Answer the statistical measures and create a box and whiskers plot for the followingset of data.4,4,5,5,5,6,6, 8, 9, 10, 12, 14, 14, 15, 17

Given:

Simplify the equation,

Answer: x = 56.

The selling price as a percent of the cost is given by the ratio between the selling price and the the cost. The selling price is given, which is $119.95 the cost is given by the difference between the selling price and the Markup($25.99). Combining all those informations in an equation, we have

To write this as a percentage, we just multiply the ratio by 100.

The selling price is 128% of the cost.

1) To solve this System of Solutions graphically, we'll need to plot those lines described by those respective equations.

2) Let's set two tables

y=-5x +4

x | y

1 -1 ( 1,-1)

2 -6 ( 2,-6)

3 -11

y=3x + 4​

x | y

1 | 7 ( 1,7)

2 |10 ( 2,10)

3 | 13

2.2 Let's plot those equations and interpret the results:

3) As these lines have point (0,4) as their common point. Therefore we can state that the solution for this consistent system is S=(0,4)

So Bill and Laura like all of the choices equally. This means that the probability of each of them choosing one out of the four is the same for each options. So this probability is 1 out of 4: 1/4. So the probability of Bill choosing apple pie is 1/4 and that of Laura choosing strawberry cheesecake is also 1/4. The probability of both making those choices at the same time is given by the product of the mentioned probabilities. Then the probability we are looking for is:

Then the answer is the fourth option.

To find a solution to the equation y = 3x - 1, we have to replace a variable by a number and compute the other variable.

Assuming x = 0, then

y = 3(0) - 1

y = 0 - 1

y = -1

Then, the point (0, -1) is a solution

Assuming x = 1, then

y = 3(1) - 1

y = 3 - 1

y = 2

Then, the point (1, 2) is a solution

Assuming x = 2, then

y = 3(2) - 1

y = 6 - 1

y = 5

Then, the point (2, 5) is a solution

In the next graph, the solutions and the line are shown

The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

Replacing with points (0, -1) and (1,2) we can compute the slope, as follows:

To convert a rectangular equation to polar forma, we use

In the equation x=18, we only have x, so

Given:

b) To find:

We know that,

Thus, the answer is,

a) To find:

We know that,

Thus, the answer is,

Answer:

72°

Step-by-step explanation:

Origin is completely 360° and its divided into 5 sides. So,360÷5=72°

The simplest form of 7 × (-2/-5) × (7/-6) is - 49/15.

A whole number or another fraction is produced when one fraction is multiplied by another fraction. We all know that a fraction has two components: a numerator and a denominator. In order to multiply any two fractions, we must multiply the numerators and denominators, respectively.    

Here we have

=> [tex]7. \frac{-2}{-5} .\frac{7}{-6}[/tex]

Can be multiplied as given below

=> [tex]7 \times\frac{-2}{-5} \times\frac{7}{-6}[/tex]  

=> [tex]7 \times\frac{1}{5} \times\frac{7}{-3}[/tex]  

=> [tex]-\frac{49}{15}[/tex]  

Therefore,

The simplest form of 7 × (-2/-5) × (7/-6) = -49/15

Learn more about Fractions at

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Given the functions below

We are to find (fg)(-x)

SOLUTION

First of all, we have to get (fg)(x)

Expand the function

Let us now solve for (fg)(-7)

Hence,

We have a problem that can be solved with a system of equations.

First we need to identify the equations of the system.

We have two unknown variables, the number of adult's tickets sold and the number of children's tickets sold. Let's call them:

- number of adult's tickets sold: x

- number of children's tickets sold: y.

The total number of tickets sold, 5600, is the sum of these:

And since the prices are 27.25 (adult) and 12.00 (children), the total revenue (117311.50) will be the sum of these prices multiplyied by the number of tickets of each of them:

So, the system of equations is:

Since we want y the number of children's tickets sold, we can solve for the other varible, x, in one equation, and substitute into the other.

Solving in the first equation, we have:

And substituting into the other:

Since y is the number of children's tickets sold, then the number of children's tickets sold is 2314.

Observe that the given number is 67,430,000.

