Marcie conducts an experiment with a bag of marbles. She draws one marble from the bag, records its color, returns the marble to the bag, and draws again. The results of her experiment are shown below.

Marble Color Number of
Times Drawn
red 5
blue 6
green 4
purple 1
yellow 4
Based on Marcie’s experiment, what proportion of the marbles in the bag would she expect to be purple?

A.
20%
B.
5%
C.
1%
D.
10%

Answer:

>> Null hypothesis; H0: μ1 - μ2 ≥ 0

Null hypothesis; Ha: μ1 - μ2 < 0

>> z = 1.85

>> p-value = 0.03

>> there is evidence sufficient to reject the claim that average weekly food expenditure of households in City 1 is more than that of households in City 2.

The economist claim is not supported by data.

Step-by-step explanation:

We are given;

Sample mean of city 1; x1¯ = 164

Sample mean of city 2; x2¯ = 159

Sample size of city 1; n1 = 35

Sample size of city 2; n2 = 30

Standard deviation of city 1; σ1 = 12.5

Standard deviation of city 2; σ2 = 9.25

Let's define the hypotheses;

Null hypothesis; H0: μ1 - μ2 ≥ 0

Null hypothesis; Ha: μ1 - μ2 < 0

Test statistic which is the z-score Formula between 2 mean is;

z = ((x1¯ - x2¯) - 0)/√((σ1)²/n1) + ((σ2)²/n2))

z = (164 - 159 - 0)/√((12.5²/35) + (9.25²/30))

z = 5/2.705

z = 1.85

From online p-value from z-score calculator attached, using z = 1.85, one tailed, significance value of 0.05, we have;

p-value = 0.03

The p-value is less than the significance value, and so we will reject the null hypothesis and conclude that there is evidence sufficient to reject the claim that average weekly food expenditure of households in City 1 is more than that of households in City 2.

Answer:

y = 3x + 41

Step-by-step explanation:

First, lets set up the slope-intercept form equation, that is...

y = mx + b

m = slope

b = y-intercept

because the y-intercept is a positive value, it cannot be y=-3x-41 or y= 3x-41

now, we know that b = 41, but what is the slope?

Well, here are tips for doing slope

if the line is gradually increasing upwards, then it is a positive slope

if the line is gradually decreasing downwards, then it is a negative slope

because the line in the picture is positive, this proves y=-3x+41 wrong, therefore making y = 3x + 41 the only correct answer

Therefore, your correct answer is y = 3x + 41

Answer:

D. 2r = 16

Step-by-step explanation:

r/2 = 16, r=32

8= r/8,    r=64

4r=16,     r=4

2r=16

/2    /2

r=8

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Answer:

1st, 4th and 5th are in arithmetic sequence.

Answer:

a) 1,2,3,4,5,6............

d) 3,0, -3 ,-6,-9,-12.............

e) 6,5,4,3,2,1...........

are arithmetic sequence

Step-by-step explanation:

Arithmetic sequence is series of numbers that the difference of consecutive terms is constant

a) 1, 2 , 3 , 4 , 5 , 6...........

Common difference = 1

d) 3,0, -3 ,-6,-9,-12.............

Common difference = second term - first term

                                  = 0 - 3 = -3

e) 6,5,4,3,2,1...........

Common difference = 5 - 6 = - 1

Answer:

n = 6

Step-by-step explanation:

Given the expression

[tex](\frac{19^8}{7^n})^4 = (\frac{19^4}{7^3})^8 \\\frac{19^{32}}{7^{4n}} = \frac{19^{32}}{7^{24}}\\\frac{1}{7^{4n}} = \frac{1}{7^{24}} \\Reciprocate \ both \ sides\\7^{4n} = 7^{24}\\4n = 24\\n = \frac{24}{4}\\n = 6[/tex]

Hence the value of n is 6

Answer:

-8x+8=-6x+20 and x= -6

Step-by-step explanation:

Reason to equation:

This image shows alternative interior angles.

Alternative interior angles are congruent to each other.

