The mean of the sample is 24.444 squares with a standard deviation of 2.45 squares. Single-ply toilet paper requires 26 squares to absorb one-quarter cup of water. Josh would like to carry out a test to determine if there is convincing evidence that the mean number of squares of Fluffy that are needed to absorb one-quarter cup of water is fewer than 26 squares. What is the appropriate test statistic and P-value of this test?

Answer: x=  −6 /5  is the answer

Answer:

x= -1 1/5 or x= -1.2

Step-by-step explanation:

-4x+-3=x+3

-5x-3=3

-5x=6

-x=6/5

x=-6/5

x=-1 1/5

or x=-1.2

Hope this helps! Pls rate brainliest

Answer: 300

We know that 5×3=15. Since we are trying to get 1500 we Multiply 300×5 and get 1500.

How do we know?

As you see when you still multiply either of those problems you have 15 in it. So we should know 300×5=1500.

Note: We can also multiply 500×3 and get 1500. You still get the same answer but just switched numbers.

Answer:

[tex]300[/tex]

Step-by-step explanation:

[tex] \frac{1500}{5} = 300[/tex]

It's very easy to find if you use a calculator.

To know whether that the answer is correct or wrong you can do like this.

[tex]300 \times 5 = 1500[/tex]

hope this helps

thanks.

Answer:

Step-by-step explanation:

So, we do not have enough evidence to conclude that the number of adolescent relationships is equal between those with an older sibling and those without.

check the attached file for explanation and solution

The student must sell at least 70 glasses of lemonade at $0.25 each, considering the initial costs of $16.00 and the additional $0.02 cost per glass for sugar, to begin to make a profit.

To calculate the minimum number of glasses of lemonade that must be sold to start making a profit, we need to consider the total costs and the revenue per glass. The student spent $12.00 on lemons and $4.00 on glasses, totaling $16.00 in costs. Additionally, each glass of lemonade has an added cost of $0.02 for sugar. The revenue from selling one glass of lemonade is $0.25.

To break even, the total revenue must equal the total costs. As costs are fixed at $16.00 and the variable cost is $0.02 per glass, we can set up the equation: (Number of glasses × $0.25) - (Number of glasses × $0.02) = $16.00. This simplifies to (Number of glasses × $0.23) = $16.00, and solving for Number of glasses gives us Number of glasses = $16.00 / $0.23, which is approximately 69.57 glasses. Since you can't sell a fraction of a glass, rounding up means the student needs to sell at least 70 glasses to begin to make a profit.

Step-by-step explanation:

a) 24 / 250 = 0.096

b) Standard error for a proportion is:

σ = √(pq/n)

σ = √(0.096 × 0.904 / 250)

σ = 0.0186

c) At 98% confidence, the critical value is 2.326.  The margin of error is therefore:

2.326 × 0.0186 = 0.0433

d) At 95% confidence, the critical value is 1.960.  The margin of error is therefore:

1.960 × 0.0186 = 0.0365

So the confidence interval is:

(0.0960 − 0.0365, 0.0960 + 0.0365)

(0.0595, 0.1325)

e) 0.10 is within the 95% confidence interval, so the null hypothesis would not be rejected.

Final answer:

a) The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is 9.6%. b) The standard error of the estimated proportion is 1.9%. c) The margin of error at the 98% confidence level is 4.4%. d) The 95% confidence interval estimate for the true proportion is approximately 5.9% to 13.3%. e) The null hypothesis that the proportion is 0.10 is rejected if the z-test statistic falls outside the range (-1.96, 1.96).

Explanation:

a) Point estimate:
The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is the number of failed components divided by the total number of components tested. In this case, the point estimate is 24/250 = 0.096, or 9.6%.

b) Standard error:
The standard error of the estimated proportion is calculated using the formula SE = sqrt((phat * (1 - phat)) / n), where phat is the point estimate and n is the sample size. In this case, the standard error is sqrt((0.096 * (1 - 0.096)) / 250) = 0.019, or 1.9%.

c) Margin of error:
The margin of error is determined by multiplying the standard error by the appropriate critical value from the standard normal distribution. For a 98% confidence level, the critical value is approximately 2.33. Therefore, the margin of error is 2.33 * 0.019 = 0.044, or 4.4%.

d) Confidence interval:
The 95% confidence interval estimate for the true proportion of components that fail to meet the specifications is given by the formula phat +/- z * SE, where phat is the point estimate, z is the appropriate critical value from the standard normal distribution (for 95% confidence, z is approximately 1.96), and SE is the standard error. Therefore, the confidence interval is 0.096 +/- 1.96 * 0.019, or approximately 0.059 to 0.133.

