In June 2008, 88%88% of automobile drivers filled their vehicles with regular gasoline, 2%2% purchased midgrade gas, and 10%10% bought premium gas. Of those who bought regular gas, 28%28% paid with a credit card. Of customers who bought midgrade and premium gas, 34%34% and 42%42%, respectively, paid with a credit card. Suppose we select a customer at random. (a) Construct a tree diagram to represent this situation. (b) Find the probability that the customer paid with a credit card. Show your work. (c) Given that the customer paid with a credit card, find the probability that she or he bought premium gas.

The sample size was not sufficiently large is the best reason why the simulation of the sampling distribution is not approximately normal.

What happens if a sample data is not big enough?

There are different variations in population size. When a sample size taken by a person or a researcher is not big or insufficient, or inadequate for the alpha level and also analyses that one have chosen to do, it will limit the study statistical power.

Due to the above, the ability to know a statistical effect in one's sample if the effect are present in the population is greatly reduces.

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The numbers are 8 and 7.

[tex]\textbf{2 x 2 system of equations : }[/tex]

➭Approach

Let x and y be the numbers.

[tex] \bold{The \: sum \: of \: 2 \: n \acute{u}mers \: \: is \: 15 \: : \: } \: \bold{x + y = 15}[/tex]

[tex] \bold{The \: difference \: between \: five \: times \: the \: first \: number \: and \: three \: times \: the \: second \ : number \: is \: 19 \: : \: } \bold{5x - 3y = 19}[/tex]

Solution by substitution method

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{cases}{ \bold{x + y= 15 \qquad \cdots(1)}}\\{ \bold{5x - 3y = 19 \qquad \cdots( 2)}} \end{cases}\end{gathered} \end{gathered} \end{gathered} [/tex]

In essence, this method of solving consists of clearing an unknown in one of the equations and then substituting the found value in the other equation.

Because it is easier, I will start solving for x in equation 1.

[tex] \bold{x = 15 - y}[/tex]

Substitute [tex]\bold{x=15-y}[/tex] into equation 2.

[tex] \bold{5 \cdot15 - y- 3y = 19}[/tex]

We are left with an equation with only one unknown, we solve to find y.

[tex] \bold{75 - 5y- 3y = 19}[/tex]

[tex] \bold{ - 5y - 3y = 19 - 75} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{-8y= -56} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{y= \dfrac{ - 56}{ - 8}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \implies{y = 7}} \: \: \: \: \: \: \: [/tex]

We have found the value of y, to find the value of x we substitute the value of y into either of the two equations.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x + y = 15} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x + 7 = 15 }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = 15 - 7}[/tex]

[tex]\bold{\implies \: x = 8}[/tex]

『 The attached graph is just to check our results 』

[tex]\therefore[/tex] The numbers are 8 and 7.

The given statement is False.

What is Function?

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

A function is defined as a set of ordered pairs in which for each value of x there is only one corresponding value of y.

However, in this case, we have multiple x-values that correspond to the same y-value.

For example, x = 12 and x = 22 both correspond to y = 12. and y=22 Therefore, y is not a function of x.

Therefore, The given statement is False.

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A stationary point of a function f(x) is a point where the derivative of f(x) is equal to 0. These points are called “stationary” because at these points the function is neither increasing nor decreasing.

Once we have identified the dy dx = 0 solutions, we may utilise the first derivative to ascertain the characteristics of the stationary points. Think about the equation y = x2 + 1.

By differentiating and setting the derivative to zero, we may determine that there is a stationary point at x = 0 since dy dx = 2x = 0. Recall that placing f by x and f by y equal to zero will reveal the location of a function f's stationary point.

In this situation, partial differentiation with regard to x while treating y as a constant results in three x squared plus six x. Any stationary point's nature can be ascertained by introducing its x coordinate into the second derivative of the function, f. (x). 

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The area of the triangle is 24 square meters.

The area of the triangle can be calculated using the formula A = 1/2bh, where b is the base and h is the height of the triangle. In this case, the base is 8 meters and the height is 6 meters. Therefore, the area of the triangle is A = 1/2bh = 1/2(8)(6) = 24 square meters. Therefore, the answer is D. 24 square meters.

To calculate the area of the triangle, first the base and the height of the triangle must be known. The base is the length of the bottom line of the triangle, and the height is the length of the line from the peak of the triangle to the base. Once the base and height of the triangle are known, the area formula A = 1/2bh can be used.

The formula can be broken down into several steps. First, the base and the height are multiplied together. In this case, it would be 8 x 6. This gives a result of 48. Then, the result is divided by 2, which gives a result of 24. Therefore, the area of the triangle is 24 square meters. When using the area formula, it is important to remember that the result must be divided by 2 in order to get the correct answer.

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The swimming pool with a volume of 53.7 kL, will be completely filled with 53,700 cubic decimeter

The problem seeks conversion from liters to cubic decimeters

From the conversion table 1 liter is equivalent to 1 cubic decimeter

Because of this, 1 kL will be equal to 1 000 cubic decimeter

Hence if 1 kL is 1 000 cubic decimeter then 53.7 kL is equal to

= 53.7 * 1000

= 53,700 cubic decimeter

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[tex]4-6x+2-2x^{2} -4x+6x^{2}[/tex]

Which of these correctly rearranges the terms in this polynomial so like terms are next to each other?

The first step is to identify the same variable.

The equation consists of variables [tex]x, x^{2}[/tex] and constant.

Terms of variable [tex]x^{2}[/tex] are [tex]-2x^{2}[/tex] and [tex]6x^{2}[/tex]

Terms of variable [tex]x[/tex] are [tex]-6x[/tex] and [tex]-4x[/tex]

Terms of constant are [tex]4[/tex] and [tex]2[/tex]

The next step is rearranges the terms in this polynomial so like terms are next to each other

[tex]-2x^{2} +6x^{2} -6x-4x+4+2[/tex] (B)

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Normal heartbeat of bat = 30 beats per minute

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given,

Bat's heart rate is about 10 beats per minute.

Normal heart rate is 300 percent of 10 beats per minute

Then normal heartbeat = (300 × 10) / 100

                              = 3 × 10

                              = 30 beats per minute.

Hence, 30 beats per minute is normal heartbeat of bat.

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The solution to the differential equation is given by R = ±1/√(C-a*x), where C is a constant of integration.

To solve this differential equation, we first separate the variables and integrate the equation:

dR/dx = a(R^2+16)

∫ dR/dx  = ∫a(R^2+16)dx

R = ±1/√(C-a*x) + K

where K is an arbitrary constant.

To find the constant of integration, we use the initial condition. We plug in the initial values for x and R to find the constant of integration. For example, if x = 0 and R = 2, then we get

2 = ±1/√(C-0) + K

2 = ±1/√C + K

K = 2±1/√C

Therefore, the solution to the differential equation is given by R = ±1/√(C-a*x) where C is the constant of integration.

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Answer: $0.075

Step-by-step explanation:

$14.95 is roughly $15

and 0.5% is 1/2 of 1/100

1/100 of 15 is 0.15 and 1/2 of that is 0.075

0.7125

Step-by-step explanation:

soln

14.25*5%

=0.7125

Answer:

The answer would be 52.8 because if the number behind the decimal you want to round is 5 or greater you round one number up. (Sorry if this is a confusing explanation)

The price of the car in 2020 dollars would be $31,620.

Price is the monetary value of a good or service that a customer is willing to pay for it. It is the result of a complex interaction between the forces of supply and demand, and is determined by the market conditions of a good or service. Price is also an important factor for companies as it is one of the primary elements used to generate revenue and profits.

In order to calculate the price of the car in 2020 dollars, we must use the Consumer Price Index (CPI). The CPI is a measure of inflation over time and is used to calculate the value of a product in the current year from its value in the past.
The CPI for 2020 is 250.6, while the CPI for 2015 is 237.9. This gives us a ratio of 250.6/237.9 = 1.054.
We can then use this ratio to calculate the value of the car in 2020 dollars:
30,000 x 1.054 = 31,620.
Therefore, the car would cost $31,620 in 2020 dollars.

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The value of the fraction 24(1/2 + 2/7) divided by 1 4/8 will be 16 3 / 7.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The value of the fraction 24(1/2 + 2/7) divided by 1 4/8 will be:

= 24(1/2 + 2/7) ÷ 1 4/8:

= 24 9/14 ÷ 1 1/2

= 345 / 14 × 2/3

= 690 / 42

= 16 3 / 7

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Complete question

24(1/2 + 2/7) divided by 1 4/8 will be:

Answer:

d. 9x^2 + 25x + 14

Step-by-step explanation:

Formula of area of a rectangle is L * W;

L being length

W being width

x + 2 is our W

9x + 7 is our L, thus;

(x+2)(9x+7)

[9x^2 + 25x + 14]

Answer:

60.26°

i have to write more so yea but do you have the answer to 83d and 91c from that chapter

The units of distance and speed should match, So kilometers per hour (kph) and miles per hour (mph) are the correct units.

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the probability of  all calculators having no defects is 16.8%. the probability of at least one defect is 83.2%.

A sample of 4 different calculators is randomly selected from a group of 16 defective and 30 non defective calculators,

So, we have to find the probability that at least one of 4 calculators in the sample is defective.

total number of calculators= 46.

the probability of one calculator being non defective is 30/46.

when a second is chosen the probability of having non defective is 29/45.

the probability of no defective in the third is 28/44

and the fourth is 27/43.

the probability of non-defective in any one of the

calculators is found by multiplying the individual probability.

[tex](\frac{30}{46})(\frac{29}{45} ) (\frac{28}{44} )(\frac{27}{43} ) =0.168.[/tex]

the probability of of all calculators having no defects is 16.8%. the probability of at least one defect is 83.2%.

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Answer:

120/20=6 pearl collected 6

Step-by-step explanation:

If Tate collected 20 times as many rare coins as Pearl, we can set up a proportion to find out how many coins Pearl collected. Let x be the number of rare coins Pearl collected. Then we have:

x / 120 = 1 / 20

To solve for x, we can cross-multiply:

20x = 120

Dividing both sides by 20, we get:

x = 6

Therefore, Pearl collected 6 rare coins.

There were approximately 5,184 graduates in 2008.

The cubic model is a useful tool for estimating the number of graduates in a given year, as it takes into account the trend of the data points. This allows us to make an educated guess about the number of graduates in a given year, despite not having data points for that year.The cubic model for the number of graduates from an online university since 2002 can be expressed as y = -7.8x^3 + 74.4x^2 + 437x - 9,150. Here, x is the number of years since 2002, and y is the number of graduates in that year. To estimate the number of graduates in 2008, we can plug in x = 6 into the equation, giving us y = 5,184. That is, there were approximately 5,184 graduates in 2008.

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The probability of the train from Le Havre having to wait at Garde du Nord for the train from Troyes to arrive on any given day is equal to the probability that the latter train is late.

This probability can be calculated using the following formula: P = (1-A)^B, where A is the average arrival time of the train from Troyes and B is the average time it takes for the train from Le Havre to depart after the first train is scheduled to arrive. The expected value of the probability can then be calculated by taking the average of this formula over the long run. For example, if the train from Troyes is typically 5 minutes late and the train from Le Havre leaves 10 minutes after it is due to arrive, the expected probability of a delay is (1-5/60)^(10/60) = 0.7355. Therefore, over the long run, the train from Le Havre will have to wait for the train from Troyes to arrive 73.55% of the time.

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All parts of the expression 10 − 5.25m have been matched with their respective quantities below.

The given expression belongs to a certain mathematical category which is linear equations.  A linear equation is an equation that can be used to denote and solve problem sums. It is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is the form Ax + B = 0. Here, x is a variable quantity, A is a coefficient and B is constant.

