The graph of Fx), shown below, has the same shape as the graph of
G(x) = x, but it is shifted up 1 unit. What is its equation?
5+
F(x) =

Answer: 15cm and 5cm

Step-by-step explanation:

A rectangle's area is the product of the length and width

Given length x and width y, 2x+2y = 40 and x*y = 75.

Verifying my answer:

2(15)+2(5) = 40

30+10 = 40

40 = 40

15*5 = 75

75= 75

This is a week late so I hope this helped.

The length and the width of the rectangle​ are 15cm and 5cm respectively

The given parameters are:

Area (A) = 75

Perimeter (P) = 40

The area of a rectangle is LW, while the perimeter is 2(L + W)

So, we have:

LW = 75

2(L + W) = 40

Divide by 2

L + W = 20

Make L the subject

L = 20 - W

Substitute L = 20 - W in LW = 75

(20 - W)W = 75

Expand

20W - W^2 = 75

Rewrite as:

W^2 - 20W + 75 = 0

Expand

W^2 - 15W - 5W + 75 = 0

Factorize

(W - 15)(W -5) = 0

Split

W - 15 = 0 or W - 5 = 0

Solve for W

W = 15 or W = 5

Recall that:

L= 20 - W

So, we have

L = 20 - 15 or L = 20 - 5

This gives

L = 5 or L = 15

Hence, the length and the width of the rectangle​ are 15cm and 5cm respectively

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(c) range, (d) variance, (e) standard deviation and (f) interquartile range measure variability.

Range, The range is the difference between the largest and smallest values in a dataset, indicating how spread out the data are.

Variance, The variance measures how far a set of numbers is spread out from their average. It provides a measure of how much the individual data points deviate from the mean.

Standard deviation, The standard deviation is the square root of the variance and is also a measure of how much the individual data points deviate from the mean. It is a widely used measure of variability, particularly in statistical analysis.

Interquartile range, The interquartile range (IQR) is the difference between the third and first quartiles of a dataset. It gives an idea of the spread of the middle 50% of the data and can help identify outliers.

The mean and median are measures of central tendency and do not directly measure variability.

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Answer:

\(A_{L} =125 in^{2}\)

Step-by-step explanation:

Let's break down the pyramid in different bidimensional figures. As you can see in the image, the pyramid has 5 total sides: 4 of them are triangles and 1 is a square (the bottom). Therefore, the total area of this pyramid is given by the area of 4 triangles of base 5 in and height 10 in, and a square whose sides measure 5 in.

1. Write an expression and find the area of all triangles.

We already know the formula for the area of a triangle: \(A=\frac{b*h}{2}\), where b is the measure of the base of the triangle, and h is the height is the triangle. We have 4 triangles, therefore, let's multiply this formula by 4 and calculate.

\(A=4*(\frac{b*h}{2})=\\ \\ \\A=4*(\frac{(5)(10)}{2})=\\ \\A=4*(\frac{50}{2})=\\ \\A=4*(25)=\\ \\A=100\)

2. Find the area of the bottom side.

The bottom side is a square whose whose sides measure 5 in. Hence, it's area is:

\(A=a^{2}\), where a is the length of one side. Then:

\(A=(5)^{2}\\ \\A=25\)

3. Add up all the areas to get the total alteral area of this pyramid.

\(A_{L} =100+25=125 in^{2}\)

Answer:

pt=%(whole)

x=1.6(65)

x=104.00

Step-by-step explanation:

or

x  =  160

65    100

160(65)=10400 divided by 100 equals 140

The slope of the line on the graph will be a negative one. Then the correct option is A.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,

m = (- 2 - 2) / (2 + 2)

m = - 4 / 4

m = - 1

The slope of the line on the graph will be a negative one. Then the correct option is A.

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The complete question is attached below.

