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Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

[tex]\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988[/tex]

The combined proportion is:

[tex]\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989[/tex]

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

[tex]Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

   [tex]=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78[/tex]

Compute the p-value as follows:

[tex]p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075[/tex]

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

     [tex]=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\[/tex]

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Answer:

4x-3

Step-by-step explanation:

9x+6-4x-1x+1-10

9x-4x-1x+7-10

5x-1x+7-10

4x-3

b)25%

espero ter ajudado

Answer:

I believe it is C

Step-by-step explanation:

Answer:

3 pens

Step-by-step explanation:

Total expenditure (Price x Quantity) on pens & pencils = $30

Let pen quantity be = x , Let pencil quantity be = y

Given : Pen (x) price = 5 , Pencil (y) price = 1.5 , Pencils (y) = Pen (x) + 5

So, 5x + 1.5y = 30

5x + 1.5 (x + 5) = 30  → 5x + 1.5x + 7.5 = 30  → 6.5x + 7.5 = 30

6.5x = 30 - 7.5  → 6.5x = 22.5

x = 22.5 / 6.5 → x = 3.46  ≈ 3 pens

Answer:

-6, -2

Step-by-step explanation:

Answer:

What do you but in the chart? Also, part 2 is 72

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

If each t-shirt costs 3.6 dollars then you would have to multiply 3.6 by 20 shirts which will equal to 72. So Charlie has to pay 72 dollars for 20 shirts.

Answer:

Simple....

you have: one is leaking 3 gallons per week and holds 256 gallons; whereas, the other one is leaking 5 gallons per week and holds 384 gallons.

Set up both the equations....

In y=mx+b form--->>>

y=-3x+256

y=-5x+384

To figure out when they will be equal..set the equations equal to each other....(remember to isolate the variable)

-3x+256=-5x+384

-3x+256=-5x+384

     -256        -256

-3x=-5x+128

-3x=-5x+128

+5x+5x

2x=128

x=64

After 64 weeks the amount of water in both tanks will be the same.

Thus, your answer.

Answer:

the general form of the equation of the line will be:

[tex]y-x=2[/tex]

Step-by-step explanation:

Finding the slope:

Taking two points from the line as shown in figure

Finding the slope between (-2, 0) and (0, 2)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:2\right)[/tex]

[tex]m=\frac{2-0}{0-\left(-2\right)}[/tex]

[tex]m=1[/tex]

Finding the y-intercept

We know that the y-intercept can be calculated by setting x=0

From the figure, it is clear that at x=0, y=2

Thus, the y-intercept is (0, 2)

We know that the slope-intercept form of the equation line is:

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept

As we have already determined the slope = m = 1 and the y-intercept b=2.

Substituting the values in the slope-intercept form of the equation line

[tex]y=mx+b[/tex]

[tex]y=(1)x+2[/tex]

[tex]y=x+2[/tex]

Writing the equation in the standard form form

As we know that the equation in the standard form is

[tex]Ax+By=C[/tex]

where x and y are variables and A, B and C are constants

As we already know the equation in slope-intercept form

[tex]y=x+2[/tex]

so just simplify the equation to write in standard form

[tex]y-x=2[/tex]

Thus, the general form of the equation of the line will be:

[tex]y-x=2[/tex]

Answer: Interior angles at Jamestown and Yorktown are 40° and 20°, respectively

Step-by-step explanation: Jamestown, Williamsburg and Yorktown form a triangle. The sum of the interior angles of a triangle is 180°.

Suppose interior angle at Yorktown is x. As Jamestown is twice the measure at Yorktown, it means this interior angle is 2x.

Then, the measures will be:

2x + x + 120 = 180

3x = 60

x = 20

Angle at Yorktown is 20°.

So, angle at Jamestown is

2x = 2.20 = 40°

The measures of the interior angles at Jamestown and Yorktown are 40° and 20°, respectively.

Answer:

12xy

Step-by-step explanation:

Each term is separated by a function sign. In this case, an addition symbol.

Answer:

16+3=y

y=19

Step-by-step explanation:

Answer:

-1.9 is to the left of -1.48.

-1.48 is closer to 0.

-1.48 is greater than -1.9.

Answer:

statements 1,4,5

Step-by-step explanation:

Answer:

f(- 3) = - 14

Step-by-step explanation:

To evaluate f(- 3), substitute x = - 3 into f(x), that is

f(- 3) = 5(- 3) + 1 = - 15 + 1 = - 14

Answer:

Antwanun waters his lawn 3 times a week, he watered his lawn 24 . So what you will need to do is divide 3 in 24 to find how many weeks he has been watering his lawn, You get 8. Mr. Antwanun has been watering for 8 weeks. Equation- Antuwantun waters his lawn 3 times a week so if he watered his lawn 24 times, 3 times a week he would have been watering his lawn for 8 weeks.

Answer:

3x=24

Step-by-step explanation:

3 times a certain amount equals 24 times in total

Answer:

m>−2

Step-by-step explanation:

3-2m<7

subtract 3 from both sides

-2m<4

divide by 2

m>−2

Answer:

B and D

Step-by-step explanation:

I'm pretty sure but definitely B

Answer:

The expression that equivalent to (g - f)(3) is 6(3) - 4 + 3² ⇒ C

Step-by-step explanation:

Let us solve the question

∵ f(x) = 4 - x²

∵ g(x) = 6x

→ Find at first (g - f)(x) by subtracting f(x) from g(x)

∵ (g - f)(x) = 6x - (4 - x²)

→ Remember (-)(+) = (-) and (-)(-) = (+)

∴ (g - f)(x) = 6x - 4 + x²

→ Substitute x by 3 to find (g - f)(3)

∵ (g - f)(3) = 6(3) - 4 + (3)²

∴ (g - f)(3) = 6(3) - 4 + 3²

The expression that equivalent to (g - f)(3) is 6(3) - 4 + 3²

Answer:

Time= 4 years

Step-by-step explanation:

Giving the following information:

Principal (P)= $12,000

Interest rate (r)= 10% = 0.10

Interest earned (I)= $4,800

To calculate the time required to gain $4,800 interest, we need to use the following formula:

T= I / (P*r)

T= 4,800/(12,000*0.1)

T= 4 years

Answer: If you want to round is so you have a small amount of decimals, you could round to the nearest tenths which would give you 17,102,740 4.3

Step-by-step explanation:

Answer:

6%

Step-by-step explanation:

Estimated distance = 80 miles

Actual distance covered = 75.5 miles

We need to find the percent error of the cyclist's estimate. Its formula is given by :

[tex]\%=\dfrac{|\text{actual value-estimated value}|}{\text{actual value}}\times 100[/tex]

Put all the values,

[tex]\%=\dfrac{80-75.5}{75.5}\times 100\\\\=5.96\%[/tex]

or

= 6%

So, the percentage error is 6%.

Answer:

5.96

Step-by-step explanation:

1.) x = 3.5

2.) x = -40

3.) x = -10

Answer:

x ≥ -7/3

Step-by-step explanation:

Pre-Algebra

Brackets

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Inequality

-15x + 4 ≤ 39

Step 2: Solve for x

Subtract 4 on both sides:                     -15x ≤ 35

Divide -15 on both sides:                      x ≥ -7/3

Here we see that any value x greater than or equal to -7/3 would work as a solution to the inequality.

Answer:

y=18

Step-by-step explanation:

pls give brainliest

Answer:

 y = − 2 x

Step-by-step Explanation:

Y + 2 = − 2 ⋅ ( − 1 )  Write in   y = m x + b  form.

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

m  in perpendicular  = − 1 2

(1,-2),y=(1)/(2)x+4

I hope I helped!

Answer:

y = -2x + 8

Step-by-step explanation:

For this problem we need to consider that the equation of a line perpendicular to another line will have a "negative reciprocal" slope so that when they cross, it forms a 90-degree angle, hence perpendicular.  Additionally, we will need to use the point-slope form and re-write it into the slope-intercept form to incorporate (2,4) into our equation.  With these things in mind, let's do that.

y = (1/2)x + (1/2)

We want a "negative reciprocal" so:

y = -2x + (1/2)

Since -2 is the "negative reciprocal" of 1/2.

And now we want to use the point-slope form to incorporate (2,4)

y - y0 = -2 ( x - x0 )

Where, y0 = 4 and x0 = 2.

y - y0 = -2 ( x - x0 )

y - 4 = -2 ( x - 2 )

y - 4 = -2x + 4

y = -2x + 8

So, the equation that is perpendicular to y = (1/2)x + (1/2) and includes the point (2,4) is y = -2x + 8.

Cheers.

Answer:

2 cups left

Step-by-step explanation:

Answer:

Hope its work for you

Step-by-step explanation:

As we know that,

As given values

take,   (X1,Y1)=(-7,-4)

           (X2-Y2)=(8,8)

hence   X1=-7  ,  Y1= -4   ,  X2=8  , Y2= 8

putt the values in the above equation of slope we get ,

m=(8-(-4))/(8-(-7)

Answer:

0.8

Step-by-step explanation:

Slope=(y2-y1) (8--4) (12)

(x2-x1)= (8--7)= (15)= 0.8

Answer:

yes, the slope is the same throughout the table

Step-by-step explanation:

Answer:

Yes, the graph shown is a proportional relationship.

Step-by-step explanation:

If you divide the distance (6) by the time (1) you get the same thing (6). Repeat for all the terms in the graphs. Since 6/1 is 6, 12/2 is 6, 18/3 is 6 and 24/4 is 6, The relationship is proportional.