Darius and his friends bought 3 pizzas. Each pizza cost $9.89. They paid for the pizzas with 20 dollar bills.

How much change did they get?

Enter your answer in the box.


$|__|

The given vectors are:(5,2), (-2,11), (7,-3), and (-8,-14).

The direction angle of a vector is the angle between the vector and the positive x-axis measured counterclockwise. Therefore, the direction angle of vector v = (x,y) is given by θ = tan⁻¹(y/x).a. For vector (5,2), direction angle is given by:θ = tan⁻¹(2/5) = 21.801 degrees (rounded to 3 decimal places)b.

For vector (-2,11), direction angle is given by:θ = tan⁻¹(11/-2) = 101.31 degrees (rounded to 3 decimal places)c. For vector (7,-3), direction angle is given by:θ = tan⁻¹(-3/7) = -23.198 degrees (rounded to 3 decimal places)Note that the direction angle here is negative because the vector points towards the negative x-axis.d.

For vector (-8,-14), direction angle is given by:θ = tan⁻¹(-14/-8) = 60.26 degrees (rounded to 3 decimal places)

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By assuming that both tests measure the same kind of ability, Bob did better in terms of the standardized Z-score.

We have provide a data about two major math's tests.

First Major test : SAT math score normally distributed with

Mean , μ = 516 and

Standard deviations, σ = 115

Second Major test: ACT math score normally distributed with

Mean, μ = 22

Standard deviations, σ = 5

Anna scores in SAT test 650

i.e x = 650

Using Z-Score formula,

Z = (x - μ)/σ

Z = (650 - 516)/115 = 154/115 = 1.17

Also, Bob score on ACT math test is 29 i.e x = 29

Z-Score = (x - μ)/σ

=> Z = (29 - 22)/5 = 7/5

=> Z = 1.4

Since, Z-Score for Bob's ACT math test is high as compared to Anna's SAT math test.

So, Bob did better in terms of the standardized z-score.

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The expression that can be used to find the perimeter of the rectangle is 62 centimeters 2(5x−2)+2(3x+1).

The perimeter of the rectangle is equal to the 2 times sum of the length and width of the rectangle.

Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper.

The expression that can be used to find the perimeter of the rectangle is given by;

\(\rm Perimeter \ of \ rectangle = 2 (length +width)\\\\\rm Perimeter \ of \ rectangle = 2 (5x-2+3x+1)\\\\ \rm Perimeter \ of \ rectangle = 2 (7x-1)\\\\ \rm Perimeter \ of \ rectangle = 16x-2\\\\When , x\ =\ 4\\\\ \rm Perimeter \ of \ rectangle = 14x-2\ = 16(4)-2\ =\ 64-2\ =\ 62\\\)

Hence, the expression that can be used to find the perimeter of the rectangle is 62 centimeters 2(5x−2)+2(3x+1).

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Answer:

  an = 5/2 +3/2(n -1)

Step-by-step explanation:

The common difference is ...

  4 -5/2 = 3/2

The general rule is ...

  an = a1 +d(n -1)

For a1 = 5/2 and d = 3/2, the rule for this sequence is ...

  an = 5/2 +3/2(n -1)

___

This can be simplified to ...

  an = 1 +3/2n

Answer:

A

Step-by-step explanation:

covert to slope intercept form

x-y=2

-y=-x+2

y=x-2

Answer: C

Step-by-step explanation:

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

Relationship is proportional ;

8 oranges

Step-by-step explanation:

Oranges (lb) 2 ___ 3 ____5 ___?

Price ($) __ 3 ___4.50___7.50_12

For proportionality :

Oranges = k * price

Where, k = constant of proportionality

2 = 3k

k = 2 /3

k = 0.666666

Using k :

Number of oranges at price = 4.50 should be:

0.66666 * 4.50 = 3

Number of oranges at price = 7.50 should be:

0.66666 * 7.50 = 5

Hence, relationship is proportional

Number of oranges at $12

0.66666 * 12 = 8

Hey there! :)

Answer:

g(x) = (x + 9)²

Step-by-step explanation:

If we look at the graph g(x), we can see that its vertex is at (-9, 0).

Recall the transformation form of a parabola is f(x) = ±a(b(x-h))+k where (h , k) are the coordinates of the vertex. In this instance it is (-9, 0), therefore:

g(x) = (x + 9)²

The expected net gain from playing this game is -0.35 dollars. To calculate the expected net gain, we need to multiply each possible outcome by its corresponding probability and sum them up.

Let's denote the winnings as X, where X = 1 represents winning 1 dollar, X = 2 represents winning 2 dollars, and X = 20 represents winning 20 dollars.

Expected net gain = (1 dollar * probability of winning 1 dollar) + (2 dollars * probability of winning 2 dollars) + (20 dollars * probability of winning 20 dollars) - (2 dollars, the cost to play the game)

Expected net gain = (1 * 0.15) + (2 * 0.05) + (20 * 0.01) - 2 = -0.35 dollars.

In this game, there are three possible outcomes with their respective probabilities: winning 1 dollar with probability 0.15, winning 2 dollars with probability 0.05, and winning 20 dollars with probability 0.01. These probabilities indicate the likelihood of winning each corresponding amount.

To calculate the expected net gain, we need to consider the potential winnings and the cost to play the game. The cost to play the game is a fixed amount of 2 dollars.

We calculate the expected net gain by multiplying each possible outcome by its probability and summing them up. For example, the expected gain from winning 1 dollar is (1 * 0.15) dollars, while the expected gain from winning 2 dollars is (2 * 0.05) dollars. Similarly, the expected gain from winning 20 dollars is (20 * 0.01) dollars.

To obtain the final expected net gain, we subtract the cost to play the game (2 dollars) from the sum of the expected gains. If the result is negative, it represents a net loss, while a positive result indicates a net gain.

In this case, the calculations are as follows:

Expected net gain = (1 * 0.15) + (2 * 0.05) + (20 * 0.01) - 2 = -0.35 dollars.

This means that, on average, a player can expect to lose approximately 35 cents per game when playing this particular gambling game.

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The solutions to the systems of equations are x = 30 and y = 54

The correct linear equation is expressed as:

4x+y+6=180 ................1

2x+2y+12=180 .................2

The equations can also be written as:

4x + y = 174 .................... 3 × 2

2x + 2y = 168 ................... 4 × 1

______________________________________

8x + 2y = 348

2x + 2y = 168

Subtract both equations

8x - 2x = 348 - 168

6x = 180

x = 180/6

x = 30

Substitute x = 30 into equation 3:

4x + y = 174

4(30) + y = 174

120 + y = 174

y = 174 - 120

y = 54

Therefore the solutions are x = 30 and y = 54

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Answer:

The answer is B

Step-by-step explanation:

By BODMAS;

2(9 - 3) = 12

2(6) = 12

12 = 12

Answer:

Step-by-step explanation:

To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:

yz + x²

Substituting the given values, we get:

(6.1 * 0.2) + (3.2^2)

This simplifies to:

1.22 + 10.24

Therefore, the value of the expression is approximately 11.46.

11.46

gimme brainlyest gang

The probability of pulling a black or red card  = 3/10

Probability that a white card will be drawn, P(white) = 1/25

Probability that a blue card will be dealt, P(black)  = 1/5

Probability that a black card will be dealt, P(red) = 1/10

Probability that a pink card will be revealed, P(pink)  = 1/15

All of these occurrences are distinct from one another and do not relate to one another.

The likelihood that any one of any two events, A and B, with probability P(A) and P(B), will occur is:

                                        P( A ∪ B ) = P(A) + P(B)

Here, event A can be compared to getting a black card, and

incident B is comparable to receiving a red card.