Here, 10 = the amount of money that you have

5.25 = Price of each sandwich

n = No. of sandwiches

5.25 = Total cost

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It's not possible to know how much the retailer spent based on the information provided. The information provided only tells us how the retailer selected a sample of receipts from the past week by numbering all the receipts, generating 25 random numbers, and sampling the receipts that correspond to those numbers. In order to know how much the retailer spent, you would need more information such as the total amount of money spent on all the receipts and the amount of money spent on each receipt.

Formulas A and B are not compared to the original formula, which makes this study poorly structured.

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This resulted in a probability of 1.0, or 100%, meaning that the puzzle was solved every time it was attempted. This indicates that the probability of successfully solving the puzzle is quite high.

Random Digits Used: 0.9, 0.3, 0.3

Repetition 1:

Successful Attempt (1)

Repetition 2:

Successful Attempt (1)

Repetition 3:

Successful Attempt (1)

Estimated Probability: 3/3 = 1.0

In this experiment, the probability of successfully solving a puzzle was estimated. Three repetitions of the simulation were completed, each using different random digits. The first repetition used the random digit 0.9, the second used 0.3, and the third used 0.3 again. For each repetition, the outcome was successful, meaning the puzzle was solved. This resulted in a probability of 1.0, or 100%, meaning that the puzzle was solved every time it was attempted. This indicates that the probability of successfully solving the puzzle is quite high.

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Answer:

14( x - 3)

Step-by-step explanation:

1/2x-6 and 2x/7x-21.

simplify (common factors)

[tex] \frac{1}{2(x - 3)},\frac{2x}{7(x - 3)} [/tex]

Find the LCM (smallest positive number that all of the numbers divide into evenly) of the denominators of those values

[tex]2(x−3),7(x−3) [/tex]

Now we get

[tex]14( x - 3)[/tex]

- if you need any further explanation let me know <3

Answer: -31

Step-by-step explanation:

f(x)=x²+x-12

f(-5)=(-5)²+(-5)-12

 =25-5-12

 =25-17

 =8

now, g(x)= -2x-15

 =(-2)×(8)-15

 = -16-15

 = -31



3.7-3.4-2n+8 = -0.3-2n+8 = 8-2n-0.3 = 8-0.3-2n = 7.7-2n

So, 3.7-3.4-2n+8 = 7.7-2n

The equation of the line is given as y = ( -2/5 )x + 162 , where the slope of the line is m = ( -2/5 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P ( -275 , 52 )

Let the first point be represented as P ( -280 , 54 )

Now , the slope of the line is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 54 - 52 ) / ( -280 - ( -275 ) )

On simplifying the equation , we get

Slope m = 2 / ( -5 )

Slope m = -2/5

Now , the equation of line is  y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 52 = ( -2/5 ) ( x - ( -275 ) )

y - 52 = ( -2/5 )x + 110

Adding 52 on both sides of the equation , we get

y = ( -2/5 )x + 162

Hence , the equation of line is y = ( -2/5 )x + 162

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The coordinates of the intersection of the diagonals of abcd with the given vertices are (0,2).

The equation of diagonal AC is the equation of the line joining

(−4,6) and (4,−2)

Using the two point formula of a line, we have

           (y−6) / (x+4) = 6−(−2) / (−4−4)

                       x + y = 2

The equation of diagonal BD is the equation of the line joining

(5,6) and (−5,−2)

Using the two point formula of a line, we have

           (y−6) / (x−5) = 6−(−2) /  5−(−5)

                           5y = 4x+10

Multiply equation x + y = 10 by 5 to get 5x+5y=10

Replace 5y=4x+46 using 5x+5y=10

        5x + (4x+10) = 10

        5x + 4x +1 0 = 10

           9x + 10 = 10

               9x=0

                 x=0

Substitute x=0 in eqn(1), To get 0+y=2

                                                         y=2

The point of intersection of the diagonals of the given quadrilateral is (0,2)

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