You decide that you want to purchase a Tesla SUV. You borrow $95,000 for the purchase. You
agree to repay the loan by paying equal monthly payments of $1,200 until the balance is paid off. If
you're being charged 6% per year, compounded monthly, how long will it take you to pay off the
loan?

Answer: The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter . The incircle touches each side of the triangle

Answer:

13. Answer: 0

17. Answer: 3

19. Answer: 2

Step-by-step explanation:

13. f(g(3))

First find g(3) on the right graph.

We see that at x = 3, g(x) = 4

So g(3) = 4

Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer

17.f(f(5))

f(5) = 1

f(f(5)) = f(1) = 3 answer

19. g(g(2))

g(2) = 0

g(g(2)) = g(0) = 2 answer

Answer:

Step-by-step explanation: Hey for the second one I got y = -3/4x -0.5 I'm not sure if its correct though sorry if not
ill try my best to explain my solution though
1. From the parallel equation (3x + 4y = 12) all we need to do is find the slope

So the easiest way to do so is to put the said equation in y-intercept form

y=mx +b
m= slope

b= y intercept

so 1. 3x + 4y = 12

=

4y = 12-3x

divide that by 4 to get only y

y=3-3/4x

-3/4 is our slope

y=-3/4x+b

than we have a point -2, -2

if we put -2 for y

-2=-3/4x+b

and then we put our -2 for x
-2 = -3/4 * -2 + b

=

-2  = -1.5 +b
b=-0.5

Answer : y=-3/4x-0.5

Answer:

302.5

Step-by-step explanation:

5 1/2 = 5.5

55 miles per hour * 5.5 hours

55*5.5

302.5

Part 1: Devon is able to contribute (a) $450 each month to a retirement plan.

a. The amount in Devon's retirement account if she makes the same monthly investment for 40 years is $733,253.26.

b. Overall, Devon's total contribution of her own money into the retirement account is $216,000.

c. The percent of the final balance in Devon's retirement account that was interest was 70.5%.

Part 2: Taylor will invest (b) $1,733.00 per month.

a. The amount that will be in Taylor's retirement account if she makes the same monthly investment for 20 years is $733,253.26.

b. By the time that Taylor retires, she will have contributed $415,920 of her own money into the account.

c. The percent of the final balance in Taylor's retirement account that will be interest is 43.3%.

3. Both Devon and Taylor had the same amount, $733,253.26, in their retirement accounts when they planned to retire.

a. None had more money at their retirement.

b. Taylor contributed more to her retirement account by $199,920 ($414,920 - $216,000).

Gross monthly income = $4,500

APR = 5.25% compounded monthly

N (# of periods) = 480 months (12 x 40 years)

I/Y (Interest per year) = 5.25%

PV (Present Value) = $0

PMT (Periodic Payment) = $450 ($4,500 x 10%)

Results:

FV = $733,253.26 ($517,253.26 + $216,000)

Sum of all periodic payments = $216,000 ($450 x 480)

Total Interest = $517,253.26

Percentage of interest out of the FV = 70.5% ($517,253.26/$733,253.26 x 100)

N (# of periods) = 240 months (12 x 20 years)

I/Y (Interest per year) = 5.25%

PV (Present Value) = $0

FV (Future Value) = $733,253.26

Results:

PMT = $1,733.00

Sum of all periodic payments = $415,920 ($1,733 x 240

Total Interest = $317,333.26

Percentage of interest out of the FV = 43.3% ($317,333.26/$733,253.26 x 100)

Thus, based on the time value of money of investments, it is more profitable to start investing early.

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g(x) is a translation of 6 units downwards.

Here we have the function:

y = f(x) = 3x + 1

Notice that the y-intercept of f(x) is:

f(0) = 3*0 + 1 = 1

The y-intercept of f(x) is y = 1.

Now, we know that the y-intercept of g(x) is -5. then:

g(x) = 3x - 5 = f(x) - 6

Meaning that g(x) is a translation of 6 units downwards.

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Answer:

translated 2

units up

g(x)= f(x-2)

Step-by-step explanation:

The two curves intersect when [tex]y=0[/tex] and [tex]y=1[/tex]. Over the range [tex]0\le y\le1[/tex], the curve [tex]x=12y^2[/tex] lies above [tex]x=12y^3[/tex]. Hence the area of the shaded region is

[tex]\displaystyle \int_0^1 (12y^2 - 12y^3) \, dy = 4y^3 - 3y^4\bigg|_0^1 = (4-3)-(0-0) = \boxed{1}[/tex]

Answer:9

Step-by-step explanation:1+2=3 6/2=3

3x3=9

Answer:

1/6

Step-by-step explanation:

You have six choices and you want to pick only 1 of those choices.