So, P(black or red) = P(black) + P (red)

= (1/5) + (1/10)

= ( 2 + 1 )/10

= 3/10

So, the likelihood that a black or red card will be pulled from the hat:

= 3/10

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Given that the boat travels upstream for 60 miles in 4 and downstream for 60 miles in 3 hours.

Let x be the rate of the boat in still water.

Let y be the rate of the boat in the current.

Downstream =x+y.

Upstream =x-y.

Using the speed formula for downstream, we get

Dividing both sides by 3, we get

Using the speed formula for upstream, we get

Dividing both sides by 4, we get

Substitute x=20-y to compute y value, we get

Substitute y=2.5 in x=20-y, we get

Hence the rate of the boat in still water is 17.5 mph and the rate of the boat in the current is 2.5 mph.

Answer:

\( \frac{1}{2} \)

Step-by-step explanation:

Given line is passing through the points (8, 0) & (0, - 4)

\(slope \: of \: line = \frac{ - 4 - 0}{0 - 8} = \frac{ - 4}{ - 8} = \frac{1}{2} \\ \)

The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1

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

Parent function: y = 2^x

The graph of the transformed exponential function g(x) passes through the points  (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)

So, we have the following transformation steps:

1st Transformation:

Reflect y = 2^x across the y-axis

So, we have

y = 2^-x

2nd Transformation:

Translate y = 2^-x down by 1 unit

So, we have

y = 2^-x - 1

This means that

g(x) = 2^-x - 1

Hence, the equation of the function g(x) is g(x) = 2^-x - 1

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Answer:

Step-by-step explanation:

So, first you add the four exam percentage which will be 314 then you multiply 80 and 5. We use 5 because there are total 5 exams which will give the mean of 80%. After you get the answer for 80x5 which will be 400. Then you do, 400 - 314 which will be 86. So, the answer is 86%. To figure out if that answer is right, You add all the scores percentage and divide that by 5 and you should get 80%.

To have an overall mean of 80% after five exams, the student needs to score 88% on the next exam.

To find the student's overall mean, we need to add up all the scores and divide by the number of exams.

We have 4 exams scores:84%, 71%, 86%, and 73%.

Therefore, the total of the four exam scores is:

84% + 71% + 86% + 73% = 314%

To find the overall mean after five exams, the total score after five exams should be 5 × 80% = 400%.

Therefore, to have an overall mean of 80%, the student must score (400 - 314)% on the fifth exam, which is equivalent to: 86%.

Hence, the student needs to score 86% on the next exam to have an overall mean of 80%.

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We can rewrite the given expression in the desired order as follows:

∫∫∫ z^2 - 2z^(4y^2) * (z^(-x/2)) dz dx dy

First, we integrate with respect to dz from 0 to z^(x/2):

∫∫ z^(2-x/2) - 2z^(4y^2 - x/2 + 1) / (4y^2 - x/2 + 1) dz dx

Next, we integrate with respect to dx from 0 to 1:

∫ z^(2-x/2) / (2-x/2) - 2z^(4y^2 - x/2 + 1) / (4y^2 - x/2 + 1) | 0 to 1 dy

Finally, we integrate with respect to dy from 0 to 1:

∫[0,1] ∫[0,1] ∫[0,1] z^(2-x/2) / (2-x/2) - 2z^(4y^2 - x/2 + 1) / (4y^2 - x/2 + 1) dz dx dy

This is the same expression as the original one, but written in the desired order of integration.

