estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the u.s., per year. suppose that there are about 3 × 108 people in the united states, approximately half of the them have cars, each car drives an average of 12,000 mi per year, and consumes a gallon of gasoline for each 20 mi .

Answer:

28/53

Step-by-step explanation:

Hey There!

So they want us to find the sine of angle S

well remember is sohcahtoa

S - sine

O - opposite

H - hypotenuse

meaning that

\(Sin=\frac{opposite}{hypotenuse}\)

The opposite side of angle S is 28 and the hypotenuse is 53

so \(sinS=\frac{28}{53}\)

Answer:

y-187.50= 1.50(x-125)

this is in point slope, but in slope intercept it would be y=1.50x+0

Step-by-step explanation:

Answer:

\(y-187.50=1.50(x-125)\)

Step-by-step explanation:

Slope = $1.50

\(x=125\)

\(y=$187.50\)

Answer:

\(M = (2,1)\)

Step-by-step explanation:

Represent the diagonals as:

\(A =(-2,-1)\)

\(B =(1,3)\)

\(C =(6,3)\)

\(D = (3,-1)\)

Required

Determine the coordinate of the intersection

To do this, we simply calculate the midpoint of AC or BD.

For AC:

\((x_1,y_1) = (-2,-1)\)

\((x_2,y_2) = (6,3)\)

The midpoint is:

\(M = \frac{1}{2}\{(x_1+x_2),(y_1+y_2)\}\)

This gives:

\(M = \frac{1}{2}\{(-2+6),(-1+3)\}\)

\(M = \frac{1}{2}\{(4),(2)\}\)

\(M = (\frac{1}{2} * 4,\frac{1}{2} * 2)\)

\(M = (2,1)\)

For BD:

\((x_1,y_1) = (1,3)\)

\((x_2,y_2) = (3,-1)\)

The midpoint is:

\(M = \frac{1}{2}\{(x_1+x_2),(y_1+y_2)\}\)

This gives:

\(M = \frac{1}{2}\{(1+3),(3-1)\}\)

\(M = \frac{1}{2}\{(4),(2)\}\)

\(M = (\frac{1}{2} * 4,\frac{1}{2} * 2)\)

\(M = (2,1)\)

Notice the midpoints are the same:

\(M = (2,1)\)

Hence, the coordinates of the intersection is (2,1)

Answer

:2.12$

Step-by-step explanation:

0.3317  is the p-value .

What is the P value?

H0 : Mu  =  10.2

H1 : Mu > 10.2

Test statistic

t=0.45          (since n is small)

P value = 0.3317

Hence P is greater than 0.10

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Answer:

1. 2/9

2. 1/3

3. 112

Step-by-step explanation:

Answer:

f(3) = -11, f(-7) = 19

Step-by-step explanation:

f(x) = -3x -2

1.

f(3) is the f(x) when x = 3 so where we see x in the equation we write 3 and calculate

f(3) = -3(3) -2 = -9 -2 = -11

2.

f(-7)  = f( x= -7) = -3(-7) -2 = 21 -2 = 19

Answer: 1) f(3)= -11 and 2) f(-7)= 19

Step-by-step explanation: f(x) means 'function of x' or just to replace x with the desired value. For example, f(3) just means x=3. Following below is written proof.

Answer:

B. The function shown on the graph has a smaller rate of change but a higher starting point

Step-by-step explanation:

Question options obtained from a similar question are;

A. The function shown on the graph has a greater rate of change and a higher starting point

B. The function shown on the graph has a smaller rate of change but a higher starting point

C. The function shown on the graph has a greater rate of change but a lower starting point

The function shown on the graph has a smaller rate of change but a higher starting point

Explanation;

The given function with which the graph is compared is y = 4·x + 2

From the given function, we have;

The rate of change of the function is the coefficient of 'x', therefore, the rate of change of the function = 4

When y = 0, 4·x + 2 = 0,

∴ x = -2/4 = -0.5

The y-intercept is given when x = 0

∴ The y-intercept, y = 4 × 0 + 2 = 2

The starting point of the function, is (0, 2)

From the graph, we have;

The y-intercept = (0, 4)

Therefore, the starting point of the line, the y-intercept, (0, 4), is higher than the starting point of the given function, (0, 2)

The coordinates of two (clear) points on the line in the graph are (0, 4) and (-2, -2)

The rate of change of the line, m = (4 - (-2))/(0 - (-2)) = 3

Therefore, the graph has a lesser rate of change, 3, than the rate of change of the given function, 4

When compared with the given function, 'the function shown on the graph has a smaller rate of change and a higher starting point'.