1/6

[tex]\displaystyle\frac{1}{6}[/tex]

Probability explains the likelihood of an event occurring. The outcome you are finding the probability for is the successful outcome. The sample size is the total number of possible outcomes.

Simple Probability

Simple probability is when there is only one single event. In this situation, the cube is only being rolled once, so it's a simple probability question. To solve this question as a fraction, the numerator should be the number of successful outcomes and the denominator should be the sample size.

Solving for P(B)

Since there are 6 sides with 6 letters, the sample size is 6. So, 6 should be the denominator. We are finding the probability of "B", which means there is 1 successful outcome. Thus, the numerator should be 1.

This means as a fraction the probability is [tex]\frac{1}{6}[/tex].

First find volume of both the cylinders:

Cylinder Volume Formula: πr²h

(r => radius, h => height)

*Container A:

r = 8

h = 15

πr²h = π(8)²(15) = 960π³

*Container B:

r = 11

h = 13

πr²h = π(11)²(13) = 1573π³

What % of container B is empty after the pumping is complete?

The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:

[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)

Hope it helps!

The point estimate of difference of the sample his will be -20.

Based on the information given, the. following can be depicted:

n1 = 13

x1 = 141

s1 = 13

n2 = 9

x2 = 161

s2 = 12

The point estimate of difference will be:

= 141 - 161

= -20

The margin of error to be used in constructing the confidence interval will be calculated by multiplying the standard error which is 5.467 and the critical value. This will be:

= 5.467 × 2.528

= 13.822

The margin of error is 13.822.

The confidence interval will now be:

= (-20 + 13.822) and (-20 - 13.822)

= -6.178 and -33.822

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It should be noted that organization was important in the thought process and calculation for an accurate solution.

It should be noted that problem-solving enables us to identify and exploit opportunities in the environment and exert control over the future.

In this case, problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations

Also, good problem solving activities provide an entry point that allows all students to be working on the same problem.

In this case, the open-ended nature of problem solving allows high achieving students to extend the ideas involved to challenge their greater knowledge and understanding and problem solving develops mathematical power.

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Answer:

135

Step-by-step explanation:

Then add the first and last number i.e.

433+107===> 540

divide 540 by 4

540/4

= 135

Answer:

134

Step-by-step explanation:

-107/4 = -26.75

429/4 = 107.25

107.25 - (-26.75)

107.25 + 26.75 = 134

Based on the number of students at Roxas Middle School and the number of students studying Chinese and Spanish, the number of students who study Spanish is 182 students.

The first thing to do is to find out the number of students who are studying either Spanish or Chinese:

= Total number of students - Students studying both Spanish and Chinese

= 374 - 100

= 274 students

Then, assuming the number of students studying Chinese alone is x, the expression to find them would be:

274 = 2x + x

Solving gives:

2x + x = 274

3x = 274

x = 274 / 3

x = 91 students

The number studying Spanish is twice this number so will be:

= 91 x 2

= 182 students

In conclusion, there are 182 student studying Spanish.

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Answer:

Step-by-step explanation:

Option C.

Step-by-step explanation:

Initial number of clients = 18

Number of Increase per week = 4

We need to use an arithmetic sequence to write a function.

So, the required arithmetic sequence for four weeks is

18, 22, 26, 30

Here, first term is 18 and common difference is 4. The range is  [18,30].

The explicit formula of n arithmetic sequence is

where, a is first term and d is common difference.

Substitute a=18 and d=4 in the above formula.

The function notation is

The function is f(x)=4x+14 and the range is  18 ≤ y ≤ 30.

Therefore, the correct option is C.

Answer:

92 degrees

Step-by-step explanation:

The sum of the exterior angles will be 360.  

67 x 4 = 268.  That means that the last angles must be 92 (360 - 268)

Step-by-step explanation:

sqrt(120) / sqrt(30) = sqrt(120/30) = sqrt(4) = 2

The quotient of √120 divided by √30 is 2.

Square root of a number is the value such that the value when multiplied to itself two times gives the original number.

It is denoted by the symbol √.

For example, square root of 16 is 4 since 4 × 4 = 16

The given numbers are √120 and √30.

We have to find the quotient when √120 is divided by √30.

Try to write each of the number as a product of perfect squares if possible.

√120 = √(4 × 30)

We know that √(ab) = √a √b

So, √120 = √4 × √30 = 2√30      (∵√4 =2)

√120 /√30 = 2√30 / √30 = 2    

Hence the required quotient is 2.

