Write as a decimal: 203% 0.203 2.03 20.3 203

Answer:

g(x) = 32x-7

Step-by-step explanation:

A vertical stretch is shown in an equation by multiplying the equation by a factor greater than 1.  Since we are stretching by a factor of 4, we multiply the equation by 4:

g(x) = 4(8x) = 32x

A vertical translation is performed by subtracting a value from a function.  To translate the function 7 units down, we will subtract 7 from the equation:

g(x) = 32x-7

The equation for g(x) = 32x - 7.

Given that,

Based on the above information, the calculation is as follows:

g(x) = 4(8x)

= 32x

Now here we subtract 7 from the equation.

So, it is  g(x) = 32x-7

Therefore we can conclude that the equation for g(x) = 32x - 7.

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Answer:

The population changed by 4.19%. The population shrank.

0.0419.

Step-by-step explanation:

We have been given that the population in Rochester, New York, was 219,773 people in 2000 and 210,565 people in 2010.

[tex]\text{Percent change}=\frac{\text{Final}-\text{Initial}}{\text{Initial}}\times 100[/tex]

[tex]\text{Percent change}=\frac{210,565-219,773}{219,773}\times 100[/tex]

[tex]\text{Percent change}=\frac{-9,208}{219,773}\times 100[/tex]

[tex]\text{Percent change}=-0.04189777\times 100[/tex]

[tex]\text{Percent change}=-4.189777\%[/tex]

[tex]\text{Percent change}\approx-4.19\%[/tex]

Therefore, the population changed by 4.19%.

Since the percent change is negative, therefore, the population decreased or shrank over the given period.

[tex]4.19\%=\frac{4.19}{100}=0.0419[/tex]

The number of squares with side length 1/4 inch that  would fit into a 1-square inch is 4

A square to a four-sided quadrilateral that has four equal sides. A square has four right angles. The sum of angles in a square add up to 360 degrees.

Area of a square = length²

Perimeter of a square = 4 x length

In order to determine how many squares would fit into the a 1 inch square, divide the length of the square by the 1/4

Number of squares = 1 ÷ 1 / 4

1 x 4 = 4 squares

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Answer: 29524

Step-by-step explanation:

Given geometric sequence : 1, 3, 9, …........................

First term of G.P. [tex]a = 1[/tex]

Second term of G.P.[tex]a_2=3[/tex]

Common ratio =[tex]r=\frac{a_2}{a}=\frac{3}{1}=3[/tex]

We know that the sum of the geometric sequence with n terms is given by :-

[tex]S=\frac{a(r^n-1)}{r-1}[/tex] for |r|>1

Substitute a = 1 , r =3 and n=10 , we get

[tex]S=\frac{1(3^(10)-1)}{3-1}\\\\=\frac{59049-1}{2}\\\\=-\frac{59048}{2}\\\\\Rightrrow\ S=29524[/tex]

By applying this formula and solving for the unknown coordinates, the coordinates of endpoint F are determined to be (6, 14).

The student is asking to find the coordinates of the other endpoint F of a line segment EF given that the midpoint M is (4,10) and one endpoint E is (2,6). To find the coordinates of F, we can use the midpoint formula which states that the midpoint's coordinates are the averages of the endpoints' coordinates:

Midpoint Formula

Mx = (Ex + Fx) / 2
My = (Ey + Fy) / 2

Knowing the coordinates of endpoint E (2, 6) and midpoint M (4, 10), we can set up two equations to solve for the coordinates of F.

Finding Fx

4 = (2 + Fx) / 2
=> Fx = 4 * 2 - 2
=> Fx = 6

Finding Fy

10 = (6 + Fy) / 2
=> Fy = 10 * 2 - 6
=> Fy = 14

Therefore, the coordinates of the other endpoint F are (6, 14).

Answer:

C. All real numbers.

Step-by-step explanation:

We have been given an image of a parabola. We are asked to find the domain of given parabola.

We know that domain of a function is all real values of x for which function has a defined value.

We know that domain of a quadratic function is all real numbers, therefore, option C is the correct choice.

Answer: R

Step-by-step explanation: The domain of a function is the set of all x-values of the function.

The x-values on a coordinate system are the left-and-right values and

we can see that the parabola is expanding infinitely to the left and

to the right so the domain of the function is all real numbers.

Although there is an all real numbers option, you can also represent

this idea using a capital R like I have done below.

The property of scaling or multiplying by a fraction is used to rename 5/6 to 10/12.

The property of multiplication used to rename 5/6 to 10/12 is the property of scaling or multiplying by a fraction. To rename a fraction, you can multiply both the numerator and denominator by the same number. In this case, we can multiply both 5 and 6 by 2 to get 10 and 12 respectively. Therefore, 5/6 = 10/12.

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16y = 164

 divide both sides by 16

y = 164 / 16 = 10.25

y = 10.25

Answer:

Step-by-step explanation:

16y=164

16/16=1    164/16= 10 1/4

164 divided by 16 is 10 1/4 when your dividing it step by step on paper.

Answer:

[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]

Step-by-step explanation:

we are given three equation of variable x, y and z.

-3x-4y-3z= -7  ------------- (1)

2x-6y+z=3     ------------- (2)

5x-2y+5z=9    ------------- (3)

Make the coefficient of z same in both equation.

Multiply equation (2) by 3

-3x - 4y - 3z = -7  

6x - 18y + 3z = 9

Add above equation to eliminate z

3x - 22y = 2 ---------------(4)

Make the coefficient of z same in both equation.

Multiply equation (2) by -5

-10x + 30y - 5z = -15  

5x - 2y + 5z = 9

Add above equation to eliminate z

-5x + 28y = -6 ---------------(5)

Make the coefficient of x same in both equation.

Multiply equation (4) by 5 and equation (5) by 3

15x - 110y = 10

-15x + 84y = -18

Add above equation to eliminate x

        -26y = -8

        [tex]y=\dfrac{4}{13}[/tex]

Substitute y into equation (5) to get x

So, [tex]-5x+28(\frac{4}{13})=-6[/tex]

[tex]x=\dfrac{38}{13}[/tex]

Substitute x and y into equation (1)

[tex]-3\cdot \frac{38}{13}-4\cdot \frac{4}{13}-3z=-7[/tex]

[tex]z=-1[/tex]

Solution:

[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]

To solve the problem, '419% of what number equals 33.52?', one sets up a proportion and solves for the unknown. The calculated result equates to approximately 7.99.

This question is asking for the base number where 419% of it equals 33.52.

Proportions play a crucial part in the calculation. Think of percentages as fractions with a denominator of 100. So, 419% can be written as 419/100. Now, let's set up a proportion to find our unknown number:

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The sample mean is calculated by adding up all the values in a sample and then dividing this total by the number of values in the sample.

When you calculate the sample mean, you divide the sum of the values in the sample by the number of values in that sample. For instance, if your sample contains the values 2, 4, and 6, you would add all these values together to get 12. Then, you would divide this total by 3, because there are three values in your sample. This would give you a sample mean of 4.

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Answer:

101.8182 pounds.

Step-by-step explanation:

He used 40 pounds of insecticide to cover 1760 square feet of lawn and 60 pounds to cover an additional 2640 square feet. So,

1760 + 2640 = 4400 square feet of lawn with 40+60 = 100 pounds of insecticide. Then, his whole lawn is 4480 square feet andn he already covered 4400, so he need to cover 4480 - 4400 = 80 square feet more.

Now, one of the data given we can do a proportion:

40 pounds to 1760 square feet = [tex]\frac{40pounds}{1760ft^2}[/tex]

x pounds to 80 square feet = [tex]\frac{xpounds}{80ft^2}[/tex]

[tex]\frac{40pounds}{1760ft^2}=\frac{xpounds}{80ft^2}[/tex]

[tex]xpounds*1760ft^2 = 80ft^2*40pounds[/tex]

[tex]xpounds = \frac{80ft^2*40pounds}{1760ft^2}[/tex]

[tex]xpounds = \frac{3200pounds}{1760}[/tex]

[tex]x = 1.8182 pounds.[/tex]

Then, to cover his whole lawn of 4480 square feet he needs 100+1.8182 = 101.8182 pounds of insecticide.

Answer:

b.

the time of year

Step-by-step explanation:

The question is to select a suitable option from the given four option to find out the factor that affects the price of room most

a) Time of day is immaterial as hotels charge 24 hours at whatever time they enter.

b) time of year -- this is a correct factor as prices of rooms depend upon demand and demand increases due to seasons, holidays, festivals, etc.

c) the gender of the person is irrelevant in determining the price of the room as equal prices for both genders.

d) nationality of the person cannot differentiate the prices charged

Hence the suitable option is

b.

the time of year

Answer:

The solution of the equation −4x−2y=−12  , 2x+4y=−12 are (6 , -6) .

Step-by-step explanation:

As given the equations are

−4x−2y = −12

Simplify the equation

-2(2x + y) = -12

2x + y = 6

Another equation

2x+4y=−12

2(x+2y) = −12

x + 2y = -6

Two equation becomes

2x + y = 6

x + 2y = -6

Multiply x + 2y = -6 by 2 and subtracted from 2x + y = 6 .

2x - 2x + y - 4y = 6 + 12

-3y = 18

[tex]y = \frac{-18}{3}[/tex]

y = -6

Putting the value of y in the equation

2x + -6 = 6

2x = 12

[tex]x = \frac{12}{2}[/tex]

x = 6

Therefore the solution of the equation −4x−2y=−12  , 2x+4y=−12 are (6 , -6) .

The average rate of change of the given function is 9.

Given that, a function f(x) = x²+9x+18, we need to find the average rate of change for the function given,

So, the average rate of change = f(b)-f(a) / b-a

Here, a and b are -10 and 10,

So, f(-10) = 100-90+18 = 28

f(10) = 100+90+18 = 208

So, the average rate of change = 208-28 / 10+10

= 180 / 20 = 9

Hence, the average rate of change of the given function is 9.

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The value of point R is -2.5 if point R is halfway between the integers on the number line; the answer is -2.5.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

The number line is shown in the picture.

Let the number is R which is halfway between the integers on the number line.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

R is between the integers -3 and -2:

R = (-3 + (-2))/2  = -5/2

R = -2.5

Thus, the value of point R is -2.5 if point R is halfway between the integers on the number line; the answer is -2.5.

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The inequality that represents the predicted possible percent of votes is 50 ≤ x ≤ 58

The margin of error (E) shows by how much the measured value can differ from the mean value.

Given that the probability of winning the election is 54% and there is a margin of error of 4%, hence:

Let x represent the predicted possible percent of votes.

x = 54% ± 4%

x = (54% - 4%, 54% + 4%)

x = (50%, 58%)

The inequality that represents the predicted possible percent of votes is 50 ≤ x ≤ 58

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The inequality representing the predicted possible percent of votes for candidate A is [tex]\( 50 \leq x \leq 58 \)[/tex].

The predicted possible percent of votes, x, for candidate A considering the margin of error can be represented as follows:

Given:

- Predicted percentage of votes for candidate A = 54%

- Margin of error = ±4%

The predicted range of percentages for candidate A can be expressed as:

[tex]\[ 54\% \pm 4\% \][/tex]

This translates to:

[tex]\[ 54\% - 4\% \leq x \leq 54\% + 4\% \][/tex]

Calculate the lower and upper bounds:

[tex]\[ 50\% \leq x \leq 58\% \][/tex]

Therefore, the inequality that represents the predicted possible percent of votes x for candidate A is [tex]\( \boxed{50 \leq x \leq 58} \)[/tex].

Complete question:- A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A?

50≤ x≤ 58

x≥ 50 or x≤ 58

x≥ 52 or x≤ 56

52≤ x≤ 56

Answer:

A

Step-by-step explanation:

I just took the test