Data on return-to-pay ratios was collected from CEOs of companies within both the low-tech industry and the consumer products industry.

Low-Tech Consumer Products
Sample size 14 12
Sample mean 157 218
Sample Variance 1563 1602
Assume population variances are unequal.

(a) The point estimate of the difference between the means of the two populations is

(b) The standard error for the difference between the two means is

(c) The correct distribution to use is :

t-distribution with 26 degrees of freedom

t-distribution with 23 degrees of freedom

normal distribution

t-distribution with 24 degrees of freedom

Answer: No

Step-by-step explanation:

Simple! No. There can be hexagonal, octagonal, and other types of prisms that do not have a triangular/rectangular base.

Hope that helped,

-sirswagger21

Answer:

a)Randomization condition: Satisfied, as the subjects were randomly selected.

10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).

Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.

b) The 90% confidence interval for the population proportion is (0.68, 0.70).

Step-by-step explanation:

a) Evaluating the necessary conditions:

Randomization condition: Satisfied, as the subjects were randomly selected.

10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).

Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.

[tex]n(1-p)=4,726\cdot (1-0.69)=4,726\cdot 0.31=1,465>10[/tex]

b) We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.69.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.69*0.31}{4726}}\\\\\\ \sigma_p=\sqrt{0.000045}=0.007[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.007=0.01[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.69-0.01=0.68\\\\UL=p+z \cdot \sigma_p = 0.69+0.011=0.70[/tex]

The 90% confidence interval for the population proportion is (0.68, 0.70).

Answer:

The length of the diameter of this circular area is of 30 miles.

Step-by-step explanation:

The area of a circular region can be represented by the following equation:

[tex]A = \pi r^{2}[/tex]

In which r is the radius. The diameter is twice the radius.

In this question:

[tex]A = 225\pi[/tex]

So

[tex]A = \pi r^{2}[/tex]

[tex]225\pi = \pi r^{2}[/tex]

[tex]r^{2} = 225[/tex]

[tex]r = \pm \sqrt{225}[/tex]

The radius is a positive measure, so

[tex]r = 15[/tex]

Area in squared miles, so the radius in miles.

What is the approximate length of the diameter of this circular area

D = 2r = 2*15 = 30 miles

The length of the diameter of this circular area is of 30 miles.

Answer:

The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.

Step-by-step explanation:

To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.

The prism and pyramid's bases is 25 cm²

The pyramid's height is 12÷2 or 6 cm

The volume formula for a prism is l×w×h

The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h

The area of the prism is 5×5×12 or 300 cm³

The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³

300 cm³-75 cm³=225 cm³

The volume outside the pyramid but inside the prism is 225 cm³.

Answer:

Step-by-step explanation:

a) The number of students sampled in both populations are large. We can assume that the populations are normally distributed. The populations are also independent.

b) This is a test of 2 independent groups. Let μ1 be the mean responses of students buying lecture notes and μ2 be the mean responses of students not buying lecture notes.

The random variable is μ1 - μ2 = difference in the mean responses of students buying lecture notes and the mean responses of students not buying lecture notes.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 8.48

x2 = 7.8

s1 = 0.94

s2 = 2.99

n1 = 86

n2 = 35

t = (8.48 - 7.8)/√(0.94²/86 + 2.99²/35)

t = 1.32

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.94²/86 + 2.99²/35]²/[(1/86 - 1)(0.94²/86)² + (1/35 - 1)(2.99²/35)²] = 0.0706/0.00192021883

df = 37

We would determine the probability value from the t test calculator. It becomes

p value = 0.195

c) Since alpha, 0.01 < than the p value, 0.195, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, the samples do not provide sufficient evidence to conclude that there is a difference in the mean responses of the two groups of the students.

d) The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 99% confidence interval, the z score is 1.2.58. This is determined from the normal distribution table.

x1 - x2 = 8.48 - 7.8 = 0.68

z√(s1²/n1 + s2²/n2) = 2.58√(0.94²/86 + 2.99²/35) = 1.33

The confidence interval is

0.68 ± 1.33

The upper boundary for the confidence interval is

0.68 + 1.01 = 2.01

The lower boundary for the confidence interval is

0.68 - 1.33 = - 0.65

We are confident that the difference in population means responses between the students buying lecture notes and the students not buying lecture notes is between - 0.65 and 2.01

d) For a 95% confidence interval, the z score is 1.96.

z√(s1²/n1 + s2²/n2) = 1.96√(0.94²/86 + 2.99²/35) = 1.01

The confidence interval is

0.68 ± 1.01

The upper boundary for the confidence interval is

0.68 + 1.01 = 1.69

The lower boundary for the confidence interval is

0.68 - 1.01 = - 0.33

Therefore, a 95% confidence interval for (μ1-μ2) would be narrower. This is seen in the values in both scenarios.

Answer: I think In short, the interior angles are all the angles within the bounds of the triangle. ... If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring exterior angle, you always get 180—a straight line, A square has 4 90 degree angles so it adds to 360, think about how triangles having half the area of a square, just like how 180 is half of 360

hope this helped

Answer: y= -15 - 3x/5 is the answer.

