Answer:
Option A) [tex]132ft[/tex]
Step-by-step explanation:
It is given that,
Radius of a circle = 21ft
We know that π = [tex]\frac{22}{7}[/tex]
So the circumference of a circle = 2πr
Substituting the values,
= [tex]2X\frac{22}{7} X 21[/tex]
So we get,
[tex]= 2X22X3[/tex]
[tex]= 132ft[/tex]
The required circumference of the circle is 132 feet. Option A is correct.
What is the circumference of the circle?To find the circumference of a circle, we use the formula C = πd, where C is the circumference, π is the mathematical constant pi (approximately equal to 3.14), and d is the diameter of the circle.
Here,
The circumference of a circle with a radius of 21 feet can be found using the formula:
C = 2πr
where "C" is the circumference, "r" is the radius, and "π" is the mathematical constant pi, which is approximately equal to 22/7.
Substituting the values given, we have:
C = 2 x (22/7) x 21
C = 132 feet
Therefore, the circumference of the circle is 132 feet. Answer: 132 feet.
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Find Y if the slope between (8, y) and (14, -13) is -2/3
Answer: The slope between two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
We are given that the slope between (8, y) and (14, -13) is -2/3. So we can use this information to set up the equation:
-2/3 = (-13 - y) / (14 - 8)
To find y, we can solve for y:
-2/3 = (-13 - y) / 6
-2 = -13 - y
y = 11
So the value of y is 11.
Step-by-step explanation:
What would need to be used to show the triangles are congruent by AAS?
A: Nothing as the triangles can not be proved congruent by AAS.
B: Angles are congruent by vertical
angles.
C: Sides are congruent by the
reflexive property.
D: Angles are congruent by the
reflexive property.
Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."
What is the congruent triangle?Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.
Given two triangles, Where the base of these triangles are same
And also given that the two angles are the same.
Since,
Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).
Thus, the third angle is also equal
From AAS:
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,
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A The numbers 4, 2, 5, ( ) have a mean of 4. What is the missing number?
B The numbers 4, 2, 7, ( ) have a mode of 2. What is the missing number?
C The numbers 8, 4, 6, ( ) have a median of 5. Write down a possible value of c
D The numbers 20, 70, 10, ( ) have a range of 80. What is the missing number? the missing number.
Based on given data, Mean is 4, missing number can be 4,2,7., So the arrangement is c,4,6,8.
a) What is meant by mean?The mean of numbers is the average value of given numbers.
Given numbers are 4,2,5
Mean is 4
Mean = sum of numbers/ total number of values given
4 = (4+2+5+x) /4
16 = 11 +x
x = 5
Therefore the missing number is 5.
b) What is mode?Mode is the number which is most frequently repeated in a list of numbers.
Given numbers are 4,2,7 and x
Mode is given as 2
So x can be any number from the given values since any number can be repeated twice.
Therefore missing number can be 4,2,7.
c) What is the median?The median of the set is the middle number after the numbers are arranged from least to greatest.
There are four numbers given. So the median is the average of middle numbers.
To get the median of 5 the middle numbers should be 4 and 6.
So the arrangement is c,4,6,8
Therefore the missing number can be any number less than or equal to 4.
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Housing prices in a small town are normally distributed with a mean of
$157,000 and a standard deviation of $8,000. Use the empirical rule to
complete the following statement.
Approximately 99.7% of housing prices are between a low price of
$ and a high price of $
Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
So, using the empirical rule, we can say that approximately 99.7% of housing prices in this small town fall within 3 standard deviations of the mean.
To find the range of prices that this corresponds to, we can use the following formula:
(mean - (3 x standard deviation), mean + (3 x standard deviation))
Plugging in the given values:
(157,000 - (3 x 8,000), 157,000 + (3 x 8,000))
(141,000, 173,000)
So, approximately 99.7% of housing prices in this small town are between $141,000 and $173,000.
Step-by-step explanation:
someone please answer and explain how to do this in steps i will give you a cookie
17. The equation can be rewritten as 2x²-8x+1=0.
18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.
How many solutions does the graph have?17.
