The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with μ = 532.2 and standard deviation σ = 26.4. (a) What is the probability that a single student randomly chosen from all those taking the test scores 539 or higher? For parts (b) through (d), consider a simple random sample (SRS) of 25 students who took the test. (b) What are the mean and standard deviation of the sample mean score x, of 25 students? - The mean of the sampling distribution for x is: - The standard deviation of the sampling distribution for x is: (c) What z-score corresponds to the mean score x of 539?
(d) What is the probability that the mean score i of these students is 539 or higher?

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

Learn more about the probability here:

https://brainly.com/question/15124899

#SPJ4

Answer: no

Step-by-step explanation: if we'd substitute the numbers, it'd look like this 10≤-10+7  which isn't true  as "≤" this symbol means more than or equals to but -10 plus 7 is equal to 3 so it doesn't fit the inequality

Answer:

2^4•2^4>2^7

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:160

Step-by-step explanation:

3:1 the difference is 2 right now

80/2=40

multiply both sides by 40 to get 120:40

120-40=80

120+40=160

Answer:

the mystery is the number 5

Answer:

here you go I hope this is right

Answer:

3 629,84

Step-by-step explanation:

4Xr^2

4(3.14)×17^2

Answer:

3629.84 yd.

Step-by-step explanation:

The radius is 17.

Using the formula, 4πr², we can plug-in the unknown value(s).

'π' means pi; 'r' means radius.

4π17² = 3629.84.

Therefore, the surface area of this sphere is 3629.84 yd.

Answer:

72

Step-by-step explanation:

If two functions are f(x) and k(x), then, The correct option is C.

A mapping demonstrates the pairings of the components. It displays the input and output values of a function, much like a flowchart would.  Every element of the domain is associated with exactly one element of the range in a function, which is a unique kind of relation. A mapping demonstrates the pairings of the components.

It displays the input and output values of a function, much like a flowchart would. The two parallel columns of a mapping diagram.

The calculation is as follows:

If two functions are f(x) and k(x),

(f o g)(x) = f[g(x)]

Now according to the picture

We have to find the value of (h o k)(1).

(h o k)(x) = h[k(x)]

             = h[k(1)]

             = h(3) [Since, k(1) = 3]

             = 28 [Since, h(3) = 28]

Learn more about functions visit: brainly.com/question/28989903

#SPJ4

Correct Question:

Select the correct answer. Consider functions h and k. What is the value of ?

In order to do well on BYU Calculus BC Explorations, you should have a solid understanding of the basic principles of calculus.

This includes understanding derivatives and integrals, as well as the fundamental theorem of calculus. Additionally, it is important to have a strong background in basic algebra and trigonometry, as these skills will be necessary for working with functions and equations. When solving problems, it is important to read the problem carefully and identify what type of calculus concept is being asked for. Once the concept is identified, you can use formulas and calculations to solve the problem. By working through problems in a systematic and logical way, you can make sure that you arrive at the correct answer.

Learn more about fundamental theorem of calculus here:

https://brainly.com/question/2293034

#SPJ4

Complete question:What is the best way to do well on BYU Calculus BC Explorations?

Answer:

$0.40

less

Step-by-step explanation:

The equation for Skylar's company is y = 3x + 1.5

and if Isabella's company charges a $4.50 pickup fee and $2.60 per mile, that makes the equation y = 2.6x + 4.5

meaning to find how much more or less, Isabella's company costs per mile than Skylar's we have to compare the terms with x (miles)

Skylar: 3x

Isabella: 2.6x

3 - 2.6 = 0.4

Therefore, your answer is $0.40 and less since 2.6 is a smaller number than 3.

Hope this helps!

Answer:

23

Step-by-step explanation:

BC is parallel to AtoF

BC = (1/2)AtoF

BC = (1/2)46

BC = 23

The length of side BC will be 23. Option C is corect.

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

Main AnswerIn the study by Hoynes (2012), the population that is of interest to the researchers are families who receive Supplemental Nutrition Assistance Program (SNAP) or more commonly known as food stamps. The study examines the impact of the policy-driven change in economic resources available in utero and during childhood on the economic health of individuals in adulthood.

The sample that the study examines are 60,782 families over the time period of 1968 to 2009, which is subsequent to the introduction of the Food Stamp Program in 1961. The data links family background in early childhood to adult health and economic outcomes.The characteristics of the population that are of interest to the researchers are the impact of a positive and policy-driven change in economic resources available in utero and during childhood on the economic health of individuals in adulthood. Specifically, the researchers looked at the long-term effect of access to food stamps in childhood on the incidence of metabolic syndrome (obesity, high blood pressure, and diabetes) and an increase in economic self-sufficiency for women.

Based on the study, the researchers concluded that access to food stamps in childhood leads to a significant reduction in the incidence of metabolic syndrome and, for women, an increase in economic self-sufficiency. Hence, the results suggest substantial internal and external benefits of SNAP.

To know more about metabolic syndrome visit:

brainly.com/question/26801801

#SPJ11

Answer:

1-2

Step-by-step explanation:

Answer:

Yes, because 9 is in the hundreths place and 3 is in the tenths

Step-by-step explanation:

Answer:

Step-by-step explanation:

no because 0.3 is the same as 3/10 and 0.9 is the same as 9/10 wich is greater

Answer:  16x^2 - 40x + 25

Step-by-step explanation:

The error that the student made was that he forgot to square.

The conversion rate of converting meter to feet (linear measurement) is given as:

1 meter = 3.28 feet.

The measures given is in area, therefore, we would need to square when doing our conversion. To convert 3.5 square meter to square feet, do the following:

3.5 m² × (3.28 ft/1 m)² (this is where the student made an error by omitting or forgetting to square)

= 3.5 × 10.8

= 37.8 square feet

Therefore, we can conclude that the error that the student made was that he forgot to square.

Learn more about Converting From Square Meter to Square Feet on:

https://brainly.com/question/17064816

#SPJ1

The volume of the Solid -

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

What is volume?

Volume is a measure of the amount of three-dimensional space occupied by an object or a region. It quantifies the extent or size of a solid object or a container. In simpler terms, volume is a measure of how much space an object takes up.

What is integral?

In mathematics, an integral is a fundamental concept in calculus that allows us to compute the total accumulation of a quantity over a given interval. It is used to find the area under a curve, the length of a curve, the volume of a solid, and many other applications.

To find the volume of the solid enclosed by the paraboloid z = 3x^2(y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 2, we need to set up a triple integral over the given region.

The limits of integration for x, y, and z are as follows:

x: -2 to 2

y: 0 to 2

z: 1 to 3x^2(y - 2)^2

The volume V can be calculated as follows:

V = ∫∫∫R dz dy dx

where R represents the region defined by the given planes.

V = ∫∫∫R 3x^2(y - 2)^2 dz dy dx

To evaluate this triple integral, we integrate with respect to z first, then y, and finally x, using the given limits of integration:

V = ∫[-2,2] ∫[0,2] ∫[1,3x^2(y-2)^2] 3x^2(y - 2)^2 dz dy dx

Performing the integration:

V = ∫[-2,2] ∫[0,2] [3x^2(y - 2)^2z]∣[1,3x^2(y-2)^2] dy dx

V = ∫[-2,2] ∫[0,2] 3x^2(y - 2)^2[3x^2(y-2)^2 - 1] dy dx

V = ∫[-2,2] [x^2(y - 2)^2(3x^2(y-2)^2 - 1)]∣[0,2] dx

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

Evaluate this integral using appropriate techniques or numerical methods, such as numerical integration or computer software, to find the volume of the solid enclosed by the paraboloid and the given planes.

To know more about integration follow the given link:

https://brainly.com/question/30094386

#SPJ4

The distance traveled along the curve is simply equal to the elapsed time from t = 0 to t = π, which is π units.


To find the distance traveled along the curve, we need to integrate the magnitude of the velocity vector with respect to time over the given interval. Given that r'(t) = ⟨−sin(t), cos(t), 0⟩,

the magnitude of the velocity vector is

||r'(t)|| = √((-sin(t))^2 + (cos(t))^2 + 0^2) = √(sin^2(t) + cos^2(t)) = √(1) = 1.

Therefore, the distance traveled along the curve when t = π is equal to the integral of the magnitude of the velocity vector from t = 0 to t = π:

∫[0,π] 1 dt = t ∣[0,π] = π - 0 = π.

Hence, the distance traveled along the curve when t = π is π.

By integrating the magnitude of the velocity vector, we obtain the instantaneous speed of the particle at each point along the curve and sum them up over the given interval. In this case, the magnitude of the velocity vector is constantly equal to 1, indicating that the particle is moving at a constant speed of 1 unit per unit of time. Therefore, the distance traveled along the curve is simply equal to the elapsed time from t = 0 to t = π, which is π units.

Learn more about integration here:-brainly.com/question/30900582

#SPJ11

The solution to the system of inequalities y ≤ 2x + 2 and y < -2x - 3 can be represented by a graph. The inequality y ≤ 2x + 2 represents a line with a slope of 2 and y-intercept of 2. The inequality y < -2x - 3 represents a line with a slope of -2 and y-intercept of -3. ( The graph attached)

The inequality y ≤ 2x + 2 represents a line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 2. To graph this inequality, we can first plot the line by using the y-intercept, which is the point (0,2) on the graph. Then, we can use the slope to find additional points that fall on the line, such as (1,4) or (-1,0). Once we have plotted several points, we can connect them to form the line.

The inequality y < -2x - 3 represents a similar line, but with a different slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. To graph this inequality, we can use the same process as before by first plotting the y-intercept (0,-3), and then using the slope to find additional points that fall on the line.

The solution to the system of inequalities is the area that lies on one side of the first line and the opposite side of the second line, which is the area between the two lines. This area can be represented by shading the region below the first line and above the second line on the graph. It is important to note that the solution region is not including the lines themselves, because the inequalities are strict inequalities.

Learn more about system of inequalities here:

https://brainly.com/question/19526736

#SPJ4

Answer:

2 1/8

Step-by-step explanation:

The function that shows the relationship between Bill's total weekly sales and total weekly income is P(x) = $300 + 0.02x.

The slope is 0.02. The slope is the rate at which weekly income increases. $300 is the y-intercept.

The total amount of weekly sales that Bill needs to earn a weekly income of $600 is $15,000.

The function that can be used to determine the total weekly income is a linear function. A linear function is a function that increases at a constant rate.

The form of a linear function is: f(x) = a + bx

Where:

a = intercept

b = slope

The linear function for the total weekly income is:

P(x) = salary + (commission x sales)

P(x) = $300 + (0.02 x x)

P(x) = $300 + 0.02x

Number of total sales that would make Bill earn a weekly income of $600 is:

$600 = $300 + 0.02x

$600 - $300 = 0.02x

$300 = 0.02x

x = $300 / 0.02

x = 15,000

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

Answer:

-14 (-7 x 2) -21 (-7 x 3) -28 (-7 x 4)

Step-by-step explanation:

Based on the information given about the exponent, the value of A is 24 and the value of n is 8.

In order to solve this problem, we can use the following steps:

Identify the exponents of x and y in the term 13440x6y4.

Write the term in the form (Ax + y)^n, where A and n are unknown.

Set the exponents of x and y in the term equal to the exponents of x and y in the expression (Ax + y)^n.

Solve the resulting equation for A and n.

Following these steps, we get the following:

The exponent of x in the term 13440x6y4 is 6.

The exponent of y in the term 13440x6y4 is 4.

The term 13440x6y4 can be written as (24x + y)^8.

Solving the equation (24x + y)^8 = 13440x6y4, we get A = 24 and n = 8.

Therefore, the value of A is 24 and the value of n is 8.

Learn more about exponents on

https://brainly.com/question/13669161

#SPJ1

Answer:

40 miles

Step-by-step explanation:

2.5 miles / .25 hours = 10 miles per hour

(10 miles per hour)(4 hours) = 40 miles

Answer:

-12 and 1

Step-by-step explanation:

If you multiply 12 by 1 you get 12, hence if you add -12 and 1 now you will get -11

The two numbers that multiply to be 12 and add to be -11, obtained using the quadratic formula are;

(-11 + √(73))/2, and 24/(-11 + √(73))

(-11 - √(73))/2 and 24/(-11 - √(73))

The quadratic formula is a formula that can be used to find the solution to a quadratic equation in the form; y = a·x² + b·x + c, where a ≠ 0, and a, b, and c are constant.

The quadratic formula can be presented as follows;

x = \(\frac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}\)

Let x represent one of the numbers,. and let y represent the other number, we get;

x × y = 12...(1)

x + y = -11...(2)

Solving for y in the first equation, we get;

y = 12/x

Substituting the value for y above in equation (2), we get;

x + 12/x  = -11

x² + 12 = -11·x

x² + 11·x + 12 = 0

Solving the above equation using the quadratic formula, we get;

x = (-11 ± √(11² - 4×1×12))/(2 × 1)

x = (-11 ± √(73))/2

When x = (-11 + √(73))/2, y = 12/((-11 + √(73))/2) = 24/(-11 + √(73))

When x = (-11 - √(73))/2, y = 24/(-11 - √(73))

The two combination of numbers that multiply to be 12 and add to be -11 are;

(-11 + √(73))/2 and 24/(-11 + √(73)), and (-11 - √(73))/2 and 24/(-11 - √(73))

Learn more on the quadratic formula here: https://brainly.com/question/17156227

#SPJ6