The volume of a cube is given by the expression s to the power of 3, and its surface area is given by the expression 6s to the power of 2, where s is the length of the cube’s side. What is the volume of a cube with a side length of 5 inches?

Answer:

75 cm (if b=10 and h=15)

Step-by-step explanation:

The formula to calculate the area of a triangle is bh1/2. So you must do (10)(15)1/2, 10 multiplied by 15 equals 150. And 150 multiplied by 1/2 equals 75. Hope this helped!

Answer:

7.1%

Step-by-step explanation:

Current yield is the ratio of coupon payment of a bond to its current market price.  It is calculated by using coupon payment and the current market value of the bond.

As per given data

Coupon rate = 7%

Face value = $1,000

Market Value = $985

Coupon Payment = $1,000 x 7% = $70

Formula for Current yield is as follow

Current Yield = Annual Coupon Payment / Current Market Price

Current Yield = $70 / $985

Current Yield = 7.11%

Answer:

a)  95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents.

( 0.0761 , 0.3239)

b) Margin of error  =  0.1264.

Step-by-step explanation:

Explanation:-

Given '8' persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents.

sample proportion of success [tex]'p' = \frac{8}{40} = 0.2[/tex]

q = 1=p

q = 1-0.2 = 0.8

a)

95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents.

[tex](p-1.96\sqrt{\frac{pq}{n} } , p+1.96\sqrt{\frac{pq}{n} } )[/tex]

[tex](0.2-1.96\sqrt{\frac{0.2X0.8}{40} } , 0.2+1.96\sqrt{\frac{0.2X0.8}{40} } )[/tex]

(0.2 - 0.1239,0.2+0.1239)

( 0.0761 , 0.3239)

b) the margin of error for a 95% confidence interval for the population proportion.

For the 95% confidence interval ∝= 0.05 and zₐ = 1.96≅2.

[tex]Margin of error = \frac{2\sqrt{pq} }{\sqrt{n} }[/tex]

[tex]Margin of error = \frac{2\sqrt{0.2X0.8} }{\sqrt{40} }[/tex]

Margin of error for a 95% confidence interval for the population proportion.

Margin of error  =  0.1264.

A)Yes they should market the wax because it thaws before 55 seconds

C) Null hypothesis: mean <55 vs Alternative =55

D) The value is 51.33 moments

When The selected samples for the champion are: 57.9, 62.9, 50.6, 50.5,48.2,47.2,50.2 and 43.1

The mean is ;

Then, Sum =57.9 + 62.9 + 50.6 + 50.5+48.2+47.2+50.2+ 43.1 =410.6

After that, Mean is = 410.6/8 =51.33= mean

Considering Significant is =0.05, therefore, applying this level will give you 51.28-51.38

if particularly, the meantime to complete their standard test course should be less than 55 seconds for a former Olympic champion, then the nullified hypothesis is correct

After that; Null hypothesis: mean <55

Hence, Alternative hypothesis: mean =55

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Answer:

32/9 or 3 5/9

Step-by-step explanation:

3.5555

3 5/9

(3×9 + 5)/9

32/9

Answer:

x = 32/9

Step-by-step explanation:

Let x = 3.55555555repeating

Multiply by 10

10x = 35.555555 repeating

Subtract the first equation

10x = 35.555555 repeating

-x = 3.55555555repeating

-------------------------------------

9x = 32

Divide each side by 9

9x/9 = 32/9

x = 32/9

Answer:

Therefore, on the graph;

The height = 7.5 units

And base = 5.0 units

Attached is an image for further information;

Step-by-step explanation:

Given that;

1 unit on the grid represent 2m of the garden;

Ratio = 1/2 unit/m

For the height;

height h = 15m

On the graph;

h = 15m × 1/2 unit/m

h = 7.5 units

For the base;

Base b = 10m

On the graph;

b = 10m × 1/2 unit/m

b = 5 units

Therefore, on the graph;

The height = 7.5 units

And base = 5.0 units

Answer:

Required total charge is [tex]256\pi[/tex] coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

[tex]x^2=y^2\leq 16[/tex] so that the charge density at (x,y) is,

[tex]\rho (x,y)=2x+2y+2x^2+2y^2[/tex]

To find total charge on the disk let Q be the total charge and [tex]x=r\cos\theta,y=r\sin\theta[/tex] so that,

[tex]Q={\int\int}_Q\rho(x,y) dA[/tex]                where A is the surface of disk.

