Jamar drove 228 miles and used 6 gallons of gas.
a) How many miles/gallon did he get on the trip?

b) On another trip, he used 9 gallons of gas. How far did he travel?

Answer:

x=6 and y=20 just took a test

Step-by-step explanation:

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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The given options are as follows: a. Neither qualitative, quantitative discrete, or quantitative continuous. b. Quantitative continuous c. Qualitative d. Quantitative discrete

Among the given options, option b. "Quantitative continuous" and option c. "Qualitative" are the correct identifications.

a. "Neither qualitative, quantitative discrete, or quantitative continuous" is not a valid identification as it does not specify the nature of the data.

b. "Quantitative continuous" refers to data that can take any numerical value within a range. For example, measuring the weight of objects on a scale is a quantitative continuous variable.

c. "Qualitative" refers to data that is descriptive or categorical, such as the color of a car or the type of fruit.

d. "Quantitative discrete" refers to data that can only take specific, distinct values. For example, counting the number of books on a shelf would be a quantitative discrete variable.

Therefore, the correct identifications are option b. "Quantitative continuous" and option c. "Qualitative."

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Darpan takes 12 / 8 * 60 = 90 minutes to run the 12km. This equation gives us a quadratic equation in terms of x is 6x^2 + 23x - 720 = 0.

To solve the problem, we can start by using the formula: Time = Distance / Speed.

Let's assume that Darpan's running speed is x km/h. Then, his cycling speed is (x+10) km/h.

For the running portion, we have: Time taken = Distance / Speed = 12 / x hours.

For the cycling portion, we have: Time taken = Distance / Speed = 26 / (x+10) hours.

The total time taken is given as 2 hours and 48 minutes, which is equivalent to 168 minutes. Thus, we can set up the equation:

12 / x + 26 / (x+10) = 168 / 60

Simplifying this equation gives us a quadratic equation in terms of x:

6x^2 + 23x - 720 = 0

Using the quadratic formula, we can solve for x:

x = 8 (to two decimal places)

Therefore, Darpan takes 12 / 8 * 60 = 90 minutes to run the 12km.

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Answer:

I think the two answers would be A & D.

Explanation:

Sorry if I'm wrong.

Answer:

The answer is D

Answer:

32 would be present and 8 would be absent

Step-by-step explanation:

Answer:

A & B

Step-by-step explanation:

A is spot-on because of the use of distributive property. B by the use of like terms.

The expression 2(a + 3b) is equivalent to the expression 2a + 6b. Then the correct option is A.

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

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The expression is given below.

⇒ 2(a + 3b)

Simplify the expression, then we have

⇒ 2(a + 3b)

⇒ 2 · a + 2 · 3b

⇒ 2a + 6b

The expression 2(a + 3b) is equivalent to the expression 2a + 6b. Then the correct option is A.

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The probability of winning $1000 a day for life is approximately 5.245 x 10^-11 and the probability of winning $1000 a week for life is approximately 1.07 x 10^-8. The probability of winning the jackpot ($1000 a day for life) is 1/(60^5 * 4), while the probability of winning $1000 a week for life is 1/(60^5).

In the Florida Lottery Cash4Life game, a player must select five numbers from 1 to 60 and then one Cash Ball number from 1 to 4. The jackpot prize is $1000 a day for life if all five numbers and the Cash Ball match the winning numbers drawn on Monday nights. If just all five numbers match the winning numbers, the player will win $1000 a week for life.
To determine the probability of winning $1000 a day for life, we can use the formula for the probability of independent events: P(A and B) = P(A) x P(B)

(a) To win the jackpot of $1000 a day for life, the player needs to match all five numbers and the Cash Ball. There are 60 options for each of the five numbers and 4 options for the Cash Ball. The total number of possible outcomes is 60^5 (60 choices for each of the five numbers) times 4 (for the Cash Ball). So the probability of winning the jackpot is 1/(60^5 * 4). (b) To win $1000 a week for life, the player needs to match only the five numbers, without considering the Cash Ball. The total number of possible outcomes for this scenario is 60^5. Therefore, the probability of winning $1000 a week for life is 1/(60^5).

