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The p-value of 4.91541E-15 (or 4.91541 x 10^-15) is considerably beneath the conventional significance level of 0.05 employed in statistical hypothesis testing.

In hypothesis testing, the p-value symbolizes the probability of detecting the test statistic (or an even larger value) under the null hypothesis. A p-value of 0.05 or below often appears statistically relevant, suggesting powerful evidence contrary to the null hypothesis.

Therefore, a p-value of 4.91541E-15 being far less than 0.05 implies very compelling evidence against the null hypothesis.

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Answer:So the instantaneous velocity at t = 0 is -20. This means that the object is moving in the negative direction at a rate of 20 units per second at t = 0.

Look at the Photo

Answer:

x^2y^4

Step-by-step explanation:

b because u have to add the exponents of the like variable. x^4 and x^-2 are the like terms in this equations so 4+(-2) so its basically flipping the signs plus and the negative sign so it's just -2

The joint costs allocated to Product B is $240,000.

We must allocate joint costs based on the relative physical quantities produced by each product.

The total physical quantity produced by both products is:

= Quantity of A + Quantity of B

= 10,000 + 40,000

= 50,000 pounds

We will calculate the proportion of physical quantity produced by product A:

= Quantity of B / Total physical quantity

= 40,000 / 50,000

= 0.8

The amount of joint costs allocated to Product B is will be

= Total joint costs x Proportion of

= $300,000 x 0.8

= $240,000.

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The domain of the function in this problem is given as follows:

all real numbers.

The domain of a function is the set of all the possible input values that can be assumed by the function.

On the graph, the domain of the function is given by the values of x of the function.

A quadratic function has no restrictions on the domain, hence it is defined by all the real values.

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Answer: The surface area of the rectangular prism is 424 square meters.

Step-by-step explanation: To find the surface area of a rectangular prism, we need to add up the areas of all six faces.

The front and back faces have an area of length x height, which in this case is 4 x 8 = 32 square meters each.

The top and bottom faces have an area of width x height, which in this case is 15 x 8 = 120 square meters each.

The left and right faces have an area of length x width, which in this case is 4 x 15 = 60 square meters each.

So the total surface area of the rectangular prism is:

32 + 32 + 120 + 120 + 60 + 60 = 424 square meters.

Therefore, the surface area of the rectangular prism is 424 square meters.

The time it will take for your account balance to reach $10,000 is given as follows:

t = 10.8 years.

The balance of an account after t years, using continuous compounding, is given as follows:

A(t) = A(0)e^(kt).

In which:

The parameters for this problem are given as follows:

A(0) = 6500, k = 0.04.

Hence the time needed for a balance of $10,000 is obtained as follows:

10000 = 6500e^(0.04t)

e^(0.04t) = 10000/6500

0.04t = ln(10000/6500) -> ln is the inverse operation of the exponential

t = ln(10000/6500)/0.04

t = 10.8 years.

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The point estimate of the population mean is 25 and the margin of error for the confidence interval is 2.04.

To determine the point estimate of the population mean, we take the midpoint of the interval.

Point estimate of population mean = (Lower bound + Upper bound) / 2 = (20 + 30) / 2 = 25

To calculate the margin of error, we need to know the level of confidence for the interval. Assuming a 95% confidence level, we can use the formula:

The margin of error = (Upper bound - Lower bound) / (2 * z-score)

Where the z-score for a 95% confidence level is 1.96.

Margin of error = (30 - 20) / (2 x 1.96) = 2.04

Hence, the population means point estimate is 25, and the confidence interval's margin of error is 2.04 percent.

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Answer:

$124 per week

Step-by-step explanation:

To fins how much she needs to save each week, divide the total cost by the amount of time. In this problem, divide $2,976 by 24 weeks to find the amount she needs to save.

$2976/24=$124 per week

Answer:2^4=4x-4 would be the answer

Step-by-step explanation: You would exponentiate both sides

The factored expression would have two brackets as shown.

We can see that the Polynomial that we have to deal with in the questions that we have here are quadratic in nature and we have to deal with them as such. We are going to have that when we deal with the quadratic;

r^2 - 25r - 150

This can be factored into (r + 5) (r - 30)

Then;

64y^2 - 49z^2

This can be factorized to give;

(8y + 7z) (8y - 7z)

Also;

16y^2 - 88y + 121

Can be factorized to;

(4y - 11) (4y - 11)

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Answer:

To solve for k, we first need to isolate k on one side of the equation by subtracting 61.1 from both sides:

K/7.8 + 61.1 - 61.1 = 17.8 - 61.1

K/7.8 = -43.3

Next, we multiply both sides by 7.8 to isolate k.

K = -43.3 * 7.8

K = -338.34

Therefore, k is approximately equal to -338.34.

The surface area of the rectangular prism is 220 square inches

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

5 in by 10 in by 4 in

The surface area of the rectangular prism is calculated as

Area = 2 * (5 * 10 + 5 * 4 + 10 * 4)

Evaluate

Area = 220

Hence, teh area is 220 square inches

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The concepts of percentage, rate, and base can be defined as follows:

In our daily lives, we utilize these three concepts in many different ways, some examples of which are outlined below:

When we go shopping, we frequently come across discounts or sale prices offered as percentages off the original price. For example, if an item was initially $40 but is now available at a discount of 20%, it will be priced at $32.

Rates enable us to measure speed when we are driving or running with unit-based measurements. In addition, rates allow us to compare prices during grocery shopping, where we might need to know the cost per pound of apples and/or calculate interests on investments or loans.