The equation can be rewritten as 2x²-8x+1=0.
Vertex:
The vertex is (4, -1). A minimum.
Axis of symmetry:
The axis of symmetry is x = 4.
The parabola opens up.
The graph has 1 solution.
18. How many solutions does the quadratic
have?
Answer: The axis of symmetry is x = 5, which is calculated by taking the coefficient of x (which is -10) and dividing it by 2. This is because the axis of symmetry is always in the middle of the two x-intercepts. The parabola opens up, which means it has a maximum at the vertex. The vertex is (5, 6), which is calculated by substituting x = 5 into the equation and solving for y.The quadratic equation has two solutions, x = 4 and x = 6. To find the solutions, one must set the equation equal to 0 and solve for x. This can be done by either factoring or using the quadratic formula. After finding the x-intercepts, the solutions can be determined by plugging in the x-intercepts into the equation and solving for y.To learn more about Solutions in the graph refer :
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17. The equation can be rewritten as 2x²-8x+1=0. 18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.
17. The equation can be rewritten as 2x²-8x+1=0.
Vertex:
The vertex is (4, -1). A minimum.
Axis of symmetry:
The axis of symmetry is x = 4.
The parabola opens up.
The graph has 1 solution.
18. The coefficient of x, which is -10, is multiplied by two to determine the axis of symmetry, which is x = 5.
This is due to the fact that the axis of symmetry is always located halfway between the two x-intercepts.
The parabola widens, indicating that the vertex is where its maximum is located. The vertex is (5, 6), which is determined by solving for y while changing x = 5 in the equation.
There are two answers to the quadratic equation: x = 4 and x = 6. The equation must be made equal to 0 in order to get the solutions.
Either factoring or applying the quadratic formula can be used to accomplish this.
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PLEASE HELP ITS MY BDAY TOMORROW
Zachary measures the area of a glacier at
the start of every year.
2
At the start of this year, the glacier had an
area of exactly 56.20 km. This is 0.2%
less than it was at the start of last year.
Work out what the area of the glacier was
at the start of last year.
2
Give your answer in km² to 2 d.p.
The area of the glacier at the beginning of the last year is given as follows:
56.31 km².
How to obtain the area of the glacier?The area of the glacier is obtained applying the proportions in the context of this problem.
The current area is given as follows:
56.20 km².
The percentage of this area relative to the area at the beginning of the last year is given as follows:
100 - 0.2 = 99.8% = 0.998.
Hence the area at the beginning of the last year is obtained as follows:
0.998x = 56.20
x = 56.20/0.998
x = 56.31 km².
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g the space complexities of bfs and dfs are o(b^d) and o(bd) respectivaly, why is one exponential with respect to d and the other not
BFS has an exponential space complexity with respect to d because it stores all the nodes at the same depth level before moving on to the next level
DFS doesn't have an exponential space complexity with respect to d because it only stores the nodes that need to be visited next.
The space complexity of breadth-first search (BFS) is O([tex]b^d[/tex]) and the space complexity of depth-first search (DFS) is O(bd), where b is the maximum branching factor of the search tree and d is the maximum depth of the tree.
The reason for the difference in the space complexities is that BFS uses a queue to store the nodes to be visited, while DFS uses a stack.
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The perimeter of a triangle is 100cm and the angles are in the ratio: 1:3:5 find the length of each side triangle
By applying the rule of sin, it can be concluded that the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.
Triangle is a 2D shape that is bounded by three sides and has three vertices. The perimeter of a triangle is the sum of the lengths of the three sides of the triangle.
Perimeter = a + b + c, where a, b, and c are the sides of the triangle
One of the most important properties of a triangle is that the sum of the angles in a triangle equals 180°.
