There are 8 pints in one gallon. How many pints are in 6 gallons?

Answer: Increase in percentage by 42% and with baggage 43.2%.

Step-by-step explanation:

we know that the price is increased from $250 to $ 335

the percentage change by increasing the price is

$355 - $ 250 = $105

percentage change will be change/original = 105/250*100 = 42%

additional charges $ 50, $105+ $50 = 155

percentage change = 155/355*100 = 43.2%

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The total medical expenses for the five people in the car are $3,000 + $3*$500 + $62,000 = $3,000 + $1,500 + $62,000 = $66,500

What does a math word problem entail?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Since Allen's personal injury protection policy covers each person up to $50,000, the insurance company must pay out $50,000*5 = $250,000 for the five people in the car.

Since the total medical expenses for the five people are $66,500, the insurance company will pay out the total medical expenses for the five people, which is $66,500.

Therefore, the insurance company must pay out $66,500 for these five people.

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Let

\(I(a) = \displaystyle \int_0^\infty \frac{\sqrt x \arctan(ax)}{1+x^2} \, dx\)

Differentiate with respect to a :

\(I'(a) = \displaystyle a \int_0^\infty \frac{x^{\frac32}}{(1+x^2)(1+a^2x^2)} \, dx\)

Substitute y = √x :

\(I'(a) = \displaystyle 2a \int_0^\infty \frac{y^4}{(1+y)(1+a^2y)} \, dy\)

Polynomial division yields

\(\dfrac{y^4}{(1+y)(1+a^2y)} \\\\ = \dfrac1{a^2}y^2 - \left(\dfrac1{a^2} + \dfrac1{a^4}\right)y + \dfrac1{a^2} + \dfrac1{a^4} + \dfrac1{a^6} - \dfrac{\left(1+\frac1{a^2} + \frac1{a^4} + \frac1{a^6}\right)y + \frac1{a^2} + \frac1{a^4} + \frac1{a^6}}{(1+y)(1+a^2y)}\)

Computing I'(a) isn't so difficult from here. You'd find (assuming a ≥ 0)

\(I'(a) = \displaystyle \frac\pi{\sqrt2\left(\sqrt a + a + a^{\frac32} + a^2\right)}\)

Integrate both sides with respect to a. On the right side, substituting b = √a yields

\(\displaystyle \int \frac{da}{\sqrt a + a + a^{\frac32} + a^2} = \int \frac{2b}{b + b^2 + b^3 + b^4} \, db \\\\ = 2 \int \frac{db}{1 + b + b^2 + b^3} \\\\ = 2 \int \frac{db}{(1+b)(1+b^2)} \\\\ = \int \left(\frac1{1+b} + \frac{1-b}{(1+b^2)}\right) \, db \\\\ = \frac14 \left(2 \arctan(b) + 2 \ln(1 + b) - \ln(1 + b^2)\right) + C \\\\ = \frac14 \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right) + C\)

Noting that a = 0 makes the integral I(a) vanish, we have

\(0 = \dfrac14 \left(2 \arctan(\sqrt0) + 2\ln(1 + \sqrt0) - \ln(1 + 0)\right) + C \implies C = 0\)

and so

\(\displaystyle I(a) = \frac\pi{4\sqrt2} \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right)\)

We recover the integral we want with a = 1, which gives a value of

\(\displaystyle \int_0^\infty \frac{\sqrt x \arctan(x)}{1 + x^2} \, dx = \boxed{\frac{\pi^2 + 2\pi\ln(2)}{4\sqrt2}}\)

The percentage of graduates who are engaged in jobs unrelated to law is about 21%

The total percentage working at jobs related to law :

Total = (74% + 3% + 2%) = 79%

Percentage working at jobs unrelated to law :

Total percentage of graduates - percentage working at jobs related to law

100% - 79% = 21%

Therefore, 21% of the graduates work at jobs unrelated to law.

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Answer:

5

Step-by-step explanation:

(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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Roselyn can drive a distance until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.Roselyn can travel 120 km before running out

Distance travelled with 20 l of petrol in solution and final answer.

Roselyn's average speed is 60 kilometers per hour, and she needs to travel 150 kilometers to reach her family's place. Therefore, she will require a total of 150/60 = 2.5 hours to complete the journey.

The car's fuel efficiency is 6 kilometers per liter, meaning it consumes 1/6 liters of fuel per kilometer. To determine the total fuel required, we multiply the fuel consumption rate by the total distance: 150 * (1/6) = 25 liters of fuel.

