What is the largest amount which can be borrowed over three years at 4.5% APR if the largest
affordable monthly payment is $279? (Round to the nearest ten dollars.)

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Explanation:

Let's say we had a circle with radius 5

It's area would be

A = pi*r^2

A = pi*5^2

A = 25pi

Now let's increase this by a factor of 4. We'll multiply the area by 4

new area = 4*(old area) = 4*(25pi) = 100pi

Now, we'll use this area value to find what the radius must be

A = pi*r^2

100pi = pi*r^2

100 = r^2

r^2 = 100

r = sqrt(100)

r = 10

The old radius r = 5 jumps to r = 10 so that the area quadruples.

We see that the radius has doubled. This must also mean the perimeter around the circle, aka circumference, must also have doubled.

C = 2*pi*r = 2*pi*5 = 10pi = old circumference

C = 2*pi*r = 2*pi*10 = 20pi = new circumference

This is directly because r has been doubled

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Here's one way to think of why this works:

Consider a square of side lengths 3. It's area is 3*3 = 9.

If we double the sides, then we have a 6 by 6 square of area 6*6 = 36.

Note the jump from 9 to 36 is "times 4". This multiplier 4 is from each side doubling and we have 2*2 = 4.

If you were to triple each side, then the area multiplier would be 3*3 = 9

Multiplying each side by k leads to an area multiplier of k^2.

The relative frequency of tails in the experiment is 0.44

In a coin flip; the outcome is either a Head(H) or Tail(T)

Since;

Total number of flips = 50

Number of heads = 28

Number of tails = 50 - 28 = 22

Recall :

Relative frequency = Number of preferred outcome / Total frequency

Hence, the relative frequency of tail will be :

Number of tails / total number of flips = 22 / 50 = 0.44

Therefore, the relative frequency of tails in the experiment is 0.44

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Here we have a problem of relative frequency.

We do know that if you perform a given experiment N times (flipping the coin in this case), and a given outcome happens n times, the relative frequency of that event is:

rf = n/N

With this, we will find that the relative frequency of tails is 0.44

We do know that:

The experiment was performed 50 times, then N = 50

The coin came up heads 28 times.

Then the other 22 times the coin came up tails.

We want to get the relative frequency of tails in this experiment, then we have n = 22

Using the general formula, we can see that:

rf = n/N = 22/50 = 0.44

The relative frequency of tails in this experiment is 0.44

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Answer:

[tex]\boxed {\boxed {\sf 9.8}}[/tex]

Step-by-step explanation:

We are asked to find the distance between two points. We will calculate the distance using the following formula;

[tex]d= \sqrt {(x_2-x_1)^2+(y_2-y_1)^2[/tex]

In this formula, (x₁ , y₁) and (x₂ , y₂) are the 2 points. We are given the points (4,0) and (0,9). If we match the value and the corresponding variable, we see that:

Substitute the values into the formula.

[tex]{d= \sqrt {(0-4)^2+(9-0)^2[/tex]

Solve inside the parentheses.

[tex]d=\sqrt{(-4)^2+ (9)^2[/tex]

Solve the exponents. Remember that squaring a number is the same as multiplying it by itself.

[tex]d= \sqrt{(16)+(81)[/tex]

Add.

[tex]d= \sqrt{97[/tex]

Take the square root of the number.

[tex]d=9.848857802[/tex]

Round to the nearest tenth. The 4 in the hundredth place tells us to leave the 8 in the tenth place.

[tex]d\approx 9.8[/tex]

The distance between the two points (4,0) and (0,9) is approximately 9.8

Given the PMF

[tex]P(X=x) = \begin{cases} 0.3 & \text{if } x \in \{-1, 2\} \\ 0.1 & \text{if } x \in \{0, 7\} \\ 0.2 & \text{if } x = 6 \\ 0 & \text{otherwise} \end{cases}[/tex]

(a)

[tex]P(-1 < X \le 2) = P(X = 0) + P(X = 2) = 0.1 + 0.3 = \boxed{0.4}[/tex]

(b) The CDF is defined as [tex]F_X(x) = P(X \le x)[/tex], so that

[tex]F_X(x) = \begin{cases} 0 & \text{if } x < -1 \\ 0.3 & \text{if } -1 \le x < 0 \\ 0.4 & \text{if } 0 \le x < 2 \\ 0.7 & \text{if } 2 \le x < 6 \\ 0.9 & \text{if } 6 \le x < 7 \\ 1 & \text{if } x \ge 7 \end{cases}[/tex]

It follows that

[tex]F(3.2) = \boxed{0.7}[/tex]

(c) Expectation is defined as

[tex]E[X] = \displaystyle \sum_x x\,P(X=x)[/tex]

We have

[tex]E[X] = \displaystyle \sum_{x\in\{-1,0,2,6,7\}} x\,P(X=x) \\\\ E[X] = -P(X=-1) + 2P(X=2)+6P(X=6)+7P(X=7) \\\\ E[X] = -0.3 + 0.6 + 1.2 + 0.7 = \boxed{2.2}[/tex]

(d) First compute the second moment of X, which is defined as

[tex]E[X^2] = \displaystyle \sum_x x^2\,P(X=x)[/tex]

We get

[tex]E[X^2] = (-1)^2P(X=-1) + 2^2P(X=2) + 6^2P(X=6) + 7^2P(X=7) \\\\ E[X^2] = 0.3 + 1.2 + 7.2 + 4.9 = 13.6[/tex]

Variance is defined as

[tex]\mathrm{Var}[X] = E[(X - E[X])^2] = E[X^2] - E[X]^2[/tex]

so it follows that

[tex]\mathrm{Var}[X] = 13.6 - 2.2^2 = \boxed{8.76}[/tex]

