Here is a solid prism.
(c) (i) Write down the mathematical name of this prism.
(ii)How many vertices does the prism have?

Answer:

x=-6, y=-7

Step-by-step explanation:

Answer:

x = -6, y = -7

Step-by-step explanation:

One way to solve for x and y is using the substitution method

(1) 3x + 4y = -46

(2) 6x + y = -43

Solve for y in equation (2)

6x + y =-43, so y = -43 - 6x

Substitute y = -43 -6x into equation (1)

3x + 4(-43 -6x) = -46

3x -172 -24x = -46

-21x -172 = -46

-21x = 126

x = -6

Find y by substituting x = -6 into equation (2)

6(-6) + y = -43

-36 + y = -43

y = -7

Answer:

Therefore, after 12 years the car will value $6,765.35.

Step-by-step explanation:

The solution to the differential equation 5y'' - 2y' = 2x + 5 - e^(-2x) using the method of undetermined coefficients is given by y = C1 + C2e^(2x) - (5/2)x + B, where C1, C2, and B are constants determined by the initial or boundary conditions.

To solve the differential equation 5y'' - 2y' = 2x + 5 - e^(-2x) using the method of undetermined coefficients, we assume a particular solution of the form:

y_p = Ax + B + Ce^(-2x)

where A, B, and C are undetermined coefficients to be determined.

Taking the derivatives:

y_p' = A - 2Ce^(-2x)

y_p'' = 4Ce^(-2x)

Substituting these derivatives into the original differential equation, we have:

5(4Ce^(-2x)) - 2(A - 2Ce^(-2x)) = 2x + 5 - e^(-2x)

Simplifying the equation:

20Ce^(-2x) - 2A + 4Ce^(-2x) = 2x + 5 - e^(-2x)

(24C)e^(-2x) - 2A = 2x + 5 - e^(-2x)

For the equation to hold for all x, the coefficients on both sides of the equation must be equal.

Matching the coefficients:

24C = 0 -> C = 0

-2A = 5 -> A = -5/2

Therefore, the particular solution is:

y_p = (-5/2)x + B

To find the value of B, we substitute the particular solution back into the original differential equation:

5(-5/2) - 2(0) = 2x + 5 - e^(-2x)

-25/2 = 2x + 5 - e^(-2x)

Solving for x and e^(-2x) in terms of B:

2x = -25/2 - 5 + e^(-2x)

2x = -35/2 + e^(-2x)

As the left side is a linear function of x and the right side is a constant plus an exponential function, there is no value of x that satisfies this equation for all x. Hence, the equation is inconsistent, and there is no particular solution in the form y_p = Ax + B.

Therefore, the solution to the given differential equation using the method of undetermined coefficients is the complementary function (homogeneous solution) plus the particular solution, which is:

y = y_c + y_p = C1 + C2e^(2x) + (-5/2)x + B

where C1 and C2 are constants determined by the initial or boundary conditions, and B is an arbitrary constant.

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In the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

The domain refers to the set of possible inputs or variables in a given context. In this case, the scatterplot is being created based on the relationship between the time students spent studying and their corresponding test grades. Therefore, the domain in this context would be the number of minutes the students studied (option D).

The domain represents the independent variable, which is the variable that is controlled or manipulated in the analysis. In this scenario, the math teacher wants to analyze the relationship between studying time and test grades, so the number of minutes studied would be the independent variable. The teacher surveys the students to collect data on the time spent studying, and this variable becomes the domain of the scatterplot.

The range, on the other hand, represents the dependent variable, which is the variable that is measured or observed as an outcome or response. In this case, the dependent variable would be the students' test grades. The scatterplot will show how the test grades correspond to the amount of time students studied.

To summarize, in the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

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A subspace must satisfy three conditions: closure under addition, closure under scalar multiplication, and containing the zero vector. Therefore, the correct statement is B. W is a subspace of P2.

In order to determine whether statement A or B is true, we need to check the subspace criteria.

Let's analyze the statements:

A. W is not a subspace of P2 because 0 € W.

If 0 € W, then W does not contain the zero vector. However, the zero vector is the polynomial 0 + 2(0)x + (0)x^2 = 0, which is an element of W. Thus, statement A is false.

B. W is a subspace of P2.

For W to be a subspace, it needs to satisfy all three subspace criteria. Let's check each criterion:

Since W satisfies all three subspace criteria, statement B is true.

Therefore, the correct statement is B. W is a subspace of P2.