e) Hypothesis test:
To test the null hypothesis H_0: p = 0.10 against the alternative hypothesis H_a: p != 0.10, we can use a two-tailed z-test. The test statistic is calculated as (phat - p_0) / sqrt((p_0 * (1 - p_0)) / n), where p_0 is the null hypothesis value (0.10), phat is the point estimate, and n is the sample size. The critical value for a significance level of 0.05 is approximately 1.96 from the standard normal distribution. If the test statistic is outside the range (-1.96, 1.96), we reject the null hypothesis. In this case, if the test statistic falls outside the range (-1.96, 1.96), we would reject the null hypothesis and conclude that the true proportion of components that fail to meet the specifications is not 0.10.

Answer:

4x+5y = 320

x+y = 70

Step-by-step explanation:

We need one equation for the total number of shirts, and one for the total cost.

Total number = 70

So that means medium shirts + large shirts = 70

So our first equation is x+y = 70

Total cost = $320

So that means $4 times medium shirts + $5 times large shirts = 320

So our second equation is 4x+5y = 320

Answer:

Heather rode the farthest

She rode 0.1km farther than Hailey.

Step-by-step explanation:

This is a conversion of units question.

Heather rode her horse 2 kilometers.

Hailey rode 1900 meters on her horse.

Each km has 1000 meters.

So 1900 meters = 1900/1000 = 1.9 km

This means that Hailey rode for 1.9 km.

Heather rode the farthest(2km is greather than 1.9km)

2 - 1.9 = 0.1km

She rode 0.1km farther than Hailey.

Answer:

Required results are [tex]\nabla .\vec{F}[/tex]=8\cos(8x+5z)-8ye^x[/tex]  and  [tex]\nabla\times \vec{F}=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]

Step-by-step explanation:

Given vector function is,

[tex]\vec{F}=\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k}[/tex]

To find [tex]\nabla .\vec{F}[/tex] and [tex]\nabla \times \vec{F}[/tex] .

[tex]\nabla .\vec{F}[/tex]

[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]

[tex]=\frac{\partial}{\partial x}(\sin(8x+5z))-\frac{\partial}{\partial z}(8ye^xz)[/tex]

[tex]=8\cos(8x+5z)-8ye^x[/tex]

And,

[tex]\nabla \times \vec{F}[/tex]

[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})\times(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]

[tex]\end{Vmatrix}[/tex]

[tex]=\uvec{i}\Big[\frac{\partial}{\partial y}(-8ye^xz)\Big]-\uvec{j}\Big[\frac{\partial}{\partial x}(-8ye^xz)-\frac{\partial}{\partial z}(\sin(8x+5z))\Big]+\uvec{k}\Big[-\frac{\partial}{\partial y}(-\sin(8x+5z))\Big][/tex]

[tex]=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]

Hence the result.

Answer:

The probability of students scored less than 60 = .0768

Step-by-step explanation:

Given -

Mean score [tex](\nu )[/tex] = 70

standard deviation [tex](\sigma )[/tex] = 7

Let X be the score of students

the probability that students scored less than 60 =

[tex]P(X< 60)[/tex]  = [tex]P(\frac{X - \nu }{\sigma}< \frac{60 - 70}{7})[/tex]

                  =  [tex]P(z < \frac{60 - 70}{7})[/tex]   put[ Z= [tex]\frac{X - \nu }{\sigma}[/tex]]

                   =  [tex]P(z < -1.428)[/tex]  using z table

                    =  .0768

Answer:

720

Step-by-step explanation:

96 * 7.5

Answer:

...

Step-by-step explanation:

...

Answer:

The z-score (value of z) for an income of $1,100 is 1.

Step-by-step explanation:

We are given that the mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100.

Let X = group of weekly incomes of a large group of executives

So, X ~ N([tex]\mu=1,000 ,\sigma^{2} = 100^{2}[/tex])

The z-score probability distribution for a normal distribution is given by;

               Z = [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean income = $1,000

            [tex]\sigma[/tex] = standard deviation = $100

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, we are given an income of $1,100 for which we have to find the z-score (value of z);

So, z-score is given by = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{1,100-1,000}{100}[/tex] = 1

Hence, the z-score (value of z) for an income of $1,100 is 1.

The z-score for an income of $1,100 is 1.0.