Since the car's tank has 20 liters of fuel at the beginning of the drive, Roselyn will need an additional 25 - 20 = 5 liters of fuel to complete the journey.

As fuel costs 0.60 dollars per liter, Roselyn will need to spend a total of 5 * 0.60 = 3 dollars to purchase the necessary fuel.

Therefore, Roselyn can drive until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.

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Answer:

C. 1/(4^10)

Step-by-step explanation:

Fοr the inequaIity given, the cοrrect representatiοns are -

C: -6x + 15 < 10 - 5x

D: A number Iine frοm negative 3 tο 3 in increments οf 1. An οpen circIe is at 5 and a bοId Iine starts at 5 and is pοinting tο the right.

In AIgebra, an inequaIity is a mathematicaI statement that uses the inequaIity symbοI tο iIIustrate the reIatiοnship between twο expressiοns. An inequaIity symbοI has nοn-equaI expressiοns οn bοth sides. It indicates that the phrase οn the Ieft shοuId be bigger οr smaIIer than the expressiοn οn the right, οr vice versa.

The inequaIity is given as -3(2x - 5) < 5(2 - x).

We need tο simpIify the inequaIity -

-3(2x - 5) = -3(2x) + -3(-5)

-3(2x - 5) = - 6x + 15

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

5(2 - x) = 10 - 5x

Sο, nοw we have -

- 6x + 15 < 10 - 5x

Subtract 15 frοm bοth sides οf the inequaIity -

- 6x < -5 - 5x

Add 5x tο bοth sides -

- x < - 5

Remember the cοefficient οf x is negative, then when yοu divide bοth sides by it yοu must reverse the sign οf inequaIity.

The cοefficient οf x is -1.

Divide bοth sides by -1.

Sο, x > 5

The cοrrect statements are -

–6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

x > 5

Sο, this is the right chοice.

The cοrrect representatiοn is x < 5 and a number Iine frοm negative -7 tο 3 in increments οf 1. An οpen circIe is at 5 and a bοId Iine starts at 5 and is pοinting tο the right.

Therefοre, οptiοn C and D are cοrrect chοices.

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Answer:

Step-by-step explanation:

3:7 = ___: 49

3 : 7 = x : 49

x = 3 × 49 ÷ 7

x = 147 ÷ 7

x = 21

3 : 7 = 21 : 49  (your answer)

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Solution

We have the following bills

8 > $1

5 > $5

4 > $10

3 > $20

Answer:

216÷4=54

Step-by-step explanation:

we have to divide the bulb he fixed in per room by how many he fixes I guess so

Answer: He can fix in a total of 54 rooms which makes 216 bulbs fixed by him.

Step-by-step explanation:

4 bulbs are present in = 1 room

thus, 216 bulbs are present in = 216/4 = 54 rooms

So, he fixes 54 rooms in total

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Answer:

x = -4, 7

Step-by-step explanation:

We are given the graph of the function f(x), and we want to find the values that make the statement f(x) = 0.

f(x) = 0 means that there are certain values that make the value of f(x) (which can be considered as y) equal to 0.

We can look to the graph to help us - we should look at where y is equal to 0, which is the x-axis.

On the x-axis, we can see that the function passes through both -4 and 7 (the graph goes up by 1) on that line.

This means that when either -4 or 7 are substituted into the function (i.e. when they are equal to x), they will make the function equal 0.

So,  it means that x = -4, 7.

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Answer:

Step-by-step explanation:

800 - 200 = 600 = range

Inter Quartile Range is hard to measure.

566 2/3 = mean = close enough to 567

The term 625 does not exist

Domain : ( – ∞ ,  ∞ ) , {x/x ∈ R }

Range : [ 0 ,  ∞ ) , { y/y ⩾ 0 }

I hope I helped you^_^

Step-by-step explanation:

180° = 2x + 70 + 4x + 10

180° = 2x + 4x + 70 + 10

180° = 6x+ 80

180 - 80 = 6x

100 = 6x

6x = 100

x = 16.66

x ≈ 17°

Answer:

m = -3/4; b = -2

Step-by-step explanation:

y = mx + b

First, we use the coordinates of the points to find the slope, m.

m = (y2 - y1)/(x2 - x1) = (-2 - (-5))/(0 - 4) = (-2 + 5)/(-4) = -3/4

The slope, m = -3/4.

Now we use the slope and the coordinates of one point in the equation y = mx + b to find b.

y = mx + b

y = (-3/4)x + b

Let's use point (0, -2).

