7) suppose that you select 4 different pizza toppings from a pizzeria that offers a total of 15 toppings. how many topping combinations are possible?

Answer:

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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.

The response variable in this study is a categorical binary variable that measures the preference of the students between two brands of instant coffee.

In mathematics, a variable is referred to as the alphanumeric symbol used to represent a number or numerical value. An unknown quantity is represented as a variable in algebraic equations.

The response variable in this study is the preference of the students between brand A and brand B of instant coffee. The students are asked to try both brands and indicate which one they prefer, so the variable is categorical with two possible outcomes: preference for brand A or preference for brand B.

In statistical research, a response variable is an outcome or result that is being studied or measured. In this particular study, the response variable is the preference of the students between two brands of instant coffee, which are brand A and brand B.

Since the students are asked to try both brands and then indicate their preference, the response variable is categorical because it involves classifying each student's response into one of two possible categories: preference for brand A or preference for brand B.

Furthermore, the response variable is binary since there are only two possible outcomes for each student. The students either prefer brand A or prefer brand B, so the variable takes on one of two values: 0 for preference for brand A or 1 for preference for brand B.

Therefore, the response variable in this study is a categorical binary variable that measures the preference of the students between two brands of instant coffee.

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The value of the correlation coefficient (r) can be equal to the value of the coefficient of determination (r2).

detail explain: The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. On the other hand, the coefficient of determination (r2) measures the proportion of the variance in one variable that can be explained by the variance in the other variable. Both coefficients are used to analyze the relationship between two variables.

The value of the correlation coefficient (r) can range from -1.0 to +1.0, with negative values indicating a negative correlation and positive values indicating a positive correlation. The closer the value of r is to -1.0 or +1.0, the stronger the correlation.

The value of the coefficient of determination (r2) can range from 0 to 1.0, with higher values indicating a stronger relationship between the two variables. Specifically, r2 represents the proportion of the variance in one variable that is explained by the variance in the other variable.

It is possible for the value of the correlation coefficient (r) to be equal to the value of the coefficient of determination (r2). This happens when there is a perfect linear relationship between the two variables. In this case, the correlation coefficient is either -1.0 or +1.0, and the coefficient of determination is 1.0.

In summary, the correlation coefficient (r) and the coefficient of determination (r2) are both used to analyze the relationship between two variables. The value of r can range from -1.0 to +1.0, indicating the strength and direction of the linear relationship. The value of r2 can range from 0 to 1.0, indicating the proportion of the variance in one variable that can be explained by the variance in the other variable. It is possible for r to be equal to r2 in the case of a perfect linear relationship between the two variables. However, this is rare and typically the values of r and r2 will differ.

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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°

Therefore, The scatter diagram indicates a linear relationship between x and y. The estimated regression equation is y = 1.8 + 2.2x, and the predicted value of y when x = 4 is 10.6.

The scatter diagram can help us identify the relationship between two variables. Based on the given data, let's plot the points:
(1,3), (2,6), (3,7), (4,11), (5,13)
Looking at the plot, there appears to be a linear relationship between x and y.
To develop the estimated regression equation, we need to calculate the slope and y-intercept. Using the formula for slope (b1) and y-intercept (b0):
b1 = (Σ(xy) - n(Σx)(Σy)/n) / (Σx^2 - n(Σx)^2/n)
b0 = (Σy - b1(Σx)) / n
Calculating the values, we get:
b1 = 2.2
b0 = 1.8
The estimated regression equation is:
y = 1.8 + 2.2x
To predict the value of y when x = 4, substitute x in the equation:
y = 1.8 + 2.2(4)
y = 10.6

Therefore, The scatter diagram indicates a linear relationship between x and y. The estimated regression equation is y = 1.8 + 2.2x, and the predicted value of y when x = 4 is 10.6.

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The vector field F = yz²i + xz²j + 2xyzk is shown to be conservative by finding a scalar potential function φ(x, y, z) = xyz² + C, where C is a constant. This demonstrates that F can be expressed as the gradient of φ, confirming its conservativeness.

To show that the vector field F = yz²i + xz²j + 2xyzk is conservative, we need to find a scalar potential function, φ, such that F = ∇φ.
Let's compute the partial derivatives of φ with respect to x, y, and z:

∂φ/∂x = yz²
∂φ/∂y = xz²
∂φ/∂z = 2xyz

Now, we will integrate each partial derivative to find φ:

1) Integrate ∂φ/∂x with respect to x:
φ(x, y, z) = xyz² + g(y, z)

2) Integrate ∂φ/∂y with respect to y:
φ(x, y, z) = xyz² + h(x, z)

Comparing the results from (1) and (2), we can conclude that g(y, z) = h(x, z) = constant, let's call it C.

3) Integrate ∂φ/∂z with respect to z:
φ(x, y, z) = xyz² + C

Therefore, the scalar potential function for the given vector field is φ(x, y, z) = xyz² + C, which shows that the vector field is conservative.

The correct question is :

show that the vector field F = yz²i + xz²j + 2xyzk  is conservative by finding a scalar potential.

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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.

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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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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We can approximate the nonlinear system by a linear system at (0,0) using the Jacobian matrix and can find the eigenvalues using the formula det(J(0,0) - λI) = 0.

We have to approximate the nonlinear system by a linear system at (0,0) and find the eigenvalues.

Identify the nonlinear system.
First, you need to provide the nonlinear system of equations you're working with. The system should be in the form of:
dx/dt = f(x, y)
dy/dt = g(x, y)

Calculate the Jacobian matrix.
To linearize the system, compute the Jacobian matrix, J, which contains the partial derivatives of f and g with respect to x and y. The Jacobian matrix is given by:

J(x, y) = [ ∂f/∂x  ∂f/∂y ]
             [ ∂g/∂x  ∂g/∂y ]

Evaluate the Jacobian at (0,0).
Substitute the point (0,0) into the Jacobian matrix to obtain J(0,0).

Find the eigenvalues.
To find the eigenvalues, solve the characteristic equation, which is given by:
det(J(0,0) - λI) = 0

Here, λ represents the eigenvalues, and I is the identity matrix. Solve the resulting polynomial equation for λ to obtain the eigenvalues of the linearized system.

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To solve this problem, we can use the M/M/1 queueing model, where "M" stands for Poisson arrivals and "M" stands for exponential service time, and "1" means there is one server.

From the problem, we know that the arrival rate, λ, is 1/7 customers per minute, and the service rate, μ, is 1/15 customers per minute. The utilization factor, ρ, is given by ρ = λ/μ = (1/7)/(1/15) = 15/7. Since ρ > 1, the system is not stable, and the average customer waiting time is infinite.

To limit the average customer waiting time to 2 minutes, we need to reduce the utilization factor. One way to do this is to increase the number of servers. Let's assume the call center has "k" servers. The average customer waiting time, W, can be approximated by the following formula:

W = (ρ^k / kμ) / (1 - ρ)

We want to find the minimum value of "k" such that W ≤ 2. Rearranging the formula, we get:

k ≥ (ρ/(1-ρ)) * (ρ^(k-1)) * (1/(2μ))

We can use trial and error or numerical methods to find the smallest integer value of "k" that satisfies this inequality. For example, starting with k = 1, we can calculate the right-hand side of the inequality and check if it is greater than or equal to 1. If it is not, we can increase k by 1 and repeat the calculation until we find the smallest integer value of "k" that satisfies the inequality.

Alternatively, we can use a formula for the Erlang C model, which is a generalization of the M/M/k model for multiple servers. The formula gives the probability that a customer has to wait for service, given the arrival rate, service rate, and number of servers. We can then use this probability to calculate the average customer waiting time using Little's law.

The minimum number of customer services needed to achieve the goal of limiting the average customer waiting time to 2 minutes is the smallest integer value of "k" that satisfies the inequality.

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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 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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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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Step-by-step explanation:

First prism volume =  L x W x H = 8 x 4 x 5 = 160 cm^3

Second prism = 14 x 8 x 1 = 112 cm^3

   Total =  160 + 112 = 272 cm^3

The volume of the composite solid will be 272 cubic cm.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

The shape is the combination of the two rectangular prisms. Then the volume is calculated as,

V = (6 x 4 x 8) + ((14 - 4) x 1 x 8)

V = (6 x 4 x 8) + (10 x 1 x 8)

V = 192 + 80

V = 272 cubic cm

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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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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 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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(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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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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In a 2 x 2 x 2 factorial design, you need to test a total of seven possible effects: three main effects (A, B, and C) and four interaction effects (A x B, A x C, B x C, and A x B x C).

In a 2 x 2 x 2 factorial design, there are three independent variables, each with two levels. The possible effects to test include main effects and interaction effects.

The main effects are the individual effects of each independent variable on the dependent variable. In this design, there are three main effects to test: the effect of the first independent variable (A), the effect of the second independent variable (B), and the effect of the third independent variable (C).

Interaction effects occur when the effect of one independent variable on the dependent variable depends on the level of another independent variable. In a 2 x 2 x 2 design, there are three possible two-way interaction effects to test: A x B, A x C, and B x C. Additionally, there is one three-way interaction effect to test: A x B x C.

In summary, in a 2 x 2 x 2 factorial design, you need to test a total of seven possible effects: three main effects (A, B, and C) and four interaction effects (A x B, A x C, B x C, and A x B x C).

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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 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 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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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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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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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 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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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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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.