Describe the graph of the function at its roots.
f(x) = (x - 2)2(x + 6)2(x + 12)
At x = 2, the graph
the x-axis.
At x = -6, the graph
the x-axis.
Atx = -12, the graph
the x-axis.
DONE

The slope of the line that is represented by the given data in the question is 3/4.

To find the slope of a line, we need to use the formula:

slope = (change in y) / (change in x)

We can choose any two points on the line and use their coordinates to calculate the change in y and the change in x. Let's choose the points (-9, 4) and (7, 16) from the given data.

Change in y = 16 - 4 = 12

Change in x = 7 - (-9) = 16

Plugging these values into the slope formula, we get:

slope = 12 / 16 = 3 / 4

We can also interpret this slope as the rate of change of y with respect to x. For every increase of 1 in x, y increases by 3/4. Similarly, for every decrease of 1 in x, y decreases by 3/4.

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Answer:

8 mins per gallon.

Step-by-step explanation:

Answer:

diameter: 2.4 mi

circumference = 38.96 mi

Step-by-step explanation:

d=2r=2·6.2=12.4

C=2πr=2·π·6.2≈38.95575

Answer:

5.5 quotient 5 and rest 1

But I would answer quotient is 5 and half

Step-by-step explanation:

11/3 ÷ 2/3 = 11/3 * 3/2 = 11/2= 5.5

So the quotient is 5 and rest is 1

Hope this helps, have a good day

Answer:

5 1/2

Step-by-step explanation:

11/3÷2/3

Applying the fractions formula for division,

=11/3×3/2

=33/6

Simplifying 33/6, the answer is

=5 1/2

The p-value for testing the claim that the mean amount of money people spend on movie tickets has changed is 0.0027.

To test the claim, we will conduct a one-sample t-test. The null hypothesis (H0) is that the mean amount of money people spend on movie tickets has not changed, while the alternative hypothesis (Ha) is that there has been a change in the mean amount.

Given the sample mean ($12.50) and the sample standard deviation ($2.40), we can calculate the t-value using the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / √n). Substituting the values, we get t = (12.50 - 12) / (2.40 / √45) ≈ 1.378.

Next, we determine the degrees of freedom (df) for the t-distribution, which is n - 1. In this case, df = 45 - 1 = 44.

Using a significance level of 5% (or 0.05), we compare the t-value to the critical t-value obtained from the t-distribution with 44 degrees of freedom. If the absolute value of the t-value is greater than the critical t-value, we reject the null hypothesis.

Looking up the critical t-value in a t-table or using statistical software, we find that the critical t-value is approximately 2.016. Since the absolute value of the calculated t-value (1.378) is less than the critical t-value, we fail to reject the null hypothesis.

To find the p-value, we compare the t-value to the t-distribution with 44 degrees of freedom. The p-value is the probability of obtaining a t-value as extreme or more extreme than the calculated t-value under the null hypothesis. Using statistical software or a t-table, we find that the p-value is approximately 0.0027 (rounded to four decimal places).

Since the p-value (0.0027) is less than the chosen significance level of 0.05, we reject the null hypothesis. This indicates strong evidence to support the claim that the mean amount of money people spend on movie tickets has changed.

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The statement "An asymmetrical layout can have balance" is true.

Asymmetrical layout is a form of visual balance that utilizes various objects' visual weights and colors to achieve an equilibrium that does not need a mirrored arrangement.

An asymmetrical design comprises two dissimilar sides of a balanced arrangement with various elements that have equal visual weight.

When it comes to graphic design, the term "asymmetrical" means any arrangement that does not appear to be balanced.

Balance is a key principle in graphic design that is defined as the even distribution of visual weight on either side of a composition.

A balanced design feels secure and comfortable, whereas an unbalanced design produces a feeling of discomfort and tension in the viewer.

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Answer:

The first Graph

Step-by-step explanation:

its not the third because it's a dotted line, so it wouldn't be equal to. it's not the second because it's shaded in the wrong place, making it less than.

In a multiple regression model, the error term (often denoted as ε or e) is assumed to be a random variable with a mean of zero.

This assumption is a key component of the regression model and is often referred to as the assumption of zero conditional mean or the assumption of homoscedasticity. The assumption of a mean of zero for the error term means that, on average, the errors have no systematic bias or tendency to overestimate or underestimate the predicted values. It implies that the model's predictions are unbiased and that any deviations from the true values are due to random chance or other factors not captured by the model. The other options presented in the answer choices (B) -1, (C) 1, and (D) any value are incorrect. The mean of the error term is specifically assumed to be zero, as it represents the average deviation of the observed values from the predicted values in the model.

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Answer:

6 or 3

Step-by-step explanation:

There are only one way to pick exactly 6 of the 7 winning numbers without regard to order.

There are "1 to 70 numbers, choose 7 " or 70C7 ways to pick 7 correctly.

AND

you must also pick 1 wrong number.  That wrong number has to be

different from any of the 7 correct numbers, and so there are

40-6 or 34 wrong numbers you could have picked.  That's 34 wrong

numbers, choose 1 or 34C1. Since AND means to multiply, the

numerator is 6C5 X 34C1=204

The denominator is the same 3838380 as in part (A)

So the desired probability is 204 / 38380 = 17 / 319865.

However that's just the probability of winning the $10000.

The words "probability of winning" could be taken as the

probability of winning either $1,000,000 OR $10,000. So

P(winning $1,000,000 OR winning $10,000) and since

"OR" means "ADD", we add the probability found in part A,

so the correct answer is 1 / 38380 + 204 / 38380 = 205 / 3838380

=41 / 767676,

the probability of winning a million or ten thousand.

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\({ \color{teal}{ \huge{ \textsf{ \textbf{Answer}}}}}\)

We can calculate supplementary angles by subtracting the given one angle from 180 degrees. To find the other angle, use the following formula: ∠x = 180° – ∠y or ∠y = 180° – ∠x where ∠x or ∠y is the given angle.

The supplementary of 97° is (180°-97°)=83°

Answer:

Step-by-step explanation:

The required work done in lifting the laptop to a height of 2 feet will be 263.79 foot-poundal.

Total weight of the laptop is 4.1 pounds

Acceleration due to gravity = 32.17 ft/\(s^{2}\)

Now the height to which the laptop has been lifted = 2 feet

Since, there is no mentioned velocity of the laptop, therefore the kinetic energy will be zero

Therefore, the total work in lifting the laptop will be equal to the change in potential energy.

Potential energy is the energy that comes by virtue of its position with reference to other

Therefore, potential energy = mgh

Where, m = mass of the laptop = 4.1 pounds

g = acceleration due to gravity = 32.17 ft/\(s^{2}\)

h = height to which the laptop is lifted =  2 feet

Therefore potential energy = (4.1)(32.17)(2) = 263.79 foot-poundal

263.79 foot-poundal is the required work done.

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Answer:

y varies inversely with x is written as

y = k /x

where k is the constant of variation

y = 8 x = 1.55

8 = k / 1.55

Multiply through by 1.55

k = 12.4

The formula is

y = 12.4 / x

when y = - 0.62

- 0.62 = 12.4/x

- 0.62x = 12.4

Divide both sides by - 0.62

x = 12.4/-0.62

x = - 20

When y = - 0.62 x = - 20

Hope this helps

Answer: From the conditions given, the total number of the problems should be 29. This means that the sum of x and y should be 29. With this and the point-system, the best system of equation that is useful for this problem is,

                                     x + y = 29

                                     5x + 2y = 100

Your first answer choice is the correct answer.

Fact: I suggest looking up the question before asking it because  sometimes others have asked the questions and it will be answered. Just letting you know to help you save points.

Answer:

x + y = 29, 5x + 2y = 100

Step-by-step explanation:

just did it

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The inequality that express the relationship between -2 and -5 is : " greater than " or " > "

\(\qquad \tt \dashrightarrow \: - 2 > - 5\)

The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.

The variance of a random variable from its true population or sample mean is expected in probability theory and statistics. The term "variance" refers to a measurement of how widely apart a group of numbers are from one another.

Here,

Variance and standard deviation are both measures of spread. They calculate the deviation of each data point from the mean. The range of data increases with increasing variation. Using the original unit of measurement, the standard deviation measures the same thing as the variance (whereas variance is the original unit squared).

Therefore ,The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.

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Answer: -1 3/14

Step-by-step explanation:

-3/6-5/7

turn into addition

-3/6+-5/7

Find The Lcm of 6 and 7

-21/42+-30/42

Add

-51/42

Simplify

-1 9/42

Simplify to lowest term

-1 3/14

Answer:

- 17/14 or -1 3/14

Step-by-step explanation:

Find the LCD and combine terms

14 is LCD

The answer is negative because negative minus a positive will be negative

The proportion of cats in the sample suffers from separation anxiety is 33%

Given 432 cats, a sample of 42 cats is taken.

Out of these 42, cats 14 are suffering from separation anxiety.

The proportion of cats suffering from separation anxiety is: 14/42

The percentage of Cats suffering from separation anxiety is:\(\frac{14}{42}*100\)%

This is equal to 33%, rounding off to the nearest percentage value.

Therefore, The proportion of cats in the sample who suffers from separation anxiety is 33%.

The sample proportion (p^hat) describes the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or items) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.

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The proportion of cats in the sample suffers from separation anxiety is 33%

Given 432 cats, a sample of 42 cats is taken.

Out of these 42, cats 14 are suffering from separation anxiety.

The proportion of cats suffering from separation anxiety is: 14/42

The percentage of Cats suffering from separation anxiety is:(14/42)*100%

This is equal to 33%, rounding off to the nearest percentage value.

Therefore, The proportion of cats in the sample who suffers from separation anxiety is 33%.

The sample proportion (p^hat) describes the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or items) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.

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By approving the drug, the FDA has accepted the alternative hypothesis that the drug is effective. Therefore, a Type I error (rejecting the null hypothesis when it is actually true) could not have been made.

If the FDA approves the drug, it means they have accepted the alternative hypothesis that the drug is effective, and therefore, a Type I error (rejecting the null hypothesis when it is actually true) could not have been made.

In hypothesis testing, a Type I error occurs when we reject the null hypothesis even though it is true. This means we falsely conclude that there is an effect or relationship when there isn't one. In the context of drug approval, a Type I error would mean approving a drug that is actually ineffective or potentially harmful.

By approving the drug, the FDA is essentially stating that they have sufficient evidence to support the effectiveness of the drug, indicating that a Type I error has been minimized or avoided. However, it is still possible to make a Type II error (failing to reject the null hypothesis when it is actually false) by failing to approve a drug that is actually effective.

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The expressions given in option A and option C on solving will have same value 3/2 or 1.5.

Numeric values can be obtained through the evaluation of numeric expressions, which consist of a mixture of numeric components including variables, numbers or functions, and operators. A blend of arrays and mathematical operators can be present within an expression to derive a numeric solution.

Now solving numerical expressions in the problem (refer to image attached)

A. \(\frac{1}{6} +(\frac{5}{6}+\frac{3}{6} ) = \frac{1+5+3}{6} = \frac{9}{6} =\frac{3}{2} =1.5\)

B. \(\frac{1}{3}+ \frac{5}{3}+ \frac{2}{3} =\frac{1+5+2}{3} =\frac{9}{3} =3\)

C. \(\frac{3}{5} +(\frac{1}{2} +\frac{2}{5} )=\frac{15}{10} =\frac{3}{2} =1.5\)

D. \(2+\frac{1}{2} =\frac{4+1}{2} =\frac{5}{2} =2.5\)

Hence, expressions in option A and option C have same values

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Answer:

36a^10

Step-by-step explanation:

Answer:

there you go

Step-by-step explanation:

angle DOB is 60 degree.