(e) Not sure what this part has to do with the rest of the question. At any rate, if Y is a random variable following a Poisson distribution with λ = 3, then Y has a PDF of

[tex]P(Y=y) = \begin{cases}\dfrac{e^{-3}\times3^y}{y!}&\text{if }y\in\{0,1,2,\ldots\}\\\\0&\text{otherwise}\end{cases}[/tex]

Then

[tex]P(Y > 5) = 1 - P(Y \le 5) = 1 - P(Y=0) - P(Y=1) - \cdots - P(Y=5) \\\\ P(Y>5) = \dfrac{5e^3-92}{5e^3} \approx \boxed{0.0839}[/tex]

Answer:

Blue = y+2 = 3

Red = y+2x = 3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I hope thats correct

Answer:

10n-2

Step-by-step explanation:

12n - 8- 2n + 10 - 4 = (12n-2n)+(-8+10-4)

Simplify.

10n-2

Happy learning!

--Applepi101

Answer:

10n - 2

Step-by-step explanation:

12n-8-2n+10-4

Group all the n together and the other numbers together:

12n-2n-8+10-4

10n-2

Answer:

22/12

Step-by-step explanation:

98-8x=14+12(2-5x)

98-8x=14+24-60x

-8x +60x=10-9

52x=88

x=22/13

Answer:

X =  1

Step-by-step explanation:

Just distribute properly, and distribute the fraction multiplying the numerator by 4 and 2

Answer:

[tex]3(2x - 1) = 1 \div 2(4x - 2) + 2 \\ 3 \times 2x - 3 \times 1 = .5 \times 4x - .5 \times 2 + 2 \\ 6x - 3 = 2x - 1 + 2 \\ x \: togather \\ 6x - 2x = - 1 + 2 + 3 \\ 4x = 4 \\ x = 4 \div 4 \\ x = 1[/tex]

Answer:

6x-8

Step-by-step explanation:

less  than means it comes after

product of 6 and a number x

6x

8 less than

6x-8

Answer associative

Step-by-step explanation:

9514 1404 393

Answer:

  119°

Step-by-step explanation:

Angles DHG and LHI are vertical angles, so have the same measure.

  angle LHI = 119°

Answer:

its very blury im sooooo sorry

Step-by-step explanation:

Answer:

[tex] - 3x(x - 4) + 2 - (5 - x) \\ = - 3 {x}^{2} + 12x + 2 - 5 + x \\ = - 3 {x}^{2} + 13x - 3[/tex]

I hope I helped you^_^

Answer: C

Step-by-step explanation:

This is 3 times 10 times 6, not 3 times the sixth power of 10.

Answer:

[tex]x = \frac{2}{65} [/tex]

Step-by-step explanation:

[tex]19 = - 4 + \frac{2}{5x} + 10[/tex]

[tex]19 = 6 + \frac{2}{5x} [/tex]

[tex] - \frac{2}{5x} = 6 - 19[/tex]

[tex] - \frac{2}{5x} = - 13[/tex]

[tex]2 = 65x[/tex]

[tex]x = \frac{2}{65} [/tex]

Answer:

Step-by-step explanations

I don’t know

Answer: Yes it is.

Step-by-step explanation:

Mixed to proper

7/3 = 2 1/3

Answer:

(I got your back pal) Your answer is -41/21

Can you give me a brainlest it would help me a lot

Answer: Most likley F - 24

Step-by-step explanation:

Each student has a 1/4 chance of getting a job and only 4 ppl get picked.

Each student has 4 jobs each since the change each job. (kinda hard to explain)

4 jobs each student (6) =

= 4x6

= 24.

Answer:

Choice a. [tex]35[/tex]

Step-by-step explanation:

Note that [tex]i=(1,0)[/tex] and [tex]j=(0,1)[/tex], so

[tex]C=2A-B=2(6i-8j)-(-16i+5j)=12i-16j+16i-5j=28i-21j=(28,-21)[/tex]

Now the magnitude of a vector [tex](x,y)[/tex] is [tex]\sqrt{x^2+y^2}[/tex], thus the magnitude of [tex]C[/tex] is

[tex]\sqrt{28^2+(-21)^2}=\sqrt{784+441}=\sqrt{1225}=35[/tex]

Answer:

the answer is 20

Step-by-step explanation:

gtttttfftuuu

Answer:

Here is your answer. Hope this helps you!

Answer:

one side is 137/4 and other is 3/4

Step-by-step explanation:

all steps are in picture

Answer:

x ≤ 11/6   or   x > 11/3

Step-by-step explanation:

6x - 2 ≤ 9 or 4 + 3x > 15

6x ≤ 11    or  3x > 11

x ≤ 11/6   or   x > 11/3

The given inequality is simplified as x≤11/6 or x>4.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, 6x-2≤9 or 4+3x>15.

Here, 6x-2≤9

Add 2 on both the sides of an inequality, we get

6x≤11

Divide 6 on both the sides of an inequality, we get

x≤11/6

Now, 4+3x>15

Subtract 4 on both the sides of an inequality, we get

3x>12

Divide 3 on both the sides of an inequality, we get

x>4

So, x≤11/6 or x>4

Therefore, the given inequality is simplified as x≤11/6 or x>4.

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Answer: The answer is 35.43 feet rounded to the nearest hundredth.

Step-by-step explanation:  

Answer:

The answer is 35.43 feet rounded to the nearest hundredth.

Step-by-step explanation:

If it is a square and the area is 1,255, the width and height of the square is the same. Find the square root of 1,255 and it will give you the length of the height and width (they are both the same being a square).