evaluate the integral. check your result by differentiation. (remember the constant of integration.) (x2 4)32x dx

The Average speed is 17.4 mph.

The average speed is calculated by dividing the total distance travelled by the total amount of motion time.

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Average speed = Distance travelled/ Time taken

Given:

Distance = 5 4/5 = 29/5 miles

Time= 1/3 hours

So, Average speed = Distance travelled/ Time taken

Average speed= 29/5 x 3/1

                         = 87/5

                         = 17.4 mph

Hence, the Average speed is 17.4 mph.

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Answer: Use your brain aka 12 and 7

Step-by-step explanation:isn't this urgent?

Answer: Steph is 16 today

Step-by-step explanation:

Austin age today = x

Austin in 4 years = x+4

Steph age today = 4x (because Austin is 1/4 her age today)

Steph age in 4 years is 4x + 4

In 4 years Austin's age is 2/5 of Steph's, so:

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

Now solve for x!

x+4 = (8/5)x + 8/5

12/5 = (3/5)x

Therefore Austin is 4 years old today (x=4) and...

Steph age today = 4x = 4x4 = 16

The distance when r = 55 mi/hr and t = 3 hours is 165 miles .

In the question ,

it is given that ,

r = 55 mi/hr which means the speed is 55 mi /hr

t = 3 hours , which means time = 3 hours .

we need to find the distance when r=55 mi/hr and t =3 hours .

the formula to calculate the distance is written as

distance = Speed × time

Substituting the value of speed = 55 and time = 3 ,

we get ,

distance = 55 × 3

distance = 165 miles .

the distance is 165 miles .

Therefore , The distance when r = 55 mi/hr and t = 3 hours is 165 miles .

The given question is incomplete , the complete question is

Find the distance when r=55 mi/hr and t = 3 hours ?

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The size that is the better one is 30.6-ounce package costs 7.98.

The 11.5-ounce package costs 3.19. The price per package will be:

= 3.19 / 11.5

= 0.27

A 30.6-ounce package costs 7.98. The cost per package will be:

= 7.98 / 30.6

= 0.26

In this case, it should be noted that the cheaper one.is the better buy. This was illustrated as the 30.6-ounce package costs 7.98.

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The new height of painting by Jacob will be 2.5 inches.

The ratio and proportion will be used to relate the original and reduced dimensions of painting. The original width and height = 42.88/33.5. Let us assume the new height be x. So, new width and height = 3.2/x. Equating these two fractions -

42.88/33.5 = 3.2/x

Rewriting the equation according to x

x = (3.2 × 33.5) ÷ 42.88

Performing multiplication in numerator

x = 107.2 ÷ 42.88

Performing division on Right Hand Side of the equation

x = 2.5

Thus, the new height will be 2.5 inches.

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the slope of the given point is m=9

The library is 5 kilometres far from the community pool.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation.

The distance between the courthouse and the library is 12 kilometres and the distance between the courthouse and the city pool is 13 kilometres. Let the distance between the library and the community pool be x and it can be observed that the Courthouse, library and Community hall form a sort of right-angled triangle

So, using Pythagoras theorem, we get

[tex]13^2=x^2+12^2\\x^2=169-144\\x^2=25\\x=5 km[/tex]

So, the library is 5 kilometres far from the community pool.

Therefore, the distance between the library and the community pool is 5 kilometres.

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Answer:

10 - x

Step-by-step explanation:

Since f(x) = 10 - 3, we can replace the "f(x)" in the equation with "10 - 3". Likewise, we can replace the "g(x)" in the equation with "-x + 3" because g(x) = -x + 3:

10 - 3 - x + 3

7 - x + 3

10 - x

The slope of the line represented by the equation  2x - 5y = 9 is 2/5  .

In the question ,

it is given that ,

the equation of the line is  2x - 5y = 9  .

we know that the equation of the line is represented as y = mx + c ,

where slope of the equation is  "m" .

So , rewriting  2x - 5y = 9 in the form of y = mx + c ,

w get ,

2x - 5y = 9

5y = 2x - 9

dividing both sides of the equation 5y = 2x - 9 by 5 ,we get

y = 2/5x - 9/5

y = (2/5)x - 9/5

the slope is = 2/5 .

Therefore , The slope of the line represented by the equation  2x - 5y = 9 is 2/5  .