Answer:

see explanation

Step-by-step explanation:

Given ∠ DOC = 90° then

∠ DOB = 90 - p and

Since AOB is a straight angle , then

4p + 90 - p = 180

3p + 90 = 180 ( subtract 90 from both sides )

3p = 90 ( divide both sides by 3 )

p = 30

4p = 4 × 30 = 120

Then

∠ DOB = 180° - 4p = 180° - 120° = 60°

(a) To find the quantity that will give maximum profit, we need to maximize the profit function. The profit function is given by:

Profit = Total Revenue - Total Cost
Profit = (Price per unit x Quantity) - (Average Cost per unit x Quantity)
Profit = (1908 - x^2) x - (900 + 8x + x^2) x
Profit = 1908x - x^3 - 900x - 8x^2 - x^3
Profit = -2x^3 - 8x^2 + 1008x

To find the maximum profit, we need to take the derivative of the profit function and set it equal to zero:

dProfit/dx = -6x^2 - 16x + 1008 = 0
Solving for x, we get:

x = (-(-16) ± sqrt((-16)^2 - 4(-6)(1008))) / 2(-6)
x = 14.37 or x = -23.63

Since x represents the quantity in hundreds of units, we can only use the positive value, which means the quantity that will give maximum profit is approximately 1437 units.

(b) To find the maximum profit, we need to substitute the value of x into the profit function:

Profit = -2(1437)^3 - 8(1437)^2 + 1008(1437)
Profit = $307,261.44

Therefore, the maximum profit is approximately $307,261.44.
To find the maximum profit, we need to first find the profit function, P(x), which is the difference between revenue, R(x), and cost, C(x). Since the demand function is given as p = 1908 - x^2, we can find the revenue function by multiplying the price with the quantity (x):

R(x) = p * x = (1908 - x^2) * x

The cost function is given as C(x) = 900 + 8x + x^2. Now, let's find the profit function P(x):

P(x) = R(x) - C(x) = (1908 - x^2) * x - (900 + 8x + x^2)

(a) To find the quantity that will give maximum profit, we need to find the critical points by taking the derivative of P(x) and setting it to zero:

P'(x) = d(P(x))/dx = 1908 - 6x^2 - 8x

Set P'(x) = 0:

0 = 1908 - 6x^2 - 8x

Solve for x, keeping in mind that x is in hundreds of units and production is limited to 1000 units (10 hundreds of units). The solution within this constraint is x ≈ 6.07 hundreds of units.

(b) To find the maximum profit, plug the value of x (6.07) into the profit function P(x):

P(6.07) ≈ (1908 - 6.07^2) * 6.07 - (900 + 8 * 6.07 + 6.07^2)

Round your answer to the nearest cent: P(6.07) ≈ $5,993.44

So, the maximum profit is approximately $5,993.44

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Answer:

Non-Linear

Includes a cluster

Positive Association

Includes an outlier

Step-by-step explanation:

The rational numbers are √10, √1000 and √100000 . Options A, C and D

A rational number can be defined as a  number that can be expressed as a fraction.

It also has the numerator and denominators as integers and expressed in decimal forms.

Given the values;

√10 = 3. 162

√100 = 10

√1000 = 31. 6

√100000 = 316. 22

Thus, the rational numbers are √10, √1000 and √100000 . Options A, C and D

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Answer:

396

Step-by-step explanation:

the volume of a rectangular is calculated as V=l×w×h

l=11, w=12, h=3

V=11×12×3

V= 396

ok

1.- Convert 1 m to mm

1 m ------------------ 100 cm 10 mm ------ 1 cm

there are 10 x 100 = 1000 mm in a meter

2.- Convert 35 cm into mm

10 mm -------------- 1 cm

x -------------- 35 cm

x = (35 x 10) / 1

x = 350 mm

3.- Total = 1000 + 350 = 1350 mm

The answer is H. 1350 mm