Write a similarlity statement for the two triangles shown below

Answer:

90/π degree

Step-by-step explanation:

length of arc, l= 20cm

length of pendulum, r= 40cm

let the angle be a:

we know that , r *a=l

                          40*a=20

                              a= 20/40=1/2 radian

                                = 1/2*(360/2π)=90/ π degree

Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

can quickly be written as a^2+b^2=c^2

where a and b are the legs and c is the hypotenuse (longest side, opposite the RIGHT/90 degree angle.

You can call either leg a or b, but the hypotenuse is always c.

Step-by-step explanation:

School to gas:

75^2-25^2 = a^2

5000=a^2

Take square root of both sides

70.7=a

So select 70.7 for school to gas.

Museum to vet office:

18^2-15^2=a^2

99=a^2

Take square root of both sides

9.9 = a.

So select 9.9 for museum to vet.

Vet to hospital:

15^2+25^2=c^2

850=c^2

Take square root of both sides

29.2=c

So select 29.2 for vet to hospital.

Museum to bakery:

60^2-45^2=a^2

1575=a^2

Take square root of both sides

39.7 = a

So select 39.7 for museum to bakery.

Bakery to house:

45^2+20^2=c^2

2425=c^2

Take square root of both sides

49.2=c

So select 49.2 for bakery to house.

Cinema to fire station:

50^2+20^2=c^2

2900=c^2

Take the square root of both sides

c=53.9

So select 53.9 for cinema to fire station.

School to fire station:

The hypotenuse (c) = 75+15=90. Look at the map to see how I got these numbers and added them up.

The leg is 30.

90^2-30^2=a^2

7200=a^2

Take the square root of both sides

84.9=a

So select 84.9 for school to fire station.

Answer: 3.525, 3.25, 3.75

Step-by-step explanation:

This makes sense because these values are all .25 or less away from 3.5

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The amount of people in the city after 2 years is 27.05 thousands

From the question, we have the following parameters that can be used in our computation:

The expression 25.75(1.025)

Express as a function

So, we have

P(x) = 25.75(1.025)ˣ

In two years, we have

x = 2

Substitute the known values in the above equation, so, we have the following representation

P(2) = 25.75(1.025)²

Evaluate

P(2) = 27.05

Hence, the population is approximately 27.05 thousands

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the final answer is 5,807 nickels to make a stack as tall as the Empire State Building.

To calculate the number of nickels required to make a stack as tall as the Empire State Building, we first need to convert the height of the building from feet to millimeters. Since 1 foot is equal to 304.8 millimeters, the height of the building in millimeters would be 381 x 304.8 = 11613.8 millimeters.

Next, we need to calculate the thickness of a single nickel in millimeters, which is 2 millimeters.

To find the number of nickels required, we divide the total height of the building (11613.8 millimeters) by the thickness of a single nickel (2 millimeters). This gives us a total of 5,806.9 nickels.

However, since we cannot have a fraction of a nickel, we need to round up to the nearest whole number. Therefore, the final answer is 5,807 nickels to make a stack as tall as the Empire State Building.

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The cost of 5 small greeting cards and 4 large greeting cards is given by $24.25.

Total cost of x small greeting cards and y large greeting cards is given by $(1.25x + 4.5y).

Given that the cost of each small cards = $1.25

the cost of each big cards = $4.50

So the cost of 5 small cards = $1.25*5 = $6.25

the cost of 4 large greeting cards = $4.5*4 = $18

So total cost to get 5 small greeting cards and 4 large greeting cards = 6.25 + 18 = $24.25

Cost of x small greeting cards = $1.25x

Cost of y large greeting cards = $4.5y

Total cost of x small greeting cards and y large greeting cards = $(1.25x + 4.5y).

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The amount of water that Mai poured into the pitcher is (y) - (x) liters.

One possible way to find the amount of water that Mai poured into the pitcher is to subtract the initial volume of the partially filled pitcher from the final volume of the pitcher after the water has been added. The amount of water that Mai poured into the pitcher is therefore (final volume) - (initial volume) liters.

Let's assume that the initial volume of the partially filled pitcher is x liters and the final volume of the pitcher after Mai has poured in water is y liters. Then, the amount of water that Mai poured into the pitcher can be found using the expression:

(final volume) - (initial volume) = (y) - (x) liters.

Therefore, the amount of water that Mai poured into the pitcher is (y) - (x) liters.

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The value of cos A in the triangle is 1 / 9.