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The pair of triangles that can be proven congruent by the HL theorem is: C. 2 right triangles having a pair of congruent hypotenuses and a pair of congruent side.

The HL theorem is a triangle congruence theorem which states that two right triangles are congruent to each other, if the hypotenuse of one is congruent to the hypotenuse, and also if one leg of one right triangle is congruent to a corresponding leg in the other right triangle.

Thus, if two triangles are right triangles having a pair of congruent hypotenuses and another pair of congruent side, then they are congruent by the HL theorem.

In conclusion, the pair of triangles that can be proven congruent by the HL theorem is: C. 2 right triangles having a pair of congruent hypotenuses and a pair of congruent side.

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Answer:

\(y = -8x + 3\)

Step-by-step explanation:

When lines are parallel to one another, their slopes are the same.  But they have different y-intercepts. To explain further, slope is the angle of measure of a line from a horizontal standpoint and knowing that parallel angles must have the same angle, it can be concluded that parallel lines would have the same slope or in other words, an equal slope.

Now solving, use algebraic concepts:

11 = -8(-1) +b    (Now solve for b)

11 = 8 + b     (Subtract 8 from both sides) (Use the "Right" to "Left")

-8   -8

3 = b  (Switch terms)

b = 3

Now let's write the equation with only slope and y-intercept.

Getting the result of:

y = -8x + 3

Calculating the factorials, we find that the person can make 2,380 different selections of 4 bags of chips out of the 17 varieties.

To find out how many different selections of chips the person can make, we need to use the combination formula. The formula for combinations is:

nCr = n! / r!(n-r)!

Where n is the total number of options (in this case, 17 varieties of chips) and r is the number of choices we want to make (in this case, 4 bags of chips).

So, plugging in the values we have:

17C4 = 17! / 4!(17-4)!
17C4 = 17! / 4!13!
17C4 = (17x16x15x14)/(4x3x2x1)
17C4 = 2380

Therefore, the person can make 2,380 different selections of chips.

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Answer:

yes

when the point is pugged into the equality, it works

Answer:

D) 2x^2 + 6x - 4

Step-by-step explanation:

I took the quiz and got a 100%

Obtuse and adjacent are the correct answers.

The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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Answer:

Graph B represents an increasing function

Step-by-step explanation:

If you look at the other graphs, they are either stagnant on one line or going downwards.

Graph B, on the other hand, is growing on both the x and y axis.

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The values of x in the rectangle are 1 or 3

A rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are parallel and equal.

The perimeter of a rectangle is given by:

Perimeter = 2(length + breadth)

From the image attached,, the length is (x + 1)/3 and the width is 1/x, hence:

\(Perimeter =2(length + width)\\\\\\\frac{10}{3} =2(\frac{x+1}{3}+\frac{1}{x} )\\\\\frac{5}{3} =(\frac{x+1}{3}+\frac{1}{x} )\\\\5x=x^2+x+3\\\\x^2-4x+3=0\)

x = 1 or x = 3

Therefore the values of x in the rectangle are 1 or 3

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Answer:

a. 5,040 ways

b. 210 ways

Step-by-step explanation:

a) We want to pick 4 numbers out of 10 given that orders matter

If orders do matter, it will be a permutation problem

Mathematically;

n P r = n!/(n-r)!

In this case, n is 10 and r is 4

Thus, we have it that;

10 P 4 = 10!/(10-4)! = 5,040

b) if orders do not matter

It will be a combination problem

n C r = n!/(n-r)!r!

n = 10 and r = 4

10 C 4 = 10! /(10-4)!4!

= 210

Work Shown:

yz = y(x^2+2x-5)

yz = y(x^2) + y(2x) + y(-5)

yz = x^2( y ) + 2x( y ) - 5( y )

yz = x^2( 3x+5 ) + 2x( 3x+5 ) - 5( 3x+5 )

yz = x^2*3x + x^2*5 + 2x*3x + 2x*5 - 5*3x - 5*5

yz = 3x^3 + 5x^2 + 6x^2 + 10x - 15x - 25

yz = 3x^3 + 11x^2 - 5x - 25

Answer:

Step-by-step explanation:

The area of a rectangle is length time width.