Answer:

1. area = 16.492

2. area = 19.798

3. area = 15.874

4. area = 13.555

5. area = 12.349

6. area = 24.37

good luck, i hope this helps :)

Answer:

1) A=16.49    2)19.8     3)15.87    4)13.56      5)14.44    6)27.04

Step-by-step explanation:

for the first 4 you should use the pythagorean theorem a^2 + b^ = c^2 to find the missing side than you use (base*Leg)/2 to find the area

If a customer service representative changes the way she envisions her job, shifting from recording complaints to being an advocate for customer rights, she engages in the form of job crafting known as task crafting.

Job crafting involves employees making changes to their job roles or tasks to align them more closely with their values, strengths, and motivations. In this scenario, the customer service representative is redefining her role from simply recording complaints to actively advocating for customer rights.

This represents task crafting, where the employee modifies the tasks and responsibilities associated with their job.

By taking on the role of a customer rights advocate, the representative seeks to go beyond the traditional boundaries of their position and make a positive impact on customer experiences and satisfaction.

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Answer:

z=8

Step-by-step explanation:

9x8=72

The probability of choosing an odd prime number from 1 to 20 is 0.35

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The odd prime numbers between 1 and 20 are 3, 5, 7, 11, 13, 17, and 19. There are 7 odd prime numbers in this range.

The total number of possible choices is 20 (since there are 20 numbers in the range 1 to 20).

Therefore, the probability of choosing an odd prime number is:

number of odd prime numbers / total number of possible choices

= 7 / 20

= 0.35

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In order to find the equilibrium solution of a differential equation, set the derivative of the dependent variable equal to zero and solve for the independent variable.

Start with a given differential equation in the form dy/dx = f(x, y), where y is the dependent variable and x is the independent variable.

To find the equilibrium solution, set the derivative dy/dx equal to zero:

dy/dx = 0.

Solve the equation dy/dx = 0 for the independent variable x to find the values of x where the derivative is zero. These values represent potential equilibrium points.

Once you have the values of x, substitute them back into the original differential equation to find the corresponding values of y.

For example, if you have found x = a as an equilibrium point, substitute x = a back into the differential equation and solve for y to find the equilibrium solution y = b, where b is a constant.

Repeat the process for all equilibrium points to find their corresponding equilibrium solutions.

To find the equilibrium solution of a differential equation, set the derivative of the dependent variable equal to zero and solve for the independent variable. The values of the independent variable where the derivative is zero represent potential equilibrium points, and by substituting these values back into the original equation, you can determine the corresponding equilibrium solutions.

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it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.

A cluster sample is a sampling technique where the population is divided into clusters or groups, and a subset of clusters is selected at random to form the overall sample. In this type of sampling, all members of the selected clusters are included in the sample.

In the given example, the airline company selects 555 flights as clusters and surveys every passenger on those flights. Each flight represents a cluster, and by selecting random flights, the company includes every passenger on those selected flights in the survey.

This cluster sampling approach is suitable when each group or cluster is representative of the overall population. It is useful when it is impractical or costly to sample every individual unit within the population, but the selected clusters are expected to reflect the characteristics of the entire population.

Cluster sampling allows for more practical data collection, particularly when dealing with large populations or geographically dispersed units. However, it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.

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The correct interpretation of the confidence interval is 90% confidence that the true proportion of all customers who have moved in the past five years is between 0.293 and 0.355.

The confidence interval is also not a guarantee that the true proportion is between 0.293 and 0.355. It is simply a statement of our confidence that the interval contains the true proportion.

This means that if the study were repeated many times, and constructed a 90% confidence interval each time, then 90% of the intervals would contain the true proportion.

In this case, the sample proportion is 0.324, which is within the confidence interval. This means that the sample data is consistent with the confidence interval. However, the sample proportion could be outside of the confidence interval if we had a different sample.

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Answer:(x-4)^2+(y+2)^2=121

Step-by-step explanation:

eqaution of circle is this

(x-h)^2+(y-k)^2=r^2

(x-4)^2+(y--2)^2=r^2

and 2 negatives make positive

(x-4)^2+(y+2)^2=r^2
and r^2=121

(x-4)^2+(y+2)^2=121

Answer:

B

Step-by-step explanation:

because of order if operations.

Answer:

B

Step-by-step explanation:

The rule of PEMDAS states to start from parenthesis. To get your correct answer, you would need to prioritize what comes first going left to right.

If you were to select A, (/5) would be prioritized. D. Has the order placed in correctly, as well as C.

