f(x)=x^2+x and g(x)=1/x+1 find the rules for (f o g)(x) and (g o f)(x) and give the domain of each composite function

Answer:

It would take [tex]2.7[/tex] seconds, correct to 1 decimal place/nearest tenth.

Step-by-step explanation:

Step 1: Understanding the formula

The formula is given as [tex]h=16t^{2}[/tex], where [tex]h[/tex] represents the height, and [tex]t[/tex] represents the time.

Step 2: Substituting and solving

The question asks for the time that would take when the height is [tex]117~\text{feet}[/tex].

So, substitute [tex]117[/tex] for [tex]h[/tex] in the formula, since [tex]h[/tex] denotes the height:

[tex]h=16t^{2}\\117=16t^{2}[/tex]

Now, let's solve the equation to find the time, [tex]t[/tex]:

[tex]117=16t^{2}\\\\\text{Divide by 16 on both sides of the equation:}\\\frac{117}{16}=\frac{16t^{2}}{16}\\\\\text{Simplify:}\\7.3125=t^{2}\\\\\text{Square root both sides of the equation:}\\\sqrt{7.3125}=\sqrt{t^{2}}\\\\\text{Calculate:}\\2.7 \approx t\\\\\text{Rearrange the equation:}\\t\approx2.7[/tex]

So, it takes about [tex]2.7[/tex] seconds to travel [tex]117[/tex] feet, according to the formula.

Answer: 5.4

Step-by-step explanation:

[tex]29.16 < 30 < 30.25 \implies 5.4 < \sqrt{30} < 5.5[/tex]

3 < x < 44

=============================================================

Explanation:

For triangles ABC and DEF we have these two pairs of congruent sides

In between sides AB and BC is angle ABC = 82

In between sides DE and EF is angle DEF = 2x-6

Since AC > DF, this must mean angle ABC is larger than angle DEF. This is because the longer a side is, the larger the opposite angle will be.

Therefore, this leads to angle ABC > angle DEF

--------------------------------------------------

This is what the steps will look like

angle ABC > angle DEF

angle DEF < ABC

0 < angle DEF < angle ABC

0 < 2x-6 < 82

0+6 < 2x-6+6 < 82+6

6 < 2x < 88

6/2 < 2x/2 < 88/2

3 < x < 44

x is between 3 and 44, excluding both endpoints.

The number of field goals the team made in the game is equal to b. 3

The number of field goals the team made can be determined using an algebraic expression. An algebraic expression can be defined as an expression or equation that consists of both letters and numbers in it.

If the team scored 14 points from touchdowns and made x goals which are worth three points each, then an algebraic expression can be given as;

3(x) + 14 = 23

Solving for x;

3x = 23 - 14

3x = 9

x = 9 ÷ 3

x = 3

Hence, the team made a total of 3 field goals that are worth three points each.

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Answer:

61608 i believe

Step-by-step explanation:

2% of 60400= 1208

60400+1208=61608

If the difference between the total surface area and curved surface area of a hemisphere is 154 cm2, then its volume is 718.66 cm³

In general, the term "hemisphere" refers to the lower half of the earth, such as the northern or southern hemispheres. A hemisphere, however, is a 3D figure that is created by splitting a sphere into two equal halves, each with one flat side, and is known as such in geometry.

In everyday life, we encounter a variety of objects that have a hemisphere shape, such as a cherry that is shaped like a hemisphere when cut in half or a grapefruit that has a hemisphere shape when cut in half.

The difference between the total surface area and curved surface area of a hemisphere is 154cm.

Total Surface Area of Hemisphere = 3πr²

And Curved Surface Area of Hemisphere = 2πr²

It is Given that

Total Surface Area of Hemisphere - Curved Surface Area of Hemisphere. = 154.

Substituting the values, we get,

⇒ 3πr² - 2πr² = 154

⇒ πr² = 154

⇒ r² = 154/π

⇒ r² = 154 × (7/22)

⇒ r² = 7 × 7

⇒ r = 7.

Now, lets find the volume which is

Volume of Hemisphere = 2/3πr³

V = 2/3π(7)³

V = 2/3(22)(7)²

V = 2156/3

V = 718.66 cm³

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The equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-7,5) is y = (-6/5)x -17/5 .