The rule of sin describes the ratio of the angles corresponding to the side lengths of the sine function.
a / sin A = b / sin B = c / sin C, where A, B, and C are the angles of the triangle
If the ratio of the angles is 1 : 3 : 5 and let x be the smallest angle, then we can put this information into the following equation:
Total angle = A + B + C
180° = x + 3x + 5x
180° = 9x
x = 20°
Then we can calculate the other angles:
A = 20°
B = 3x = 3 * 20° = 60°
C = 5x = 5 * 20° = 100°
Now we put the value of A, B, and C into the rule of sin equation:
a / sin A = b / sin B
a / sin 20° = b / sin 60°
a / 0.34 = b / 0.87
a = 0.34 * b / 0.87
a = 0.39b
c / sin C = b / sin B
c / sin 100° = b / sin 60°
c / 0.98 = b / 0.87
c = 0.98 * b / 0.87
c = 1.13b
Then we go back to the perimeter formula:
perimeter = a + b + c
100 = 0.39b + b + 1.13b
100 = 2.52b
b = 39.68 cm
Then we can calculate the length of the other sides, a and c:
a = 0.39b
= 0.39 * 39.68
= 15.48 cm
c = 1.13b
= 1.13 * 39.68
= 44.84 cm
Thus, the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.
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a company produces a product for which the variable cost is $12.13 per unit, and the fixed costs are $92,000. the product sells for $17.10. let x be the number of units produced and sold.(A). The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost C as a function of the number of units produced. C = _____(B). Write the revenue ft as a function of the number of units sold. R = _____(C). Write the profit P as a function of the number of units sold. P = _____
a. The total cost C as a function of the number of units produced is C = $12.13x + $92,000
b. The revenue R as a function of the number of units sold is R = $17.10x
c. The profit P as a function of the number of units sold is P = $5.97x - $92,000
(A) The total cost for a business is the sum of the variable cost and the fixed costs.
The variable cost per unit is $12.13, so the total variable cost for x units produced is $12.13x.
The fixed costs are $92,000 and do not change with the number of units produced, so the total cost C as a function of the number of units produced is given by -
C = $12.13x + $92,000
(B) The revenue is the total amount of money earned from selling the product. The product sells for $17.10 per unit, so the revenue R as a function of the number of units sold is given by -
R = $17.10x
(C) The profit is the difference between the revenue and the total cost. Using the equations from (A) and (B), the profit P as a function of the number of units sold is given by -
P = R - C = $17.10x - ($12.13x + $92,000) = $5.97x - $92,000
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O $132.50
7) Kiron is buying $84 worth of groceries at the store. The sales tax rate is 8.75%. What is the total
cost of his groceries in dollars and cents?
The total cost of his groceries in dollars and cents is 91.35 on 8.75% sales tax.
A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.
Sales tax is an indirect fee that is always applied at the point of exchange or purchase and is calculated as a percentage of the item's worth. Retail, manufacturing, wholesale, use, and value-added taxes are the various types of sales taxes (VAT). Note: As of July 1, 2017, the Goods and Services Tax (GST) has taken the place of the Sales Tax.
Sales tax = 8.75%
⇒ 8.75/100 × 84
⇒ 7.35
Total price = 7.35 + 84
⇒ $ 91.35
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question approximately 38 percent of people living in region w have the blood type o positive. a random sample of 100 people from region x revealed that 35 people in the sample had the blood type o positive. consider a hypothesis test to investigate whether the percent of people in region x with o positive blood is different from that of in region w. which of the following is the appropriate null hypothesis for the investigation? Ha: proportion 0.38 Ha: proportion >0.38 Ha: proportion =0.38 O Ha: proportion <0.38
Null hypothesis for the investigation Ha=0.38
The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.
This hypothesis is either rejected or not rejected based on the viability of the given population or sample.
In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance.
It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H0.
Here, the hypothesis test formulas are given below for reference.
The formula for the null hypothesis is:
H0: p = p0
The formula for the alternative hypothesis is:
Ha = p >p0, < p0≠ p0
The formula for the test static is:
[tex]z=\frac{p-p0}{\sqrt{\frac{p0(1-p0)}{n} } }[/tex]
Remember that, p0 is the null hypothesis and p – hat is the sample proportion.