The triangle is given as ABC. The side lengths are a, b and c. Therefore, cos A of the triangle can be found using cosine rule as follows:

a² = b² + c² - 2bc cos A

a = 4

b = 3

c = 3

Therefore,

4² = 3² + 3² - 2(3)(3) cos A

16  = 9 + 9 - 18 cos A

16 - 18 = - 18 cos A

-2 = - 18 cos A

divide both sides by - 18

cos A = - 2 / - 18

cos A = 1 / 9

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The values of each expression are as follows:

5. ac = 48

6. 1 / 2 b = 3 / 2

7. abd = 324

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.

Therefore, let's find the values of each expression by find substituting the values.

Hence,

5.

a = 12

c = 4

ac = 12 × 4 = 48

6.

b = 3

1 / 2 b = 1 / 2 (3) = 3 / 2

7.

abd = 12 × 3 × 9

abd = 324

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The circumference and area, correct to the nearest tent of a circle with diameter are:

C = 16.6 units.

A = 22.1 square units.

In Mathematics and Geometry, the circumference of a circle can be determined by using the following mathematical equations:

C = πD or C = 2πr

Where:

By substituting the given parameters into the formula for the circumference of a circle, we have the following;

Circumference of circle, C = 3.14 × 5.3

Circumference of circle, C = 16.6 units.

In Mathematics and Geometry, the area of a circle can be calculated by using this formula:

Area of circle = πd²/4

Area of circle = 3.14 × 5.3²/4

Area of circle = 22.1 square units.

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Mr. cruz is selling coupons for a carnival. he has 2745 food coupons and some game coupons. Mr. Cruz has 734 game coupons.

Let's start by setting up some equations based on the information given:

Mr. Cruz has 2745 food coupons and some game coupons.

He sells 639 of the food coupons, so he has 2745 - 639 = 2106 food coupons left.

He has 1372 more food coupons than game coupons. Let's call the number of game coupons "x". Then, the number of food coupons he has left is x + 1372.

Putting these equations together, we can create the following equation:

x + 1372 = 2106

To solve for x, we can subtract 1372 from both sides:

x = 2106 - 1372

x = 734

Therefore, Mr. Cruz has 734 game coupons.

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The coefficient of determination, denoted by R^2, is a measure of how well the regression model fits the data. It represents the proportion of the total variation in the dependent variable (sales dollars) that is explained by the independent variable (number of contacts).

In this case, we can use the formula:

R^2 = SS_regression / SS_total

where SS_regression is the sum of squares of the regression (13,591.17) and SS_total is the total sum of squares (14,249.12).

Thus,

R^2 = 13,591.17 / 14,249.12

R^2 = 0.953

Therefore, the coefficient of determination is 0.953 or 95.3%. This means that 95.3% of the variation in sales dollars can be explained by the number of contacts made by the salesperson, and the remaining 4.7% is due to other factors not included in the model.

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Answer:

55r737tdfrrgutyrvytuyt

Answer:

  (6, 3) and (6, -4)  or  (-4, 3) and (-4, -4)

Step-by-step explanation:

You want the coordinates of the remaining two vertices of a rectangle with area 35 square units, the endpoints of one side being (1, 3) and (1, -4).

A rectangle is a quadrilateral with adjacent sides at right angles. The area of it is the product of its length and width.

The given side is a vertical line (x=1) with points on it that are 7 units apart:

  3 -(-4) = 7

The area being 35 square units means the length of an adjacent side must be ...

  LW = 35

  7W = 35

  W = 35/7 = 5 . . . . units

The opposite side of the rectangle will be 5 units away, on a vertical line that is either x = 1+5 = 6, or x = 1 -5 = -4.

The y-coordinates of the endpoints of the opposite side will be the same as the y-coordinates of the given points. That is because the top and bottom edges of the rectangle are horizontal lines.

For the rectangle to the right of the given line, the missing coordinates are (6, 3) and (6, -4).

For the rectangle to the left of the given line, the missing coordinates are (-4, 3) and (-4, -4).

__

Additional comment

The attachment shows the two possible sets of answers.

(a) A{2} = A. This statement is an identity

(b) AU{2} = A. This statement is not an identity.

(c) An Am = An+m. This statement is an identity.

(d) A*A = A. This statement is not an identity.

(e) A UA A* = A*. This statement is an identity.

(f)  (4*)* = A*. This statement is not an identity.

a. A{2} = A

This statement is an identity, meaning it is always true for any set of strings A. A{2} represents the concatenation of A with itself, so A{2} consists of all possible strings that can be formed by concatenating two strings from A. Since A is a set of strings over V, all possible strings that can be formed by concatenating two strings from A are also in A, so A{2} is a subset of A. And since A is a set, it contains all of its subsets, so A is also a subset of A{2}. Therefore, A{2} = A, and this is true for any set of strings A.

b. AU{2} = A

This statement is not an identity. If A is the set of all possible strings over V, then AU{2} is the set of all possible strings that can be formed by concatenating zero, one, or two strings from A. But if nobody receives an R and exactly two students receive a C, then not all possible strings from AU{2} are in A. For example, the string "CC" is in AU{2}, but it is not in A because not all possible strings in A contain at least two Cs and no Rs. Therefore, AU{2} is a subset of A, but it is not necessarily equal to A, so this statement is not an identity.

c. An Am = An+m

This statement is an identity. An is the set of all possible strings that can be formed by concatenating n strings from A, and Am is the set of all possible strings that can be formed by concatenating m strings from A. Therefore, An Am is the set of all possible strings that can be formed by concatenating n+m strings from A. And An+m is the set of all possible strings that can be formed by concatenating n+m strings from A. Since both sets consist of the same strings, they are equal, so this statement is true for any set of strings A.

d. A*A = A

This statement is not an identity. AA represents the concatenation of all possible pairs of strings from A, which may result in new strings that are not in A. For example, if A = {"a", "b"}, then AA = {"aa", "ab", "ba", "bb"} includes the string "aa" which is not in A. Therefore, A*A is a subset of A, but it is not necessarily equal to A, so this statement is not an identity.

e. A UA A* = A*

This statement is an identity. A* is the set of all possible strings that can be formed by concatenating any number of strings from A, including zero strings. Therefore, A UA A* is the set of all possible strings that can be formed by concatenating zero or more strings from A, which is equal to A*. This is because any string in A* can be formed by concatenating zero or more strings from A, and any string that can be formed by concatenating zero or more strings from A is in A UA A*. Therefore, this statement is true for any set of strings A.

f. (4*)* = A*

This statement is not an identity. (4*)* represents the set of all possible strings that can be formed by concatenating zero or more strings from 4*, where 4* is the set of all possible strings of length 4 over V. A* is the set of all possible strings that can be formed by concatenating any number of strings from A, including zero strings.

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If someone wins 2 blue balls and loses 3 red balls every day for 5 days, and ends up with the same number of blue and red balls, then they must have started with 25 red balls.

Explanation:

Let x be the number of red balls the person started with. After 5 days, they would have won 2 × 5 = 10 blue balls and lost 3 × 5 = 15 red balls. So, the person would have a total of (x - 15) red balls and (10 + 2 × 5) = 20 blue balls. We know that the person ends up with the same number of blue and red balls, so we can set up the equation:

x - 15 = 20

Solving for x, we get:

x = 35

Therefore, the person started with 35 red balls. However, this does not satisfy the condition that the person ends up with the same number of blue and red balls, since 35 - 15 = 20 ≠ 20 blue balls. So, we made a mistake in our assumption that the person started with x red balls. Let's try again:

Let y be the number of red balls the person started with. After 5 days, they would have won 2 × 5 = 10 blue balls and lost 3 × 5 = 15 red balls. So, the person would have a total of (y - 15) red balls and 20 blue balls. We know that the person ends up with the same number of blue and red balls, so we can set up the equation:

y - 15 = 20

Solving for y, we get:

y = 35

Therefore, the person started with 35 red balls and ended up with 20 blue balls and 20 red balls, satisfying the given condition. So, the answer is that the person started with 25 red balls.

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The perimeter of the points is 18.61 units

The perimeter of an object is the sum of the lengths of the sides of the object.

The formula to find the distance (length) between the two points is usually given by d =√((x₂ – x₁)² + (y₂ – y₁)²)

(-3,1) and (1,3):

(-3,1) : x₁ = -3 , y₁ = 1

(1,3) : x₂ = 1 , y₂ = 3

d =√((1 – (-3))² + (3 – 1)²) = 4.47 units

(1,3) and (2,-4):

d =√((2 – 1)² + (-4 – 3)²) = 7.07 units

(2,-4) and (-3,1)

d =√((-3 – 2)² + (1 – (-4))²) = 7.07 units

Perimeter = 4.47 + 7.07 + 7.07

Perimeter = 18.61 units

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Answer:

$0.16

Step-by-step explanation:

It is 16 cents because a singular jar of caramel sauce is modeled by 6.4/2=3.2 then you multiply 1/20 x 3.2 and you get 0.16, so it costs 16 cents in caramel sauce to make one banana.