In the question ,

it is given that the required line is perpendicular to  y=5/6x+7/6 .

on comparing it with the slope intercept form of the line , we get

slope(m₁)= 5/6

So, the slope of the perpendicular(m₂)  line will be

m₂= -1/m₁

m₂= -6/5

hence,  slope(m₂) of the perpendicular line = -6/5

Given that the perpendicular line is  passing through (-7,5)

substituting the values in slope intercept form (y=mx+c) of the line , we get

5 = (-6/5)(-7) + c

5 = 42/5 + c

c = 5-42/5

= (25-42)/5

= -17/5

y intercept = -17/5

so , the equation of the perpendicular line is y = (-6/5)x -17/5   .

Therefore , the equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-7,5) is y = (-6/5)x -17/5 .

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Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.

Let x be the number of minutes water has been added.

(a)

For each pool, write an expression for the amount of water in the pool after x minutes.

Amount of water in the first pool (in liters) = 23x + 728

Amount of water in the second pool (in liters) = 37x

(b)

Write an equation to show when the two pools would have the same amount of water.

this is when:

23x + 728 = 37x

subtract 23x from both sides:

23x + 728 - 23x = 37x - 23x

728 = 14x

divide both sides by 14:

728/14 = 14x/14

x = 52

So, pools are equal after 52 minutes.

Likert scales are designed to be ordinal in measurement.

What is Likert scale and why is it used ?

The Likert scale is a psychometric scale that is used in survey questions that are based on it. It is one of the most popular sorts of survey questions. Respondents in a Likert scale survey are given precise options based on whether they "agree" or "disagree" with a particular survey question rather than just selecting "yes" or "no."

Likert scale survey questions are crucial for gauging a respondent's attitude or view toward a certain topic and are therefore a vital component of market research. Likert scales are commonly used to gauge respondents' levels of agreement with diverse claims using a five-, seven-, or nine-point scale. The Likert Scale was created by organizational psychologist Rensis Likert to evaluate the degree of agreement or disagreement on a symmetric agree-disagree scale. In general, a series of statements is used, each intended to look at a construct from a little different angle. The effectiveness of this method lies in the fact that it can be applied to both social science and marketing constructs.

Therefore, likert scales are designed to be ordinal in measurement.

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Answer:

40

Step-by-step explanation:

Go through PEMDAS

Exponents: 4∧0 = 1 and 1³ = 1

Multiply: 4 × 5 = 20 × 2 = 40

Add: 1 + 40 = 41

Subtract: 41 - 1 = 40

Answer:

1 is 2 and 2 is 2

Step-by-step explanation:

10 miles per hour is the average journey speed.

Given that,

Some pupils choose to ride bikes. They move at a 15 mph average speed for the first two hours, and then they stop for lunch for an hour. The pupils ride at a 10 mph speed for an additional hour.

Average speed is ( total distance ) / ( total time )

During the 1st 2 hrs:

distance = speed * time

distance = 15 *2 = 30 miles

During the last hour:

distance = speed * time

distance = 10 *1 = 10 miles

Average speed = 30+10 / 2+1+1 = 40/4 = 10 mil/hr

Therefore, their average speed for the trip is 10 mil/hr

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The range of the function in this situation as required in the task content is; Choice D; 0 ≤ y ≤ 3.

It follows from the task content that the range of the function described by the situation is to be determined.

The set of all possible output values of a function, otherwise termed the dependent variable, y is called the Range.

It follows that since the distance he has remaining, y is a function of how long he has been riding the bike, x and it's said that; the boy lives 3 miles from the library; the range of the function described is; Choice D ; 0 ≤ y ≤ 3.

Please Note: The term, domain encompasses the set of all possible input values, otherwise termed the independent variable, x.

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Using proportions, it is found that the value of x would be 28.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We have been given two triangle, we need to find the value of x.

Then using proportions;

12/(x-7) = 8 / 14

Cross multiplication;

12 (14/8) = x - 7

3 (14/2) = x - 7

21 = x - 7

x = 21 + 7

x = 28

Therefore, the value of x is 28.

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The perimeter of the rectangle given its dimensions is 24x - 4.

A rectangle is a two-dimensional quadrilateral with four right angles that sum up to 360 degrees. A rectangle has two diagonals of equal length that bisect each other at right angles.

The perimeter of  rectangle is the sum of the lengths of the four sides of the rectangle.

Perimeter of a rectangle = 2 x (length + width)

2 x [(12x - 7) + 5)

2 x (12x - 2)

24x - 4

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what in your opinion is the moral in the story ?

we know that

The parent function is

The transformation is to shift 1 unit to the left

so

The rule of this translation is given by

(x,y) -----> (x-1,y)

so

the equation for the transformed function is

Answer:

bbbbbbbbbbbbbbbb

kjajs

Answer:

10 and 5[tex]\sqrt{6}[/tex]

Step-by-step explanation:

these cannot be solved as they are not equations, but can be simplified

using the rule of radicals

[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]

then

2[tex]\sqrt{25}[/tex] = 2 × 5 = 10

[tex]\sqrt{150}[/tex]

= [tex]\sqrt{25(6)}[/tex]

= [tex]\sqrt{25}[/tex] × [tex]\sqrt{6}[/tex]

= 5[tex]\sqrt{6}[/tex]

Step-by-step explanation:

loga(x) calculates simply the exponent of a needed to get x as result.

so, 5 "to the power of the exponent of 5 needed to get 7" is 7 (we give 5 the exponent that it needs to create 7, so it creates 7).

the same thing with 2, where we give 2 the exponent it needs to create 1/49. so, it creates 1/49.

we get therefore

7 × 1/49 = 7/49 = 1/7

Considering the relative frequencies in this problem, the association between scoring 21 points and winning the game is as follows:

There is a strong, positive association.

The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

From the table given at the end of the answer, we have that when the team scored at least 21 points, an interval composed of 28 games, the team won 25 games and lost only 3, hence the relative frequency of wins when the team scores at least 21 points is of:

25/28 = 0.8929 = 89.29%.

Due to this high frequency of wins, there is a strong and positive association between scoring 21 points and winning the game

The table with the team's results is given by the image at the end of the answer.

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The total number of engineering students is 176 approximately among the 750 students enrolled in the college by using the proportionate formula.

It is mentioned here that a college has 19 students of engineering for every 81 students who got enrolled.

Therefore the ratio of engineering students to total number of students is as follows:

No. of engineering students = 19

Total number of students = 81

Ratio = [tex]\frac{19}{81}[/tex]

Now if the total number of students that the college has is 750 then the number of engineering students can be found by using the proportionate formula as the ratio of the engineering to the total students will remain same.

Total number of students = 750

Let the number of engineering students be y

Ratio = [tex]\frac{y}{750}[/tex]

Comparing it with the above ratio and using the proportionate formula,

[tex]\frac{19}{81} = \frac{y}{750}[/tex]

⇒ y = [tex]\frac{19*750}{81}[/tex]

⇒ y = 175.925

So approximately 176 were the engineering students among 750 students enrolled.

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Answer:

  128

Step-by-step explanation:

You want the total number of bedrooms in a mix of 1-, 2-, and 3-bedroom apartments.

The total number will be the sum of the products ...

  1 × number of 1-bedroom apartments = 1 × 32 = 32

  2 × number of 2-bedroom apartments = 2 × 24 = 48

  3 × number of 3-bedroom apartments = 3 × 16 = 48

That total is ...

  32 +48 +48 = 128

There are 128 bedrooms in the apartment building.

The formula for time, t = d/s which means time exists equivalent to distance divided by speed.

The times taken to travel 441 miles apart exists 8.25 hours

Time can be defined as the dimension based on which the evolution of any system takes place. It can be measured in terms of seconds, minutes, hours, days, weeks, months, and years.

The formula for time, t = d/s which means time exists equivalent to distance divided by speed.

Given: Train running in the opposite direction

Speed of one train (S1) = 65 mph

Speed of one train (S2)= 63 mph

Distance to be covered = 1056 miles

Train exists running in the opposite direction, so their relative speed = (S1 + S2)

Relative speed = (65 + 63) = 128 mph

Now, time is taken to travel 1056 miles apart

Time = Distance / relative speed

Time = 1056/128 = 8.25 hours

Therefore, the times taken to travel 441 miles apart exists 8.25 hours

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Answer: x= -18

Step-by-step explanation:

Your equation would be (x/9)+6=4

Subtract 6 by both sides.

Multiply 9 by both sides.

Then you should get -18.