8. let y = (x 2 5)2 . find dy when x = 2 and dx = 0.3.

Answers

Answer 1

For the function y = ( x² + 5 )² and x = 2 and dx = 0.3 then the value of differential dy is equal to 21.6.

y = (x² + 5)²

Calculate the differential dy with respect to x  we get,

dy / dx = d /dx (x² + 5)²

⇒ dy / dx = 2 ( x² + 5 )²⁻¹ × ( 2x )

⇒ dy = 4x ( x² + 5 ) dx

Now substitute the value of  x = 2, and dx = 0.3 to get the value of differential dy we get,

dy = 4( 2 ) ( 2² + 5 ) ( 0.3 )

⇒ dy = 8 × 0.3 × ( 9 )

⇒ dy = 21.6

Therefore, the value of the differential function dy for the function          y = ( x² + 5 )²  is equal to 21.6.

The above question is incomplete, the complete question is :

Let y = (x² + 5)². find the differential dy when the value of x = 2 and dx = 0.3.

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Related Questions

a second-stage smog alert has been called in a certain area of los angeles county in which there are 70 industrial firms. an inspector will visit 10 randomly selected firms to check for violations of regulations. (a) if 28 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of at least one regulation?

Answers

The required pmf is P(X=x) = [tex]\frac{\binom{28}{x}\binom{70 - 28}{10 - x}}{\binom{70}{10}}[/tex]

A probability mass function (pmf) is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value. Let X be a discrete random variable on a sample space S . Then the probability mass function f(x) is defined as. f(x)=P[X=x]. f ( x ) = P [ X = x ] .

as given, if 28 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of at least one regulation.

so,

Let X denote the number of firms that violate at least one regulation from 10 randomly selected firms out of 70 firms of which 28 violate at least one regulation.

P(X=x)

= Hyper(x; n = 10, M = 28, N = 70)

= h(x; 10, 28, 70)

= [tex]\frac{\binom{28}{x}\binom{70 - 28}{10 - x}}{\binom{70}{10}}[/tex]

Thus, the required pmf is P(X=x) = [tex]\frac{\binom{28}{x}\binom{70 - 28}{10 - x}}{\binom{70}{10}}[/tex]

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The required pmf is P(X=x) = 28Cx * (70-28)C(10-x))/70C10

A probability mass function (pmf) is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value. Let X be a discrete random variable on a sample space S . Then the probability mass function f(x) is defined as. f(x)=P[X=x]. f ( x ) = P [ X = x ] .

as given, if 28 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of at least one regulation.

so,

Let X denote the number of firms that violate at least one regulation from 10 randomly selected firms out of 70 firms of which 28 violate at least one regulation.

P(X=x)

= Hyper(x; n = 10, M = 28, N = 70)

= h(x; 10, 28, 70)

= 28Cx * (70-28)C(10-x))/70C10

Thus, the required pmf is P(X=x) = 28Cx * (70-28)C(10-x))/70C10

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Describe the end behavior of the graph of the function
f(x)=−5(4) x−6
. For[infinity], type in the word infinity. For−[infinity], type in -infinity (a minus sign followed by the word infinity). Make sure that you type in the word infinity with a lower case
. As x→−[infinity],f(x)→
As x→[infinity],f(x)→

Answers

End behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. In other words, the end behavior of a function explains the graph's trend when we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

What is function?

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter anything for x, you will only get one output for y. Because x represents the input value, we may say that y is a function of x.

Here,

End behavior of a function f specifies how the function's graph behaves at the "ends" of the x-axis. In other words, when we look to the right end of the x-axis (as x approaches +) and to the left end of the x-axis (as x approaches ), the end behavior of a function explains the graph's trend.

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Suppose that the universal set s is defined as S= {1, 2, 10} and and c 17, 8, 9, 10 a. Find AUB b. Find (AUC) - B c. Find Au(B-C) d. Do A, B, and c form a partition of s?

Answers

AUC - B = 17 and AUB = 1, 2, 8, 9, 10, The partition of S formed by A, B, and C is not Au(B-C) = 1, 2, 8, 9, 10, or 17.

Finding the union of A and B requires us to identify every element that is either in A, B, or both. Here, A = 17 and B = 8, 9, and 10 respectively. So AUB = {1, 2, 8, 9, 10, 17}.

Finding (AUC) - B requires us to identify the components of the union of A and C minus the components of B. Here, A equals 17, B equals 8, 9, and 10, and C equals 17. Therefore, (AUC) - B = 17.

To determine Au(B-C), we must first identify the components of the union of A and the difference between B and C. Here, A equals 17, B equals 8, 9, and 10, and C equals 17. Therefore, Au(B-C)=1, 2, 8, 9, 10, and 17.

d. S cannot be partitioned by A, B, or C since S includes items that are not present in any of those three. As an illustration, elements 1 and 2 are present in S but not in A, B, or C. Therefore, S cannot be divided into A, B, and C.

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how many double letter mutations are possible in 23 dna string

Answers

There are 4 possible nitrogenous bases, so for each position in the DNA sequence there are 4 options to choose from. Therefore, in a single base position there are 4 possible mutations. In a double base position, there are 4 * 4 = 16 possible mutations. This means that for 11 double base positions, there are 11 * 16 = 176 possible double letter mutations.

DNA (Deoxyribonucleic Acid) is the genetic material that encodes the instructions for the development and function of all living organisms. DNA is made up of four nitrogenous bases: adenine (A), cytosine (C), guanine (G), and thymine (T).

The sequence of these nitrogenous bases is what determines the genetic information of an organism. Mutations are changes in the DNA sequence that can occur naturally or as a result of environmental factors.

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Devi had five time a many weet a Sally. Both of them bought an equal number of weet. In the end, Sally had 48 weet and Devi had twice a many weet a Sally. What i the difference in the number of weet between the two girl at firt?

Answers

The difference between the two girl at first is 120 - 24 = 96 weet.

Difference in Weet Number

I determined the answer by using algebra. I started by defining the original number of weet that Sally had as x. Then, I used the information given in the problem to set up two equations:

x + x = 48 (because both of them bought an equal number of weet and in the end, Sally had 48 weet)2x = 48 (because Devi had twice as many weet as Sally in the end)

Next, I solved for x by dividing both sides of the second equation by 2:

       x = 24

Now that I know that Sally originally had 24 weet, I can use that information to find the original number of weet that Devi had. According to the problem, Devi had five times as many weet as Sally, so:

Devi = 5 * 24 = 120

Finally, I subtracted Sally's original number of weet (24) from Devi's original number of weet (120) to find the difference between the two:

Difference = 120 - 24 = 96

So, the difference between the two girls at first was 96 weet.

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Select whether the relation is a function or not.
((-3, 1), (-1, 3), (1, -2), (3, 3))

A. not a function
B. function

Answers

A function is a mathematical relationship where each input has a unique output. In the given relation, the input value of 1 has two different output values of -2 and 3. This means that the relation is not a function as the same input value has more than one output value

A. Not a function

Josiah has a points card for a movie theater.

He receives 70 rewards points just for signing up.

He earns 11. 5 points for each visit to the movie theater.

He needs 139 points for a free movie ticket.


Write and solve an equation which can be used to determine vv, the number of visits Josiah must make to earn a free movie ticket

Answers

Answer:

6

Step-by-step explanation:

70 sign up

11.5 each visit  assuming w visits

so to get to 139

11.5w +70=139

11.5w =69

w= 6

What is the distance between (2, 5) and (-3, 5)?

Answers

The distance between (2, 5) and (-3, 5) is 5 units.

Answer:

5 units

Step-by-step explanation:

since the y- coordinates are equal, both 5, then this is a horizontal line.

the distance between the points is then the absolute difference of the x- coordinates, that is

distance = | - 3 - 2 | = | - 5 | = | 5 | = 5 units

or

distance = | 2 - (- 3) | = | 2 + 3 | = | 5 | = 5 units

Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all ten questions, find the indicated probabilities. (Round your answers to three decimal places.)
(a) What is the probability that he will answer all questions correctly?
(b) What is the probability that he will answer all questions incorrectly?
(c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table.
Then use the fact that P(r ≥ 1) = 1 − P(r = 0).
(d) What is the probability that Richard will answer at least half the questions correctly?

Answers

Richard has a 1/5 probability of accurately answering all of the questions.

What is probability?

Probability is simply the possibility that something will happen.

When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.

The study of events that fit into a probability distribution is known as statistics.

How likely something is to happen is determined by its probability.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

So, we know he probability formula which is:

P(E) = Favourable events/Total events

So, the correct answers are 10 and there are 10*5 total options.

Then, P(F) = 10 and P(T) = 10*5 = 50.

Now, insert values in the formula and calculate as follows:

P(E) = Favourable events/Total events

P(E) = 10/50

P(E) = 1/5

Therefore, Richard has a 1/5 probability of accurately answering all of the questions.

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Complete question:

Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended a class recently, he doesn't know any of the answers. Assuming that Richard guesses on all ten questions, find the indicated probabilities. (Round your answers to three decimal places.)

What is the probability that he will answer all questions correctly?

Raina deposited $5000 into an account with a 9. 4% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will

it take for the investment to grow to $8935?

Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answers

It will take 0.6431 years or approximately 7.7 quarters for the investment to grow to $8935.

Raina deposited $5000 into an account with a 9. 4% annual interest rate, compounded quarterly.

To calculate the time it takes for an investment to grow to a certain amount at a given interest rate, you can use the formula:

T = [tex]\frac{log(\frac{A}{P}) }{log(1+\frac{r}{n}) }[/tex]

where:

T is the time in years

A is the final amount ($8935)

P is the initial amount ($5000)

r is the annual interest rate (9.4%)

n is the number of times compounded per year (quarterly = 4 times)

Plugging in the values, we get:

T = (log(8935 / 5000)) / (log(1 + 0.094 / 4))

T = [tex](\frac{log(1.787)}{log(1.0225)} )[/tex]

T = 0.6431 years or approximately 7.7 quarters (rounded to 2 decimal places).

Therefore, it will take 0.6431 years or approximately 7.7 quarters.

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Find (f/g) (x). include any restrictions on the domain.
(image attached

Answers

[tex]\huge\begin{array}{ccc}A.&\left(\frac{f}{g}\right)(x)=\frac{\sqrt[3]{2x}}{2x+1},&x\neq-\frac{1}{2}\end{array}[/tex]

Funkction.

We have the functions:

[tex]f(x)=\sqrt[3]{2x}\\\\g(x)=2x+1[/tex]

Let's define the domain of the functions:

[tex]D_f:x\in\mathbb{R}\\\\D_g:x\in\mathbb{R}[/tex]

Make the function

[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{\sqrt[3]{2x}}{2x+1}[/tex]

Let's define the domain of the function:

[tex]D:2x+1\neq0\\\\2x+1-1\neq0-1\\\\2x\neq-1\\\\\dfrac{2x}{2}\neq\dfrac{-1}{2}\\\\x\neq-\dfrac{1}{2}[/tex]

Answer: A.

let f be a polynomial function with values f'(x) at selected values of x given in the table above. which of the following would be true for -2 < x <6?

Answers

[tex]f'(-2) = 4[/tex]This means that the rate of change of the function is 4 for all values of x within the given interval.

The derivative of a polynomial function tells us the rate of change of the polynomial function at any given point. Therefore, if we look at the table above, we can see that for x = -2, the derivative of the function (f') is equal to 4. So the statement that [tex]"f'(-2) = 4"[/tex] is true for -2 < x < 6.

The derivative of a polynomial function is a measure of the rate of change of the function at any given point. In the table provided, we can see that for x = -2, the derivative of the function (f') is equal to 4. As such, this statement is true for the interval -2 < x < 6 since f'(-2) = 4. This means that the rate of change of the function is 4 for all values of x within the given interval.

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complete the first step in determining the sum of 14 and 38.

Answers

When the two number of columns are added together, the result is 52. Therefore, 14 + 38 = 52.

14 + 38 =

The first step in determining the sum of 14 and 38 is to add the two numbers together.

14 + 38 = 52

The first step in determining the sum of 14 and 38 is to add the two numbers together. This is done by lining up the numbers according to their place values, and then adding the numbers in each column. In this case, the ones column is 4 and 8, which adds up to 12. The tens column is 1 and 3, which adds up to 4. When the two columns are added together, the result is 52. Therefore, 14 + 38 = 52.

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4 in
6 in.
4 in

Find the aria of the shaded region

Answers

Check the picture below.

first off let's get the area of the "circular ring", and then let's add to that the area of the innermost circle with a radius of 6.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=14\\ r=10 \end{cases}\implies A=(14^2-10^2)\implies A=96\pi \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6 \end{cases}\implies A=\pi (6)^2\implies A=36\pi \\\\[-0.35em] ~\dotfill\\\\ 96\pi ~~ + ~~36\pi \implies 132\pi ~~ \approx ~~ \text{\LARGE 414.69}~in^2[/tex]

Check whether
(

3
,

2
)
is a solution to the system, then choose all true statements from the list.

Equation 1:

7
x

4
y
=
29

Equation 2:
3
x
=

7
+
y

Group of answer choices

The point satisfies both equation 1 and 2

The point satisfies only equation 2

The point is not a solution to the system

The point satisfies only equation 1

The point does not satisfy either equation

The point is a solution to the system

Answers

The point satisfies both equation 1 and 2" and "The point is a solution to the system.

What do you mean by equation?

An equation is a mathematical statement that shows the equality of two expressions. Equations can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

For example, the equation 2x + 3 = 7 is an equation that states that the expression on the left side (2x + 3) is equal to the expression on the right side (7). The goal is to find the value of the variable x that satisfies the equation. In this case, x = 2 is a solution to the equation.

To check whether a point is a solution to a system of equations, we can substitute the values of the variables into the equations and see if the resulting expressions are equal.

So, for the point (-3, -2), we can substitute these values into the equations:

Equation 1: -7x - 4y = 29

Substituting x = -3 , y = -2:

-7(-3) - 4(-2) = 29

21 + 8 = 29

29 = 29

Equation 2: 3x = -7 + y

Substituting x = -3 , y = -2:

3(-3) = -7 + (-2)

-9 = -9

Since both equations are true, the point (-3, -2) satisfies both equation 1 and 2, and is a solution to the system.

Therefore, the true statement from the list is "The point satisfies both equation 1 and 2" and "The point is a solution to the system".

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How long will it take to fill a cylinder-shaped vat (with a radius of 32.5 ft and depth of 33.9 ft) with a certain liquid (d = 1.77 g/mL) if it is spilling out of the hose at 12,757.9 g/s? a. 1.23×102hr
b. 1.53×10−7hr
c. 1.08×108 hr
d. 1.98 hr
e.6.65×109hr

Answers

Answer:A 1.23 x 102hr

Step-by-step explanation:

It will take 1.23 x 10^2 hours to fill a cylinder-shaped vat.

What is the volume of the cylinder?

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

The volume of the cylinder-shaped vat can be calculated as follows:

V = π * r^2 * h

= π * 32.5^2 * 33.9 ft^3

The mass of the liquid in the vat can be calculated as the product of its volume and density:

m = d * V

= 1.77 g/mL * π * 32.5^2 * 33.9 ft^3

The time it takes to fill the vat can be calculated as the ratio of the mass of the liquid to the rate at which it is spilling out of the hose:

t = m / (12,757.9 g/s)

Converting the volume to liters, the density to kg/m^3, and the time to hours, the answer is approximately 1.23 x 10^2 hours.

Hence, it will take 1.23 x 10^2 hours to fill a cylinder-shaped vat.

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Question 9
Solve 9x + 11 < 10x + 16

Answers

Answer:

[tex]x > -5[/tex]

Step-by-step explanation:

Flip the equation over- [tex]10x+16 > 9x+11[/tex]

Now do [tex]10x-9x=x[/tex]

So the equation now looks like this [tex]x+16 > 11[/tex]

Now subtract 16 from both sides to give you the answer [tex]x > -5[/tex]

Answer: [tex]x > \Large\boxed{-5}[/tex]

Step-by-step explanation:

Given inequality

[tex]9x+11 < 10x+16[/tex]

Subtract 9x on both sides

[tex]9x+11-9x < 10x+16-9x[/tex]

[tex]11 < x+16[/tex]

Subtract 16 on both sides

[tex]11 -16 < x+16-16[/tex]

[tex]-5 < x[/tex]

[tex]x > \Large\boxed{-5}[/tex]

A rectangular prism has a height of 10 inches in a width of 19 inches and a length of 20 inches in what is the volume of the prism​

Answers

The volume of a rectangular prism is a measure of the space occupied by the prism. It is calculated by multiplying the area of the base of the prism by its height.

In a rectangular prism, the base is a rectangle, and the height is the perpendicular distance between the top and bottom faces of the prism.

To find the volume of the rectangular prism, we simply multiply the length, width, and height of the prism. The length and width give us the area of the base, and the height gives us the perpendicular distance between the top and bottom faces. So, the formula for the volume of a rectangular prism is:

V = length * width * height

In this case, the height of the rectangular prism is 10 inches, the width is 19 inches, and the length is 20 inches. So, we can plug these values into the formula and calculate the volume:

V = 20 * 19 * 10

V = 3800 cubic inches

So, the volume of the rectangular prism is 3800 cubic inches.

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A rectangular prism has a height of 10 inches in a width of 19 inches and a length of 20 inches in what is the volume of the prism​?

We need only multiply the rectangular prism's length, breadth, and height to determine its volume. The area of the base is determined by the length, breadth, and height, while the angle between the top and bottom faces is determined by the height. So, the following is the formula for a rectangle prism's volume:

V: length, breadth, and height

In this instance, the rectangular prism measures 10 inches in height, 19 inches in breadth, and 20 inches in length. As a result, we can determine the volume by entering these values into the formula:

V = 20 * 19 * 10

Dionne can fold 175 packing boxe in 50 minute. Elia can fold 120 packing boxe in 40 minute. Ue unit rate to find how much time it will take each peron to fold 210 packing boxe. Drag the number to explain and how your anwer. Number may be ued once or not at all. 60 returned to choice lit. 370803. 54. 550604
Dionne can fold
boxe in 1 minute and Elia can fold
boxe in 1 minute. Dionne will fold 210 boxe in
minute and Elia will fold 210 boxe in
minute

Answers

It will take Dionne 60 minutes and Elia 70 minutes to fold 210 packing boxes.

To find the unit rate for each person, divide the number of boxes they can fold by the time it takes them to fold them:

Dionne: 175 boxes / 50 minutes = 3.5 boxes/minute

Elia: 120 boxes / 40 minutes = 3 boxes/minute

Next, divide the total number of boxes to be folded (210) by each person's unit rate:

Dionne: 210 boxes / 3.5 boxes/minute = 60 minutes

Elia: 210 boxes / 3 boxes/minute = 70 minutes

So, it will take Dionne 60 minutes and Elia 70 minutes to fold 210 packing boxes.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

Destiny is using ribbon to create girls' hair barrettes. For a craft fair in Booneville, she made 12 small barrettes and 14 large barrettes, using a total of 148 yards of ribbon. Then, for another craft fair in Newport, she made 12 small barrettes and 10 large barrettes, which used a total of 116 yards. How many yards of ribbon does Destiny use for each?

Destiny uses
yards of ribbon on each small barrette and
yards on each large one.

Answers

The number of yards of ribbon used to make small barrettes is 3 yards and the number of yards of ribbon used to make large barrettes is 7 yards.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, Destiny is using ribbon to create girls' hair barrettes.

Let the number of yards of ribbon used to small barrettes be x and the number of yards of ribbon used to large barrettes be y.

For a craft fair in Booneville, she made 12 small barrettes and 14 large barrettes, using a total of 148 yards of ribbon.

Now, the equation is 12x+14y=148 -------(i)

For another craft fair in Newport, she made 12 small barrettes and 10 large barrettes, which used a total of 116 yards.

So, the equation is 12x+10y=116 -------(ii)

Subtract equation (ii) from equation (i), we get

12x+14y-(12x+10y)=148-116

4y=32

y=8

Substitute y=7 in equation (i), we get

12x+14(8)=148

12x+112=148

12x=36

x=3

Therefore, the number of yards of ribbon used to make small barrettes is 3 yards and the number of yards of ribbon used to make large barrettes is 7 yards.

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Yui is buying beverages for her friends. She buys a total of 6 bottles of water and sports drinks. Bottles of water cost $1.50 each, and sports drinks cost $2.50 each. She spends a total of $10. Write a system of equations to represent the information, and use substitution to determine how many of each type of drink Yui buys.

Answers

Answer:

Let x be the number of bottles of water that Yui buys, and y be the number of sports drinks. The first equation represents the total number of bottles:

x + y = 6

The second equation represents the total cost:

1.5x + 2.5y = 10

To solve for x and y, we can use substitution. Solving the first equation for y in terms of x:

y = 6 - x

Substituting this expression for y into the second equation:

1.5x + 2.5(6 - x) = 10

Expanding and simplifying the right side:

1.5x + 15 - 2.5x = 10

-x + 15 = 10

Subtracting 15 from both sides:

-x = -5

Dividing both sides by -1:

x = 5

Substituting this value for x back into y = 6 - x:

y = 6 - 5

y = 1

So Yui buys 5 bottles of water and 1 bottle of sports drink.

Step-by-step explanation:

PLSS HELP ALSO SHOW HOW U DID IT

Answers

y = -x - 9 is the equation of the line that passes through the points (-5. -4) and (-2, -7).

What is a Linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a line Pass through the points (-5. -4) and (-2, -7)

The slope-intercept form of the equation of a line:

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

m = (-7 + 4)/(-2 + 5)

m = -3/3

m = -1

Thus the equation of the line will be:

y = - x  +b

Since, point (-5, -4) passes through the equation of the line

-4 = 5 + b

b = -9

So,

The equation of the line:

y = -x - 9

Therefore, the equation of the line that passes through the points (-5. -4) and (-2, -7) is y = -x - 9.

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The distribution of age for players of a certain professional sport is strongly skewed to the right with mean 26.8 years and standard deviation 4.2 years. consider a random sample of 4 players and a different random sample of 50 players from the population. What would be true about the sampling distributions of the sample mean ages for samples of size 4 and samples of size 50?

Answers

Answer:

For a random sample of 4 players, the sampling distribution of the sample mean age would have:

the mean wouldn't be close to 26.8 years, as a sample mean will be an unbiased estimator of the population mean but the sample here is far smaller than a sample of 50.

A larger standard deviation compared to the standard deviation of individual player ages (4.2 years), as the standard deviation of the sample mean decreases with larger sample sizes (i.e., the Central Limit Theorem). The standard deviation of the sample mean for a sample of 4 players can be calculated using the formula:

s_mean = s / sqrt(n)

where s is the population standard deviation (4.2 years) and n is the sample size (4).

For a random sample of 50 players, the sampling distribution of the sample mean age would have:

A mean close to 26.8 years, as the sample mean will be an unbiased sample mean for a sample of 4 players, as the standard deviation of the estimator of the population mean.

A smaller standard deviation compared to the standard deviation of the sample mean decreases with larger sample sizes (i.e., the Central Limit Theorem). The standard deviation of the sample mean for a sample of 50 players can be calculated using the formula:

s_mean = s / sqrt(n)

where s is the population standard deviation (4.2 years) and n is the sample size (50).

find the solution of the initial value problem y'' 4y = t^2 7e^t, y(0) = 0, y'(0) = 2

Answers

The values of A,B,C are 1/4,0.-1/8 respectively.

If the degree of both f(x,y) and g(x,y) are the same, a differential equation of the form f(x,y)dy = g(x,y)dx is said to be homogeneous. For k>0, a homogeneous function of degree n is a function of type F(x,y) that may be expressed in the form kn F(x,y). As a result, f and g are the same-degree homogeneous functions of x and y.

The characteristic equation of homogeneous problem and its zeros:

r²+4=0

r= ±2i

Homogeneous solution:

yc=c1 cos 2t+ c2 sin 2t

set Y1= At²+ Bt+C

Plugging in Y1 into the starting equation:

2At+ 4At²+ 4Bt+4C=t²

A=1/4

B=0

2A+4C= 0

4C= -1/2

C= -1/8

Thus, the values of A,B,C are 1/4,0.-1/8 respectively

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Evaluate the expression 10(x + 2) + 10 • 2 for x = 2. A. 20 B. 60 C. 40 D. 80

Answers

The value of the expression when x = 2 is

How to evaluate the expression

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

10(x + 2) + 10 • 2

The expression 10(x + 2) + 10 * 2 for x = 2 is:

10(2 + 2) + 10 * 2

So, we have the following representation

10 * 4 + 10 * 2 =

So, we have the following representation

40 + 20

Lastly, we have

= 60

So, the answer is B. 60.

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A bathtub holds 42 gallons of water filling at a rate of 4 gallons per minute how long will it take to fill a tub?

Answers

Answer:

10 minutes 30 seconds

Step-by-step explanation:

begin by dividing the overall size of the tub by the amount of gallons per minute.

42/4=10.5

This means that in 10.5 minutes the tub would be full. .5 is half and half of one minute is 30 seconds.

Match the correlation coefficient with the correct association:

Question 8 options:

0.52


-0.86


0.93


-0.66


-0.01

1.
Strong association

2.
Weak association

3.
Moderate association

Answers

Note that the correlation coefficients matched with the correct association are given as follows:


0.52: Moderate association

-0.86: Strong association

0.93: Strong association

-0.66: Moderate association

-0.01: Weak association

What is a correlation coefficient?

A correlation coefficient is a quantitative measure of a statistical connection between two variables.

The variables might be two columns from a specified data set of observations, commonly referred to as a sample, or two factors of a multivariate random variable with a known distribution.

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Which ofthe following is the LU-factorization of the matrix a) b) 1. c) -1 [1 01 0] d) -3

Answers

For the matrix [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex] , the LU-factorization is option D:  [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

Lower-upper (LU) decomposition, also known as factorization of a matrix, is the process of breaking a matrix into its lower and upper triangular components.

The given matrix is - [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex].

Generate a matrix A = LU such that L is the lower triangular matrix with principal diagonal elements being equal to 1 and U is the upper triangular matrix.

Take a matrix I =  [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

Apply the elementary row operation such that - R2 → 3R1 + R2

So, it is obtained that I = [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex]

Here, lower matrix is [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex].

Here. upper matrix is  [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].

Therefore, the matrix is  [tex]\left[\begin{array}{ccc}1&0\\-3&1\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].

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Let f be the function defined above, where k is a positive constant. For what value of k, if any, is continuous? 2.081 2.646 8.550 There is no such value of k.

Answers

k=2.081, f(x) is continuous at x=3. So correct option is A.

What do mean by continuity in function?

In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities, or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter. Any function that is not continuous is said to be discontinuous. Mathematicians up until the 19th century mostly used intuitive ideas of continuity and only took into account continuous functions. To formalize the idea of continuity, the epsilon-delta definition of a limit was established.

Since f(x)[tex]\left \{ {{k^{3}+x } for x < 3 \atop {\frac{16}{k^{2}-1 }for x\geq 3 }} \right.[/tex]

We have to check continuity at x=3, for the value of k.

So, [tex]\lim_{x \to-3 \ } f(x)= \lim_{x \to +3\ } f(3)[/tex], eq.(1)

[tex]\lim_{x \to -3\ } f(x)=k^{3} + 3\\ \lim_{x \to +3\ } f(x)= \frac{16}{k^{2}-3 } and f(3)=\frac{16}{k^{2}-3 } \\from eq.(1)\\k^{3}+3=\frac{16}{k^{2} -3}[/tex]

By option (A), put k= 2.081= 2.081³ + 3= [tex]\frac{16}{2.081^{2} -3}[/tex]

=9.01189744+3= [tex]\frac{16}{4.330561-3}[/tex]

=12.01189744=[tex]\frac{16}{1.330561}=12.0118974[/tex]

Hence, k=2.081, f(x) is continuous at x=3.

So, option A is correct.

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(ii) The quadratic equation whose solution set is {0, 2}, is:

Answers

The quadratic equation whose solution set is {0, 2}, is: x²-2x = 0

What are quadratic equations?

A Quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given that, the solution of a quadratic equation is {0, 2},

The equation of a quadratic polynomial in form sum and product of solutions is given by,

x²-(α+β)x+αβ = 0, where α, β = solution of equation

α+β = 0+2

α+β = 2

αβ = 0×2

αβ = 0

Therefore, equation is x²-2x+0 = 0

Hence, the quadratic equation whose solution set is {0, 2}, is: x²-2x = 0

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