The scatter plot shows the median household income x in thousands of dollars, and the number of adults per 1,000 people with bachelors degree y of 50 U.S states. The line y=4.08x+63.13 is a good fit for this data

EXPLANATION

This is a combinatory, as there are 12 groups, the combinatory will be as follows:

16C12 = 16!/[12!*(16-12)!] = 1820

In conclusion, there will be 1820 possible groups of 12 appetizers.

The values of the functions are:

a. (f + g)(x) = 9x + 1

b. (f - g)(x) = -7x - 17

c. (f * g)(x) = 8x² - 55x - 72

d. (f/g)(x) = (x - 8)/(8x + 9)

To evaluate a function for a given value of input, substitute the value of the input, x, into the function equation, evaluate and simplify.

Given the following:

f(x) = x - 8

g(x) = 8x + 9

a. (f + g)(x) = (x - 8) + (8x + 9)

Combine like terms

(f + g)(x) = 9x + 1

b. (f - g)(x) = (x - 8) - (8x + 9)

(f - g)(x) = x - 8 - 8x - 9

Combine like terms

(f - g)(x) = -7x - 17

c. (f * g)(x) = (x - 8)(8x + 9)

Expand

(f * g)(x) = x(8x + 9) -8(8x + 9)

(f * g)(x) = 8x² - 55x - 72

d. (f/g)(x) = (x - 8)/(8x + 9)

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Let's call C to the cups of chocolate chips and S to the cups of sugar. We are told that the cups of sugar are 2 2/3 times the cups of chocolate, then we can formulate the following equation:

In the case 4 1/3 of sugar is added, we can replace 4 1/3 for S to get:

By dividing both sides by 2 2/3 we get:

We can rewrite the mixed fractions to get:

By changing the division symbol to a multiplication symbol and flipping the 8/3, we get:

Then, 1 5/8 cups of chocolate chips are needed

Answer:

50 + 6x = 62

Explanation:

If x represents the cost of one box of pencils and the teacher got snacks for $50, purchased 6 boxes of pencils, and spent a total of $62, we can write the equation that models the above situation as shown below;

In order to estimate the interest the average househould accumulates in 1 year, you use the following formula:

A = Prt

where P is the initial credit card debt ($7,281), r is the interest rate per period (16.99%) and t is the number of time periods. In this case the value of r is given by the APR, then, there is one period of 1 year.

To use the formula it is necessary to express 16.99% as 0.1699. Thus, you have:

I = 7,281 x 0.1699 x 1

I = 1,237.04

Hence, the interest accumulated is of $1,234.04

By identifying the intercepts in the given image, we conclude that the solutions of the system of equations are points B and F.

When we have a system of 2 equations:

y = f(x)

y = g(x)

To solve it graphically, we have to graph both functions in the same coordinate axis and see in which points the graphs intercept (if they do). Each of these interceptions in the form (x, y) will be a solution for the equation f(x) = g(x) = y

In this case, we can see a line and a parabola (each of these is a different equation from the system), and we can see that the graphs intercept at points F and B (i think, the image is really small). Then the two solutions of the system of equations graphed are the points F and B

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Answer:

solution: F and B

NOT solution: the rest of the letters

Step-by-step explanation:

I did the work on imagine math

1) We are going to tackle this question starting with the total outcomes of dice rolled twice in succession.

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

So we can see that there are 36 possibilities.

2) Let's examine the events.

a) P (>7)

Let's bold the combinations of outcomes whose sum is greater than 7

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

So, we can see that there are 15 favorable outcomes.

Now, we can find the Probability of rolling the dice twice and get a sum greater than 7:

b) Now, for the other event: The sum is divisible by 3 or 6, or both:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Hence, the favorable outcomes are: 12

So now, let's find the probability of getting a sum that way:

The time needed to look over the resumes depends on how many papers is the resume

But it is convenient to have a speed looking on each one

so, the answe will be 50 seconds

The given function is:

By using a graphing calculator, we found that the local maximum is located at:

x=0.41, then f(0.41)=-0.88

The answer is (0.41, -0.88)

Given:

The volume of the hemisphere = 281,250

Find-:

Radius of hemisphere

Explanation-:

The volume of the hemisphere is:

Given volume is 281250

So, the radius is 51.209 cm

Given:

S={(5,6),(-2,-9),(-9,6)}

To find the domain and range:

The domain is,

{-9, -2, 5}

The range is,

{-9, 6}

A exponential growth or decay function has the next general form:

If it is :

(1+r) , (>1) the function growth

(1-r) , (<1) the function decay

------

The given equation:

In (1+r) the r is the percent of growth, then for the given equation you have:

Let us calculate the move-in costs of both properties.

Rental Property

The monthly rent is $1,350.

The move-in costs are:

First month = $1,350

Last month = $1,350

Security deposit = 55% of one month's rent

Therefore, the move-in cost is:

Purchase Property

The purchase price is $195,450.

The move-in costs are:

Down payment of 18% of purchase price:

Closing costs of 2.1% of purchase price:

Therefore, the move-in cost is:

Difference in Total Move-In Cost

This is calculated to be:

ANSWER

The difference in total move-in cost is $35,842.95

First, we need the next equivalence

1 hour = 60 min

we have 330 min in order to know the number of hours we need to divide the 330 min between 60

He will record 5.5 hours

Given the points:

(−1, 7) and (4, −1)

The slope of the line passing through the points is given by:

So, the answer will be Slope = -8/5

Answer

The drug cannot be completely eliminated from one's system.

This is because the kidney removes 25% of the drug, leaving 75% at any time; the 75% of any number will give a smaller number, but never zero.

So, the amount of the drug in the body system can become extremely low, but it can never be 0.

