Robin invested $1000 in a 12% simple interest savings deposit for 3
years. He also invested an equal amount in a 10% compound interest
savings deposit for 3 years. At the end of 3 years, how much more
interest did he get from the simple interest deposit?

Answer:

a

  [tex]P( \^ p > 0.775 ) = 0.12798[/tex]

b

 [tex]P( 0.6718 < p < 0.775 ) =0.87183[/tex]

Step-by-step explanation:

From the question we are told that

    The population proportion is  [tex]p = 0.75[/tex]

Considering question a  

     The sample size is  [tex]n = 387[/tex]

Generally the standard deviation of this sampling distribution is  

         [tex]\sigma = \sqrt{ \frac{p(1 - p)}{ n } }[/tex]    

=>      [tex]\sigma = \sqrt{ \frac{0.75(1 - 0.75)}{ 387 } }[/tex]    

=>      [tex]\sigma = 0.022[/tex]    

The sample proportion of cans that are recycled is

                 [tex]\^ p = \frac{ 300}{387 }[/tex]

=>              [tex]\^ p = 0.775[/tex]

Generally the probability that 300 or more will be recycled is mathematically represented as

         [tex]P( \^ p > 0.775 ) = P( \frac{\^ p - p }{ \sigma } > \frac{0.775 - 0.75 }{ 0.022} )[/tex]

[tex]\frac{\^ p  - p }{\sigma }  =  Z (The  \ standardized \  value\  of  \ \^ p  )[/tex]

       [tex]P( \^ p > 0.775 ) = P( Z > 1.136 )[/tex]

From the z table  the area under the normal curve to the left corresponding to  1.591   is

      [tex]P( Z > 1.136) = 0.12798[/tex]

=>    [tex]P( \^ p > 0.775 ) = 0.12798[/tex]

Considering question b

Generally the lower limit of  sample proportion of cans that are recycled is

                 [tex]\^ p_1 = \frac{ 260 }{387 }[/tex]

=>              [tex]\^ p_1 = 0.6718[/tex]

Generally the upper limit of  sample proportion of cans that are recycled is

                 [tex]\^ p_2 = \frac{ 300}{387 }[/tex]

=>              [tex]\^ p_2 = 0.775[/tex]

Generally probability that between 260 and 300 will be recycled is mathematically represented as

           [tex]P( 0.6718 < p < 0.775 ) = P( \frac{0.6718 - 0.75 }{ 0.022}< \frac{\^ p - p }{ \sigma } <\frac{0.775 - 0.75 }{ 0.022} )[/tex]

=>      [tex]P( 0.6718 < p < 0.775 ) = P( -3.55 < Z < 1.136 )[/tex]

=>        [tex]P( 0.6718 < p < 0.775 ) = P(Z < 1.136 ) - P( Z < -3.55 )[/tex]

From the z table  the area under the normal curve to the left corresponding to  1.136 and  -3.55  is

       [tex]P( Z < -3.55 ) = 0.00019262[/tex]

and

       [tex]P(Z < 1.136 ) = 0.87202[/tex]

So

       [tex]P( 0.6718 < p < 0.775 ) = 0.87202- 0.00019262[/tex]

=>   [tex]P( 0.6718 < p < 0.775 ) =0.87183[/tex]

Answer:

x ≥ 10 or x ≤ -8

Step-by-step explanation:

2|x - 1| - 3 ≥ 15

Add 3 to both sides;

2|x - 1| ≥ 18

Divide both sides by 2

|x - 1| ≥ 9 or |x - 1| ≤ -9

x - 1 ≥ 9 or x - 1 ≤ -9

Add 1 to both sides;

x ≥ 10 or x ≤ -8

Answer:

The larger wheel is 10979.04098 more than the smaller wheel.

Step-by-step explanation:

Given that,

The circumference of the great wheel was twelve thousand and forty-one thousandth inches.

C = 12000.041 inches

The circumference of the lesser wheel was only one thousand twenty-one and two hundred-thousand inches.

C' = 1021.00002 inches

We need to find how much larger was the great wheel. To find it, take the difference of C and C'.

C-C' = 12000.041 inches - 1021.00002 inches

= 10979.04098 inches

Hence, the larger wheel is 10979.04098 more than the smaller wheel.

Answer:

C

Step-by-step explanation:

The GCF of 18 and 24 is 6. So divide both 18 and 24 individually by six and you get 3 and 4.

Answer:

3/4

Step-by-step explanation:

divide both sides by 6

Answer:

B

Step-by-step explanation:

Only one in which x is not more than one number matching y in function.

The table 4 represent the function.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

The function should have distinct input with corresponding output.

If there are 2 same input vales then it not said to be a function.

So, according the definition the table 4 represent the function because the table 1, 2 and 3 have repeated input value,

Hence, the table 4 represent the function.

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Answer:13

Step-by-step explanation:

7x + 2 = 28 + 5x

subtract 5x on both sides

7x - 5x + 2 = 28

2x = 28 -2

2x = 26

x = 13

if correct mark braliest! :)

hope this helps

Answer:

-7/2 or -3.5

Explanation:

The slope is rise over run.

The rise is how much it went up and the run is how much it went right

The line went up 7 units while going -2 units to the right (meaning it went 2 units to the left)

This makes our slope 7/-2 which is the same as -7/2 or -3.5

Answer:

All of them except for the 3rd one

Step-by-step explanation:

2) 15 - 3x = 5(x + 4) - 8x

15 - 3x = 5x + 20 - 8x

15 - 3x ≠ -3x + 20

4) 2(x - 7) = 2x - 10

2x - 14 ≠ 2x - 10

1) 24x - 22 = -4(1 - 6x)

24x - 22 ≠ -4 + 24x

3) 12 - 2x = 6(2x + 2)

12 - 2x = 12x + 12

0 = 14x

0 = x, only one that has a solution

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the 2 other sides, that is

x² + 6² = 17²

x² + 36 = 289 ( subtract 36 from both sides )

x² = 253 ( take the square root of both sides )

x = [tex]\sqrt{253}[/tex] → C

Answer:

y = 2x + 9

Step-by-step explanation:

The y-intercept: 9

Slope: 2x

-12 * 4= 48 and -12+4= -8

Answer:

x = -2

y = -10

( -2, -10)

Step-by-step explanation:

set them equal

5x = 9x + 8

subtract 9x

-4x = 8

divide by -4

x = -2

plug in x

y = 5(-2)

y = -10

Answer:

I dont know if this is right but I think its 125/343

Answer:

she will need one box to make one gallon. If the question is correct, she will ned one box.

Step-by-step explanation:

Answer:

1. A

2. C

3. B

Step-by-step explanation:

1. we can create an equation y = 48x + 96

if we plug in 1 we get 144

2. we can create an equation y = 10x to represent how much battery you will lose every hour

if we plug in 5 to x, we get y = 50

so we get the plot point: (5, 50)

3. process of elimination

Answer:

37.8

Step-by-step explanation:

Answer:

7x+18

Step-by-step explanation:

add both 4x and 3x to get 7x and add 10 and 8 to get 18. therefore 7x+18

The final expression of (4x + 10) + (3x + 8) is 7x + 18.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(4x + 10) + (3x + 8)

Combine like terms.

4x + 3x + 10 + 8

7x + 18

Thus,

The final expression is 7x + 18.

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Answer:

Because they both have 65 degree angles and are both triangles

Step-by-step explanation:

Answer:

because they have the same bottom degrees

Step-by-step explanation:

Answer:

Where is the question?

Step-by-step explanation:

Answer: 4z + 3

Step-by-step explanation:

Number of books read by Zeke = z

Michelle read twice as many book as Zeke. This will be: = 2 × z = 2z

Tay read 3 more books than Zeke. This will be: = z + 3

The expression that represents the total number of books read over the summer by Zeke, Michelle and Tay would be the addition of the books read by each person. This will be:

= z + 2z + z + 3

= 4z + 3

Answer: is 10

Step-by-step explanation:input :

Changes made to your input should not affect the solution:

(1): "3.4" was replaced by "(34/10)". 4 more similar replacement(s)

STEP

1

:

17

Simplify ——

5

Equation at the end of step

1

:

89 14 65 17

((——-(——•x))+(——•x))+——

10 10 10 5

STEP

2

:

13

Simplify ——

2

Equation at the end of step

2

:

89 14 13 17

((——-(——•x))+(——•x))+——

10 10 2 5

STEP

3

:

7

Simplify —

5

Cannot determine the nature of roots.

The Nature of roots simply means the category in which the roots are falling upon. The roots may be imaginary, real, unequal or equal. If the discriminate is negative, the roots will be imaginary.

The nature of roots of quadratic equations (in the form ax^2 + bx +c=0) we need to calculate the discriminant, which is b^2 - 4 a c. When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real.

The Discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial.

Given that ,

 b2 – 4ac

first we arrange terms in descending order -4ac + 2b

then find discriminant of quadratic equation :Δ =  4

Identify a, b, c through co-efficient:

a = 0

b= -4c

c = 2b

Substitute the value of a, b, c and calculate discriminant

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

Δ = [tex]16c^{2}[/tex] determine number of solutions with discriminant:

Can't determine the nature of roots.

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Answer:

The required inequality is:

[tex]\mathbf{x >60\: and\: x<135}[/tex]

Step-by-step explanation:

Minimum Money students should bring = $60

Maximum Money students should bring= $135

We need to write compound inequality  that  represents the amounts of money a student can bring.

Compound inequalities are combination of two inequalities combined with "and" , and "or"

And is used, when both inequalities should be true.

Or is used when one of the inequality should be true.

In our case we would use and because we need  both inequalities to be true.

The required inequality is:

[tex]\mathbf{x >60\: and\: x<135}[/tex]

Answer:

r = -1

Step-by-step explanation:

-6 + 4r = 2(r - 4)

-6 + 4r = 2r - 8

+6 +6

4r = 2r - 2

-2r -2r

2r = -2

/2 /2

r = -1

hope this helps

Answer:

C. 1 day

Step-by-step explanation:

Chris:

10 - 4d

Evan:

8 - 2d

How many days will it take before they both have the same number of bags remaining?

Equate both expressions and solve

10 - 4d = 8 - 2d

Collect like terms

10 - 8 = -2d + 4d

2 = 2d

Divide both sides by 2

d = 2/2

= 1

d = 1 day

It will take 1 day before they both have the same number of bags remaining

Answer: 255

Step-by-step explanation: