20
For the next school play, there are 69 students who tried out for the play. The number of
students who tried out but did not get a role is 52. Let g be the number of students who got a
role in the school play. The equation model this situation. Solve the equation to find the
number of students who will be in the play.
* (2 Points)
69
g
52

The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Answer:

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

What factors determine if one relationship is proportional?

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

What are the two proportional relationships principles?

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Step-by-step explanation:

Answer:

D. \(\sqrt{27}\)

Step-by-step explanation:

A, B, and C are all perfect squares being square rooted. This means that they will all result in whole numbers.

For example: A.   \(\sqrt{9}=3\)

However, D.         \(\sqrt{27}=3\sqrt{3}\), which is not rational because it contains an unsimplifiable square root (sqrt 3)

Answer:

√27

Step-by-step explanation:

√9 = 3

√81 = 9

√36 = 6

√27 = not whole number

The random variable r has a mean μ = 10 and σ = 4. For the variable s, the μ = 7 and σ = 3. The mean of r-s will be obtained by arithmetic subtraction of the μ for r and a. The standard deviation isn't independent since it's obtained by square root of the variance of a distribution. The standard deviation will be obtained by obtained through the square root of the squared sum of σ.

μ (r-s) = μ(r) -μ(s)

μ (r-s) = 10 -7 = 3

σ (r) -σ(s) = √(σ (r))²+ (σ (s))²

σ (r) -σ(s) = √(4²+ 3²)

σ (r) -σ(s) = √(16+ 9)

σ (r) -σ(s) = √25 = 5

thus, the mean is 3 and the standard deviation is 5.

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The signal \(x[n] = \cos (\pi n)\) is periodic because it is a discrete-time cosine function with a frequency of \(\pi\) and an integer period of 2. Therefore, it repeats every 2 samples. the signals (i) and (iv) are periodic with periods of 2 and 4, respectively, while the signals (ii), (iii), and (v) are not periodic.

A periodic signal repeats itself after a certain interval called the period. To determine if a signal is periodic, we need to check if there exists a positive integer \(N\) such that \(x[n] = x[n + N]\) for all values of \(n\). Let's analyze each signal:

(i) \(x[n] = \cos (\pi n)\):

The cosine function has a period of \(2\pi\). In this case, the argument of the cosine function is \(\pi n\). Since \(\pi\) is irrational, the cosine function will not repeat itself exactly after any integer \(N\). However, if we consider \(N = 2\), we have:

\(x[n] = \cos (\pi n) = \cos (\pi (n + 2)) = \cos (\pi n + 2\pi) = \cos (\pi n)\)

Therefore, \(x[n]\) is periodic with a period of 2.

(ii) \(x[n] = \cos \left(\frac{3\pi n}{2} + \pi\)\):

The argument of the cosine function is \(\frac{3\pi n}{2} + \pi\). This function has a period of \(\frac{4}{3}\pi\) since \(\frac{3\pi}{2}\) is the coefficient of \(n\) and the \(+\pi\) term shifts the function by \(\pi\) units. Since \(\frac{4}{3}\pi\) is not an integer multiple of \(\pi\), the signal is not periodic.

(iii) \(x[n] = \sin (3.15 n)\):

The sine function has a period of \(2\pi\). In this case, the argument of the sine function is \(3.15 n\). Since \(3.15\) is irrational, the sine function will not repeat itself exactly after any integer \(N\). Therefore, the signal is not periodic.

(iv) \(x[n] = 1 + \cos \left(\frac{\pi n}{2}\right)\):

The cosine function in this signal has a period of \(4\) since the coefficient of \(n\) is \(\frac{\pi}{2}\). Adding 1 to the cosine function does not affect its period. Therefore, the signal is periodic with a period of 4.

(v) \(x[n] = e\):

The signal \(x[n] = e\) is a constant signal and is not dependent on \(n\). A constant signal is not periodic since it does not exhibit any repetitive pattern.

In summary, the signals (i) and (iv) are periodic with periods of 2 and 4, respectively, while the signals (ii), (iii), and (v) are not periodic.

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Step-by-step explanation:

\(\frac12(8k+12k^2+6k^3)\\=4k+6k^2+3k^3\\\)

Rearrange into descending order:

\(\boxed{3k^3+6k^2+4k}\)

To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.

Given matrix D:

D = | k 0 0 |

| 3 k² k³ |

| 0 kª k³ kº |

| k k k |

| 0 0 0 |

| k¹⁰ |

The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

- 0(det | 3 k² k³ |

| 0 kª k³ |

| k k k |)

+ 0(det | 3 k² k³ |

| k k k |

| k k k |)

Simplifying further, we have:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

Now, we can calculate the determinant of the 3x3 submatrix:

det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |

This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:

det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº

Now, we can set det(D) equal to 1024 and solve for k:

k⁴+kº = 1024

Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.