How to find x:

-8x+8=-6x+20

We subtract 8 from both sides

-8x=-6x+12

We add 6x to both sides

-2x=12

We divided -2 from both sides

-2x/-2x = 12/2

Leaving us with x=-6

Answer:

Step-by-step explanation:

Use FOIL method.First multiply (5x + 1) and (3x - 4). Then multiply (15x² - 17x - 4) by (x +2)

Volume of the rectangular prism = length *width * height

              = (5x + 1) (3x -4)(x +2)

              = [ 5x*3x + 5x*(-4)  + 1*3x + 1*(-4) ] (x + 2)

             = [15x² - 20x + 3x - 4] (x +2)    {Combine like terms}

             = [15x² - 17x - 4] (x + 2)

             =[15x² -17x - 4]*(x) + [15x² - 17x  -4]*2

            = [15x²*x - 17x*x - 4*x ]+ 15x²*2 - 17x *2  - 4*2

            = 15x³ - 17x² - 4x  + 30x² - 34x - 8

           = 15x³ - 17x² + 30x²  - 4x - 34x - 8    {Combine like terms}

           = 15x³ + 13x²  - 38x - 8

Answer:

x = -2

y = 5

Step-by-step explanation:

7y - 5x = 45    -------------------(I)

x = 8 - 2y -----------------------(II)

Substitute x = 8 - 2y in equation (II)

7y - 5(8-2y) = 45

7y + 8 *(-5) - 2y*(-5) = 45

7y - 40 + 10y = 45

17y - 40 = 45

17y = 45 + 40

17y = 85

y = 85/17

y = 5

Plugin y = 5 in equation (II)

x = 8 - 2*5

x = 8 - 10

x = -2

Answer:

Yes, Yes, No, Yes.

Step-by-step explanation:

2/5 as a decimal = 0.4

4 ÷ 0.4 = 10

1 is correct.

2 x 10 = 20

2 is correct.

6 x 10 = 60

3 is incorrect.

10 ÷ 2 = 5

4 is correct.

Answer: it's 10, not 210.

Answer:

D) $5385.10

Step-by-step explanation:

Exponential equation of decay:

The exponential equation for the decay of an amount after t years is given by:

[tex]A(t) = A(0)(1-r)^t[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

If you buy a motorcycle for $12,500 in 2015 and it depreciates (shrinks) in value by 15.5% every year

This means that [tex]A(0) = 12500, r = 0.155[/tex]

So

[tex]A(t) = A(0)(1-r)^t[/tex]

[tex]A(t) = 12500(1-0.155)^t[/tex]

[tex]A(t) = 12500(0.845)^t[/tex]

How much will it be worth in 2020?

2020 is 2020 - 2015 = 5 years after 2015, so this is A(5). So

[tex]A(5) = 12500(0.845)^5 = 5385.10[/tex]

The correct answer is given by option D.

Answer:

The monthly loan payment is of $458.88.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Amount owed after 5 years:

Loan of 24000 means that [tex]P = 24000[/tex]

5 years means that [tex]t = 5[/tex]

Interest rate of 2.75% means that [tex]r = 0.0275[/tex]

Compounded monthly means that [tex]n = 12[/tex]

The amount is A(5). So

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(5) = 24000(1 + \frac{0.0275}{12})^{12*5}[/tex]

[tex]A(5) = 27533[/tex]

What is your monthly loan payment?

$27,533 in 5 years = 5*12 = 60 months. So

27533/60 = 458.88

The monthly loan payment is of $458.88.

Answer:

C

Step-by-step explanation:

It is one whole shaded diagram (100%) and half of the diagram (50%), making 150%

Answer:

a or c

Step-by-step explanation:

Use the formula A = p(1 + r/n)^(nt).

Here is the set up:

A = 6500[1 + (0.08/4)]^(4•7)

Solve for A.

Answer:

3/100 × 30000 is the answer to your question.

Answer:

[tex]f(x) = 5 {x}^{2} + 2x + 5 \\ when \: x = 2 \\ f(2) = 5( {2})^{2} + 2(2) + 5 \\f(2) = 29[/tex]

Answer:

i think the answer is B, good luck

Answer:

c i do believe good luck with the answer

Answer:

1 1/3 cups of flour

Step-by-step explanation:

1/3 x 4 = 4/3 = 1 1/3

Hope that helps! :)

-Aphrodite

Answer:

just substitute the value of x as 1

f(x)=3(12)x+1

f(1)=3(12)(1)+1

f(1)=3(12)(1)+1

f(1)=36+1

f(1)=37

Answer:

This is the answer!!!

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

3 1/3-2 2/3=  2/3

Answer:

19.50

Step-by-step explanation:

If the scarf is 25% off, you have to pay 100% -25% = 75%

26 *75%

26 *.75

19.5

Answer:

n has no value.

There is no solution to this equation

Step-by-step explanation:

let n be the number

In pieces:

sum of the number and 1: (n + 1)

8 times the sum: 8(n + 1)

-7 times a number: -7n

sum of -7 times and...: -7n + 8(n + 1)

number minus 7: n - 7

the same as: =

All together:

-7n + 8(n + 1) = n - 7

-7n + 8(n+1)=n-7

-7n + 8n+8=n-7

0=-15