Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B
Explain the expression written in Part A. Include the final product and how it is shown with the model.

g( x ) = 2x² + 12x + 22 is the standard form of the the function g( x ) = 2( x + 3 )² + 4.

Polynomials in standard forms are written in a way that arrange the terms in descending order.

Given the data in the question.

g( x ) = 2( x + 3 )² + 4

First, we expand; ( x + 3 )² → ( x + 3 )( x + 3 )

g( x ) = 2( ( x + 3 )( x + 3 ) ) + 4

Using FOIL Method

g( x ) = 2( x² + 3x + 3x + 9 ) + 4

g( x ) = 2( x² + 6x + 9 ) + 4

Apply distributive property

g( x ) = 2( x² + 6x + 9 ) + 4

g( x ) = ( 2x² + 12x + 18 ) + 4

Add 18 and 4

g( x ) = 2x² + 12x + 18 + 4

g( x ) = 2x² + 12x + 22

Therefore, the function in standard form is g( x ) = 2x² + 12x + 22

Learn more about functions here: brainly.com/question/2541698

#SPJ1

Considering the situation described, it is found that:

a) The numeric values of the piecewise function are as follows:

b) The new piece-wise function is:

c) The new piece-wise function is:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

In this problem, the rule is one for times up to 40 hours, and another for times greater than 40 hours, hence the numeric values are given as follows:

For item b, the new reference is of 38 hours, hence the function is:

For item c, the new hourly wage is of 12 hours, hence the rule is:

More can be learned about piecewise functions at brainly.com/question/19358926

#SPJ1

Remember that the slope-intercept equation of the line is:

where 'm' is the slope and b is the y-intercept.

In this case, we have the following:

therefore,, the slope is m = 2

Answer:

D

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = πd ( d is the diameter ) , then

C = π × 8 = 8π

Answer: C=2pir or diameter(pi)

Step-by-step explanation:

The diameter of a circle stretches from one side to the other, the Radius (r) goes from the center to the side meaning it is twice the diameter.

To solve this just half the diameter and insert it into the first equation or just plug it in for diameter.

The answer is

D. 8pi

Answer:

3.456 × 10^11

Step-by-step explanation:

= 3.456 × 10^11

scientific notation

= 3.456e11

scientific e notation

= 345.6 × 10^9

engineering notation

billion; prefix giga- (G)

= 3.456 × 10^11

standard form

11

Order of Magnitude

for scientific and standard forms

= 345600000000

(real number)

= three hundred forty-five billion six hundred million

word form

I hope this helps!! :D

In order to calculate the total spending in the town each year, first, multiply by the 70% that is spent within the town,

Also, multiply by 70% of the amount people will spend after they receive it in town,

Answer:

The total spending in the town each year is $1,960,000

Answer:

Step-by-step explanation:

what 15/60 as a decimal?

so

15 : 60 =

0.25   (1/4 as a fraction)

A.  P(BB) = P( GG) ,P(BG), P(GB) .1/4 the sample space and probability measure that describes the genders of the two children in the order in which they are born.

B.    = 1/2 is the probability that the other child is a boy.

C.   1/2 is the probability that the older child we have not yet seen is a boy.

A. sample space s. {BB,GG,BG,GB}

    P(BB) = P( GG) ,P(BG), P(GB) .1/4

B. P(other child is boy / at least one girl

therefore P(A/B) = P(A∩B)/P(B)      ( Additional probe)

P(B) = P (at least one girl)

      = P (GG)+P(BG)+P(GB)

      = 1/4+1/4+1/4

      = 3/4

P (A∩B) = P (One boy and one girl)

             = P (BG)+P(GB)

             = 1/4+ 1/4

            = 1/2

Therefore, P(A/B) = [tex]\frac{\frac{1}{2} }{\frac{3}{4} }[/tex] = 2/3

C. P (older child is a boy/ younger child is a girl)

   P [tex]\frac{older child\ is a\ boy}{youngerchild is a girl}[/tex]

P(BG)/P (BG)+ P (GG) = 1/4/1/4+1/4 = 1/2

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

To learn more about probability, refer;

https://brainly.com/question/14210034

#SPJ4

In linear equation, 3 number of cups will be needed to marinade 4 pounds of chicken for grill.

What are a definition and an example of a linear equation?

Here we have the data from the question:-

Marcy will use 6 fluid ounces of lemon-garlic marinade for every pound of chicken.

Marcy plans to grill 4 pounds of chicken.

So total marinade required will be:-

Total marinade  =6x4=24 ounces

Now we know that the conversion:-

1 fluid Ounce = 0.125 Cup

24 fluid ounce =0.125 Cup

Hence 3 number of cups will be needed to marinade 4 pounds of chicken for grill.

Learn more about linear equation

brainly.com/question/11897796

#SPJ10

Answer:

y=65/100x+2.5

Step-by-step explanation:

Equation: w - 12 = 14

Answer: 26

Step-by-step explanation:

Lost 12, left with 14.

Let W be water balloons before the trip.
w - 12 = 14

14 + 12 = 26

Proof:

26 - 12 = 14

The multiplication expression is given as L × w

The expression is given as N = r+ g + w + b

The final product of the expression is 200 boxes

Note that the formula determining the area of a rectangle is expressed as;

Area = lw

Where;

The area of the figure can be calculated by multiplying the length and the width and then addition of the number of boxes.

This is given as;

10( 4 + 5 + 4 + 7)

Also

L × w =  r + g + w + b

The expression L×w is a multiplication expression.

Total number of boxes vertically is the length = 20

Total number of boxes horizontally is the width = 10

Total area = L×w = 20 × 10 = 200

Then,

N= r + g + w + b

We have;

L×B =  3r + w

Hence, a multiplication expression is expression having variables that are multiplied.

Learn more about algebraic expressions here:

https://brainly.com/question/4541471

#SPJ1

The equation of the line in standard form is -1/2x + y = 1 or y = 1/2x + 1 in slope-intercept form.

(note: none of the option given is correct).

In standard form, the equation of a line can be expressed as Ax + By = C, where x and y are coordinate of a point on the line, A, B, and C are integers.

This equation can be rewritten in slope-intercept form as y = mx + b, where b is the y-intercept and m is the slope.

Given:

Substitute m = 1/2, x = 4, and y = 3 into y = mx + b to find b:

3 = 1/2(4) + b

3 = 2 + b

3 - 2 = b

1 = b

b = 1

Write the equation by substituting b = 1 and m = 1/2 into y = mx + b:

y = 1/2x + 1

Rewrite in standard form

- 1/2x + y = 1

Thus, none of the options is correct, The equation is: y = 1/2x + 1 in slope-intercept form or - 1/2x + y = 1 in standard form.

Learn more about equation of a line on:

https://brainly.com/question/13763238

#SPJ1

The chances that radio transmissions from Earth or messages sent on distant space probes will ever be received by living beings are very low.

In radio transmission, a radio transmitter's antenna couples electromagnetic energy into the atmosphere or other open space. Electromagnetic radio waves are caught by a receiving antenna during radio reception and coupled into a receiver for detection.

Radio waves have a low frequency, which limits their ability to deliver large amounts of data at once.

There are extremely slim odds that radio signals from Earth or messages placed on far-off space probes will ever be received by living things, it is acceptable to the state. Remember that some scientists have held this belief about the existence of extraterrestrial life for years without any convincing evidence.

To learn more about radio transmission refer to:

https://brainly.com/question/13033832

#SPJ4

The error term, which refers to the sum of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.

Y=αX+βρ+ϵ

where:

α,β=Constant parameters

X,ρ=Independent variables

ϵ=Error term

To Learn more About error term refer to:

https://brainly.com/question/8050273

#SPJ1

The volume of the cube with the shortest possible side lengths is 216 cubic inches.

If a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths, then the side lengths of the cube must be equal to the diameter of the sphere.

side length of cube = diameter of sphere

side length of cube = 2 x radius of sphere

side length of cube = 2 x 3 inches

side length of cube = 6 inches

The volume of the cube can be calculated using the formula below.

V = s³

where V = volume and s = side length of cube

V = (6 inches)³

V = 216 cubic inches

Learn more about volume of cube here: https://brainly.com/question/8738162

#SPJ4

Answer: B=30

Step-by-step explanation:

because of corresponding angles

Hope this helps! have a great day!

sorry also if you can could you please give a brainliest it would help a lot

the diameter of a circle is 20

The radius of circle is the half of the diameter of the circle :

Radius = Diamter/2

In the given question , we have Diameter = 20

So,

Radius = 20/2

Radius = 10

The expression for the radius 'r' of the circle is express as :

Substitute the value of Radius r = 10 in the expression of the area of circle:

Area of the circle is 314

Answer : 314 unit square.

Let's begin by identifying key information given to us:

A is a 3 x 2 matrix

B is a 2 x 3 matrix

AB is the product of 3 x 2 matrix & 2 x 3 matrix. We obtain a 3 x 3 matrix

Therefore, the size of the product of A & B (that is AB) is a 3 x 3 matrix whenever these products exist

Answer:

Step-by-step explanation:

The perimeter of the given polygon rounded to the nearest tenth is; 24.7

What is the perimeter of the Polygon?

The given polygon as we can see has 10 sides.

Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.

Thus, the other two angles will be; (180 - 36)/2 = 72° each

Using sine rule, we can find the length of a side of the polygon as;

x/sin 36 = 4/sin 72

x = (4 * sin 36)/sin 72

x = 2.472

Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7

Answer: 1320 ways.

Step-by-step explanation:

For this problem you should use the formula for variations in combinatorics. You use this when choosing a few objects from a group in which the order of the objects is of importance:

[tex]P^{12} _{3}=\frac{12!}{(12-3)!}=\frac{12 \cdot 11\cdot 10\cdot ...\cdot 1}{9 \cdot 8 \cdot ... \cdot 1} = 12 \cdot 11 \cdot 10 = 1320[/tex]

where ! stands for factorial.

Answer:

Step-by-step explanation:

yes it does

Answer:

70

Step-by-step explanation:

Proportional means in a ratio.

Picking any L/W from the table works. Set that equal to 42/W.

[tex]\frac{6}{10} =\frac{42}{W}[/tex]

Solve for W.

6W = 42 * 10

6W=420

W=70

Since the ages of students at a university are normally distributed with a mean of 21, the percentage of the student body that is at least 21 years old is: 50%.

A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which indicate that all data near the mean have a higher frequency than the data that are far from the mean.

For all normal distributions, the mean is always located at the center with 50 percent (50%) or 0.5 of the distribution to either side, which is right or left of the distribution.

In this context, the percentage of student body that is at least 21 years old is represented by the percentage to the left of the normal distribution, which is 50 percent (50%):

P(x ≤ 21) = 50%

P(x ≤ 21) = 50/100

P(x ≤ 21) = 0.5.

Read more on normal distribution here: brainly.com/question/27068375

#SPJ1

Answer:

Explanation: We need to find the answer to the inequality

Solution:

Graph:

The solution as found through solving inequality and demonstrated in the graph is

Answer:

$754.92

Step-by-step explanation:

699.00 plus 8% of 699.00 is 754.92

Notice that the intersection between both functions on the positive values of x is near the line x=2. From the provided options, the closest to that value is 1.7

Then, the positive solution to f(x)=g(x) is closest to:

The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Steel rods are produced by a firm. The lengths of the steel rods have a mean of 140.9 cm and a standard deviation of 1 cm, and they are regularly distributed. 22 steel rods are packaged together for shipping. determine the likelihood that the average length of a bundle of steel rods chosen at random is less than 140.7 cm.

mean is N (M) (109,1.6)

Looking for P(M 108.7) to P(z ???) conversion utilizing N(0,1) z-statistic transformation

P(z [M - population mean]/[SD/square root(sample size)]) = P(z [108.7-109)/[1.6/sqrt(27)] = P(z -0.974] = 0.165.

To learn more about Probability distribution refer to:

https://brainly.com/question/28021875

#SPJ4

Answer:

8x - 4 = 60 (alternate angles, parallel lines a and b)

8x = 64

x = 8