Given f = <4, -3> and g = <-2, 1>, what is f - 2g ?<2, -2><8, -5><6, -4><0, -1>

The inverse of the function f(x) = x + 4 is given as f⁻¹(x) = x - 4

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, the function given is f(x) = x + 4;

We can find the inverse of the function as;

y = x + 4;

Let's switch the variables by replacing x as y and y as x;

x = y + 4

Solving for y;

y = x - 4

f⁻¹(x) = x - 4

The graph of the function is attached below

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Answer:

\(r=4.38\)

Step-by-step explanation:

Step 1: Arrange the equation so that you are calculating rate (divide both sides by t)

\(\frac{d}{t} = \frac{rt}{t}\)

\(t\) cancels out on the right side.

Step 2: Substitute in the numerals

\(r=\frac{d}{t}\)

\(r=\frac{5.7}{1.3}\)

Step 3: Divide

\(r=4.38\) \(mph\)

There's your answer!

Hope this helps you!

(7x + (3)/(4))^(2)-(x-1)

784

x

2

+

152

x

+

25

16

Answer:

x+6=40

Subtract 6

x=34

Answer:

n + 6 = 40

n = 34

Step-by-step explanation:

Sum of a number and 6. That means you got to add n and 6.

'is' means you need to put an equal sign.

n + 6 = 40

Now, lets find what n is.

Isolate the variable by subtracting 6 from both sides.

n = 34

The rate at which the depth of the liquid is increasing when it reaches one-third of the height of the bowl is (7/3)π cm³/s.

To ascertain the rate at which the liquid's depth rises, let's find the derivative of the depth function with respect to time.

Let;

The rate of change of the volume of the liquid with respect to time is constant and equal to 7π cm³/s.

To determine the height of the bowl, we can evaluate the curve y = [-4 / (8 - x)] - 1 when x = 4 and y = 7.6 and then find the absolute difference between the values.

h = |[-4 / (8 - 4)] - 1 - [-4 / (8 - 7.6)] - 1|

Let's calculate the rate at which the depth rises when it reaches one-third of the bowl's height.

D = depth of bowl

Using this relationship from the question given;

D = (1/3) * h

In order to determine the rate at which D will change with respect to time, let's differentiate both sides of the equation.

dD/dt = (1/3) * dh/dt

Since dh/dt is the rate at which the depth of the liquid is changing, which is constant and equal to 7π cm³/s, we can substitute it into the equation:

dD/dt = (1/3) * (7π)

Simplifying, we have:

dD/dt = (7/3)π cm³/s

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Using the formula of margin of error, the margin of error on this data is 6.7%

The formula for the margin of error is calculated by multiplying a critical factor (for a certain confidence level) with the population standard deviation. Then the result is divided by the square root of the number of observations in the sample.

The formula is given as;

\(MOE = Z*\sqrt{\frac{p(1 - p)}{n} }\)

where:

In this case, the Z-score for a 95% confidence level is 1.96, p is 0.38, and n is 220.

Let substitute the values and solve;

\(MOE = 1.96*\sqrt{\frac{0.38(1 - 0.38)}{220} } \\MOE = 0.067\)

Converting this into percentage;

The margin of error is 6.7%

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The probability of observing such an extreme result by chance alone is 0.0124.

To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.

Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:

P-value = 2 * 0.0062

P-value = 0.0124

This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.

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The scale factor used is:

1 centimeter equals half millimiter.

The scale factor tells us how many units in the sculpture represent a real unit.

We know that:

Real length = 9mm

Length in the sculpture = 18cm

Then we have the relation between the lengths:

18cm = 9mm

Dividing both sides by 18 we will get:

1cm = 9mm/18

1cm = 0.5mm

So the scale is 1 centimeter equals half millimiter.

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Answer:

The equation would be:

58 times 65

The answer:

3,770

Step-by-step explanation:

a) The Reynolds number for a sphere moving in air is 83,333.33.

b) Yes, Based on the Reynolds number, the flow around the sphere is turbulent (Re > 4000).

c) The Reynolds number for a sphere moving in water is 150,000.

a) To calculate the Reynolds number for a sphere moving in air at 15 m/s with a diameter of 10cm, we can use the formula:

Re = (density * velocity * diameter) / viscosity

Where density of air is 1.2 kg/m³, viscosity of air is 1.78 x 10⁻⁵ Ns/m² and diameter is 0.1m.