38 percent of people living in region w have the blood type o positive.
w region
38% - o positive
x region
100 random sample
35 o positive
means 35/ 100*100
35% 0 positive
a hypothesis test to investigate whether the percent of people in region x with o positive blood is different from that of in region w
The formula for the null hypothesis is:
H0: p = p0 =0.38
Ha = p >p0, < p0≠ p0
Ha=0.38
Null hypothesis for the investigation Ha=0.38
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Michelle has 4 1/5 feet of yarn. She cuts the yarn into pieces that each measure 3/5 foot long. How many pieces of yarn did Michelle cut?
Answer: 7
Step-by-step explanation:
yarn = 4 1/5 = 21/5
measure of one piece = 3/5
no. of pieces of yarn = 21/5÷3/5
= 21/5×5/3
= 105/15 = 7
So the number of pieces of yarn cut will be 7
Answer:
7
Step-by-step explanation:
4.2' yarn
cut into 0.6' pieces
4.2/0.6 =7
i could really use some help please
The coordinate of the circumcentre of ΔABC is (-1, 0.15).
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle ABC.
A = (-5, -4)
B = (3, -4)
C = (-1, 6)
The circumcentre of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.
Now,
Let the circumcentre be M = (x, y).
The length from each side of the triangle to the circumcentre is equal.
So,
AO² = BO² = CO²
Now,
AO² = BO²
(x + 5)² + (y + 4)² = (x - 3)² + (y + 4)²
x² + 10x + 25 + y² + 8y + 16 = x² - 6x + 9 + y² + 8y + 16
10x + 25 = -6x + 9
16x + 16 = 0
x + 1 = 0
x = -1
BO² = CO²
(x - 3)² + (y + 4)² = (x + 1)² + (y - 6)²
x² - 6x + 9 + y² + 8y + 16 = x² + 2x + 1 + y² - 12y + 36
-6x + 9 + 8y + 16 = 2x + 1 - 12y + 36
20y - 8x + 25 - 36 = 0
20y - 8x - 11 = 0
20y = 11 + 8x
y = (11 + 8x)/20
y = (11 - 8)/20
y = 3/20
y = 0.15
Thus,
Circumcentre M = (-1, 0.15)
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SOLVE FOR Y 32=16Y+64X
Answer: y = 2-4x
Step-by-step explanation:
Use the distributive property to write each expression as an equivalent
algebraic expression.
6(4+x)
Answer:
= -6x + 24
Step-by-step explanation:
6(4-x) = 6*4 + 6*-x
= 24 - 6x
= -6x + 24
sam buys a computer for $590.00 plus $32.45 in sales tax find the sales tax rate?
Answer:
Is this what youre asking?
Step-by-step explanation:
Price before tax: $ 590.00
+ Sales tax (32.45%): $ 191.46
Total price including tax: $ 781.46
Christian is making a circular pizza. The diameter of the pizza is 12 inches. Approximately, how many inches of the pizza will be the outer
edge crust?
Christian is making a circular pizza. The diameter of the pizza is 12 inches. The pizza crust on the outside will be about 12 inches thick.
How is the pizza's circumference determined using this formula?The formula for determining a pizza's circumference is C = 2πr, where C is the circumference, pi is a constant that is roughly equivalent to 3.14, and r is the pizza's radius.
We must determine the pizza's circumference in order to locate the crust on the pizza's outer edge. C = 2πr is the formula for a circle's circumference, where C is the circumference, pi is a constant that is roughly equivalent to 3.14, and r is the circle's radius.
The pizza has a diameter of 12 inches, so the radius, or 6 inches, is half of that. Thus, the pizza's circumference is:
C= 2π6 = 12π
The pizza's circumference represents the crust's outer edge. C = 26 inches = 12 inches As a result, the pizza's crust on the outside measures about 12 inches.
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"Dondarrion's Wood," Galshore said to herself as she approached the dense growth of trees. She spied all kinds of trees and shrubs. Galshore prided herself on her knowledge of plant life, but there were three trees that she did not recognize. She regarded the strange trees for a moment then turned to the trees she knew. She saw ten sprightly maple trees eager to catch the sun. She saw four ancient and venerable oaks placidly lording over the wood. She saw two cedars, four pines, a birch and seven sycamores. A crow quorked. Galshore looked up searching. She spotted the crow perched at the top of one of the maple trees hidden behind the sycamores. The crow quorked again. Galshore was a little afraid. The wood was dark. She felt a coolness linger and caress her face. Galshore concentrated on listening and noticed other sounds coming from the wood. They were strange sounds. She wondered what sort of animals made such sounds and shivered. Galshore turned and sat on a boulder.