[tex]=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA[/tex]

[tex]=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta[/tex]

[tex]=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta[/tex]

[tex]=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta[/tex]

[tex]=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta[/tex]

[tex]=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi[/tex]

[tex]=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi[/tex]

[tex]=256\pi[/tex]

Hence total charge is [tex]256\pi[/tex] coulombs per square meter.

To find the total charge on a disk with a given charge density, we need to integrate the charge density over the entire area of the disk. In this case, the charge density is not constant, so we convert the cartesian coordinates to polar coordinates which simplifies the integral. The final solution is obtained by performing a double integral over r and θ.

The student is asking for the total electric charge on a disk with a given charge density. The disk being referred to is defined by the equation x² + y² ≤ 16, i.e., a disk of radius 4 units, and the charge density at any point (x, y) on the disk is given by rho(x, y) = 2x + 2y + 2x² + 2y².

In such problems, we find the total charge by integrating the charge density over the entire area of the disk. But in this case, we first need to convert the cartesian coordinates (x, y) to polar coordinates. which simplifies the integral. In polar coordinates, the area element is r dr dθ and the charge density funciton becomes rho(r, θ) = 2r cosθ + 2r sinθ + 2r². We perform a double integral of this function over r from 0 to 4 and θ from 0 to 2π.

This is a classic example of a problem in electrostatics, particularly involving the calculation of electric charge given a non-uniform charge density.

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Answer:

a) Null hypothesis: [tex]p \leq 0.44[/tex]

b) Alternative hypothesis: [tex]p > 0.44[/tex]

c) For this case our parameter of interest is a proportion "reduced rate of first heart attacks for a new drug". for this reason the answer would be 1 proportion and we can conduct the hypothesis with a 1 z proportion test  

Step-by-step explanation:

For this case the pharmaceutical company thinks they have a drug that will be more effective than aspirin and on this case that means a better rate in order to reduce the heart attacks (that represent the alternative hypothesis since that;s what they want to proof), and the complement would be the null hypothesis.

Part a

Null hypothesis: [tex]p \leq 0.44[/tex]

Part b

Alternative hypothesis: [tex]p > 0.44[/tex]

Part c

For this case our parameter of interest is a proportion "reduced rate of first heart attacks for a new drug". for this reason the answer would be 1 proportion and we can conduct the hypothesis with a 1 z proportion test  

Answer:

there is a 1/18th percent chance Darlene and bob will go in that order

Step-by-step explanation:

Answer:

The answer is c

Step-by-step explanation:

the graph shows the equations y=3x-2 and y=1/2+3 and if y is greater than the otherside you shade above and if it's less than the otherside you shade below. y=3x-2 is sahded above the line and y=1/2+3 is shaded below the line.

Answer:

  see below

Step-by-step explanation:

The line with the shallow slope has a slope of 1 unit of rise for each 2 units of run, so a slope of 1/2. It has a y-intercept of 3. The shading is below it, so you're looking for an inequality that looks like ...

  y ≤ 1/2x + 3

Only one answer choice matches.

Answer:

Probability of event

0.34

Step-by-step explanation:

Final answer:

The probability that exactly 3 people out of a sample of 20 Americans are afraid of being alone in a house at night, given that 5% of Americans have this fear, is approximately 13.98%.

Explanation:

The question asks for the probability that exactly 3 people in a sample of 20 Americans are afraid of being alone in a house at night, given that 5% of Americans have this fear. This can be solved using the binomial probability formula, which is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on an individual trial, and C(n, k) is the number of combinations of n items taken k at a time.

Plugging in the values, we get P(X = 3) = C(20, 3) * 0.05³* 0.95¹⁷ First, calculate C(20, 3) = 20! / (3!(20-3)!) = 1140. Then calculate the probability: P(X = 3) = 1140 * 0.05³* 0.95¹⁷.

Doing the math, P(X = 3) ≈ 0.1398, or approximately 13.98%.

Final answer:

The probability that exactly 3 out of 20 Americans are afraid of being alone at night is found by using the binomial probability formula, which incorporates the number of people in the sample, the number who are afraid, and the overall chance of fear of being alone at night.

Explanation:

To find the probability that exactly 3 people out of a random sample of 20 Americans are afraid of being alone at night when it is known that 5% of Americans have this fear, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

n is the number of trials (in this case, 20)

k is the number of successes (in this case, 3)

p is the probability of success on an individual trial (5% or 0.05)

C(n, k) is the number of combinations of n things taken k at a time

Let's calculate:

Compute C(20, 3): This is 20! / (3! * (20-3)!).

Calculate p^k, which is 0.05^3.

Calculate (1-p)^(n-k), which is (1-0.05)^(20-3).

Multiply these together to get the probability.

After performing the calculations, we determine the probability of exactly 3 out of 20 Americans being afraid of being alone at night.

Answer:

[tex]5.5-2.701\frac{1.1}{\sqrt{42}}=5.04[/tex]    

[tex]5.5+2.701\frac{1.1}{\sqrt{42}}=5.96[/tex]    

So on this case the 99% confidence interval would be given by (5.04;5.96)

And the best option would be:

a. 5.04 and 5.96

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X=5.5[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s=1.1 represent the sample standard deviation

n=42 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

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

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

[tex]df=n-1=42-1=41[/tex]

Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,41)".And we see that [tex]t_{\alpha/2}=2.701[/tex]

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

[tex]5.5-2.701\frac{1.1}{\sqrt{42}}=5.04[/tex]    

[tex]5.5+2.701\frac{1.1}{\sqrt{42}}=5.96[/tex]    

So on this case the 99% confidence interval would be given by (5.04;5.96)

And the best option would be:

a. 5.04 and 5.96

Answer:

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron. (OR) A face is a 2D shape that makes up one surface of a 3D shape, an edge is where two faces meet and a vertex is the point or corner of a geometric shape.

Step-by-step explanation:

The question is incomplete. The complete question is as follows.

Consider the reduction of the rectangle. A large rectangle has a length of 16.8 feet and width of 2.3 feet. A smaller rectangle has a length of 4.5 feet and width of x feet. Not drawn to scale (The drawing is in the attachment). Rounded to the nearest tenth.  

What is the value of x?

A. 0.1 feet

B. 0.6 feet

C. 1.6 feet

D. 2.0 feet

Answer: B. 0.6 feet

Step-by-step explanation: Two quantity are proportional if the ratio of them is constant. From the drawing and the question, we have that the two rectangles are proportional between them.

[tex]\frac{x}{2.3} = \frac{4.5}{16.8}[/tex]

[tex]x = \frac{4.5*2.3}{16.8}[/tex]

x = [tex]\frac{10.35}{16.8}[/tex]

x = 0.6

The width of the smaller rectangle is 0.6 feet.

Answer: 0.6 ft.

Step-by-step explanation: 16.8/4.5= 3.733333333 repeating. The scale factor is 3.73333333333 repeating. 2.3/3.733333333333 Repeating equals .61607142857. We can shorten it to .61, and it says rounded to the nearest tenth, so .61 rounded is 0.6.

Answer:

Attached

Step-by-step explanation:

On a cartessian plane, we take four points as shown. Point A has coordinates as (4, 0) while point B is (32, 0). Since the y cordinates are zero, don't change, only x change. Change in x coordinates is 32-4=28 units.

Point C is (32, 12) where x has not changed when compared to point B but y changes by 12-0=12 units

Therefore, the diagram is triangle whose length is 28 units while width is 12 units.

Answer:

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{15-5}=\frac{1}{10};\ 5<X<15[/tex]

Step-by-step explanation:

A continuous Uniform distribution is the probability distribution of a random outcome of an experiment that lies with certain specific bounds.

Consider that random variable X follows a continuous Uniform distribution and the value of X lies between a and b.

The probability density function of the random variable X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

Now, in this case it is provided that the amount of salad taken is uniformly distributed between 5 ounces and 15 ounces.

The random variable X is defined as:

Χ = Salad plate filling weight.

The probability density function of the salad plate filling weight is:

[tex]f_{X}(x)=\frac{1}{15-5}=\frac{1}{10};\ 5<X<15[/tex]

In mathematics at a college level, this answer explains how to find the probability density function of a uniformly distributed random variable representing the amount of salad taken by customers at TAB.

Given: Customers at TAB take salad that is uniformly distributed between 5 ounces and 15 ounces. Let X = Salad plate filling weight.

i. Find the probability density function of X: Since the salad amount is uniformly distributed, the probability density function is a horizontal line, given by f(x) = 1/(b-a), where a = 5 and b = 15, so f(x) = 1/10 for 5 ≤ x ≤ 15.

Answer: x^2+9 and x^2+3x+9

Step-by-step explanation:

A polynomial is prime if it cannot be factored into polynomials of lower degree. In this case, x² +9 and x² + 3x + 9 are prime polynomials while x² -9 and -2x² +8 are not.

In mathematics, a polynomial is said to be prime if it cannot be factored into polynomials of lower degree, at least one of which must be non-constant. To determine if a polynomial is prime, we try to factor it. In our case:

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Answer:

The probability is 0.503

Step-by-step explanation:

If the ghost appearances occur in the house according to a Poisson process with mean m, the time between appearances follows a exponential distribution with mean 1/m. so, the probability that the next ghost appearance happens before x hours is equal to:

[tex]P(X\leq x)=1-e^{-xm}[/tex]

Then, replacing m by 1.4 ghosts per hour we get:

[tex]P(X\leq x)=1-e^{-1.4x}[/tex]

Additionally, The exponential distribution have a memoryless property, so if it is now 1:00 p.m. and we want the probability that ghost appear before 1:30 p.m., we need to find the difference in hours from 1:00 p.m and 1:30 p.m. no matter that the last ghost appearance was at 12:35 p.m.

Therefore, there are 0.5 hours between 1:00 p.m. and 1:30 p.m, so the probability that the 7th ghost will appear before 1:30 p.m is calculated as:

[tex]P(x\leq 0.5)=1-e^{-1.4*0.5} =0.503[/tex]

Final answer:

The probability that the 7th ghost will appear before 1:30 p.m. in an old house in Pomona, CA can be calculated as approximately 0.5034, or 50.34%. This calculation is based on the Poisson distribution, with a rate of 1.4 ghosts per hour and the last ghost appearance occurring at 12:35 p.m.

Explanation:

The probability of the 7th ghost appearing before 1:30 p.m. can be calculated using the Poisson distribution. We know that the rate of ghost appearances is 1.4 ghosts per hour, which means the average time between ghost appearances is 1/1.4 hours. From 12:35 p.m. to 1:00 p.m., there are 25 minutes, or 25/60 hours. So, the probability that the 7th ghost will appear before 1:30 p.m. is equal to the probability that there will be at least 1 ghost in the remaining time, i.e., the probability that at least one ghost appears in the next 30 minutes.

We can use the complementary probability method to calculate this. The complementary probability is the probability that none of the ghosts appears in the next 30 minutes. Since the time follows a Poisson process, we can use the Poisson probability formula. Let's calculate:

Therefore, the probability that the 7th ghost will appear before 1:30 p.m. is approximately 0.5034, or 50.34%.

Answer:

Test statistics = 3.74

P-value = 0.0001

Step-by-step explanation:

We are given that an experiment to compare the tension bond strength of polymer latex modified mortar to that of unmodified mortar resulted in x = 18.11 kg f/[tex]cm^{2}[/tex] for the modified mortar (m = 42) and y = 16.83 kg f/[tex]cm^{2}[/tex] for the unmodified mortar (n = 30).

Assume that the bond strength distributions are both normal and assuming that σ1 = 1.6 and σ2 = 1.3.

Let [tex]\mu_1[/tex] = true average tension bond strengths for the modified mortars

      [tex]\mu_2[/tex] = true average tension bond strengths for the unmodified mortars

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1-\mu_2=0[/tex]  or  [tex]\mu_1=\mu_2[/tex]    {means that true average tension bond strengths for the modified and unmodified mortars are same}

Alternate Hypothesis, [tex]H_a[/tex] : [tex]\mu_1-\mu_2>0[/tex]  or  [tex]\mu_1>\mu_2[/tex]    {means that the true average tension bond strengths for the modified mortars is greater than that for unmodified mortars}

The test statistics that will be used here is Two-sample z test statistics as we know about population standard deviations;

