The volume of a triangular prism is 1380 cubic centimeters. Its base is a right triangle with legs measuring 8 centimeters and 15 centimeters. What is the height of the prism?

A. 34.5 \mathrm{~cm}
B. 23 \mathrm{~cm}
C. 17cm
D. 11.5 \mathrm{~cm}

The degrees of freedom used in the the t distribution is 86.

We have to calculate the degrees of freedom using the given formula. The t distribution is used as the population mean and standard deviation is not known. The data of two samples from two different population are given, using which we have to compute degrees of freedom.

Given,

n1=40, n2=50

\(\bar{x_{1} }\)=32.2 , \(\bar{x_{2} }\)= 30.1

s1=2.8 , s2= 4.1

The

The degrees of freedom formula is given by

\(df=\frac{\left(\frac{s_1{ }^2}{n_1}+\frac{s_2^2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s_1^2}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s_2^2}{n_2}\right)^2} \\\)

Substituting the given values, we get

\(df=\frac{\left(\frac{2.8^2}{40}+\frac{4.1^2}{50}\right)^2}{\frac{1}{40-1}\left(\frac{2.8^2}{40}\right)^2+\frac{1}{50-1}\left(\frac{4.1^2}{50}\right)^2}\)

Further simplifying, we get

\(d f=\frac{(0.5322)^2}{0.0032917}\)

df= 86.04

Therefore, the degrees of freedom used after rounding off to the nearest integer is 86.

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Answer: 98 mins

Step-by-step explanation:

First find out the number of minutes it takes him to decorate a single cupcake:= Number of minutes / Number of cupcakes decorated = 28 / 16= 1.75 minutes per cupcakeIf he had to decorate 56 cupcakes, the amount of time he would take is:= Number of cupcakes to be decorated x Time taken per cupcake = 56 x 1.75= 98 minutes 

Answer & Step-by-step explanation:

We can assume that Adrian decorates cupcakes at a constant rate, so we can use a proportion to solve the problem.

If Adrian can decorate 16 cupcakes in 28 minutes, we can set up the proportion:

16/28 = 56/x

where x is the number of minutes it will take to decorate 56 cupcakes.

To solve for x, we can cross-multiply and simplify:

16x = 28 * 56

16x = 1568

x = 1568/16

x = 98

Therefore, if Adrian can continue at the same pace, it will take him 98 minutes to decorate 56 cupcakes.

Answer:

9

Step-by-step explanation:

Answer:

Nine = 9

Step-by-step explanation:

Answer: A. To find the number of glass squares each student will receive, we need to divide the total number of squares by the number of students.

We can write this as:

x = number of glass squares per student

x = 1240 / 121

B. To find the number of squares each student will receive, we need to solve for x by dividing 1240 by 121.

1240 ÷ 121 = 10.246753246753247

C. Each student will get 10 whole glass squares.

D. The remainder in this context is the number of glass squares that cannot be distributed evenly among the students. In this case, the remainder is 30. It means that there will be 30 glass squares left over after each student has received 10 squares. It's like remainder in division where after dividing 1240 by 121 the quotient is 10 and the remainder is 30.

Step-by-step explanation:

The interest paid in the 11th year of a $95,000 mortgage with a 5.5% interest rate and a 25-year term is approximately $3,638.

This is calculated by first determining the remaining balance after 10 years, which is $64,516. Then, the interest paid for each monthly payment in the 11th year is calculated, and the sum of these monthly interest payments is $3,638.

Here are the steps involved in calculating the interest paid in the 11th year:

Input the loan amount ($95,000), the interest rate (5.5%), and the loan term (25 years) into a mortgage calculator.

Determine the remaining balance after 10 years.

Calculate the monthly payment for the mortgage.

Calculate the interest paid for each monthly payment in the 11th year.

Sum the monthly interest payments to get the total interest paid in the 11th year.

The total interest paid in the 11th year can also be calculated using the following formula:

Interest paid = (Remaining balance × Interest rate) / 12

In this case, the interest paid in the 11th year is:

Interest paid = ($64,516 × 0.055) / 12 = $3,638

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Answer: -19.2

Step-by-step explanation:

Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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Answer:

it´s no

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

3 I think forgive me if im wrong.

Step-by-step explanation:

it would be the second one because it is exactly the same the first one is a little bit shorter so there not exactly the same

Answer:

$14.00

Step-by-step explanation:

So, the 20 peaches all weigh 4 oz, and there are 16 oz in 1 pound. 16 oz divided by 4 is also equal to 4 oz, so we need to divide $2.80 by 4, which would be $0.70. That means that a 4 oz peach would be $0.70, so we multiply that by 20, which gives us $14.00, so Stacey will need $14.00 to buy 20 peaches that each weigh 4 oz.

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring, this statement is false.

The union of two or more sets refers to the set with all the elements belonging to each set. An element is said to be in the union if it lies to at least one of the sets.

The intersection of two or more sets refers to the set of elements universal to each set. An element is in the intersection if it occurs in all of the sets.

The event that both A and B occur is the intersection of the events A occurs and B occurs. As such, it is a subset of each and cannot, therefore, have a larger probability than either one individually.

