A computer monitor is 20 inches wide. The aspect ratio, which is the ratio of the width of the screen to the height of the screen, is
16:9
What is the length of the diagonal of the screen, to the nearest whole inch?
Enter your answer in the box.

(A) sample of 13 mature female pink seaperch was collected in winter, with a mean length of 109 millimeters and a standard deviation of 11 millimeters.

(B)  The critical value(s) and rejection region(s) are determined based on the significance level of 0.10 and the degrees of freedom

(c) The standard test statistic, also known as the t-value, is calculated using the formula:

t = (mean₁ - mean₂) / sqrt[(s₁²/n₁) + (s₂²/n₂)]

In order to determine whether the mean length of mature female pink seaperch is different in fall and winter, a hypothesis test is conducted with a significance level (alpha) of 0.10. The marine biologist collected a sample of 14 mature female pink seaperch in fall, with a mean length of 113 millimeters and a standard deviation of 10 millimeters. Another sample of 13 mature female pink seaperch was collected in winter, with a mean length of 109 millimeters and a standard deviation of 11 millimeters.

To support or refute the biologist's claim, the following steps are taken:

(b) The critical value(s) and rejection region(s) are determined based on the significance level of 0.10 and the degrees of freedom. Since the sample sizes are relatively small and the population variances are assumed to be equal, the appropriate test statistic to use is the t-distribution. The critical values are obtained from the t-distribution table or a statistical software. The rejection region(s) correspond to the extreme values in the tails of the t-distribution.

(c) The standard test statistic, also known as the t-value, is calculated using the formula:

t = (mean₁ - mean₂) / sqrt[(s₁²/n₁) + (s₂²/n²)]

where mean₁ and mean₂ are the sample means, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.

By plugging in the given values, the standard test statistic is calculated.

In order to reach a conclusion about the biologist's claim, the test statistic is compared to the critical value(s) obtained in step (b). If the test statistic falls in the rejection region, the null hypothesis (mean length is the same in fall and winter) is rejected, providing support for the biologist's claim. Conversely, if the test statistic falls outside the rejection region, there is not enough evidence to support the claim, and the null hypothesis cannot be rejected.

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The radius is approximately 3.78 inches.

We can solve the question using the formula for the surface area of a sphere:

S=4πr^2

We are given that the surface area is 225 square inches, so we can substitute this value into the formula and solve for r:

\(225=4\pi r^2\frac{225}{4\pi}\)

      = r^2

r={{225}{4π}}

approx  3.78

A sphere does not have any edges or vertices, like other 3D shapes. The points on the surface of the sphere are equidistant from the center.

Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere.

The Radius of a circle or sphere is equal to the Diameter divided by 2.

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Answer:

Step-by-step explanation:

Jill needs to make 2 full glasses of orange drink for each of the 50 people, which means she needs to make a total of 100 glasses of orange drink. Since each glass requires 250 millilitres of orange drink, Jill needs a total of 25 litres (100 glasses x 250 millilitres per glass) of orange drink.

According to the instructions, Jill needs to mix 1 part of orange squash with 4 parts of water. This means that for every 5 parts of drink, 1 part is orange squash and 4 parts are water. Therefore, Jill needs to use 5 times the amount of water as the amount of orange squash.

If Jill needs to make 25 litres of orange drink, then she needs to use 1/5th of that amount (5 parts) or 5 litres of orange squash.

A one litre bottle of orange squash costs £2. Therefore, Jill needs to buy 5 bottles of orange squash at a total cost of £10.

I hope this helps you with your calculations!

Answer:

20.25    

Step-by-step explanation:

304/15=20.25

Answer:

a+b+c = 180

48+59+b=180

107+b=180

b=180-107

b=73

Answer: b equals to 73 Degrees

Step-by-step explanation:

make two of this figure and keep one like that and rotate the other until they line up correctly an make a rectangle, then you will see the 30 degree angle is only half of the top square. since this is true, the top square= 60 degrees. y= 20   x= 40

Answer:

3+13i

Step-by-step explanation:

(10+10i)+(-7+3i)

Combine the real parts

10+-7 = 3

And the imaginary parts

10i +3i = 13i

Combine them to make the complex number

3+13i

The correct answer choice for the MPC (marginal propensity to consume) when the multiplier is 6 is not provided among the options A. 0.16, B. 0.83, C. 0.71, or D. 0.86.

The MPC is calculated as the ratio of the change in consumption to the change in income. When the multiplier is given, we can derive the MPC using the formula MPC = 1 / (1 + MPC). In this case, the multiplier is stated to be 6.

To find the corresponding MPC, we can solve the equation 1 / (1 + MPC) = 6 for MPC.

Rearranging the equation, we have 1 + MPC = 1 / 6. Subtracting 1 from both sides, we get MPC = 1 / 6 - 1 = -5 / 6.