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The total number of apples, oranges, and tangerines in the fruit basket is in the ratio 10 or 10x

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

We know that : the ratio of apples : oranges : tangerines = 3 : 2 : 5.

The total number of apples, oranges, and tangerines in the fruit basket is the total number of ratio, that is 3 + 2 + 5 = 10.

Because of the question is not contain information about the number of pieces, we can describe the dividend with x (or unknown value). So, the total number of apples, oranges, and tangerines in the fruit basket with ratio, that is 10 or 10x.

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The Law of detachment states that if m then n and m is true then q is true.

If two angles are complementary, then the two angles' sum is 90 degrees.

This is m∠E + m∠F = 90.

Option C is the correct answer

The Law of detachment states that if m then n and m is true then q is true.

We have,

If two angles are complementary, then the sum of their measures is 90°.

This is in the form of,

If M then N and if M is true then N must be true.

So,

If two angles are complementary, then the two angles' sum is 90 degrees.

If the two angles are m∠E and m∠F.

m∠E + m∠F = 90

Thus,

If two angles are complementary, then the two angles' sum is 90 degrees.

This is m∠E + m∠F = 90.

Option C is the correct answer

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The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.

Given,

In the question:

His juggling instructor divides a box of bean bags equally among the 16 clowns in Jason's class. each clown gets 6 bean bags.

Now, According to the question:

The equation that can be used to determine the number of bean bags in the instructor's box is b = 16 x 6.

The number of bean bags in the instructor's box is 96.

What is multiplication?

Multiplication is a mathematical operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.

Hence, The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.

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Answer:

Step-by-step explanation:

this slope of a line question is such a common question.  I feel like math teachers all over don't understand how to teach this subject.  Just so you know,  I answer a question like this about 10 times a day when I am on here.  It's like one of the most common questions.  

Here is my copy and paste answer for this...

point P1 (-3,7.2)  in the form (x1,y1)

point P2(2,-2.3)  in the form (x2,y2)

slope = m

m = (y2-y1) / (x2-x1)

m = (-2.3-7.2) / (2-(-3))

notice all the minus signs and how i'm being very careful to keep close track of them.  Also, who ever has written this question is intentionally trying to trip you up by putting in all the minus signs,  there is no need for so many minus signs to teach this well.  Anyway...

m = -8.5 / 5

m = - 1.7

the problem question ends there , but there is a common place this question is supposed to take you.   to the point slope formula.  but for another question.

The slope of (-3, 7.2) and (2, -2.3) is -1.9.

Consider,

(x1, y1) = (-3, 7.2)

(x2, y2) = (2, -2.3)

slope = (y2 - y1)/(x2-x1)

slope = ((-2.3) - (7.2))/((2) - (-3))

slope = (-9.5)/(5)

slope = -1.9

Therefore, the slope of the given points (-3, 7.2) and (2, -2.3) is -1.9.

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Answer: x=7°

Combine like terms and divide.

8x+5°+3x+8°=90°

(8x+3x)+(5°+8°)=90°

11x+13°=90°

-13°       -13°

11x=77°

[tex]\frac{11x}{11} =\frac{77}{11}[/tex]

x=7°

The elevation of the hole after placing the bush in the hole is 17/8 feet

Given: Davis digs a hole at a rate of 3/4 feet every 10 minutes

After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole

This involves subtraction and multiplication of fractions

Since the rate of digging = 3/4 feet every 10 minutes

Thus, after digging for 40 minutes, the depth will be:

3/4 × 4 = 3 feet

If Davis places a bush in the hole that fills exactly 7/8 feet of the hole, the remaining depth or elevation will be:

3 feet - 7/8 feet = 17/8 feet

Therefore,  after placing the bush in the hole, the elevation of the hole is 17/8 feet

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Answer:

box a - 252 inches squared (6 x 7 x 6)

box b - 216 inches squared (3 x 8 x 9)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

-4x + 9 ≥ -3  Subtract 9 from both sides

-4x ≥ -12  Divide both sides by -4.  When you divide both sides by a negative number, you must flip the inequality sign.

x ≤ 3

D: 5 is not a solution.

Answer:

D) 5

Step-by-step explanation:

To solve this problem, we must first isolate the variable and simplify the inequality. Isolating the variable means having the variable on one side of an equation or inequality without any other terms?

How do you isolate a variable?

