Suppose that the functions g and h are defined as follows.g(x) = x-8h(x) = (x+4)(x+5)(a) Find(-3).h(b) Find all values that are NOT in the domain of8hIf there is more than one value, separate them with commas.

First we need to factorate the number 40:

The possible numbers we can create using these factors are 2, 4, 5, 8, 10 and 20.

So If the product of the two factors (let's call them 'a' and 'b') is 40 and the sum is 14, we have:

Using the quadratic formula to solve this equation, we have:

So the factors which product is 40 and the sum is 14 are 4 and 10.

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

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

For an initial ammount borrowed I, an term of the loan t, and an annual interest rate r, the simple interest S due on the loan is given by:

For I = $12000, r = 0.065 and t = 150 days, we have:

If Kevin were to randomly select a boy from this table, this means that we need to add up the total number of boys in this sample in order to find the denominator of the fraction we are dealing with.

Let's add the number of boys up:

Now, the probability that a randomly selected boy likes History is the number of boys who said they like History divided by the total number of boys.

We already have the total number of boys, so now we need to find the number of boys who said they like History, which is 18 based off of the table.

The probability that Kevin will pick a boy who likes History is C) 35.3%.

Distance = rate x time

Gloria = X mph

Doug = 5X mph

Where X is the rate of speed

And we have that they are 858 miles apart after 6.5 hours

6.5 X + 5( 6.5 X) = 858 mph

6.5X + 32,4X= 858 mph

39X = 858mph

X = (858mph)/39 = 22

5X = 110

So Gloria is traveling at 22 mph and Doug is traveling at 110 mph. This meand that Gloria rate of speed is 22 and Doug is 110

Given:

To express it as a function of reference angle:

Since the angle lies in the fourth quadrant.

So, the reference angle will be,

Therefore, the function of the reference angle is,

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:

Answer:

14,938

Step-by-step explanation:

i mean multiply it out

Solution

Domain

Range

we have the coordinates

(-11,-8)

(-11,0)

(0,0)

(0,-8)

step 1

plot the give points

using a graphing tool

see the attached figure below

The figure is a rectangle

where

L=0-(-11)=11 units (subtract x-coordinates)

W=0-(-8)=8 units (subtract y-coordinates)

step 2

Find out the area

A=L*W

A=11*8=88 unit2

step 3

Find out the perimeter

P=2(L+W)

P=2(11+8)

P=2(19)=38 units

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.

Interger numbers: are whole numbers (numbers without fractional part). Can be negtive and possitive numbers.

Whole numbers: Positive whole numbers

Rational numbers: A number that can be made by dividing two intergers. A number that can be written as a fraction

As in the given numbers not all are whole numbers it can not be intergers or whole.

All the given numbers can be written as fractions:

Then, all are rational numbers

Explanation

the y-intercept is the point where the line intersects the y-axis, it is when x=0

and

the x-intercept is the point where the line intersects the x-axis,this is when y=0

so

Step 1

y-intercept

let x=0 and replace

so, the ordered pair is ( 0,-13)

Step 2

x-intercept

let y=0 and solve for x

hence, the ordered pair is (13/5, 0)

I hope this helps you

we have

Z1=0

Z2=-2.18

so

using the z-scores table values

Using simple mathematical operations, the funding for 3 years is:

So, let the funding in 1995 be 'x'.

Now, the equation will be formed as:

Hence,

Therefore, using simple mathematical operations, the funding for 3 years is:

Know more about mathematical operations here:

https://brainly.com/question/28937023

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Given:

The equation that represents the given situation is

Required:

We need to find the y-intercept of the given function.

Explanation:

The y-intercept is the intersection point where the line crosses the y-axis.

Substitute x =0 in the equation to find the y-intercept.

Divide both sides by 4.

The y-intercept is 2,800.

We know that x represents the cost of general admission and y represents the student tickets to a high school football.

We get y =2800.

This tells us that only student's attended the high school football game.​

Final answer:

The y-intercept is 2,800. This tells us that only student's attended the high school football game.​

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,

Step 1:

Step 2:

Write the corresponding sides of the similar triangle

Next

Cross multiply

Final answer

PQ ? = 117

The intercept on the equation of line is represented by c, where the equation of line is y = mx + c

Now, ( 2,2 ) means x=2, y=2 , the slope is m which is -3/2 ( from the question )

Hence, substitute all into the equation of line to find c

Recall, equation y = mx + c

Hence, we say that the intercept of the slope C is 5

The equation form is y = -3/2 x + 5 ( since m = -3/2 and c = 5 )

Given the function f(x) = x

We will find the function g(x) whose graph is produced by the following transformations on the graph of f(x)

First, The graph of f is reflected vertically

So,

Second, expanded horizontally by a factor of 2

So,

Finally, shifted right 6 units, and shifted down 4 units.

So,

Simplifying the function g(x):

The graph of the function (f) and (g) will be as shown in the following figure:

For any line passing through the points (x1,y1) and (x2,y2), its slope is given by:

a = (y2 - y1)/(x2 - x1)

And its intercept is given by:

b = y1 - ax1 = y2 - ax2

And the equation of this line, in the slope-intercept form, is y = ax + b

Then, for a line passing through the points (3,4) and (-6,5), we have:

a = (5 - 4)/(-6 - 3) = -1/9

Then, the intercept is:

b = 4 + 3/9 = 13/3

Therefore, the equation of the line is given by:

y = -x/9 + 13/3

Solution;

To the describe the error on the graph;

The graph is supposed to pass through point(1/3, -1).

Step 1- Write out the Future Value Ordinary Annuity formula:

Where,

Step 2- Write out the given values and substitute them into the formula:

Substituting the given values into the formula, we have:

Hence,

Hence, the future value is approximately:

Hence, the amount in the account in 3 years is:

$61109.00

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.

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.

Explanation:

The slope of the altitude drawn to side DN is the reciprocal and opposite to the slope of side DN, because the altitude is perpendicular to the side.

First we have to find the slope of side DN. The formula for the slope of a line with points (x1, y1) and (x2, y2) is:

In this problem the points are D(-6, -1) and N(-3, 10). The slope of side DN is:

Therefore the slope of the altitude is:

Answer:

The slope of the altitude is -3/11

To do a quotient between two numbers in scientific notation we must do the usual division with the number, and subtract the exponents, for example:

Therefore, we must divide

Do the division:

Now we do the division of the exponents

Now we put it all together:

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.