She stared into the wood for fifteen minutes wondering about the strangeness of the wood and trying to peer through the shadows of leaf and branch to discover what awaited her in the wood. "It is the only way to Ten Alders," she said under her breath.
A light breeze shimmered through the cedars. Galshore smelled oak and pine and remembered.
"Father, what will we do when the Kargs come to Oranea?" Galshore asked.
The stout merchant sat down by the fire with a book. "Galshore dear child, fear not for our safety." He leaned forward in his high backed chair. "The walls of our city are strong. We are well protected by stone and metal."
"What about food?" Galshore asked. "Do we have enough food to survive if the Kargs stay outside our walls for a long time?"
Galshore's father took a sip of Merasha tea. "We have been storing grain for quite some time. I have calculated that we have enough grain to give each of the 2200 inhabitants of Oranea one and one half pounds of grain each week. Never fear, you shall continue to enjoy cakes and cookies even if the Kargs come." He folded his hands and looked down at Galshore. "We shall not be troubled by mindless Kargs.
Our hard work will not be undone by savages and brutes. The beauty we have created here will be protected. We are safe. asked.
"What about your Merasha? Maybe we should give it to the Kargs," Galshore Galshore's father hooked his thumbs under his belt and smiled. "So you would invite the Kargs to tea my little dear? Even if they could learn to precisely measure the proper proportions of 5 parts black lion's fennel leaf to two parts greebe root and seven parts prisic, they don't believe in medicines of any kind. They have some sort of superstition that medicines weaken the body and rob the true warrior of his strength and turn him into a zombie or some such nonsense."
Galshore's father picked up his book.
Galshore was curious, "Why do the Kargs want to attack us?"
Galshore's father sighed. "The Kargs are not nice. They do not build and work.
They plant no crops. They only know how to destroy, so they have nothing of their own. They steal from others. They know nothing of peace or beauty. They know only the violence and disorder they bring wherever they go."
Galshore clasped her knees. "Why don't we give them some food if they have none of their own? I want to give them half of my one and a half pounds of grain I am to receive each week."
Galshore's father smiled. "I am afraid my dear that would only insult the
Kargs. There is no reasoning with them. They must destroy or be destroyed. Misery is like a comfortable warm blanket for them."
The crow left its tree and perched on a rock in front of Galshore and cawed loudly. Galshore started. The crow regarded her curiously. "I wish you had been right father," Galshore whispered into the darkness of the wood. "I wish you had been right." She stepped into a green unknown world of shade and shadows.
QUESTIONS:
1. What percentage of the trees were oaks?
2. If over the span of one year the number of pines were increased by 3, cedars by 2, sycamores by 1 , oaks by 5 and birches by 4; by what fraction would the total number of trees have increased?(don’t forget the unknown trees)**
3. Make a table of the propagation of the trees in Dondarrion’s Wood over a year. The table should include information about the fractional changes in tree proliferation over the year. (use all the info at your disposal including the info from question 2 -and don’t forget the unknown trees)**
4. What percentage of the trees were unknown to Galshore?(first year)
5. How much grain would it take to feed the inhabitants of Oranea for one year?
6. If Galshore gave 24% of her grain to the Kargs for one week, how much grain would she have left for that week?
7. How much prisic would be contained in 13 pounds of Merasha Tea?. **
8. How much greebe root would be contained in 13 pounds of Merasha Tea?**
In reality, only 55% of the calories produced by crops around the world are consumed directly by humans. Animal feed accounts for an additional 36% of usage.
