Answer:2/30
Step-by-step explanation:
1/15*1/15=2/30
Alanna goes to the pet store to buy fish for her new 15-gallon fish tank. Each large fish costs $8 and requires 2 gallons of water. Each small fish costs $3 and requires 0.5 gallon of water. She has $100 to spend on fish at the pet store. Which combinations of large and small fish can Alanna purchase for her fish tank?
Let's set up the cost constraint inequality.
x = number of large fish, some nonnegative integer
y = number of small fish, some nonnegative integer
8x = cost of just the large fish only
3y = cost of just the small fish only
8x+3y = total cost
The total cost must be $100 or smaller, so Alanna keeps to her budget.
We form the inequality 8x+3y ≤ 100 as the cost constraint.
Because x and y are nonnegative, this means x ≥ 0 and y ≥ 0
----------------
Now let's form the water constraint inequality.
x = number of large fish
y = number of small fish
2x = amount of water needed for the large fish only
0.5y = amount of water needed for the small fish only
2x+0.5y = total amount of water needed
This total must be 15 gallons or fewer.
2x+0.5y ≤ 15
Let's multiply both sides by 2 to make that 0.5 turn into a whole number.
2x+0.5y ≤ 15
2*(2x+0.5y) ≤ 2*15
4x+y ≤ 30
This represents the water constraint.
----------------
Here are the inequalities we found
8x+3y ≤ 100
4x+y ≤ 30
x ≥ 0
y ≥ 0
The first two items represent the cost constraint and water constraint in that order. The last two items make sure that x and y can't be negative.
Valid (x,y) solutions will be found in the shaded region of that system of inequalities. Points on the boundary are included in the shaded region due to the "or equal to" as part of each inequality sign.
Below is the graph of this system of inequalities. I used Desmos to make the graph. GeoGebra is another good choice. Let me know if you need to make the graph by hand rather than use technology.
The purple shaded region represents all possible (x,y) solutions.
For example, (5,5) is in that shaded region. I've marked it in the drawing below. This means x = 5 large fish and y = 5 small fish can be bought. Alanna will stick to her budget and she'll have enough water to go around.
On the other hand, (5,25) is NOT in the shaded region. This means Alanna cannot buy x = 5 large fish and y = 25 small fish (she'll either go over budget or she won't have enough water, or both happens).
ten identical protein samples were analyzed by the bradford method for protein analysis. the following values for protein concentration were obtained. observation number protein concentration (mg/ml) 1 1.02 2 0.98 3 0.99 4 1.01 5 1.03 6 0.97 7 1.00 8 0.98 9 1.03 10 1.01 calculate sample mean
The sample mean protein concentration obtained using the Bradford method for protein analysis is 1.00 mg/ml.
We must add together all the protein concentrations and divide the total by the number of observations in order to determine the sample mean for the protein concentrations acquired using the Bradford technique for protein analysis.
We have ten identical protein samples in this instance, and the measured protein concentrations are as follows:
Protein concentration (mg/ml) observations: 1: 1.02, 2: 0.98, 3: 0.99, 5: 1.01, 6: 0.97, 8: 1.00, 9: 1.03, and 10: 1.01.
We add up the protein concentrations and divide the total by the number of observations to determine the sample mean:
[tex](1.02 + 0.98 + 0.99 + 1.01 + 1.03 + 0.97 + 1.00 + 0.98 + 1.03 + 1.01) / 10[/tex] is the sample mean.
= 1.00 mg/ml
As a result, the Bradford method for protein analysis yielded a sample mean protein content of 1.00 mg/ml.
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Find the area of the regular octagon.
Answer:
48 square centimeters
Step-by-step explanation:
[tex] \frac{1}{2} (4)(8)(3) = 48[/tex]
A number cube is rolled
twice. What is the probability
of getting a 6 on the first roll,
then a number less than 5
on the second roll?
A) 1/9
B) 2/3
C) 5/36
D 5/12
E) 1/36
Therefore , the solution of the given problem of probability comes out to be the response is A 1/9.
What is probability exactly?The primary goal of the systems inside a procedure known as criteria is to determine the average possibility that a statement is true or that a specific occurrence will occur. Any value from 0 to 1, when 0 is frequently utilized to denote that something is likely and 1 is typically used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.
