Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more than 2 times the width what is the largest possible length

Answer:

The demand function is  [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

Step-by-step explanation:

A firm has the​ marginal-demand function [tex]D' x = \dfrac{-1200}{\sqrt{25-x^2 } }[/tex].

Find the demand function given that D = 16,000 when x = $4 per unit.

What we are required to do  is to find the demand function D(x);

If we integrate D'(x) with respect to x ; we have :

[tex]\int\limits \ D'(x) \, dx = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

Let represent   t  with [tex]\sqrt{25-x^2}}[/tex]

The differential of t with respect to x is :

[tex]\dfrac{dt}{dx}= \dfrac{1}{2 \sqrt{25-x^2}}}(-2x)[/tex]

[tex]\dfrac{dt}{dx}= \dfrac{-x}{ \sqrt{25-x^2}}}[/tex]

[tex]{dt}= \dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]

replacing the value of  [tex]\dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]  for dt in   [tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

So; we can say :

[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = 1200\int\limits{\dfrac{- x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = 1200\int\limits \ dt[/tex]

[tex]D(x) = 1200t+ C[/tex]

Let's Recall that :

t  = [tex]\sqrt{25-x^2}}[/tex]

Now;

[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex]

GIven that:

D = 16,000 when x = $4 per unit.

i.e

D(4) = 16000

SO;

[tex]D(x) = 1200(\sqrt{25-x^2}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{25-4^2}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{25-16}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{9}})+ C[/tex]

[tex]D(4) = 1200(3}})+ C[/tex]

16000 = 1200 (3) + C

16000 = 3600 + C

16000 - 3600 = C

C = 12400

replacing the value of C = 12400 into [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex], we have:

[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

∴ The demand function is  [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

Answer:

The correct option is (B).

Step-by-step explanation:

The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.

In this case, we need to test the claim that the majority of voters oppose a proposed school tax.

The hypothesis can be defined as follows:

H₀: The proportion of voters opposing a proposed school tax is not a majority, i.e. p ≤ 0.50.

Hₐ: The proportion of voters opposing a proposed school tax is a majority, i.e. p > 0.50.

It is provided that the test statistic value and p-value are:

z = 1.23

p-value = 0.1093

The probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic is 0.1093.

The significance level of the test is:

α = 0.05

The p-value of the test is larger than the significance level of the test.

p-value = 0.1093 > α = 0.05

The null hypothesis will not be rejected.

Concluding that there is not enough evidence to support the claim.

Thus, the correct option is:

"If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is not surprising (or considered unusual) and could easily happen by chance"

Answer:

i feel as if in the United States, both the metric system and the English system of measurement are used, although the English system predominates. This discussion question has three parts:

Look around you to find something in the U.S. that is measured in metrics. Describe it to the class.

Give an example of how you think the metric system will be used in your future career.

Do you think the U.S. should switch to metric system exclusively? Why or why not?

This week we learned about the metric and U.S. customary measurement systems. Please upload and submit your responses to the following questions in at least 150 words:

In reflecting on both measurement systems, what did you find most important?

Explain how both measurement systems could relate to your life, community, or current/future career.

Expert Answer

Step-by-step explanation:

An outlier in statistics is a data point that deviates considerably from other observations. The given data set has no outlier.

An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.

To find the outlier for the given data set follow the given steps.

Step one: The first step is to find the quartiles for the data set.

For this data set, the quartiles are:

Q1 = 45.5

Q3 = 62.5

Step Two: Find the Interquartile Range

The interquartile range is the difference between the first and third quartiles.

IQR = Q3 - Q1

IQR = 45.5 - 62.5

IQR = 17

Step Three:

The next step is to set up a fence beyond the first and third quartiles using the interquartile range.

Lower Fence = Q1 - (1.5 × IQR)

Lower Fence = 45.5 - (1.5 × 17)

Lower Fence = 20

Upper Fence = Q3 + (1.5 × IQR)

Upper Fence = 62.5 + (1.5 × 17)

Upper Fence = 88

Step Four: Find the Outliers

Any numbers in the data that are above or below the fences are outliers.

Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.

Learn more about Outlier:

https://brainly.com/question/26958242

#SPJ2

Answer:

Option(A) is correct

Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Step-by-step explanation:

The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58

the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:

Highest = 97

Lowest = 71

Range = highest value - Minimum value

Range = 97 - 26 = 71

[tex] Range= 71[/tex]

mean of the data is the summation of all the numbers in the data set divided by the number of given samples.

Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11

= 647/11

[tex]Mean value =58.7[/tex]

Now to find the variance of the data set by using below formular

σ²=[ (xᵢ -mean)²]/n-1

[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10

[tex]Variance=546[/tex]

Now, we will calculate standard deviation by taking square root over variance

σ =√(variance)

σ =√(546)

[tex]Standard deviation= 23.4[/tex]

Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,

Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Answer:

The correct answer for the best line of fit is C: y = 1/3x+12

Step-by-step explanation:

So our goal here is to find the best equation that matches the line of fit.

So right away we can already eliminate two of the options because in the scatter point it shows that the starting y-intercept is 12 and two of the options have a y-intercept of 15. So we are able to tell that Option B and Option D isn't the equation for the lien of fit.

Now we are left with Option A and Option C, which both have a y-intercept of 12. To find the right equation that best matches the line of fit we look at the slope. Option A has a slope of 3x while Option C has a slope of 1/3x, to tell what slope the line of has we applied both option's slope and see which one matches it.

When we match Option A's slope which is 3x it doesn't match because a slope of 3x is going first going up the y-axis 3 times then moving through the x-axis 1 time. Which would had made the line of fit more steep.

Next we match Option C's slope which is 1/3x this slope matches the line of fit because in the scatter plot it clearly shows  it going up 1 time on the y=axis and 3 times through the x-axis. Which made the line of fit not that steep.

So the correct answer to this question is C:  y = 1/3x+12.

Here a picture of the line of fit if it has a slope of 3x.

Answer:

correct answer  C: y = 1/3x+12

Step-by-step explanation:

i just did the problem

Answer:

x = log (7)/ 2log 5

Step-by-step explanation:

25^ x = 7

Replace 25 with 5^2

5^ 2x = 7

Take log  on each side

log (5 ^2x) = log ( 7)

We know that log a^ b = b log a

2x  log 5 = log (7)

Divide each side by log 5

2x  log 5/ log 5= log (7)/ log 5

2x = log (7)/ log 5

Divide each side by 2

x = log (7)/ 2log 5

Answer:

Step-by-step explanation:

tan(pi\4+A)tan(3pi\4+A) =-1

using the tangent sum of angle formula

Answer:

3

Step-by-step explanation:

336 / n = k + 2/n, where k is an integer

336 = kn + 2

334 = kn

2007 / n

(2004 + 3) / n

(334×6 + 3) / n

334×6/n + 3/n

6k + 3/n

The remainder is 3.

Answer:

57.6 km/h

Step-by-step explanation:

We are told that At noon, ship A is 70 km west of ship B.

Thus, coordinates of initial position of A and B is;

A(0,0) and B(70,0)

Now, we are told that Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. Thus, the final position of ship A and B after t hours are;

A(0,-35t) and B(70,25t)

Thus, distance between the two ships at time t hours is;

d(t) = √[(70 - 0)² + (25t - (-35t))²]

d(t) = √(4900 + 3600t²)

Now, to find how fast the distance between the ships changing, let's differentiate using the chain rule;

d'(t) = [1/(2√(4900 + 3600t²))] × 7200t

d'(t) = 3600t/√(4900 + 3600t²)

d'(t) = 3600t/10√(49 + 36t²)

d'(t) = 360t/√(49 + 36t²)

Now, at 4pm,it would have been 4 hours from noon. Thus, t = 4.

So;

d'(t) = (360×4)/√(49 + 36(4²))

d'(t) = 1440/√(49 + 576)

d'(t) = 1440/√625

d'(t) = 1440/25

d'(t) = 57.6 km/h

Answer:

I guess that we have the linear equation:

y = 32*x

Where y is the profit, and x is the number of games sold.

Then the first step may be doing a table.

Give x different values, then find the value of y.

if x = 0

y = 32*0 = 0

if x = 1, y = 32*1 = 32

if x = 2, y = 2*32 = 64

Then the points:

(0,0) (1,32) and (2, 64) belong to this line, now we need to conect them with a straigth line and its ready.

The graph will be:

Answer:

[tex](A)7.5 ft^2\\(C)20 ft^2[/tex]

Step-by-step explanation:

The diagram is attached below.

Area of the Rectangular Faces

[tex]8 X 6.5 =52$ ft^2\\8 X 2.5 =20$ ft^2\\8 X 6= 48$ ft^2[/tex]

Area of the Triangular face

[tex]=\dfrac12 X 2.5 X 6 =7.5$ ft^2[/tex]

Therefore, Options A and C could be the area of one lateral face of the triangular prism.

Answer:

C

Step-by-step explanation:

Answer:

Likely

Step-by-step explanation: Mathematically it is likely because there are 4 options certain is the thing that will defiantly happen so it would be 4/4. The impossible thing would be 1/4 this is because 1/4 is the smallest so it is obviously going to be impossible. Likely would be 3/4 and unlikely would clearly be 2/4

Answer:

it is likely

Step-by-step explanation:

it is not certant because it is not 4/4 but it is not impossible because its not 0/4 so the answer is likely 3/4

Answer:

$0.26

Step-by-step explanation:

To find the unit price, divide the cost by the amount you have.

$2.86/11 = $0.26

The unit price is $0.26.

Answer:

Bridge = 300 m

Speed = 10 m/s

Step-by-step explanation:

If a goes past you in 10 seconds, it means the train has speed of

100 m/ 10 seconds as it is 100 m long

The speed in m/s is:

Then it take 3 times of 10 seconds to cross the bridge, so

The length of the bridge is:

Answer:

Length  : 50m

Speed   : 5 m  /  s

Answer:

the car overtake the truck at time 11:40 am.

Step-by-step explanation:

We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.

We will express the time in hours (and decimals of hours).

The truck speed can be calculated estimating the time between arrival and start:

- The arrival time is 1.15 pm. This is t2=13.25.

- The starting time is 9:15 am. This is t1=9.25.

The truck took t2-t1=13.25-9.25=4 to go from city a to b.

The average speed is then:

[tex]v_t=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{4}[/tex]

We can write the equation for the position x(t) for the truck as:

[tex]x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t[/tex]

For the car we have:

- The arrival time is 12:45 am. This is t2=12.75.

- The starting time is 10 am. This is t1=10.

The car took t2-t1=12.75-10=2.75.

The average speed is then:

[tex]v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}[/tex]

We can write the equation for the position x(t) for the car as:

[tex]x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t[/tex]

The time at which the car overtake the car is the time when both vehicles have the same position:

[tex]x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65[/tex]

The car overtakes the truck at t=11.65 hours or 11:39 am.

Answer:

z = 70°

y = 103°

Step-by-step explanation:

From the picture attached,

110° + z° = 180° [Supplementary angles]

z = 180 - 110

z = 70°

Since sum of interior angles of a polygon = (n - 2)×180°

where n = number of sides of the polygon

For a quadrilateral (n = 4),

Sum of interior angles = (4 - 2) × 180°

                                     = 360°

z° + y° + 100° + 87° = 360°

70° + y° + 187° = 360°

y = 103°

Therefore, measure of the angles x = 70° and y = 103°.

Answer:

C. (x-3)(x+2)(x+1)

Step-by-step explanation:

We can use the rational roots test to help factor out the original equation.

The leading term is 1 and the constant is 6

p/q= 6/1

Now we find factors (all these are plus and minus)

1,2,3,6

1

We find the common ones (+1 and -1) and use -1 because it ends up being the root of the function

Factor, (x+1)

Now we have (x+1)(x^2-x-6)

Factor this with whatever method you perfer, I use AC method

Find two that are a product of -6 and add to -1 (-3 and 2)

We get (x+1)(x-3)(x+2)

C

Answer:

[tex]\boxed{C}[/tex]

Step-by-step explanation:

Let's solve all of the option and see which equals x³-7x-6

Option A)

[tex](x-4)(x-2)(x+1)[/tex]

=> [tex](x^2-6x+8)(x+1)[/tex]

=> [tex]x^3+x^2-6x^2-6x+8x+1\\x^3-5x^2+2x+1[/tex]

So, A is not correct

Option B)

[tex](x-6)(x-1)(x+1)\\(x+6)(x^2-1)\\x^3-x+6x^2-6\\x^2+6x^2-x-6[/tex]

This is also not correct

Option C)    ← Correct

[tex](x-3)(x+2)(x+1)\\(x^2-x-6)(x+1)\\x^3+x^2-x^2-x-6x-6\\x^3-7x-6[/tex]

This equals to x³-7x-6, So, this is the correct option. No need to do Option D since we have the right option now!

S = sample space = set of all possible outcomes

S = set of whole numbers 1 through 6

S = {1,2,3,4,5,6}

E = event space = set of outcomes we want to happen

E = set of odd numbers between 1 through 6

E = {1,3,5}

We have 3 items in set E and 6 items in set S. So there are 3 ways to get what we want to happen out of 6 ways total. The probability is therefore 3/6 = 1/2

Answer:

C. It is an angle that has its vertex at the center of a circle.

Step-by-step explanation:

That's the definition.

A. is wrong. An angle with a measure greater than 180° is an obtuse angle,

B. is wrong. An angle that has its vertex on the circle is an inscribed angle.

D. is wrong. Part of the circumference of a circle is an arc.

Answer:

Well if (a,b) is in Quadrant IV which is the last quadrant the a or x is a positive number and the b or y is a negative number.

Answer:

a should be a positive number

b should be a negative number

Answer:

x = -4/3 and x = 5/2.

Step-by-step explanation:

6x² - 7x = 20

6x² - 7x - 20 = 0

To solve this, we can use the quadratic formula to solve this.

[please ignore the A-hat; that is a bug]

[tex]\frac{-b±\sqrt{b^2 - 4ac} }{2a}[/tex]

In this case, a = 6, b = -7, and c = -20.

[tex]\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}[/tex]

= [tex]\frac{7±\sqrt{49 + 80 * 6} }{12}[/tex]

= [tex]\frac{7±\sqrt{49 + 480} }{12}[/tex]

= [tex]\frac{7±\sqrt{529} }{12}[/tex]

= [tex]\frac{7±23 }{12}[/tex]

[tex]\frac{7 - 23 }{12}[/tex] = [tex]\frac{-16 }{12}[/tex] = -8 / 6 = -4 / 3

[tex]\frac{7 + 23 }{12}[/tex] = [tex]\frac{30}{12}[/tex] = 15 / 6 = 5 / 2

So, x = -4/3 and x = 5/2.

Hope this helps!  

Answer:

Step-by-step explanation:

[tex]6 {x}^{2} - 7x = 20[/tex]

Move constant to the left and change its sign

[tex] {6x}^{2} - 7x - 20 = 0[/tex]

Write -7x as a difference

[tex]6 {x}^{2} + 8x - 15x - 20 = 0[/tex]

Factor out 2x from the expression

[tex]2x(3x + 4) - 15x - 20 = 0[/tex]

Factor out -5 from the expression

[tex]2x(3x + 4) - 5(3x + 4) = 0[/tex]

Factor out 3x + 4 from the expression

[tex](3x + 4)(2x - 5) = 0[/tex]

When the product of factors equals 0 , at least one factor is 0

[tex]3x + 4 = 0[/tex]

[tex]2x - 5 = 0[/tex]

Solve the equation for X1

[tex]3x + 4 = 0[/tex]

Move constant to right side and change its sign

[tex] 3x = 0 - 4[/tex]

Calculate the difference

[tex]3x = - 4[/tex]

Divide both sides of the equation by 3

[tex] \frac{3x}{3} = \frac{ - 4}{3} [/tex]

Calculate

[tex]x = - \frac{4}{3} [/tex]

Again,

Solve for x2

[tex]2x - 5 = 0[/tex]

Move constant to right side and change its sign

[tex]2x = 0 + 5[/tex]

Calculate the sum

[tex]2x = 5[/tex]

Divide both sides of the equation by 2

[tex] \frac{2x}{2} = \frac{5}{2} [/tex]

Calculate

[tex]x = \frac{5}{2} [/tex]

[tex]x1 = - \frac{4}{3} [/tex]

[tex]x2 = \frac{5}{2} [/tex]

Hope this helps...

Best regards!!

Answer:

A)$ 45

B) $105

Step-by-step explanation:

Bag and a belt cost $255

Let bag = x

Let belt = y

X+y= 255 equation 1

Let total money be z first

Remaining money= z-255

X-30 = z-255

Y +15 = z-255

Equating the left side of the equation

X+30 = y+15

X-y= 45 equation 2

Solving simultaneously

X+y= 255

X-y= 45

2x = 300

X= 150

If x= 150

150-y= 45

150-45= y

105=y

Bag = $150

Belt = $105

Bag Is 150-105 more than the belt

150-105= $45

Answer:

[tex]\mathbf{V = 1296 \pi }[/tex]

Step-by-step explanation:

Given that :

Find the volume of the region enclosed by the cylinder [tex]x^2 + y^2 =36[/tex] and the plane z = 0 and y + z = 36

From y + z = 36

z = 36 - y

The volume of the region can be represented by the equation:

[tex]V = \int\limits \int\limits_D(36-y)dA[/tex]

In this case;

D is the region given by [tex]x^2 + y^2 = 36[/tex]

Relating this to polar coordinates

x = rcosθ    y = rsinθ

x² + y² = r²

x² + y² = 36

r² = 36

r = [tex]\sqrt{36}[/tex]

r = 6

dA = rdrdθ

r → 0 to 6

θ to 0  to 2π

Therefore:

[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r sin \theta ) (rdrd \theta)[/tex]

[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r^2 sin \theta ) drd \theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [\dfrac{36r^2}{2}- \dfrac{r^3}{3}sin \theta]^6_0 \ d\theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [648- \dfrac{216}{3}sin \theta]d\theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [648+\dfrac{216}{3}cos \theta]d\theta[/tex]

[tex]V = [648+\dfrac{216}{3}cos \theta]^{2 \pi}_0[/tex]

[tex]V = [648(2 \pi -0)+\dfrac{216}{3}(1-1)][/tex]

[tex]V = [648(2 \pi )+\dfrac{216}{3}(0)][/tex]

[tex]V = 648(2 \pi )[/tex]

[tex]\mathbf{V = 1296 \pi }[/tex]

Answer:

Total number of required ways = 18480

Step-by-step explanation:

Given that

Total appetizers = 11

Total main courses = 8

Total desserts = 4

To be selected 9 appetizers

3 main courses and

2 desserts.

To find:

Number of ways of selecting them.

Solution:

Number of ways to select 'r' number of items out of 'n' number of items is given as:

[tex]_nC_r = \dfrac{n!}{(n-r)!r!}[/tex]

One important property:

[tex]_nC_r = _nC_{n-r}[/tex]

Here we have 3 items, we will find each items' number of ways of selecting and then will multiply all of them.

Number of ways to select 9 appetizers out of 11 appetizers:

[tex]_{11}C_9\ or\ _{11}C_2 = \dfrac{11 \times 10}{2} = 55[/tex]

Number of ways to select 3 out of 8 main courses:

[tex]_{8}C_3= \dfrac{8 \times 7 \times 6}{6} = 56[/tex]

Number of ways to select 2 desserts out of 4:

[tex]_{4}C_2= \dfrac{4 \times 3}{2} = 6[/tex]

Total number of ways = [tex]55 \times 56 \times 6[/tex] = 18480

Let x be the number.

Set up an equation:

2x - 2/3x = 20

Simplify:

1 1/3x = 20

Divide both sides by 1 1/3

X = 15

The number is 15

Answer:median:249    

Step-by-step explanation:

median:198] 216} 220] 236] 246 252 [253[ 260 {290[ 369

246 +252=498

498/2=249

as for the mean  i will give you that later

Answer:

x = 65°

Step-by-step explanation:

Naming the sides of the parallelogram formed ABCD as shown in the attached image to this solution.

Angle A = 2x (vertically opposite angles are equal)

Angle A = Angle C (opposite angles of a parallelogram are equal)

Angle A = Angle C = 2x

(Angle C) + 50° = 180° (Sum of angles on a straight line is 180°)

2x + 50° = 180°

2x = 180° - 50° = 130°

x = (130°/2) = 65°

Hope this Helps!!!

Answer:

65 degrees

Step-by-step explanation:

Answer: a) Mean = [tex]=37.80[/tex]

Standard deviation=[tex]=1.9442[/tex]

b) Mean = [tex]56.00[/tex]

Standard deviation=[tex]4.0988[/tex]

c) Mean = [tex]=24[/tex]

Standard deviation=[tex]2.4495[/tex]

Step-by-step explanation:

To compute Mean and standard deviation , we use following formula:

Mean = [tex]n\pi[/tex]

Standard deviation=[tex]\sqrt{n\pi(1-\pi)}[/tex]

a. [tex]n=42,\ \pi=0.90[/tex]

Mean = [tex]42\times0.90=37.80[/tex]

Standard deviation=[tex]\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442[/tex]

b. [tex]n=80,\ \pi=0.70[/tex]

Mean = [tex]80\times0.70=56.00[/tex]

Standard deviation=[tex]\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988[/tex]

c. [tex]n=32,\ \pi=0.75[/tex]

Mean = [tex]32\times0.75=24[/tex]

Standard deviation=[tex]\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495[/tex]

Answer:

[tex]7.5cm^2[/tex]

Step-by-step explanation:

Well using the following formula,

[tex]\frac{b*h}{2}[/tex]

5*3 = 15

15 / 2

7.5cm^2

Answer:[tex]7.5cm^{2}[/tex]

Step-by-step explanation:

h=3

b=5

area=1/2 x b x h

1/2 x 5 x 3

area=7.5