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Answer:

2cm

Step-by-step explanation:

Given data

Capacity/volume of liquid held=  6π cm^3

Height= 6cm

Required

The diameter d of the tube

let us apply the expression for the volume of cylinder

V=πr^2h

6π=πr^2*6

6=r^2*6

r^2= 6/6

r^2=1

r= √1

r=1cm

Hence the diameter d = 2r= 2*1= 2cm

a) The volume of the solid E in rectangular coordinate system is given by: [tex]$$\iiint_{E}[/tex] dx dy dz = [tex]\int_{-2}^{2} \int_{0}^{\sqrt{z^2}} \int_{-\sqrt{z^2 - y^2}}^{\sqrt{z^2 - y^2}} dx dy dz$$[/tex]

b) The volume of the solid E in cylindrical coordinate system is given by:  [tex]$$\iiint_{E} \rho d\rho d\theta dz = \int_{0}^{2} \int_{0}^{\frac{\pi}{2}} \int_{0}^{\sqrt{4 - z^2}} \rho d\rho d\theta dz$$[/tex]

c) The volume of the solid E is 11π/3.

a) The solid E that lies between the cone z² = x² + y² and the sphere x² + y² + (z + 2)² = 2.

Let the limits of x, y, z be X, Y, Z respectively.

The limits of X:

From the equation, z² = x² + y²

Z² = X² + Y²

X² = Z² - Y²

Let Z = 0, then X² = - Y² which is impossible. Therefore, Y can take any value such that Y < Z.

The limits of Y:

From the equation, z² = x² + y²

Z² = X² + Y²

Y² = Z² - X²

Let Z = 0, then Y² = - X² which is impossible. Therefore, X can take any value such that X < Z.

Limits of Z:

From the equation x² + y² + (z + 2)² = 2z² + 4z + 8 = 2(Z + 1)² + 6

The limits of z are Z < 2 and Z > - 2.

Volume in rectangular coordinate system:

[tex]$$\iiint_{E}[/tex] dx dy dz = [tex]\int_{-2}^{2} \int_{0}^{\sqrt{z^2}} \int_{-\sqrt{z^2 - y^2}}^{\sqrt{z^2 - y^2}} dx dy dz$$[/tex]

b) Volume of solid E in cylindrical coordinate system

Let the limits of ρ, θ, z be R, Θ, Z respectively.

The limits of R:

From the equation, z² = ρ² cos²θ + ρ² sin²θ

Z² = ρ²

Rho² = Z²/ cos²θ + sin²θ

Rho = Z/ cosθ

Let Z = 0, then Rho = 0. Therefore, R can take any value such that 0 ≤ R < 2.

Limits of Θ:

From the equation, z² = ρ² cos²θ + ρ² sin²θ

Z² = ρ² sin²θ

Theta² = tan⁻²(Z²/ ρ²)

Let Z = 0, then Θ = 0. Therefore, Θ can take any value such that 0 ≤ Θ ≤ π/2.

Limits of Z:

From the equation x² + y² + (z + 2)² = 2z² + 4z + 8 = 2(Z + 1)² + 6

The limits of Z are -2 ≤ Z < 2.

Volume in cylindrical coordinate system:

[tex]$$\iiint_{E} \rho d\rho d\theta dz = \int_{0}^{2} \int_{0}^{\frac{\pi}{2}} \int_{0}^{\sqrt{4 - z^2}} \rho d\rho d\theta dz$$[/tex]

c) Evaluation of the volume of solid E:

Using rectangular coordinate system, the volume of solid E is

[tex]$$\iiint_{E} dx dy dz[/tex] = [tex]\int_{-2}^{2} \int_{0}^{\sqrt{z^2}} \int_{-\sqrt{z^2 - y^2}}^{\sqrt{z^2 - y^2}} dx dy dz$$$$[/tex]

[tex]=\int_{-2}^{2} \int_{0}^{\sqrt{z^2}} [x]_{-\sqrt{z^2 - y^2}}^{\sqrt{z^2 - y^2}} dy dz$$$$=\int_{-2}^{2} \int_{0}^{\sqrt{z^2}} 2\sqrt{z^2 - y^2} dy dz$$$$=\int_{-2}^{2} \left[-\frac{1}{2}(z^2 - y^2)^{3/2}\right]_{y=0}^{y=\sqrt{z^2}} dz$$$$=\int_{-2}^{2} \frac{1}{2}z^3 dz = 0$$[/tex]

Therefore, the volume of solid E using rectangular coordinate system is 0.

Using cylindrical coordinate system, the volume of solid E is

[tex]$$\iiint_{E} \rho d\rho d\theta dz = \int_{0}^{2} \int_{0}^{\frac{\pi}{2}} \int_{0}^{\sqrt{4 - z^2}} \rho d\rho d\theta dz$$$$=\int_{0}^{2} \int_{0}^{\frac{\pi}{2}} \left[\frac{\rho^2}{2}\right]_{0}^{\sqrt{4 - z^2}} d\theta dz$$$$=\int_{0}^{2} \int_{0}^{\frac{\pi}{2}} 2 - \frac{z^2}{2} d\theta dz$$$$=\int_{0}^{2} \left[2\theta - \frac{\theta z^2}{2}\right]_{\theta = 0}^{\theta = \frac{\pi}{2}} dz$$$$=\int_{0}^{2} \pi - \frac{\pi z^2}{4} dz = \frac{11\pi}{3}$$[/tex]

Therefore, the volume of solid E using cylindrical coordinate system is 11π/3.

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Answer:

A is the answer

Step-by-step explanation:

All you have to do is follow the order pair such as 2, 100 and see if that is a correct pair.

Hope that helps

Answer: A. (2, 100)

Step-by-step explanation:

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{48}[/tex]

= [tex]\sqrt{16(3)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]

= 4[tex]\sqrt{3}[/tex]

...............................................

Answer:

2 km < 4,000 m

Step-by-step explanation:

2 km = 2,000 m

Therefore, 2,000 m is less than 4,000 m.

Answer:

Step-by-step explanation:

Look at the graph, look at homework and then look at the number right outside of it.

Answer:

8/7

Step-by-step explanation:

12*2=24.

7*3=21

24/21 is divisible by 3

=8/7

Answer:

the answer is 14 I pinkie promise!

Answer:

Step-by-step explanation:

Answer:

C is the answer also can I have brian list

Step-by-step explanation:

Answer:

Your answer would be D. I know this is kind of late, but maybe other people that come up here could get some help

Step-by-step explanation:

During an experiment of acceleration changes, the value that must stay constant during these trials is d. Mass

Inertia, a basic characteristic of all matter, may be measured quantitatively using mass. When a force is applied, an item effectively provides resistance to changes in velocity or position. The change brought about by an applied force is less the more mass an item has. According to Newton's second law of motion an object's acceleration is inversely proportional to its mass and directly proportional to the net force that has been applied to it. It may be expressed mathematically as F = ma.

The goal of this experiment is to see how variations in force impact acceleration. It is crucial to maintain the mass constant throughout the trials in order to isolate the impact of force on acceleration. Any observable variations in acceleration may be entirely attributable to variations in the applied force by maintaining the mass constant.

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Answer:

D 19,905

Step-by-step explanation:

19,905.22×25%=4976.31

19905.22-4976.31=14,928.91

14928.91×8%=1194.31

14928.91-1194.31=13734.6

Answer:

0.0129449838188

Answer: Should be 7

Step-by-step explanation:

14/2 is 7

Based on the sample data, we can construct a 99% confidence interval estimate for the percentage of girls born as approximately 85.1% to 94.9%.

To construct a confidence interval estimate for the percentage of girls born, we can use the formula for estimating a proportion.

First, we calculate the sample proportion, which is the number of successes (girls) divided by the total number of trials (babies born):

Sample proportion (p-hat) = Number of girls / Total number of babies born

= 288 / 320

= 0.9

Next, we can construct the confidence interval using the sample proportion. Since we want a 99% confidence interval, we need to find the critical value corresponding to that level of confidence. For a two-tailed test, the critical value is obtained from the standard normal distribution (Z-distribution).

Using a Z-table or calculator, the critical value for a 99% confidence level is approximately 2.576.

The margin of error (E) can be calculated as:

Margin of error (E) = Critical value * Standard error

The standard error (SE) for estimating a proportion is given by:

Standard error (SE) = [tex]\sqrt {(p-hat * (1 - p-hat)) / n}[/tex]

where p-hat is the sample proportion and n is the sample size.