Bases have utility while dealing with ratios or proportions. For instance, if we wish to prepare food for eight people instead of four, one can take the existing recipe as a base and adjust ingredient quantities proportionally.

The formulas P = B × R, B = P / R, and R = P / B are basic calculations that correspond to different values based on the given percentage, rate, or base. For instance, P = B × R allows us to obtain the value of P given the input of B and R.

Meanwhile, B = P / R enables us to get the value of B by punching in P and R much like calculating interest paid out each month in compound-interest cases.

Finally, R = P / B yields the value of R using inputs for P and B. These formulas find rampant use in fields like finance, economics, and mathematics.

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Answer:

There are 36 possible outcomes when two dice are rolled (6 outcomes for the first die and 6 outcomes for the second die). To find the probability that the sum of the two numbers on the dice will be greater than 9, we need to count the number of outcomes where the sum is greater than 9.

The possible outcomes where the sum is greater than 9 are (4,6), (5,5), (5,6), and (6,5), for a total of 4 outcomes. Therefore, the probability of getting a sum greater than 9 is 4/36 or 1/9.

Answer: C) 1/12.

Answer:

45

Step-by-step explanation:

The coordinates of the points B' and C' are B' = (-1, 10) and C' = (-6, -5)

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

A = (-2, -4)

This point is translated to

A' = (-3, -1)

This means that the rule of transformation is

(x, y) = (x - 1, y + 3)

Given that

B = (0, 7) and C = (-5, -8)

When this transformation is applied on B and C, we have

B' = (0 - 1, 7 + 3) and C' = (-5 - 1, -8 + 3)

Evaluate

B' = (-1, 10) and C' = (-6, -5)

Hence. the coordinates of B' and C' are B' = (-1, 10) and C' = (-6, -5)

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Answer:

12

Step-by-step explanation:

PEMDAS (Parenthesis, exponents, multiplication/division, addition/subtraction

(-1)² + 5(4) - 9

1 + 5(4) - 9

1 + 20 - 9

=12

Answer:  the best answer is option A: the data is symmetric with an approximate range of 20. The lowest value of 6 might mean that most students did not participate in activities.

Step-by-step explanation: From the line plot, we can see that the data is not symmetric because the dots are not equally distributed on both sides of the plot. Therefore, we can eliminate options A and C.

Option D suggests that the data is bimodal, meaning that there are two peaks in the distribution. However, there is no clear indication of two peaks in the plot. Therefore, we can eliminate option D.

Option B suggests that the data is skewed, and the most frequent number of activities is 16 or more. However, this is not the case as the highest number of dots is above 14 and 16. Therefore, we can eliminate option B.

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[tex]\cos C=\dfrac{CE}{AC}\\=\dfrac{8}{\sqrt{8^2+3^2}}\\=\dfrac{8}{\sqrt{64+9}}\\=\dfrac{8}{\sqrt{73}}\\=\boxed{0,936}[/tex]

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Answer:

multiply the number of meters by 100

The 90% confidence that the proportion of yellow peas is between 23.5% and 29.5%

and, 25% estimate falls within the 90% confidence limits.

We have,

Green peas= 445

Yellow peas= 161

So, Total peas:

= 445 + 161

= 606.

Now, the Proportion of yellow

= 161/606

= 0.265676

= 26.56%

Now, p= 0. 265 and q= 1-0.265= 0.735

So, np = 606 (0.265)= 160.59

nq = 606(0.735) = 445.41

As, both results are ≥ 5 and the sample can be approximated by a normal distribution.

For 90% confidence, z = 1.645.

Now, the margin error

= 1.645 √ (0.265)(0.735) / 606

= 1.645 / 0.0179

= 0.0294

Now, The confidence limits are the point estimate ± the margin of error. =

= 0.265 + 0.03

= 0.295

= 29.5%;

or, 0.265 - 0.030

= 0.235

= 23.5%

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Answer:

t = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

calculate the gradient (slope) of AB using the slope formula and equate to the slope of the perpendicular line.

given line with slope 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex]

calculate [tex]m_{AB}[/tex] using slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (2, - 3 ) and (x₂, y₂ ) = B (- 2, t )

[tex]m_{AB}[/tex] = [tex]\frac{t-(-3)}{-2-2}[/tex] = [tex]\frac{t+3}{-4}[/tex]

equating corresponding slopes

[tex]\frac{t+3}{-4}[/tex] = - [tex]\frac{4}{5}[/tex] ( multiply both sides by - 4 to clear the fraction )

t + 3 = - [tex]\frac{4}{5}[/tex] × - 4 = [tex]\frac{16}{5}[/tex] ( subtract 3 from both sides )

t = [tex]\frac{16}{5}[/tex] - 3 = [tex]\frac{16}{5}[/tex] - [tex]\frac{15}{5}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

9w - 35

Step-by-step explanation:

-3(w + 5) + 4(3w - 5)

(Use the distributive property to multiply -3 by w + 5.)

-3w - 15 + 4(3w - 5)

(Use the distributive property to multiply 4 by 3w - 5)

-3w - 15 + 12w - 20

(Combine -3w and 12w to get 9w.)

Subtract 20 from -15 to get -35.

9w - 35.

Answer:

Step-by-step explanation:

[tex]\mathrm{-3(w+5)+4(3w-5) }[/tex]

Expand (Apply the distributive property) :-

[tex]\mathrm{-3w-15+12w-20}[/tex]

Combine like terms:-

[tex]\mathrm{-3w+12w=\bf 9w}[/tex]

[tex]\matherm{-15-20=\bf-35}[/tex]

[tex]\mathrm{9w-35}[/tex]

______________________

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