A=LW

In this case,

A=32x^2+12

W=4x

Solve for L

L=A/W

Substitute

L=(32x^2+12)/4x

L=(8x^2+3)/x

Answer:

∠ ADB = 59°

Step-by-step explanation:

The vertices of a rectangle are right angles, then

∠ ADB + 31° = 90° ( subtract 31° from both sides )

∠ ADB = 59°

The height of this hill is given as :  51.88 feet.

How to solve for the height of the hill

We can use trigonometry to find the height of the hill. Let's call the height of the hill "h".

From the information given, we know that:

tan(27°) = h / (103/2)

h = (103/2) * tan(27°)

Using a calculator, we would have to go ahead to get the value of the variable h or height.

So  that h ≈ 51.88 feet.

So, the height of the hill is approximately 51.88 feet.

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Answer:

135.04 - 125.62 = 9.42

9.42/125.62=0.07498805

0.07498805 X 100 = 7.49880592

sales tax = 7.5%

The information that can be illustrated from the table that shows the relationship between x and y is that the expression is y = x + 6.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations

Based on the information, at 0, y is 6. At 1, y is 10. It should be noted that the expression will be:

y = x + 6.

This illustrates the expression.

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A player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.

To determine how fast a player needs to make a goal to be sponsored by the puck company, we'll need to find the

time cutoff for the top 10% quickest goals.

Step 1: Determine the z-score for the 90th percentile (since we want the top 10%).

We can use a standard normal distribution table (or a calculator) to find that the z-score for the 90th percentile is

approximately 1.28.

Step 2: Use the z-score formula to find the time cutoff.

The formula is: Z = (X - μ) / σ

Where Z is the z-score, X is the time cutoff we're looking for, μ is the mean (12.56 minutes), and σ is the standard

deviation (4.91 minutes).

Step 3: Solve for X.

Rearrange the formula to solve for X: X = Z × σ + μ

Plug in the values: X = 1.28 × 4.91 + 12.56

X ≈ 6.29 + 12.56

X ≈ 18.85

So, a player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.

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The measure angle EBF is (5b-24)°.

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

Give that, m∠ABF =(7b-24)° and m∠ABE =2b°.

From the figure,

m∠ABF =m∠ABE + m∠EBF

(7b-24)°=2b° + m∠EBF

m∠EBF = 7b-24-2b

m∠EBF = (5b-24)°

Therefore, the measure angle EBF is (5b-24)°.

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To solve this problem, we need to find the x-values where the curve intersects the x-axis, which occurs when y=0.
0=x²-2kx ,We can factor out an x: 0=x(x-2k) .So the x-intercepts are at x=0 and x=2k.

To find the value of k, we need to follow these steps:

Step 1: Find the points of intersection between the curve y = x^2 - 2kx and the x-axis.
To do this, set y = 0:
0 = x^2 - 2kx
x(x - 2k) = 0

This means that the curve intersects the x-axis at x = 0 and x = 2k.

Step 2: Determine the limits of integration.
Since we are looking for the region in the fourth quadrant, we will have limits 0 and 2k for our integration.

Step 3: Calculate the area using integration.
Area = ∫[0 to 2k] (x^2 - 2kx) dx

Step 4: Solve the integral.
Area = [1/3x^3 - kx^2] evaluated from 0 to 2k
Area = (1/3(2k)^3 - k(2k)^2) - (1/3(0)^3 - k(0)^2)
Area = (8k^3/3 - 4k^3)

Step 5: Set the area equal to 36 and solve for k.
36 = 8k^3/3 - 4k^3
36 = (8k^3 - 12k^3)/3
36 = -4k^3/3

Now, multiply both sides by 3 and divide by -4:
-108/-4 = k^3
27 = k^3

Take the cube root of both sides:
k = 3

The value of k is 3 (Option b).