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Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Answer:

d

Step-by-step explanation:

3 multiplied by ricks salary minus 150

Answer:

I think you have it

Step-by-step explanation:

It's not -4.44, and if it was -3.14 it would be closer to the -3 tick on the line. With the negative square root of 17 being 4.12 it's not that either. -11/3 is 3.6666667 or something along those lines so it would be closer to the -4 tick on the line, so I'm pretty sure you got it.

Simple interest analysis reveals that

a) The installment was $321.53 per month.

b) The total amount of the payments is $11,575.

c) Interest was paid of $1,575.

After t years, the amount of simple interest is calculated using:

A(t) = p(1 + rt)

that where:

The initial deposit is known as the primary, or P.

The interest rate in decimal form is r.

In this issue:

Hence, a $10,000 loan.

APR of 5.25%, which equals 3 years, therefore

Item c:

The result is A(3), so:

A(t) = P( 1 + rt)

A(3) = 10000[ 1 + 0.0525(3)]

A(3) = 11575

The total amount of the monthly installments is $11,575.

Item d:

I = A(3)  - P = 11575 - 10000 = 1575

When interest is calculated, the principal is removed, so:

Interest was paid of $1,575.

Item b:

36 payments were made over a period of 3 years, or 3 x 12 months.

Item a:

11575/3 = 321.53

The amount due each month was $321.53.

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A linear system of equations has a unique solution if and only if the number of equations is equal to the number of variables, and the determinant of the coefficient matrix is non-zero.

1. Write down the given system of linear equations. Let's assume there are n equations and n variables.

2. Check if the number of equations (n) is equal to the number of variables (n). If they are equal, proceed to the next step. Otherwise, the system does not have a unique solution.

3. Construct the coefficient matrix by taking the coefficients of the variables from the system of equations.

4. Calculate the determinant of the coefficient matrix.

5. If the determinant is non-zero, then the system of equations has a unique solution. If the determinant is zero, it means the equations are linearly dependent, and the system either has no solutions or infinitely many solutions.

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What we know:

Lets first convert the mixed partial fraction --> improper fraction

       --> for easier calculation

After Conversion:

To find how many scoops of birdseed will Samantha put into the feeder we must:

  --> divide the total capacity by the scoop's capacity

       --> find the number of scoops:

Solve:

  \(Total-number- of -scoops = \frac{\frac{14}{5} }{\frac{7}{10} } =\frac{14}{5} *\frac{10}{7} =\frac{14*10}{5*7} =\frac{14}{7} *\frac{10}{5} =2*2=4\)

Thus the total number of scoops that Samantha will put into the bird feeder is 4

Answer: 4

Hope that helps!

Answer:

not completely sure but I think it's it's 13.4

 The probability of rolling a non 2, 3, 7, 11, or 12 on the first roll and then matching that total on the second roll, when rolling two 6-sided dice two times in a row, is 5/36.

When rolling two 6-sided dice, there are a total of 36 possible outcomes (6 options for the first die and 6 options for the second die). Out of these 36 outcomes, there are 5 outcomes that are not 2, 3, 7, 11, or 12, which are (1, 4), (1, 5), (4, 1), (4, 6), and (6, 4).
To find the probability of rolling a non 2, 3, 7, 11, or 12 on the first roll and matching that total on the second roll, we need to determine the number of favorable outcomes. For each of the 5 non-restricted outcomes, there is only one way to match that total on the second roll. Therefore, there are a total of 5 favorable outcomes.
Since there are 36 possible outcomes, the probability of rolling a non 2, 3, 7, 11, or 12 on the first roll and matching that total on the second roll is 5/36.

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Answer:

Step-by-step explanation:

To determine what was her gas mileage, divide the total miles driven by the gallons of gas;

The circled section represents the range of solving times for children and adults at a Rubik's cube competition, indicating variability in performance.

The circled section represents the range of times it took both children and adults to solve a Rubik's cube at a competition. The range is the difference between the highest and lowest times recorded for each group.

It provides an overview of the variability in solving times within each age group. In competitions, participants are timed while solving the cube, and the circled section helps visualize the spread of solving times.

A larger circled section indicates a wider range of solving abilities within the group, while a smaller circled section suggests a more consistent performance.

By examining the circled section, one can gain insights into the skill levels and proficiency of both children and adults in solving Rubik's cubes at the competition.

