Could someone please give me the answer to this?

Could Someone Please Give Me The Answer To This?

Answers

Answer 1

Answer:

36.87

Step-by-step explanation:

The cosine of an angle in a right triangle is the length of the adjacent side divided by the length of the hypotenuse, which in this case is 4/5. Therefore, the measure of this angle is the arc cosine of 4/5, or about 36.87 degrees. Hope this helps!

Answer 2
The correct answer is 36.86 because the cos of 4/5 is 36.86

Related Questions

An experiment was done to look at whether there is an effect of the number of hours spent practising a musical instrument and gender on the level of musical ability. A sample of 30 (15 men and 15 women) participants who had never learnt to play a musical instrument before were recruited. Participants were randomly allocated to one of three groups that varied in the number of hours they would spend practising every day for 1 year (0 hours, 1 hours, 2 hours). Men and women were divided equally across groups. All participants had a one-hour lesson each week over the course of the year, after which their level of musical skill was measured on a 10-point scale ranging from 0 (you can’t play for toffee) to 10 (‘Are you Mozart reincarnated?’). An ANOVA was conducted on these data, and the results revealed significant main effects of gender and the number of hours spent practising. Which of the following contrasts could we use to break down the effect of gender?
A- Helmert contratst
B- Simple contrast
C- Repeated contrast
D- None

Answers

Answer: Repeated contrast

Step-by-step explanation:

In the two way ANOVA that was performed above, there were 3 groups of which 30 people (15 men and 15 women) participants who had never learnt to play a musical instrument before were recruited and divided equally.

The ANOVA is of repeated measures. There is within group effect, between group effect and interaction effect. The result also shows significant main effect for the gender and the hours used practicing. Hence, to breakdown the effect of gender, the repeated contrast method will be utilized. The repeated contrast method compares the mean of every level with the succeeding level except the last level.

Can someone help me With This

Answers

Answer:

D

Step-by-step explanation:

Find out if they match in all of them

Hope this helps

What is the circumference of the circle shown below (round your answer to nearest tenths)

Answers

Answer:

A. 38.3

Step-by-step explanation:

[tex]circumference \\ \: \: \: \: \: = 2 \times radius \times \pi \\ or =diameter \times \pi \\ thus \: the \: answer \: is \\ 12.2 \times 3.14 = 38.3 \\ ( \: a \: ) [/tex]

What is six thousandths as a number?

Answers

Answer:

6000

Step-by-step explanation:

6 six

60 sixty

600 six hundred

6000 six thousand

//have a great day//

The answer for six thousandths as a number is 0.006

Multiply
4.2
x0.6

Type
Type an integer or a decir​

Answers

Answer:

2.52

Step-by-step explanation:

4.2 × 0.6

Multiply the terms.

= 2.52

Answer:

2.52

hope it helps

Step-by-step explanation:

4.2 x 0.6

To solve this first, you simply multiply 42*06

(Exclude the decimal point)

42 x 6

= 252

Now since there are two numbers after the point (one is 4.2 and one is 0.6)

Move 252 two decimal places to left

= 2.52

What is the value of x?

Answers

Answer:

Oioj[

Step-by-step explanation:

Step-by-step explanation:

Write the equation to solve it in order to know the exact value of X.

In how many ways you can put 20 books on 50 shelves so that there is not more than one book on a shelf?

Answers

9514 1404 393

Answer:

47129212243960 ≈ 4.713×10^13 if order doesn't matter114660755112113373922453094400000 ≈ 1.147×10^32 if it does

Step-by-step explanation:

If order doesn't matter, the number is the combinations of 50 things taken 20 at a time:

  50C20 = 47129212243960 ≈ 4.713×10^13

If order does matter, then the number of ways is this value multiplied by 20!:

  50P20 = 114660755112113373922453094400000 ≈ 1.147×10^32

_____

nCk = n!/(k!(n-k)!)

nPk = n!/(n-k)!

Which calculation could not be used to find the percentage change
between 16 and 20?

look at the image attached and explain why​

Answers

Answer:

Option (B).

Step-by-step explanation:

Percentage change between two numbers a and b can be calculated by the formula,

% change = [tex]\frac{|b-a|}{a}\times 100[/tex]

Where, (b - a) = Change in values

a = Initial value

If a = 16 and b = 20

Percentage change between 16 and 20 will be,

= [tex](\frac{20-16}{16})\times 100[/tex]

= [tex]\frac{4}{16}\times 100[/tex]

= 25%

If a = 20 and b = 16,

Percentage change = [tex]\frac{|16-20|}{20}\times 100[/tex]

                                 = 20%

Therefore, %change between 16 and 24 may be 16% or 20%.

Option (A),

[tex]\frac{20-16}{16}\times 100[/tex] = 25%

Option (B),

[tex]\frac{20}{16}-1\times 100[/tex] = 1.25 - 1 × 100

                   = 1.25 - 100

                   = -98.75%

Option (C),

[tex]100\times \frac{1}{4}[/tex] = 25%

Option (D),

[tex]\frac{(20-16)}{20}\times 100[/tex] = 20%

Therefore, we can not use the calculation used in Option (B).

The formula for the volume of a cube of side length L is: V = L X L X L What is the value of V when L= 5? *

Answers

Answer:125

Solution,

Length=5

Volume of cube=(L)^3

= 5*5*5

=125

hope it helps

Good luck on your assignment

Find the value of x in the parallelogram below.

Answers

Answer:

x=106 degrees

Step-by-step explanation:

The two opposite angles in a parallelogram are always the same and we know 360 degrees in a parallelogram.

x+x+74+74=360.

2x+148=360

2x=212

x=106 degrees

Joanna went school supply shopping. She spent $33.33 on notebooks and pencils. Notebooks cost
$1.85 each and pencils cost $1.39 each. She bought a total of 21 notebooks and pencils. How many of
each did she buy?

Answers

Answer:

Joanna bought 21 items that come out to a total of $33.33. She bought 9 notebooks and 12 pencils.

Step-by-step explanation:

Notebooks (N) = $1.85 Pencils (P) = $1.39

9N+12P= $33.33

9*1.85=16.65

12*1.39=16.68

16.65+16.68=33.33

what can you say about the end behavior of the function f(x)=-4x^6+6x^2-52

Answers

Answer:

As x gets smaller, pointing to negative infinity, the value of f decreses, pointing to negative infinity.

As x gets increases, pointing to positve infinity, the value of f decreses, pointing to negative infinity.

Step-by-step explanation:

To find the end behaviour of a function f(x), we calculate these following limits:

[tex]\lim_{x \to +\infty} f(x)[/tex]

And

[tex]\lim_{x \to -\infty} f(x)[/tex]

In this question:

[tex]f(x) = -4x^{6} + 6x^{2} - 52[/tex]

At negative infinity:

[tex]\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} -4x^{6} + 6x^{2} - 52[/tex]

When the variable points to infinity, we only consider the term with the highest exponent. So

[tex]\lim_{x \to -\infty} -4x^{6} + 6x^{2} - 52 = \lim_{x \to -\infty} -4x^{6} = -4*(-\infty)^{6} = -(\infty) = -\infty[/tex]

So as x gets smaller, pointing to negative infinity, the value of f decreses, pointing to negative infinity.

Positive infinity:

[tex]\lim_{x \to \infty} f(x) = \lim_{x \to \infty} -4x^{6} + 6x^{2} - 52 = \lim_{x \to \infty} -4x^{6} = -4*(\infty)^{6} = -(\infty) = -\infty[/tex]

So as x gets increases, pointing to positve infinity, the value of f decreses, pointing to negative infinity.

f(x) = -4x^6 +6x^2-52

The leading coefficient is negative so the left end of the graph goes down.

f(x) is an even function so both ends of the graph go in the same direction.

A truncated cube is a convex polyhedron with 36 edges and 24 vertices. A truncated tetrahedron is a convex polyhedron

with 18 edges and 12 vertices.

How do the number of faces of a truncated cube and a truncated tetrahedron compare?

The truncated cube has 6 more faces than the truncated tetrahedron.

The truncated cube has 8 more faces than the truncated tetrahedron.

The truncated cube has 12 more faces than the truncated tetrahedron.

The truncated cube has 18 more faces than the truncated tetrahedron.

Answers

Answer:

The truncated cube has 6 more faces than the truncated tetrahedron.

Step-by-step explanation:

==>Given:

truncated cube=>

edges (E) = 36

vertices (V) = 24

faces (F) = ? (unknown)

According to Euler's polyhedron formula, Vertices (V) - Edges (E) + Faces (F) = 2, let's find how many faces the truncated cube has

=> 24 - 36 + F = 2

- 12 + F = 2

F = 2 + 12

F = 14

truncated tetrahedron=>

edges (E) = 18

vertices (V) = 12

faces (F) = ? (unknown)

Using V - E + F = 2, find F

=>12 - 18 + F = 2

- 6 + F = 2

F = 2 + 6

F = 8

Comparing the faces of the truncated cube (14) and the truncated tetrahedron (8), the truncated cube has 6 more faces than the truncated tetrahedron (14 - 8 = 6)

Answer:

Answer A:The truncated cube has 6 more faces than the truncated tetrahedron.

Step-by-step explanation:

Find the value of x a)10 b)6 c)5

Answers

C) 5 hope this helped
The answer is c I think

What are the solution(s) to the quadratic equation 50 - x2 = 0?
x = +2,5
x = +63
x = +5,2
no real solution

Answers

Answer:

Step-by-step explanation:

Please use " ^ " for exponentiation:  50 - x^2 = 0.

Solving for x^2, we get:                      x^2 = 50

Taking the square root of both sides:    x = ±√(50), or x = ±7.07

None of the three possible answers here is correct.

I have a question about this.

Answers

I'm pretty sure it's rectangle

3 lines intersect. A horizontal line with points G, N, K intersects a vertical line with points J, N, M at point N and forms a right angle. The third line contains points H, N, L and intersects the other lines at N. It is diagonal and cuts through angles J N G and M N K. Which statements are true regarding the diagram? AngleGNH and AngleHNJ are complementary. AngleJNK and AngleKNL are supplementary. AngleKNL and AngleLNM are complementary. mAngleHNK + mAngleKNL = 180° mAngleMNG + mAngleGNH = 90°

Answers

Answer:

A, C, D

Step-by-step explanation:

Answer: A , C , D

Step-by-step explanation: edge2022

Suppose that two people standing 2 miles apart both see the burst from a fireworks display. After a period of​ time, the first person standing at point A hears the burst. Six seconds ​later, the second person standing at point B hears the burst. If the person at point B is due west of the person at point A and if the display is known to occur due north of the person at point​ A, where did the fireworks display​ occur? Note that sound travels at 1100 feet per second.

Answers

Answer: approximately 5148 feet directly north of point A

This is equivalent to 0.975 miles

==============================================================

Explanation:

Check out figure 1 (attached image below) to see how the drawing is set up.

Points A and B are separated by 2 miles, or 10560 feet. Use the conversion factor 1 mile = 5280 feet.

Because sound travels at roughly 1100 feet per second (assuming all of the conditions are right), this means that after x seconds, the sound wave has traveled a total distance of 1100x feet. This is the distance from A to C. Point C is the firework location.

The distance from B to C is 1100(x+6) feet because it takes 6 more seconds for the soundwave to travel from C to B, compared from C to A.

Note that triangle ABC is a right triangle. The 90 degree angle is at point A.

We can use the pythagorean theorem to solve for x

See figure 2 in the attached images to see the steps on solving for x. The numbers get quite big, though in the end x is fairly small. We end up with x = 4.68, which is approximate due to the 1100 figure being approximate.

This means the sound wave takes about 4.68 seconds to go from point C to point A.

With this x value, we can compute the expression 1100x to get

1100*x = 1100*4.68 = 5,148 feet

To convert this to miles, divide by 5280

(5148)/(5280) = 0.975

Therefore,

5148 feet = 0.975 miles

The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume the standard deviation is σ = $2,400.
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean for each of the following sample sizes: 20, 50, 100, and 500? (Round your answers to four decimal places.)
b. What is the advantage of a larger sample size when attempting to estimate the population mean?
a. A larger sample increases the probability that the sample mean will be a specified distance away from the population mean.
b. A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.
c. A larger sample lowers the population standard deviation.
d. A larger sample has a standard error that is closer to the population standard deviation.

Answers

Answer:

(a)                             n :      20           50          100         500

P (-200 < X - μ < 200) : 0.2886    0.4444    0.5954    0.9376

(b) The correct option is (b).

Step-by-step explanation:

Let the random variable X represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.

The mean amount of deductions is, μ = $16,642 and standard deviation is, σ = $2,400.

Assuming that the random variable X follows a normal distribution.

(a)

Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:

For a sample size of n = 20

[tex]P(\mu-200<X<\mu+200)=P(\frac{(16642-200)-16642}{2400/\sqrt{20}}<\frac{X-\mu}{\sigma/\sqrt{n}}<\frac{(16642+200)-16642}{2400/\sqrt{20}})[/tex]

                                           [tex]=P(-0.37<Z<0.37)\\\\=P(Z<0.37)-P(Z<-0.37)\\\\=0.6443-0.3557\\\\=0.2886[/tex]

For a sample size of n = 50

[tex]P(\mu-200<X<\mu+200)=P(\frac{(16642-200)-16642}{2400/\sqrt{50}}<\frac{X-\mu}{\sigma/\sqrt{n}}<\frac{(16642+200)-16642}{2400/\sqrt{50}})[/tex]

                                           [tex]=P(-0.59<Z<0.59)\\\\=P(Z<0.59)-P(Z<-0.59)\\\\=0.7222-0.2778\\\\=0.4444[/tex]

For a sample size of n = 100

[tex]P(\mu-200<X<\mu+200)=P(\frac{(16642-200)-16642}{2400/\sqrt{100}}<\frac{X-\mu}{\sigma/\sqrt{n}}<\frac{(16642+200)-16642}{2400/\sqrt{100}})[/tex]

                                           [tex]=P(-0.83<Z<0.83)\\\\=P(Z<0.83)-P(Z<-0.83)\\\\=0.7977-0.2023\\\\=0.5954[/tex]

For a sample size of n = 500

[tex]P(\mu-200<X<\mu+200)=P(\frac{(16642-200)-16642}{2400/\sqrt{500}}<\frac{X-\mu}{\sigma/\sqrt{n}}<\frac{(16642+200)-16642}{2400/\sqrt{500}})[/tex]

                                           [tex]=P(-1.86<Z<1.86)\\\\=P(Z<1.86)-P(Z<-1.86)\\\\=0.9688-0.0312\\\\=0.9376[/tex]

                                 n :      20           50          100         500

P (-200 < X - μ < 200) : 0.2886    0.4444    0.5954    0.9376

(b)

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ([tex]\bar x[/tex]) approaches the whole population mean ([tex]\mu_{x}[/tex]).

Consider the probabilities computed in part (a).

As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.

So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

Thus, the correct option is (b).

Using the normal distribution and the central limit theorem, it is found that:

a)

0.2886 = 28.86% probability that a sample size of 20 has a sample mean within $200 of the population mean.

0.4448 = 44.48% probability that a sample size of 50 has a sample mean within $200 of the population mean.

0.5934 = 59.34% probability that a sample size of 100 has a sample mean within $200 of the population mean.

0.9372 = 93.72% probability that a sample size of 500 has a sample mean within $200 of the population mean.

b)

b. A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

It 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, which is the percentile of X.By the Central Limit Theorem, the standard deviation of the sampling distribution of sample sizes of n is: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

Hence, the probability of sample of size n having a sample mean within 200 is the p-value of [tex]Z = \frac{200}{s}[/tex] subtracted by the p-value of [tex]Z = -\frac{200}{s}[/tex]

In this problem:

The standard deviation is [tex]\sigma = 2400[/tex].

Item a:

For samples of 20, [tex]n = 20[/tex], and thus:

[tex]s = \frac{2400}{\sqrt{20}}[/tex]

Then

[tex]Z = \frac{200}{s} = \frac{200}{\frac{2400}{\sqrt{20}}} = 0.37[/tex]

Z = 0.37 has a p-value of 0.6443.Z = -0.37 has a p-value of 0.3557.

0.6443 - 0.3557 = 0.2886.

0.2886 = 28.86% probability that a sample size of 20 has a sample mean within $200 of the population mean.

For samples of 50, [tex]n = 50[/tex], and thus:

[tex]s = \frac{2400}{\sqrt{50}}[/tex]

Then

[tex]Z = \frac{200}{s} = \frac{200}{\frac{2400}{\sqrt{50}}} = 0.59[/tex]

Z = 0.59 has a p-value of 0.7224.Z = -0.59 has a p-value of 0.2776.

0.7224 - 0.2776 = 0.4448.

0.4448 = 44.48% probability that a sample size of 50 has a sample mean within $200 of the population mean.

For samples of 100, [tex]n = 100[/tex], and thus:

[tex]s = \frac{2400}{\sqrt{100}}[/tex]

Then

[tex]Z = \frac{200}{s} = \frac{200}{\frac{2400}{\sqrt{100}}} = 0.83[/tex]

Z = 0.83 has a p-value of 0.7967.Z = -0.83 has a p-value of 0.2033.

0.7967 - 0.2033 = 0.5934

0.5934 = 59.34% probability that a sample size of 100 has a sample mean within $200 of the population mean.

For samples of 500, [tex]n = 500[/tex], and thus:

[tex]s = \frac{2400}{\sqrt{500}}[/tex]

Then

[tex]Z = \frac{200}{s} = \frac{200}{\frac{2400}{\sqrt{500}}} = 1.86[/tex]

Z = 1.86 has a p-value of 0.9686.Z = -1.86 has a p-value of 0.0314.

0.9686 - 0.0314 = 0.9372

0.9372 = 93.72% probability that a sample size of 500 has a sample mean within $200 of the population mean.

Item b:

A larger sample size reduces the standard error, as [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], that is, the standard error is inversely proportional to the square root of the sample size n, meaning that values are closer to the mean. Thus, the correct option is:

b. A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

A similar problem is given at https://brainly.com/question/24663213

OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT

Answers

Answer:

252

Step-by-step explanation:

BACTROBAN ointment contains 2% w/w mupirocin. How many grams of a polyethylene glycol ointment base must be mixed with the contents of a 22-g tube of the BACTROBAN ointment to prepare one having a concentration of 5 mg/g?

Answers

Answer:

66g of polyethylene ointment base!

Please answer this correctly without making mistakes

Answers

Since the radius for either the quarter or the whole circle is the same the radius of the circle shall be divided into 4 parts
Please refer to the photograph to know more about the answer

Area = 0.785

Area=0.79

I hope it helps

Which numbers are the extremes of the proportion shown below

Answers

Answer:

3 and 8 are the extremes of the given proportion (first listed answer option)

Step-by-step explanation:

In a proportion of the type:

[tex]\frac{A}{B} =\frac{C}{D}[/tex]

the values "A" and "D" are called "extremes of the proportion, while "B" and "C" are called the "means" of the proportion.

This comes from writing it as:   A : B = C : D

where we observe that A and D are the more "extreme" values being further away from the equal sign than the quantities B and C which are more towards the middle (center of the proportion).

So in your case, the numbers 3 and 8 are the extremes

Answer:

3 and 8

Step-by-step explanation:

can someone help me?​

Answers

U-U glad u asked yes I can U-U

For A: V = B · h  V = 8 · 14  V = 784 units^3.

For B: V = B · h  V = 9 · 9  V = 729 units^3.

For C: V = B · h  V = 5 · 11  V = 220 units^3.

Can anyone help me with this question?

Answers

Answer:

x= 60°, y = 80°, z = 40°

Step-by-step explanation:

Look at the line substending 40° and Z°; you would see that both lines are parallel and so their angles are they the same.

Hence z= 40° { corresponding angles of parallel lines}

Similarly;

Look at the line substending 60° and x°; you would see that both lines are parallel and so their angles are they the same.

60° = x° { corresponding angles of parallel lines}

Now looking at the angle between x and y; let's call the angle between them r

And you would observe closely that r = z° = 40°{ vertically opposite angles are equal}

Note that x + r + y = 180°{ angle on a straight line}

y = 180° - ( x + r)

y = 180 - (60+40)

y = 180° - 100°

= 80°

Keep getting this wrong please help!!

Answers

Answer:

139.316148[tex]\pi[/tex]cubed inches

Step-by-step explanation:

If needed, use a calculator. Not sure if there's rounding for the final answer, so I will give you the precise answer.

1. Find the radius of the ball. If you know the circumference is 9.42 inches, divided it by 2, which the quotient is 4.71.

2. Remember the formula is V= [tex]\frac{4}{3} \pi r^3[/tex]

3. [tex]\frac{4}{3} \pi (4.71)^3[/tex]

4. [tex]\frac{4}{3} \pi (104.487111^3)[/tex]

5. [tex]4\pi (34.829037)[/tex]

6. 139.316148[tex]\pi[/tex]cubed inches

The congressional committees on mathematics and computer science are made up of five representatives each, and a congressional rule is that the two committees must be disjoint. If there are 385 members of congress, how many ways could the committees be selected?

Answers

Answer:

The committes can be selected in [tex]1.752507297 \times 10^{19}[/tex] ways

Step-by-step explanation:

The order in which the members are chosen to the committee is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The two committees must be disjoint.

This means that a person cannot be part of both committes.

If there are 385 members of congress, how many ways could the committees be selected?

Since the committes are disjoint, 5(math) + 5(computer science) = 10 people will be chosen from the set of 385. So

[tex]C_{385,10} = \frac{385!}{10!(385-10)!} = 1.752507297 \times 10^{19}[/tex]

The committes can be selected in [tex]1.752507297 \times 10^{19}[/tex] ways

The total cost (in dollars) for a company to manufacture and sell x items per week is C = 40 x + 640 , whereas the revenue brought in by selling all x items is R = 66 x − 0.2 x 2 . How many items must be sold to obtain a weekly profit of $ 200 ?

Answers

Answer:

The company must sell 60 or 70 items to obtain a weekly profit of 200.

Step-by-step explanation:

The profit is the difference between the revenue and the cost of a given task, therefore:

[tex]\text{profit} = R - C\\\text{profit} = 66*x - 0.2*x^2 - (40*x + 640)\\\text{profit} = 66*x - 0.2*x^2 - 40*x - 640\\\text{profit} = - 0.2*x^2 + 26*x - 640[/tex]

To have a profit of 200, we need to sell:

[tex]-0.2*x^2 + 26*x - 640 = 200\\-0.2*x^2 + 26*x -840 = 0\text{ } *\frac{-1}{0.2}\\x^2 -130 + -4200 = 0\\x_{1,2} = \frac{-(-130) \pm \sqrt{(-130)^2 - 4*1*(-4200)}}{2*1}\\x_{1,2} = \frac{130 \pm \sqrt{16900 + 16800}}{2}\\x_{1,2} = \frac{130 \pm \sqrt{100}}{2}\\x_{1,2} = \frac{130 \pm 10}{2}\\x_{1} = \frac{130 + 10}{2} = \frac{140}{2} = 70\\ x_{2} = \frac{130 - 10}{2} = \frac{120}{2} = 60[/tex]

The company must sell 60 or 70 items to obtain a weekly profit of 200.

Miles draws three cards at random from a standard deck of 52 cards, without replacement.
(a) Find the probability that all three cards are red.

(b) Find the probability that all three cards have the same rank.

Answers

Answer:

P( red, red, red no replacement ) =  2/17

P( 3 cards with same rank, no replacement) =  1/425

Step-by-step explanation:

There are 52 cards, 26 are red

P( red) =  red/total =26/ 52 = 1/2

Now draw the second card without replacement

There are 51 cards, 25 are red

P( red) =  red/total =25/51

Now draw the third card without replacement

There are 50 cards, 24 are red

P( red) =  red/total =24/50 = 12/25

P( red, red, red no replacement ) = 1/2 * 25/51 * 12/25 = 2/17

P ( all have the same rank)

There are 52 cards,  4 of each rank

We don't care what the first rank is, now the second and third draw have to have the same rank as the first

P( rank) = 1/1

Now draw the second card without replacement

There are 51 cards, 3 are left with the same rank

P( same rank) = cards with same rank/total = 3/51

Now draw the third card without replacement

There are 50 cards, 2 are left with the same rank

P( same rank) = cards with same rank/total = 2/50 = 1/25

P( 3 cards with same rank, no replacement) = 1 * 3/51*1/25 = 1/425

The Office of Student Services at UNC would like to estimate the proportion of UNC's 28,500 students who are foreign students. In their random sample of 50 students, 4 are foreign students. Unknown to them, the proportion of all UNC students that are foreign students is 0.061. For each student, let x=1 if the student is foreign and let x=0 if the student is from the U.S.Find the mean and the standard deviation of the sampling distribution of the sample proportion for a sample of size 50.

Answers

Answer:

For the sampling distribution of the sample proportion for a sample of size 50, the mean is 0.061 and the standard deviation is 0.034.

Step-by-step explanation:

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.061, n = 50[/tex]

So

Mean:

[tex]\mu = p = 0.061[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{0.061*0.939}{50}} = 0.034[/tex]

For the sampling distribution of the sample proportion for a sample of size 50, the mean is 0.061 and the standard deviation is 0.034.

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