Which of the following are possible examples of sampling distributions? (Select all that apply.) O all mean trout lengths in a sampled lake O mean trout lengths based on samples of size 5 O heights of college students at a sampled university O average SAT score of a sample of high school students
O average male height based on samples of size 30 X

Answers

Answer 1

The potential instances of sample distribution are options C and E.

Option E. Average male height based on samples of size 30.

Option C. Mean trout lengths based on samples of size 5.

The sampling distribution of the mean is the distribution of the variable x (all feasible sample means of size n) for a variable x and a given sample size n.

The mean is the most typical kind of sample distribution. Plotting the data points and computing the means of each sample group drawn from the population are its main goals.

This idea, which is a form of the probability distribution, is frequently used to gather precise data from a sizable population that is divided into a number of randomly chosen samples. This idea is further divided into three categories: T-Sampling, proportional sampling, and the sampling distribution of the mean.

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The correct questions should be like this:

Which of the following are possible examples of sampling distributions? (Select all that apply.) average SAT score of a sample of high school students

all mean trout lengths in a sampled lake

mean trout lengths based on samples of size 5

heights of college students at a sampled university

average male height based on samples of size 30


Related Questions

A plane slices a double-napped cone parallel to the slanted edge of the cone. Which conic section is formed?
Circle
Ellipse
Hyperbola
Parabola

Answers

It is both of the pair of intersecting lines and degenerate hyperbola.

What is conic section?

A conic section, conic or quadratic curve is a curve formed by the surface of a cone crossing a plane. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, however it was frequently referred to as a fourth type. Parabolas, ellipses, circles, and hyperbolas are the four main forms of conics. Examine the diagrams below to discover how a conic is defined geometrically. The plane does not travel through the vertex of a non-degenerate conic.

Here,

It consists of a pair of intersecting lines as well as a degenerate hyperbola.

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A quantity with an initial value of 7800 decays continuously at a rate of 0. 1%

per hour. What is the value of the quantity after 1. 25 days, to the nearest

hundredth?

Answers

The question is asking for the value of a quantity that decays continuously at a rate of 0.1% per hour. We are given that the initial value of the quantity is 7800 and are asked to find the value after 1.25 days (30 hours).

What is a ratio in mathematics?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

We can use the following formula to find the final value of the quantity after a certain amount of time:

final value = initial value * (1 - decay rate)^time

Where decay rate is given as a decimal (0.1% = 0.001)

Plugging in the given values, we get:

final value = 7800 * (1 - 0.001)^30

The final value is around 7396.65

Rounding the final value to the nearest hundredth, the final value after 1.25 days is:

7396.65 ≈ 7396.66

The value of the quantity after 1.25 days, to the nearest hundredth is 7396.66.

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witch are linear and witch are not linear!?

Answers

Step-by-step explanation:

a linear relationship or function is described by

y = ax + b

that means that the difference from one y value to the next is defined by a constant ratio of y diff / x diff.

so, the first one is not linear.

because the difference ratios are not constant :

(1-0)/(1-0) = 1

(4-1)/(2-1) = 3

(9-4)/(3-2) = 5

the second one is linear.

the difference ratios are constant :

(1-0)/(1-0) = 1

(4-1)/(4-1) = 1

(9-4)/(9-4) = 1

the third one is not linear.

the difference ratios are not constant :

(3-1)/(3-2) = 2

(9-3)/(4-3) = 6

(27-9)/(5-4) = 18

the fourth one is linear.

the difference ratios are constant :

(5-1)/(4-2) = 4/2 = 2

(9-5)/(6-4) = 4/2 = 2

(13-9)/(8-6) = 4/2 = 2

The circle below has center H. Suppose that mLFEG=46°. Find the following.

Answers

From given circle, Measure of arc FG = 23πr/45 and ∠FHG = 92°.

The distance between the two locations along a segment of a curve is known as the arc length. Any portion of the circumference is an arc in a circle. The angle that an arc occupies at any given point is the angle created by the two line segments that connect that point to the arc's endpoints.

Length of an Arc = r, where is in radians, is the formula used to express the arc length of this arc OP.

The measure of ∠FHG = 2 × 46° [As Angle at center equals twice at circumference]

So, ∠FHG = 92°

Measure of the arc FG = 2πr(θ/360°)

FG = 2πr(92/360)

FG = 23πr/45

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I’m doing homework and this may be easy for others but I’m not that good at learning quickly. Take ur time it’s fine. Please help

Answers

the statement that "you walk at a constant rate" tells us that the relationship is indeed proportional, namely, there's a value in the input that's consistent or common yielding the output.

Check the picture below.

to get the equation of any straight line, we simply need two points off of it, for the distance "from school" table, let's use those two points in that table

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{0.5})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{1.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1.5}-\stackrel{y1}{0.5}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{10}}}\implies \cfrac{1}{20}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0.5}=\stackrel{m}{\cfrac{1}{20}}(x-\stackrel{x_1}{10})\implies y-0.5=\cfrac{1}{20}x-\cfrac{1}{2} \\\\\\ y=\cfrac{1}{20}x-\cfrac{1}{2}+0.5\implies y=\cfrac{1}{20}x-\cfrac{1}{2}+\cfrac{1}{2}\implies \boxed{y=\cfrac{1}{20}x}[/tex]

Karime walks 3/4 of a mile each day for 5 days.the number of miles karime walks altogether is between which two whole numbers?

Answers

Answer:

Step-by-step explanation:

To find the total number of miles Karime walks, we need to multiply the number of miles she walks each day by the number of days:

3/4 mile/day * 5 days = 15/4 miles

We can simplify this fraction to be:

15/4 = 3 3/4

The whole number portion of this result is 3, and the fractional portion is 3/4. Therefore, the total number of miles Karime walks is between 3 and 4.

In other words, the two whole numbers between which the total number of miles Karime walks are 3 and 4.

Total number of miles Karime walks altogether is,

⇒ 5 miles

We have to given that,

Karime walks 3/4 of a mile each day for 5 days.

Hence, To find number of miles Karime walks altogether, we can multiply 3/4 by 5.

So, We get;

Total number of miles Karime walks altogether is,

⇒ 3/4 x 5

⇒ 15 / 4

⇒ 3.75

⇒ 4 miles

Because 3.75 is nearest to 4.

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Mrs. Remeto separate would like to buy a television TV set payable for 6 months starting at the end of the month how much is the cost at the TV set if her monthly payment is P3,000 and interest is 9% compounded semi annually?​

Answers

If her monthly payment is P3,000 and interest is compounded semi-annually at 9%, the cost of the TV set comes to P17,545.08.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest.

In finance and economics, compound interest is common.

In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time.

The interest per period multiplied by the number of periods in a year yields the simple annual interest rate.

According to our question-

9% = 0.09 / 2

=0.045 + 1 =1.045^(1/6)

=1.00736312 - 1 x 12 x 100

=8.836%

PV=0;

PMT=3000;

R=0.08836/12; N=6; PV

=PMT*(((1 + R)^N - 1)*((1 + R)^-N)* R^-1)

PV==17,545.08

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What is the probability that all the members of your mathematics class have different birthdays? What is the probability that there is a birthday coincidence in the group?

Answers

Supposing a band of 20 members, we have that the probabilities are given as follows:

All have different birthdays: 0.9466 = 94.66%.There is a birthday coincidence: 0.0534 = 5.34%.

What is the binomial distribution formula?

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

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

The parameters are given by:

n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.

The parameter values for this problem are given as follows:

n = 20, as the band has 20 members.p = 1/365, as the year has 365 days, hence the probability of a person having a given day as a birthday is of 1/365.

The probability that all members have different birthdays is of P(X = 0), hence:

P(X = 0) = (1 - 1/365)^20 = 0.9466.

Hence the probability that there is a birthday coincidence is of:

P(X > 0) = 1 - P(X = 0) = 1 - 0.9466 = 0.0534.

Missing Information

This problem is incomplete, hence we suppose a band of 20 members.

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Solve the system of linear equations by substitution. Check your solution.
3
1. y = -2x + 4 and -x +3y = -9

2. 3 over 4x -5y = 7 and x= -4y +12

3. 5x - y= 4 and 2x + 2y = 16

4. 2x + 3y = 0 and 8x +9y = 18

Answers

The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

What is function?

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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Solving provided question, we can say that the given linear equation is  y = -2x + 4 and -x -x +3(-2x + 4 ) + 9 = x = 7/3

What is a linear equation?

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

the given linear equation is

y = -2x + 4 and -x +3y = -9

now,

-x +3(-2x + 4 ) + 9

-x - 6x - 12 +9 = 0

-7x = -3

x = 7/3

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please help will mark brainliest

Answers

After diving the polynomials, the quotient and remainder is q(x)=-x^2+1 and r(x)=-1 respectively.

What are polynomials?

The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases." There is no limit to the number of terms that can exist in a polynomial.

The polynomials are -

a(x)=-x^4

b(x)=x^2+1

Divide a(x) by b(x).

-x^4/x^2+1 = -x^2+1 with remainder as -1.

The quotient is obtained as q(x)=-x^2+1 and the remainder is r(x)=-1.

The given equation is -

a(x)/b(x)=q(x)+[r(x)/b(x)]

Plugging in all the values -

-x^4/x^2+1=-x^2+1+[-1/x^2+1]

[-x^4/x^2+1]-[-1/x^2+1]=-x^2-1

-x^4+1/x^2+1=-x^2-1

-x^4+1=[-x^2+1][x^2+1]

-x^4+1=(-x)^2[x^2+1]+(1)[x^2+1]

-x^4+1=-x^4-x^2+x^2+1

-x^4+1=-x^4-1

So, LHS=RHS is proved using the equation.

Therefore, the quotient is q(x)=-x^2+1 and the remainder is r(x)=-1.

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Explain how the Quotient of Powers property was used to simplify this expression. 2 to the fifth power, over 8 = 22

Answers

The Quotient of Powers was used to simplify this expression is By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents

We have given that,

2 to the fifth power, over 8 = 22

What is the simplified form of expression?

The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form or to rewriting the same algebraic expression with no like terms and in a compact manner.

By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.

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an airplane is flying from new york city to los Angeles the distance it travels in miles, d, is related to the time in seconds, t, by the equation d=0.15t how long will it take to go 12.75 milles

Answers

Answer: 85 seconds

Step-by-step explanation: 12.75/0.15=85

What are interval examples?

Answers

An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

Interval

An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

Interval Notation

Interval notation is a simplified way of describing a particular interval. Let’s see how it’s done.

Step 1: We write the first and last number of the interval, which are the endpoints of the interval. For example, if the interval is from 6 to 20, we write 6, 20.

Step 2: We use a round or square bracket on each side of the two numbers. We use:

A square bracket [ ], if we want to include the endpoints

A round bracket ( ), if we don’t want to include the endpoints

So in this example, we use:

[6, 20] if the interval includes 6 and 20(6, 20) if the interval excludes 6 and 20 (6, 20] if the interval excludes 6 but includes 20[6, 20) if the interval includes 6 but excludes 20 Types of Intervals

So, we can see that some intervals include the endpoints, some partially include them, and some do not include them. Based on this, there are three types of intervals

These are:

Open intervalClosed intervalHalf-open and half-closed intervalOpen Interval

This type of interval does not include the endpoints. For example, (5, 10) does not include endpoints 5 and 10.

Closed Interval

This type of interval includes the endpoints. For example, [4, 9] includes the endpoints 4 and 9.

Half-Open and Half-Closed Interval

This type of interval includes only one of the endpoints.

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Coach Taylor asked his team to record the distance they ran during practice. It’s a dot plot so someone plssss help me I’ll give them 10 points!

Answers

The range between 3/16 & 3/8 is where the line plot with the difference of daily mileage logged by each racer in a group is still most obvious.

Line plot: what is it?

A line graph, liner plot, or line chart is a graph that uses lines to link the individual data points. For a specific time period, quantitative values are displayed as a line graph. Line graphs are widely used in finance to depict the past market movements of a securities or asset.

Here,

calculation

The number line indicates that there's more than or equal to 3 marks when there are 7 markings either on or to the right of 3. The fraction must first have the same denominators.

=> 3/8 x 2 = 6/16

=> 1/2 x 8 = 8/16, 3/8 x 2 = 6/16

=> 5/8 x 2 = 10/16, 1/2 x 8 = 8/16

Since they all have the same numerator, we can now compare them.

=> 3/16 - 1/16 = 2/16

=> 6/16 - 3/16 = 3/16

=> 8/16 - 6/16 - 2/16

=> 10/16 - 8/16 = 2/16

The largest distinction is between 3/16 and 3/8 (6/16 vs. 3/16).

The range between 3/16 and 3/8 is where the line plot with the difference in daily mileage logged by each runner in a group is most obvious.

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The complete question is " Coach Taylor asked his team to record the distance they ran during practice The line plot shows the number of miles the individual members in a group of runners run each day. How many runners run at least 3 miles per day?."

When Edna's phone is fully charged, it can operate for up to 18 hours before running out of battery. It has been 6 hours since Edna's phone was fully charged. Let x represent how many more hours Edna's phone can operate without running out of battery. Which inequality describes the problem? 6 + x < 18 6 +xs 18 Solve the inequality. Then, complete the sentence to describe the solution. Edna's phone can operate for up to more hours without running out of battery. ​

Answers

Edna's phone can operate for up to 12 more hours without running out of battery. ​

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

fully charged

T = 18Hr

It has been 6 hours since Edna's phone was fully charged.

remaining battery =18- 6= 12Hr

x=12Hr

6 + x < 18

6 +x > 18

neither nor.

both equations are wrong.

6 +x = 18

Edna's phone can operate for up to 12 more hours without running out of battery. ​

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Question 3
Determine if this statement is always, sometimes, or never true.
If a < 0, then |a| = -a

Answers

Answer:

the answer is neither

Step-by-step explanation:

An integer is a whole number that can be either greater than 0, called positive, or less than 0, called negative. Zero is neither positive nor negative. Two integers that are the same distance from the origin in opposite directions are called opposites.

What is the XYZ axis called?

Answers

The XYZ axis is called as X-axis, Y-axis, and Z-axis, respectively.

The term axis in math is defined as  a line with respect to which a curve or figure is drawn, measured, rotated, etc.

Here we have given that XYZ axis, in math are no standard names for the coordinates in the three axes

Based on these the coordinates are often denoted by the letters X, Y, and Z, or x, y, and z.

And these axes may then be referred to as the X-axis, Y-axis, and Z-axis, respectively.

Here in the graph x-axis and y-axis represent the first two dimensions where as the z-axis, the third dimension. Which is also defines the x and y denote width and height and the z denotes depth.

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Are undecidable problems unsolvable?

Answers

Therefore , the solution to the given problem of algorithm comes out to be it fall under the category of undecidable questions, which is a subtype of unsolvable problems.

Define algorithm.

An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.

Here,

A problem is considered undecidable if there is no algorithm that can be created that will consistently return a true or false answer for each input value.

Only issues that should have a yes-or-no response (such as: does my code contain a bug?) fall under the category of undecidable questions, which is a subtype of unsolvable problems.

Therefore , the solution to the given problem of algorithm comes out to be it fall under the category of undecidable questions, which is a subtype of unsolvable problems.

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What is the importance of constructing a probability distribution for a random variable in interpreting data?​

Answers

A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.

A probability distribution is a list of all of the possible outcomes of a random variable, along with its corresponding probability values.

A probability distribution links each outcome of a random variable or process with its probability of occurrence.

A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.

These models have a mathematical background, and can be very picky. For them to work properly, the random variable you are trying to fit in must meet different assumptions so that the outcomes of the model have the correct probabilities, and also so that you can test and validate the model against real data from the random variable.

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Uri buys two burgers and a soda for $\$2.10$, and Gen buys a burger and two sodas for $\$2.40$. How many cents does a soda cost

Answers

The cost of soda as calculated from the data given is found to be as 0.9 cents.

the price of 1 burger = x

the price of 1 soda =y

Therefore, the equation for Uri and Gen becomes,

2x + y = $2.10

x+ 2y = $2.40

On solving these two equations we will get the value of x and y which represents their cost.

on multiplying equation 2 with 2 , we will get ,

2x + 4y = 4.80

Therefore , on subtracting equation 1 and 2 ,

 2x + y = $2.10

- 2x + 4y = 4.80

=> -3y = - 2.7

=> y = 0.9

Therefore x will be ,

x+ 2y = $2.40

x+ 2(0.9) = $2.40

x + 1.8 = $2.40

x = 2.40 - 1.8

  = 0.60

Therefore, cost of soda is 0.9 cents.

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How to do elimination with 3 variables?

Answers

Elimination is a method used to solve systems of linear equations with two or more variables. One possible method to solve a equation with 3 variables using elimination is solving algebraically.

To use elimination to solve a system of equations with three variables, you can follow these steps:

1. Write the system of equations. For example, if you have the equations:

3x + 2y - z = 5

2x - 4y + 2z = 6

5x - 2y + 3z = 10

2. Multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say y in two of the equations.

3. Next, you can multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say x in two of the equations.

4. Now substitute this value of z in the first or the second equation to solve for x

5. Now substitute this value of x and z in the second equation or any other equation to solve for y

This is one possible way to use elimination to solve a system of equations with three variables. Depending on the specific problem, there may be different ways to eliminate variables, but the general idea is to use scalar multiplication and addition or subtraction to create a new equation with one variable having the same coefficient but with opposite signs. One can also use Gaussian elimination or matrix inversion method.

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The scale model of a statue is 1 inch to 11.2 feet. If the model is 5.8 inches, what is the length, in feet, of the actual statue?

Answers

The length of the actual statue in feet would be = 64.96 ft

What is scale model?

A scale model is defined as the the exact type of an object but with a different measurement.

The scale model of a statue = 1 In = 11.2 ft

The length of the model = 5.8 inches

Therefore it length in feet = X ft

That is; 1 in = 11.2 ft

5.8 in = X ft

make X ft the subject of formula;

X ft = 5.8 × 11.2 = 64.96 ft

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Help me, its geometry pls show everything.

Answers

It is assumed the given figure is a parallelogram.

Use properties of a parallelogram:

opposite sides are parallel and congruent,diagonals bisect each other.

Find the missing values:

ML = NP = 12 m, opposite sides are congruent,LP = MN = 10 m, opposite sides are congruent,m∠LPM = m∠NMP = 62°, alternate interior angles are congruent, as LP║MN and MP is transversal,LN = LQ*2 = 9*2 = 18 m, as Q is the midpoint of LN,m∠MLN = m∠PNL = 32°, alternate interior angles are congruent, as ML║NP and LN is transversal,QN = QL = 9 m, as Q is the midpoint of LN.

∆ABC is divided into three smaller triangles and one quadrilateral. Area of ∆AFE is 4, Area of ∆AFC is 9, area of ∆DFC is 7. Find the area of quadrilateral BEFD.

Answers

The area of quadrilateral BEFD is 15.32units²

How to find the area of quadrilateral BEFD?

Let the area of  ∆ABC be A

Let the area of ∆AFE be X

Let the area of ∆AFC be Y

Let the area of ∆DFC be Z

Using Ladder theorem:

1/A + 1/Y = 1/(X+Y) + 1/(Y+Z)

Since X = 4, Y = 9 and Z = 7, we have:

1/A + 1/9 = 1/(4+9) + 1/(9+7)

1/A + 1/9 = 1/13 + 1/16

1/A = 1/13 + 1/16 - 1/9

1/A = 53/1872

A = 1872/53

A = 35.32

area of  ∆ABC = area of ∆AFE + area of ∆AFC + area of ∆DFC + area of quadrilateral BEFD

35.32 = 4 + 9 + 7  + area of quadrilateral BEFD

35.32 = 20 + area of quadrilateral BEFD

area of quadrilateral BEFD = 35.32 - 20

area of quadrilateral BEFD = 15.32unit²

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Neville buys a triangular box with three chocolate cauldrons. The box is an equilateral triangle with three circles with a radius of 6 inches inscribed inside it. What is the perimeter of the triangle?

Answers

Using the radius of the circle given, the perimeter of the equilateral triangle is 48 inches

What is Perimeter of Equilateral Triangle

The perimeter of an equilateral triangle is three times the length of one side. Thus, if the length of one side is 'l', the perimeter of the triangle is 3l.

In this problem, the equilateral triangle has 3 circles inside with radius of 6 inches each.

Assuming the circles when combined will cover the entire triangle.

The diameter of the circle = 6 * 2 = 12 in

The length of the equilateral triangle = 2 * 12 = 24in

However, we already know the perimeter of an equilateral triangle is three times the side length of the triangle.

Perimeter of equilateral triangle = 3 * 24

Perimeter = 48 in

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Find the area under the graph

Answers

Therefore , the solution of the given problem of function comes out to be 4 log2  + 3/4 is the are required.

What is meant by the word function?

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.

Here,

Given :

=>  f(x) = x.2ˣ

=>A = [tex]\int\limits^2_{-1} x.2^{x}[/tex]dx

=> A = [tex]2^{x} \int\limits^2_{-1} x. + x\int\limits^2_{-1} 2^{x}[/tex]

=>  [ xlog2 + x²/2 +  x²log2 ]₋₁²

=>  log2 + 3/4 + 3log2

=> 4 log2  + 3/4

Therefore , the solution of the given problem of function comes out to be 4 log2  + 3/4 is the are required.

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Joy is solving a quadratic equation of the form a2+bx+c=0 where b
and care integers.
She correctly solves the equation to get a = 3 ± √/13
Work out the values of b and c.
(3 marks)
b=
=

Answers

To find the values of b and c, we can use the quadratic formula:

[tex]x = (-b ± \sqrt{ (b^2 - 4ac)}) / 2a[/tex] which will give us the value B = -6 & C = -4

What is a quadratic equation.

A quadratic equation is a second-order polynomial equation in one variable using the formula [tex]x = ax2 + bx + c = 0[/tex] and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

So the equation that she get is [tex]x^{2} -6x-4[/tex]

this means that x=3+√13 or 3-√13

which also equals to x=3+√13 & x-3-√13=0 and

x=3-√13

x-3+√13=0

which if you try to find the quadratic equation for this. you need to do it by this

(x-3+√13)(x-3-√13)

which will get you

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How do you find the f of G in a pair of functions?

Answers

To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.

What is function ?

A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Have given ,

f of G in a pair of functions ,

Let a example that f(x) = [tex]x^{2}[/tex] and g(x) = √x + 2

To find f(g(x)), we take f(x) and everywhere there's an x, we replace it with g(x).

f(x) = x2

f(g(x)) = g(x)2

= (√x + 2)2

= x + 2√x + 4

To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.

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The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.

Answers

The solution of the system of equations is:

x = 5t - 4

y = -5t + 1

z = t

Option B is the correct answer.

What is a matrix?

A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.

We have,

From the row-echelon form of the augmented matrix of a system of equations, we get,

x + 0y -5z = -4

x - 5z = -4

x = 5z - 4

0x + y + 5z = 1

y + 5z = 1

y = -5z + 1

0x + 0y + 0z = 0

Now,

Put z = t (any real number)

We get,

x = 5t - 4

y = -5t + 1

Thus,

The solutions are:

x = 5t - 4

y = -5t + 1

z = t

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Valentina is baking jumbo cinnamon rolls for a family breakfast. She uses all the dough she made to form 12 cinnamon rolls of equal weight. The recipe usually makes 36 ounces of dough, but Valentina made more dough than that so she can have larger cinnamon rolls.

Answers

The required inequality to represent the above data regarding Valentina is x > 3.

How to illustrate the inequality?

Valentina uses more than 36 ounces of dough 12 cinnamon rolls made by Valentina of weight ounces of dough represented by x ,then required inequality is given by 12x > 36.

Number of cinnamon rolls made by Valentina = 12

Weight of all 12 cinnamon rolls are equal

x represents the ounces of dough used by Valentina to make cinnamon roll.

Ounces of dough used by Valentina is more than 36.

Required inequality to represent the above data is given by:

12x > 36

Divide by 12 form both the sides we get,

12x /12 > 36/12

x > 3

The inequality is x > 3.

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Complete question

Valentina is baking jumbo cinnamon rolls for a family breakfast. She uses all the dough she made to form 12 cinnamon rolls of equal weight. The recipe usually makes 36 ounces of dough, but Valentina made more dough than that so she can have larger cinnamon rolls. Let x represent how many ounces of dough Valentina uses for each cinnamon roll. Which inequality describes the problem?

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