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Step-by-step explanation:

Assume the number of double matches is x (matches)

the number of single matches is y (matches)

(Condition: x > 0 and y > 0)

Because there are 13 matches in progress, so:

x + y = 13 (1)

Because there are 38 people playing (4 people on each double match and 2 people on each single match), so:

4x + 2y = 38 (2)

A system of equation is made by combining (1) and (2):

x + y = 13 (1)

4x + 2y = 38 (2)

Take (2) - 2×(1):

=> 2x = 12

=> x = 6

Substitute the result on (1)

=> y = 7

So there are 6 double matches and 7 single matches being played

Answer:

x+y=5a

5a is added to b which is the sum of x and y multiplied by 3. That is, b=x+y×3=5a×3=15a

Since, 5a is added to b= 5a+15a=20a,

Answer:

For any value

Step-by-step explanation:

Answer:

Anything substituted for p should be correct

Step-by-step explanation:

Given that the angle between the two cities, a and b, is 32°. The distance between the two cities, a and b, is approximately _____ miles (round to the nearest whole number as needed).

To find the distance between the two cities, let us assume a triangle with vertices A, B, and C, where A represents city A, B represents city B, and C represents a point on the surface of the Earth directly beneath the plane containing the two cities, as shown below.

The angle between the cities A and B is 32°, and the distance between the cities is given to be 4000 miles. \(AB = 4000 miles\)In the triangle ABC, \(cos 32° = \frac{AB}{AC}\)\(\Rightarrow AC = \frac{AB}{cos32°}\)\(\Rightarrow AC = \frac{4000}{cos32°}\)\(\approx 4663.39\)Thus, the distance between the two cities, a and b, is approximately 4663 miles (rounded to the nearest whole number).Therefore, the distance between two cities, a and b, to 4000 miles is approximately 4663 miles.

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The area of the triangular dock is 19.5 square feet and the area of the rectangular box is 10 feet. The box will fit under the dock.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Calculate the area of the triangle first,

Area = 1 / 2 x B x H

Area = 1/2 x 12 x 3.25

Area = 19.5 square feet

Calculate the area of the rectangle,

Area = L x W

Area = 2 x 5

Area = 10 square feet

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Answer:

P(3) = 57/150 = 19/50 = .38 = 38%

Without the actual data, it's not possible to calculate the estimated regression equation, coefficient of determination, F test statistic, and p-value. However, I can explain the process of finding them.

To find the estimated regression equation, we use the method of least squares to find the values of the coefficients β0, β1, and β2 that minimize the sum of squared residuals. The equation would be of the form: y = β0 + β1x + β2x^2. The coefficient of determination (R^2) measures the proportion of variation in the dependent variable (traffic flow) that is explained by the independent variable (vehicle speed) and the model. It ranges between 0 and 1, with higher values indicating a better fit. It can be calculated as the ratio of explained variance to total variance. The F test statistic is used to test the overall significance of the model by comparing the variance explained by the model to the unexplained variance. It is calculated as the ratio of explained variance to unexplained variance, adjusted for the degrees of freedom. The p-value is the probability of obtaining an F test statistic as extreme or more extreme than the observed one, assuming the null hypothesis that the model has no significant effect. It is compared to a significance level (α) to decide whether to reject or fail to reject the null hypothesis. Using a significance level of .01, we can reject the null hypothesis of no significant effect if the p-value is less than .01. To predict the traffic flow for a speed of 39 miles per hour, we plug x = 39 into the estimated regression equation and solve for y. The result would be rounded to the nearest whole number.

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The distance from Jade's house to the coffee shop is 5 miles.

Let's assume the distance from the coffee shop to Jade's school is represented by the variable "x."

According to the given information, the distance from Jade's house to the coffee shop is 3 miles more than twice the distance from the coffee shop to Jade's school. We can express this as:

Distance from Jade's house to the coffee shop = 2x + 3

Furthermore, the total distance from Jade's house to her school is 5 times the distance from the coffee shop to her school. Mathematically, we can write:

Distance from Jade's house to her school = 5x

Since we're looking for the distance from Jade's house to the coffee shop, we can set up an equation by equating the two expressions for the total distance:

2x + 3 = 5x

To solve for x, we can subtract 2x from both sides of the equation:

3 = 3x

Dividing both sides by 3, we find:

x = 1

Now that we know x represents the distance from the coffee shop to Jade's school, which is 1 mile, we can substitute this value back into the equation for the distance from Jade's house to the coffee shop:

Distance from Jade's house to the coffee shop = 2x + 3 = 2(1) + 3 = 2 + 3 = 5

Therefore, the distance from Jade's house to the coffee shop is 5 miles.

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An example of the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.

This is the term that is used to refer to the fraction that is represented by the use of a rational fraction. That is there is denominator and a numerator.

The denominator must have a variable and this variable has to be of degree 1. Hence the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.

First you have to know if it is an inequality or not. Then you have to assign x and y variables to numbers. From here you form an equation. This equation is plotted on a graph.

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Answer:

11 x 11 x 11 x 11 x 11 x 11 = 1771561

Answer:

1, 771, 561

Step-by-step explanation:

multiply 11 in 6 places that is 11*11*11*11*11*11

Answer:

3/4 of a mile

Step-by-step explanation:

.5+.25=.75