The z-score is a measure of how many standard deviations a particular value, in this case, income, is from the mean of a normally distributed dataset. The formula to calculate the z-score is:

z = (x - μ) / σ

Where:

Given the mean (μ) is $1,000 and the standard deviation (σ) is $100, we can substitute these values into the formula to find the z-score of an income of $1,100.

z = ($1,100 - $1,000) / $100

z = $100 / $100

z = 1

Therefore, the z-score for an income of $1,100 is 1.0. This means the income of $1,100 is one standard deviation above the mean.

Answer:

   look for the x-intercepts

Step-by-step explanation:

A "zero" is a value of x where the function value is zero. On a graph, that point is where the graph meets the x-axis. Every x-intercept is a zero of the function.

__

If there are no x-intercepts, then there are no real zeros. The roots (zeros) will be complex.

B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and  it takes 2.6 hours when both drains are turned on.

Step-by-step explanation:

The given is,

                   A alone can empty the pool in 4.75 hours.

                   It takes 2.6 hours when both drains are turned on.

Step:1

            One hour work drains A and B =

                  One hour work of drain A + One hour work of Drain B.........(1)

            One hour work of Drain A = [tex]\frac{1}{4.75}[/tex]

                     One hour of ( A + B ) = [tex]\frac{1}{2.6}[/tex]

            Equation (1) becomes,

                     One hour work of B = One hour work of ( A + B )

                                                                  - One hour work of A

            Substitute the values,

                     One hour work of B =  [tex]\frac{1}{2.6} - \frac{1}{4.75}[/tex]

                                                       = [tex]\frac{4.75-2.6}{(4.75)(2.6)}[/tex]

                                                       = [tex]\frac{2.15}{12.35}[/tex]

                                                       = [tex]\frac{1}{5.744}[/tex]

                    One hour work of B  = [tex]\frac{1}{5.744}[/tex]

             B alone can empty the pool in 5.744 hours

Result:

           B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and  it takes 2.6 hours when both drains are turned on.

Answer:

24 guppies

Step-by-step explanation:

Assuming a linear relationship,  the volume required per guppy is given by:

[tex]g=\frac{576\ in^3}{3\ guppies}\\ g= 192\ in^3/guppy[/tex]

The volume of the fish tank is given by the product of its length, by its width and its height:

[tex]V = 24*12*16\\V=4,608\ in^3[/tex]

The number of guppies that this tank can safely hold is:

[tex]n=\frac{V}{g}=\frac{4,608}{192} \\n=24\ guppies[/tex]

The tank can safely hold 24 guppies.

Answer:

[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]    

[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]    

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

Step-by-step explanation:

Data provided

[tex]\bar X=9797[/tex] represent the sample mean for the steps

[tex]\mu[/tex] population mean

s=2313 represent the sample standard deviation

n=61 represent the sample size  

Solution

The confidence interval for the true population mean is given by :

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

Since we need to find the critical value [tex]t_{\alpha/2}[/tex] we need to calculate first the degrees of freedom, given by:

[tex]df=n-1=61-1=60[/tex]

The Confidence is 0.90 or 90%, the value for the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,60)".And we see that [tex]t_{\alpha/2}=1.67[/tex]

Now we have everything in order to replace into formula (1):

[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]    

[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]    

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps.

To construct a 90% confidence interval for the mean number of steps taken on a typical workday for people working in New York City who wear activity trackers, you can use the following formula:

Confidence Interval = X ± Z * (σ/√n)

Where:

X is the sample mean (9,797 steps).

Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645, but you can use a Z-table or calculator to get the exact value).

σ is the population standard deviation (2,313 steps).

n is the sample size (61).

Now, let's plug in the values and calculate the confidence interval:

Z for a 90% confidence level is approximately 1.645.

Confidence Interval = 9,797 ± 1.645 * (2,313/√61)

Confidence Interval = 9,797 ± 1.645 * (299.98)

Confidence Interval ≈ 9,797 ± 494.06

Now, calculate the lower and upper bounds of the confidence interval

Lower Bound = 9,797 - 494.06 ≈ 9,302.94

Upper Bound = 9,797 + 494.06 ≈ 10,291.06

Interpretation:

We are 90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps. This means that if we were to take many random samples and calculate a 90% confidence interval for each sample, we would expect about 90% of those intervals to contain the true population mean.

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The equation we've developed to represent the rabbit population over time, where 't' is the number of months since January, is P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650. This equation covers the oscillations in the population and the steady yearly increase.

The subject matter falls under the discipline of Mathematics, particularly in the topics involving functions. We can create a sinusoidal (sine or cosine) function to represent the oscillation of the population of rabbits.