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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Step-by-step explanation:

l = length

w = width

l = 2w + 5

l × w = 63

using the identity of the first equation in the second :

(2w + 5) × w = 63

2w² + 5w = 63

2w² + 5w - 63 = 0

the general solution to such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = w

a = 2

b = 5

c = -63

w = (-5 ± sqrt(5² - 4×2×-63))/(2×2) =

= (-5 ± sqrt(25 + 504))/4 = (-5 ± sqrt(529))/4 =

= (-5 ± 23)/4

w1 = (-5 + 23)/4 = 18/4 = 4.5 ft

we = (-5 - 23)/4 = -28/4 = -7

a negative Stilton does not make any sense for a side length, so, the only valid solution is w = 4.5 ft.

l = 2w + 5 = 2×4.5 + 5 = 9 + 5 = 14 ft

so,

the length = 14 ft

the width = 4.5 ft

Armed force and other for Henderson high school is greater than

Johnson High School.

The mode for each school is college.

Options F and G are the correct answer.

We have,

The number of students in Henderson High School.

Work = 96

College = 114

Armed forced = 48

Other = 42

The number of students in Johnson High School.

Work = 30

College = 40

Armed forced = 15

Other = 15

From the information,

The number of students in Work for Henderson High School is greater than Johnson High School.

Now,

Henderson High School:

Armed force and other = 48 + 42 = 90

Mode = college

Johnson High School.

Armed force and other = 15 + 15 = 30

Mode = college

Thus,

Armed force and other for Henderson high school is greater than

Johnson High School.

The mode for each school is college.

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the graph of the equation y = 2 x - 2 is being obtained.

We are given the equation:

y = 2 x - 2

We need to make the graph of the equation.

We will first find some points on this equation:

x              y

0             -2

1               0

2              2

3              4

4              6

5              8

Now, we will plot these points on the graph and join them with a dark line to obtain the graph of the equation y = 2 x - 2.

Therefore, the graph of the equation y = 2 x - 2 is being obtained.

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Answer:

surely it's 200 marbles bc 2/4 is equal to 1/2 and if u then half 400 you get 200

Step-by-step explanation:

Answer:

200 marbles

Step-by-step explanation:

She starts with 400 marbles.

She gives away 2/4 of them

How many does she have left?

How can we simplify this?

Well, 2/4. It makes the problem seem longer and more complicated then it really is. 2/4 is the same as 1/2.

Now what's one half of 400?

200!

You could subtract the 200 from the 400 to officially see how much he has left, but knowing that 200 is half of 400, there will still be 200 left over.

If you ever need more help, don't be afraid to reach out! I hope this helps!

Answer:

Option 3: -2

Step-by-step explanation:

The slope of the graph is negative, and the only option with a negative term for the slope is -2.

So the slope of the graph is -2.

Answer:

The calculated χ² = 21.455       falls in the critical region χ² ≥  7.815  so we reject the null hypothesis that the type of hard drive and the store where the computers were bought are dependent and accept the claim the type of hard drive and the store where the computers were bought are independent.

Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0: the type of hard drive and the store where the computers were bought are dependent

against the claim

Ha: the type of hard drive and the store where the computers were bought are independent

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency

which has an approximate chi square distribution with ( 4-1) (2-1)=  3 d.f

4) Computations:

Using the calculator we summarize the results as

Under H0 , the observed frequencies are :

Observed         Expected  E        χ²= (O-E)²/E

13                          (23.58)            [4.75]                

11                           (10.63)             [0.013]                  

19                          (14.69)              [1.264]

9                            (3.09)              [11.282]

109                       (98.42)              [1.138]

44                          (44.37)            [0.003]

57                           (61.31)               [0.303]

7                             (12.91)               [2.703]                            

∑                                                            21.455        

5) Conclusion:

The calculated χ² = 21.455       falls in the critical region χ² ≥  7.815  so we reject the null hypothesis that the type of hard drive and the store where the computers were bought are dependent and accept the claim the type of hard drive and the store where the computers were bought are independent.

The p-value is .000085.

The result is significant at p < .05 meaning the claim is accepted.

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

School related questions please

Step-by-step explanation:

And thanks for telling me

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

A. Margin of error=0.0346

B. Confidence interval=0.4854 to 0.5546

Step-by-step explanation:

A. Computation the margin of error

First step is to calculate the Confidence level using this formula

Confidence level= 1 -α

Where,

α=0.95

Let plug in the formula

Confidence level= 1-0.95

Confidence level= 0.05

Second step is to find Z using this formula

Zα/2

Let plug in the formula

Z= 0.05/2

Z=0.025

Third step is to find the Z score of Z=0.025

Zα/2=1.96

Now let calculate the margin of error using this formula

Margin of error=Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Margin of error=1.96√0.52(1-0.52)/800

Margin of error=1.96√0.52(0.48)/800

Margin of error=1.96√0.2496/800

Margin of error=1.96√0.000312

Margin of error=0.0346

Therefore Margin of error will be 0.0346

B. Computation for the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009

Computation for the boundaries of confidence interval

Using this formula

p- Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52-1.96√0.52(1-0.52)/800

Confidence interval=0.52-1.96√0.52(0.48)/800

Confidence interval=0.52-1.96√0.2496/800

Confidence interval=-0.52-1.96√0.000312

Confidence interval=0.4854

Computation for the boundaries of confidence interval

Using this formula

p+ Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52+1.96√0.52(1-0.52)/800

Confidence interval=0.52+1.96√0.52(0.48)/800

Confidence interval=0.52+1.96√0.2496/800

Confidence interval=-0.52+1.96√0.000312

Confidence interval=0.5546

Therefore the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009 is 0.4854 to 0.5546

The domain and range of the function in interval notation are (-∞, ∞) and [-5, ∞) respectively. Option D is correct.

The given function is y = (x+3)^2 - 5.

The domain of the function is all real numbers, since any value of x can be plugged into the function.

To find the range of the function, we can consider the vertex of the parabola, which is (-3,-5) since the coefficient of x^2 is positive. The lowest value of the function occurs at the vertex, which is -5. Therefore, the range of the function is y ≥ -5, meaning that the function can output any value greater than or equal to -5.

Therefore, the domain of the function is all real numbers and the range of the function is y ≥ -5.

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Angie' s grandma drive 376 miles in each day.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The two cities are 752 travel miles apart.

And, It take 12 hours to drive that far.

Now,

Since, Angie' s grandma want to do the drive in two day.

So, The distance cover by Angie' s grandma in each day is,

= 752 / 2

= 376 miles

Thus, Angie' s grandma drive 376 miles in each day.

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Answer:

\(33\) times

Step-by-step explanation:

Distance between Earth and the sun \((D)\) = 9 × \(10^{7}\) miles = \(90,000,000\) miles

Distance between Neptune and the sun \((d)\) = 3 × \(10^{9}\) miles = \(3,000,000,000\) miles

Find \(\frac{d}{D}\).

\(\frac{d}{D}=\frac{3,000,000,000}{90,000,000} =33.3\) ≈ \(33\)

Therefore,

Neptune is approximately \(33\) times farther from the sun than earth

Answer:

180

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is mable

Answer:4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Answer:

third angle = 180-4m

Step-by-step explanation:

m+3m + third angle =180

so third angle = 180-4m

Answer:

she needs 15/6 or 2 3/6 ir 2 1/2 cups of sugar

Step-by-step explanation:

1 2/3=5/3 5/3+5/6 10/6+5/6

Answer:5/6 cup of sugar?

Step-by-step explanation:

Usually sugar isn’t measured in sixths but mathematically it would be 1 2/3 divided by 2 which would be 5/6 and that can’t really be converted into standard baking measurements?

Answer:

x = 5

Step-by-step explanation:

We know that AB = 2x - 3 and AB = 7, therefore:

2x - 3 = 7

2x - 3 + 3 = 7 + 3

2x = 10

2x / 2 = 10 / 2

x = 5

The answer that correctly fills the missing portions is option A.

The full sentence is: When the Bureau of Labor Statistics (BLS) calculates an increasing Consumer Price Index (CPI); the Federal Reserve (FED) may choose to Quantitative Easing.

Quantitative easing is a monetary policy operation in which a central bank buys government bonds or other financial assets to infuse monetary reserves into the economy in order to encourage economic activity.

The goal of QE is to level the playing field in order to make spending and investing money more enticing and accessible to people. Lower interest rates may improve the possibility that company and civilian borrowers will borrow to make purchases, promoting economic activity.

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Full Question:

When the ___ calculates an increasing ___ ; the ___ may choose to decrease______.

A) BLS, CPI. FED, QE

B) OECD, QE, BLS, CPI

C) BEA, GDP, BLS, CPI

D) BEA, CPI, OECD, GDP

Answer:

2!

Step-by-step explanation:

hope this helps! will appreciate brainliest!