A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below. 20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27 It is known that the population standard deviation is 7. The instructor has recommended that students devote 2 hours per week for the duration of the 12-week semester, for a total of 24 hours. Test to determine whether there is evidence at the 0.07 significance level that the average student spent less than the recommended amount of time. Fill in the requested information below.A. The value of the standardized test statistic:Note: For the next part, your answer should use interval notation. An answer of the form (−[infinity],a) is expressed (-infty, a), an answer of the form (b,[infinity]) is expressed (b, infty), and an answer of the form (−[infinity],a)∪(b,[infinity]) is expressed (-infty, a)U(b, infty). B. The rejection region for the standardized test statistic:C. The p-value isD. Your decision for the hypothesis test: A. Reject H0. B. Do Not Reject H1. C. Do Not Reject H0. D. Reject H1.

Answer:

a

   [tex]\= x = 18.5[/tex]  ,  [tex]\sigma = 5.15[/tex]

b

 [tex]15.505 < \mu < 21.495[/tex]

c

 [tex]14.93 < \mu < 22.069[/tex]

Step-by-step explanation:

From the question we are are told that

    The  sample data is  21, 14, 13, 24, 17, 22, 25, 12

     The sample size is  n  = 8

Generally the ample mean is evaluated as

        [tex]\= x = \frac{\sum x }{n}[/tex]

        [tex]\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}[/tex]

         [tex]\= x = 18.5[/tex]

Generally the standard deviation is mathematically evaluated as

         [tex]\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}[/tex]

[tex]\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}[/tex]

[tex]\sigma = 5.15[/tex]

considering part b

Given that the confidence level is  90% then the significance level is evaluated as

         [tex]\alpha = 100-90[/tex]

         [tex]\alpha = 10\%[/tex]

         [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex]  from the normal distribution table the value is  

     [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]

The margin of error is mathematically represented as

      [tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =1.645 * \frac{5.15 }{\sqrt{8} }[/tex]

=>     [tex]E = 2.995[/tex]

The 90% confidence interval is evaluated as

       [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

       [tex]18.5 - 2.995 < \mu < 18.5 + 2.995[/tex]

       [tex]15.505 < \mu < 21.495[/tex]

considering part c

Given that the confidence level is  95% then the significance level is evaluated as

         [tex]\alpha = 100-95[/tex]

         [tex]\alpha = 5\%[/tex]

         [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex]  from the normal distribution table the value is  

     [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

The margin of error is mathematically represented as

      [tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =1.96 * \frac{5.15 }{\sqrt{8} }[/tex]

=>     [tex]E = 3.569[/tex]

The 95% confidence interval is evaluated as

       [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

       [tex]18.5 - 3.569 < \mu < 18.5 + 3.569[/tex]

       [tex]14.93 < \mu < 22.069[/tex]

Answer:

1. elements it contains =  (1,3)

2.  elements it contains = 35

3.  elements it contains = 8

4.  elements it contains = 17

Step-by-step explanation:

A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.

The red die shows 1 and the numbers add to 4.

How many elements does it contain?

B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]

The numbers do not add to 2.

How many elements does it contain?

C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 11 or the red die shows a 1.

How many elements does it contain?

D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 5, or they add to 9, or at least one of them is 1.

How many elements does it contain?

NB. Attached is the solution to the problems stated above

Answer:

Hi, there!!!

I hope you mean to evaluate cosA+ sonA /cosA - sinA.

so, i hope the answer in pictures will help you.

Answer:

The total   profit is [tex]p = 17x + 2124[/tex]

Step-by-step explanation:

From the question we are told that

   The profit made on each mp3 is  k  =  $35

    The profit made on each mp3 is  y =  $18

     The total amount sold is   n  =  118

 Now given that the amount of mp3 sold is x then the amount of  DVD sold is mathematically evaluated as

                      [tex]n - x[/tex]

Now the profit made on the x number of mp3 sold is  

                      [tex]x * 35 = 3x[/tex]

And the the profit made from the n-x number of  DVD  sold is  18 (n-x ) =  18 - 18x

 So the total profit made last week from the sales of both mp3 and DVD  is  

                   [tex]p = 35x + 18n - 18x[/tex]

                    [tex]p = 17x + 18(118)[/tex]

                    [tex]p = 17x + 2124[/tex]

Answer:

m∠AOD = 140°

Step-by-step explanation:

In the diagram attached,

OA⊥OC and OB⊥OD

m∠AOD = 3.5(m∠BOC)

Since, m∠BOD = 90°  [Given: OA⊥OC]

m∠BOC + m∠COD = 90° ---------(1)

Similarly, m∠AOC = 90° [Given : OA⊥OC]

m∠AOB + m∠BOC = 90° --------(2)

Equation (1) - Equation(2)

(m∠BOC + m∠COD) - (m∠AOB + m∠BOC) = 90°- 90°

m∠COD = m∠AOB

m∠AOB + m∠BOC + m∠COD = m∠AOD --------(3)

m∠AOB + m∠BOC + m∠AOB = 3.5(m∠BOC) [Since m∠COD = m∠AOB]

2m∠AOB = 3.5(m∠BOC) - m∠BOC

2m∠AOB = 2.5(m∠BOC)

m∠AOB = 1.25(m∠BOC)

From equation (2),

m∠AOB + m∠BOC = 90°

1.25(m∠BOC) + m∠BOC = 90°

2.25(m∠BOC) = 90°

m∠BOC = 40°

From equation (1),

m∠BOC + m∠COD = 90°

m∠COD + 40° = 90°

m∠COD = 50°

Now by putting these values in equation (3)

m∠AOB + m∠BOC + m∠COD = m∠AOD

m∠COD + m∠BOC + m∠COD = m∠AOD

50° + 40° + 50°= m∠AOD

m∠AOD = 140°

Answer:

0.4 cm

Step-by-step explanation:

The magnifying glass basically zooms into smaller objects. If the insect appears to be 2cm, then it is actually smaller than this. It cannot be 10 cm.

If the scale factor is 5, then this means that the insect is zoomed in 5 times through the magnifying glass. Use the following ratio:

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

This fraction can also be seen as division, so:

[tex]2[/tex]÷[tex]5=0.4[/tex]

The insect is actually 0.4 cm long.

(or 4 millimeters)

:Done

The inverse function theorem says

[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(f^{-1}(16))}[/tex]

We have

[tex]f(x)=x^2+4x-5[/tex]

defined on [tex]x>-2[/tex], for which we get

[tex]f^{-1}(x)=-2+\sqrt{x+9}[/tex]

and

[tex]f^{-1}(16)=-2+\sqrt{16+9}=3[/tex]

The derivative of [tex]f(x)[/tex] is

[tex]f'(x)=2x+4[/tex]

So we end up with

[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(3)}=\dfrac1{10}[/tex]

Answer:

The events are independent.

The probability of showing heads on both toss is equal to 1/2

Step-by-step explanation:

The sample space for this experiment consists of 2⁴= 16 sample points, as each toss can result in two outcomes we assume that the events are equally likely.

Two events are independent in the sample space if the probability of one event occurs, is not affected by whether the other event has or has not occurred.

In general the k events are defined to be mutually independent if and only if the probability of the intersection of  any 2,3,--------, k  equals the product of their respective probabilities.

P (A∩B) = P(A). P(B)

P (A∩B)   = 1/2. 1/2= 1/4

                                                                  Head          Tail

 P(E1)= 1/2  ----------          Coin 1               H,H              T,H

                                                                1/4                  1/4

  P(E2)= 1/2  ---------------  Coin 2             H, H               H,T

                                                                      1/4           1/4

So the events are independent.

The probability of showing heads on both toss is equal to 1/2

The sample space for this experiment consists of 2⁴= 16 sample points, out of which eight will have heads on both toss.

Or in other words ( 1/4* 1/4) = 2/4 = 1/2

Answer:

(1) B

(2) A

(3) C

Step-by-step explanation:

A random variable is a variable that denotes a set of all the possible outcomes of a random experiment. It is denotes by a single capital letter such as X or Y.

There are two types of random variables.

(1)

Exact weight of quarters now in circulation in the United States.

The variable weight is a continuous variable.

Thus, the exact weight of quarters now in circulation in the United States is a continuous random variable.

(2)

Shoe sizes of humans.

The shoe size of a person are discrete and finite values.

Thus, the shoe sizes of humans are discrete random variables.

(3)

Political party affiliations of adults in the United States.

This variable is not a quantitative variable.

It is a qualitative variable.

Thus, the political party affiliations of adults in the United States is no random variable.

Answer:

First use the protractor then round the number to the nearest 10

Answer:

Round to the nearest tenth

Step-by-step explanation:

Answer:

4110

Step-by-step explanation:

One ton is equal to 2000 pounds and one ounce is equal to 0.0625 pounds.

2 tons*2000 lbs per ton  = 4000 lbs

1760 ounces*0.0625 lebs per ounce = 110 lbs

4000+110=4110 lbs

Answer: 44

Step-by-step explanation:

Answer:

15x - y = - 126

or y = 15x + 126

Step-by-step explanation:

will make it simple and short

to find the equation... we need to find slope first.

                   y2 - y1             -9  -   6

slope = m  = ---------    =       -----------  =  15

                   x2 - x1             -9  -  (-8)

so we know that the equation of the line using point (-8,6) and slope 15             y - 6 = 15( x + 8)

y - 6 = 15x + 120

Writing the equation in the form   Ax + By = C

15x - y = -120-6

therefore.... 15x - y = - 126   or simplify it as or y = 15x + 126

Hope this helps

Answer:

A) C = 1/96

B) P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places

C) P(x+y<=1) = 5/2305, or 0.0021701 to 7 places

Step-by-step explanation:

f(x,y) = C x (1+y)

A)

To find C, we need to integrate the volume under region bound by

0 <= x <= 4, and

0 <= y <= 4

This volume equals 1.0.

Find integral,

int( int(f(x,y),x=0,4), y = 0,4) = 96C

therefore C = 1/96

or

F(x,y) = x (1+y) / 96  ............................(1)

B)

P(x<=1, y<=1)

Repeat the integral, substitute the appropriate limits,

P = int( int(F(x,y),x=0,1), y = 0,1)

= 1/128 or 0.0078125

P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places

C)

P(x+y<=1)

From the function, we know that this is going to be less than one half of the probability in (B), closer to 1/4 of the previous.

It will be again a double integral, as follows:

P = int( int(F(x,y),x=0,1-y), y = 0,1)

= 5/2304

= 0.0021701 (to 7 decimals)

P(x+y<=1) = 5/2305, or 0.0021701 to 7 places

Answer:

0.9995

Step-by-step explanation:

10% = 0.10

1 - 0.10 = 0.9

n = number of light bulbs = 7

we calculate this using binomial distribution.

p(x) = nCx × p^x(1-p)^n-x

our question says at most 4 is defective

= (7C0 × 0.1⁰ × 0.9⁷) + (7C1 × 0.1¹ × 0.9⁶) + (7C2 × 0.1² × 0.9⁵) + (7C3 × 0.1³ × 0.9⁴) + (7C4 × 0.1⁴ × 0.9³)

= 0.478 + 0.372 + 0.1239 + 0.023 + 0.0026

= 0.9995

we have 0.9995 probability that at most 4 light bulbs are defective.

Answer:

About $1.75 per tennis balls

Step-by-step explanation:

A tin of 4 tennis balls costs $6.99. We are asked to find the price of one tennis ball.

We need to find the unit price, or price per ball.

Divide the cost by the number of tennis balls.

cost / tennis balls

cost = $6.99

tennis balls = 4 tennis balls

$6.99 / 4 tennis balls

Divide 6.99 by 4.

$1.7475 / 1 tennis ball

Round to the nearest cent or hundredth. The 7 in the thousandth place tells us to round the 4 to a 5 in the hundredth place.

$1.75 / 1 tennis ball

It would cost approximately $1.75 for one tennis ball.

Answer:

i. Has a liver problems?

= 0.08

ii. Is a heavy drinker ?

= 0.066

iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem?

= 0.303

iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker?

= 0.25

v. If a person is found to be a non –drinker, what is the probability that this person has liver problems?

= 0.104

Step-by-step explanation:

We have 2 Events in this question

Event A: People with liver problems

Event B : People without liver problems

Event A: People with liver problems

Let us represent people with liver problems as = (L)

a)8% have liver problems. = P(L)

Under liver problems we have:

b) 25% are heavy drinkers = P( L & H)

c) 35% are social drinkers = P( L & S)

d) 40% are non-drinkers. = P( L & N)

Event B( no liver problem)

Let us represent no liver problem as NL

We are not given in the question but Probability of having no liver problem = 100 - Probability of having liver problem

= 100 - 8% = 92 %

P(NL ) = 92%

From the question, For people without liver problems, we have:

a) 5% are heavy drinkers = P(NL & H)

b) 65% are social drinkers = P( NL & S)

c) 30% do not drink at all = P( NL & N)

An adult is chosen at random, what is the probability that this person

i. Has a liver problems?

P(L) = 8% or 0.08

ii. Is a heavy drinker ?

From the question, we have:

Probability of people that have liver problems and are heavy drinkers P(L & H) = 25% = 0.25

Probability of people that have do not have liver problems and are heavy drinkers P(NL & H) = 5% = 0.05

Probability ( Heavy drinker) =

P(L) × P(L & H) + P(NL) × P(NL & H)

= 0.25 × 0.08 + 0.05 × 0.92

= 0.066

iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem?

Probability (Heavy drinker and has liver problem) = [P(L) × P(L & H)] ÷ [P(L) × P(L & H)] + [P(NL) × P(NL & H) ]

= [0.25 × 0.08] ÷ [0.25 × 0.08] + [0.05 × 0.92]

= 0.303030303

Approximately = 0.303

iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker?

P(L & H) = 25% = 0.25

v. If a person is found to be a non –drinker, what is the probability that this person has liver problems.?

People with liver problems are non-drinkers. = P( L & N) = 40% = 0.4

People without liver problems and do not drink at all = P( NL & N) = 30% = 0.3

Probability (non drinker and has liver problem) = [P( L & N) × P(L & H)] ÷ [P( L & N) × P(L & H)] + [ P( NL & N) × P(NL & H) ]

= [0.4× 0.08] ÷ [0.4 × 0.08] + [0.3 × 0.92]

= 0.1038961039

Approximately ≈ 0.104

Answer:

204

Step-by-step explanation:

To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.

For height of the prongs, take 4 from 6.

6 - 4 = 2

Divide by 2 as there are 2 prongs.

2 / 2 = 1

Remember L * W * H

6 * 3 * 1 = 18

Remember that there are two prongs!

3 + 4 = 7

6 * 7 * 4 = 168

168 + 2(18) = 204

Answer:

a. Quadratic--[tex]y=x^{2}[/tex]

b. Absolute Value--[tex]y=|x|[/tex]

c. Linear--[tex]y=x[/tex]

d. Reciprocal Squared--[tex]y=\frac{1}{x^{2} }[/tex]

e. Cubic--[tex]y=x^{3}[/tex]

f. Square Root--[tex]y=\sqrt{x}[/tex]

g. Reciprocal--[tex]y=\frac{1}{x}[/tex]

h. Cube root--[tex]y=\sqrt[3]{x}[/tex]

Answer:

Step-by-step explanation:

y=[tex]x^{2}[/tex] is quadratic

y=x  is an absolute value

y= |x| os linear

y= [tex]\frac{1}{x}[/tex] is reciprocal

y= [tex]x^{3}[/tex] is cubic

y= [tex]\sqrt{x}[/tex] is square root

y= [tex]\frac{1}{x^{2} }[/tex] is reciprocal squared

y= [tex]\sqrt[3]{x}[/tex] is cube root

Answer: There will 486 bacteria in 31 hours.

Step-by-step explanation:

The population decay in bacteria is exponential.

Exponential function : [tex]y=Ab^x[/tex], where A = initial population, b multiplication decay factor, t= time:

As per given:

Initial population: [tex]A=120,000[/tex]

After 36 hours, population = [tex]120000(b^{36})=200[/tex]

Divide both sides by 120,000 we get

[tex]b^{36}= 0.00167[/tex]

Taking natural log on both sides , we get

[tex]36\ln b=\ln 0.00167\\\\\Rightarrow\ b=e^{\left(\frac{\ln0.00167}{36}\right)}=0.83724629\approx0.8372[/tex]

At x= 31,

[tex]y=120000(0.8372)^{31}=120000\times0.00405234\approx486[/tex]

Hence, there will 486 bacteria in 31 hours.

Answer:

x = 3, y = -2

Step-by-step explanation:

Since y=y

then, -3x +7 = 2x-8

7+8 = 3x+2x

15 = 5x

x=3

substitute

y = 2(3) - 8

y = -2

Hope that helped!!! k

Answer:

y = -2

x = 3

Step-by-step explanation:

Solve using elimination

1. Rearrange the equations to make it easier to solve

y = -3x + 7 → 3x + y = 7

y = 2x - 8 → 2x - y = 8

2. Multiply the equations to have a matching coefficient

2(3x + y = 7) = 6x + 2y = 14

3(2x - y = 8) = 6x - 3y = 24

3. Subtract

 6x + 2y = 14

- 6x - 3y = 24

  0 + 5y = -10

4. Solve for y

5y = -10

y = -2

5. Substitute y in any equation to solve for x

-2 = -3x + 7

-3x = -9

x = 3

Answer:

The answer is option B

Step-by-step explanation:

To find the coefficient of the third term in

[tex](x + 5)^{7} [/tex]

Rewrite the expansion in the form

[tex](a + x)^{n} [/tex]

where n is the index

So we have

[tex] ({5 + x})^{7} [/tex]

After that we use the formula

[tex]nCr( {a}^{n - r} ) {x}^{r} [/tex]

where r is the term we are looking for

For the third term we are looking for the term containing x²

that's

r + 1 = 3

r = 2

So to find the coefficient of the third term

We have

[tex]7C2[/tex]

Hope this helps you

first of all, the notation is wrong it should be [tex] {}^nC_r \text{ and more usual notation is } {n \choose k} [/tex]

second, the

[tex](r+1)^{\text{th}} \text{ term } T_{r+1} \text{ in the expansion of } (x+a)^n \text{ is } {n \choose r}x^{(n-r)}a^r[/tex]

here [tex] a=5 \text{ and } n=7 \text{ and for } 3^{\text{rd}} \text{ term } T_3, \quad r+1=3 \implies r=2 [/tex]

so the coefficient of third term is, [tex]{7 \choose 2}={7\choose 5}[/tex]

an important property of binomial coefficient you should know:

[tex] {n \choose k}={n \choose {n-k}}[/tex]

and if you interchange [tex] x \text{ and } a[/tex]

only the "order" will get reversed. i.e. the series will start from back.

another thing, the [tex] k^{\text{th}} \text{ term from beginning, is the } (n-k+2)^{\text{th}} \text{ term from behind}[/tex]

Answer: The missing number is 5.

Step-by-step explanation:

In the table we can only have numbers between 1 and 9,

The pattern that i see is:

We have sets of 3 numbers.

"the bottom number is equal to the difference between the two first numers, if the difference is negative, change the sign, if the difference is zero, there goes a 9 (the next number to zero)"

Goin from right to left we have:

9 - 6 = 3

6 - 2 = 4

4 - 9 = - 5 (is negative, so we actually use -(-5) = 5)

4 - 4 = 0 (we can not use zero, so we use the next number, 9)

3 - 3 = 0 (same as above)

? - 1 = 4

? = 4 + 1 =  5

The missing number is 5.

Answer:

(D) 48​

Step-by-step explanation:

Let English book = x

Let french book = y

In 1995 x= 10

Y= 7

In 1996

Y = 2x

Total book read in the two years

0.6(Total) = y

0.4(total) = x

We don't know the exact amount of books read in 1996.

Total = 10 + 7 +x +2x

Total = 17+3x

0.6(total) = 7+2x

0.6(17+3x) = 7+2x

10.2 +1.8x= 7+2x

10.2-7= 2x-1.8x

3.2= 0.2x

3.2/0.2= x

16= x

So she read 16 English book

And 16*2 = 32 french book Making it a total of 16+32= 48 books in 1996

Answer:

[tex]\boxed{\frac{1}{2} }[/tex]

Step-by-step explanation:

Hey there!

Well given,

[tex]\frac{2}{5} * 1 \frac{3}{12}[/tex]

We need to make 1 3/12 improper,

1*12 = 12

12 + 3 = 15

[tex]\frac{2}{5} * \frac{15}{12}[/tex]

2*15 = 30

5*12 = 60

[tex]\frac{30}{60}[/tex]

Simplified

[tex]\frac{1}{2}[/tex]

Hope this helps :)

Answer:

Option A. 4√5

Step-by-step explanation:

To obtain the value of x, we must first obtain the value of y as shown in the attached photo.

The value of y can be obtained by using the pythagoras theory as illustrated below:

In this case y is the longest side i.e the Hypothenus.

y² = 4² + [4√3]²

y² = 4² + [4² × (√3)²]

y² = 4² + [4² × 3]

y² = 16 + [16 × 3]

y² = 16 + 48

y² = 64

Take the square root of both side

y = √64

y = 8

Finally, we shall determine the value of x by using the pythagoras theory as illustrated below.

Note: x is the longest side i.e the Hypothenus in this case.

x² = 4² + 8²

x² = 16 + 64

x² = 80

Take the square root of both side

x = √80

x = √(16 × 5)

x = √16 × √5

x = 4√5

Therefore, the value of x is 4√5.

Answer:

2.8

Step-by-step explanation:

11.1-8.3=2.8

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Answer:

The probability that he answered neither of the problems correctly ​is 0.0625.

Step-by-step explanation:

We are given that a student ran out of time on a multiple-choice exam and randomly guess the answers for two problems each problem have four answer choices ABCD and only one correct answer.

Let X = Number of problems correctly ​answered by a student.

The above situation can be represented through binomial distribution;

[tex]P(X=r)=\binom{n}{r}\times p^{r}\times (1-p)^{n-r};x=0,1,2,3,....[/tex]    

where, n = number of trials (samples) taken = 2 problems

           r = number of success = neither of the problems are correct

           p = probability of success which in our question is probability that

                 a student answer correctly, i.e; p = [tex]\frac{1}{4}[/tex] = 0.75.

So, X ~ Binom(n = 2, p = 0.75)

Now, the probability that he answered neither of the problems correctly ​is given by = P(X = 0)

             P(X = 0) = [tex]\binom{2}{0}\times 0.75^{0}\times (1-0.75)^{2-0}[/tex]

                            = [tex]1 \times 1\times 0.25^{2}[/tex]

                            = 0.0625

Answer:

C° = 71.6056

Step-by-step explanation:

Law of Cosines: c² = a² + b² - 2abcosC°

Step 1: Plug in known variables

29² = 30² + 15² - 2(30)(15)cosC°

Step 2: Evaluate

841 = 900 + 225 - 900cosC°

-59 = 225 - 900cosC°

-284 = -900cosC°

71/225 = cosC°

cos⁻¹(71/225) = C°

C° = 71.6056

And we have our answer!

Answer:

  79.0°

Step-by-step explanation:

The Law of Cosines is used for this purpose. It tells you ...

  a² = b² +c² -2bc·cos(A)

Solving for A gives ...

  cos(A) = (b² +c² -a²)/(2bc) = (15² +29²-30²)/(2(15)(29)) = 166/870

Using the inverse cosine function, we find the angle to be ...

  A = arccos(166/870) ≈ 79.00026°

  A ≈ 79.0°

Answer:

Total amount in dollars= $64614.00

Step-by-step explanation:

Initial starting salary is $40000.

Rate of increase is 3%

Number of years is 16 years

The salary is compounded yearly.

Amount A after 16 years is given as

A= p (1+r/n)^ (nt)

A=40000(1+0.03/16)^(16*16)

A= 40000(1.001875)^(256)

A=40000(1.61534824)

A= 64613.92959

Total amount in dollars= $64614.00

Answer: the answer is $806275

Step-by-step explanation:

A p e x