Only questions 8 and 9 help please!!!

Their headquarters contains 28000 employees.

Step-by-step explanation:

Given,

Total number of employees = 30000

Let,

Number of employees in headquarters = x

Number of employees in overseas branch = y

According to given statement;

x+y=30000     Eqn 1

x = 14y             Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]14y+y=30000\\15y=30000\\[/tex]

Dividing both sides by 15

[tex]\frac{15y}{15}=\frac{30000}{15}\\y=2000[/tex]

Putting y=2000 in Eqn 2

[tex]x=14(2000)\\x=28000[/tex]

Their headquarters contains 28000 employees.

Keywords: linear equation, division

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The overseas branch has 2,000 employees, and since the headquarters has 14 times as many employees, it contains 28,000 employees.

We need to determine the number of employees at the headquarters of a company given that the headquarters has 14 times as many employees as the overseas branch, and the total number of employees in both buildings is 30,000.

Let's denote the number of employees in the overseas branch as x. Then, the number of employees in the headquarters is 14x. According to the problem, the total number of employees in both buildings is:

x + 14x = 30,000

Combining the terms:

15x = 30,000

To find x, we divide both sides by 15:

x = 30,000 / 15

x = 2,000

This means the overseas branch has 2,000 employees.

Now, since the headquarters contains 14 times as many employees as the overseas branch, we calculate:

14x = 14 * 2,000 = 28,000

Therefore, their headquarters contains 28,000 employees.

Answer:

3718 ways

Step-by-step explanation:

How many ways can a person toss a coin 13 times so that the number of tails is between 7 and 9 inclusive

Probability is the likelihood for an event to occur  or not

The formula for a combination is:

n choose r = n! / (r! x (n-r)!)  

n=13

r=7 to 9

We are going to add up the cases for 7 through 9:

[tex]^{n } C_{r}[/tex]

[tex]^{13 } C_{7}[/tex]+[tex]^{13 } C_{8}[/tex]+[tex]^{13 } C_{9}[/tex]

[tex]\frac{n!}{r!(n-r)!}[/tex]

[tex]\frac{13!}{7!(13-7)!}[/tex]+[tex]\frac{13!}{8!(13-8)!}[/tex]+[tex]\frac{13!}{9!(13-9)!}[/tex]

1716+1287+715

3718 ways

Answer:

Marginal Product of Labour = 5K

Step-by-step explanation:

Marginal product of labor is the change in output when additional labor is added,

To calculate marginal product of labor you simply divide the change in total product by the change in labour.

Marginal product of labour (MPL) = Change in total products/ Change in labour

Here, change in labour = 5KL

Change in labour = L

MPL = 5KL/L

MPL = 5K

The marginal product of labor for Joe's coffee house, where the production function is q = 5KL, is found by differentiating q with respect to L, resulting in 5K, which indicates that each additional employee increases output by 5 times the number of coffee machines available.

The marginal product of labor (MP) is the additional output generated by employing one more unit of labor while holding other factors of production constant. In Joe’s coffee house, where the production function is given by q = 5KL (with q as the number of cups produced per hour, K as the number of coffee machines, and L as the number of employees), the marginal product of labor can be found by differentiating the production function with respect to labor. As capital (K) is held constant, the marginal product of labor will be calculated as follows:

MP = d(q)/d(L) = d(5KL)/d(L) = 5K

This equation indicates that the marginal product of labor is 5 times the number of coffee machines in use because K is constant in the short run. Therefore, every additional employee hired will increase the output (q) by an amount equal to 5 times the number of coffee machines that Joe has in his coffee house.

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Answer:

Step-by-step explanation:

The max and min values exist where the derivative of the function is equal to 0. So we find the derivative:

[tex]y'=9x^2+28x-11[/tex]

Setting this equal to 0 and solving for x gives you the 2 values

x = .352 and -3.464

Now we need to find where the function is increasing and decreasing.  I teach ,my students to make a table.  The interval "starts" at negative infinity and goes up to positive infinity.  So the intervals are

-∞ < x < -3.464           -3.464 < x < .352             .352 < x < ∞

Now choose any value within the interval and evaluate the derivative at that value.  I chose -5 for the first test number, 0 for the second, and 1 for the third.  Evaluating the derivative at -5 gives you a positive number, so the function is increasing from negative infinity to -3.464.  Evaluating the derivative at 0 gives you a negative number, so the function is decreasing from -3.464 to .352.  Evaluating the derivative at 1 gives you a positive number, so the function is increasing from .352 to positive infinity.  That means that there is a min at the x value of .352.  I guess we could round that to the tenths place and use .4 as our x value.  Plug .4 into the function to get the y value at the min point.

f(.4) = -48.0

So the relative min of the function is located at (.4, -48.0)

Answer:

The lateral surface area of square pyramid is 448 square units.

Step-by-step explanation:

We are given the following in the question:

Side length of square pyramid = 11.2 units

Slant height of square pyramid = 20 units

Lateral area of a square pyramid =

[tex]L = \dfrac{1}{2}Ph[/tex]

where P is the perimeter of square base and h is the slant height.

Perimeter of square base =

[tex]P = 4\times \text{Base edge}\\= 4\times 11.2 = 44.8\text{ units}[/tex]

Putting the values, we get:

[tex]L = \dfrac{1}{2}\times 44.8\times 20 = 448\text{ square units}[/tex]

Thus, the lateral surface area of square pyramid is 448 square units.

Answer:

[tex]448 cm^{2}[/tex]

Step-by-step explanation:

s = 11.2; l = 20

L.A.  = [tex]4 (\frac{1}{2} sl)[/tex]

L.A.= [tex]\frac{1}{2}(4 * 11.2)20[/tex]  Multiply 4 * 11.2 to get perimeter 44.8

L.A. = [tex]\frac{1}{2} pl[/tex]

L.A. = [tex]\frac{1}{2} (44.8)20\\[/tex] Simplify 44.8 * 20

L.A. = [tex]\frac{1}{2}(896)\\[/tex] Divide 896 by 2

L.A. = [tex]448cm^{2}[/tex]

Answer:

$1040

Step-by-step explanation:

As 80/20 insurance policy is a form of coinsurance in which deductible is satisfied first and then the client would pay 20% of additional medical costs and the remaining 80% is paid by the insurance company. Under the current scenario, Veronica will bear an amount of $250 and $790(i.e. 20% of the amount after deductible), totaling to $1040.

Answer:

Step-by-step explanation:

Tex wants to make a lawn in the front of his house. The total yards are 30 by 30 yards. This means that the total area of the lawn is

30 × 30 = 900 yards^2

he gets 20 by 10 yards. This means that the total area of what he got would be

20 × 10 = 200 yards^2

Since what he needs is 900 yards^2 and it is greater than what he got, 200 yards^2, then it won't be enough.

What he needs more would be

900 - 200 = 700 yards^2

Answer:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{0.8^2}{1.0^2}=0.64[/tex]

[tex]p_v =P(F_{15,10}<0.64)=0.2105[/tex]

Since the [tex]p_v > \alpha[/tex] we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.  

Step-by-step explanation:

Data given and notation  

[tex]n_1 = 11 [/tex] represent the sampe size for the Old

[tex]n_2 =16[/tex] represent the sample size for the New

[tex]\bar X_1 =6.25[/tex] represent the sample mean for Old

[tex]\bar X_2 =5.95[/tex] represent the sample mean for the New

[tex]s_1 = 1.0[/tex] represent the sample deviation for Old

[tex]s_2 = 0.8[/tex] represent the sample deviation for New

[tex]\alpha=0.05[/tex] represent the significance level provided

Confidence =0.95 or 95%

F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:

[tex]F=\frac{s^2_2}{s^2_1}[/tex]

Solution to the problem  

System of hypothesis

We want to test if the variation for New sample it's lower than the variation for the Old sample, so the system of hypothesis are:

H0: [tex] \sigma^2_2 \geq \sigma^2_1[/tex]

H1: [tex] \sigma^2_2 <\sigma^2_1[/tex]

Calculate the statistic

Now we can calculate the statistic like this:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{0.8^2}{1.0^2}=0.64[/tex]

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_2 -1 =16-1=15[/tex] and for the denominator we have [tex]n_1 -1 =11-1=10[/tex] and the F statistic have 15 degrees of freedom for the numerator and 10 for the denominator. And the P value is given by:

P value

Since we have a left tailed test the p value is given by:

[tex]p_v =P(F_{15,10}<0.64)=0.2105[/tex]

And we can use the following excel code to find the p value:"=F.DIST(0.64,15,10,TRUE)"

Conclusion

Since the [tex]p_v > \alpha[/tex] we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.  

if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is 1.56. The option (d) is correct.

To test whether the new seed results in less variability in individual potato length compared to the old seed, we can perform an F-test for comparing variances.

The F-test statistic for comparing two variances is given by:

[tex]\[ F = \frac{s_1^2}{s_2^2} \][/tex]

where [tex]\( s_1^2 \)[/tex] is the variance of the old seed and [tex]\( s_2^2 \)[/tex] is the variance of the new seed. The larger variance should be the numerator to ensure the F-value is greater than or equal to 1.

Given data:

- Old Seed:

[tex]- \( n_1 = 11 \)\\ - \( \bar{x}_1 = 6.25 \) inches\\ - \( s_1 = 1.0 \) inch[/tex]

- New Seed:

[tex]- \( n_2 = 16 \)\\ - \( \bar{x}_2 = 5.95 \) inches\\ - \( s_2 = 0.80 \) inch[/tex]

First, calculate the variances:

- Variance of old seed, [tex]\( s_1^2 = (1.0)^2 = 1.0 \)[/tex]

- Variance of new seed, [tex]\( s_2^2 = (0.80)^2 = 0.64 \)[/tex]

Since [tex]\( s_1^2 \)[/tex] (old seed) is larger than [tex]\( s_2^2 \)[/tex] (new seed), we use:

[tex]\[ F = \frac{s_1^2}{s_2^2} = \frac{1.0}{0.64} \][/tex]

Now, calculate the F-value:

[tex]\[ F = \frac{1.0}{0.64} = 1.5625 \][/tex]

The calculated test statistic is approximately 1.56. Therefore, the correct answer is (d) 1.56.

The complete question is:

The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given: Old Seed - Number of Seeds = 11, Average length = 6.25 inches , Standard Deviation = 1.0 inches New Seed - Number of Seeds = 16, Average length = 5.95 inches Standard Deviation = 0.80 inches. On this data, if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is:

(a) 1.25

(b) 0.80

(c) 0.64

(d) 1.56

Answer:

60 times will they ring together at the same second in one hour excluding the one at the end.

Step-by-step explanation:

Given : Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively.

To find : How many times will they ring together at the same second in one hour excluding the one at the end?

Solution :

First we find the LCM of 3, 6, 10, 12 and 15.

2 | 3  6  10  12  15

2 | 3  3   5   6  15

3 | 3  3   5   3  15

5 | 1    1  5   1    5

  | 1    1   1   1     1

[tex]LCM(3, 6, 10, 12,15)=2\times 2\times 3\times 5[/tex]

[tex]LCM(3, 6, 10, 12,15)=60[/tex]

So, the bells will ring together after every 60 seconds i.e. 1 minutes.

i.e. in 1 minute they rand together 1 time.

We know, 1 hour = 60 minutes

So, in 60 minute they rang together 60 times.

Therefore, 60 times will they ring together at the same second in one hour excluding the one at the end.

Answer:

(B) 0.8+0.0025y

Step-by-step explanation:

Total houses =80

First y houses was painted at the rate of x hours per week

Remaining houses was painted at 1.25x hours per week

Remaining houses= 80-y

Rate = quantity/ time

Time = quantity/ rate

Time for the first painting = y/x

Time for the second painting = 80-y/1.25x

Total time y/x + 80-y/1.25x

= 0.25y +80/1.25x

If it was being painted at the original rate

Time = 80/x

The time to paint in this scenario as a fraction of the time it will take to paint in the original rate.

(0.25y+80/1.25x) /(x/80)

=( 0.25y +80)/100

=0.0025y +0.8

Answer:

B

Step-by-step explanation:

radius=24/2=12

eq. of circle is

x²+y²=12²

Answer:

b. x² + y² = 12²

Step-by-step explanation:

A circle has a general equation of:

(x + h)² + (y – k)² = r²

where h and k are the center (h,k) and r is the radius.

The circle is centered at origin (0, 0), so h=0, k=0.

The diameter is 24, but we want the radius instead. So divide the diameter by 2 to get the radius. r = 24/2 = 12

Plug it into the equation

(x + h)² + (y – k)² = r²

(x + 0)² + (y – 0)² = 12²

x² + y² = 12²

Answer:

D) 12%

Step-by-step explanation:

The merchant marks his wares 40% more than the real price.

The merchant also allows 20% discount.

Let the real price = 100

After a 40% mark up, the price becomes

(40 /100) * 100

= 40

So we have 100 +40= 140

Discount of 20% = (20/100)* 140

= 28

The price is 140 - 28 = 112

Profit = 112 -100

= 12%

Answer:

No positive value of n

Step-by-step explanation:

we have to find out for how many positive values of n are both

[tex]n^3 , 3^n[/tex] our-digit integers

Let us consider first cube

we get 4digit lowest number is 1000 and it has cube root as 10.

Thus 10 is the least integer which satisfies four digits for cube.

The highest integer is 9999 and it has cube root as 21.54

or 21 the highest integer.

Considering 3^n we get,

3^10 is having 5 digits and also 3^21

Thus there is no positive value of n which satisfy that both n cube and 3 power n are four digits.

Answer: the original length was

3 1/2 cm longer than the length of the dragon

Step-by-step explanation:

The original length of the paper is

6 cm. Mia folds the 6 cm piece of into a dragon that is 2 1/2 cm long. Converting 2 1/2 cm to decimal, it be comes 2.5cm

To determine How much longer the original paper was than the dragon, we would determine difference in length between the original paper and the dragon. It would be

6 - 2.5 = 3.5 = 3 1/2 cm

Answer: The original paper is longer by the difference btw the length

6cm - 2½cm

3½cm

Step-by-step explanation:

Answer:

c =$607

200 ft deep

Step-by-step explanation:

A sale transaction closes on April 15th. The day oIf a lot contains 48,000 square feet and is 240’ wide, how deep is the lot? closing belongs to the seller. Real estate taxes for the year, not yet billed, are expected to be $2,110. According to the 365-day method, what is the seller's share of the tax bill?

a. $626

b. $675

c. $607

d. $721

Since there are 90 days between january and March, we add that to the 15 days in April. which will give us 105 days.

Applying the 365-day method,

therefore 2110/365

5.78*105

606.98

approximately=$607

b. the day golf contains 48000 square feet

then 48000 divided by how wide it is

48,000 sq ft ÷ 240' = 200'

Answer:

  8

Step-by-step explanation:

We observe that the logarithm bases are ...

  5√5 = √125 . . . . . 125 is the 2nd power of this

  2√2 = √8 . . . . . . . 8 is the 2nd power of this; 64 is the 4th power of √8

If we define ...

  [tex]p=\sqrt{125}\\q=\sqrt{8}[/tex]

Then our logarithms are ...

  [tex]\log_{p}{p^2}=x=2\\\\\log_{q}{q^4}=y=4\\\\xy=2\cdot 4=8[/tex]

The product of x and y is 8.

Answer:The total cost of Loren's ticket is $352

Step-by-step explanation:

Loren is flying round trip from Dallas, Texas, to Minneapolis, Minnesota. The total fare for her ticket is $308.

Each airport charges a $16 airport fee. This means that the total airport charges would be 16 × 2 = $32

There is also a tax of $12 on the fare.

The total cost of Loren's ticket would be

308 + 32 + 12 = $352

The total cost of Loren's round-trip ticket from Dallas to Minneapolis, including the fare, airport fees, and tax, is $352.

To find the total cost of Loren's round-trip ticket from Dallas to Minneapolis, we need to add the base fare, airport fees, and the tax.

We then add these amounts together to find the total cost:

$308 (fare) + $32 (airport fees) + $12 (tax) = $352

Therefore, the total cost of Loren's ticket is $352.

Answer:

  angle measures are 32°, 53°, 95°.

Step-by-step explanation:

The problem statement asks you to report the angle measures after telling you what they are. The mention of side lengths (without any numbers for them) seems irrelevant.

  "The measures of the angles of the triangle are 32, 53, 95."

Answer: 0.0001

Step-by-step explanation:

Given : For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1.

i.e. [tex]\mu=114.8\ \ \ \&\ \ \sigma=13.1[/tex]

Sample size =4

Let x be the sample mean systolic blood pressure.

Then the probability that their mean systolic blood pressure is greater than 140 will be

[tex]P(x>140)=1-P(x\leq140)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{140-114.8}{\dfrac{13.1}{\sqrt{4}}})\\\\\ =1-P(z\leq3.85)\ \ [\because \ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9999\ \ \text{[By z-table]}\\\\= 0.0001[/tex]

Hence, the required probability = 0.0001

Answer:

Hence, the required probability = 0.0001

Step-by-step explanation:

Answer:

Aaron needs 2 more rolls to complete the path.

Step-by-step explanation:

Given:

Total rolls Aaron has = 4

Part of path covered by using [tex]\frac{3}{4}[/tex] of a roll = [tex]\frac{1}{8}[/tex]

So, in order to find the number of rolls required to cover the complete path is given using the unitary method.

Rolls used for [tex]\frac{1}{8}[/tex] of a path = [tex]\frac{3}{4}[/tex]

Therefore, rolls used to cover the whole path is given by dividing the rolls used for one-eighth of the path and the path covered. This gives,

[tex]=\frac{3}{4}\div \frac{1}{8}[/tex]

[tex]=\frac{3}{4}\times \frac{8}{1}[/tex]

[tex]=\frac{3\times 8}{4\times 1}[/tex]

[tex]=\frac{24}{4}[/tex]

[tex]=6\ rolls[/tex]

Now, rolls required to complete the path is 6. But Aaron has only 4 rolls.

So, he will need 6 - 4 = 2 rolls more to complete the path.

Aaron can cover 6 portions of the path with his 4 rolls. Since the path has 8 portions, he needs 2 more rolls of rope to complete the path.

In this question, Aaron uses 3/4 of a roll for 1/8 of the path. Therefore, he will need one roll for (1/8) / (3/4) = 2/3 of the path. Now, we want to know how many rolls he needs for the complete path. The full path will be 1/(2/3) = 3/2 = 1.5 times bigger than the amount of path he can cover with one roll. Since he has four rolls to start with, he can cover 4 * 1.5 = 6 portions of the path. But to cover a full path, he would need 8 portions (as 1/8 of the path corresponds to one portion). So, he needs 8 - 6 = 2 more rolls.

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Answer:

Step-by-step explanation:

let width=x

length=x+3

x(x+3)=54

x²+3x-54=0

x²+9x-6x-54=0

x(x+9)-6(x+9)=0

(x+9)(x-6)=0

x=-9,6

x=-9 (rejected)

as width can't be negative.

hence width=6 units

Answer:

Therefore,  the probability that at least half of them need to wait more than 10 minutes is 0.0031.

Step-by-step explanation:

The formula for the probability of an exponential distribution is:

P(x < b) = 1 - e^(b/3)

Using the complement rule, we can determine the probability of a customer having to wait more than 10 minutes, by:

p = P(x > 10)

  = 1 - P(x < 10)

  = 1 - (1 - e^(-10/10) )

  = e⁻¹

  = 0.3679

The z-score is the difference in sample size and the population mean, divided by the standard deviation:

z = (p' - p) / √[p(1 - p) / n]

  = (0.5 - 0.3679) / √[0.3679(1 - 0.3679) / 100)]

  = 2.7393

Therefore, using the probability table, you find that the corresponding probability is:

P(p' ≥ 0.5) = P(z > 2.7393)

P(p' ≥ 0.5) = 0.0031

Therefore,  the probability that at least half of them need to wait more than 10 minutes is 0.0031.

Jill put 10.3 gallons of gas into her car. She drove for 473.8 miles.

So we have to find how many miles per gallon she drove.

473.8 into 10.3 = 46

To make sure= 10.3 x 46 = 473.8

So Jill drove 46 miles per gallon.

Answer:

2/3

Step-by-step explanation:

A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded.

Probability is the likelihood that an event will occur. Probability is a selection over the number of observation.

There are 4 shaded portion of the spinner and two unshaded portion.

The probability that when the spinner is spinned the portion will liand on four is simply

4/6, divided to its lowest term.

2/3

The probability that when the spinner is spined the portion will land on four is simply [tex]\frac{2}{3}[/tex].

Given information:

A certain spinner is divided into [tex]6[/tex] sectors of equal size, and the spinner is equally likely to land in any sector. Four of the [tex]6[/tex] sectors are shaded, and the remaining sectors are not shaded.

According to question,

[tex]P(E)=\frac{\rm{No\;of\;favourable\;outcomes}}{\rm{Total\;no\;of\;outcomes}}[/tex]

Four of the [tex]6[/tex] sectors are shaded, and the remaining sectors are not shaded.

There are [tex]4[/tex] shaded portion of the spinner and two unshaded portions.

[tex]P(E)=\frac{4}{6}=\frac{2}{3}[/tex]

Hence, The probability that when the spinner is spined the portion will land on four is simply [tex]\frac{2}{3}[/tex].

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Answer:

He needs 23 containers

Step-by-step explanation:

1 container = 12 toy boxes

X container= 278 toy boxes

12x= 278

X= 278/12

X= 23 containers

Answer:No, the hat will not fit into the box.

Step-by-step explanation:

The length of the hat is 27 inches long. The only box available is 15-by-20-by-15 inches. This represents the height , width and length of the box

Since all sides of the box are lesser than 27 inches, then the hat will not fit into the box.

Answer: the speed of the plane is 7.4 miles per minute.

the speed of the wind is 0.93 miles per minute.

Step-by-step explanation:

Let x represent the speed of the plane.

Let y represent the speed of the wind.

Distance of Las Cruses, NM from Dallas, TX is 600 miles.

Distance = speed × time

One plane flies from Dallas to Las Cruses in 1 hr 12 min(72 minutes). Assuming the plane flew in the same direction with the wind, then

600 = 72(x + y)

600 = 72x + 72y - - - - - - - - 1

Another plane with the same air speed flies from Las Cruses to Dallas in 1 hr 30 min(90 minutes). Assuming it flew in opposite direction to that of the wind, then

600 = 90x - 90y - - - - - - - 2

Adding equation 1 and equation 2, it becomes. 1200 = 162x

x = 1200/162 = 7.4 miles per minute.

x + y = 600/72 = 8.33

y = 8.33 - x = 8.33 - 7.4 = 0.93 miles per minute

Answer:

Hi am sitting in my post office waiting for you to come over and then I’ll come over to you

Step-by-step explanation:

Inside the post office office became offices when offices are offices

The amount of each of the 6 payments will be $41.50

Step-by-step explanation:

Given,

Cost of bike including taxes = $349

Down payment = $100

Amount left to pay = Cost of bike - Down payment

Amount left to pay = 349 - 100

Amount left to pay = $249

She agrees to pay in 6 equal payments, therefore, we will divide the total amount to pay by 6.

Amount to pay for one month = [tex]\frac{Amount\ left\ to\ pay}{No.\ of\ months}[/tex]

Amount to pay for one month = [tex]\frac{249}{6} = \$41.50[/tex]

The amount of each of the 6 payments will be $41.50

Keywords: division, subtraction

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Answer:

[tex]p_v =P(t_5>1.965)=0.0533[/tex]

We can use the following excel code to find it :"=1-T.DIST(1.965,5,TRUE) "

Step-by-step explanation:

Data given and notation  

[tex]\bar X[/tex] represent the average score for the sample  

[tex]s[/tex] represent the sample standard deviation  

[tex]n=6[/tex] sample size  

[tex]\mu_o =98.6[/tex] represent the value that we want to test  

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to apply a one upper tailed test.  

What are H0 and Ha for this study?  

Null hypothesis: [tex]\mu \leq 98.6[/tex]  

Alternative hypothesis :[tex]\mu > 98.6[/tex]  

Compute the test statistic  

The statistic for this case is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

The calculated value on this case is given t=1.965

Give the appropriate conclusion for the test  

First we need to calculat ethe degrees of freedom given by:

[tex]df=n-1=6-1=5[/tex]

Since is a one side right tailed test the p value would be:  

[tex]p_v =P(t_5>1.965)=0.0533[/tex]

We can use the following excel code to find it :"=1-T.DIST(1.965,5,TRUE) "

Conclusion  

If we compare the p value and a significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 98.6 at 5% of significance.  

Answer:

A. 93%

Step-by-step explanation:

Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit.

So each children started with 0.2A, in which A is Arthur's fortune.

Alice

In the first year, she earned a profit of 50 percent. In the second year, she earned a profit of 10%. So her part is

0.2A*(1+0.5)*(1 + 0.1) = 0.33A

Bob

In the first year he earned a profit of 50 percent. In the second year, he earned a profit of 10%. So his part is

0.2A*(1+0.5)*(1 + 0.1) = 0.33A

Carol

In the first year, she earned a profit of 50 percent. In the second year, she lost 60 percent. So

0.2A*(1+0.5)*(1-0.6) = 0.12A

Dave

In the first year, he lost 40 percent. In the second, he earned a profit of 25%. So

0.2A*(1-0.4)*(1 + 0.25) = 0.15A

Errol

Lost all the money he had. So he has 0A.

What percentage of Arthur's fortune currently remains?

This is the sum of the results of all five of his children.

0.33A + 0.33A + 0.12A + 0.15A = 0.93A

So the correct answer is:

A. 93%