The mathematical proof is shown under explanation.

Explanation

We are told that the kidney filters off 25% of the drug out of the system every 4 hours.

This means that 75% of the dosage of the drug remains in the person's system every 4 hours.

If one starts with A₀ of the drug and classify every 4 hour time period as n

At n = 1,

A₁ = 0.75 (A₀)

A₂ = 0.75 (A₁) = 0.75² (A₀)

Aₙ = 0.75ⁿ (A₀)

For this question, we start wit 1000 mg

A₀ = 1000 mg

We are then asked to calculate if Aₙ, the amount of drug in the system after n time periods, can ever be 0

Aₙ = 0.75ⁿ (A₀)

0 = 0.75ⁿ (1000)

To solve for n, if there's an n for when the value of Aₙ = 0, we first divide both sides by 1000

0 = 0.75ⁿ (1000)

0 = 0.75ⁿ

We then take the natural logarithms of both sides

In 0 = In (0.75ⁿ)

In (0.75ⁿ) = In 0

n (In 0.75) = In 0

But, since In 0 does not exist, it shows that there is no value of n that can make the value of Aₙ go to 0.

Hope this Helps!!!

Answer: 31 electricians

Step-by-step explanation:

We could set up a ratio for this problem. It takes 14 electricians 18 days to wire a new housing subdivision, so it would take 24 electricians x days to do the same job. 14/18 = 24/x. We can then cross multiply to find x.

X = 30.8 or approximately 31.

The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .

In the question ,

let the time travelled by the slower motorcycle be "t" .

given , the faster one travelled 1 hour longer ,

So , the time travelled by faster motorcycle = "t+1" hour .

the speed of slower motorcycle = 60 miles per hour .

the speed of faster motorcycle = 80 miles per hour .

So , the distance covered by slower motorcycle = speed * time

                                                                                 = 60*(t)

the distance covered by the faster motorcycle = 80*(t+1) .

given that faster motorcycle travels twice the distance of the slower motorcycle

So According to the question

80*(t+1) = 2*60*(t)

simplifying further , we get

80t + 80 = 120t

120t - 80t = 80

40t = 80

t = 2 hours

distance covered by slower motorcycle = 60(2) = 120 miles

distance covered by faster motorcycle = 80(2+1) = 80*3 = 240 miles .

Therefore , The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .

The given question is incomplete , the complete question is

One motorcycle travels 80 miles per hour and the second motorcycle  travels 60 miles per hour,  if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcycle . What distance does each of the motorcycle travel ?

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8x² + 16x = 42​

x² + 16/8x = 42​/8 dividing by 8 at both sides

x² + 2x = 5.25

x² + 2x - 5.25 = 0

If we compute (x + 1)², we get:

(x + 1)² = x² + 2*x*1 + 1² = x² + 2x + 1

Then,

x² + 2x - 5.25 + 1 - 1 = 0

(x² + 2x + 1) + (-5.25 - 1) = 0

(x + 1)² - 6.25 = 0

(x + 1)² = 6.25

x + 1 = √6.25

This has 2 solutions,

x + 1 = 2.5 or x + 1 = -2.5

x = 2.5 - 1 x = -2.5 - 1

x = 1.5 x = -3.5

Step 1:

Step 2:

a)

Total possible outcome = 2640

Total number of freshman = 625

Step 3:

b)

Total number of senior and large cafeteria = 350

Step 4:

c)

Number of Sophomore or student center = 650 + 595 - 125 = 1120

Step 5:

d)

Given the functions

1) To find f(g(2))

Hence, f(g(2)) = 3

2) To find f(g(x))

Hence, f(g(x)) = 18x²-60x+51

3) To find g(f(x))

Hence, g(f(x)) = 6x²-2

4) To find (gog)(x)

Answer:

Explanation:

We start by having a diagrammatic representation as follows:

Explanation:

From the graph,

we can see that the graph is symmetric about the y axis

Hence,

We can say that the Polynomial is even

Also, Because th opwning of the function is downwards,

Hence the leading coefficient is negative

Also we can see that the y-intercept is positive

That is when x=0, y=3

Hence,

The constant term of the polynomial is positive.

Therefore,

The final answers are OPTION A,OPTION D,OPTION E

As per given by the question,

There are given that a graph of line.

Now,

h

Part a: Pot the points X, Y and Z are obtained on graph.

Part b: Distances; XY = 3, YZ = 5 and XZ = √34 units.

Part c: Measure of angles; X = 59.04 degrees and Z = 30.96 degrees.

For the given question, Triangle XYZ with the vertexes are given.

Part a: Pot the points.

X = (6, 6)

Y = (6, 3)

Z = (1, 3)

The points on the graph are plotted.

Part b: Distances;

XY = 6 - 3 = 3 units

YZ = 6 - 1 = 5 units

XZ , use Pythagorean theorem.

XZ² = XY² + YZ²

Put the values.

XZ² = 3² + 5²

XZ² = 9 + 25

XZ² = 34

XZ = √34 units.

Part c: Measure of angles.

In right triangle XYZ

cos X = XY/XZ

cos X = 3/ √34

X = 59.04 degrees.

cos Z = ZY/XZ

cos Z = 5/ √34

Z = 30.96 degrees.

Thus, the value of the triangle are obtained.

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In order to calculate the area of the triangle, given the length of its three sides, we can use Heron's formula:

Where p is the semi-perimeter.

So, calculating the value of p and then the area of the triangle, we have:

Rounding to the nearest square foot, the area is 170 ft².

Consider all the different possible combinations of 4 members of the committee (b,b,b,b), (b,b,b,g),...(g,g,g,g). We need to use the binomial distribution given below

In our case

Then,