The result MPC = -5 / 6 implies a negative MPC, which does not align with any of the given answer choices.

Additionally, all the answer choices provided (0.16, 0.83, 0.71, and 0.86) are positive values, further confirming that none of them represents the correct MPC when the multiplier is 6.

Therefore, the correct answer choice for the MPC when the multiplier is 6 is not listed among the options A. 0.16, B. 0.83, C. 0.71, or D. 0.86.

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Answer:

He payed $643.50 for the bike

Step-by-step explanation:

Because $585 + 10% = $643.50

(Sorry if wrong!)

Answer:

he paid $643.5 for it originally

585 x .1 = 58.5

585+58.5= 643.5

hope this helps

Step-by-step explanation:

All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.

1.1 Formulation:

The problem can be formulated as follows:

Minimize: 0 (since it is a feasibility problem)

Subject to:

α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1

α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2

α1, α2, α3, α4 are unrestricted

β is unrestricted

y_i ≥ 0 for all points in S1

z_i ≥ 0 for all points in S2

The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.

1.2 Finding a feasible solution:

To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.

Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.

For S1:

(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible

(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible

(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible

(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible

For S2:

(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible

(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible

(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible

(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible

Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

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Answer:

The bull weighs 1,900 pounds.

Step-by-step explanation:

2,000 pounds = 1 ton

0.95 x 2,000 = 1,900 pounds

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Answer: 1,900 pounds

Step-by-step explanation:

     There are 2,000 pounds in a ton, so we will multiply 0.95 tons by 2,000 to figure out the weight of the bull in pounds.

0.95 * 2,000 = 1,900 pounds

Answer:

A. A translation 4 units to the left and 3 units down.

Step-by-step explanation:

Answer:

A = 1160

B = 1160 is already in standard form.

C = 1200

Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

Answer:

2.9

18 \(m^{2}\)

Step-by-step explanation:

According to the following graph, the y intercept is 0, the asymptote is ∞ and the range is (-∞, ∞)

In math the term called graph is defined as  a pictorial representation or a diagram that represents data or values in an organized manner and the points on the graph often represent the relationship between two or more things.

Here we know that the function is f(x) = 8x.

When we plot the function then we get the graph like the following.

While we looking into plotted graph, then we have identified that the y-intercept is 0.

And the horizontal asymptote is the limit as x goes to ∞.

And the range is the set of values above the horizontal asymptote (-∞, ∞).

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Answer:

90,000

Step-by-step explanation:

Answer: The general solution of the differential equation is in the screenshot provided

Step-by-step explanation:

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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The probability that a random sample of 4 of the articles will contain a defective article is approximately 0.2916, or about 29.16%.

To find the probability that a random sample of 4 articles will contain a certain number of defective articles, we can use the binomial probability formula:

P(X = k) = (nCk) * (p^k) * (1-p)^(n-k)

where:
- n is the total number of articles in the sample (4 in this case)
- k is the number of defective articles we want to find the probability for
- p is the probability of an article being defective (1/10)
- 1-p is the probability of an article not being defective (9/10)
- nCk represents the number of combinations of n items taken k at a time

It appears that you haven't mentioned the specific number of defective articles you want in the sample of 4. However, you can use the formula above and plug in the values for k (0, 1, 2, 3, or 4) to find the probability for any desired number of defective articles in the sample.

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Answer:

B

Step-by-step explanation:

Refer to the attached images.

Taking into account the definition of a system of linear equations, the price of each drink and each taco is $1.54 and $2.75 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related. This is, systems of linear equations are sets of equations with multiple unknown values.

The solution of a system of equations is a set of real numbers that satisfies all the equations at the same time.

A system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

3x + 6y= 21.12

4x + 9y=30.91

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "y" from the first equations:

6y= 21.12 - 3x

y= (21.12 - 3x)÷ 6

y= 21.12÷6 - 3÷6x

y= 3.52 -0.5x

Substituting the expression in the second equation:

4x + 9×(3.52 -0.5x)=30.91

Solving:

4x + 9×3.52 -9×0.5x=30.91

4x + 31.68 -4.5x=30.91

4x -4.5x=30.91 - 31.68

-0.5x= -0.77

x= (-0.77)÷ (-0.5)

x= 1.54

Remembering that y= 3.52 -0.5x, you get:

y= 3.52 -0.5×1.54

y= 2.75

Finally, the price of each drink is $1.54 and the price of each taco is $2.75.

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Answer:5.97

Step-by-step explanation.  

you have to look at the question.

you have to look around the question

The very last step is you have to answer it  

Answer: 8 hours

Step-by-step explanation:  

(804 miles)/(12 hours) = 67 miles/hour

(536 miles)/(67 miles/hour) = 8 hours

Answer:

0.0625

Step-by-step explanation:

Answer: Choice B) 50 square meters

Work Shown:

A = pi*r^2

A = 3.14*4^2

A = 50.24

A = 50