Billy took out a 15 year loan with a principal of $25,000. He made monthly payments of $250 for the entire period, at which point the loan was paid off. How much did Sam pay in interest?
1. $20,000
2. $40,000
3. $30,000
4. $10,000

Answer:

10

Step-by-step explanation:

You have to look at the corresponding length of each figure i.e. 9 on figure A and 90 on figure B. You then divide the numbers from each other

90 ÷ 9 = 10

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

Answer:

The given equations are;

y = a·(x - h)² + k or y = a·x² + b·x + c

We have;

(x - h)² = 4·p·(y - k),

Where;

(h, k) are the x, and y coordinates of the vertex

p = The distance from the focus to vertex distance;

Comparing, we have;

y - k = a·(x - h)²

(y - k)/a = (x - h)²

(x - h)² = 4·p·(y - k)

4·p·(y - k) = (x - h)²

∴ 4·p = 1/a

p = 1/(4·a)

Therefore, the focus to vertex distance inversely proportional to the value of a

The distance of every point on the parabola is equidistant from the directrix and the focus

Therefore, the equation of the directrix is y = k - p

For example, we have;

y = 2·x² + 3·x + 1

h = -b/2a = -3/4

k = (4ac - b²)/4a = (4×2×1 - 3²)/(4×2) = -1/8

The coordinate of the focus is (h, k + p) = (-3/4, -1/8 + 1/8) = (-3/4, 0)

The directrix, y = k - p = -1/8 - 1/8 = -1/4

For a point x = 2, we have, y = 2·2² + 3·2 + 1 = 15

The coordinate of the point is (2, 15)

The distance of the point from the directrix = 15 - (-1/4) = 15 + 1/4 = 15.25

The distance of the point from the focus is √((2 - (-3/4))² + (15 - 0)²) = 15.25

Therefore, all points on the parabola have equal distances from the focus and the directrix

Step-by-step explanation:

The total that Tony has is 1465 while Gene has a total of 1565, hence they are not equivalent.

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

14 hundreds, six tens, and 5 ones = 14(100) + 6(10) + 5(1) = 1465

1 thousand, 4 hundreds, 16 tens. and 5 ones = 1(1000) + 4(100) + 16(10) + 5(1) = 1565

The total that Tony has is 1465 while Gene has a total of 1565, hence they are not equivalent.

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Answer:

Step-by-step explanation:

Gene has more, also, by the way, aren't you in my school? Do you know Ezekiel?

The equation represents the total cost of turkey and amount is y= 3.25x.

We have,

The turkey costs $3. 25 per pound.

let x be the amount in pounds and y be the total cost in dollar.

Then, the relation between x and y

Total cost = 3.25 (amount in  poind)

y = 3.25 x

Thus, the required equation is y= 3.25x.

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Answer:

\(52.8cm^{2}\)

Step-by-step explanation:

Perimeter = 26.4 cm

Apothem = 4.0 cm

The area of an regular octagon can be defined as the \(\frac{perimeter*apothem}{2}\)

when we plug in our values we get the equation \(\frac{26.4cm*4.0cm}{2}=52.8cm^{2}\)

Answer:

7 workers

Step-by-step explanation:

\(\frac{workers first time}{workers second time} = \frac{hours second time}{hours first time}\)

\(\frac{3}{x} = \frac{12}{28}\)

cross multiply and it becomes

12x = 3x28

12x = 84

x = 84/12

x = 7 workers

Answer

4

Step-by-step explanation:

3/28=x/12

that is 7 and you need to find how many more workers so you subtract

7-3=4

Answer:

Lesser = -\(\sqrt{11}\) - 7 = -10.317

Greater = +\(\sqrt{11}\) - 7 = -3.683

Step-by-step explanation:

I am assuming you are asking for the lesser x solution and greater x solution.

(x + 7)^2 – 11 = 0

(x + 7)^2 = 11

x+7 = ±\(\sqrt{11}\)

x = ±\(\sqrt{11}\) - 7

Lesser = -\(\sqrt{11}\) - 7 = -10.317

Greater = +\(\sqrt{11}\) - 7 = -3.683

Answer:

lesser= -14

greater= 0  (:

The problem involves determining the average temperature of a cup of coffee during the first 18 minutes using Newton's Law of Cooling. The temperature function is given as \(T(t) = 22 + 67e^(-t/47)\), where t represents time in minutes.

To find the average temperature of the coffee during the first 18 minutes, we need to calculate the integral of the temperature function over the interval [0, 18] and divide it by the length of the interval.

The average temperature is given by the formula:

Average Temperature =\((1/b - a) ∫[a to b] T(t) dt\)

In this case, the temperature function is T(t) = 22 + 67e^(-t/47), and we want to find the average temperature over the interval [0, 18]. Therefore, we need to evaluate the following integral:

Average Temperature \(= (1/18 - 0) ∫[0 to 18] (22 + 67e^(-t/47)) dt\)

To calculate the integral, we can use the antiderivative of e^(-t/47), which is -47e^(-t/47).

The integral becomes: Average Temperature = \((1/18) [22t - 67(-47e^(-t/47))]\) evaluated from 0 to 18

Evaluating the integral over the interval [0, 18], we can compute the average temperature of the coffee during the first 18 minutes.

By performing the necessary calculations, we can determine the numerical value of the average temperature during the first 18 minutes.

