Question 6
Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car
results in 310 miles on 20 gallons of gas. Which equation below represent the gas milage of the
car? Select ALL answers that apply.
Oy=310-20x
Oy = 15.5x
Oy = 310x + 20
Oy = 31/2x

The odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three are approximately 31%.

To determine the odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three,

we first need to identify the possible outcomes. The possible sums of rolling two dice range from 2 to 12. We then need

to find the multiples of three within that range, which are 3, 6, 9, and 12.

Next, we need to find the number of ways that we can roll each of these multiples of three. To do this, we can create a

chart:
Sum | Ways to roll
---|---
3 | 1
6 | 5
9 | 4
12 | 1

So there are a total of 11 ways to roll a multiple of three with two dice.

To find the odds, we need to divide the number of favorable outcomes (11) by the total number of possible outcomes

when rolling two dice (36), and then convert the fraction to a percentage or a ratio.

11/36 = 0.3056 or approximately 31%

Therefore, the odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three are approximately 31%.

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To verify that fxy = fyx for the given function f(x,y)=e^(x+y+3), we need to find the partial derivatives of f with respect to x and y, and then check if they are equal.

Let's begin by finding the partial derivative of f with respect to x (f_x): f_x = (∂f/∂x) = (∂/∂x) e^(x+y+3) = e^(x+y+3) * (∂/∂x) (x+y+3) [using chain rule] = e^(x+y+3)

Now, let's find the partial derivative of f with respect to y (f_y): f_y = (∂f/∂y) = (∂/∂y) e^(x+y+3) = e^(x+y+3) * (∂/∂y) (x+y+3) [using chain rule] = e^(x+y+3)

Now, let's find the mixed partial derivative of f with respect to x and y (f_xy): f_xy = (∂^2 f/∂y∂x) = (∂/∂y) e^(x+y+3) = e^(x+y+3) * (∂/∂y) (x+y+3) [using chain rule] = e^(x+y+3)

Similarly, the mixed partial derivative of f with respect to y and x (f_yx) can be found as: f_yx = (∂^2 f/∂x∂y) = (∂/∂x) e^(x+y+3) = e^(x+y+3) * (∂/∂x) (x+y+3) [using chain rule] = e^(x+y+3)

Now, we can see that fxy = fyx, as both are equal to e^(x+y+3). Hence, we have verified that the given function f(x,y)=e^(x+y+3) satisfies the condition fxy = fyx.

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The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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The correct statement regarding the two functions is given as follows:

f(1) = g(1).

Considering the graph containing the equations for the system, the solution of the system of equations is given by the point of intersection of all the equations of the system.

The point of intersection for this problem is given as follows:

(1,3).

Which means that at x = 1, function f(x) and g(x) have the same numeric value, thus the correct statement is given as follows:

f(1) = g(1).

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Answer:

z > - [tex]\frac{11}{9}[/tex]

Step-by-step explanation:

7z + 7 > - 2z - 4

9z + 7 > -4

9z > - 11

z > - [tex]\frac{11}{9}[/tex]

Buddy's answer of 19 feet for the maximum height of his punt is correct, based on the given quadratic function.

How to solve the question?

To determine the maximum height of the punt, we need to find the vertex of the parabolic function h(x) = −.02x² + 1.2x + 4, which represents the height of the football at any given horizontal distance x from the point of impact.

The vertex of a parabola in the form y = ax² + bx + c can be found using the formula x = -b / 2a, which gives the x-coordinate of the vertex, and then substituting that value into the function to find the corresponding y-coordinate.

In this case, we have a = -.02, b = 1.2, and c = 4. So the x-coordinate of the vertex is x = -b / 2a = -1.2 / (2*(-.02)) = 30, and the corresponding maximum height is h(30) = -.02(30)2 + 1.2(30) + 4 = 19 feet.

Therefore, Buddy's answer of 19 feet for the maximum height of his punt is correct, based on the given quadratic function.

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The solution to the system equation after it is solved, would be x = 3 and y = 7.

To solve the given system of linear equations:

8x - 3y = 3

3x - 2y = -5

We can use the method of substitution or elimination. In this case, I will use the elimination method.

First equation x 2:

16x - 6y = 6

Second equation x 3:

9x - 6y = -15

Now, subtract the second equation from the first equation to eliminate the y variable:

(16x - 6y) - (9x - 6y) = 6 - (-15)

16x - 9x = 21

7x = 21

x = 21 / 7

x = 3

Next, substitute the value of x back into either of the original equations to find the value of y.

8x - 3y = 3

8(3) - 3y = 3

24 - 3y = 3

-3y = -21

y = -21 / -3

y = 7

So, the solution to the system of equations is x = 3 and y = 7.

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Answer:

Let's start by using a proportion to find the total number of questions on the test. We know that Charles answered 23 questions correctly and received a grade of 92%, which means he missed 8% of the questions.

Let x be the total number of questions on the test. Then 8% of the questions that Charles missed can be expressed as 0.08x.

The number of questions that Charles answered correctly plus the number of questions he missed must add up to the total number of questions on the test:

23 + 0.08x = x

Simplifying and solving for x, we get:

0.92x = 23

x = 23 / 0.92

x ≈ 25

Therefore, the total number of questions on the test was approximately 25.

Answer: 7x+4y=12 answer is x = (12/7, 0) and y (0,3) and the x+2y=-4 is

x intercepts (-4,0) and y intercepts is (0,-2)

Step-by-step explanation:

Add to one side and then divide

Answer:

Based on the information provided that one corner of the parallelogram measures 128 degrees, we can determine the measures of the other three angles x, y, and z.

In a parallelogram, opposite angles are congruent, which means that x and z are congruent to 128 degrees.

So, x = z = 128 degrees.

The sum of the measures of the interior angles of a parallelogram is always 360 degrees. Since x and z both measure 128 degrees, the sum of x and z is 2 * 128 = 256 degrees.

Therefore, we can find the measure of y by subtracting the sum of x and z from 360 degrees:

360 degrees - 256 degrees = 104 degrees

So, y measures 104 degrees.

To summarize:

x = z = 128 degrees

y = 104 degrees

Answer: The problem states that the proportion of people who throw away a portion of what they buy at the grocery store is p = 0.4. We want to find the probability that the sample proportion exceeds a certain value, which we will denote as p-hat.

The sample size is n = 100, which is large enough to use the normal approximation to the binomial distribution.

The formula for the standard error of the sample proportion is:

SE = sqrt[p * (1 - p) / n]

Substituting the values given in the problem, we get:

SE = sqrt[0.4 * 0.6 / 100] = 0.049

To find the z-score corresponding to a sample proportion of , we use the formula:

z = (p-hat - p) / SE

Substituting the values given in the problem, we get:

z = ( - 0.4) / 0.049 = -2.04

Using a standard normal table, we find that the probability of obtaining a z-score of -2.04 or lower is 0.0207. Therefore, the probability that the sample proportion exceeds is approximately 0.0207, rounded to three decimal places.

Step-by-step explanation:

The time series component that reflects the random changes in a time series that are not caused by any other components, and tends to hide the existence of the more predictable components, is called the "random" or "irregular" component.

It represents the noise or fluctuations in the time series that cannot be explained by any of the other components, such as trend, seasonality, or cyclical variations. The irregular component is also known as the "white noise" or "error" component, and it is typically modeled as a random process with zero mean and constant variance. It is important to separate out the irregular component from the other components in order to identify the underlying patterns and trends in the time series, and to make accurate forecasts and predictions.

what is white noise?

In time series analysis, "white noise" refers to a random process where the values at each point in time are independently and identically distributed with a mean of zero and a constant variance.

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Answer:

the answer is 145°

Step-by-step explanation:

the sum of other two non adjecent interior angle are equal to remot exterior angle . so 80° + 65° = 145°

The measure of angle 1 is 67.4°. The measure of angle 2 is 104.5°.

An angle is the measure of the amount of rotation between two lines or two planes that meet at a point. It is typically measured in degrees or radians. An angle can be acute, meaning it is less than 90 degrees, right, meaning it is exactly 90 degrees, obtuse, meaning it is greater than 90 degrees but less than 180 degrees, or straight, meaning it is exactly 180 degrees. An angle can also be positive or negative, depending on the direction of rotation between the lines or planes. Angles are used in various fields such as mathematics, engineering, physics, and geometry.

Here,

180-121.8=58.2°

180-(58.2+17.3)=104.5°

180-104.5=75.5°

180-(75.5+37.1)=67.4°

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Step-by-step explanation:

probability that the first die shows six = 1/6

probability that the other die shows an odd number = 1/2

The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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Answer: 7/9

Step-by-step explanation:

To find how many reams of paper the printing press used for each book, we need to divide the total number of reams used by the number of books printed.

Let's convert 2 1/3 reams of paper to an improper fraction:

2 1/3 = (2 × 3 + 1) / 3 = 7/3

So the printing press used 7/3 reams of paper to print 3 books. To find how many reams of paper were used per book, we can divide the total amount of paper used by the number of books:

(7/3) ÷ 3 = 7/9

Therefore, the printing press used 7/9 of a ream of paper for each book.

Therefore , the solution of the given problem of inequality comes out to be  x< 3, which denotes that x can be any real number below 3.

The distinction in algebra can be expressed by an amalgamation or set of two numbers since there is no indicator for it. Equity usually comes after equilibrium. The persistent gap in standards is what causes inequality. Disparity and equality are not the same thing. As was the least favourite symbol, despite the fact that its components are typically neither connected nor adjacent to one another.

Here,

We can use the procedures listed below to solve the inequality 4x - 1 11:

To isolate the term with x on one side of the inequality, add 1 to both sides of the inequality in step 1:

=> 4x - 1 + 1 < 11 + 1 4x < 12

Step 2: To find x, multiply both sides of the inequality by 4.

=> 4x/4 < 12/4 x < 3

The answer to the inequality 4x - 1 11 is therefore x< 3, which denotes that x can be any real number below 3.

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Let's start by setting up some equations to represent the information given in the problem.

Let's assume that Mitchell read x sports books last year. According to the problem, he read 5 mysteries for every 2 sports books, so he must have read (5/2)x mysteries.

We also know that he read 12 more mysteries than sports books, so:

(5/2)x - x = 12

Simplifying this equation, we get:

(3/2)x = 12

Multiplying both sides by 2/3, we get:

x = 8

So Mitchell read 8 sports books last year. To find out how many mysteries he read, we can use the equation we derived earlier:

(5/2)x = (5/2)(8) = 20

Therefore, Mitchell read 20 mysteries last year.

To find the absolute maximum and absolute minimum of a function using the closed interval method.

Determine the function, f(x), and the closed interval [a, b].
Calculate the critical points of the function by finding the derivative, f'(x), and setting it equal to zero.

Solve for x to find the critical points.

Keep in mind that only the critical points within the closed interval are relevant to this problem.
Evaluate the function, f(x), at the critical points and the endpoints of the closed interval, a and b.
Compare the function values obtained in step 3.

The highest value corresponds to the absolute maximum, and the lowest value corresponds to the absolute minimum.
Identify the points (x, f(x)) corresponding to the absolute maximum and absolute minimum.

These points represent the locations and values of the absolute maximum and absolute minimum on the given closed interval.

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The area of 0.6808 to its left using the Standard Normal Table.

steps: 1. Identify the area: In this case, the area to the left of the z-score is given as 0.6808.

2. Consult the Standard Normal Table: This table shows the area to the left of various z-scores, ranging from negative to positive values.

3. Locate the closest area value: Look for the value in the table that is closest to the given area (0.6808). The table is typically organized into rows and columns, with the row header representing the first two digits of the z-score and the column header representing the third digit.

4. Identify the z-score: Once you've found the closest area value, determine the corresponding z-score by combining the row and column headers where the value is located.

Upon checking the Standard Normal Table, the closest area value to 0.6808 is 0.6800, which corresponds to a z-score of 0.47.

Keep in mind that the Standard Normal Table may not have the exact area value of 0.6808, so you need to find the closest possible value.

In summary, the z-score with an area of 0.6808 to its left using the Standard Normal Table is approximately 0.47.

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Answer:

16

Step-by-step explanation:

To round 15.98 to the nearest tenth, we look at the digit in the hundredths place which is 8. Since 8 is greater than or equal to 5, we round up the digit in the tenths place which is 9. Therefore, rounding 15.98 to the nearest tenth gives us 16.

Answer:

16

Step-by-step explanation:

15 . 98

8 round up is 10

0.10 + 0.9 = 1

15 + 1 = 16

If we throw, a coin in twice, then pay off for throw exactly two heads is $120. The expected win value in the game in 742 trials is equals to the $1669.5.

We have to two tosses a coin and we gift with payouts according to results of tossing. When we throw exactly two heads in two tosses of a coin, then pay out is $120. If not throw two heads then payout is $37… Now, number of times we play the game that is trials = 742

We have to determine value of expected value to win or loss for 742 trials. First we determine the excepted value of proposition. Total possible outcomes on two tosses of a coin = 4 = {HH,TT, HT, TH}

Probability of throwing two heads = 1/4

= 0.25

Probability of not throwing two heads

= 1 - 1/4 = 3/4 = 0.75

That is when x (pay off) = $120, P( x)

= 0.25 ; x (payout) = -$37, P( X) = 0.75. Now, the excepted value formula is written as, [tex]E( x) = \sum x× P(x) [/tex]

= $120 × 0.25 - $37 ×0.75

= $2.25

So, the expected value of win with 575 trials of gane = 2.25 × 742

= 1669.5

Hence, required excepted win value is $1669.5.

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The area in units of square meter is 2,090,318.4 sq cm,  under the given condition that  a house has a floor area of 2,250 square feet. So , the correct option from the following is  Option B.

To convert 2,250 square feet to square centimeters, we can use the conversion factor of 1 square foot = 929.0304 square centimeters⁵. Therefore,

2,250 sq ft = 2,250 x 929.0304 sq cm/ sq ft = 2,090,318.4 sq cm.

The area in units of square meter is 2,090,318.4 sq cm,  under the given condition that  a house has a floor area of 2,250 square feet. So , the correct option from the following is  Option B.

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Answer:

18.8651

Step-by-step explanation:

(im not the best at explaining, so sorry if i dont explain it well, but ill try!)

so rounding a number to a certain amount of sig figs is a pretty easy concept to grasp, in my opinion.

ex: lets say you need to round 231.45 to 3 sif figs.

basically what you have to do in this situation is count the digits up to you get to the 3rd digit.

check if the digit that follows it is smaller or bigger than 5 to see if the 3rd number will stay the same or has to go up a number.

for this problem the third digit is 1, and the digit that follows it is 4. but 1 is less than 4, so that means that it will stay as 1.

thus the answer would be 231.

if that didnt make sense, comment on my answer and ill try to give you more examples

Answer: 5 (first round) + 25 (second round) + 125 (third round) + 625 (fourth round) = 780

So, at the end of 4 rounds, including Jacob himself, 780 people will have gotten fliers.

Step-by-step explanation: In the first round, Jacob hands out fliers to 5 people.

In the second round, each of the 5 people from the first round hands out 5 fliers to 5 other people. So, there are now 5 x 5 = 25 people with fliers (including the original 5).

In the third round, each of the 25 people from the second round hands out 5 fliers to 5 other people. So, there are now 25 x 5 = 125 people with fliers (including the original 5 and the 25 from the second round).

In the fourth round, each of the 125 people from the third round hands out 5 fliers to 5 other people. So, there are now 125 x 5 = 625 people with fliers (including the original 5, the 25 from the second round, and the 125 from the third round).

The journal entries fro the transaction for October 31 and November 19 are as follows:

Oct. 31: Cash                                              $3,840,000

             ($12 x 320,000)

                       Common Stock                                      $1,600,000

                       ($5 x 320,000)

                       Paid-In Capital in Excess of Par-com.   $2,240,000  

                       ($3,840,000 - $1,600,000)

Nov. 19: Cash                                            $3,240,000

              ($72 x 45,000)

                       Preferred Stock                                     $2,700,000

                        ($60 x 45,000)

                       Paid-In Capital in Excess of Par-Pre.    $540,000

                        ($3,240,000 - $2,700,000)

Full question "On October 31, Pidgeon Stones Inc. , a marble contractor, issued for cash 320,000 shares of $5 par common stock at $12, and on November 19, it issued for cash 45,000 shares of preferred stock, $60 par at $72. Journalize the entries for October 31 and November 19".

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