Here,
If a 6 is rolled on the first roll, the probability of spinning a number less than 5 on the second roll is 2/3,
since there are the four possible outcomes on the third roll that are less than 5 (rolling a 1, 2, 3, or 4) out of an overall of six possible outcomes (rolling any plenty from 1 to 6),
so the probability of a favorable outcome is 4/6, which simplifies to 2/3.
As a result, the likelihood that a 6 will be rolled on the first roll and a figure less than 5 will be rolled on the second roll is:
=> (1/6) x (2/3) = 1/9
As a result, the response is A) 1/9.
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Question 20
After months of negotiations, Jabu's annual salary was increased by 6. 35% to R330 000. Determine his
previous monthly salary and the monthly increase he will be getting.
Original salary of R20 955. 00, with an increase of R6 545. 00 per month.
[2] Original salary of R25 858. 02, with an increase of R1 641. 98 per month
(3) Original salary of R27500. 00, with an increase of R1 746. 25
per
month.
14] Original salary of R25 858. 02, with an increase of R1 746. 25 per month.
Jabu's Monthly salary is of R27500.00, with an increase of R1 746.25 per month. Jabu's monthly increase is R1 746.25. The correct answer is option 3.
To find Jabu's previous monthly salary, we can use the formula:
Previous monthly salary = (Annual salary / 12)
Since Jabu's new annual salary is R330 000, his previous annual salary would be:
Previous annual salary = (New annual salary / 1.0635) = (R330 000 / 1.0635) = R310 020.10
Therefore, Jabu's previous monthly salary would be:
Previous monthly salary = (Previous annual salary / 12) = (R310 020.10 / 12) = R25 835.01
To find the monthly increase, we can subtract Jabu's previous monthly salary from his new monthly salary:
Monthly increase = (New monthly salary - Previous monthly salary) = (R27 618.38 - R25 835.01) = R1 783.37
Therefore, Jabu's monthly increase is R1 746.25 (rounded to the nearest cent).
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Kyle is playing a game where he rolls a number cube twice and flips a coin twice. The number cube is labeled 1 to 6. The coin can land on heads or tails.
If the number cube lands on 5 both times and the coin lands on heads both times, Kyle wins a prize. What is the probability that Kyle wins the prize?
The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is [tex]1/144[/tex]
What is the probability?The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.
Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:
P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)
[tex]= (1/6) \times (1/6) \times (1/2) \times (1/2)[/tex]
[tex]= 1/144[/tex]
Therefore, the probability that Kyle wins the prize is ,[tex]1/144[/tex] or approximately [tex]0.0069[/tex] (rounded to four decimal places).
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Suppose we have a solid with volume 10 cubic units.
It's dilated, and the volume of the image is 40 cubic
units.
How can you find the scale factor that was used?
Answer:
Step-by-step explanation:
We can use the fact that the ratio of the volumes of two similar solids is equal to the cube of their corresponding linear dimensions, also known as the volume-scale factor:
(volume of image) / (volume of original) = (linear dimension of image / linear dimension of original)^3
(40 cubic units) / (10 cubic units) = (linear dimension of image / linear dimension of original)^3
4 = (linear dimension of image / linear dimension of original)^3
Taking the cube root of both sides, we get:
(cube root of 4) = (linear dimension of image / linear dimension of original)
Simplifying, we have:
2 = (linear dimension of image / linear dimension of original)
Therefore, the linear dimensions of the image are two times greater than those of the original. Thus, the scale factor is 2.
the circle below has center O, and its radius is 5 ft. Given that m AOB = 70, Find the area of the shaded region and the length of the arc ADB
The area of the shaded region of the circle is 63.24 ft²
How to find the shaded area?We know that the area of a circle of radius R is given by the formula:
Area = pi*R²
Where pi = 3.14
If we have only a section of a circle defined by an angle θ, the area of that section will be:
area = (θ/360°)*3.14*R²
Here we know that the radius is 5 feet, and that AOB (the non-shaded part) is 70°, then we will have:
θ = 360° - 70° = 290°
Then the area of the shaded region is:
area = (290°/360°)*3.14*(5 ft)² = 63.24 ft²
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Benzoic acid is used to determine the heat capacity of bomb calorimeters because it can be obtained in pure form and its energy of combustion is known very accurately (-26.43 kJ/g).