If we express it as a scientific notation, then we would have to move the decimal point 7 spots to the left.

We will illustrate on how to find the inverse function.

First, recall that the inverse function is a function that given the output of a function, it will give you back the input out of which that output came from.

when athe function has a formula, we can follow some steps to find the inverse function. Suppose we are given the function

Now, we first change f(x) with the letter y. So we get

now, we interchange variables x and y. So we get

Finally we solve this equation for y. We will first subtract 5 on both sides and then divide both sides by 3. So we get

and now we replace the y with the symbol of the inverse function. So we have that

10x - 2y = -4 ==== (1)

4x + 5y = -19 ==== (2)

To solve the system we should make the coefficients of y have the same values to eliminate it, then

Multiply equation (1) by 5 and equation (2) by 2

5(10x) - 5(2y) = 5(-4)

50x - 10y = -20 ===== (3)

2(4x) + 2(5y) = 2(-19)

8x + 10y = -38 ===== (4)

Now add equations (3) and (4) to eliminate y

(50x+8x) + (-10y + 10y) = (-20 + -38)

58x + 0 = -58

58x = -58

Divide both sides by 58 to find x

x = -1

Substitute the value of x in equation (1) or (2) to find the value of y

4(-1) + 5y = -19

-4 + 5y = -19

Add 4 to both sides

-4 + 4 + 5y = -19 + 4

0 + 5y = -15

5y = -15

Divide both sides by 5 to find y

y = -3

The solution of the system is (-1, -3)

SOLUTION:

Step 1:

In this question, we have the following:

Step 2:

Given:

m = -13

-16 = m - 3

Add 3 to both sides of the equation

-16 + 3 = m - 3 + 3

-13 = m

m = -13

The given system is

We can multiply the first equation by 8, then we sum and solve for x.

Then we, solve for x.

Now we use this value to find y.

The popcorn balls cost $1.00 each

Jumbo candy bars cost $1.50 each

This week they have made a total of $229 and have sold 79

popcorn balls.

First, let's make a function with includes this information.

Let's say that popcorn balls are x and Jumbo candy bars are y.

So the function would be

1.00x+ 1.50y = 229

We already have the x value which represents the total of popcorn balls sold this week, so replace this value in the function:

1.00x+ 1.50y = 229

1.00(79)+ 1.50y = 229

79.00 + 1.50y = 229

Solve the equation for y to find the total of candy bars sold.

79 + 1.50y = 229

1.50y = 229 - 79

1.50y = 150

y = 150/1.50

y = 100

So the have sold 100 candy bars this week

SOLUTION:

We want to find the inverse of f(x);

We solve for x;

Thus the answer is OPTION A

(-5, 2)

1) Solving this Linear System with the method of Addition/Elimination:

2x + 3y=-4

x + 9y = 13​ x-2 Multiply the whole equation by -2

2x +3y = -4

-2x -18y= -26

--------------------

-15y= -30

15y= 30 Divide both sides by 15

y = 2

2) Plug into the simpler equation y=2

x +9y = 13

x + 9(2) = 13

x +18 = 13

x =13-18

x= -5

3) So the answer is (-5, 2)

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solve for T:

Therefore, the correct answer is option 2.

The given expression is

We will use the distributive property to solve it

Divide each term in the bracket by 10

Simplify each term

The answer in standard form is 4s + 10t

The unit rate = 0.6 holes per hour

Number of holes dug by the team = 12

Total time taken = 20 hours

The unit rate = (Number of holes) / (Time)

The unit rate = 12/20

The unit rate = 0.6 holes per hour

Solve the following inequality for p. Write your answer in simplest form.

8p + 10 > -5p - 1

group terms

8p+5p > -1-10

13p > -11

p > -11/13

In order to find the correct answers, let's simplify the equation by calculating the square root of both sides of the equation:

Therefore the correct options are 3√7 and -3√7.