Use PEDMAS for order of operation:

a: 100 – 8 × √25 + 3

First solve the root:

100 – 8 × 5 + 3

Next multiply:

100 - 40 + 3

Now solve from left to right:

100-40 = 60

60+3 = 63

Answer: 63

b. 100 – (11 – 4)² × 2

First parentheses:

100 - 7^2 x 2

Next the power:

100 - 49 x 2

Multiplication:

100 - 98 = 2

Answer: 2

Answers: sin(2∅) = 120/169,  cos(2∅) = 119/169, tan(2∅) = 120/119

Trigonometric functions are used to establish the relationship between the sides and the angles of a right angle triangle.

Analysis:

If cos∅ = adjacent/hypotenuse =  12/13,

Then, opposite of the right angled triangle = \(\sqrt{13^{2} - 12^{2} }\) = 5

sin∅ = 5/13, cos∅ = 12/13, tan∅ = 5/12

sin(2∅) = 2sin∅cos∅ = 2(5/13)(12/13) = 120/169

cos(2∅) = \(cos^{2}\)∅ - \(sin^{2}\)∅ = \((\frac{12}{13}) ^{2}\) - \((\frac{5}{13} )^{2}\) = 144/169 - 25/169 = 119/169

tan(2∅) = sin(2∅) / cos(2∅)  = 120/169 ÷ 119/169 = 120/119

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Answer:

115 peices ignore this woejdndnsja

Answer:

There would be 115 pieces because 5.75 divided by 0.05 is 115

Step-by-step explanation:

Answer:

$8

Step-by-step explanation:

25% is .25, also known as 1/4. So if you think of it that way, $2 is 1/4 of the entire payment that was added to it. 2*4 is 8, so the price of the tacos was $8 before any tip was added. Andrea paid $10 in total if you include the tip.

Answer:

-50x - 66

Step-by-step explanation:

Answer:

-50x - 66

Step-by-step explanation:

Adding and subtracting fractions with unlike denominators is an important skill for students to master in order to understand basic math concepts.

Unlike denominators are two fractions that have different denominators, such as 1/3 + 1/4. When fractions are added together with unlike denominators, the result is a fraction with a denominator that is a common multiple of the two original denominators.

Worksheets can provide students with the practice and repetition needed to become fluent in this skill.

Worksheets can help to provide context for the concept by explaining the steps involved in solving the problem. This can give students a better understanding of the concepts behind adding and subtracting fractions with unlike denominators and make them more confident in their abilities.

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Answer:

add a graph so we can help you

Step-by-step explanation:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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The area is given by A = 2π ∫[a,b] y √(1 + (dx/dt)²) dt, where a and b are the limits of integration. By substituting the given parametric equations and evaluating the integral from t = 0 to t = 1, we can find the exact area of the surface.

To determine the area of the surface generated by rotating the parametric curve x = ln(et) + et, y = √(16et) around the y-axis, we utilize the formula for surface area of revolution. The formula is A = 2π ∫[a,b] y √(1 + (dx/dt)²) dt, where a and b are the limits of integration.

In this case, the given parametric equations are x = ln(et) + et and y = √(16et). To find dx/dt, we differentiate the equation for x with respect to t. Taking the derivative, we obtain dx/dt = e^t + e^t = 2e^t.

Substituting the values into the surface area formula, we have A = 2π ∫[0,1] √(16et) √(1 + (2e^t)²) dt.

Simplifying the expression inside the integral, we can proceed to evaluate the integral over the given interval [0,1]. The resulting value will give us the exact area of the surface generated by the rotation.

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Answer:

Domain are the x's in an ordered pair and it is usually the left side of diagrams. So everything on the left is a domain. So 5,10,15 is correct.

Step-by-step explanation:

Answer:

A.) 5, 10, 15

Step-by-step explanation:

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

The given data is

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

(a) calculate mean value of x:

μ = E(x)

  = ∑(xi.P(xi))

 = 4.13

(b)  calculate variance of x:

σ² = ∑(xi - E(x))².P(xi)

   = 1.81331

(c)  calculate standard deviation of x:

σ = √σ²

σ = √1.831

σ = 1.3539

The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:

P(μ  - σ < x < μ  + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)

                                = P(2.7761 < x < 5.4839)

                                = P(x = 3) + P(x = 4) + P(x = 5)

                                = 0.13 + 0.30 + 0.31

                                = 0.74

Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

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The complete question is-

Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

What is the probability that the number of systems sold is within 1 standard deviation of its mean value?

Answer:

4

Step-by-step explanation:

Answer:

4 because half of 8 is 4