Re = (1.2 * 15 * 0.1) / (1.78 x 10⁻⁵)

Re = 83333.33

b) Based on the Reynolds number, the flow around the sphere is turbulent (Re > 4000). So, the answer is yes.

c) To calculate the Reynolds number for a sphere moving in water at 15 m/s with a diameter of 10cm, we can use the formula:

Re = (density * velocity * diameter) / viscosity

Where density of water is 1000 kg/m³ and viscosity of water is 0.001 Ns/m².

Re = (1000 * 15 * 0.1) / (0.001)

Re = 150000

Based on the Reynolds number, the flow around the sphere is turbulent (Re > 4000).

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The solution to the inequality is -3 ≤ x ≤ -1/3

Given the inequality:

4|3x+5| ≤ 16

Let us simplify it by dividing both sides by 4 to get:

|3x+5| ≤ 4

Next, we can break the inequality into two cases, depending on whether 3x+5 is positive or negative:

First: 3x+5 ≥ 0

In this case, the inequality simplifies to:

3x+5 ≤ 4

Subtracting 5 from both sides, we get:

3x ≤ -1

Dividing by 3 (which is positive) gives:

x ≤ -1/3

Second: 3x+5 < 0

In this case, the inequality simplifies to:

-3x-5 ≤ 4

Adding 5 to both sides, we get:

-3x ≤ 9

Dividing by -3 (which is negative and requires us to flip the inequality), gives:

x ≥ -3

Therefore, the solution to the inequality is:

-3 ≤ x ≤ -1/3

The interval [-3,-1/3] is the solution set, and it includes all values of x between -3 and -1/3, including the endpoints.

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23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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If  it travels 135 miles with the current in the same length of travels 87 miles against the current,  The speed of the current is 8.

Let speed of water current = x mph

Let speed with the current = x+37 mph

Time = distance/time =135/x+37 hrs

Speed against the current = 37-x mph

Hence,

Time = 87 /37-x

87 /37-x  =135 /37+x

87 (37+x)= 135 (37-x)

3219 +87 x=4995 -135x

Combine like terms

87x+135 x= 4995  - 3219

222x = 1776

Divide both side by 222x

x = 1776/222

x = 8

Therefore the speed is 8.

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Answer:

Kate's photo got 14 likes.

Step-by-step explanation:

42 ÷ 3 = 14

Given:-

To find:-

Decompose the fraction in two ways.

Way one,

Way two,

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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The area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1) coordinates is 6 square units

We first need to plot all the given points A  (2,-2), B (2,1), C (4,2), D (6,2)and E (4,-1) which is coordinate geometry

After joining the Points which is a pentagon and it can be divided in two shapes one is triangle CDE and a quadrilateral ABCE

Using the distance formula

BC = \(\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }\) = \(\sqrt{(2-1)^{2} + (4-2^{2} }\) = √5

Since BC = AE and BC ll AE , we can say ABCE is a parallelogram

area of a parallelogram = base × Altitude

                                      = 2 × 2= 4

Area of triangle CDE where CD is perpendicular and CE is the base

                        = 1/2 ( 2×2)

                        = 1/2 (4)

                         = 2 square units

So the area of ABCDE = Area of ABCE + area of CDE

                                     = 4 square units + 2 square units

                                      = 6 square units

Hence, the area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1)coordinates is 6 square units

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Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = \(H_0\\\) * D

where

v = velocity = 8254

\(H_0\\\) = hubble constant = 70

D = v/\(H_0\\\)

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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Answer:

3.25x50=21

Step-by-step explanation:

Sample size falls within the range from the mean Standard deviation (3.5±1.75).

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given, Suppose that the mean of your 50 rolls is x = 3.25.

Therefore,  Sample size falls within the range from the mean Standard deviation (3.5±1.75).