Determine the calorimeter constant of the calorimeter that had a temperature increase of 9.199 degrees Celsius when 3.500 g of benzoic acid was used.
Benzoic acid is used to determine the heat capacity of bomb calorimeters because it can be obtained in pure form and its energy of combustion is known very accurately (-26.43 kJ/g).
The calorimeter constant is -2873.5.
Determine the calorimeter constant of the calorimeter that had a temperature increase of 9.199 degrees Celsius when 3.500 g of benzoic acid was used.To determine the calorimeter constant, follow these steps:
Explanation:
1. Calculate the energy released by the benzoic acid combustion: Multiply the mass of benzoic acid by its energy of combustion.
Energy released = mass × energy of combustion
Energy released = 3.500 g × -26.43 kJ/g = -92.505 kJ
2. Convert the temperature increase to a change in energy: Multiply the temperature increase by the mass of benzoic acid.
ΔEnergy = temperature increase × mass of benzoic acid
ΔEnergy = 9.199°C × 3.500 g = 32.1965 J
3. Determine the calorimeter constant: Divide the energy released by the change in energy.
Calorimeter constant = Energy released / ΔEnergy
Calorimeter constant = -92.505 kJ / 32.1965 J
Note: We need to convert the units to be consistent, either to J or kJ.
1 kJ = 1000 J, so -92.505 kJ = -92505 J.
Calorimeter constant = -92505 J / 32.1965 J = -2873.5
The calorimeter constant is -2873.5.
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hey there mide helping me⭒What is the missing numerator and denominator? Three (?) times (?) fourths equals nine twentieths⭒ this is for my ↣⭒exam⭒↢ (=^・ェ・^=)⭒meow⭒ will get brainiest
The answer is in numerator = 3 and denominator = 5
What are numbers?Numbers are present in every part οf οur everyday lives, including the number οf laps we cοmplete οn the racetrack, the number οf hοurs we sleep at night, and many οther things.
In math, a number can be even, οdd, prime, cοmpοsite, decimal, fractiοnal, ratiοnal, irratiοnal, natural, integer, real, whοle, οr any cοmbinatiοn οf these.
Numbers are the basis οf mathematics
We must learn abοut numbers if we are tο understand math.
There are many different kinds οf numbers.
There is a lengthy list that includes whοle numbers, οrdinal numbers, οrdinal numbers, natural numbers, οdd numbers, even numbers, cοnsecutive numbers, and sο οn.
3*3 = 9
5*4=20
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an ai that plays the game of go has a 90\% chance of winning each game it plays against a human grandmaster. what is the binomial probability of the human beating the ai 1 out of 3 games?
The probability of the human Grandmaster winning one out of three games against the AI is approximately 0.243 or 24.3%.
Let's denote the probability of the human Grandmaster winning one game as p. Then the probability of the AI winning one game is 0.9, which means the probability of the human winning one game is 0.1. Since we want to calculate the probability of the human winning one game out of three, we can use the binomial distribution formula:
[tex]P(X=k) = (^n _k) \times p^k \times (1-p)^{(n-k)}[/tex]
Where:
P(X=k) is the probability of getting k successes in n trials
(n choose k) is the binomial coefficient, which is the number of ways to choose k successes from n trials
p is the probability of success in one trial
(1-p) is the probability of failure in one trial
k is the number of successes we are interested in (in this case, k=1)
n is the total number of trials (in this case, n=3)
Plugging in the values, we get:
P(X=1) = (3 choose 1) * 0.1^1 * 0.9^(3-1) = 3 * 0.1 * 0.81 = 0.243 or 24.3%
This means that there is a decent chance for the human to win at least one game, but it is still more likely for the AI to win all three games.
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a large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, find the probability of selecting 3 red marbles
A large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, the probability of selecting 3 red marbles is 1/54.
The probability of selecting 3 red marbles is 1/54.What is a probability?
Probability refers to the likelihood or chance of an occurrence. The probability of an event occurring is the ratio of the number of favourable outcomes to the total number of possible outcomes.
A fraction or a decimal is used to express it.The total number of marbles in the bag is 10 + 5 + 7 = 22 marbles.
There are ten red marbles in the large bag, so the number of ways to select 3 red marbles from ten red marbles is:
[tex]10C_3 = (10 \times 9 \times 8) / (3 \times 2 \times 1) = 120[/tex]
There are 22 marbles in the bag, therefore, the total number of ways to pick 3 marbles from 22 is:
[tex]22C_3 = (22 \times 21 \times 20) / (3 \times 2 \times 1) = 1540[/tex]
Hence, the probability of choosing 3 red marbles out of the 22 marbles in the bag without replacement is:120/1540 = 1/54
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
40 min 25 min
Answer:
Part A is 8/13 of the whole
Part B is 5/13 of the whole
Step-by-step explanation:
Assuming there are no other parts,
the Whole = A + B is the denominator:
Whole = 40 + 25 = 65
Part A = 40 and Part B = 25 are numerators for each fraction.
The fractions are then:
40/65 and 25/65
Meaning:
Part A is 40/65 of the whole
Part B is 25/65 of the whole
Reducing the fractions, it is also true that:
Part A = 8/13 of the whole
Part B = 5/13 of the whole
Last sentence was find the volume of the larger pyramid
a)the ratio of the heights of the pyramids is 5:3. b)the volume of the larger pyramid is 23.04 cm³.
what is volume ?
Volume is a measure of the amount of space that a three-dimensional object occupies. It is usually measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be calculated using different formulas depending on its shape.
In the given question,
a. Let the height of the smaller pyramid be h₁ and the height of the larger pyramid be h₂. Since the two pyramids are similar, their corresponding linear dimensions are in the same ratio as the areas of their bases. Therefore, we have:
(base area of smaller pyramid)/(base area of larger pyramid) = (linear dimension of smaller pyramid)² / (linear dimension of larger pyramid)²
Since the linear dimension is the height in this case, we can substitute the given ratio of the base areas to obtain:
25/9 = (h₁/h₂)²
Taking the square root of both sides, we get:
h₁/h₂ = 5/3
Therefore, the ratio of the heights of the pyramids is 5:3.
b. Since the volume of a pyramid is proportional to the cube of its height, we have:
(volume of smaller pyramid) / (volume of larger pyramid) = (h₁/h₂)³ = (5/3)³ = 125/27
Substituting the given volume of the smaller pyramid, we get:
108 / (volume of larger pyramid) = 125/27
Solving for the volume of the larger pyramid, we obtain:
volume of larger pyramid = (27/125) * 108 = 23.04 cm³ (rounded to two decimal places)
Therefore, the volume of the larger pyramid is 23.04 cm³.
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650 of those surveyed said their favorite color was blue. if 65% of the students surveyed said their favorite color was blue, how many students were surveyed in total?
Answer:
let X be the value of the total students
[tex] \frac{65}{100} \times x = 650 \\ \\ \frac{65x}{100 } = 650 \\ if \: w \:e \: crossmultipl \\ 65x = 65000 \\ x = 65000 \div 65 \\ x = 1000[/tex]
Which expression is equivalent to
-5
28p9q5
12pq
7 ? Assume P≠0,q≠0.
The expression -5 + 28p9q5 - 12pq + 7 is equivalent to 7. Since all the terms except the last one contain variables, we can use algebra to solve for the value of the expression.
What is algebra?Algebra is a branch of mathematics which deals with the manipulation of equations, inequalities, and other mathematical expressions. Algebra is used to solve equations, simplify expressions, and model real-world problems.
To begin, we can add -5 and 7 to obtain 2. This means that the expression is now equal to 2 + 28p9q5 - 12pq. We can then simplify this expression by combining like terms.
Since 28p9q5 and -12pq are both products of the same variables, we can add them together. When we do so, we obtain 16p9q5, which means that the expression is now equal to 2 + 16p9q5.
Finally, we can simplify the remaining term by breaking down the product. We can divide 16 by 8 to obtain 2, and then divide 9 by 3 to obtain 3. This means that the expression is now equal to 2 + 2p3q5. Since there are no more terms to simplify, we can conclude that the answer is 2.
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For 5 days mr fransico had a total 10. 5 hours of overtime in the office what was his average daily overtime?
Mr. Fransico had average overtime in a day is 2.1 hours.
In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.
For 5 days Mr fransico had a total of 10. 5 hours of overtime in the office
Then the average daily overtime is-
10.5÷5 = 2.1 hours
Hence Mr. Fransico had total overtime in a day is 2.1 hours.
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I just need help with this, please! 10 points!
The given data comprises of a right triangle in which the base is denoted by x whose value is found to be 10.01.
Define trigonometric identity of sine?It states that the ratio of the length of the side opposite to the angle to the length of the hypotenuse is equal to the sine of the angle.
The given data comprises of a right triangle in which the base is denoted by x and the perpendicular is 8. The angle formed between the base and hypotenuse is 53 degree.
To solve this problem, we can use the trigonometric identity of sine.
Mathematically, it can be expressed as:
sin 53° = Perpendicular/Hypotenuse
8/x = sin 53°
x = 8/sin 53°
x = 8/ 0.7986
x ≈ 10.01
Hence, the value of x is 10.01.
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circle project represented in a graph
1. Draw a point at (1,-2).
2. Draw a long radius of 8 units.
3.Using a compass, draw a circle with your point from step one as its center and the point from step two as the side.
4.Using a protractor, draw a 70 degree arc
5. draw a central angle that intersects your arc
6. Draw an inscribed angle that intersects an arc of 40 degrees
7.draw a tangent line
8. draw a secant line
9. write the equation of your circle
Answer:
search up the answers
Step-by-step explanation:
you spin two wheels with equal size wedges labeled with numbers 1 through 8. what is the probability that at least one wheel lands on an even value and the first value is less than or equal to 4?
The probability that either of spin two wheel lands on an even value is 1.
Define the term probability?
Probability is a way to gauge how likely something is to happen. Even though no event can be predicted with absolute certainty, probability can be used to express how likely it is that it will happen.
For the stated question-
Total number marked on the wheel (1 to 8) = 8 numbers.
Total even number (2,4,6,8) = 4numbers
Probability of getting an even number on one wheel = 4/8 = 1/2.
Let the probability of getting an even number on one wheel P(A).
Then, the Probability of getting an even number on the second wheel P(B).
Then,
Only only wheel have the even number,
P(A∩B) = 0.
Thus,
Probability that either wheel lands on an even value;
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 1/2 + 1/2 - 0
P(A∪B) = 1
Thus, probability that either wheel lands on an even value is 1.
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Can someone please help me answer these I’m gonna have a lot of these on my test I just need help answering this one and if you could please try to explain it to me to that would be great
The formula for percent from the board can be expressed this way:
The total number of students that like pineapple pizza * 100.
The total number of students
A (i). The part is the number of students that like pineapple pizza which is 5.
(ii). The whole is the total number of students namely; 7 + 12+ 5 + 3 + 6 = 33.
(iii). Plugging the part and whole into the equation, we will have: 5/33 * 100
(iv). Final answer is = 15.15%
What is a percentage?A percentage is a mathematical expression that is aimed at calculating the proportion of a given quantity out of 100. In the question, we are requested to find what proportion of students like pineapple pizza.
To get the answer, we first have to determine the number of students that like pineapple pizza which is 5 according to the table. Next, we get the sum of students which is 33. The percentage will then get the fraction and multiply the result by 100. The final answer is 15.15%.
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a car dealership pays $8,350 for a car, they mark up the price by 17.4% to get the retail price. What is the retail price of the car at this dealership
Factor out the GCF from the polynomial.
3x³y² - 9xz4 + 8y²z
The expression 3x³y² - 9xz⁴ + 8y²z have no GCF greatest common factor but the terms 3x³y² and 8y²z have GCF equal to y².
What is (GCF) greatest common factor?The GCF defines the highest common factor present in between given two or more numbers or algebraic expressions.
we shall determine the GCF greatest common factor for the algebraic expression 3x³y² and 8y²z as follows:
3x³y² = y² × 3x³
8y²z = y² × 8z
both terms 3x³y² and 8y²z have y² common to them, so we can write;
3x³y² + 8y²z = y² × 3x³ + y² × 8z
3x³y² + 8y²z = y²(3x³ + 8z)
In conclusion, the expression 3x³y² - 9xz⁴ + 8y²z have no GCF greatest common factor but the terms 3x³y² and 8y²z have GCF equal to y².
