A service station on the interstate charges $2.29 per gallon for gasoline and $1.89 per quart for oil. What would be a reasonable amount to pay for 10 gallons of gasoline and 2
quarts of oil?
O $20
O $23
O $25
O $27

If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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Answer:

A

Step-by-step explanation:

The answer is option (A) 8560. This combination cannot be the correct combination for your brother's lock because it contains the digit '6' in the same position as the correct combination (6348), but the other digits do not match.

The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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The probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

Since there are 8 cameras in the box, the total number of ways to choose 2 cameras from the box is given by the combination formula:

C(8,2) = 8!/(2!×(8-2)!) = 28

So there are 28 possible ways to choose a sample of 2 cameras.

Now, let's calculate the probability of each possible value of x:

When x = 0, both cameras in the sample are non-defective. The number of ways to choose 2 non-defective cameras from the 4 non-defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 0 is:

P(x=0) = (number of ways to choose 2 non-defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

When x = 1, one camera in the sample is defective and the other is non-defective. The number of ways to choose 1 defective camera from the 4 defective cameras in the box and 1 non-defective camera from the 4 non-defective cameras in the box is given by the product of the corresponding combinations:

C(4,1) × C(4,1) = 4×4 = 16

So the probability of x = 1 is:

P(x=1) = (number of ways to choose 1 defective camera and 1 non-defective camera)/(total number of ways to choose 2 cameras)

= 16/28

= 0.571

When x = 2, both cameras in the sample are defective. The number of ways to choose 2 defective cameras from the 4 defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 2 is:

P(x=2) = (number of ways to choose 2 defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

Therefore, the probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

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The relation between these three variables is demonstrated by

the formula for Ohm's Law: E = (I)(Z) is 12i.

What is Ohm's Law?

According to Ohm's law, the resistance of the circuit and the current or energy travelling through the resistance are both exactly proportional to the voltage or potential difference between two places. V=IR is the equation for Ohm's law.According to Ohm's Law, assuming the temperature and other physical parameters don't vary, the current flowing through a conductor is precisely proportional to the potential difference applied across its ends. Through a resistor, current is inversely proportional to the voltage difference.

(3+3 i)(2+2 i)

Apply complex arithmetic rule: (a+b i)(c+d i)=(a c-b d)+(a d+b c) i

=(3 .2-3. 2)+(3 .2+3 . 2) i

Simplify \($(3 \cdot 2-3 \cdot 2)+(3 \cdot 2+3 \cdot 2) i: \quad 12 i$\)

\($=12 i$\)

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The vertices of the feasible region is (4, 3)

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

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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The equation represents the image of the line y = 3x +1 is y' = 3(x - 3) +1.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

The transformation that translates function y = f(x) by h units right and k units up is

y' = f(x -h) +k

We have y= 3x+ 1

So, After translating 3 units to x axis the function will become

y' = 3(x - 3) +1

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The market equilibrium point, assuming the supply snd demand functions are linear, is (10, 95)

Let's first define the demand and supply functions as linear equations in terms of the price (p) and quantity (q):

Demand function: q = -5p + 145

Supply function: q = 5p - 100

The demand function represents the quantity of radios that the retailer is willing to buy at a given price, and the supply function represents the quantity of radios that the wholesaler is willing to sell at a given price.

To find the market equilibrium point, we need to set the demand and supply functions equal to each other and solve for the price and quantity:

-5p + 145 = 5p - 100

Adding 5p and 100 to both sides, we get:

10p + 45 = 145

Subtracting 45 from both sides, we get:

10p = 100

Dividing both sides by 10, we get:

p = 10

So the equilibrium price is $10 per radio. To find the equilibrium quantity, we can plug the equilibrium price into either the demand or supply function and solve for q:

q = -5(10) + 145

q = 95

Therefore, the market equilibrium point is (10, 95), which means that at a price of $10 per radio, the quantity demanded by the retailer is equal to the quantity supplied by the wholesaler, resulting in a market equilibrium.

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Answer:

25%

Step-by-step explanation:

$60 times ? = $45

$60 - $45 = $15

$15 were reduced and 15/60 = 25%

Answer: 25%

Step-by-step explanation:

25

In statistics, a residual is defined as the difference between the predicted value of an outcome variable and the observed value of that variable. Residuals are used to evaluate how well a regression model fits the data.In order to calculate the residuals for a scatterplot, follow these steps:

Step 1: Plot the data on a scatterplot.

Step 2: Perform a regression analysis on the data to find the equation of the regression line. This equation should take the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Step 3: Using the equation of the regression line, calculate the predicted value of y for each data point in the scatterplot.

Step 4: Subtract each predicted value of y from the actual value of y for each data point in the scatterplot. This difference is the residual for that data point.

Step 5: Plot the residuals on a new scatterplot. The x-axis of this scatterplot should be the independent variable, and the y-axis should be the residual values.

Step6: This scatterplot is called a residual plot.Residuals are useful for identifying patterns in data that the regression model fails to capture. If the residuals are randomly scattered around the horizontal axis, then the regression model is a good fit for the data. If there are clear patterns in the residual plot, then the regression model may not be a good fit for the data and further analysis is required.

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The probability that 17 adults in a sample of 100 adults pass the fitness test is 0.  0106. option B

Probability is simply:

We can use the binomial formula to solve this problem.

\(P(X) = \frac{n!}{x!(n - x)!} * p^x(1 - p) ^n^-^x\)

Where:

Let's calculate the probability

\(P(17) = \frac{100!}{17! (100 - 17)!} * 0. 1^1^7 ( 1 - 0. 1)^ 1^0^0 ^-^1^7\)

P = 0.  0106

Thus, the probability that 17 adults in a sample of 100 adults pass the fitness test is 0.  0106. option B

The complete question is:

It is known that 10% of adults can pass a fitness test. What is the probability that 17 adults in a sample of 100 adults pass this fitness test?