The fewest number of coins that Kevin can use to make exactly 90 cents is six coins: three 25-cent coins and three 5-cent coins.

To determine the fewest number of coins that Kevin can use to make exactly 90 cents, we need to consider the values of the coins and how they can add up to 90 cents. We want to use the fewest number of coins possible, so we should start with the highest-value coins first. In this case, the highest-value coin is the 25-cent coin.

Since Kevin needs exactly 90 cents, he could use three 25-cent coins, which would give him 75 cents. He would then need 15 more cents to make 90 cents. The only coins that he has left are 5-cent coins and 10-cent coins. If he were to use two 10-cent coins, he would have to use three 5-cent coins to make up the remaining 5 cents, for a total of five coins. However, if he uses three 5-cent coins instead of two 10-cent coins, he will have used six coins in total, which is the fewest number of coins possible. Therefore, the fewest number of coins that Kevin can use to make exactly 90 cents is six coins: three 25-cent coins and three 5-cent coins.

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The account increases in value by 1% every quarter, which is equivalent to 1/4% every month.

Savings interest is calculated on a daily basis and deposited into the account on the first day of the next quarter. The interest rate will depend on the balance in the account. Now it's between 3% and 3.5%.

To find the increase in value for an account with an APR of 4% and quarterly compounding, we'll first need to convert the APR to a quarterly interest rate.
1. Divide the APR by the number of compounding periods in a year: 4% / 4 = 1%.
2. The account increases in value by 1% every quarter.

Your answer: a. 1%

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Rick sold 99 cans of popcorn

To find the number of popcorn cans sold by Rick,

First, we need to calculate the total number of cans sold by all the students, which is the sum of the cans sold by each student. The total number of cans sold is

76 + 84 + 119 + 81 + Rick = Total cans sold

The mean number sold is given as 91.8. So, we can write it as a equation using the mean formula,

Mean = sum of all values / total number of values

91.8 = (76 + 84 + 119 + 81 + Rick) / 5

Now, we can simplify the equation by multiplying both sides by 5 to eliminate the fraction:

5 x 91.8 = 76 + 84 + 119 + 81 + Rick

459 = 360 + Rick

Rick = 459 - 360

Rick = 99

Therefore, Rick sold 99 cans of popcorn

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The expression that represents the surface area of the prism is 2(3x4 + 4x5 + 3x5), which simplifies to 94.

To find the surface area of a prism, you need to calculate the area of each face and add them together. In this case, the prism has a rectangular base with dimensions of 3 units by 4 units, and the height of the prism is 5 units. So, the area of the two rectangular faces is 3x4 = 12 units² each, and the area of the top and bottom faces (which are also rectangles) is 5x3 = 15 units² each. The area of the two triangular faces is (1/2)(3)(5) = 7.5 units² each. Adding all of these areas together gives:

2(12 + 15 + 15 + 7.5 + 7.5) = 2(57) = 114 units²

However, since the question asks for an expression rather than a specific value, we can simplify this expression by factoring out a common factor of 2 and using distributive property:

2(3x4 + 4x5 + 3x5) = 2(12 + 20 + 15) = 2(47) = 94

Therefore, the expression that represents the surface area of the prism is 2(3x4 + 4x5 + 3x5), which simplifies to 94.

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Which expression represents the surface area of the prism?

3, 4, 5, 10.

A distribution in which all the values have the same frequency is called a uniform distribution. This type of distribution is characterized by an equal probability of each value occurring within a given range or interval.

In a uniform distribution, the probability density function is a constant value, indicating that all values have the same chance of occurring.
Uniform distributions are often used in statistical analyses and probability theory, particularly in cases where there is no reason to expect one value to occur more frequently than any other. For example, rolling a fair die would result in a uniform distribution, with each of the six possible outcomes having an equal chance of occurring.
Uniform distributions can be visualized using histograms or probability density functions, which display the frequency or likelihood of each value occurring. In practice, many real-world distributions are not perfectly uniform, but they may approximate a uniform distribution in certain circumstances.
Overall, uniform distribution is an important concept in statistics and probability theory, helping to understand the likelihood and frequency of different values occurring within a given data set or range.

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The length of the other leg of the right triangle is 6 m.

The length of the hypotenuse of a right triangle is 10 m and the length of one of the legs is 8 m.

We can use the Pythagorean theorem to find the length of the other leg of the triangle:

a^2 + b^2 = c^2

where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.

Substituting the given values, we get:

8^2 + b^2 = 10^2

64 + b^2 = 100

b^2 = 36

b = 6

Therefore, the length of the other leg of the right triangle is 6 m.