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Answer:

  263.08 m²

Step-by-step explanation:

The fraction of circle area that a sector represents is proportional to the central angle.

  circle area/circle angle = sector area/sector angle

  circle area / 360° = 85.5 m² / 117°

Multiplying by 360°, we have ...

  circle area = (360/117)(85.5 m²) = 263.08 m²

The area of the circle is about 263.08 m².

Answer:

(a - b)(a + b)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )

Step-by-step explanation:

by repeated use of the difference of squares factorising method, that is

a² - b² = (a - b)(a + b)

given

[tex]a^{8}[/tex] - [tex]b^{8}[/tex]

= ([tex]a^{4}[/tex] )² - ([tex]b^{4}[/tex] )²

= ([tex]a^{4}[/tex] - [tex]b^{4}[/tex] )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis using difference of squares

= ( a² - b²)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis by difference of squares

= (a - b)(a + b)(a² + b² )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )

The  techniques that can be used to best explain for each equation that I have created are:

A)  For  graphing -  This is often used in checking if your answer is correct, if the math is known to be a little tedious, graphing is recommended

(b) For factoring:  x^2 -3x +4 '

Where: (x-4)(x+1)=0

Then x=-1, 4

(c) For  square root method:   x^2 = 64

Therefore x = + or - [tex]-\sqrt{64}[/tex] = + or - 8

(d) For  completing the square:  x^2 + 4x = 11 and x^2 +4x + 4

Note that:  x^2 +4x + 4

= x^2 + 4x = -4

= x^2 +4x + 4 = -4 + 4

= (x+2)^2 = 0

So, x = -2

(e) For quadratic formula: 6x² + 7x -19 =0  

x= [-b + or - sqr(b² - 4ac)]/2a

Note that b=7

a=6

c=-19

Therefore

x= [-7+ or - sqr(49+4(6)(9)]/2

2.  if the discriminant is said to be negative,   then the equation is one that is made up of two imaginary or complex solutions.

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See full question below

You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.

a. graphing

b. factoring

c. square root method

d. completing the square

e. quadratic formula

2. What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?

The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:

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There is no answer because there cannot be one to one function inverse.

Answer:

129792

Step-by-step explanation:

         156

     ×  832

    ----------

         312

      468

+  1248

---------------

  129792

Answer:

  3.9¢ per cup per week

Step-by-step explanation:

Revenue is the product of price and quantity sold. The rate of change in any of these quantities can be found by solving the derivative equation at using the given values.

Revenue (r) is the product of price (p) and quantity sold (q):

  r = pq

Differentiating with respect to time, we have ...

  r' = p'q +pq'

The values given for the problem are ...

Using the above derivative relation, we have ...

  0 = p'(50) +39(-5) . . . . . . fill in given values

  p' = 195/50 = 3.9 . . . . . . add 195, divide by 50

The price must be raised at the rate of 3.9 cents per week to maintain unchanging revenue.

The functions, q(x) and r(x) are defined as 2•x + 1, and -5•x - 3, respectively, therefore;

[tex] \: (q \: \circ \: r) (1)= - 15[/tex]

[tex] \: (r \: \circ \: q) (1)= -18[/tex]

The given functions are;

q(x) = 2•x + 1

r(x) = -5•x - 3

The evaluation of the composite functions can be presented as follows;

[tex](q \: \circ \: r) (x)= q(r(x))[/tex]

Therefore;

[tex](q \: \circ \: r) (1)= q(r(1))[/tex]

Which gives;

[tex](q \: \circ \: r) (1)= q( - 8)[/tex]

q(-8) = 2×(-8) + 1 = -15

Therefore;

[tex](q \: \circ \: r) (1)= - 15[/tex]

Similarly, we have;

[tex](r \: \circ \: q) (1)= r(q(1))[/tex]

q(1) = 2×1 + 1 = 3

r(3) = -5×3 - 3 = -18

Which gives;

[tex](r \: \circ \: q) (1)= -18[/tex]

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Answer:

OB:.242.T gives it's area in square inches

Answer:

[tex](2,-1.5)[/tex]

Step-by-step explanation:

The midpoint formula goes as follows:

[tex](x,y)=(\frac{x1+x2}{2} , \frac{y1+y2}{2})[/tex]

Lets plug in our values, let x1 be -3, x2 be 7, y1 be 2, y2 be -5.

[tex](\frac{-3+7}{2} , \frac{2+-5}{2})[/tex]

Solve numerators

[tex](\frac{4}{2} , \frac{-3}{2})[/tex]

Solve

[tex](2 , -1.5)[/tex]

Therefore the midpoint must be at [tex](2,-1.5)[/tex]

Answer: 8.7 the mean is 20

Step-by-step explanation: