Give a rule of the piecewise-defined function.

The volume of aggregate that she needs to build the patio is 13.18 ft^3

We know that the backyard is 14ft long, 6 feet wide and 4 inches deep.

Rememeber that:

1ft = 12 in

Then:

4 in = (4/12) ft = (1/3) ft

Then the volume of the backyard is:

V = (14ft)*(6ft)*(1/3 ft) = 28ft^3

Now we know that we have a mix of 4 parts aggregate to 4.5 parts loose cement that need to fill these 28 cubic feet.

Note that:

4 + 4.5 = 8.5

How many times we have 8.5 in 28?

28/8.5 = 3.294

Now for each of these we have 4 parts of aggregate, then the volume of aggregate that we need is:

4*3.294 ft^3 = 13.18 ft^3

The volume of aggregate that she needs to build the patio is 13.18 ft^3

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Answer: x=-3, x=3

Step-by-step explanation:

Answer:

4-[x]=1

-4.    -4

-[x]=-3

x=3

The total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6) has been found as  51 square units.

A graph is described as a mathematical representation of a network and it describes the relationship between lines and points.

The first step is to divide the figure is into two rectangles and a triangle.

we notice that the points B, C, E, and F will form a rectangle with base BC and height of 7 units.

We also notice that the  points A, D, and G form a rectangle with base AG and height 5 units.

we notice that  points C, D, and E form a triangle with base CE and height 4 units.

we notice that the  length of BC is 4 - 4 = 0, therefore  the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.

In conclusion, the total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6)  is 45 + 6 = 51 square units.

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The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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Answer:

  see below

Step-by-step explanation:

First of all, you want to find the data set the matches the extreme values of 5 and 35. That eliminates the 2nd and 4th choices.

Then you want to find the data set that has a median of 15. The first data set has a middle value (median) of 20, so that choice is eliminated.

The data set of the 3rd choice matches the box plot extremes, median, and quartile values.

Answer:

The third choice, (5, 6, 10, 12, 13, 15, 17, 25, 30, 35) would be your best answer.

Step-by-step explanation:

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.

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Answer:

31.42cm

Step-by-step explanation:

Answer. We know that C = πd. Since the diameter is 10cm, we know that C = π x 10cm = 31.42cm (to 2 decimal places).

Answer:

2

Step-by-step explanation:

3/4= 6/8 if you need 3/8 for one batch you made two batches. found it on brainly

Step-by-step explanation:

For example: Subtract 4x - 10y + 15z from 5x + 8y - 20z.

Step 1: Arrange the polynomials in standard form. In this example, it is already arranged.

Step 2: Place them horizontally.

(4x - 10y + 15z) - (5x + 8y - 20z)

Step 3: Change the sign of the second polynomial through the parentheses.

4x - 10y + 15z - 5x - 8y + 20z

Step 4: Arrange the like terms together.

4x - 5x - 10y - 8y + 15z + 20z

Step 5: Solve the equation

-x - 18y + 35z

Therefore, when we subtract 4x - 10y + 15z from 5x + 8y - 20z = -x - 18y + 35z.

Step-by-step explanation:

(a/b*b/c=1/2*3/4)(a/c=3/8)

Step-by-step explanation:

65 km / h = 65,000 m / 3600 s

what do we need to multiply 3600 with to get 3 ?

3600 × f = 3

f = 3/3600 = 1/1200

now, we need to multiply 65,000 by the same factor to get how many meters the car is driving in these 3 seconds :

65000 × 1/1200 = 65000/1200 = 54.16666666...

so, rounded, it travels 54 meters in 3 seconds.

Answer:

4.75 megabytes per second

Step-by-step explanation:

500-25 = 475

475 / 100 = 4.75

Answer:

$20

Step-by-step explanation:

Gym city fees are:

Sign up = 30

6 monthly sub = 6 x 25 = 150

Total fees = 30 + 150

FitnessExpress fees are:

Sign up = 20

6 monthly sub = 6 x 30 = 180

Total fees = 20 + 180 = 200

Therefore, the difference between the two is $20

9514 1404 393

Answer:

  2.4

Step-by-step explanation:

We can see that this is a 3-4-5 right triangle, so side AB is 5 units long.

The area of the triangle is ...

  A = 1/2bh = 1/2(3 units)(4 units) = 6 units

This is true also when side AB is the base and CD is the height.

 A = 1/2(AB)(CD)

  6 = 1/2(5 units)(CD) . . . . . substitute given information

  6/2.5 = CD = 2.4 . . . . . . . divide by the coefficient of CD

The length of side CD is 2.4 units.

__

In the attached, the height to vertex C is given on the bottom line.

4.5y

subtract 2.9y from 7.4y, and you get 4.5y

Answer:

\(\frac{5}{6}\)

Step-by-step explanation:

sin =opposite/hypotenuse

sinQ=5/6

From the given information it cannot be determined whether it is a relation or function.

In mathematics, a function is a relationship between two sets of elements, where each element in the first set (the domain) corresponds to a unique element in the second set (the range). In other words, a function takes an input from the domain and produces a unique output from the range.

In mathematics, a relation is a set of ordered pairs that describes a relationship between two sets of elements. The ordered pairs typically consist of one element from each set, and the relationship between the two elements is defined by some rule or condition.

To determine whether the relation is a function, we need to check whether each input (type of washing machine) has a unique output (amount of water used per load), or whether there are multiple outputs for some inputs.

If each type of washing machine has a unique amount of water used per load, then the relation is a function. If there are multiple amounts of water used per load for some types of washing machines, then the relation is not a function.

Without knowing the data that Keon recorded, we cannot determine whether the relation is a function. We would need to see the data and check whether there are any types of washing machines that have multiple amounts of water used per load recorded, or whether each type of washing machine has a unique amount of water used per load recorded.

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Answer:

My opinion Camilo Madrigal

Step-by-step explanation:

Because his gift is shapeshifting.

Answer: Isabela and dolores yes yes:)

Complete question is;

Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.

Claim: μ ≥ 8300,α= 0.10

Sample statistics: ¯x = 8000, s = 440, n = 24

a. What are the null and alternative hypotheses?

b. What is the value of the standardized test statistic? (Round to 2 decimal places as needed.)

c. What is the p-value? (Round to three decimal places as needed.)

d. Decide whether to reject or fail to reject the null hypothesis.

Answer:

A) Null hypothesis:H0: μ ≥ 8300

Alternative Hypothesis:Ha:μ < 8300

B) t = -3.34

C) p-value = 0.001

D) we will reject the null hypothesis

Step-by-step explanation:

A) We are told that the claim is: μ ≥ 8300. Thus, the null hypothesis would be the claim. So;

Null hypothesis:H0: μ ≥ 8300

Also, alternative hypothesis would be;

Alternative Hypothesis:Ha:μ < 8300

B)Formula for standardized test statistic with a t-test is;

t = (¯x - μ)/√(s/n)

Plugging in the relevant values, we have;

t = (8000 - 8300)/√(440/24)

t = -3.34

C) From online p-value from t-score calculator attached using t = -3.34, n = 24, significance level = 0.01, DF = 24 - 1 = 23 and a one - tailed test, we have;

p-value = 0.001421 ≈ 0.001

D) The p-value of 0.001 is less than the significance value of 0.01,thus we will reject the null hypothesis

The area of triangle YCX is given as follows:

G. 2 units squared.

The area of square WXYZ is 16, hence the side length is given as follows:

s² = 16

s = 4.

Considering the midpoints, we have that the sides of the right triangle are given as follows:

YC = CX = 4/2 = 2

Hence the area of the triangle is given as follows:

0.5 x 2 x 2 = 2 units squared.

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Answer: 1/2 a pound is more, because 1/2 a pound is 8 ounces

I hope this helped!

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Answer:

1/2 of a pound.

Step-by-step explanation:

Its because 16 ounces = 1 pound, and 16/2 = 8, which is bigger than 6.

Answer:

90% confidence interval is ( -149.114, -62.666   )

Step-by-step explanation:

Given the data in the question;

Sample 1                                Sample 2

x"₁ = 259.23                            x"₂ = 365.12

s₁  = 34.713                              s₂ = 48.297

n₁ = 5                                       n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

\(S_p^2\) = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

\(S_p^2\) = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

\(S_p^2\) = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [  4 + 9 ]

\(S_p^2\) = [ 4819.9692 + 20993.4 ] / [  13 ]

\(S_p^2\) = 25813.3692 / 13

\(S_p^2\) = 1985.64378

Now the Standard Error will be;

\(S_{x1-x2\) = √[ ( \(S_p^2\) / n₁ ) + ( \(S_p^2\) / n₂ ) ]

we substitute

\(S_{x1-x2\) = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

\(S_{x1-x2\) = √[ 397.128756 + 198.564378 ]

\(S_{x1-x2\) = √595.693134

\(S_{x1-x2\) = 24.4068

Critical Value = \(t_{\frac{\alpha }{2}, df\) = \(t_{0.05, df=13\) = 1.771  { t-table }

So,

Margin of Error E =  \(t_{\frac{\alpha }{2}, df\) × [ ( \(S_p^2\) / n₁ ) + ( \(S_p^2\) / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666   )

Answer:

I don't speak Spanish

Step-by-step explanation:

Given:

Two spheres have a scale factor ratio of 1:3. The smaller sphere has a surface area of 16ft. square.

Required:

Find the surface area of the larger sphere?

Explanation:

3/12 is equivalent to 1/4 because 1 x 3 = 3 and 4 x 3 = 12. 4/16 is equivalent to 1/4 because 1 x 3 = 4 and 4 x 3 = 16. and so on ... Equivalent fractions may look different, but when you reduce then to the lowest terms you will get the same value.

Answer:

y = 3/5x + -9

or y = 3/5x - 9

Step-by-step explanation:

Since you are already given the slope for this equation all you have to do is plug in the ordered pair in this equation: y = mx+b

Here is what this equation stands for:

y = the y in the order pair you are given, in this case it would be -6

m = This is the slope, sometimes you may not be given the slope so you would have to find it, but in this case, you are given it, the slope is 3/5

x = the x in the ordered pair you are given, in this case it would be 5

b = This is the y-intercept, you will mostly be solving for this most of the time

(5,-6)

(x, y)

y = mx+b (Use this Formula)

-6 = 3/5(5) +b (The numbers have been substituted within the formula)

-6 = 3+b (simplify the equation by multiplying the slope by the x)

-6-3 = b ( once simplified the left side of the equation, go to the right side, but remember when you do that you have to change the sign because you are eliminating 3 on the left side completely, "what you do on one side, do it to the other side")

-9 = b (solve)

y = 3/5x + -9 (plug in the slope and B(y-intercept) within the formula - y = mx+b, make sure that you are not plugging in x and y for this step)

I Hope This Helped You Understand this Problem Better/More!!! Stay Safe and Healthy!

Step-by-step explanation:

therefore, the correct option should be A.