You have the following expression for the function f(x):

f(x) = 2x + 3

In order to calculate the value of f(4), just replace x=4 into the function f(x) and simplify it:

f(4) = 2(4) + 3

f(4) = 8 + 3

f(4) = 11

Hence, the answer is:

A) 11

we know that

the total surface of a cylinder is equal to

where

B us the area of the circular base

P is the circumference of the circular base

h is the height of the cylinder

we have

h=2r

so

substitute

substitute the value of h

therefore

The proportion of the first row with the second row is

that is, we have the proportionality 1:2, which correspond to the pink square.

Answer:

I call this a simple solution because it does not involve probability distributions. It just requires simple knowledge of probability, that’s it!

The question says any 15-minute interval, so one hour can be thought of as four 15-minute intervals.

Now, the question asks the probability of seeing at least one shooting star in those four 15-minute intervals.

Such a probability is the same as the complement of the probability of not seeing any shooting star in those four 15-minute intervals.

All of those four 15-minute intervals are independent of each other. So, their combined probability is the product of the individual probabilities.

The individual probability of not seeing any shooting star in an interval of 15 minutes is 1 - 0.2 = 0.8.

So, the combined probability of not seeing any of the shooting stars in the four intervals is: 0.8 * 0.8 * 0.8 * 0.8 = 0.8⁴ = 0.4096

Now, the complement of its probability is 1 - 0.4096 = 0.5904

So, that is the answer or the probability of seeing at least one shooting star in an interval of an hour.

Step-by-step explanation:

Why?

Before diving into the Poisson process, let me explain why such a demonstration is helpful even if the problem can be solved simply.

The problems we encounter in the real-life can’t be solved by mere simple probability formulas. That is the reason more complex concepts are developed in mathematics. They help model real-life scenarios. When the scenarios are not exactly the same as the mathematical model, we do some assumptions and approximate the scenarios with mathematical models. Then, we do the modeling.

Mathematical modeling requires prior practice. To visualize the mathematical models and naturalize ourselves to such (abstract) models, good practice with the problems always helps. So, even if these problems can be solved easily using simpler methods, such problems provide us a good opportunity to practice mathematics and modeling.

Assumptions

At first, let’s see if the assumptions of the Poisson process hold here. The number of events can be counted. The occurrences of the events are independent of each other. The average rate at which the events occur can be calculated and let’s assume two events can not occur exactly at the same instant in time.

So, all the assumptions of the Poisson process hold here. That gives us the green light to move forward.

Mathematical Work

Let’s assume the rate of λ per minute. Then, the rate corresponds to 15λ per quarter.

Now, the formula for the probability distribution is:

P(X = x) = μ^x * e^-μ / x!

Before we go further, let’s understand the mathematical statement. The mathematical statement expresses the probability of seeing x events in a time period. μ is the average number of events seen in the time period. The time period can be a minute, an hour, or even a day. It can be any time period.

At first, let’s see the first statement — In any 15-minute interval, there is a 20% probability that you will see at least one shooting star.

Here, the interval is of 15 minutes. So, the average number of events in the interval is 15λ. The probability of seeing 0 events (i.e X = 0) is:

P(X = 0) = μ⁰ * e^-(15λ) / 0! = 1 / e^(15λ) — — (1)

(1) is equal to 80% as the probability of at least one event happening is 20%.

So, 1 / e^(15λ) = 0.8

or, e^(15λ) = 1.25

or, 15λ = ln(1.25) = 0.2231

=> λ = 0.0149 / min

So, the average number of events (shooting stars) is 0.0149 per minute.

Now, the average number of events in an hour is:

0.0149 * 60 = 0.8926 / hour

So, the Poisson distribution expression becomes:

P(X = x) = 0.8926^x * e^-0.8926 / x! — — (2)

Here, the time period is an hour.

Now, let’s find the probability of not having even a single event in an hour:

P(X = 0) = 0.8926⁰ * e^-0.8926 / 0! = 0.4096

So, the probability of having at least one event is the complement of the above probability.

So, P(X≥1) = 1 - P(X=0) = 1 - 0.4096 = 0.5904

Step-by-step explanation:

We need to simply use the triangle inequality Theorem, This theorem state that the sum of the two side lengths of a triangle must always be greater than the third side.

Now let's check from the given lengths

16 + 21 = 37 and 37 is less than 39 which is the third side

Hence, it cannot form a triangle