Given that the population fluctuates 19 above and below the average, and the average increases by 160 each year, this suggests a sinusoidal period of 12 months (a year) with a vertical shift (midline) that increases linearly.

Considering t as the number of months since January, the equation for the population P in terms of the months since January t would be:

P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650

The 19 is the amplitude, (2π/12)t - π/2 represents the sinusoidal oscillation adjusted to start at the minimum in January, (160t/12) is the yearly change in population that increases per month, and 650 is the average population at the start.

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To find the population equation in terms of months since January considering oscillations and growth, use the formula p(t) = 650 + 160t + 19sin(2πt/12).

Population Equation: The equation for the population p in terms of the months since January t can be written as p(t) = 650 + 160t + 19sin(2πt/12). This equation takes into account the initial population of 650 rabbits, an increase of 160 rabbits per year, and the oscillation of 19 above and below the average population.

Answer:

90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)

Step-by-step explanation:

We have the following data:

Sample size = n = 1000

Proportion of travelers who prefer window seat = p = 60%

Standard Error = SE = 0.015

We need to construct a 90% confidence interval for the proportion of travelers who prefer window seat. Therefore, we will use One-sample z test about population proportion for constructing the confidence interval. The formula to calculate the confidence interval is:

[tex](p-z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}}, p+z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}})[/tex]

Since, standard error is calculated as:

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

Re-writing the formula of confidence interval:

[tex](p-z_{\frac{\alpha}{2}} \times SE, p+z_{\frac{\alpha}{2}} \times SE)[/tex]

Here, [tex]z_{\frac{\alpha}{2}}[/tex] is the critical value for 90% confidence interval. From the z-table this value comes out to be 1.645.

Substituting all the values in the formula gives us:

[tex](0.6 - 1.645 \times 0.015, 0.6 + 1.645 \times 0.015)\\\\ = (0.575, 0.625)[/tex]

Therefore, the 90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)

Answer:

18.86 feet

Step-by-step explanation:

The circumference of the inner circle is 88 ft.

Circumference of a Circle[tex]=2\pi r[/tex]

Therefore:

[tex]2\pi r =88\\r=88 \div (2*\frac{22}{7})=14 ft[/tex]

Radius of the inner circle=14 feet

If the distance between the inner circle and the outer circle is 3 ft, the radius of the outer circle=14+3 =17 feet.

Therefore. circumference of the outer Circle[tex]=2\pi r[/tex]

[tex]=2*\frac{22}{7}*17=106.86 ft[/tex]

Difference in Circumference=106.86-88 =18.86 feet

The circumference of the outer circle is greater than that of the inner circle by 18.86 feet.

18.9

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

So we are given the formula for the slope of a hyperbola in this form:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex].

That formula for the slope is [tex]m=\frac{b^2x}{a^2y}[/tex]

If we compare the following two equations, we will be able to find [tex]a^2[/tex] and [tex]b^2[/tex]:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

[tex]\frac{x^2}{8}-\frac{y^2}{4}=1[/tex]

We see that [tex]a^2=8[/tex] while [tex]b^2=4[/tex].

So the slope at [tex](x,y)=(4,2)[/tex] is:

[tex]m=\frac{b^2x}{a^2y}=\frac{4(4)}{8(2)}=\frac{16}{16}=1[/tex].

Recall: Slope-intercept form of a linear equation is [tex]y=mx+b[/tex].

We just found [tex]m=1[/tex]. Let's plug that in.

[tex]y=1x+b[/tex]

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

To find [tex]b[/tex], the [tex]y[/tex]-intercept, we will need to use a point on our tangent line. We know that it is going through [tex](4,2)[/tex].

Let's enter this point in to find [tex]b[/tex].

[tex]2=4+b[/tex]

Subtract 4 on both sides:

[tex]2-4=b[/tex]

Simplify:

[tex]-2=b[/tex]

The equation for the tangent line at [tex](4,2)[/tex] on the given equation is:

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

Answer: y = x - 2

Step-by-step explanation:

First you take the derivative of each term. d/dx(x²/8) - d/dx(y²/4) = d/dx(1)

x/4 - (y/2)dy/dx = 0

Then you solve for dy/dx: dy/dx = x/2y

Plug in the values: dy/dx = 1

To find the y-intercept, plug in values for y = mx+ b. 2 = 4 + b, b = -2

The equation is y = x - 2

Answer: +/- 7

Step-by-step explanation:

3x² = 147

To solve for x divide through by three first.