How much grain is used for animal feed?The percentage of crops grown for human consumption compared to all crops farmed for animal feed or biofuels is fascinatingly depicted on this National Geographic map:In reality, only 55% of the calories produced by crops around the world are consumed directly by humans. Animal feed accounts for an additional 36% of usage. The remaining 9% is used for biofuels and other industrial applications. (Those numbers are from a study by Emily Cassidy and colleagues at the Institute on the Environment at the University of Minnesota.)Just 27% of crop calories in the US are directly ingested, such as wheat or Californian fruits and vegetables. In the US, these figures are even more startling.As opposed to this, animal feed accounts for almost 67 percent of all crops, especially the soy farmed in the Midwest. Ethanol and other biofuels receive a part of the remaining funds.Of course, some of that feed for animals does eventually end up as food, but the process is a lot, lot more deceptive. Just 12 calories of chicken or 3 calories of beef, for example, are made from grain, which requires roughly 100 calories.The Complete Question.
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14.3 percentage of the trees were oaks, The total number of trees have increased by: 15/28.
How to solve the following?There were 4 ancient oaks and a total of ten sprightly maple trees, four ancient oaks, two cedars, four pines, a birch, and seven sycamores, so the percentage of oaks would be 4/(10+4+2+4+1+7) = 4/28 = 14.3%.The total number of trees was 10+4+2+4+1+7 = 28, and the increase over one year was 3+2+1+5+4 = 15. The fractional increase would be 15/28 = 0.5357.The fractional change in tree proliferation for each type of tree over the year is not specified in the text.The total number of trees was 28, and Galshore did not recognize three of the trees, so the percentage of unknown trees would be 3/28 = 10.7%.2200 people would each receive one and a half pounds of grain per week for 52 weeks in a year, so the total amount of grain required would be 2200 x 1.5 x 52 = 183,400 pounds.If Galshore received 1.5 pounds of grain each week, and gave away 24% of it, she would have 1.5 x (1 - 0.24) = 1.5 x 0.76 = 1.14 pounds left for the week.The proper proportions of 5 parts black lion's fennel leaf to two parts greebe root and seven parts prisic are not specified.The amount of prisic contained in 13 pounds of Merasha Tea is not specified, so this question cannot be answered.To know more about percentage visit:
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please help will mark BRAINLIEST
The composite translation for this problem is represented as follows:
<3, -9>
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.Another notation is the <x,y> notation, in which:
x is the horizontal movement.y is the vertical movement.For the composition of translations, we add the movements, hence:
6 - 3 = 3.-4 - 5 = -9.Meaning that the first option is the correct option.
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consider the triangles shown below. which of the following would also need to be true in order to prove that ABD = ABC?
A.BC BD must be true in order to demonstrate that triangles ABD and ABC are congruent by SSS.
How does the SSS Congruence Theorem work?The SSS Congruence Theorem requires three pairs of corresponding sides to be congruent for two triangles to be considered congruent to one another.
We may infer the two triangles' characteristics from the provided image by looking at them:
AB ≅ AB (reflexive property) (reflexive property)
AC ≅ AD (provided) (given)
The two pairs of corresponding congruent sides are so present. As a result, for SSS to demonstrate that ABD ABC, the following must be true: A. BC BD.
A.BC BD must be true in order to demonstrate that triangles ABD and ABC are congruent by SSS.
The complete question is,
Have a look at the triangles below. In order to demonstrate that ABDABC, which of the following would also need to be true?
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In Problems 13 through 16, substitute y = e^rx into the given differential equation to determine all values of the constant r for which y = e^rx is a solution of the equation. 13. 3y' = 2y 14. 4y" = y 15. y" + y' - 2y = 0 16. 3y" + 3y' - 4y = 0
The values of given differential equation constant r are = 1/5 and -3.
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x)
Here “x” is an independent variable and “y” is a dependent variable.
For example, dy/dx = 5x A differential equation contains derivatives which are either partial derivatives or ordinary derivatives.
The derivative represents a rate of change, and the differential equation describes a relationship between the quantity that is continuously varying with respect to the change in another quantity.
There are a lot of differential equations formulas to find the solution of the derivatives.
