As per the geometric sequence, the common ratio is -7.
Firstly, let's start with a brief introduction to what a sequence is. A sequence is simply a list of numbers that follow a certain pattern or rule. For example, the sequence 1, 3, 5, 7, 9 is a sequence of odd numbers.
Now, let's talk about a geometric sequence specifically.
Now, let's apply this to the sequence you were given: -3, 21, -192. To find the common ratio, we need to look at the ratio of any term to the previous term. For example, we can look at the ratio of the second term (21) to the first term (-3):
r = 21 / (-3) = -7
This means that the common ratio of the sequence is -7, since each term is found by multiplying the previous term by -7.
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Find the x-intercept of 3 tan(3x) over the interval (pi/6,3pi/6)
Express your answer in terms of pi.
The x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:
x = π/3 and x = 2π/3
What is function ?
A function is a mathematical object that takes one or more inputs, called the arguments or variables, and produces a unique output. The output is determined by a set of rules that specify how the function operates on the inputs. In other words, a function is a relationship between inputs and outputs.
Functions are typically denoted by a symbol or a name, such as f(x) or g(t). The input is usually represented by a variable, such as x or t, while the output is represented by the function value, such as f(x) or g(t).
Functions are used extensively in mathematics, science, engineering, and many other fields. They provide a way to model and analyze real-world phenomena, and they are essential tools for solving many problems in these fields. Examples of functions include polynomial functions, exponential functions, trigonometric functions, and logarithmic functions.
To find the x-intercept of the function 3 tan(3x) over the given interval, we need to find the values of x where the function equals zero.
Let's first simplify the function:
3 tan(3x) = 0
tan(3x) = 0
We know that tan(π/2) is undefined and that tan(π) = 0. Since the period of the tangent function is π, we can say that:
tan(3x) = 0 --> 3x = nπ for n ∈ ℤ
Now we solve for x:
3x = nπ
x = nπ/3
Since the interval is (π/6, 3π/6), we need to find the values of x that satisfy:
π/6 < x < 3π/6
π/6 < nπ/3 < 3π/6
1/2 < n < 3/2
So the values of x that satisfy the given condition are:
x = π/3 and x = 2π/3
Therefore, the x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:
x = π/3 and x = 2π/3
Expressed in terms of π, the x-intercepts are:
π/3π and 2π/3π, which simplify to:
x = 1/3 and x = 2/3.
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9. The linear regression equation is = 34.38x - 91.75. Use the equation to predict how far this
4.38x-91-75 Use
person will travel after 10 hours of driving.
The answer of the given question based on the linear regression is , the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.
What is Distance?Distance is measurement of length between the two points or objects. It is a scalar quantity that only has a magnitude and no direction. In mathematics, distance can be measured in various units such as meters, kilometers, miles, or feet, depending on the context.
Distance can be calculated using the distance formula, which is based on the Pythagorean theorem in two or three dimensions.
Assuming the equation you meant to write is y = 34.38x - 91.75, where y is the predicted distance traveled in miles and x is the number of hours driven, we can use this equation to predict how far the person will travel after 10 hours of driving:
y = 34.38x - 91.75
y = 34.38(10) - 91.75
y = 343.8 - 91.75
y = 252.05
Therefore, the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.
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During 10 hours of driving, the projected distance according to linear regression is roughly 252.05 miles.
What is Distance?The term "distance" refers to the length between two points or objects. Having merely a magnitude and no direction, it is a scalar quantity. Depending on the situation, distance in mathematics can be expressed in a variety of ways, including meters, kilometers, miles, or feet.
The distance formula, which depends on the Pythagorean theorem in either two or three dimensions, can be used to compute distance.We may use this equation to forecast how far the individual would go after 10 hours of driving, assuming the equation you meant to write is
y = 34.38x - 91.75, where y is the expected distance travelled in miles and x is the number of hours driven:
y = 34.38x - 91.75
y = 34.38(10) - 91.75
y = 343.8 - 91.75
y = 252.05
The estimated distance that the driver will cover after 10 hours on the road is 252.05 miles.
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The complete question is,
The equation for linear regression is = 34.38x - 91.75. Calculate this person's estimated distance after 10 hours of driving using the equation: 4.38x-91-75.
each time a hurricane arrives, a new home has a 0.4 probability of experiencing damage. the occurrences of damage in different hurricanes are mutually independent. calculate the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes.
As per the given probability, the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes is either one or two hurricanes, depending on which sequence is more likely to occur.
The probability of the DD sequence is 0.4 x 0.4 = 0.16. This means that there is a 16% chance that the home will experience damage in both the first and second hurricanes.
The probability of the DN sequence is 0.4 x 0.6 = 0.24. This means that there is a 24% chance that the home will experience damage in the first hurricane but not in the second hurricane.
The probability of the ND sequence is 0.6 x 0.4 = 0.24. This means that there is a 24% chance that the home will not experience damage in the first hurricane but will experience damage in the second hurricane.
To determine the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes, we need to consider which sequence is most likely to occur.
In this case, the DN and ND sequences have the same probability, which means that there are two possible modes: one and two hurricanes.
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If h = 13 units and r = 6 units, then what is the volume of the cone shown above?
The vοlume οf the cοne is 156π cubic units
What is cοne?A cοne is a three-dimensiοnal geοmetric fοrm with a flat base and a smοοth tapering tip οr end. A cοne is made up οf a cοllectiοn οf line segments, half-lines, οr lines that link the apex—the cοmmοn pοint—tο every pοint οn a base that is in a plane οther than the apex.
Given,
h = 13 units and r = 6 units
We knοw the fοrmula tο determine vοlume οf cοne; that is
(1/3)πr²h
Where r= radius οf the cοne
h= height οf the cοne
We put the value οf h and r in the fοrmula
(1/3)πr²h
= (1/3)π6² *13
=156π cubic units
The vοlume οf the cοne is 156π cubic units
Hence the cοrrect answer is 156π cubic units
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< Back to task
In the quadrilateral below, angles DAB and BCD are the same size.
What is the size of angle DAB?
D
228
34° -B
Answer >
The size of angle DAB in the quadrilateral is 49°.
How to find the size of angle DAB?The sum of the interior angles of a quadrilateral is 360°. We can say:
∠A + ∠B + ∠C + ∠D = 360°
∠A + 34° + ∠C + 228° = 360°
∠A + ∠C + 262° = 360°
∠A + ∠C = 360 - 262
∠A + ∠C = 98
Since angles DAB and BCD are the same size. This implies ∠A = ∠C. Thus:
∠A + ∠A = 98
2∠A = 98
∠A = 98/2
∠A = 49°
Therefore, the size of angle DAB is 49°.
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Complete Question
Check the attached image
a newsletter publisher believes that under 69% 69 % of their readers own a rolls royce. is there sufficient evidence at the 0.10 0.10 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69
A newsletter publisher believes that under 69% of their readers own a Rolls Royce.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.
Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.
Null Hypothesis (H0): p ≤ 0.69
Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.
Alternative Hypothesis (H1): p > 0.69
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You are offered a job that pays $34,000 during the first year, with an annual increase of 6% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.06 times what it was in the previous year. What can you expect to earn in your fourth year on the job? Round your answer to the nearest dollar.
plot four different points whose -coordinates are half their -coordinates. do these points lie on a line?
The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.
To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example
If x = 0, then y = 0/2 = 0, so the first point is (0,0).
If x = 2, then y = 2/2 = 1, so the second point is (2,1).
If x = 4, then y = 4/2 = 2, so the third point is (4,2).
If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).
We can plot these points on a coordinate plane
As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.
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a man standing 11 feet from the base of a lamppost casts a shadow 3 feet long. if the man is 6 feet tall and walks away from the lamppost at a speed of 200 feet per minute, at what rate, in feet per minute, will the length of his shadow be changing?
Step-by-step explanation:
Insects can show three types of development. One of them, holometaboly (complete development), consists of the stages of egg, larva, pupa and sexually mature adult, which occupy different habitats. Insects with holometaboly belong to the most numerous orders in terms of known species. This type of development is related to a greater number of species due to the a) protection in the pupa stage, favoring the survival of fertile adults. b) production of many eggs, larvae and pupae, increasing the number of adults. c) exploration of different niches, avoiding competition between life stages. d) food intake at all stages of life, ensuring the emergence of adults. e) use of the same food in all stages, optimizing the body's nutrition.
