Find the necessary sample size.
Scores on a certain test are normally distributed with a variance of 68. A researcher wishes to estimate the mean score achieved by all adults on the test. Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 4 units.
2- A college statistics professor has office hours from 9:00 A.M. to 10:30 A.M. daily.
A sample of waiting times to see the professor (in minutes) is 10, 12, 20, 15, 17, 10, 30, 28, 35, 28, 19, 27, 25, 22, 33, 37, 14, 21, 20, 23.
Assume alpha equals 7.84 find the 95.44% confidence interval for the population mean.

Answer: Triangle, Square, Rectangle, Trapezium

Step-by-step explanation:

Cutting the cube from above, in a way that the slice is diagonal, making the slice touches two points that's almost at the edges diagonally facing each other of the cube will give a Trapezium (A)

Cutting the cube from above, in a way that the slice cuts exactly through the edges diagonally facing each other will give a Triangle (B)

Cutting the cube from above perpendicularly to the length, the two new faces made from the cube are squares (C)

Cutting the cube from above perpendicularly too will give two rectangles from the above face (D)

Answer:

  7h +11r = 350

Step-by-step explanation:

Let h and r represent minutes of hiking and running, respectively. Then calories burned by a 150-lb person doing these activities will total 350 when ...

  7h +11r = 350

_____

7 calories per minute are burned by hiking, so 7h will be the calories burned by hiking h minutes.

11 calories per minute are burned by running, so 11r will be the calories burned by running r minutes.

The total of calories burned in these activities will be 7h+11r, and we want that total to be 350.

Answer:1260 tickets were sold on the first game

Step-by-step explanation:

For the second game, the ratio of the number of sold tickets to number of unsold tickets is 13:2

Total ratio = 13+2 = 15

There were 240 unsold tickets for the second game. Let total number of tickets for the second game be x

This means that

240 = 2/15 × x

2x/15 = 240

2x = 15 × 240= 3600

x = 3600/2 = 1800

1800 tickets were sold for the second game. Assuming total number of tickets for the first game is equal to total number of tickets for the second game. Therefore,

Total number of tickets sold for the first game is 1800

The ratio of sold tickets to unsold tickets for the first game was 7:3.

Total ratio = 7+3 = 10

Number of sold tickets for the first game would be

7/10 × 1800 = 12600/10

= 1260 tickets

The mathematical solution involves understanding and applying the concept of ratios. From the information given, we deduce that 840 tickets were sold for the first baseball game.

The student's question is about a mathematics problem involving ratios. We know that the ratio of sold tickets to unsold tickets for the first game was 7:3, and for the second game, it was 13:2. We are also given that there were 240 unsold tickets for the second game.

Firstly, let's deal with the second game tickets. If we say the ratio 13:2 represents 13x:2x, where x is a common multiplier. Since the unsold tickets (2x) were 240, we can solve for x by the equation: 2x = 240. So, x = 240/2 = 120. However, we don't need the number of sold tickets for the second game now.

For the first game, we know the ratio of sold tickets to unsold tickets was 7:3. Yes, it's the same x because ratios are the same across the populated places. We can then figure out the number of sold tickets as 7x. So, just multiply 7 by our common multiplier 120 to get 840 tickets sold for the first game.

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Erica will take 4.5 minutes to run from home to school

Given that , Arica can run [tex]\frac{1}{6}[/tex] of a kilometer in a minute  

Her school is [tex]\frac{3}{4}[/tex] th of a kilometer away from her home  

We have to find at this speed how long will it take Erica to run from home to school

The relation between speed distance and time is given as:

[tex]\text { Distance }=\text { speed } \times \text { time }[/tex]

Plugging in values, we get

[tex]\frac{3}{4}=\frac{1}{6} \times \text { time taken }[/tex]

[tex]\begin{array}{l}{\text { Time taken to reach school }=\frac{3}{4} \times 6} \\\\ {\text { Time taken to reach home }=\frac{3}{2} \times 3} \\\\ {\text { Time taken to reach home }=\frac{9}{2}=4.5}\end{array}[/tex]

Hence, she takes 4.5 minutes to reach school from her home

Step-by-step explanation:

The domain of f(x) is all values of x for which f(x) is defined.

For f(x) to be defined, the expression under the radical must be non-negative.

Therefore, the domain is x ≥ 0, or in interval notation, [0, ∞).

Answer:

5000(1+0.0245) raise to 5

$5643.26

Step-by-step explanation:

The amount of money that will received after 5 years is $5643.256

Compound Interest

The compound interest of a primary money P with rate of interest r for time t is the total money that include interest and primary as well and can be calculated with the formula

[tex]A=P(1+\frac{r}{100})^t[/tex]

Here we have given

Primary money = P = $5000

Rate of interest = r = 2.45 %

Time = 5 year

Substitute these values into above formula and we get

[tex]A=5000(1+\frac{2.45}{100})^5[/tex]

[tex]A=5000(1.0245)^5[/tex]

A = $5643.256

Therefore the total amount that will received after 5 year is $5643.256

Learn more about compound interest here-

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Answer:

Yes this makes sense

Step-by-step explanation:

When their is one outlier it makes the average spike which can present misleading data while with median the outlier is left relatively unaffected.

Answer:

Yes this makes sense.

Step-by-step explanation:

The given dataset consists of 15 apartment rents. A data value which is an outlier (much larger than the rest) will increase the overall mean value of the population but it may not affect the median. Let us take an example of 15 sample rent value in ascending order,

100,120,130,140,150,170,175,185,190,200,220,250,280,290,1000

Here , mean rent will become high due to the single high rent datapoint(1000) but the median won't be impacted.

Final answer:

To find the sample mean difference, multiply the t statistic by the standard error. With a t statistic of 2.00 and a standard error of 4 points for samples with n = 16 scores, the sample mean difference is 8 points.

Explanation:

The student asks how to calculate the sample mean difference given the standard error and the t statistic for two samples each with n = 16 scores. This information is used to conduct a hypothesis test to compare two population means, using the t distribution when the population standard deviations are unknown and the sample sizes are small.

The formula to find the sample mean difference when given the t statistic and the standard error is:

sample mean difference = t statistic × standard error

Plugging the given values:

sample mean difference = 2.00 × 4 = 8

Therefore, the estimated sample mean difference is 8 points.

The answer is 240 chairs.

Answer:the car was traveling at a speed of 80 ft/s when the brakes were first applied.

Step-by-step explanation:

The car braked with a constant deceleration of 16ft/s^2. This is a negative acceleration. Therefore,

a = - 16ft/s^2

While decelerating, the car produced skid marks measuring 200 feet before coming to a stop.

This means that it travelled a distance,

s = 200 feet

We want to determine how fast the car was traveling (in ft/s) when the brakes were first applied. This is the car's initial velocity, u.

Since the car came to a stop, its final velocity, v = 0

Applying Newton's equation of motion,

v^2 = u^2 + 2as

0 = u^2 - 2 × 16 × 200

u^2 = 6400

u = √6400

u = 80 ft/s

To find out how fast the car was traveling when the brakes were first applied, we need to solve a quadratic equation. After simplifying and rearranging the terms, we find that the car's initial velocity is not equal to 0, indicating that the car was already moving before the brakes were applied.

To determine how fast the car was traveling when the brakes were first applied, we can use the equation of motion relating distance, initial velocity, deceleration, and time. In this case, the given distance is 200 feet and the deceleration is 16 ft/s². Initially, the car was traveling at a certain velocity, which we need to find.

Using the equation x = xo + vot + 1/2at², where x is the final distance, xo is the initial position, vo is the initial velocity, a is the deceleration, and t is the time, we can plug in the known values and solve for vo:

200 ft = 0 + vo * t + 1/2 * (-16 ft/s²) * (t)²

Simplifying the equation and rearranging terms gives us a quadratic equation:

-8t² + vot - 200 = 0

Using the quadratic formula, we can solve for t:

t = (-vo ± √(vo² - 4 * (-8) * (-200))) / (2 * (-8))

Since the car is initially traveling, the positive root is used:

t = (-vo + √(vo² + 6400)) / (-16)

Simplifying the equation further:

t = (-vo + √(vo² + 6400)) / (-16)

Now we can solve for vo by substituting t = 0 into the equation:

0 = (-vo + √(vo² + 6400)) / (-16)

vo - √(vo² + 6400) = 0

Squaring both sides of the equation:

vo² - (vo² + 6400) = 0

Subtracting vo² from both sides of the equation:

-6400 = 0

This is a contradiction, which means that the car's initial velocity vo is not equal to 0. Therefore, the car was already moving when the brakes were first applied.

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Answer:

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

Step-by-step explanation:

Given lines,

y = 2x - 5,

y = -x + 1

Subtracting these two equations,

0 = 3x - 6

[tex]\implies 3x = 6[/tex]

[tex]\implies x = \frac{6}{3}=2[/tex]

By first equation,

[tex]y=2(2) -5=4-5 = -1[/tex]

Thus, point of intersecting would be (2, -1).

Now, the equation of a line is y = mx + c,

Where,

m = slope of the line,

So, the slope of the line [tex]y=\frac{1}{2}x+4[/tex] is 1/2.

∵ two parallel lines have same slope.

Hence,

Equation of the parallel line passes through (2, -1),

[tex]y+1=\frac{1}{2}(x-2)[/tex]

[tex]y+1=\frac{1}{2}x - 1[/tex]

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

Answer: The correct option is C

Step-by-step explanation:

Looking at the right angle triangle ABC, three sides are known and the angles are unknown. To find sin A, we will take A to be our reference angle, we will have the following

Hypotenuse = AB = 26

Opposite side = BC = 24

Adjacent side = AC = 10

Applying trigonometric ratio

SinA = opposite/hypotenuse

SineA = 24/26

To find cos A, A remains our reference angle, we will have the following

Hypotenuse = AB = 26

Opposite side = BC = 24

Adjacent side = AC = 10

Applying trigonometric ratio

CosA = adjacent/hypotenuse

CosA = 10/26

The correct option is C

Answer:

[tex]z=-2.32[/tex]  

[tex]p_v =P(Z<-2.32)= 0.010[/tex]  

If we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significant lower than the proportion 2 at 5% of significance.  

Step-by-step explanation:

1) Data given and notation  

[tex]X_{1}=37[/tex] represent the number of people with characteristic 1

[tex]X_{2}=58[/tex] represent the number of people with characteristic 2

[tex]n_{1}=139[/tex] sample 1 selected

[tex]n_{2}=147[/tex] sample 2 selected

[tex]p_{1}=\frac{37}{139}=0.266[/tex] represent the proportion of people with characteristic 1

[tex]p_{2}=\frac{58}{147}=0.395[/tex] represent the proportion of people with characteristic 2

z would represent the statistic (variable of interest)  

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

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion 1 is less than the proportion 2, the system of hypothesis would be:  

Null hypothesis:[tex]p_{1} \geq p_{2}[/tex]  

Alternative hypothesis:[tex]p_{1} < p_{2}[/tex]  

We need to apply a z test to compare proportions, and the statistic is given by:  

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex]   (1)

Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{37+58}{139+147}=0.332[/tex]

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

[tex]z=\frac{0.266-0.395}{\sqrt{0.332(1-0.332)(\frac{1}{139}+\frac{1}{147})}}=-2.32[/tex]  

4) Statistical decision

For this case we don't have a significance level provided [tex]\alpha[/tex] we can assuem it 0.05, and we can calculate the p value for this test.  

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

[tex]p_v =P(Z<-2.32)= 0.010[/tex]  

So if we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significant lower than the proportion 2 at 5% of significance.  

Final answer:

To determine the length of a Bengal tiger's tail, which is 30% of its total length of 96 cm, we calculate 30% of 96 to get a tail length of approximately 28.8 cm.

Explanation:

The question asks us to calculate the length of a Bengal tiger's tail given that it is 30% of its total length. If the total length of the tiger is 96 cm, we can find the length of the tail by calculating 30% of 96 cm.

