assume that x1, x2, x3, and x4 are independent random variables. read the following statements. (a) the joint pmf or pdf for x1, x2, x3, and x4 is f1(x1)f2(x2)f3(x3)f4(x4). (b) if x1, x2, x3, and x4 are identically distributed then they are considered to be a random sample of size n. (c) if x1, x2, x3, and x4 have the same mean and variance then they are called a statistic. (d) identically distributed x1, x2, x3, and x4 can be thought of as measurements on outcomes of 4 random experiments. now choose the correct answer. group of answer choices all statements (a), (b), (c), and (d) are correct. statements (a) and (d) only are correct. statements (a), (b), and (c) only are correct. statements (a) and (b) only are correct. none of these answers are correct. statements (a), (b), and (d) only are correct.

Answer: 6 days and 18 hours

Step-by-step explanation: 9/4=1.25 1.25x3=6.75 and so on

Answer:  -27≥x  OR  x>7

Step-by-step explanation:

[tex]\displaystyle\\a)\ -7\geq \frac{x}{3}+2 \\\\\-7-2\geq \frac{x}{3}+2-2\\\\ -9\geq \frac{x}{3} \\\\[/tex]

Multiply both parts of the equation by 3:

[tex]\displaystyle\\-9(3)\geq \frac{x}{3}(3)\\\\\boxed {-27\geq x}[/tex]

[tex]\displaystyle\\b)\ \frac{3x+1}{2} > 11[/tex]

Multiply both parts of the equation by 2:

[tex]\displaystyle\\\frac{3x+1}{2}(2) > 11(2)\\\\3x+1 > 22\\\\3x+1-1 > 22-1\\\\3x > 21[/tex]

Divide both parts of the equation by 3:

[tex]\boxed{x > 7}[/tex]

Initial velocity of the function = 109 ft/sec.

The given quadratic function is-

h(t) = -16t² + 109t

maximum height;

dh/dt = 0 and d²h/dt² < 0.

Then,

dh/dt = -32t + 109

dh/dt = 0

-32t + 109 = 0

t = 3.4 seconds.

Time when maximum height is reached by the ball is 3.4 second.

Maximum height;

h(t) = -16(3.4)² + 109(3.4)

h(t) = 185.6 ft

Thus, the maximum height obtained by the ball is 185.6 ft.

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The complete question is-

A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. Use the quadratic function

h(t) = -16t2 + 109t to find how long it will take for the ball to reach its maximum height, and then find the maximum height.

Answer: The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.

Given :

Expression - 8 + (n - 4)

To simplify the given expression following steps can be used:

Step 1 - Rewrite the given expression.

= (n - 4) + 8

Step 2 - Now, remove the parenthesis in the given expression.

= n - 4 + 8

Step 3 - Now, write 8 as the addition of 4 and 4.

= n - 4 + 4 + 4

Step 4 - Subtract 4 by 4.

= n + 4

Therefore ,the heart beat the time per beat in units of seconds is 0.5s/beat.

A well-formed equation in algebra unites two variables with the equals sign to indicate the equality of the two terms. An equation, for instance, is any well-formed formula that consists of two expressions joined by the equals sign in English. An équation, on the other hand, is described as consisting of one or more variables in French.

Here,

Given: your heart rate is 120 beats per minute during strenuous exercise

Thus to calculate time per beat in units of seconds

We,

time  per second per beat =  total second in a minute /heart rate

time  per second per beat =60/120

time  per second per beat =1/2

time  per second per beat = 0.5 s/beat

Therefore ,the heart beat the time per beat in units of seconds is 0.5s/beat.

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The 20% off of Jeremy's purchases is $5.50.

What is discount?

Discount is a noun that designates a sum or a portion taken off of a product's suggested retail price. Check to see if you really need all of that stuff before waiting until after the holiday to buy it. A good or service's price being reduced is referred to by the noun discount.

Given:

Jeremy has a 20%-off coupon for his purchases at a store.

His total purchases are $27.50 without the coupon.

We have to find the 20% off (discount) of Jeremy's purchases.

The 20% off on $27.50 is.

$27.50 x 20% = $27.50 x 0.20 = $5.50

Hence, the 20% off of Jeremy's purchases is $5.50.

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The new coordinates are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

A 180 degrees rotation denoted by R(180, 0) is a rotation that has the same effect as the 180 degrees counterclockwise of a figure.

And it has the algebraic rule of its rotation to be changed from (x, y) to (-x, -y) i.e  (x, y) ⇒ (-x, -y)

The coordinates of the parallelogram are given as

M(1, 7), N(8, 5), O(4, 2), and P(-3, 4)

The rotation is given as 180° rotation

As mentioned above,

We have (x, y) ⇒ (-x, -y)

Substitute M(1, 7), N(8, 5), O(4, 2), and P(-3, 4) in (x, y) ⇒ (-x, -y)

So, we have

M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

Hence, the coordinates of the image are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

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The solution to the graph of the linear inequality is the point of intersection which is (-5, 3)

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system

In this problem, to find the solution to the system of linear inequality, we have to find the point of intersection. This gives the exact solution to the graph.

Looking at this graph, the point of intersection is (-5, 3)

The solution to the graph is (-5, 3)

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Turn a percent into a decimal by moving the decimal point two to the left.

10 x 6% = 10 x .06

10 x .06 = .60

Sales tax: 60 cents

Total price: $10.60

Answer:

  21.35 inches

Step-by-step explanation:

You want to know the circumference of a hat that has a diameter of 6.8 inches.

The circumference is given by ...

  C = πd

  C = 3.14 × 6.8 in = 21.352 in

  C ≈ 21.35 in

The distance around the hat is about 21.35 inches.

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The average acceleration is - 1.24 m/s². The result is calculated by using calculator. See the picture in the attachment!

Average acceleration is the rate of change in velocity per unit time. The formula can be expressed as

[tex]\overline{a} = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex]

Where

Calculate this average acceleration using calculator!

[tex]\overline{a} = \frac{-3.7 \: m/s \: - 13.9 \: m/s}{21.4 \: s- 7.2 \: s}[/tex]

See the picture in the attachment!

The average acceleration after rounding is

[tex]\overline{a} = -1.23943661972 \: m/s \: /s[/tex]

[tex]\overline{a} = -1.24 \: m/s^{2}[/tex]

Hence, the average acceleration from the data is - 1.24 m/s².

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The value of y in the triangle is 20°

Consider the labeling on the image I attached

Since vertically opposite angles are equal. Thus:

x = 50°

Since the sum of angles on a straight line is 180°. Thus:

t + 70° = 180°

t = 180°-70°

t = 110°

Since the sum of angles in a triangle is 180°. Thus:

x + t + y =  180°

50 + 110 + y =  180°

160 + y = 180

y = 180 - 160

y = 20°

Therefore, the value of y is 20°

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Answer:

17 feet

Step-by-step explanation:

We can use the Pythagorean therom, since the triangle has a 90 degree angle:

         8^2 + 15^2 = x^2

         64  +  225 = x^2

          x^2 = 289

           x = 17 feet

See the attached worksheet.

Answer: answer below

Step-by-step explanation:

4 (a). 900 grams of flour
work 150x6=900 grams

4 (b). 3 large eggs
work 450÷150=3
5 (a). 2.99

work 11.96÷4=2.99

5 (b). 26.91

work 2.99x9=26.91

6 (a). Can't help
6 (b). 6:12
6 (c). 16:8
6 (d). 10 paws

Can't help on problem 7

A dictator

Step-by-step explanation:

The percentage discount for the good bought by Nora is 17%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

In this situation, Nora has a loyalty card good for a discount at her local pharmacy. The item she wants to buy is priced at $28, before discount and tax. After the discount, and before tax, the price is $23.24.

The percentage discount will be:

= Discount / Original value × 100

= (28 - 23.24) / 28 × 100

= 4.76 / 28 × 100

= 17%

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If Sebastian has x nickels and y pennies. He has at least 20 coins worth at most $0.65 combined then he has 27 nickels.

Two or more expressions with an Equal sign is called as Equation.

Given,

x represents nickels and y represents dimes.

x+y=20...(1)

0.05x+0.10y=0.65...(2)

From equation 1,

y=20-x

0.05x+0.10y=0.65

0.05x+0.10(20-x)=0.65

0.05x+2-0.10x=0.65

2-0.05x=0.65

Subtract 2 from both sides

-0.05x=0.65-2

-0.05x=-1.35

Divide both sides by -0.05

x=27

x+y=20

27+y=20

y=20-27

y=-7

Hence the number of nickels are 27 and dimes are minus seven.

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Answer:

y = x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 1 , then

y = x + c ← is the partial equation

to find c substitute (5, 3 ), that is x = 5, y = 3 into the partial equation

3 = 5 + c ⇒ c = 3 - 5 = - 2

y = x - 2 ← equation of line

a) The formula for the area of the triangle is given as follows:

Area = 0.5 x base x height.

b. The length of the base is given as follows: 6.3 units.

c. The length of the height is given as follows: 5 units.

d. The area of the triangle is given as follows: 15.75 units squared.

The area of a triangle is calculated as half the multiplication of the triangle's base by the triangle's height, as follows:

Area = 0.5 x base x height.

The vertices for the right triangle in this problem are given as follows:

(-4, -1), (2,1), (2,6).

Hence the base of the triangle is of:

[tex]B = \sqrt{(2 - (-4))^2 + (1 - (-1))^2} = 6.3[/tex]

The height is given as follows:

6 - 1 = 5.

Which means that the area of the triangle is of:

Area = 0.5 x 5 x 6.3 = 15.75.

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The given statement that 'the batter's distance from the first base bag is a function of time.' is false.

If we need to call any quantity a function of any other quantity, we need to know what it means first. For this, we take the example of velocity. If we say that velocity is a function of time, what we mean is that the function is such that we input time and get velocity as the output. That quantity changes as the input increases or decreases.

We can deem distance as a function of time when it changes with respect to it. Here, it is evident that the distance between the batter and the first base is not going to change. Thus, it is not a function of time and the given statement is false.

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According to the question,

Given data in the question,

In July, the price of a gallon of gasoline rose=12%

In august, it fell 15% of its final July price,

Ending the month at 1.19 rupees

Let us consider,

x is the original price at the beginning of July,

then the price of gasoline rose is 112%

=100+2

=112%

=112/100

=1.12

In august it fells 15%=100-15%

=.85%

With the help of given data

the original price is---- x

(1.12) × (.85) x = 2.29

find the value of x

x = 2.29/0.952

x=2.41

x=2.41 was its price at the beginning of July.

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Answer:

9z^2 -7

Step-by-step explanation:

(z9z−5)−2.

(9z^2−5)−2.

9z^2-5 -2

9z^2-7

Write the problem as a mathematical expression.

Multiply

z9 by z  by adding the exponents.

Subtract

2 from  −5  .

ANSWER:

z^10 − 7

On solving the provided question, we have the followings roots of the equations as -  x3 - 23x2 + 142x - 120 = (x - 1) (x - 10) (x - 12) and (x-1)(x-2)(x-3)=0

f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real integers and a 0. The cubic function is the cubic polynomial function. The higher cube function, or the fundamental cubic function, is defined as f(x) = x3.

x3 – 6x2 + 11x – 6 = 0.

(x-1)(x-2)(x-3)=0

x3 – 23x2 + 142x – 120.

first factorize

[tex]x3 - 23x2 + 142x - 120 = (x - 1) (x2 - 22x + 120)\\ But x2 - 22x + 120 = x2 - 12x - 10x + 120\\ = x (x - 12) -10(x - 12)\\ = (x - 12) (x - 10)\\ Therefore,\\ x3 - 23x2 + 142x - 120 = (x - 1) (x - 10) (x - 12)[/tex]

Equate each factor to zero to get;

x = 1

x = 10

x = 12

The roots of the equation are x = 1, 10 and 12.

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The happening in the graph is that the speed of the roller skater increases and decreases with time

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following axes

x-axis = Time

y-axis = Speed

The x-axis is continually increasing while the y-axis decreases and increases (as in a sine function)

This means that the speed increases and decreases with time

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We can factor this polynomial with 4 terms without grouping.

Factor is a thing that influence decision or the situation.

How to factor polynomials with 4 term without groupingLet P(x) be a polynomial with four terms.

To factor P(x) without grouping, substitute

x = -1, 1, -2, 2, -3, 3.......

P(-1) = 0 ----> (x + 1) is a factor of P(x)

P(1) = 0 ----> (x - 1) is a factor of P(x)

P(-2) = 0 ----> (x + 2) is a factor of P(x)

P(2) = 0 ----> (x - 2) is a factor of P(x)

If P(-1) ≠ 0, then (x + 1) is not a factor of P(x).

Then, try x = 1, x = -2, x = 2 and so on.

Once one of the linear factors of P(x) is found, the other factors can bound easily (the rest of the process has been explained in the following examples).

Factor the following polynomials without grouping :

d as (x2 + ax + b).

Then,

(x + 1)((x2 + ax + b) = x3 - 2x2 - x + 2

Comparing the coefficients of x and constants,

b + a = -1 ----(1)

b = 2

Substitute b = 2 in (1).

2 + a = -1

a = -3

x2 + ax + b = x2 - 3x + 2

Factors of (x2 - 3x + 2) are (x - 1) and (x - 2).

Therefore,

x3 - 2x2 - x + 2 = (x + 1)(x - 1)(x - 2)

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The locations on the function's graph that are most near the specified point f(x) = x2, (0,9) are approximately 3 units to the right and left, respectively, or (sqr8.5, 8.5).

The initial estimate would be rough to the right and left by around 3 units, or (sqr8.5, 8.5), rounded to the nearest decimal place.

Visually, it is most likely just below y=9 and just below x=3. Additionally, roughly (-3, 9) slightly lower than 3 and 9

Connect the parabola's nearest point to the point at (0,9). Where the two intersect, its slope is the negative inverse of the parabola's slope. The derivative's slope is 2x for the equation f(x) = x2. -1/2x is its inverse negative. The line from (0,9) to the parabola's nearest point has a slope that is perpendicular to the tangent to the parabola at that location.

Get the equation of the line joining (0,9) and the nearest point (x,y) on the parabola using the point-slope formula: 8.5 or y=-1/2 + 9 = (-1/2x)(x)

The closest point's y coordinate is that. The square root of 8.5, including both positive and negative square roots, is the closest point's x coordinate (-sqr8.5, 8.5)

Sqr8.5 =[tex]\sqrt{8.5}[/tex], or approximately 2.91 or -2.91

The process entails finding the equation for the line connecting (0,9) with the parabola's nearest point and then setting the two equations equal. Set the line equation to y=(-1/2x), the parabola equation. The parabola equation is y=[tex]x^{2}[/tex] and the line equation is x + 9.

Equalize them, then find x using the square of the result. The closest point is at x,y. There are two places that are equally far from (0,9), both of which are as close as they can be to 3 at (3,9). (0,9). At the parabola point, that line is not perpendicular to the tangent line (3,9). The line must be perpendicular to the tangent line, which is the slope of the parabola, in order to be closest.

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You can select numerous impressions with the Tableau Lasso Selection tool by tracing a freehand shape around them.

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Answer:

The first expression to represent the new price of an item after the markdown would be:

new price = d * (1 - 0.70)

This expression uses the original price (d) and multiplies it by (1 - 0.70), which is equal to 0.30. This results in the new price being equal to 30% of the original price.

Another way to write this expression would be:

new price = d - (d * 0.70)

This expression also uses the original price (d) and subtracts from it the product of the original price and 0.70. This also results in the new price being equal to 30% of the original price.

Step-by-step explanation:

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years.

a) The hypotheses that can be used to challenge the validity of the claim made by the shareholders' group.

H₀ : u ≤ 9

Hₐ : u > 9

So, the correct option is option (A).

b) T- statistic value is -2.571 for a sample of 90 companies.

c) The critical value for t i.e P-value is 0.0059

d) P-value < α = 0.01, implies reject the null hypothesis. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid. So, the correct option is option(D).

We have given that,

x-bar= 7.27 , σ = 6.38, n = 90

a) Test that the mean tenure for a chief executive officer (CEO) was atleast nine years .

Null and alternative hypothesis is

H₀ : u <= 9

Hₐ : u > 9

b) test statistic:

t =( x-bar - μ ) /σ/√n

=> t = (7.27 - 9 )/6.38/90

=> t = - 1.73/0.67251

=> t = -2.571

c) P-value :

P-value = P( tₙ₋₁ < t) = P(t₉₀₋₁ < t )

=> P-value = P( t₈₉< - 2.571)

=>P-value = P( t₈₉ >2.571)

=> P-value = 1 - P( t₈₉< 2.571)

P-value = 1 - 0.9941 = 0.0059

d) Significance level, = 0.01

we see that p-value= 0.0059 < 0.01

Decision : Reject the null hypothesis H₀

We have no evidence to support the claim.

Hence, we calculate all the required result.

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Complete Question :

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.27 yearsfor CEOs with a standard deviation of

s = 6.38 years.

(a)Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group. multiple choice:

i)H0: μ ≤ 9

Ha: μ > 9

ii)H0: μ ≥ 9

Ha: μ < 9

iii) H0: μ > 9

Ha: μ ≤ 9

iv)H0: μ < 9

Ha: μ ≥ 9

v) H0: μ = 9

Ha: μ ≠ 9

(b)Assume 90 companies were included in the sample. What is the test statistic? (Round your answer to three decimal places.)

c)What is the p-value for your hypothesis test? (Round your answer to four decimal places.)

p-value =

(d) At = 0.01,what is your conclusion? MULTIPLE CHOICE:

Answer:

  20%

Step-by-step explanation:

You want to know the percentage change from 1120 to a final number that is 100 less, 130 more, and 254 less.

The percentage change is given by ...

  percent change = change/(original amount) × 100%

Here, the total amount of change is the sum of the given changes:

  -100 +130 -254 = -224

Then the percentage change is ...

  -224/1120 × 100% = -20%

The percent decrease is 20%.

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