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(a) The total expected payoffs for Tech when going for one point are (0.98)($7.2 million) + (0.02)(-$1.7 million) = $7,014,000 (0.02)(0.20)($7.2 million) + (0.02)(0.80)(-$1.7 million) = -$108,000 Therefore, based on the expected payoffs, Tech should go for one point.

(b)  Tech’s probability of winning the game in overtime should be 76.82% to make Tech indifferent to going for either 1 or 2 points.

Decision tree analysis is a graph with different decision options and their potential consequences. Tech can go for two points or one point, and if one point is successful, it will go over time. The decision tree analysis is as follows: The following probabilities and outcomes will be used for decision tree analysis if Tech goes for two points: Probability of winning = 0.33 The payoff for a win is $7.2 million The payoff for a loss is -$1.7 million The probability of losing is 0.67 The payoff for a win is -$1.7 million The payoff for a loss is -$1.7 million If Tech goes for one point, the following probabilities and outcomes will be used: Probability of winning = 0.98 The payoff for a win is $7.2 million The payoff for a loss is -$1.7 million The probability of losing is 0.02 The payoff for a win is -$1.7 million The payoff for a loss is -$1.7 million If it goes for one point and loses, it will have a 20% chance of winning in overtime. Therefore, the probability of going for one point and winning is 0.98, while the probability of going for one point and losing is 0.02. If Tech goes for one point and goes to overtime, the probability of winning in overtime is 0.20. The total expected payoffs for Tech when going for two points are: (0.33)($7.2 million) + (0.67)(-$1.7 million) = $1,386,000 The total expected payoffs for Tech when going for one point are: (0.98)($7.2 million) + (0.02)(-$1.7 million) = $7,014,000 (0.02)(0.20)($7.2 million) + (0.02)(0.80)(-$1.7 million) = -$108,000 Therefore, based on the expected payoffs, Tech should go for one point.

(b) Let P be the probability that Tech will go for one point, and 1 – P be the probability that Tech will go for two points. Then, the overall probability of Tech winning the game is given by: P(Tech wins) = P(Tech wins, goes for one point) + P(Tech wins, goes for two points)Let A denote the event that Tech goes for one point and wins, B denote the event that Tech goes for two points and wins, and C denotes the event that Tech goes for two points and loses. Then we have: P(Tech wins) = P(A) + P(B) = 0.98P + 0.33(1 – P)If Tech goes for one point, there is a 0.98 probability of winning, and if Tech goes for two points, there is a 0.33 probability of winning. Let D denote the event that the game goes into overtime. Then: P(A) = P(Tech wins | A)P(A) = 0.98P(1 – 0.2)P(B) = P(Tech wins | B)P(B) = 0.33P(C) = P(Tech loses | C)P(C) = 0.67(1 – P)Hence: P(Tech wins) = P(A) + P(B) = 0.98P + 0.33(1 – P)If Tech is indifferent between going for one point and going for two points, it follows that the payouts for the Sugar Bowl and the Gator Bowl must be equalized. We have: P(Tech wins) = P(Tech wins, goes for one point) + P(Tech wins, goes for two points) = $7.2 million x P(A) + $7.2 million x P(B) + $1.7 million x P(C)Now we can solve for P as follows:0.98P + 0.33(1 – P) = $7.2 million x P(A) + $7.2 million x P(B) + $1.7 million x P(C)0.98P + 0.33 – 0.33P = $7.2 million x 0.98P + $7.2 million x 0.33P + $1.7 million x 0.67(1 – P)0.65P = $7.2 million x 0.98P + $7.2 million x 0.33P + $1.139 million – $1.139 P0.481P = $7.2 million x 0.98P + $7.2 million x 0.33P + $1.139 millionP = $1.139 million/$1.4815 millionP = 0.7682, or 76.82%Therefore, Tech’s probability of winning the game in overtime should be 76.82% to make Tech indifferent to going for either 1 or 2 points.