To find 30% of 96, we convert the percentage into a decimal by dividing by 100 and then multiply by the total length:

30% = 30/100 = 0.3

0.3 x 96 cm = 28.8 cm

Therefore, the length of the Bengal tiger's tail is approximately 28.8 cm.

The slope of a line perpendicular to the line with equation y=4x+1 is -1/4. This is found by taking the negative reciprocal of the original line's slope, which is 4.

The slope of a line that is perpendicular to a given line can be determined by taking the negative reciprocal of the slope of the given line.

Given the equation y=4x+1, we can see that the slope (m) is 4.

Therefore, a line that is perpendicular to this line would have a slope that is the negative reciprocal of 4, which is -1/4.

The concept of perpendicular lines in coordinate geometry implies that two lines are perpendicular if the product of their slopes is -1.

Our given line has a positive slope, hence the slope of its perpendicular counterpart must be negative. A positive slope indicates that the line moves up as we move from left to right, whereas a negative slope indicates that the line moves down.

Answer:

A) First number: 13

B) Second number: 21

C) Third number: 63

Step-by-step explanation:

Let x, y and z be 1st, 2nd and 3rd numbers respectively.

We have been given that sum of three numbers is 97. We can represent this information in an equation as:

[tex]x+y+z=97...(1)[/tex]

The 3rd number is 3 times the second. We can represent this information in an equation as:

[tex]z=3y...(2)[/tex]

The second number is 8 more than the first. We can represent this information in an equation as:

[tex]y=x+8...(3)[/tex]

Substituting equation (3) in equation (2), we will get:

[tex]z=3(x+8)[/tex]

Substituting [tex]z=3(x+8)[/tex] and [tex]y=x+8[/tex] in equation (1), we will get:

[tex]x+x+8+3(x+8)=97[/tex]

[tex]x+x+8+3x+24=97[/tex]

[tex]5x+32=97[/tex]

[tex]5x+32-32=97-32[/tex]

[tex]5x=65[/tex]

[tex]\frac{5x}{5}=\frac{65}{5}[/tex]

[tex]x=13[/tex]

Therefore, the first number is 13.

Now, we will substitute [tex]x=13[/tex] in equation (3) as:

[tex]y=21[/tex]

Therefore, the second number is 21.

Now, we will substitute [tex]y=21[/tex] in equation (2) as:

[tex]z=3(21)[/tex]

[tex]z=63[/tex]

Therefore, the third number is 63.

Staement 1 and statement 4 are true

Staement 1: It is incorrect because thirds and eighths cannot be divided to make ninths

Statement 4: It is incorrect because a quotient cannot be greater than the number that is divided.

Given that, Eli evaluated 23 ÷ 38 and got an answer of 179.

Now, let us check the given statements

1) It is incorrect because thirds and eighths cannot be divided to make ninths

It seems right because when 3 is divided by 8, it will give an fractional value. So this statement is correct

2) It is correct because 38 of 23 is 179

It is wrong as 38 x 23 ≠ 179 and not even related to the question.

3) It is correct because 179 • 38 equals 23

It is wrong because 179 x 38 ≠ 23

4) It is incorrect because a quotient cannot be greater than the number that is divided.

It is right as the dividend can not be smaller than the quotient.

Hence, the 1st and 4th statements are right.

Answer:

E(X) = 6.0706

Step-by-step explanation:

1) Define notation

X = random variable who represents the number of heads in the 10 first tosses

Y = random variable who represents the number of heads in range within toss number 4 to toss number 10

And we can define the following events

a= The first coin has been selected

b= The second coin has been selected

c= represent that we have 2 Heads within the first two tosses

2) Formulas to apply

We need to find E(X|c) = ?

If we use the total law of probability we can find E(Y)

E(Y) = E(Y|a) P(a|c) + E(Y|b)P(b|c) ....(1)

Finding P(a|c) and using the Bayes rule we have:

P(a|c) = P(c|a) P(a) / P(c) ...(2)

Replacing P(c) using the total law of probability:

P(a|c) = [P(c|a) P(a)] /[P(c|a) P(a) + P(c|b) P(b)] ... (3)

We can find the probabilities required

P(a) = P(b) = 0.5

P(c|a) = (3C2) (0.4^2) (0.6) = 0.288

P(c|b) = (3C2)(0.7^2) (0.3) = 0.441

Replacing the values into P(a|c) we got

P(a|c) = (0.288 x 0.5) /(0.288x 0.5 + 0.441x0.5) = 0.144/ 0.3645 = 0.39506

Since P(a|c) + P(b|c) = 1. With this we can find P(b|c) = 1 - P(a|c) = 1-0.39506 = 0.60494

After this we can find the expected values

E(Y|a) = 7x 0.4 = 2.8

E(Y|b) = 7x 0.7 = 4.9

Finally replacing the values into equation (1) we got

E(Y|c) = 2.8x 0.39506 + 4.9x0.60494 = 4.0706

And finally :

E(X|c) = 2+ E(Y|c) = 2+ 4.0706 = 6.0706

In this problem, we have to consider a conditional expected value for the flips of a randomly chosen misshapen coin. We start with a known result (2 heads in 3 flips) and then compute the expected outcome for the next 7 flips for both coins. The final answer is the average of these expectations.

This question involves the realm of probability theory and specific concept of expected value. Given two distinct coins with varying chances of landing on heads, we need to calculate the expected number of heads when one of these coins is randomly chosen and flipped 10 times.

The usual expected number of heads will be the sum of the individual expected values for each, which in turn is the product of the number of trials (10 flips) and the probability of success (landing on a head). However, the condition that two of the first three flips landed on heads slightly modifies this calculation process.

The main challenge here is that we start with a known result (2 heads in 3 flips), and we then have 7 additional flips with unknown results. Since we don't know which coin we have, we must consider the expected outcomes for both coins and then divide by 2. The theoretical probability does not predict short-term results, but gives information about what can be expected in the long term.

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Answer:

  431,646

Step-by-step explanation:

The problem statement tells us ...

  34,100 = 0.079 × (sold to date)

Dividing by 0.079, we get ...

  34,100/0.079 = (sold to date) ≈ 431,646

About 431,646 copies have been sold to date.

The total number of books sold to date is approximately 431,646. This was determined by using the percentage of the total sales represented by the first month's sales (7.9%) and the number of books sold in the first month (34,100 copies).

To solve this problem, we need to understand that the 34,100 books sold in the first month represent 7.9% of the total number of copies sold to date. In mathematics, percentage is a way of expressing a number as a fraction of 100. Here, we need to find the whole, where 7.9% is equivalent to 34,100 copies.

To do this, we use this formula:

So, the calculation would be:

The result we get from the calculator is approximately 431,646 copies. This means, approximately 431,646 copies were sold to date.

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Answer: 2w

Step-by-step explanation: if the garden is shaped like a square, then all the sides are equal,

length = breadth, and the Area of a square or rectangle is the length multiplied by the breadth

and to find the length and breadth, we find the square root of the area

The area is 4w2

We know that 4 is the perfect square of 2, making 2 the square root of 4

And w2 is the square of w

This is elementary algebra, a x a = a2

b x b = b2, w x w = w2

So adding both together, the square root of 4w2 = 2w

The length of each side of the square-shaped garden with area 4w2 is 2w.

The student has given the area of a square-shaped garden as 4w2. Since the area of a square is calculated by squaring the length of one of its sides (side2), to find the length of each side, we need to find the square root of the area. The square root of 4w2 is 2w, because (2w)2 equals 4w2. Therefore, the length of each side of the garden is 2w.

Answer:

A) 20ml

Step-by-step explanation:

You have a 2.5% solution (in 100 of the solution you have 2.5 of solvent), then if the dose that is being supplied to the cat is 5mg / kg it means:

if    1000 gr is equivalent to 100%

           5 gr is equivalent to X;    

X= (100%*5gr)/1000gr → X= 0.5%,  , Therefore the amount of milliliters that should be supplied of 2.5% is:

if   100ml  hava a concentration of 2.5,  how many mililiters are necesary in a concentration 0.5

X=(0.5%*100ml)/2.5% → X=20ml

Answer: The answer is $49.10

Step-by-step explanation: Because it is .30 cents per extra minute

So you will take 47 for the minuets and multiply by .30 and get $14.10

Then you add $14.10 to your monthly fee of $35 and get $49.10

Answer:

Step-by-step explanation:

Independent samples t-test

Answer:

The person will pay $ 510 more as income tax per month .

Step-by-step explanation:

Given as :

The monthly income of person = $ 25000

The amount paid as income tax per year =$ 9000

So,The amount paid as income tax per month =$ [tex]\frac{9000}{12}[/tex] = $750

Or, x% is the income tax of the monthly income

I.e x % of 25000 = 750

∴ x % = [tex]\frac{750}{25000}[/tex]

Or, x =  [tex]\frac{750}{25000}[/tex] × 100

I.e x = 3 %

Now, since the income tax is increase by 0.5 % per month

So, x' = 3 % + 0.5 % = 3.5 %

And The monthly income increase by $ 11000

I.e New monthly income = $ 25000 + $ 11000 = $ 36000

Now, The income tax which the person pay now is 3.5 % of $ 36000

i.e The income tax which the person pay now = 0.035×36000 = 1260 per month

so, The income tax which the person pay now as per year = 1260 × 12 =        $ 15,120

∴ The increase income tax per month = $ 1260 - $ 750 = $ 510

Hence The person will pay $ 510 more as income tax per month . Answer

Final answer:

To calculate the additional income tax the person will pay per month, we add the tax increase due to the salary increase to the original increased tax after the 0.5% hike. The total increased monthly tax payment amounts to $930.

Explanation:

The question is asking how much more income tax a person will pay per month after their salary is increased and the government increased income tax by 0.5%. To find the additional income tax that a person will pay, we need to consider the initial monthly income, the new monthly income, the old annual tax amount, and the increased tax rate.

Originally, the person earned $25,000 per month and paid $9,000 in income tax yearly. With the 0.5% monthly increase in tax, we first need to calculate the monthly increase based on the initial salary. The monthly increase is 0.5% of $25,000, which is $125. Therefore, the new monthly tax without accounting for the salary increase is the old monthly tax plus the $125 increase.

The monthly tax paid before the income increase was $9,000 / 12 months = $750 per month. After the 0.5% monthly increase, the tax becomes $750 + $125 = $875 per month. But the person's monthly earnings were increased by $11,000, resulting in a new monthly income of $25,000 + $11,000 = $36,000.

To calculate how much more in income tax the person will pay on the additional $11,000 monthly earnings at the increased rate: 0.5% of $11,000 is $55. So the additional tax per month is $55. Therefore, the total increased monthly tax is $875 + $55 = $930.

Answer:

  783.9

Step-by-step explanation:

The same tool that gave you the answer to the second part will give you the answer to the first part.

_____

You will note the box is checked saying "Log Mode". This mode uses linear regression on the logarithms of the y-values. When the box is unchecked, regression is used on the actual y-values.

The latter method tends to favor matching the larger y-values at the expense of matching smaller ones. It gives a different equation.

Answer:

55 trees per hectare.

Step-by-step explanation:

An apple orchard contains 50 trees per hector. The average yield per tree is 600 apples.

If the trees are spaced more closely, when being planted, the yield per tree drops by 10 apples for each extra tree.

Let x extra tree is planted and then the average yield per tree reduces by 10x.

Therefore, yield as a function of x can be written as  

Y(x) = (50 + x)(600 - 10x) = 30000 + 100x - 10x²

Therefore, condition for maximum yield is [tex]\frac{dY(x)}{dx} = 0[/tex]

So, 100 - 20x = 0

⇒ x = 5

So, when the number of trees that should be planted per hectare is (50 + 5) = 55, then only the yield will be maximum. (Answer)

Answer: There are 50 ways to select in this way and there is only 1 combination is possible i.e. 3 students and 4 professors.

Step-by-step explanation:

Since we have given that

Number of professors = 5

Number of students = 5

We need to find the number of ways of 7 members in such that number of professors must be one more than students.

So, if we select 3 students, then there will be 4 professors.

So, Number of ways would be

[tex]^5C_3\times ^5C_4\\\\=10\times 5\\\\=50[/tex]

Hence, there are 50 ways to select in this way and there is only 1 combination is possible i.e. 3 students and 4 professors.

The value of Bill Casler's CD (certificate of deposit) when it matures is $1060 and Bill receives $1036.36 from his friend.

First, we'll calculate the value of the CD (certificate of deposit) when it matures. To do this, we can use the formula for simple interest, which is PRT (Principal, Rate, Time). Here, P = $1000, R = 8% (or 0.08) and T = 9/12 years (converted to years).

So, the interest earned = 1000 * 0.08 * (9/12) = $60. The value of the CD when it matures would thus be the principal plus the interest earned, which is $1000 + $60 = $1060.

Now, for the second part of the question, we need to find out how much Bill received from his friend. The friend wants to earn a 10% annual simple interest return on his loan to Bill, so we'll equate the maturity value to the formula for simple interest. Here, P represents the amount loaned and we need to solve for P. Thus 1060 = P + P*0.10*(3/12).

Solving for P, we get P = $1036.36. So, Bill received $1036.36 from his friend.

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To find the value of the CD when it matures, use the simple interest formula. Add the interest earned to the principal to find the value. To find how much Bill received from his friend, set up an equation with the interest earned by the friend as 10% of the loan amount.

To find the value of the CD when it matures, we can use the formula for simple interest which is I = PRT, where I is the interest, P is the principal, R is the interest rate, and T is the time in years. In this case, P = $1000, R = 8%, and T = 9/12 years. Plugging the values into the formula, we get:
I = $1000  imes 0.08  imes (9/12)

I = $60

So, the interest earned is $60. To find the value of the CD when it matures, we simply add the interest to the principal:

Value = $1000 + $60

Value = $1060

For the second question, we need to find how much Bill received from his friend. Since the friend will earn a 10% annual simple interest return on his loan to Bill, we know that the interest earned by the friend is 10% of the amount he lent. Let's call this amount X. So, the interest earned by the friend is 10% of X. To find X, we can set up an equation:

10% of X = $1060

0.10X = $1060

X = $1060 / 0.10

X = $10,600

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Answer: B

Step-by-step explanation:

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. Since the machines are identical and running at the same constant rate, it means each of them as the same rate. The rate of each machine can produce would be determined by dividing the combined unit rate by 6. It becomes

270/6 = 45 bottles per minutes

The rate for 10 machines running at the same constant rate would be

10 × 45 = 450 bottles per minutes.

If the 10 machines produce 450 bottles per minutes, then,

In 4 minutes, the 10 machines will produce 4 × 450 = 1800 bottles

Answer:

  2

Step-by-step explanation:

We can use the formula for the derivative of the arcsin function:

  f'(x) = 1/√(1 -x²)

Filling in x=(√3)/2, we get ...

  f'((√3)/2) = 1/√(1 -3/4) = 1/(1/2)

  f'((√3)/2) = 2

To find the value of f'(√3/2) for f(x) = sin⁻¹(x), we can use the chain rule and substitute the given value into the derivative expression.

To find the derivative of f(x) = sin⁻¹(x), we can use the chain rule. Let's denote u = x, then y = sin⁻¹(u). Taking the derivative of y with respect to u, we get dy/du = 1/√(1 - u²). Now, substituting u = √3/2, we can find the value of f'(√3/2) in simplest form.

Substituting u = √3/2 into the derivative, we have dy/du = 1/√(1 - (√3/2)²) = 1/√(1 - 3/4) = 1/√(1/4) = 1/√1/4 = 1/(1/2) = 2.

Therefore, the value of f'(√3/2) is 2.

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