-2 = (-3/4)(0) + b

b = -2

Answer: m = -3/4; b = -2

Answer:

the answer is true......

Answer:

false

Step-by-step explanation:

Answer:

B. W = (P - 2L) / 2

Step-by-step explanation:

(I'm gonna use capitals so it's easier to identify length and width variables)

P = 2L + 2W

Isolate w:

P - 2L = 2W

(P - 2L) / 2 = W

Answer:

x = -5

Step-by-step explanation:

-6 + x = -11

x = -11 + 6

x = -5

Answer:

x=17

Step-by-step explanation:

17+ -6= 11

pls mark brainlest for real ('>')

Answer:

What are the phrases?

Step-by-step explanation:

The statement that is not necessary is (b) For each given value of x, the values of the response variable y are dependent.

From the question, we have

Test = significance test for the slope of a regression line

Take for instance, the regression is a linear regression

This is represented as

y = bx + a

Where

Also, the variable y is dependent on the variable x

However, this is not always needed when the slope of a regression is to pass through a test of significance

Hence, the statement that is not necessary is (b)

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Answer:

64% of 300 is the same as 64 times the value of 1% of 300

Step-by-step explanation:

64% of 300 is the same as 64 times the value of 1% of 300 because 64/1 is 64.

Meaning:

0.64 * 300 = 64(0.01*300)

192 = 64(3)

192 = 192

Hope this helps :)

Have a great day!

Answer:

1% of 300 is 3, so 64% of 300 is 192.

Have a beautiful day.

The function f(x) = 4x + 4 means that for each value of x, the player will receive 4 times that value plus 4 points, and domain for the function is Domain = {1, 2, 3, 4, 5, 6}.

What is the domain?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The function f(x) = 4x + 4 describes the number of points awarded to a player based on the value rolled on a six-sided die labeled 1 to 6.

To find the function value for a given roll, we simply substitute the roll value for x and evaluate the function. For example, if the roll is 3, then the function value is:

f(3) = 4(3) + 4 = 12 + 4 = 16

This means that the player is awarded 16 points for rolling a 3.

The domain of the function is the set of possible input values, which in this case are the numbers 1, 2, 3, 4, 5, and 6. This is because the die is labeled with these numbers and only these numbers, so it is not possible to roll any other value. Therefore, we can write the domain as:

Domain = {1, 2, 3, 4, 5, 6}

Interpretation: The function f(x) = 4x + 4 means that for each value of x, the player will receive 4 times that value plus 4 points.

The function provides a linear relationship between the roll value on the die and the points awarded to the player.

The function has a positive slope, which means that higher roll values result in more points awarded.

Hence, The function f(x) = 4x + 4 means that for each value of x, the player will receive 4 times that value plus 4 points, and the domain for the function is Domain = {1, 2, 3, 4, 5, 6}.

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9514 1404 393

Answer:

Step-by-step explanation:

ΔBCD is isosceles, so ∠CDB = ∠CBD = x. The sum of angles in the triangle is 180°, so you have ...

  x + x + 50° = 180°

  2x = 130° . . . . . . . . . subtract 50°, collect terms

  x = 65° . . . . . . . divide by 2

__

Triangle ABC is also isosceles, so ∠BAC = ∠BCA = y. Angle ABC is the supplement of angle x. The sum of angles in ΔABC is 180°:

  y + y + (180° -x) = 180°

  2y - 65° = 0 . . . . . . . . . . subtract 180°, substitute the value of x

  y -32.5° = 0 . . . . . . . divide by 2

  y = 32.5° . . . . . . . . . . add 32.5°

Answer:

7 to 8 months / most probably 8 months

7.5 months to be exact

Step-by-step explanation:

Hi there!! Let's work!

So lets Break it down,

Given: $40 every month

Prove: How many months till he has in total $300

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400 x (months) = $300 / (or how much ever we get)

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We have 2 final equations because we don't have a straight forward answer. (Refer to explanation below)

40 x 7 = 280

and

40 x 8 = 320

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So in problems like these we have to think like we would in real life, if you have an option you can write 7 to 8 months or you should write 8 instead of seven since they may be asking for a specific amount of months and after 8 months Gage will reach (surpass) his goal of $300 by $20.

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Answer:

the answer is 4 (option C)

Step-by-step explanation:

Since the triangles are similar, and in triangle UTV both sides are equal, we can consider QTR also has two equal sides.

therefore, the equation forms:

13x + 3 = 55

13x = 55 - 3

13x = 52

x = 52/13

x = 4