               T.S.  =  [tex]\frac{(x-y)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{m}+\frac{\sigma_2^{2} }{n} } }[/tex]  ~ N(0,1)

where, x = sample mean tension bond strengths for the modified mortars = 18.11 kg f/[tex]cm^{2}[/tex]

         y = sample mean tension bond strengths for the unmodified mortars = 16.83 kg f/[tex]cm^{2}[/tex]

         [tex]\sigma_1[/tex] = population standard deviation for modified mortars = 1.6

         [tex]\sigma_2[/tex] = population standard deviation for unmodified mortars = 1.3

         m = sample of modified mortars = 42

         n = sample of unmodified mortars = 30

So, test statistics  =  [tex]\frac{(18.11-16.83)-(0)}{\sqrt{\frac{1.6^{2} }{42}+\frac{1.3^{2} }{30} } }[/tex]

                               =  3.74

Now, P-value is given by the following formula;

         P-value = P(Z > 3.74) = 1 - P(Z [tex]\leq[/tex] 3.74)  

                                            = 1 - 0.9999 = 0.0001

Here, the above probability is calculated by looking at the value of x = 3.74 in the z table which gives an area of 0.9999.

To test the hypothesis H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 > 0 at level 0.01, calculate the test statistic and the P-value. The test statistic is Z = (x - y) / √((σ1² / m) + (σ2² / n)). Substituting the values gives Z = 1.278. The P-value is approximately 0.1019.

To test the hypothesis H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 > 0 at level 0.01, we calculate the test statistic and the P-value. The test statistic is given by:

Z = (x - y) / √((σ1² / m) + (σ2² / n))

where x = 18.11, y = 16.83, σ1 = 1.6, σ2 = 1.3, m = 42, and n = 30.

Substituting the values, we get Z = (18.11 - 16.83) / √((1.6² / 42) + (1.3² / 30)).

Calculating Z gives Z = 1.278. To determine the P-value, we find the area to the right of Z in the standard normal distribution. The P-value is the probability that Z > 1.278. Consulting a Z-table or using a calculator, we find the P-value to be approximately 0.1019.

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Based on the experimental design and the data collected the statistical test that should be used is the correlation coefficient.

The statistical tests are tests that are used by researchers to determine the progress of a set process and make a quantitative decision during analysis of test results.

Example of statistical tests include the following:

The correlation coefficient which is a type of statistical test is used to assess the strength and direction of the linear relationships between pairs of variables.

Therefore, the relationship between cognitive reflectivity and cognitive impulsivity in human data can be statistically analysed using correlation coefficient.

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Answer:

Step-by-step explanation:

We are given that [tex] R(x) = 108\sqrt[]{x}[/tex] is the revenue for having x employees.

Let us calculate the following

[tex]R(12)-R(11) = 108\sqrt[]{12}-108\sqrt[]{11} = 15.93[/tex] REcall that is amount represents the revenue that having one extra employee would have.

We have that the salary of the 12th employee would be 26000. One criteria to define if it's a good idea to hire the 12th employee is to check if the profit for having an extra employee is positive. We will take the revenue of the extra employee minus the cost and check if it is positiv. Then,

[tex](108\sqrt[]{12}-108\sqrt[]{11})\text{(revenue for 12 employees)}-26000\text{(cost for the 12th employee} =-25984<0[/tex]

Since it is a negative amount, this means that it would be more expensive to have one extra employee than the revenue it would generate. Therefore, it won't be suitable to hire the 12th employee

Answer:

[tex]z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933[/tex]  

[tex]p_v =2*P(z<-1.933)=0.0532[/tex]  

Step-by-step explanation:

Information given

n=370 represent the sample selected

[tex]\hat p=0.4[/tex] estimated proportion of  readers owned a laptop

[tex]p_o=0.45[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Creating the hypothesis

We need to conduct a hypothesis in order to test if the true proportion of readers owned a laptop is different from 0.45, the system of hypothesis are:  

Null hypothesis:[tex]p=0.45[/tex]  

Alternative hypothesis:[tex]p \neq 0.45[/tex]  

The statistic is:

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

Replacing we got:

[tex]z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933[/tex]  

Calculating the p value  

We have a bilateral test so then the p value would be:

[tex]p_v =2*P(z<-1.933)=0.0532[/tex]  

Answer:

[tex]t_{1} \approx 9.943\,s[/tex] and [tex]t_{2} \approx 0.057\,s[/tex]

Step-by-step explanation:

The following polynomial is needed to be solved:

[tex]-16\cdot t^{2} + 160\cdot t - 9 = 0[/tex]

The roots are found by means of the General Equation for Second-Order Polynomials:

[tex]t_{1} \approx 9.943\,s[/tex] and [tex]t_{2} \approx 0.057\,s[/tex]

Physically speaking, both solutions are reasonable.

Answer:

t = 0.0625

Step-by-step explanation:

Given that,

Height, h = -16t + 160t

To obtain time,t at height,h = 9feet

We substitute h = 9 into the given equation to have:

9 = - 16t + 160t

: 9 = 144t

t = 9/ 144 = 0.0625

The chip amount that represents the 67th percentile is 48.588.and this can be determined by using the formula of z-score.

Given :

The amount of corn chips dispensed into a bag by the dispensing machine has been identified as possessing a normal distribution with a mean of μ = 48.5 ounces and a standard deviation of σ = 0.2 ounces.

To determine the chip amount that represents the 67th percentile, the below formula can be used:

[tex]\rm z = \dfrac{x-\mu}{\sigma}[/tex]

Now, substitute the values of known terms in the above formula:

[tex]\rm 0.44 = \dfrac{x - 48.5}{0.2}[/tex]

Cross multiply in the above equation.

[tex]\rm 0.44\times 0.2 = x - 48.5[/tex]

Now further, simplify the above equation.

0.088 = x - 48.5

x = 48.5 + 0.088

x = 48.588

So, the chip amount that represents the 67th percentile is 48.588.

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The weight that represents the 67th percentile of the corn chip bags, with a given mean of 48.5 ounces and a standard deviation of 0.2 ounce, is 48.59 ounces, calculated using the z-score provided.

To determine the amount of corn chips that represents the 67th percentile, p67, for a bag's weight distribution with a mean of μ = 48.5 ounces and a standard deviation of σ = 0.2 ounce. Given that the z-score for the 67th percentile is z = 0.44, we can use the percentile to z-score formula to find the corresponding weight.

To convert a z-score to a specific value within a normal distribution, we use the formula:

X = μ + zσ

For the 67th percentile:

X = 48.5 + (0.44 × 0.2)

X = 48.5 + 0.088

X ≈ 48.59 ounces (rounded to two decimal places)

This means that the weight that represents the 67th percentile of corn chip bag weights, to the nearest hundredth, is 48.59 ounces.

To predict the number of golden retrievers G that will be registered in year t, use the linear equation G = -6.4t + 12868.9.

To predict the number of golden retrievers G that will be registered in year t, we can use a linear equation. We have two data points: (2001, 62.5) and (2002, 56.1). We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Step 1: Determine the slope (m) using the formula m = (y2 - y1) / (x2 - x1) = (56.1 - 62.5) / (2002 - 2001) = -6.4

Step 2: Choose one of the data points and substitute the values into the equation to solve for b. Using (2001, 62.5), we can substitute x = 2001 and y = 62.5.

62.5 = -6.4 * 2001 + b
62.5 = -12806.4 + b
b = 12868.9

Step 3: The linear equation to predict the number of golden retrievers G is G = -6.4t + 12868.9.

Answer:

The value of the t-statistic for this test is 1.138.

Step-by-step explanation:

We are given that a new manager of a small convenience store randomly samples 20 purchases from yesterday’s sales. The mean was $45.26 and the standard deviation was $20.67.

We wish to test for evidence that the overall mean purchase amount is at least $40

Let [tex]\mu[/tex] = overall mean purchase amount

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] $40   {means that the overall mean purchase amount is at least $40}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < $40   {means that the overall mean purchase amount is less than $40}

The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;

                           T.S.  = [tex]\frac{\bar X -\mu}{{\frac{s}{\sqrt{n} } } }[/tex]  ~ [tex]t_n_-_1[/tex]

where,  [tex]\bar X[/tex] = sample mean sale = $45.26

              s = sample standard deviation = $20.67

              n = sample of purchases = 20

So, test statistics  =  [tex]\frac{45.26-40}{{\frac{20.67}{\sqrt{20} } } }[/tex]  ~ [tex]t_1_9[/tex]

                               =  1.138

Hence, the value of the t-statistic for this test is 1.138.