PLEASE HELP - WORTH 30 POINTS
Answer: 1,023 combinations & 4/5 chance
Step-by-step explanation: A bunch of weird math with the first answer, but the 2nd answer is just every clothing article that isn't red over the total amount of articles simplified (8/10 = 4/5).
Hope this helped!
A farmer wants to fence in a rectangular portion of land along one side of her barn. She uses the side of the barn for one side of the rectangle, and makes the other three sides from a total of 60 feet of fencing. Find the side lengths that give the maximum area she can fence in, as well as the maximum area. Show all of your work.
the answer is 62x IAM take a guess so
A plane is 148 mi north and 167 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree
Therefore, the pilot should turn by approximately 41.8 degrees to fly directly to the airport.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It has applications in various fields, such as engineering, physics, architecture, and astronomy. Trigonometry is based on the use of six fundamental trigonometric functions, which are sine, cosine, tangent, cosecant, secant, and cotangent. These functions are defined in terms of the ratios of the sides of a right triangle. In a right triangle, one angle is a right angle, which measures 90 degrees, and the other two angles are acute angles, which are less than 90 degrees. The three sides of a right triangle are called the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the longest side, and it is always opposite to the right angle. The adjacent side is the side that is adjacent to the angle of interest, and the opposite side is the side that is opposite to the angle of interest.
Here,
We can use trigonometry to find the angle x that the pilot should turn in order to fly directly to the airport.
First, let's draw a diagram of the situation:
A(airport)
|\
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
P x mi
In the diagram, P represents the position of the plane, which is 148 miles north and 167 miles east of the airport A. The line labeled "x mi" represents the distance that the plane needs to fly in order to reach the airport, and the angle x is the angle between the line x mi and the line representing the eastward direction.
To find x, we can use the trigonometric ratio for tangent (tan):
tan(x) = opposite/adjacent
In this case, the opposite side is 148 miles (the distance north of the airport) and the adjacent side is 167 miles (the distance east of the airport). Therefore:
tan(x) = 148/167
Using a calculator, we can find that:
tan(x) ≈ 0.8868
To find x, we need to take the arctangent (tan⁻¹) of both sides:
x = tan⁻¹(0.8868)
Using a calculator, we find that:
x ≈ 41.8°
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DUE FRIDAY WELL WRITTEN ANSWERS ONLY!!!!!!!!!!!
Complete the table
All the trigonometric values for sin θ, cos θ and tan θ are valued below. Each trigonometric value is mentioned.
sin θ has boundaries from 0 to 1.
sin [tex]-\pi /2[/tex] = -1
sin [tex]-\pi /3[/tex] = -0.87
sin [tex]-\pi /6[/tex] = -0.5
sin 0 = 0
sin [tex]\pi /6 \\[/tex] = 0.5
sin [tex]\pi /3[/tex] = 0.87
sin [tex]\pi /2[/tex] = 1
sin [tex]2\pi /3[/tex] = [tex]\sqrt{3}/2[/tex]
sin [tex]5\pi /6[/tex] = 1/2
sin [tex]\pi[/tex] = 1
sin [tex]7\pi /6[/tex] = -0.5
sin [tex]4\pi /3[/tex] = -0.87
sin [tex]3\pi /2[/tex] = -1
sin [tex]5\pi /3[/tex] = -0.87
sin [tex]11\pi /6[/tex] = -0.5
sin [tex]2\pi[/tex] = 0
Similarly cos θ has boundaries.
cos [tex]-\pi /2[/tex] = 0
cos [tex]-\pi /3[/tex] = 0.5
cos [tex]-\pi /6[/tex] = 0.87
cos 0 = 1
cos [tex]\pi /6 \\[/tex] = 0.87
cos [tex]\pi /3[/tex] = 0.5
cos [tex]\pi /2[/tex] = 0
cos [tex]2\pi /3[/tex] = -0.5
cos [tex]5\pi /6[/tex] = -0.87
cos [tex]\pi[/tex] = -1
cos [tex]7\pi /6[/tex] = -0.87
cos [tex]4\pi /3[/tex] = -0.5
cos [tex]3\pi /2[/tex] = 0
cos [tex]5\pi /3[/tex] = 0.5
cos [tex]11\pi /6[/tex] = 0.87
cos [tex]2\pi[/tex] = 1
But tan θ has no boundaries.
tan [tex]-\pi /2[/tex] = undefined
tan[tex]-\pi /3[/tex] = -0.8
tan [tex]-\pi /6[/tex] = -1.73
tan 0 = 0
tan[tex]\pi /6 \\[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]
tan [tex]\pi /3[/tex] = [tex]\sqrt{3}[/tex]
tan [tex]\pi /2[/tex] = undefined
tan [tex]2\pi /3[/tex] = -3
tan [tex]5\pi /6[/tex] = -0.5774
tan [tex]\pi[/tex] = undefined
tan [tex]7\pi /6[/tex] = -1.73
tan[tex]4\pi /3[/tex] = 1.73
tan [tex]3\pi /2[/tex] = undefined
tan [tex]5\pi /3[/tex] = -1.73
tan [tex]11\pi /6[/tex] = -0.58
tan [tex]2\pi[/tex] = 0
Hence, all the values mentioned in the table, were written above.
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9r subtract three fifths greater than 3 and 9 tenths
the baker needs 15 gallons of milk to make 80 chocolate pies for the community festival. To translate the phrase "9r subtract three fifths greater than 3 and 9 tenths" into an expression, we first need to understand what it's asking us to do.
"Three fifths greater than 3 and 9 tenths" means we need to add 3 and 9 tenths to three fifths of 3. Three fifths of 3 is 1.8 (since 3/5 * 3 = 9/5 = 1.8), so we can write:
3 + 9/10 + 1.8
We can simplify this to a single mixed number by adding the whole numbers and the fractions separately:
3 + 1 + 8/10 + 8/5
= 4 + 1 3/5
= 5 3/5
So "three fifths greater than 3 and 9 tenths" is equal to 5 3/5.
Now we can subtract this value from 9r:
9r - 5 3/5
We can simplify this expression further by converting 5 3/5 to a fraction with a common denominator of 5:
9r - 5 3/5 = 9r - (28/5) = (45/5)r - (28/5) = (9r - 28) / 5
So the final expression is:
(9r - 28) / 5
In summary, "9r subtract three fifths greater than 3 and 9 tenths" can be translated to the expression (9r - 28) / 5. This expression represents a quantity that is 9 times "r" minus 5 3/5. We can simplify this expression further by converting the mixed number to an improper fraction and combining the terms, as shown above.
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Compare the amount of sand in the top cone of the hourglass to the amount there will be when the height of the sand in the top cone is only 1 inch.
HINT: The cones are similar
the amount of sand in the top cone when the height of the sand is only 1 inch is (h-1)/h times the amount of sand in the top cone originally.
the cones are similar, their volumes are proportional to the cube of their heights. Let's denote the height of the top cone as h, and the radius of the top and bottom bases as r. Then, the volume of the top cone can be expressed as:
V₁ = (1/3)π[tex]r^2[/tex]h
If the height of the sand in the top cone is reduced to 1 inch, then the height of the remaining sand in the top cone is (h-1) inches. The volume of the remaining sand in the top cone can be expressed as:
V₂ = (1/3)π[tex]r^2[/tex](h-1)
To compare the amount of sand in the top cone in these two scenarios, we can take the ratio of their volumes:
V₂/V₁ = [(1/3)π[tex]r^2[/tex](h-1)] / [(1/3)π[tex]r^2[/tex]h] = (h-1)/h
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the perimeter of an isosceles triangle is 56 in. the ratio of the sides is 5:4. find the lengths of the sides and the base of the triangle
The perimeter of an isosceles triangle is the sum of the length of the sides. In this case, the perimeter is 56 inches. The ratio of the sides is [tex]5:4.[/tex]
To calculate the lengths of the sides and base, we need to first calculate the lengths of the two equal sides. To do this, divide the perimeter (56 inches) by the sum of the ratio (5 + 4) which is 9. This gives us a result of 6.2 inches for the two equal sides.
To calculate the length of the base, multiply the two equal sides by the ratio of 5:4, which gives us a result of 7.5 inches for the base.
Therefore, the lengths of the sides and the base of the triangle are: two equal sides of 6.2 inches, and a base of 7.5 inches.
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What is 4.8 x 0.1 ?
Question :
4.8 x 0.1 =
Answer: 0.48
Step-by-step explanation:
× 0.1 = ÷10
÷ 0.1 = ×10
× 0.01 = ÷100
÷ 0.01 = ×100
So, we do=
4.8 x 0.1 = 4.8 ÷ 10
= 0.48
So our answer is 0.48
PLEASE HELP ME!!
A beach ball has a volume of approximately 10,332 in³. Find the approximate radius of the beachball. Use 3.14 for π. Round your answer to the nearest tenth
Answer:
Step-by-step explanation:
Given diameter of a beach ball is d=10 inches.Let us find the radius of the beach ball:d=2 r10=2×rr=102∴r=5Therefore, the radius of a beach is 5 inches.Let us find the volume of air contained inside the beach ball:V=43 π×r3=43 π×53=43 π×125=500π3∴V=523.59877Therefore, the volume of air contained inside the beach ball is approximately 523.6 in3.
Answer:
The formula for the volume of a sphere is:
V = (4/3)πr³
We can rearrange this formula to solve for the radius (r):
r = [(3V) / (4π)]^(1/3)
where V is the volume of the sphere.
Substituting the given volume of the beach ball, we get:
r = [(3 × 10,332 in³) / (4 × 3.14)]^(1/3)
r = 10.27 in
Rounding to the nearest tenth, the approximate radius of the beach ball is 10.3 inches.
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHelp
Answer:
first box (pies): 3, 6, 9, 12, 15, 18, 33
-> increments of 3
2nd box [cost ($)]: 11, 22, 33, 44, 55, 66, 121
-> increment of 11
Step-by-step explanation:
$44 ÷ 12 pies = $3.67 per 1 pie
3 × $3.67 = $11.01
same process: (number of pies) × $3.67 ≈ COST
Answer:
Step-by-step explanation:
So start off with 66 x 33. That will equal 2,178. Divide 2,178 by 18, like this: 2,178/18. That will equal 121. that will mean that 33 = 121. So 9 = 33 because 9 x 44 = 396 so you will divide that by 12 meaning that 9 equals 33. So now you will multiply 9 and 22 and then divide that answer by 33 making 6 = 22. now divide 22 by 6. That will equal 3.67. So 3.67 is the cost of one pie.
For the boxes above 12 and 44 it will be 16 = 59.
I hope it helped
Which inequality statement describes the two numbers on a number line? "2 and a number 9 units to the left of 2"
Answer:
Step-by-step explanation:
The inequality statement that describes the two numbers on a number line "2 and a number 9 units to the left of 2" would be:
x < 2
where x represents the number that is 9 units to the left of 2.
please help me solve this i’ll mark brainliest
Answer:
Step-by-step explanation:
From the parallel lines, we know that corresponding angles are congruent, so:
(2y+78) = X
We also know that vertically opposite angles are equal:
X=5y
Substitute for X:
2y+78=5y
Solve:
2x-5x=-78
-3x=-78
x=26
Therefore, the measure of angle WXZ is 26.
Duri wants their backpack to weigh less than 45 pounds.
Use w to represent weights where Duri can carry their backpack.
This inequality represents that the weight of Duri's backpack is w < 45
How to represent the backpack as an expressionGiven that
Weight = Less than 45 pounds
We can use the inequality symbol to represent Duri's weight limit as follows:
w < 45
This inequality states that the weight of Duri's backpack, represented by w, must be less than 45 pounds.
Any weight value for w that satisfies this inequality is within Duri's weight limit and can be carried in their backpack.
For example, if Duri's backpack weighs 30 pounds, then w = 30 satisfies the inequality w < 45, so Duri can carry this weight.
However, if the backpack weighs 50 pounds, then w = 50 does not satisfy the inequality w < 45, so Duri cannot carry this weight.
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Complete the table
Original Price
Percent of Discount
15%
Sale Price
$146.54
The final result for the money is [tex]172.40[/tex] after you multiply it by a percent.
What does a maths percent mean?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage.
What does the word "percentage" actually mean?Rather than being stated as a fraction, a percent is a piece of an entire thing expressed as just a number between zero and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the total by its entirety and multiply the result by 100 to get the percentage.
[tex]w-[0.15]=146.54[/tex]
so [tex]w-85p=146.54[/tex]
[tex]146.54[/tex] divided by [tex]80=1.724[/tex] so when you make it a percent it turns it into [tex]172.40[/tex] which is the final answer for the money.