As y = e power rx
y¹= dy/dx= re power rx
and y'' = r²e power rx
Hence 5y'' +14y' – 3y = 0 can be written as
5r²e - 14re** - 3e¹² - 0
or 5r2 + 14r - 3 - 0
or 5r2 + 15r - r - 3 - 0
or (5r − 1)(r + 3) = 0
r=1/5 or r= -3
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A 5 foot wide painting should be centered on a 13 foot wall type the left side of an equation that can be used to determine how many feet should be on each side of the painting
The number of feet that should be on each side of the painting is 4 feet.
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Let x be the number of feet on each side of the painting.
The equation to determine the number of feet on each side of the painting would be:
x + 5 + x = 13
So x = (13-5)/2
x = 4
So there should be 4 feet on each side of the painting.
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The total average monthly expenditure in 2010 was £1200.
What was it in 2020?
The total average monthly expenditure in 2020 was £2400.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The expenditure in 2020 will be calculated as:-
Average monthly expenditure in 2020 = 600 + 500 + 400 + 300 + 200 + 100 = £2400
So, the total average monthly expenditure in 2020 was £2400.
The complete question is given below:-
Average monthly expenditure (£)
600
500
400
300
200
100
The total average monthly expenditure in 2010 was £1200. What was it in 2020?
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the mean of an iq test are normally distributed with a mean of 100 points and a standard deviaiton of 15. calculate the following probability in r using the pnorm() function. what is the probability a student taking the exam scores below 125 points?
The percentage of scores below 112 is equal to 78.81.
Let X represent a test's score. X is regularly distributed, hence
P(X < 112)
= P[(X - 100)/15 < (112 - 100)/15]
= P[ SNV < 0.8] .8]
SNV stands for Standard Normal Variable,
A normal distribution with a mean of 0 and a standard deviation of 1 is the standard normal distribution. When referring to a random variable that has this typical normal distribution, the letter Z is frequently employed.
z = (X – μ) / σ
If X is a normal random variable, represents its mean, and represents its standard deviation. The normal distribution formula is also available here.
and the value is 0.7881.
Thus, the percentage of scores below 112 is equal to 78.81.
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The full question
If the scores for a test have a mean of 100 and a standard deviation of 15, what is the percentage of scores that will fall below 112? Assuming a normal distribution
Exercise 2: ABC is a triangle such that B=80°. BC=5cm and Ĉ=40°. 1) Construct the triangle ABC. 2) The bisector of the angle ABC cuts [AC] at M. a. Calculate MBC. b. What is the nature of triangle MBC? Justify. c. Deduce that MB=MC.
Answer:
Step-by-step explanation:
Exercise 2:
1.To construct the triangle ABC, start by drawing a line segment BC of length 5cm. Using a protractor, measure and mark an angle of 80° at B and an angle of 40° at C. Connect the two marked angles with a line to form triangle ABC.
2.The bisector of angle ABC cuts the line segment AC at M.
a. To calculate MBC, we can use the Angle Bisector Theorem, which states that the ratio of the lengths of the bisector of a given angle of a triangle to the sides of the triangle is equal to the ratio of the other two sides of the triangle. So, MBC/AC = BC/AB. Since angle B=80° and angle C=40°, angle A is (180-(80+40))=60°. Therefore, AB/BC = MC/MB.
b. Using the Angle Bisector Theorem again, we can see that MBC/AC = BC/AB, which means that MBC/5 = 5/AB. And since AB/BC = MC/MB, we can deduce that MB = MC. Therefore, triangle MBC is an isosceles triangle.
c. As we know that MB=MC, we can say that triangle MBC is an isosceles triangle.
Note: To construct the triangle in a more accurate way, you may need a ruler and a compass, and the angles and sides should be measured and drawn with more precision.
Need help with question 12.
The length of the rectangle be 12 and Width be 6.
What is meant by rectangle?With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width.
A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.
4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other.
Let the equation be L = 2W and
P = 36 = 2 × ( L + W )
simplifying the equation, we get
⇒ 18 = L + W
⇒ 18 = 2W + W
⇒ 6 = W and L = 2 × W = 2 × 6 = 12
Therefore, the length of the rectangle be 12 and Width be 6.
The complete question is:
The length of a rectangle is twice the width. The perimeter of the rectangle is 36. What is the length and width of the rectangles?