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Complete question:

Answer:

a and d

Step-by-step explanation:

brainliest if you want :)

Answer:

A or 18 – 0.25(18)

and

D or 0.75(18)

Step-by-step explanation:

Have great rest of your day. I know this works because I got it correct on the assignment. Good luck! :)

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

Yes. A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.

The sides of the triangle ABC are 6, 10, and 8. The sides of the triangle LMN are 12, 20, and 16. The ratio of the respective sides is the same for the two triangles because they are comparable. Therefore, BC is 10 miles long.

Due to the equal ratio of their corresponding sides, the triangles ABC and LMN are comparable. This indicates that the lengths of the sides of LMN may be obtained by multiplying the lengths of the sides of ABC by the same factor. For instance, side AB in ABC is 6 inches long, whereas side LM in LMN is 12 inches long. The lengths are 6:12, or 1:2, apart. The ratio remains the same for all matching. We can examine the other two sides of ABC to verify this response. Ten is the length of AC, and twenty is the length of MN. These two sides must likewise be multiplied by the same factor (1/2), since the ratio of the corresponding sides is the same. This results in AC and MN having lengths of 10 and matching ABC's dimensions. This demonstrates that BC is eight miles long.

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the complete question is

triangles abc and lmn are similar with measurements as shown. what is the measurement of bc, rounded to an integer find BC?

Answer:

A. (3,2)

Step-by-step explanation:

One way to solve without graphing

equate both equations to each other:

\(2x - 4 = - x + 5\)

add x on both sides:

\(2x + x - 4 = 5\)

add 4 on both sides:

\(2x + x = 5 + 4\)

collect like terms:

\(3x = 9\)

divide 3 on both sides, so

\(x = 3\)

now that we have x, go back to any one of the equations and substitute x=3 to find y. I'll use y=2x-4

\(y = 2x - 4\)

sub x=3

\(y = 2(3) - 4\)

2 × 3 is 6

\(y = 6 - 4\)

\(y = 2\)

we now have x and y, so the coordinates are (3,2)

If you want to use the graphing method, substitute in x values of your choice, for example -2 to 2 into each equation to find y and when there is a same coordinate in both equations that is the solution.

y = 2x - 4

when x is -2, y = 2(-2)-4 = -8. (-2,-8)

when x is -1, y = 2(-1) - 4= -6. (-1,-6)

when x is 0, y = 2(0)-4 = -4. (0,-4)

when x is 1, y = 2(1) - 4 = -2. (1,-2)

when x is 2, y = 2(2) - 4 = 0. (2,0)

when x is 3, y = 2(3) - 4 = 2. (3,2)

do the same thing of substituting to the other equation

y = -x + 5

when x is -2, y is 7 (-2,7)

when x is -1, y is 6. (-1,6)

when x is 0, y is 5. (0,5)

when x is 1, y is 4. (1,4)

when x is 2, y is 3. (2,3)

when x is 3, y is 2. (3,2)

plot these coordinates on a graph

they both have same x value (3) and same y value (2)

The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:

Between 20 and 30 bags.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.

In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:

Number of bags = Number of treats / Treats per bag.

The values of these parameters are given as follows:

Hence the numeric value of the expression is:

Number of bags = 78/3 = 26.

Which is a number between 20 and 30.

The problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.

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Answer:

I'm not sure exactly me myself

Answer:

-18^6

Step-by-step explanation:

(-18^2)^3   = -18^(2*3)  =  -18^6

The solutions to the dividing fractions prompts are as follows:

6. 4/3

7. 2/13

8. 33/2

9. 24/35

10. 63/20

To solve the divisions, note that the second divisor is inversed and multiplied. For the following problems, the divisions can be gotten as follows:

6. 8/9 ÷ 2/3

= 8/9 × 3/2

=24/18

=4/3

7. 12/13 ÷ 6

= 12/13 × 1/6

= 12/78

=6/39

= 2/13

8.  11/5 ÷ 2/15

= 11/5 × 15/2

165/10

= 33/2

9. 6/7 ÷ 5/4

6/7 × 4/5

= 24/35

10. 7/2 ÷ 10/9

7/2 × 9/10

63/20

So, the above are ways to determine the step-by-step answers.

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