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Unit 1 is m feet, unit 2 is n feet unit 3 is k dollars per square feet, write an expression that could result in a final unit measure of dollars
The expression that could result in a final unit measure of dollars is given by (mnk²) dollars.
To write an expression that could result in a final unit measure of dollars, we need to consider the units given.
We have three units, i.e., m feet, n feet, and k dollars per square foot.
To convert these units to dollars, we need to multiply the given units with appropriate conversion factors.
The conversion factor for the given units is as follows:
Unit 1: 1 foot = k dollars (Conversion factor)
Unit 2: 1 foot = k dollars (Conversion factor)
Unit 3: 1 square foot = 1 x k dollars = k dollars (Conversion factor)
Now, let us write the expression that results in a final unit measure of dollars.
The expression should be written in HTML format.
Let us begin: Final Unit Measure = (Unit 1) x (Unit 2) x (Unit 3)
Final Unit Measure = (m feet) x (n feet) x (k dollars per square foot)
Final Unit Measure = m x k dollars x n x k dollars per square foot
Final Unit Measure = (m x k x n x k) dollars
Final Unit Measure = (mnk²) dollars.
Thus, the expression that could result in a final unit measure of dollars is given by (mnk²) dollars.
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in 2005 the population of a district was 35,700 with a continuous annual growth rate of approximately 4%, what will the population be in 2030 according to the exponential growth function?
The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.
The formula for the continuous exponential growth is given by the formula:
P = Pe^(rt)
where,P is the population in the future.
P0 is the initial population.
t is the time.
r is the continuous interest rate expressed as a decimal.
e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.
Therefore, t = 25.We will now use the formula:
P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.
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Answer: I got 97,042.7
Step-by-step explanation:
9 N = 480 ´ 109
(a) Write N as a number in standard form.
(1)
(b) Write N as a product of powers of its prime factors.
Show your working clearly.
(3)
(c) Find the largest factor of N that is an odd number.
Answer:
(a) To write 9 N as a number in standard form, we need to express it as a number between 1 and 10 multiplied by a power of 10. To do this, we can divide 9 N by 10 until we get a number between 1 and 10:
9 N = 480 × 10^9
9 N ÷ 10 = 48 × 10^9
9 N ÷ 10^2 = 4.8 × 10^9
9 N ÷ 10^3 = 0.48 × 10^9
9 N ÷ 10^4 = 0.048 × 10^9
9 N ÷ 10^5 = 0.0048 × 10^9
Therefore, 9 N = 4.8 × 10^10.
(b) To write N as a product of powers of its prime factors, we can first factorize N:
480 × 10^9 = 2^5 × 3 × 5 × 10^9
Then, we can express 10^9 as 2^9 × 5^9 and substitute it in the factorization:
2^5 × 3 × 5 × 2^9 × 5^9 = 2^14 × 3 × 5^10
Therefore, N = 2^14 × 3 × 5^10.
(c) To find the largest factor of N that is an odd number, we need to remove all factors of 2 from the factorization of N. We can do this by dividing N by 2 as many times as possible:
N = 2^14 × 3 × 5^10
N ÷ 2 = 2^13 × 3 × 5^10
N ÷ 2^2 = 2^12 × 3 × 5^10
N ÷ 2^3 = 2^11 × 3 × 5^10
N ÷ 2^4 = 2^10 × 3 × 5^10
N ÷ 2^5 = 2^9 × 3 × 5^10
N ÷ 2^6 = 2^8 × 3 × 5^10
N ÷ 2^7 = 2^7 × 3 × 5^10
N ÷ 2^8 = 2^6 × 3 × 5^10
N ÷ 2^9 = 2^5 × 3 × 5^10
N ÷ 2^10 = 2^4 × 3 × 5^10
N ÷ 2^11 = 2^3 × 3 × 5^10
N ÷ 2^12 = 2^2 × 3 × 5^10
N ÷ 2^13 = 2 × 3 × 5^10
N ÷ 2^14 = 3 × 5^10
Therefore, the largest factor of N that is an odd number is 3 × 5^10.
What would be the new coordinates of W' after a dilation of 3? W
The new coordinates would be
W' (12 , 6)
X'( 24 , 18 )
Z'(24 ,6 )
What exactly does coordinate geometry mean?