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Answer:

See below

Step-by-step explanation:

Stephanie's profit relationship:

Bryson's Tomato Sales, using the pairs of numbers let's find the relationship.

Since it is also linear relationship, we'll find a slope and y-intercept:

y-intercept is:

So the function is:

Comparing the functions:

The slope of g(x) is greater than f(x) but the y-intercept is smaller

It translates as:

The equation f(x) = (-9 - 3x)(x + 4), as represented is in its factored form

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

f(x) = (-9-3x)(x+4)

Express properly

f(x) = (-9 - 3x)(x + 4)

The above equation is a quadratic function

As a general rule, a quadratic function in factored form is represented as

f(x) = (ax + b)(cx + d)

When the equation are compared, we have

a = -3, b = -9

c = 1 and d = 4

This means that the equation f(x) = (-9 - 3x)(x + 4) is in factored form

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Answer:

I'm guessing it's D

Step-by-step explanation:

It says D is the answer

Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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Answer:

7.211

Step-by-step explanation:

Answer:

2/15

Step-by-step explanation:

I think not 100% on this but not so sure-

Subtract 5 1/10 from 5 3/4

5 3/4 - 5 1/10

• Subtract the whole numbers (5 and 5)

5 - 5 = 0

• LCM of the denominators (4 and 10)

= 13/20

She put an extra 13/20

Answer:

1725 square feet

Step-by-step explanation:

\(area \: of \: yard = \frac{1}{2} (50 + 65) \times 30 \\ = 115 \times 15 \\ = 1725 \: {ft}^{2} \\ \)

Answer:

1725 sq ft

Step-by-step explanation:

50+65=115

115/2=57.5

57.5*30=1725

Therefore, the solution to the system of equations is: x = 13/12, y = -3/4 that is option C.

In mathematics, an equation is a statement that asserts the equality of two expressions, separated by an equals sign (=). The expressions on either side of the equals sign are referred to as the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between variables and to solve problems.

Here,

To solve the system of equations:

4y + 12x = 10 ...(1)

2y - 6x = -8 ...(2)

We can use the method of elimination or substitution.

Method of elimination:

We can eliminate x by multiplying equation (2) by 2 and adding it to equation (1) to obtain:

4y + 12x = 10

(4y - 12x = -16)

8y = -6

Dividing both sides by 8, we get:

y = -6/8

y = -3/4

Substituting this value of y in equation (1), we get:

4(-3/4) + 12x = 10

Simplifying and solving for x, we get:

-3 + 12x = 10

12x = 13

x = 13/12

So the answer is C. x = 13/12, y = -3/4.

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Answer:

-6x-5y+2

Step-by-step explanation:

The hypothesis test is left-tailed because the financial analyst wants to test if the proportion of stock portfolios containing high-risk stocks is lower than 0.10.

In other words, they are interested in determining if the proportion is significantly less than the specified value of 0.10. A left-tailed hypothesis test is used when the alternative hypothesis suggests that the parameter of interest is smaller than the hypothesized value. In this case, the alternative hypothesis would be that the proportion of stock portfolios with high-risk stocks is less than 0.10.

By conducting a left-tailed test, the financial analyst is trying to gather evidence to support their claim that their clients have a lower proportion of high-risk stock portfolios. They want to determine if the observed data provides sufficient evidence to conclude that the true proportion is indeed less than 0.10, which would support their claim of a lower proportion of high-risk stocks.

Therefore, a left-tailed hypothesis test is appropriate in this scenario.

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The eigenvalues for the given system dx/dt = 4x - 2y, dy/dt = x + y are λ1 = 3 and λ2 = 2.

The associated eigenvectors are v1 = (1, 1) and v2 = (-1, 2). Using HPGSystemSolver, you can sketch the direction field, plot straight line solutions, and create the phase portrait.

To find the eigenvalues:
1. Write the system as a matrix: A = [[4, -2], [1, 1]]
2. Calculate the characteristic equation: det(A - λI) = 0, which gives (4 - λ)(1 - λ) - (-2)(1) = 0
3. Solve for λ, yielding λ1 = 3 and λ2 = 2

For eigenvectors:
1. For λ1 = 3, solve (A - 3I)v1 = 0, resulting in v1 = (1, 1)
2. For λ2 = 2, solve (A - 2I)v2 = 0, resulting in v2 = (-1, 2)

Using HPGSystemSolver or similar software, input the given system to sketch the direction field, plot straight line solutions (if any), and generate the phase portrait. This visual representation helps in understanding the system's behavior.

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The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

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The equation for temperature change is T = -1.5t + 29 and the number line is plotted.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

Let T represent the temperature in degrees Celsius, and let t represent the time in hours after lunchtime.

Then write an expression for the situation as follows:

T = -1.5t + 29

Here, -1.5t represents the decrease in temperature per hour, since the temperature is dropping at a rate of 1.5 degrees Celsius per hour.

Adding 29 to -1.5t gives the initial temperature of 29 degrees Celsius at lunchtime.

To illustrate this situation on a number line diagram, we can plot the temperature T as a function of time t.