3x² = 147

x² = 49, now we take the square root of both side by trying to apply laws of indices.

√x² = √49

The square root will neutralize the effect of the square because

√a = a¹/² so (x²)¹/², and (x²)¹/² =

x²×¹/² = x, therefore the solution is

x = +/- 7.

Answer:

(a) The least-square regression line is: [tex]y=4.662+2.709x[/tex].

(b) The number of households using online banking at the beginning of 2007 is 31.8.

Step-by-step explanation:

The general form of a least square regression line is:

[tex]y=\alpha +\beta x[/tex]

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

(a)

The formula to compute intercept and slope is:

[tex]\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \end{aligned}[/tex]

The values of ∑X, ∑Y, ∑XY and ∑X² are computed in the table below.

Compute the value of intercept and slope as follows:

[tex]\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}[/tex]

The least-square regression line is:

[tex]y=4.662+2.709x[/tex]

(b)

For the year 2007 the value of x is 10.

Compute the value of y for x = 10 as follows:

[tex]y=4.662+2.709x[/tex]

  [tex]=4.662+(2.709\times10)\\=4.662+27.09\\=31.752\\\approx 31.8[/tex]

Thus, the number of households using online banking at the beginning of 2007 is 31.8.

Answer:7^6

Step-by-step explanation:

Answer:

7^6

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

8*5

Answer:

the correct graph is pictured below

Step-by-step explanation:

the graph is below

Answer:

At 95% confidence level, the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois is -7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237

Step-by-step explanation:

Here we are required to construct the 95% confidence interval of the difference between two proportions

The formula for the confidence interval of the difference between two proportions is as follows;

[tex]\hat{p}_1-\hat{p}_2\pm z^{*}\sqrt{\frac{\hat{p}_1\left (1-\hat{p}_1 \right )}{n_{1}}+\frac{\hat{p}_2\left (1-\hat{p}_2 \right )}{n_{2}}}[/tex]

Where:

[tex]\hat{p}_1 = \frac{34}{1679}[/tex]

[tex]\hat{p}_2 = \frac{24}{1366}[/tex]

n₁ = 1679

n₂ = 1366

[tex]z_{\alpha /2}[/tex] at 95% confidence level = 1.96

Plugging in the values, we have;

[tex]\frac{34}{1679}- \frac{24}{1366} \pm 1.96 \times \sqrt{\frac{ \frac{34}{1679}\left (1- \frac{34}{1679}\right )}{1679}+\frac{\frac{24}{1366} \left (1-\frac{24}{1366} \right )}{1366}}[/tex]

Which gives;

-7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237.

At 95% confidence level, the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois = -7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237.

Answer:

  5.892×10^-2

Step-by-step explanation:

Scientific notation has one digit to the left of the decimal point. To write the number in scientific notation, it can work to start by writing the number with that as one of the factors:

  0.05891 = 5.891 × 0.01

  = 5.891 × 1/10^2

  = 5.891 × 10^-2

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You can also enter this number into your calculator and change the display mode to SCI.

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It helps to understand the decimal place-value number system in terms of the power of 10 that multiplies each number place.

Answer:

This would be -9 to the 5th power. (-9^5)

Step-by-step explanation:

-9 to the 5th power when put in a calculator equals -59,049.

The exponent is how many times the number is multiplied by itself.

Answer:

-59049

Step-by-step explanation:

(-9).(-9).(-9).(-9).(-9)

=81.(-9).(-9).(-9)

= -729.(-9).(-9)

= 6561.(-9)

= -59049

By calculating the average speed of Tomos in the 525-meter race, we can estimate that he would take about 3 minutes 12 seconds to complete an 800-meter race if he maintains the same average speed.

To solve this problem, we first need to figure out Tomos's average speed in the 525-meter ski race that he completed in 2 minutes and 6 seconds. We convert the time to seconds for ease of calculation. So, 2 minutes 6 seconds equals 126 seconds. Now, we calculate his average speed by dividing the length of the race by the time he took to complete it:

Average speed = Distance / Time
Average speed = 525m / 126s
Average speed = 4.17 m/s

Now to calculate how long Tomos should take to complete an 800 m race, we rearrange the formula to solve for time. Time = Distance / Average Speed:

Time = 800m / 4.17 m/s
Time = 191.84 seconds

Learn more about Average Speed here:

https://brainly.com/question/17661499

#SPJ11

Answer:

330+77= 407

Step-by-step explanation:

*Danganronpa flashbacks*