The term "coordinate geometry" refers to the study of geometry using coordinate points (or analytic geometry). Calculating distances between points, segmenting lines into m:n pieces, finding a line's midpoint, figuring out a triangle's area in the Cartesian plane, and other operations are all achievable with coordinate geometry.
Remember that the rule for a dilation by a factor of k about the origin is
(x,y) = (kx, ky)
Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.
w = (4,2)
x = ( 8, 6 )
z = ( 8,2)
Apply a dilation by a factor of 3:
W(4,2) ⇒ W'(3 * 4, 3 * 2) = W' (12 , 6)
X(8 ,6 ) ⇒ X'(3 * 8 , 3 * 6 ) = X' ( 24 , 18 )
Z(8 , 2 ) ⇒ Z'(3*8 , 3 * 2) = Z'(24 ,6 )
Therefore, the new coordinates would be
W' (12 , 6)
X'( 24 , 18 )
Z'(24 ,6 )
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Write an equation for line t. Show or explain how you determined your equation.
Enter your equation and your work or explanation in the box provided.
Answer:
[tex]y - 3 = \frac{2}{3} (x - 3)[/tex]
[tex]y = \frac{2}{3} x + 1[/tex]
[tex]2x - 3y = - 3[/tex]
Step-by-step explanation:
[tex]m = \frac{ - 5 - 3}{ - 9 - 3} = \frac{ - 8}{ - 12} = \frac{2}{3} [/tex]
[tex]y - 3 = \frac{2}{3} (x - 3)[/tex]
[tex]y - 3 = \frac{2}{3} x - 2[/tex]
[tex]y = \frac{2}{3} x + 1[/tex]
[tex]3y = 2x + 3[/tex]
[tex] - 2x + 3y = 3[/tex]
[tex]2x - 3y = - 3[/tex]
Work out the length of side BC in each triangle
Give your answers correct to 3 significant figures
In triangle ABC as per given measurements the measure side length BC is equal to 7.26cm (Rounding to three significant figures).
In triangle ABC,
Measure of angle A = 36 degrees
Measure of angle B = 90 degrees
length of AB = 8.7cm
Use trigonometry to solve for the length of BC.
First, Measure of angle C,
In triangle ABC,
Measure of (Angle A + Angle B + Angle C ) = 180
⇒ 36 + 90 + Measure of angle C = 180
⇒ Measure of angle C = 54 degrees
Now , use the sine function to solve for BC,
sin(C) = opposite side /hypotenuse
Substitute the values we have,
⇒ sin(54) = BC/AB
⇒BC = AB × sin(54)
⇒ BC = 8.7 × 0.834
⇒ BC = 7.2558
Rounding to three significant figures, we get,
BC ≈ 7.26 cm.
Therefore, the measure of length BC in triangle ABC is equal to 7.26cm.
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The above question is incomplete, the complete question is:
ABC is a right-angled triangle. Angle B = 90. Angle A = 36. AB = 8.7 cm. Work out the length of BC. Give your answer correct to 3 significant figures.
PLEASEEEEE HELPPPPPPP!!!!!!!
A line segment contains endpoints A(-1, 2) and B(2, 5).
Determine the point that partitions line segment AB into a 3: 6 ratio.
A 4,5/3
B 0,3
C 1/3,3
D -2,1
Answer:
We can find the point that partitions line segment AB into a 3:6 ratio by using the formula for finding a point that divides a line segment into two parts in a given ratio.
Let's call the point we're looking for "P". According to the formula, the coordinates of point P can be found using the following equations:
x-coordinate of P = [(6 * x-coordinate of A) + (3 * x-coordinate of B)] / 9
y-coordinate of P = [(6 * y-coordinate of A) + (3 * y-coordinate of B)] / 9
Using the coordinates of points A and B given in the problem, we can plug them into these equations and simplify to find the coordinates of point P:
x-coordinate of P = [(6 * -1) + (3 * 2)] / 9 = 0
y-coordinate of P = [(6 * 2) + (3 * 5)] / 9 = 3.33 (rounded to two decimal places)
Therefore, the point that partitions line segment AB into a 3:6 ratio is approximately (0, 3.33), which is closest to option A: 4,5/3.