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Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

Answer:

\(\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}\)

Step-by-step explanation:

Fundamental Theorem of Calculus

\(\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))\)

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

\(\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x\)

Take partial fractions of the given fraction by writing out the fraction as an identity:

\(\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}\)

Calculate the values of A and B using substitution:

\(\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}\)

\(\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}\)

Substitute the found values of A and B:

\(\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x\)

\(\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}\)

If the terms are multiplied by constants, take them outside the integral:

\(\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x\)

\(\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}\)

\(\implies \dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}\)

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For an alternative approach, expand and complete the square in the denominator to write

\((x-4)(x+2) = x^2 - 2x - 8 = (x - 1)^2 - 9\)

In the integral, substitute \(x - 1 = 3 \sin(u)\) and \(dx=3\cos(u)\,du\) to transform it to

\(\displaystyle \int \frac{x+5}{(x - 1)^2 - 9} \, dx = \int \frac{3\sin(u) + 6}{9 \sin^2(u) - 9} 3\cos(u) \, du \\\\ ~~~~~~~~~~~~ = - \int \frac{\sin(u) + 2}{\cos(u)} \, du \\\\ ~~~~~~~~~~~~ = - \int (\tan(u) + 2 \sec(u)) \, du\)

Using the known antiderivatives

\(\displaystyle \int \tan(x) \, dx = - \ln|\cos(x)| + C\)

\(\displaystyle \int \sec(x) \, dx = \ln|\sec(x) + \tan(x)| + C\)

we get

\(\displaystyle \int \frac{x+5}{(x - 1)^2 - 9} \, dx = \ln|\cos(u)| - 2 \ln|\sec(u) + \tan(u)| + C \\\\ ~~~~~~~~~~~~ = - \ln\left|\frac{(\sec(u) + \tan(u))^2}{\cos(u)}\right|\)

Now, for \(n\in\Bbb Z\),

\(\sin(u) = \dfrac{x-1}3 \implies u = \sin^{-1}\left(\dfrac{x-1}3\right) + 2n\pi\)

so that

\(\cos(u) = \sqrt{1 - \dfrac{(x-1)^2}9} = \dfrac{\sqrt{-(x-4)(x+2)}}3 \implies \sec(u) = \dfrac3{\sqrt{-(x-4)(x+2)}}\)

and

\(\tan(u) = \dfrac{\sin(u)}{\cos(u)} = -\dfrac{x-1}{\sqrt{-(x-4)(x+2)}}\)

Then the antiderivative we found is equivalent to

\(\displaystyle - \int \frac{x+5}{(x - 1)^2 - 9} \, dx = - \ln\left|-\frac{3(x+2)}{(x-4) \sqrt{-(x-4)(x+2)}}\right| + C\)

and can be expanded as

\(\displaystyle - \int \frac{x+5}{(x - 1)^2 - 9} \, dx = -\ln\left| \frac{3(x+2)^{1/2}}{(x-4)^{3/2}}\right| + C \\\\ ~~~~~~~~~~~~ = - \ln\left|(x+2)^{1/2}\right| + \ln\left|(x-4)^{3/2}\right| + C \\\\ ~~~~~~~~~~~~ = \boxed{\frac32 \ln|x-4| - \frac12 \ln|x+2| + C}\)

Answer:

The Zero Product Property simply states that if ab=0 , then either a=0 or b=0 (or both). A product of factors is zero if and only if one or more of the factors is zero. This is particularly useful when solving quadratic equations .

Step-by-step explanation:

Answer:

Answer. Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units.

Step-by-step explanation:

Answer. Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units.

The likelihood of randomly selecting a terrier from the shelter would be unlikely. That is option B

The formula that can be used to determine the probability of a selected event is given as follows;

Probability = possible event/sample space.

The possible sample space for terriers = 15%

Therefore the remaining sample space goes for Labradors and Golden Retrievers which is = 75%

Therefore, the probability of selecting the terriers at random is unlikely when compared with other dogs.

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Answer:

11

Step-by-step explanation:

If n=7, you would substitute n in the equation with 7.

h=7+4

h=11

Answer:

h=11

Step-by-step explanation:

h = n + 4

but n = 7

h = 7 + 4

h=11

Answer:

z=56

Step-by-step explanation:

trust me

z=56  pay attention in school‍

Answer:

n ≥ 10

Step-by-step explanation:

Given

8 + 3n ≥ 38 ( subtract 8 from both sides )

3n ≥ 30 ( divide both sides by 3 )

n ≥ 10

Answer:

25

Step-by-step explanation:

PLS GIVE BRAINLIEST

Answer:

25

Step-by-step explanation:

PLEASE GIVE ME BRAINLEIST

Answer:

Range: 22

Median: 79

Mode: 80

Step-by-step explanation:

I hope this helped and have a nice day! Also can I have brainliest?

Answer:

ranalllldooo

Step-by-step explanation:

suiiiiiii

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as small as that provided by the sample

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

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Answer:

0.00676

Step-by-step explanation:

Answer:

I did the math, and I think it is .00676. Hope this helps!

Step-by-step explanation:

Answer:

(-3,2) is located in the solution region.

Step-by-step explanation:

Answer:

4 days

Step-by-step explanation:

First Convert minutes to Hours

5760/60=96 Hours

Then convert hours to days

96 Hours/24 = 4 days

the given expression is,

so the factors are (3v - 7) (v + 1)

the given equation is,

so the answer is

(3v-7)(v+1)

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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Answer:

fuel

Step-by-step explanation:

Josh j.g dhbsnsnjsnsheuwbb

Answer:

its the third one more girls than boys!!

Step-by-step explanation: