Draw the graph of the line that is parallel to Y -3 = 1/3(x+2) and goes through the point (1, 7)

For every 5.75 feet, here is one post.

Determine the number of posts in a wall of 166.75 feet.

So 29 posts needed for the wall.

Answer

f(x)

domain: all real numbers, range: all real numbers

f⁻¹(x)

domain: all real numbers, range: all real numbers

Step-by-step explanation

Given the function:

This is the equation of a line.

The domain and range of a linear function are all real numbers.

On the other hand, the range of an inverse function is the domain of the original function and the domain of an inverse function is the range of the original function. Then, the domain and range of the inverse of f(x) are all real numbers.

Answer:

C. 84

Explanation:

First, we will calculate the percentage of left-handed students in the group of 60 that the teacher asked.

So, the percentage is equal to:

Therefore, 30% of the randomly selected students are left-handed.

Now, we can use this percentage to estimate the number of left-handed students in the group of 280.

Then, 30% of 280 is equal to:

So, the answer is C. 84.

The equation that represents the relationship between x and y in the table is (L.) y = -5x + 3.

In mathematics, an equation is a relationship between two expressions that are expressed as equality on each side of the equal to sign.

Given in the table is the relationship between x and y respectively.

Substitute the values of x in the respective equations to find the value of y, the resulting value which matches the value of y in the table determines the correct equation.

J. y = -5x -27

⇒ For x = -3, y = -5(-3) - 27 = 15 -27 = -12 ≠ 18

K. y = -5x + 18

⇒ For x = -3, y = -5(-3) + 18 = 15 + 18 = 33 ≠ 18

L. y = -5x + 3

⇒ For x = -3, y = -5(-3) + 3 = 15 + 3 = 18 ≈ 18

For x = -1, y = -5(-1) + 3 = 5 + 3 = 8

For x = 2, y = -5(2) + 3 = -10 + 3 = -7

For x = 6, y = -5(6) + 3 = -30 + 3 = -27

All the values of x and y in the table satisfy the equation y = -5x + 3. Hence this is the required equation that represents the relationship.

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Using the binomial distribution, the probabilities are given by the image at the end of the answer.

The probability mass function is given as follows:

[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 of the function are described as follows:

In the context of this problem, the values of these parameters are given as follows:

To complete the table, we find each probability, as follows:

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

[tex]P(X = 0) = C_{8,0}.(0.46)^{0}.(0.54)^{8} = 0.0072[/tex]

[tex]P(X = 1) = C_{8,1}.(0.46)^{1}.(0.54)^{7} = 0.0493[/tex]

[tex]P(X = 2) = C_{8,2}.(0.46)^{2}.(0.54)^{6} = 0.1469[/tex]

[tex]P(X = 3) = C_{8,3}.(0.46)^{3}.(0.54)^{5} = 0.2503[/tex]

[tex]P(X = 4) = C_{8,4}.(0.46)^{4}.(0.54)^{4} = 0.2665[/tex]

[tex]P(X = 5) = C_{8,5}.(0.46)^{5}.(0.54)^{3} = 0.1816[/tex]

[tex]P(X = 6) = C_{8,6}.(0.46)^{6}.(0.54)^{2} = 0.0774[/tex]

[tex]P(X = 7) = C_{8,7}.(0.46)^{7}.(0.54)^{1} = 0.0188[/tex]

[tex]P(X = 8) = C_{8,8}.(0.46)^{8}.(0.54)^{0} = 0.0020[/tex]

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If halved a recipe that calls for 5 c chicken broth, then you would end up using 2.5 c chicken broth (that is two and half c of chicken broth).

The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?​

we have that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube.

so

Find the scale factor

ratio volumes=40.5/12=3.375

3.375=(scale factor)^3

scale factor=1.5

To find out the diameter of the larger balloon multiply the scale factor by the diameter of the smaller balloon

so

1.5*(10)=15 inches

Hello there. To answer this question, we need to remember some properties in simple and coumpound interests investments.

For simple interest, the balance will be equal to P(1 + rt), in which P is the amount invested, r is the interest rate in years and t is the time (can be either years of months).

For compound interest, the balance will be equal to P(1 + r)^t.

So, using the values P = $19,000.00 and the time is equal to 30 years, we have for:

a) 7% simple interest

It means that r = 7% and then we can use the first formula

19000(1 + 0.07*30)

We converted the rate to decimals above

Multiplying the values, we have:

19000(1 + 2.1)

19000*3.1

$58.900

b) 7% compounded monthly

First, we need to convert the time from years to months, multiplying by 12

30*12 = 360 months

Using the second formula, we have:

19000(1 + 0.07)^(360)

Sum the values into parenthesis

19000*1.07^(360)

We want to know the total of blankets that Greg's collected.

As there are 38 people in the group, and they each gave 2 blankets, they brough a total of 79 blankets.

As they got 29 asking door-to-door, and got another 52, we will sum the values, as shown:

This means that the Greg group collected a total of 160 blankets, instead of 121, and the Greg statement is false.

solve for y

then, solve for x

x = 3

y = -2

The combined volume is:

The volume of the rectangular prism is:

The volume of a cylinder is:

Then, the combined volume is:

Turn into inches:

Then, the volume in inches is 12,223,047 cubic inches (200.3 cubic meters)

The total social security and medicade for the first quarter of the year is $17,781.66.

The computation will be:

Gross earning per week = 15 * 365 + 9 * 385

= $8,940 per week

Here, the number of weeks is 13 in each quarter:

Gross earning =$8,940 * 13

= $116,220

Social security tax = $116,220 * 6.2%

= $7,205.64

Medicare tax = $116,220 * 1.45%

= $1,685.19

Total = $7,205.64 + $1,685.19

= $8,890.83

Now, to involve the employer's share it is required to multiply the total tax by 2

Therefore,

Total tax remitted to IRS = $8,890.83 * 2

= $17,781.66

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Imagine the following, we will place a tube under the snow. So we have the following

After one hour, the tube will be filled with 1 inch of snow.

After 2 hours, we will have one inch more

So, one way to calculate the amount of snow after a specific amount of hours, is simply multiplying the hours by the rate at which the height of the snow changes. IN here, the height changes 1 inch per hour. So after x hours the height of the snow would be

We want to find x, such that the height of the snow is 12.

So we have the equation

which gives us that in 12 hours we will have 12 inches of snow.

Markup (or price spread) is the difference between the selling price of a good or service and cost. It is often expressed as a percentage over the cost.

Given:

cost = $9.00

percent markup = 30%

Let the selling price be x

The formula form percent markup is:

Substituting we have;

Solving for x:

Hence, the selling price is $11.7

Answer: $11.7

Answer:

Explanation: We have to find the center of the circle, the equation of the circle is as follows:

Ploting the equation (0) gives the following result:

Therefore the center of the circle has the coordinates (0,4).

Solution

Given:

2x - 4y = -2

3x + 2y = 3

Substitution method

Graphical method:

Plot the graph of the two equations on the same graph

The point of intersection of the two graphs gives the solution to the system of equations

The point of intersection is (0.5, 0.75)

Which in fraction gives (1/2, 3/4)

Thus. x = 1/2, y= 3/4

Answer:  73.1%

Step-by-step explanation:

620/453 = 73.1%

Pls check so you can see if correct

For the two given functions, the compositions are:

Here we have two functions:

f(x) = √x

g(x) = 2x + 3

Now we want to get the compositions:

(f o g)(x) = f( g(x))

So here we just need to evaluate f(x) in g(x), we will get:

(f o g)(x) = √g(x) = √(2x + 3)

The other composition is:

(g o f)(x) = g(f(x)) = 2*f(x) + 3 = 2*√x + 3

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Answer:

The coordinates of point B is;

Explanation:

Given the attached image;

The coordinate of point A is;

The coordinate of point C is;

If AB is 1/5 of AC;

So; let (x,y) represent the coordinates of B;

The same applies to y coordinate;

So;

Therefore, the coordinates of point B is;

Let the point estimate be x and the margin of error be e.

Then, we must have

Add the equation (1) and equation(2) to eliminate the variable e, we have

Subtracting equation (2) from equation(1) to eliminate the variable x, we have

Hence, the point estimate is $50233 and the margin of error is $392, The Third option

The most appropriate choice for equation of line in slope intercept form will be given by-

y = 2x - 8 is the required equation of line

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line

Here,

The given equation of line is y= 2x +3

Slope of this line = 2

Slope of the line parallel to this line = 2

The line passes through (-2, -12)

Equation of the required line = y - (-12) = 2(x - (-2))

                                                = y + 12 = 2x + 4

                                                = y = 2x + 4 - 12

                                                = y = 2x - 8

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Given

PR and SU are parallel lines.

To find the pair of corressponding angles.

Explanation:

From, the figure,

Since PR and SU are parallel and the corressponding angles lie in the same corner.

Then,

Hence, the answer is Option c).

Given the 3° degree function:

Graph:

The given function can be represented f(x) and g(x) as below

What are functions?

A function from X to Y is an assign of each constituent of Y to each variable of X. The set X is known as the function's scope, while the set Y is known as the function's image domain. The notation f: XY denotes a function, its domain, and its codomain, and the value of a function f at an element x of X, indicated by f(x), is known as the image of x under f, or the value of f applied to the argument x. When defining a function, the domains and codomain are not often explicitly specified, and without performing some (complicated) calculation, one may only know that perhaps the domain is included in a larger package.

The functions are

(a) f(x) = 3x+2 and g(x) = |x|

so, H(x) = f(g(x)) = |3x+2|

(b)  f(x) = 5x+4 and g(x) = √√√√x

so, H(x) = f(g(x)) = √√√√5x+4

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Given the function f(x) defined as:

We need to obtain the graph after performing two shifts: 1 unit up and 2 units left. For the first shift, we do the transformation:

Now, for the second shift:

Combining these transformations:

The solution of the given equation is [tex]-3+\sqrt{6}[/tex] and [tex]-3-\sqrt{6}[/tex].

Given equation:-

[tex](x+3)^2=6[/tex]

We have to find the value of x by solving the given equation.

We can rewrite the given equation as:-

[tex]x^2+6x+9=6\\x^2+6x+3=0[/tex]

We can solve the the quadratic equation by finding the discriminant.

[tex]x = \frac{-6+-\sqrt{6^2-4*1*3} }{2*1}[/tex]

[tex]x = \frac{-6+-\sqrt{36-12} }{2}[/tex]

[tex]x=\frac{-6+-2\sqrt{6} }{2}=-3+-\sqrt{6}[/tex]

Hence, the values of x are [tex]-3+\sqrt{6}[/tex] and [tex]-3-\sqrt{6}[/tex].

Discriminant

In arithmetic, a polynomial's discriminant is a function of the polynomial's coefficients.

Quadratic equation

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

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Given: A regular pentagonal prism with base edge 8cm and height 20 cm .

Find: wrap need to cover the box.

Explanation: for to find the length of wrap we need to find the area of regular pentagonal prism .

where a=base edge=8cm and h =height=20 cm

Final answer: the required answer is 1020 square centimeter.

Answer:

C. 1,020 [tex]cm^{2}[/tex]

Hope this helps!

Step-by-step explanation:

Given the inequality:

4m < 24

Let's solve for m.

To solve for m, divide both sides of the inequality by 4:

ANSWER:

m < 6

It is predicted that sales over time can be approximated by the function:

It is required to find the predicted sales in 15 years to the nearest whole number.

To do this, substitute t=15 into the given function:

Evaluate and round to the nearest whole number as required:

The sales in 15 years is about 3708.

Step 1

To change word problem to an inequality, you must take the word problem step by step and translate it into an inequality.

Step 2

Take the word problem step by step