If f(x) = 3x²-4 and g(x) = x+2, find (f - g)(x).
А. 3x3-8
B. 3x²-x-6
C. x-3x²-2
D. 3x²-x-2

Answer:

95% confidence interval for the percentage of students who change their major

(0.69881 , 0.86119)

Step-by-step explanation:

Step(i):-

Given that the sample size 'n' = 100

Given that the sample proprtion

                        p = 78% = 0.78

Level of significance =0.05

Critical value Z₀.₀₅ = 1.96

Step(ii):-

The 95% of confidence interval is determined by

\((p^{-} -Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p^{-} +Z_{0.05} \frac{\sqrt{p(1-p)} )}{\sqrt{n} })\)

\((0.78 - 1.96 \frac{\sqrt{0.78(1-0.78)} }{\sqrt{100} } , 0.78 +1.96 \frac{\sqrt{0.78(1-0.78} )}{\sqrt{100} })\)

(0.78 -  0.08119,0.78 + 0.08119 )

(0.69881 , 0.86119)

Final answer:-

95% confidence interval for the percentage of students who change their major

(0.69881 , 0.86119)

The correct option is (D) The subject would not receive treatment and could spread the disease.

The probability is 0.04

and, The unfavorable consequence of error is "The subject would not receive treatment and could spread the disease."

In mathematics, probability defines the occurrence of something. Or we can say that it defines the chance of something to be happen or occur.

Probability is the mathematical branch that studies and deal with the possible outcomes of some given events together or some set of event with the outcomes of distributions.

The minimum value of probability is 0 while the maximum value is 1 .

Suppose if there are some favorable outcomes whose probability we have to find out then the formula is :

\(prob ( fav \ outcome) = \frac{number \ of \ favorable \ outcome}{total \ number \ of \ outcomes}\)

In the given question :

total outcomes = 333 + 14 = 347

favorable outcome = 14

thus, probability = 14 / 347 = 0.04

and unfavorable consequence of error is "The subject would not receive treatment and could spread the disease."

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Hey there! I'm happy to help!

Let's call our number n. Here is the information we have.

n+5=5n

We subtract 5n from both sides.

n+5-5n=0

Combine like terms.

-4n+5=0

Subtract 5 from both sides.

-4n=-5

Divide both sides by -4.

n=5/4

Our number is 5/4 or 1 1/4. If you add 5 to 5/4, you get 6 1/4. If you multiply 5/4 by 5, you get 25/4 which is also 6 1/4.

Have a wonderful day! :D

The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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Answer:

x-5=18 because x would be the number with "5 less"  being the "-5."

Hoped I helped

mark me as brainliest

The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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Answer:

it's commutstive property but

-8.4 x 8.3

Answer:

3.1-3.9/7 can be the answer.

Step-by-step explanation:

this is because you asked between and not exactly in half. 3.5/7 would be halfway

A, the relation is not a function

in order for something to be a function, x (the input) can't repeat itself more than once

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

y

Step-by-step explanation:

Answer:

x>3

Step-by-step explanation:

The length of segment CD is approximately 28.84.

To calculate the length of segment CD, we need to use the properties of a tangent line and the given information.

In a circle, when a line is tangent to the circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle AEC is a right triangle.

Given that AE = 12 and EC = 8, we can use the Pythagorean theorem to find the length of AC, which is the hypotenuse of triangle AEC.

AC^2 = AE^2 + EC^2

AC^2 = 12^2 + 8^2

AC^2 = 144 + 64

AC^2 = 208

Taking the square root of both sides:

AC = √208

AC ≈ 14.42

Now, segment CD is a part of the diameter of the circle and passes through the center of the circle. Therefore, it is twice the length of the radius.

CD = 2 * AC

CD = 2 * 14.42

CD ≈ 28.84

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Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.

Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.

What is an Angle?

An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths

To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:

Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.

Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees

Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees

Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

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Step-by-step explanation:

So if you need to use 4/3 of a cheese block that is 1 1/3 of those cheese blocks so keep adding until you get to 6 blocks of cheese or just about 6 blocks

Answer:

the answer is y=8x+42

Step-by-step explanation:

y-y=m(x-x¹)

y-2=8(x-(-5))

y-2=8x+40

+2 +2

y=8x+42

The selection can be made in 15 different ways, taking into account the distinct combinations of a boy and a girl from the given group of 5 boys and 3 girls.

To determine the number of ways a boy and a girl can be selected from a group of 5 boys and 3 girls to attend a conference, we can use the concept of combinations.

The number of ways to choose one boy from 5 boys is 5C1, which is equal to 5. Similarly, the number of ways to choose one girl from 3 girls is 3C1, which is equal to 3.

To select one boy and one girl, we need to multiply the number of ways to choose a boy and a girl together. Using the multiplication principle, we multiply the number of choices for each category: 5C1 * 3C1 = 5 * 3 = 15.

Therefore, there are 15 ways to select a boy and a girl from the given group to attend the conference.

Each combination represents a unique pair consisting of one boy and one girl. For example, if the boys are labeled as B1, B2, B3, B4, and B5, and the girls are labeled as G1, G2, and G3, the possible pairs could be (B1, G1), (B1, G2), (B1, G3), (B2, G1), (B2, G2), and so on, up to (B5, G3).

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Answer:

To investigate the different sizes of ponds and their effects on the garden, I followed these steps:

1. I drew several sizes of ponds on a grid paper, using the given dimensions of 18 ft2, 24 ft2, and 30 ft2. I made sure that the length and width of each pond were whole numbers. I also drew borders around the ponds to represent the tiles needed for each pond. Here is an example of how I drew a 24 ft2 pond:

| | | | | | | | | | |

| | | | | | | | | | |

|X|X|X|X|X|X|X|X|X|X|

|X|O|O|O|O|O|O|O|O|X|

|X|O|O|O|O|O|O|O|O|X|

|X|O|O|O|O|O|O|O|O|X|

|X|X|X|X|X|X|X|X|X|X|

In this drawing, X represents a tile and O represents water.

2. I recorded the number of tiles needed for each pond in a table, as well as the length and width of each pond. Here is the table I made:

Pond size (ft2) Length (ft) Width (ft) Number of tiles

18 6 3 22

24 6 4 28

30 6 5 34

3. I looked for patterns in the table and noticed that the number of tiles increased by 6 for every increase of 1 ft in width. I also noticed that the number of tiles was always equal to twice the length plus twice the width minus four.

4. I came up with a numerical expression that relates the length and width to the number of tiles needed. The expression is:

Number of tiles = 2 x Length + 2 x Width - 4

This expression works for any pond size with whole number dimensions.

By following these steps, I was able to compare different pond sizes and their tile requirements. I hope this helps you decide on the best size for your pond and garden.

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Answer:

4 1/2

Step-by-step explanation:Because 2x2 =4 and 2x1/4 = 1/2 so it is 4 1/2

Answer:C. [12.35+(2.25x3)-2]÷3

The diagram is showing the length of each line segment.

• NM has length 110 + 4x

• ML has length x + 103 (this is the one you have to find)

• LK has length 70

• NK has length x + 243

The segment NK has length equal to the sum of the lengths of NM, ML, and LK. So we have

x + 243 = (110 + 4x) + (x + 103) + 70

Solve this equation for x :

x + 243 = (110 + 103 + 70) + (4x + x)

x + 243 = 283 + 5x

x - 5x = 283 - 243

-4x = 40

x = 40/(-4)

x = -10

Now solve for x + 103 by adding 103 to this result:

x + 103 = -10 + 103 = 93

So ML has length 93.

The percentage of women with weights that are within the limits is:

60.93%

Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:

z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74

z-score for upper limit = (217 - 168.7) / 48.8 = 0.99

Next, we can use a z-table to find the corresponding probabilities for these z-scores:

Probability for lower limit = 0.2296

Probability for upper limit = 0.8389

Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093

Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.

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We know, the probability of an event = Favorable outcomes / Total outcomes.

In a case of two dices,

Total outcomes = 6 × 6 = 36

A.T. Q favorable outcome is a sum of 6,

Ways of obtaining a sum of 6

(1,5), (5,1), (2,4),(4,2) and (3,3). Total 5 ways in which 6 can be obtained using two dices.

Therefore, required probability (P),

P = 5/ 36

Answer:

a. The present value of these receivables is $42,123.64

b. The total value at the end of 10 years is $69,257.02

c. The present value of these payments is $10,059.37

Step-by-step explanation:

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Answer:

x=1 or x=5

Step-by-step explanation:

x2−6x+5=0

Step 1: Factor left side of equation.

(x−1)(x−5)=0

Step 2: Set factors equal to 0.

x=1 or x=5

Answer:

[-0.2  0.4]

[0.8   -0.6]

Answer:

A .

length : 2x + 2 + x - 4 + x-2

        =  2x + 2 + - 4 + x-2

         = 2x + x - 4 + x - 2

         = 4x -6

width :  x - 2 + x

         = 2x -2

B.

to find the perimeter

perimeter of rectangle = 2 ( l + b)

                                      = 2  (4x -6 + 2x -2)

                                      = 2 ( 6x - 8)

                                      = 12x - 16

perimeter of Marlene's house in simplest form is 12x - 16

C.

perimeter = 142  finding the value of x ..

142 = 12x - 16

12x = 142 + 16

12x = 158

x = 158/12

x = 13.16

22.

area of living room = length × breadth

                               = 2x + 2 ×x

                                = 2 (13.16) + 2 × 13.16 (distributive property used)

                                = 26.32 + 2 × 13.16

                                = 28.32 × 13.16

                                = 372.6912

area of her living room = 372.6912

23. to find the length and width of Marlene's living room

length = 2x + 2

            = 2 (13.16) + 2

            = 26.32 + 2

            = 28.32

Width = x

          = 13.16

A .

The actual length of her living room is  28.32

The actual width of her living room is 13.16

B.

The actual area of Marlene's Living room is 372.6912 feet (given above) using actual dimensions

24.

Actual area of living room = length × breadth

                                = 2x + 2 ×x

                                = 2 (13.16) + 2 × 13.16 (distributive property used)

                                = 26.32 + 2 × 13.16

                               = 28.32 × 13.16

                                = 372.6912

Actual area of her living room = 372.6912

25.

Yes the answers to Question 23B and Qestions 24 are same .

We can conclude by saying that the x value doesn't change

The  quotient of 302 ÷ (9.1 x \(10^4)\) in scientific notation is approximately 3.31868131868 x \(10^1\)

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x\(10^1\)

Therefore, the quotient of 302 ÷ (9.1 x \(10^4\)) in scientific notation is approximately 3.31868131868 x\(10^1\)

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