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For each of the following, count the number of four-digit numberssatisfying the condition and with digits in {1, 2,3, 4,5, 6}:(a) The digits are distinct(b) The number is even(c) The number is even and the digits are distinct.
(a) The number of four-digit numbers with distinct digits in {1, 2, 3, 4, 5, 6} is 6543 = 360.
(b) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even is (3543)/2 = 270.
(c) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even and have distinct digits is (321*1)/2 = 3.
Four-Digit Numbers CountingFor (a) the total number of four-digit numbers with digits in {1, 2, 3, 4, 5, 6} is 6 options for the first digit, 5 for the second, 4 for the third and 3 for the last one. So, 654*3 = 360.
For (b) since digits in {1, 2, 3, 4, 5, 6} the even digits are 2,4,6. for each of the even digits we have 5 options for the second digit, 4 for the third and 3 for the last one. In total, we have 354*3= 270 even numbers.
For (c) The total number of four-digit numbers with distinct digits that are even is 211 = 2, since there are 2 even digits in {1,2,3,4,5,6} and only one of each can be used. However, this count is double-counting the numbers, so we divide by 2 to get 3.
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(1 point) A company received a shipment of 42 laser printers, including 8 that are defective. 2 of these printers are selected to be used in the copy room. (a) How many selections can be made? (b) How many of these selections will contain no defective printers?
The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.
(a) There are 6,632 selections that can be made.
(b) There are 5,832 selections that will contain no defective printers.
(a)The number of selections can be found using the nCr formula: nCr = n!/(r!(n-r)!), where n is the total number of items (42) and r is the number of items selected (2). So nCr = 42!/(2!(42-2)!) = 42!/(2!40!) = 6,632.
(b) The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.
There are 6,632 selections that can be made when two printers are chosen from a shipment of 42, including 8 that are defective. Out of these selections, 5,832 will contain no defective printers.
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athletes in a particular sport are classified as either offense or defense. the distribution of weights for the athletes classified as offense is approximately normal, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. the distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. there are 1,000 athletes in each classification. which of the following is the best description of a histogram of the weights of all 2,000 athletes?
A histogram of the weights of all 2,000 athletes would be a graph with two normal distributions, one for offense and one for defense.
The offense distribution would have a bell shaped curve centered at 200 pounds, with a range of 150-250 pounds. The defense distribution would have a bell shaped curve centered at 300 pounds, with a range of 250-350 pounds. Each of the distributions would have the same area, representing 1,000 athletes in each group. The total area of the histogram would represent the combined 2,000 athletes with weights ranging from 150-350 pounds. It is important to note that the histogram would not represent the exact weights of the athletes, but rather the relative frequency of each weight.
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jeremy is looking for a good auto loan in his city. He is willing to pay no more than an effective rate of 7.000% annually. which if any of the following loans meet jermeys criteria?
loan A : 6.785% normal rate compounded semi annually
loan B : 6.795% nominal rate compounded, manually
loan C : 6.659% nominal rate, compounded weekly.
Answer: To determine which loan(s) meet Jeremy's criteria of no more than an effective rate of 7.000% annually, we need to calculate the effective rate for each loan.
The effective rate is the true annual interest rate that a borrower will pay on a loan, taking into account the frequency of compounding.
Loan A: 6.785% normal rate compounded semi-annually
To calculate the effective rate, we can use the formula:
(1+ (nominal rate/2))^2 - 1
Effective rate = (1+ (6.785/2))^2 - 1 = 6.897%
Loan B: 6.795% nominal rate compounded, manually
Since the loan is compounded manually, the effective rate is the same as the nominal rate.
Effective rate = 6.795%
Loan C: 6.659% nominal rate, compounded weekly
To calculate the effective rate, we can use the formula:
(1+ (nominal rate/number of compounding periods per year))^(number of compounding periods per year) - 1
Effective rate = (1+ (6.659/52))^52 - 1 = 6.759%
Since 6.897% > 7.000% and 6.795% > 7.000% and 6.759% < 7.000%. So Loan C with 6.659% nominal rate, compounded weekly meets Jeremy's criteria.
Step-by-step explanation: