The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= 0.2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012, where x = 0 corresponds to 2003, x = 1to 2004, and so on, and y is in millions of students.(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is millions.(Type an integer or decimal rounded to the nearest tenth as needed.)

A line is given by the expression:

y=mx+b

where, m is the slope of the line and since we have to write an equation that is parallel to the given line, both lines have the same slope:

We can find the equation of the line by the slope-point form of a line, with the given point (-8, -7) and the slope of -4

From the question, we were told:

TUVW is a rhombus

Angle SUV = 4z + 56˚

We are asked to find the value of z.

From the diagram, we can see that angle SVU is 90˚

So, to get the value of z, we equate the value of SVU to 90˚

4z + 56˚ = 90˚

subtract 56˚ from both sides:

4z + 56 - 56 = 90 - 56

4z = 34

divide both sides by 4 to make z the subject of formula:

z = 34/4

z = 8.5

Given,

x-3y=-3

2x+3y=-6

Plotting it in graph we have,

Since we have only one point of intersection so that would be only one solution.

The point of intersection is (-3,0)

Thus x=-3 and y=0

Plan 1:

Initial (fixed) fee: $60

Variable fee: $0.50 per mile

Plan 2:

Initial (fixed) fee: $0

Variable fee: $0.70 per mile

If we call x to the number of miles driven by Tony, then the cost of Plan 1 is:

P1 = 60 + 0.5x

The cost of Plan 2 is:

P2 = 0.7x

It's required to find the number of miles Tony should drive for both plans to cost the same, that is:

60 + 0.5x = 0.7x

Subtracting 0.5x:

60 = 0.7x - 0.5x

Operating:

60 = 0.2x

Dividing by 0.2:

x = 60 / 0.2

x = 300

Tony should drive 300 miles for both plans to cost the same.

Under that condition, both plans cost the same. Plan 1 cost:

P1 = 60 + 0.5*300

P1 = 60 + 150

P1 = $210

Plan 2 cost:

P2 = 0.7*300

P2 = $210

Both costs are equal

Answer:

Where's the chart?

Step-by-step explanation:

In polar coordinates, the x variable is given as

So, we have the equation

By dividing both sides by cosine of thetat, we get

since

The above result is equivalent to:

Let:

x = Number of points Juan earned on the second text

n = Total number of points of each test

First, let's find the total number of points of each test using the information provided:

Now, we can find how many points Juan earned on the second test:

Answer:

40 points

The principal amount with the given parameters if $165.

Given that, Amount = $192,000, Time period = 15 years and Rate of interest = 4%.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100} )^{nt}[/tex]

Now, [tex]192,000=P(1+\frac{4}{100} )^{15\times 12}[/tex]

⇒ [tex]P=\frac{192,000}{(1.04)^{180}}[/tex]

⇒ P = $164.93

≈ $165

Therefore, the principal amount with the given parameters if $165.

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Answer:

Step-by-step explanation:

Use the compound interest formula and substitute the values given: $192,000=P(1+.0412)12(15). Simplify using order of operations: $192,000=P(1+.0412)180

P=192,000(1+.0412)180

P≈$105477.02

Solution:

Given that a store sells flour for $0.86 per pound, this implies that

Given that a baker paid $15.05, let y represent the amount of flour the baker bought.

Thus,

To solve for y,

Hence, the baker bought 17.5 lb of flour.

From the question:

Let f(x) = 2x² + 2x - 8

g(x) = √x - 2

We are aske to write f(g(x))

f(x) = 2x² + 2x - 8, g(x) = √x - 2

g(x) = √x - 2

= f(√x - 2)

f(√x - 2): 2x + 2√x - 2 - 12

f(g(x)) = 2x - 12 + 2√x - 2.

The z-score formula is given to be:

where

From the question given, the mean and standard deviations are provided as:

Therefore, the z-score of exactly 1 gallon is calculated to be:

Therefore, the z-score is -0.583.

This tells us that a container with exactly one gallon of milk lies 0.583 standard deviations below the mean.