The diagram would have time t on the horizontal axis and temperature T on the vertical axis.

Label the point (0, 29) on the diagram to represent the temperature at lunchtime, and the point (x, 16) to represent the temperature at sunset, where x is the number of hours after lunchtime.

Then draw a straight line connecting these two points to represent the linear relationship between temperature and time.

The line slopes downward from left to right, indicating that the temperature is decreasing over time.

Therefore, the number line diagram is plotted.

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On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

Answer:

aggregate, total, totality, whole, summation, entirety, full, tally, all, body

Step-by-step explanation:

Answer:

in this topic, students will use ribbon diagrams and / or number lines to represent and solve problems involving addition and subtraction of fractions in word problems. consider this example.

Answer:

c

Step-by-step explanation:

S=B+1/2Pl

-b from both sides

s-b=1/2Pl

x2 to both sides

2(S-B)=Pl

divide both sides by l

you get c

The xy-term in the equation \(x^2 + 14xy - y^2 + 5 = 0\), we can use the rotation formulas with either \(\theta\) = 0 or \(\theta\) = π. The resulting equations will have no xy-term, but the solutions will differ in the signs of x and y depending on the choice of rotation.

What is the polynomial equation?

A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.

To eliminate the xy-term in the equation \(x^2 + 14xy - y^2 + 5 = 0\), we can use a rotation transformation to align the coordinate axes with the principal axes of the conic section. The appropriate rotation formula to use is:

\(x = x' \cos(\theta) - y' \sin(\theta) \ y = x' \sin(\theta) + y' \cos(\theta) \end{cases}\)

By choosing the angle \(\theta\)  appropriately, we can eliminate the xy-term in the transformed equation. Let's proceed step by step.

Step 1: Set up the original equation:

\(x^2 + 14xy - y^2 + 5 = 0\)

Step 2: Introduce the new variables \(x' \ and \ y'\) using the rotation formulas:

\(x = x' \cos(\theta) - y' \sin(\theta) \ y = x' \sin(\theta) + y' \cos(\theta) \end{cases}\)

Step 3: Substitute the new variables into the original equation:

\((x' \cos(\theta) - y' \sin(\theta))^2 + 14(x' \cos(\theta) - y' \sin(\theta))(x' \sin(\theta) + y' \cos(\theta)) - (x' \sin(\theta) + y' \cos(\theta))^2 + 5 = 0\)

Step 4: Expand and simplify the equation:

\(x'^2 \cos^2(\theta) - 2x'y' \cos(\theta) \sin(\theta) + y'^2 \sin^2(\theta) + 14x'^2 \cos^2(\theta) \sin(\theta) + 14xy' \cos^2(\theta) + 14x'y' \sin^2(\theta) + 14y'^2 \cos(\theta) \sin(\theta) - x'^2 \sin^2(\theta) - 2x'y' \cos(\theta) \sin(\theta) - y'^2 \cos^2(\theta) + 5 = 0 \end{align*}\)

Step 5: Group terms and simplify further:

\((x'^2 - y'^2)\cos^2(\theta) + (14xy' - 2x'y')\cos(\theta) \sin(\theta) + (x'^2 - y'^2)\sin^2(\theta) + 14xy' \cos^2(\theta) + 14y'^2 \cos(\theta) \sin(\theta) + 5 = 0 \end{align*}\)

Step 6: Determine the angle \(\theta\)  such that the coefficient of the cross-term cos(\(\theta\) ) sin(\(\theta\) ) becomes zero. In this case, we want:

\(14xy' - 2x'y' = 0\)

Step 7: Solve the equation \(14xy' - 2x'y' = 0\) to find the value of \(\theta\) :

\(14xy' = 2x'y' \Rightarrow 14x = 2x'\)

From the equation 14xy' = 2x'y', we can deduce that 14x = 2x', which implies x' = 7x. Substituting this value back into the rotation formulas, we have:

x = 7x cos(\(\theta\) ) - y sin(\(\theta\))

y = 7x sin(\(\theta\) ) + y cos(\(\theta\) )

To eliminate the xy-term, the coefficient of xy' should be zero. In this case, the coefficient is 14x, which implies 14x = 0. Therefore, x = 0.

Substituting x = 0 into the rotation formulas, we get:

0 = -y sin(\(\theta\) )

y = y cos(\(\theta\) )

From the equation 0 = -y sin(\(\theta\) ), we can deduce that sin(\(\theta\) ) = 0, which means theta = 0 or theta = pi (180 degrees).

When theta = 0, the rotation formulas become:

x = x'

y = y'

When theta = pi, the rotation formulas become:

x = -x'

y = -y'

Either of these rotations will eliminate the xy-term from the equation. However, it's important to note that rotating by an angle of pi will result in the same equation, just with the signs of x and y reversed.

Hence, the xy-term in the equation \(x^2 + 14xy - y^2 + 5 = 0\), we can use the rotation formulas with either \(\theta\) = 0 or \(\theta\) = π. The resulting equations will have no xy-term, but the solutions will differ in the signs of x and y depending on the choice of rotation.

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