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Okay, let's break this down step-by-step:

* The sum of angles in a quadrilateral is 360 degrees

* Angles DAB and BCD are the same size

* Angle ABC is not given, so we'll call it 'x' degrees

* Putting this together:

360 = 38 + x + 226 + 38

360 = 302 + x

x = 58

Therefore, angle DAB = 58 degrees.

The answer is:

DAB = 58°

The answer is not one of the options given, but the correct scale factor is 1.5.

To find the scale factor of the dilation from the black triangle to the blue triangle, we need to compare the corresponding side lengths of both triangles.

Looking at the black triangle, we can see that the length of the side opposite the right angle is 6 cm, while the length of the shorter adjacent side is 2 cm.

In the blue triangle, the corresponding side opposite the right angle is 9 cm, while the shorter adjacent side is 3 cm.

We can see that the length of the corresponding sides in the blue triangle are 1.5 times the length of the corresponding sides in the black triangle. Therefore, the scale factor of the dilation from the black triangle to the blue triangle is:

9 cm / 6 cm = 3/2 = 1.5

So the answer is not one of the options given, but the correct scale factor is 1.5.

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A standard normal random variable (Z) has a mean of 0 and a standard deviation of 1. The probability of Z being greater than 0 is equal to the area under the normal curve to the right of 0, which is exactly half of the total area under the curve (since the curve is symmetric around the mean of 0). Therefore, P(Z>0) is equal to 0.5.

A standard normal random variable, like Z in your question, follows a standard normal distribution, which is a special type of normal distribution with a mean of 0 and a standard deviation of 1. Now, you're asked to find the probability P(Z > 0).

Since the standard normal distribution is symmetrical around the mean (0), the probability of Z being greater than 0 is equal to the probability of Z being less than 0. In other words, half of the distribution is on the right side of the mean, and the other half is on the left side.

Therefore, P(Z > 0) = 0.5, which is your answer.

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The calculated value of the degree measure of angle c is 16°

From the question, we have the following parameters that can be used in our computation:

The figure (see attachment)

The sum of angles in a triangle is 180 degrees

This means that

x + 20 + 62 = 180

Evaluate the like terms

This gives

x + 82 = 180

So, we have

x = 98

The measure of angle c is then calculated as

c + 2 * (180 - 98) = 180

Collect the like terms

c = 180 - 2 * (180 - 98)

Evaluate

c = 16

Hence, the degree measure of angle c is 16°

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The expression of the integral that quantifies the increase in volume of a sphere as its radius r quadruples from r to 4·r is therefore;

∫dV/dr, r, r, 4·r = 84·π·r³

An integral is a function which when differentiated, yields a specified function.

The volume of the sphere with radius r is V = (4/3) × π × r³

The increase in volume with a change in radius from r to 4·r is the difference between the volume at r and the volume with a radius of 4·r, as follows;

ΔV = ∫dV/dr, r, r, 4·r = [tex]V_{final}[/tex] - [tex]V_{initial}[/tex]

Therefore;

ΔV = ∫dV/dr, r, r, 4·r = ∫4·π·r², r, r, 4·r =  (4/3) × π × (4·r)³ - (4/3) × π × r³ = 84·π·r³

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To order the critical values for the most area in the tails of the distribution, we need to look at the degrees of freedom and the type of test.  the correct order is (b), (c), (a).

For a one-tailed test, we want to find the critical value that cuts off the highest percentage of the distribution, and for a two-tailed test, we want to find the critical values that cut off equal percentages in both tails.
(a) z0.10 is the critical value for a one-tailed test with alpha = 0.10. It cuts off 10% in the upper tail, so we want to place it last.
(b) t0.10 with 25 degrees of freedom is the critical value for a one-tailed t-test with alpha = 0.10 and 25 degrees of freedom. It cuts off more than 10% in the upper tail, so we want to place it first.
(c) 0.10 with 40 degrees of freedom is the critical value for a two-tailed t-test with alpha = 0.10 and 40 degrees of freedom. It cuts off 5% in each tail, so we want to place it in the middle.
Therefore, the correct order is (b), (c), (a).

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The percent of discount, rounded to the nearest tenth, is approximately 30.7%.

To find the percent of discount, we need to calculate the difference between the original price and the selling price, and then divide that by the original price. Finally, we multiply by 100 to express it as a percentage.

Discount = Original Price - Selling Price = $23,505 - $16,295 = $7,210

Percent of Discount = (Discount / Original Price) * 100 = ($7,210 / $23,505) * 100 ≈ 30.7%

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