A. 0.9900

B. 0.0106

C. 0.1000

D. 0.0343

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I used to know a Camilla, she cheated on me for my brother...pain

Rain minus the \

The probability that either event will occur is 0.33

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

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 8 + 7 + 30

Evaluate

Total = 45

So, we have

P(A) = 8/45

P(B) = 7/45

For either events, we have

P(A or B) = 8/45 + 7/45

P(A or B) = 15/45

Evaluate

P(A or B) = 0.33

Hence, the probability that either event will occur is 0.33

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The amount invested in the account that earns 7% interest is $6,000 and the amount invested in the account that earns 8% interest is $14,000.

The system of equations that represent the information in the question is:

a + b = 20,000 equation 1

0.07a + 0.08b = 1540 equation 2

Where:

a = amount invested in the account that earns 7% interest

b = amount invested in the account that earns 8% interest

The elimination method would be used to solve the equations.

Multiply equation 1 by 0.07

0.07a + 0.07b = 1,400 equation 3

Subtract equation 3 from equation 2

0.01b = 140

Divide both sides of the equation by 0.01

b = 140/ 0.01

b = 14,000

Substitute for b in equation 1:

a + 14,000 = 20,000

a = 20,000 - 14,000

a = 6,000

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Answer:25

Step-by-step explanation:

The correct option is C) 48.9 units. To find the perimeter of the equilateral triangle, we first need to determine the length of one side of the triangle. Since the triangle is equilateral, all three sides are of equal length.

We can use the distance formula to find the length of one side of the triangle. Let's choose the two vertices located at (-8, -5) and (3, 7) to find the distance between them.

Distance between (-8, -5) and (3, 7) = √[(3 - (-8))² + (7 - (-5))²]

= √[11² + 12²]

= √(121 + 144)

= √265

Since the triangle is equilateral, all three sides are of the same length, so the length of one side of the triangle is also √265.

Therefore, the perimeter of the triangle is 3 times the length of one side:

Perimeter = 3 × √265

= 48.91 (rounded to two decimal places)

Therefore, the correct option is C) 48.9 units.

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Increasing 2400 by 5% gives us 2520

we can increase the value by using the formula:

\(initial value+ percentage increase *initial value\) = increased percentage

in the aforementioned question we have

initial value = 2400

percentage increase = 5%

thus we can find out the increased percentage by:

2400 + 2400 X (5/100)

=2400 + 120

=2520

the value by which 2400 is increased is 120

to arrive at the increased value which is 2520

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Answer:

x = 58.03°

Step-by-step explanation:

Given:

Solve for x:

1. \(x=cos^{-1}(\frac{9}{17})=58.03\)

Answer:

So, the measure of angle x is equal to 58.03.

To make a profit Kelsey must make and sell more than 49  additional pendants

in this given sum we need to find how many additional pendents kelsey need to make and sell to make profit .  The information that are give in the sum

she has to pay $200 for the rent

materials for each pendant is $ 7.8 .

for 10 pendants  the total will be 10*7.8 = $78

Therefore she will spend a total of $(78 +200) = $278

So to make a profit the amount of pendants kelsey make multiply it by 13.50 should be greater than the totall amount she spend in making 10 pendants $278 added to the number  of pendants she makes multiply by 7.8 that is the total cost

let the no. of pendants she need to make be x

we can write then above explanation as

13.50x >278 + 7.8x

=> 13.5x - 7.8x > 278 +7.8x - 7.8x      [subtracting 7.8x on both side]

=> 5.7x > 278

=> x > 278/5.7 = 48.77 = 49 (approx.)

Kelsey needs to make more than 49 pendants rto make a profit.

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Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.

Minutes | Distance Traveled (in miles)

50 | 20

20 | f

40 | 60

100 | a

125 | 80

100 | 100

To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:

Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.

Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.

Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.

Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.

Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.

Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:

Slope = Distance Change / Time Change

= 20 miles / 25 minutes

= 0.8 miles per minute

So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

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Step-by-step explanation:

(x + 3) × -7 = -7x - 7×3 = -7x - 21

Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

Answer:

y = 2/x

Step-by-step explanation:

You cannot divide by zero because you will get an undefined value, and this will create a hole in the graph.

Answer:

\(y = \frac{2}{x\\}\)

Explanation:

Let's check all the answers to be sure we are correct!

Choice A)  y = 2x

The domain for y = 2x is represented by the interval (-∞,∞). This shows that the domain is all real numbers.

Choice B)  y = 2 + x

The domain is represented by the interval (-∞,∞). This shows that the domain is all real numbers.

Choice C)  \(y=\frac{2}{x}\)

We know that the denominator can not be equal to zero. You must remember this! So, now we find that the domain is represented by the interval,

                                              (-∞,0) ∩ (0,∞)

This shows that the domain is all real numbers except the number zero.

Choice D) \(y = x^{2}\)

The domain is represented by the interval (-∞,∞). This shows that the domain contains all real numbers.

Therefore, our answer is choice C!

Nice job everyone!

Answer:

20%

Step-by-step explanation:

5 divided by 25 multiplied by 100 will give you 20%.

I hope you understand

Answer:

Elena scored 22 points.

Step-by-step explanation:

Mai scored 5 points, and Noah scored three times as many. This means Noah scored 15 points and if Tyler scored four points fewer, he scored 11 points. If Elena scored twice as many as Tyler, she scored 22.

Answer:

d

Step-by-step explanation:

Because you need to substitute the variable first, multiply that and add 8.

Answer:

k=1

Step-by-step explanation:

The rise over run is 1, so the slope/constant of proportionality is 1.