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Answer:

the sampling distribution of proportions

A sample is a small group of observations which is a subset of a larger population containing the entire set of observations. The proportion of success or measure of a certain statistic from the sample, (in the scenario above, the proportion of obese observations on our sample) gives us the sample proportion. Repeated measurement of the sample proportion of this sample whose size is large enough (usually greater Than 30) in other to obtain a range of different proportions for the sample is called the sampling distribution of proportion. Hence, creating a visual plot such as a dot plot of these repeated measurement of the proportion of obese observations gives the sampling distribution of proportions

Step-by-step explanation:

Hope this helps:)

The area of the shaded region is 294.4 square meters

The given parameters are represented on the figure

By this;

The area of the shaded region is the sum of the area of the major sector and the area of the triangle

The area of the major sector is

A1= ∅/360 * πr²

The area of the triangle is

A2 = 0.5r²sin(x)

So, the total area is

Total = ∅/360 * πr² + 0.5r²sin(x)

This gives

Total = (360 - 130)/360 * 3.14 * 11.1^2 + 0.5 * 11.1^2 * sin(130 deg)

Evaluate

Total = 294.4

Hence, the area of the shaded region is 294.4 square meters

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Answer:

5³

Step-by-step explanation:

kira rides = 5 miles

cory rides = 5 * 5

tina rides : 5 * 5 * 5

therefore tina rides = 5³

Answer:

The answer would be 5 with 3.

Step-by-step explanation:

By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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The probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

Let X denote the time required to process a package of five tasks. X is an exponentially distributed random variable with mean 2 minutes.

The probability of X being less than 8 minutes is given by:

P(X ≤ 8) = 1 - P(X > 8)

= \(1 - (1 - e^{(-8/2)}^{5}\)

= 0.963

Therefore, the probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

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A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.

Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.

A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.

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Answer:

The graph in the lower left corner.

Step-by-step explanation:

The graph of  \(y=2^x\)  is in the upper right-hand corner.

The graph of  \(y=-2^x\)  (reflected about the x-axis) is in the upper left-hand corner.

The graph of  \(y=-\frac{1}{2}(2^x)\) is a vertical compression of \(y=-2^x\),  the points are half as far away from the x-axis -- squeezed closer to the x-axis by half.

Answer:

\(x^2+8x+15\)

Step-by-step explanation:

\(f(x)=x+4 \\\\g(x)=x^2-1 \\\\(g\circ f)(x)=(x+4)^2-1=\\\\x^2+8x+16-1=\\\\x^2+8x+15\)

Hope this helps!

Answer:

x² + 8x + 15

Step-by-step explanation:

(gºf)(x) = g((f(x)) = (x+4)² - 1 = x² + 8x + 16 - 1 = x² + 8x + 15

The probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.

When events A and B are independent, the probability of them occurring together is the product of their individual probabilities.

P(A and B) = P(A) * P(B) = 0.31 * 0.76 = 0.2356

P(A|B) = P(A and B) / P(B) = 0.2356 / 0.76 = 0.31 (It is same as P(A) because events A and B are independent)

P(B|A) = P(A and B) / P(A) = 0.2356 / 0.31 = 0.76 (It is same as P(B) because events A and B are independent)

P(A or B) = P(A) + P(B) - P(A and B) = 0.31 + 0.76 - 0.2356 = 0.8144

Therefore, the probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.

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Answer:

Step-by-step explanation:

(x - 6)/2= -2

x - 6 = -4

x = 2

(y + 3)/2 = 2

y + 3 = 4

y = 1

(2, 1) coordinates of B

Answer:

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -3x-4y-9 = 0 and calculate its properties. Graph of a Straight Line : Calculate the Y-Intercept : Notice that when x = 0 the value of y is 9/-4 so this line "cuts" the y axis at y=-2.25000. y-intercept = 9/-4 = -2.25000.

Step-by-step explanation:

Find the X and Y Intercepts 3x-4y=9. 3x − 4y = 9 3 x - 4 y = 9. Find the x-intercepts. Tap for more steps... To find the x-intercept (s), substitute in 0 0 for y y and solve for x x. 3 x − 4 ⋅ 0 = 9 3 x - 4 ⋅ 0 = 9. Solve the equation. Tap for more steps... Simplify 3 x − 4 ⋅ 0 3 x - 4 ⋅ 0.