Sophie invested $93,000 in an account paying an interest rate of 5.6% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $170,500?

Answer:

Step-by-step explanation:

You want to set up a system. We are given some points fo we can set up inputs and outputs. F(0) = 5, given by point (0,5). and F(3)=135, given by point (3,135). The exponential function general equation is F(x)= a(b)^x. plug in out functions into the general equation to get a(b)^0=5 and a(b)^3=135. Then you simplify and solve for a. In the equation a*b^0=5, anything to the power of 0 is 1. so a*1=5. Therefore a=5. we plug in the a to the second equation to find b. 5*b^3=135. b^3=27. b=3 from simplifying. Therefore, the equation should be 5(3)^x. THATS IT!

Answer:

Shirt A, Skirt A, Shoe A

Shirt A, Skirt A, Shoe B

Shirt A, Skirt B, Shoe A

Shirt A, Skirt B, Shoe B

Shirt A, Skirt C, Shoe A

Shirt A, Skirt C, Shoe B

The number of ways Natalie has to choose outfits for her first day school is 28 ways.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Given that, Natalie is trying to pick out an outfit for the first day of school. She can choose from 7 pairs of pants, 2 t-shirts, and 2 pairs of shoes.

Let 7 pairs of pants be P1, P2, P3, P4, P5, P6 and P7.

Let 2 t-shirts be T1 and T2

Let 2 pairs of shoes be S1 and S2

Now,

1) P1, T1, S1                                      

2) P1, T2, S2

3) P2, T1, S1

4) P2, T2, S2

5) P3, T1, S1

6) P3, T2, S2

7) P4, T1, S1

8) P4, T2, S2

9) P5, T1, S1

10) P5, T2, S2

11) P6, T1, S1

12) P6, T2, S2

13) P7, T1, S1

14) P7, T2, S2

15) P1, T1, S2                                      

16) P1, T2, S1

17) P2, T1, S2

18) P2, T2, S1

19) P3, T1, S2

20) P3, T2, S1

21) P4, T1, S2

22) P4, T2, S1

23) P5, T1, S2

24) P5, T2, S1

25) P6, T1, S2

26) P6, T2, S1

27) P7, T1, S2

28) P7, T2, S1

Other way = 7×2×2

= 28 ways

Therefore, the number of ways is 28 ways.

To learn more about the permutation visit:

https://brainly.com/question/3867157.

#SPJ3

The cross-section cut by the plane yields a quadrilateral with length and width equal to the length and width of the face that is parallel to the plane.

Answer:

Step-by-step explanation:

8

Answer: x=16

Step-by-step explanation:

2x+4=36

Subtract 4 from both sides and get

2x=32

Divide both sides by 2 to isolate x and you get

x=16

Answer:

The popsicle stick is 11 and 6/10 inches and 4.9 centimeters.

The pencil is 7 and 3/10 inches and 2.14 centimeters.

The paperclip is 6 and 3/10 inches and 2.8 centimeters.

Step-by-step explanation:

Just look at where the red dotted lines are

hope this helps

Answer:

Step-by-step explanation:

4. odd number, odd number

5. 2, 3

6. 1, 3

7. 7, 1

Answer:

,,,,,,,,,,,,,,,,,,,,,

Answer: 6 tenths

Step-by-step explanation:

3/5 = 6/10 (multiply by 2)

Answer:

the expresion its equal at the d9feremce between you and the excercise so its 7

Answer:12x+8y

Step-by-step explanation:Simplify the expression

The expression equivalent to 4(3x+2y) is 12x +8y.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Create an expression equivalent to 4(3x+2y).

The equivalent expression is determined in the following steps given below.

[tex]\rm =4(3x+2y)\\\\=4 \times 3x+4\times 2y\\\\=12x+8y[/tex]

Hence, the expression equivalent to 4(3x+2y) is 12x +8y.

Learn more about equivalent expression here;

https://brainly.com/question/14735698

#SPJ2

The answer would be 30°.

I believe the answer is B) 6/81

Answer:

The answer is 4ws - 12

Step-by-step explanation:

1) Collect like terms.

[tex]4ws + (4 - 16)[/tex]

2) Simplify.

[tex]4ws - 12[/tex]

therefor, the answer is 4ws - 12.

Answer:

45

Explanation:

No explanation

Answer:

(-3,3)

Step-by-step explanation:

Using elimination:

Multiply the first equation by 8 and the second by 5 which equals

40x+56y=48

-40-60y=-60

Now you add them together

40x+(-40x)=0 so that crosses out

56y+(-60y)= -4y

48+(-60)=-12

You now have -4y=-12

Divide by -4

y=3

Now plug in y to any of the equations

5x+7(3)=6

5x+21=6

Subtract 21 from both sides

5x=-15

Divide by 5

x=-3

Your final solution is (-3,3)

The amplitude of the function is the range A = 3

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the amplitude of the function be represented as A

Now , the value of A is

The range of the function = Amplitude x 2

And , Amplitude of the function A = | max - min | / 2

On simplifying , we get

A = | -4 - 2 | / 2

A = 6/2

A = 3

Therefore , the value of A is 3

Hence , the amplitude is A = 3

To learn more about domain and range click :

https://brainly.com/question/28135761

#SPJ2

Answer:

Well theres Texas of course then Taxes..then i dont know any more that make sense

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☁Brainliest is greatly appreciated☁

Hope this helps!!

- Brooklynn Deka

There are 120 ways to arrange 5 letter wor with each letter is used only once.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.

Here, 5 letters are arranged in 5! ways

         5! = 5 X 4 X 3 X 2 X 1

             = 120

Thus, there are 120 ways to arrange 5 letter wor with each letter is used only once.

Learn more about Permutations from:

https://brainly.com/question/1216161

#SPJ2

Answer:

x = 11

x = 7

Step-by-step explanation:

divide each side by 3 to get:

(x-4)² = 9

(x-4)² is the difference of two squares and has these factors:

(x+2)(x-2) = 9

x + 2 = 9;  x = 7

x - 2 = 9;  x = 11

Answer:

Step-by-step explanation:

Correct choice is C or orange tile

Answer:

x = -4y

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

f(x) = 4x + 7

so

f(a + h) = 4(a + h) + h

          = 4a + 4h +h

          = 4a + 5h

f(a) = 4a + 7

now by the question

[tex]\frac{f(a+h) - f(a)}{h}\\=\frac{4a + 5h - 4a + 7}{h}\\=\frac{ 5h + 7}{h} \\= \frac{5h}{h} + \frac{7}{h} \\= 5 +\frac{7}{h}[/tex]

hope it helps :)

Answer:

C,D,E,F

Step-by-step explanation:

A amplitude is 2

B period is 4pi

Answer:

f option is write

Step-by-step explanation:

because it is true

mark me brainlist

Answer:

8cm & 514 squared are correct answers

Step-by-step explanation:

Answer:

25

100

55

Step-by-step explanation:

Givens

Let the first angle = x

Let the second angle = 4x

Let the third angle = 2x + 5

All triangles have 180

Equation

x + 4x + 2x + 5 = 180

Solution

Begin by combining like terms

7x + 5 = 180

7x = 180 - 5

7x = 175

7x/7 = 175/7

x = 25

Answer

First angle = x    =          25

Second angle = 4x =    100

Third angle = 2x + 5 =    55

Total                               180

Answer:

24

Step-by-step explanation:

Answer:

[tex] {3}^{2} [/tex]

Step-by-step explanation:

♡ Good Lessons ♡

Answer:

it's indices tho so you'll use addition/subtraction rule