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Colleen paid $13.70 to download 12 songs from an online music service. Some of the songs were on sale and cost $0.99 each. The rest were regularly priced at $1.25 per song. Let x represent the number of sale priced songs, and let y represent the number of regularly priced songs. This situation can be represented by the system x+y=12 and 0.99x+1.25y=13.7 . How many of each type of song did Colleen purchase?
Using equations, we can find that the number of sale-priced songs is 5 and the number of regularly priced songs is 7.
What exactly is an equation system?Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol.
As per the question, equation given are:
x + y = 12
x = 12 - y
Now, substituting the value in:
0.99x+1.25y = 13.7
= 0.99(12-y) +1.25y = 13.7
= 11.88 - 0.99y + 1.25y = 13.7
= 0.26y = 13.7 - 11.88
0.26y = 1.82
y = 1.82/0.26
y = 7
Now, substitute this value,
x = 12 - 7
x = 5
As a result, there are 5 songs on sale and 7 songs that are regularly priced.
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Please help me this is due after class (20 mins) (I-Ready Math)
YOU GET 20 POINTS!!!!
Here's the picture
The value of h in the given parallelogram is 6 units, which can be found by using the formula for the area of a parallelogram.
In the given parallelogram, we can see that the base is 12 units long and the distance between the base and the opposite side is 6 units.
To find the value of h (the height or distance between the base and the opposite side), we can use the formula for the area of a parallelogram which is:
Area = base x height
Since we know the area of the parallelogram is 72 square units (given in the diagram), we can plug in the values we know and solve for h:
72 = 12 x h
h = 72/12
h = 6
Therefore, the value of h in the parallelogram is 6 units.
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What did I do wrong? (#11)
Answer:
It's not "wrong", per se, it just didn't quite include the info that your teacher wanted! I personally would have said "Rotate 180 degrees about F", so I think that may be it.
Let me know if this helped by hitting the thanks button/marking brainliest! If not, please comment and I'll get back to you ASAP.
Use the given information to prove the following theorem.
Answer: two right-angled triangle, equilateral triangle
Step-by-step explanation:
It is a combination of two right-angled triangle or it is an equilateral triangle.
Explanation:
You want to prove a point P on the perpendicular bisector of segment YZ is equidistant from Y and Z.
Statement . . . . Reason1. PX is the perpendicular bisector of YZ . . . . given
2. angles at X are right angles . . . . definition of perpendicular
3. YX = XZ . . . . definition of bisector
4. PX = PX . . . . reflexive property of congruence
5. ∆PXY ≅ ∆PXZ . . . . LL congruence theorem
6. YP ≅ ZP . . . . CPCTC
divide the circumference of a pumpkin by its diameter and what do you get?
Dividing the circumference of a pumpkin by its diameter gives a value approximately equal to pi (π)
When you divide the circumference of a pumpkin by its diameter, you get a value that is approximately equal to the mathematical constant pi (π), which is approximately 3.14159.
This is because pi represents the ratio of the circumference of a circle to its diameter, and a pumpkin is roughly spherical in shape. So, no matter how big or small the pumpkin is, if you measure its circumference and diameter and divide them, the result will be very close to pi.
Mathematically, this can be represented by the formula
pi ≈ circumference / diameter
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scores on an iq test are normally distributed with a mean of 100 and a standard deviation of 15. what is the z-score for an iq score of 122?
The z-score for an IQ score of 122 is 2.
This is calculated by subtracting the mean (100) from the score (122) and dividing by the standard deviation (15). So, 122-100=22, 22/15=2.
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find the area, to the nearest hundredth, of a circle with a circumference of 19 centimeters. use 3.14 for pi
The area of the circle with circumference 19cm is 6.42cm²( nearest hundredth).
What is area of circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2. Where r is the radius.
The circumference of a circle is given as ;
C = 2πr
C = 9cm
therefore, 9 = 2× 3.14 × r
9 = 6.28r
r = 9/6.28
r = 1.43 cm
Area of circle = πr²
= 3.14 × 1.43²
= 6.42cm²( nearest hundredth)
therefore the area of the circle is 6.42cm²
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