SOLUTION:

Case: Area of plane shapes

Method:

a) Parallelogram

To find the area we need to find the perpendicular height (using Pythagoras theorem)

The Area of a parallelogram is given as:

b) Triangle

To find the area of the triangle, we need to find the base first

First, lets find 'a'

The base, b

b= 2(a)

b= 2 (36.06)

b= 72.12

The area of the triangle is:

Final answer:

a) Parallelogram,

A= 552 square feet

b) Triangle

A= 2163.6 square feet

Probability of selecting a black three or a red jack = 1/13

There are a total of 52 cards in a deck of cards

Total number of ways of selecting one card from 52 cards = 52C1 = 52 ways

There are two red jacks in a deck of cards

Number of ways of selecting a red jack = 2C1 = 2 ways

There are two blacks 3s in a deck of cards

Number of ways of selecting a black three = 2C1 = 2 ways

Probability of selecting a black three or a red jack = (1/26) + (1/26)

Probability of selecting a black three or a red jack = 2/26 = 1/13

1) To better set the measurements in that picture, we need to consider that parallel line segments in this picture have the same measurements.

2) Based on that, we can look at that picture this way:

And set the following equation, given that Perimeter is the sum of all lengths of a polygon:

Answer:

• x=1

• HG=8 units

Explanation:

If triangles HFG and RPQ are similar, the ratios of their corresponding sides are:

Substitute the given values:

First, we solve for x:

Finally, calculate the length of HG.

Tim should order approximately 6 pizza.

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on. One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction. Mathematicians use addition, subtraction, multiplication, and division as their four fundamental arithmetic operations. The division is one of these four operations that we employ most frequently in our daily work. It involves dividing a huge group into equally sized smaller units. Divide 25, for instance, by 5.

Given Data

Number of employees = 22

Slice of pizza one should get = 1/4

Dividing 22 by 1/4

[tex]\frac{22}{4}[/tex]

5 and [tex]\frac{1}{2}[/tex]

Tim should order approximately 6 pizza.

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The answer is the third choice

Where all probability are equal

The equation d = 65t

represents the distance (d) the car travels at a 65 mile speed in t hours

a. 65 tells us the speed at which the car travels

b. If the car travels in 1.5 hrs, then

d = 65(1.5)

= 97.5 milestone.

c. To travel 26 miles, we have d = 26

26 = 65t

t = 26/65

= 0.35 (approximately)

he had 40 biscuits in the beginning

to solve this we can use a rule of three

so

Step 1

let x represents the total treats he had in the beginning , so

so, the proportion is

therefore,

he had 40 biscuits in the beginning

I hope this helps you

Solution

The final answer

Since x is given in cubic inches, let's split the expression like this:

For x = 2:

Answer:

look below

Step-by-step explanation:

The function is:

to check witch is true we have to evaluate the function in -1, 1, 1 and 0 so:

for

Given: A matrix

Required: To perform the following matrix row operation

Explanation: The operation is to be applied on the first row of the given matrix. Hence the second row will be same as that of the initial matrix.

The elements of the first row are first multiplied by 3 and then added with second row to give the required matrix.

Hence,

which gives

Final Answer: The required matrix is

Given:

The accumulated value of investment is A = 13,407.58.

The invested amount is P = 12,000.00.

The time period is 4 years and 6 months.

Explanation:

The formula for the accumulated value at r rate of interest is compounded semi-annually.

Substitute the values in the formula to determine the value of r.

So the rate of interest is 2.48%.

We are going to use Binomial Probability Distribution

Probability that they have no landline = q = 27/100 = 0.27

Probability that they have landline = p = 1 - 0.27 = 0.73

Now, to find the probability that at least one of them does not have a landline, we have to find the probability that all the five have a landline first.

So let's find the probability that all the five have a landline:

So the probability that all the five have a landline = 20.73%

Now is the time to find the probability that at least one of them does not have a landline:

P(at least one has no landline) = 1 - P(All have landline)

= 1 - 0.2073

= 0.7927

So the probability that at least one of them does not have a landline = 79.27%

That's all Please

• A ,Reflection

• A ,Vertical Shift 4 units down

1) Considering the parent function, i.e. the simplest form of a family of functions, in this case, to be:

2) Then we can state that this transformed function:

We can see the following transformations:

• A ,Reflection,, pointed out by the negative coefficient

• A ,Vertical Shift 4 units down

As we can see below, to better grasp it:

Answer:

Step-by-step explanation:

A composite function is created when one functions is substituted into another function.

Given:

Therefore,

Now, graphing this function...

the given expression is,

so the answer is option A