Using these values, we can calculate the margin of error:

Standard error (SE) = [tex]\sqrt {(0.9 * (1 - 0.9)) / 320}[/tex]

≈ 0.019

Margin of error (E) = 2.576 * 0.019

≈ 0.049

Finally, we can construct the confidence interval:

Confidence interval = Sample proportion ± Margin of error

= 0.9 ± 0.049

≈ (0.851, 0.949)

Therefore, based on the sample data, we can construct a 99% confidence interval estimate for the percentage of girls born as approximately 85.1% to 94.9%.

Since the interval includes the value of 0.5 (50%), which represents an equal chance of having a girl or a boy, it suggests that the method used in the clinical trial does not significantly increase the probability of conceiving a girl.

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The maximum possible cost in dollars is $226.76 (approx).

Standard deviation = $88

Let X be the cost of the automobile repair, then X ~ N(367, 88^2) (normal distribution)

Now, we need to find the following probabilities:

(a) P(X > 480)(b) P(X < 240)(c) P(240 < X < 480)(d)

Find X such that P(X < X1) = 0.05, where X1 is the lower 5% point of X(a) P(X > 480)

We need to find P(X > 480)P(X > 480) = P(Z > (480 - 367)/88) [Standardizing the random variable X]P(X > 480) = P(Z > 1.2955)

Using the standard normal table, the value of P(Z > 1.2955) = 0.0983 (approx)

Hence, the required probability is 0.0983 (approx)(b) P(X < 240)

We need to find P(X < 240)P(X < 240) = P(Z < (240 - 367)/88) [Standardizing the random variable X]P(X < 240) = P(Z < -1.4432)

Using the standard normal table, the value of P(Z < -1.4432) = 0.0749 (approx)

Hence, the required probability is 0.0749 (approx)(c) P(240 < X < 480)

We need to find P(240 < X < 480)P(240 < X < 480) = P(Z < (480 - 367)/88) - P(Z < (240 - 367)/88) [Standardizing the random variable X]P(240 < X < 480) = P(Z < 1.2955) - P(Z < -1.4432)

Using the standard normal table, the value of P(Z < 1.2955) = 0.9017 (approx)and the value of P(Z < -1.4432) = 0.0749 (approx)

Hence, the required probability is 0.9017 - 0.0749 = 0.8268 (approx)(d)

Find the maximum possible cost in dollars, if the cost for your car repair is in the lower 5% of automobile repair charges.

This is nothing but finding the lower 5% point of X.We need to find X1 such that P(X < X1) = 0.05.P(X < X1) = P(Z < (X1 - 367)/88) [Standardizing the random variable X]0.05 = P(Z < (X1 - 367)/88)

Using the standard normal table, the value of Z such that P(Z < Z0) = 0.05 is -1.645 (approx)

Hence, we get,-1.645 = (X1 - 367)/88

Solving for X1, we get: X1 = 88*(-1.645) + 367 = $226.76 (approx)

Therefore, the maximum possible cost in dollars is $226.76 (approx).

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The variance of the sampling distribution for the difference of the two means is 0.0147142857.

The correct option is D. 0.051.

The variance of the sampling distribution for the difference of two means of sample populations can be calculated using the formula given below:

[tex]\Large\frac{{{\sigma }_{1}}^{2}}{n_{1}}+\frac{{{\sigma }_{2}}^{2}}{n_{2}}[/tex]

Where,[tex]{{\sigma }_{1}}$ and ${{\sigma }_{2}}[/tex] are the standard deviations of the two populations respectively, and [tex]{{n}_{1}} and ${{n}_{2}}[/tex] are the sample sizes of the first and second populations respectively.

Substituting the given values, we get

[tex]\Large\frac{0.9^2}{25}+\frac{0.8^2}{35}=0.009+0.0057142857[/tex]

=0.0147142857

Therefore, the variance of the sampling distribution for the difference of the two means is 0.0147142857.

Sampling distribution approaches normal distribution:

True. Regardless of the shape of the population, the sampling distribution of the mean approaches a normal distribution as the sample size increases.

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Answer:

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored. Equation at the end of step 2 : 2n2 - 7n - 5 = 0. Step 3 : Parabola ...

Step-by-step explanation:

Answer:

100-47=53 so 53$ profit

Step-by-step explanation:

Answer:

n=2

Step-by-step explanation:

[tex]\frac{3.3.3.3.3.3}{3.3.3.3} = 3^{n}[/tex]

[tex]3^{2}[/tex]= [tex]3^{n}[/tex]

n=2

Answer:

[tex]3^1[/tex]

Step-by-step explanation:

[tex]\frac{3*3*3*3*3}{3*3*3*3} =3^1[/tex]