Step-by-step explanation:

Answer:

The second graph

Step-by-step explanation:

Answer:

The answer would be 1,853,614,297

Answer:

  A, C, D, E

Step-by-step explanation:

According to the rational root theorem, any rational roots will be of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

The constant is 8, and its divisors are 1, 2, 4, 8.

The leading coefficient is 6, and its divisors are 1, 2, 3, 6.

So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:

Answer:

Step-by-step explanation:

BRUH YOU STUPID

Answer:

0

[tex] \\ solution \\ - 2( -5) - 7 + 1( - 3) \\ = 10 - 7 + ( - 3) \\ = 10 - 7 - 3 \\ = 3 - 3 \\ = 0 \\ hop \: it \: helps...[/tex]

Answer:

GH¢. 18098.46

Step-by-step explanation:

Let the first investment giving 12% interest per annum be Bank A

Let the 2nd investment giving 10% per annum be bank B

Let the first amount invested be

GH¢. X and let the second amount invested be GH¢. X + 580

Thus; In bank A;

Principal amount in first = GH¢. x

rate = 12 %

time = 1 year

Formula for simple interest = PRT/100

Where P is principal, R is rate and T is time.

So, interest in his investment = 12X/100 = 0.12X

while in bank B;

principal amount = GH¢. X + 580

rate = 14%

time = 1 yr

So, interest in his investment = [(X + 580) × 14]/100

= 0.14(X + 580)

So, total accumulated interest is;

0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2

Now, we are given accumulated interest = GH¢. 2,358.60

Thus;

2358.60 = (0.26X + 81.2)

2358.6 - 81.2 = 0.26X

X = 2277.4/0.26

X = 8759.23

So,

first amount invested = GH¢. 8759.23

Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23

Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46

Answer:

1.2 km

Step-by-step explanation:

The first thing that we should go over is the formula for the area of a trapezoid.

Recall that it is [tex]A= \frac{b_1 +b_2}{2} *h[/tex]

From this image, we have the following information

[tex]b_1=2.5\\\\b_2=1.5\\\\A=2.4[/tex]

Now, we can plug this information into our formula and then solve for h.

[tex]2.4=\frac{2.5+1.5}{2} *h\\\\2.4=\frac{4}{2} *h\\\\2.4=2h\\\\h=1.2[/tex]

Another method that can be employed is to use the pythagorean theorem.

A trapezoid can be be broken into a rectangle and two triangles.

If we look at the difference in the sizes of the bases, the bottom base is 1 km larger. This means that the base of each triangle would be 0.5 km long.

As we have two side lengths of the triangle, we can now use the Pythagorean theorem to find the third side, which is h.

[tex](1.3)^2=h^2+(0.5)^2\\\\h^2=1.69-0.25\\\\h=\sqrt{1.44} \\\\h=1.2[/tex]

Answer:

h=1.2 km

Step-by-step explanation:

This is the formula of a Trapezium

A=[tex]\frac{h(a+b)}{2}[/tex]

[tex]2.4=\frac{(2.5+1.5)h}{2}\\ 2.4=\frac{4h}{2}\\ 2.4*2=4h\\4.8=4h\\h=1.2[/tex]

Answer:

  see below

Step-by-step explanation:

Considering the last two table entries, we can find the slope of the line to be ...

  Δy/Δx = (24 -14)/(10 -6) = 10/4 = 5/2

The point-slope form of the equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

For (h, k) = (-2, -6) and m = 5/2, this is ...

  y -(-6) = 5/2(x -(-2))

  y +6 = 5/2(x +2) . . . . . matches the last choice

Answer:

d is the right choice

Step-by-step explanation:

Answer:

8 yds

Step-by-step explanation:

The sides have to have the same length

14 yd = 6yd + ?

Subtract 6 from each side

14-6 = 8

8 yds

Answer:

[tex] V =\frac{1}{3} \pi r^2 h[/tex]

For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:

[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]

And the best option would be:

[tex] V = \frac{539}{3} \pi cm^3 [/tex]

Step-by-step explanation:

For this case we know that the volume of the cone is given by:

[tex] V =\frac{1}{3} \pi r^2 h[/tex]

For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:

[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]

And the best option would be:

[tex] V = \frac{539}{3} \pi cm^3 [/tex]

Answer:

All the elements in the sample share a common characteristic. All of them read the magazine, so we may have a biased sample. And we also have the bias of the fact that only the volunteers will respond to this survey, so this is a biased sample.

This type of sample is usually called convenience sampling, where the elements in the sample are the most readily available (and what is most readily available for a magazine than its own readers?)

Then the type of sample is a convenience sample and a biased sample.

Answer:

6.68% probability that the mean weight is below 68.5g.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]

Probability that the mean weight is below 68.5g:

This is 1 subtracted by the pvalue of Z when X = 68.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{68.5 - 70}{1}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% probability that the mean weight is below 68.5g.

Answer:

P(x ∠ 68.5) = 0.07

Step-by-step explanation:

Got it right on khan.

Answer:

76

Step-by-step explanation:

The two angles are vertical angles so they are equal

3x+7 = 4x-16

Subtract 3x from each side

3x-3x+7 = 4x-3x-16

7 = x-16

Add 16 to each side

7+16 = x-16+16

23 =x

We want YAX

YAX = 3x+7

3*23+7

69+7

76

Answer:

x = 54°

h = 7.5cm

w= 6cm

Step-by-step explanation:

Find attached the diagrams as found at Maths made easy.

Similar shapes have same shapes but different sizes.

When two shapes are similar, the ratios of the lengths of their corresponding sides are equal.

B is an enlargement of A with scale factor 1.5. That is, each of the sides of B = 1.5 of each side of A

To determine the value of x, h and w, let's look at the relationship of A and B.

h = 1.5 × 5cm

h = 7.5cm

9cm = 1.5 × w

w = 9cm/1.5

w= 6cm

Since the angles do not change when a shape is enlarged, the value of x = 54°

x = 54°

Answer:

The capital B refers to the base of the area

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The capital B means the area of the base

Answer:

A unit cube has one cubic unit of volume.

Another unit cube with the same length, width and height as the unit cube shown would have the same volume

Step-by-step explanation:

A cube is a shape formed from the combination of a square.

A cube has equal sides.

But a unit cube has equal sides and equal volume to be equal to one, i.e unity.

Answer:

the base is 5 meters long.

Step-by-step explanation:

To find the a missing side when given the area you have to multiply the area by 2 which in this case would be 50 so 50/10 would be 5m which is your answer.

So the right answer is 5m

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

-1, 1

13, 15

Step-by-step explanation:

x and x+2 are the integers

Roots of the quadratic equation are: -1 and 13.

So the integers pairs are: -1, 1 and 13, 15

Answer:

k = -4 (0, -14) also lies on the graph

Step-by-step explanation:

6 = (7 - 2)2 + k

6 = 10 + k

-4 = k

y = (0 - 5)2 - 4, y = -14

Answer:

x=135

Step-by-step explanation:

We know that sin(270) = -1/2

So 2x = 270

x = 135

Answer:

The critical values of F at 95% confidence are 0.359 and 2.788.

Step-by-step explanation:

We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:

Store A                     Store B    

nA = 21                      nB = 16

SA = 28.284              SB = 20

And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.

AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.

The test statistics for F-test is =  [tex]\frac{S_A^{2} }{S_B^{2} } \times \frac{\sigma_B^{2} }{\sigma_A^{2} }[/tex]  ~ [tex]F__n_A_-_1,_ n_B_-_1[/tex]

where, [tex]S_A[/tex] and [tex]S_B[/tex] are sample standard deviations.

Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;

2.788 for right-part and 0.359 for the left-part.

Answer:

Step-by-step explanation:

_______________________________

Hey!!

Solution,

X+61+42=180[ sum of angle in triangle]

or,X+103=180

or,X=180-103

X=77°

So the value of X is 77°

Hope it helps..

Good luck on your assignment

____________________________

Answer:

Answer: 4615.66667

Steps: 1 foot=0.33333

total feets=30.5×454=13847

13847 feets=46.1566667 yards

Answer:

The age difference between oldest the youngest is of 48 years.

Step-by-step explanation:

We can solve this question using a system of equations.

I am going to say that:

Kissi's age is x.

Esinam's age is y.

Lariba's age is z.

The ratio of the ages of Kissi and Esinam is 3:5

This means that [tex]\frac{x}{y} = \frac{3}{5}[/tex], so [tex]5x = 3y[/tex]

That of Esinam and Lariba is 3:5

This means that [tex]\frac{y}{z} = \frac{3}{5}[/tex], so[tex]5y = 3z[/tex]

The sum of the ages of all 3 is 147 years

This means that [tex]x + y + z = 147[/tex]

What is the age difference between oldest the youngest

z is the oldest

x is the youngest.

First i will find y.

We have that, from the equations above: [tex]x = \frac{3y}{5}[/tex] and [tex]z = \frac{5y}{3}[/tex]

So

[tex]x + y + z = 147[/tex]

[tex]\frac{3y}{5} + y + \frac{5y}{3} = 147[/tex]

The lesser common multiple between 5 and 3 is 15. So

[tex]\frac{3*3y + 15*y + 5*5y}{15} = 147[/tex]

[tex]49y = 147*15[/tex]

[tex]y = \frac{147*15}{49}[/tex]

[tex]y = 45[/tex]

Youngest:

[tex]x = \frac{3y}{5} = \frac{3*45}{5} = 27[/tex]

Oldest:

[tex]z = \frac{5y}{3} = \frac{5*45}{3} = 75[/tex]

Difference:

75 - 27 = 48

The age difference between oldest the youngest is of 48 years.

Answer:

Step-by-step explanation:

Let the first term is n, then the second term must be an where a is a common ratio, and the third term is a^2 n

so, n + an = 24

n + an + a^2 n = 26

solve for a, then solve for n