Here's an example.

x+3=18

What can we do to have x on its own side of the equation? Currently, 3 is also with it. If we subtract 3 on both sides, we are leaving the equation with the same answer.

x + 3 - 3= 18 - 3

Combine like terms.

x = 21

That's how you solve for an equation.

Next, an example with division.

3x = 21

How do we solve for x this? Well, we know that 3x = 3 times x. So, to solve for x, we remove the 3. Since its 3 times x, lets divide by 3 on both sides.

[tex]\frac{3x}{3} =\frac{21} {3}[/tex]

Simplify:

3x/3 means 3 times x divided by 3. 3/3 = 1

1x = 21/3

21/3 = 7

x = 7

Now lets get to the problem.

[tex]-4x + 9 \geq -3[/tex]

The first step is to subtract by 9 on both sides so we can work our way to isolating the variable and solving the problem.

[tex]-4x + 9 -9\geq -3 - 9[/tex]

Simplify.

[tex]-4x \geq -12[/tex][tex]-4x \geq -12[/tex]

Now heres the tricky part. To solve for an equation, we must remove -4 from x, or -4 times x. In an equality, which states that:

A [tex]\geq , \leq , > , or < B[/tex]

If you divide or multiply both sides by a negative number, which means the number is less than 0, you must flip the sign!

When you multiply/divide by a negative number or both sides in an equality:

[tex]\leq[/tex] [tex]\geq[/tex]

[tex]\geq[/tex] [tex]\leq[/tex]

> <

< >

So, we currently have:

[tex]-4x \geq -12[/tex]

Divide by -4 on both sides.

[tex]\frac{-4x}{-4} \geq \frac{-12}{-4}[/tex]

Simplify. (Use the rule which states that a negative number multiplied or divided by another negative number equates to a positive number).

[tex]x \geq 3[/tex]

Flip the sign (This is a crucial step!)

[tex]x \leq 3[/tex]

Now, [tex]x \leq 3[/tex] means any number equal to or lower than 3 satisfies the conditions of the inequality.

Is -3 lower than or equal to 3?

Yes; Lower

Is -1 lower than or equal to 3?

Yes;

Is 3 lower than or equal to 3?

Yes; Equal

Is 5 lower than or equal to 3?

No; Greater

D, 5 is your answer as it does not satisfy the inequality.

The given sequence is geometric sequence not arithmetic.

An arithmetic sequence is a sequence in which the difference between every two consecutive terms is constant

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. It is found by taking any term in the sequence and dividing it by its preceding term.

Difference between arithmetic and geometric sequence:

An arithmetic sequence has a constant difference between each consecutive pair of terms

while

A geometric sequence has a constant ratio between each pair of consecutive terms.

Here, we have a sequence 5,10,20.

So a₁ = 5, a₂ = 10, a₃ = 20

Difference = a₃- a₂ = 20 - 0 = 10

                    a₂ - a₁ = 10 - 5 = 5

Since the difference is not constant, therefore the given sequence is not arithmetic.

Now ratio a₃/a₂ = 20/10 =2 and a₂/a₁ = 10/5 =2 which is same which shows the sequence is geometric.

Therefore, the sequence is geometric sequence.

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Answer:

Erin would need $10 more dollars in order to buy all three books.

Step-by-step explanation:

Step one: find the cost of all books

12 +16 +11 = 39

Step two: subtract

39 -29 = 10

Step two: Get your Answer!

Erin would need $10 more dollars in order to buy all three books.

The probability that 72% or more of the women in the sample have been on a diet is, 0.1736.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

As given a sample survey interviews an SRS of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months.

p = 0.69

1 - p = 0.31

n = 209

μp = p = 0.69

σp = √(p(1-p))/n = √(0.69*0.31)/209 = 0.03199

= 1 - p(p < 0.72)

= 1 - p((p - μp) / σp < (0.72 - 0.69) / 0.03199)

= 1 - p(z < 0.94)

= 1 - 0.8264

= 0.1736

Hence, the probability is 0.1736.

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Answer: 9.

Step-by-step explanation:

These are all multiples of 9, meaning that they can all be divided by 9 into a whole number.

90/9 =10

81/9 =9

72/9 =8

63/9 =7

Answer:

9:N

Step-by-step explanation:

90-9=81

81-9=72

72-9=63

The same number (9) is used to fing the sum of the next number in the sequence therefore that is your nth term

Answer:

-160 I think so

Step-by-step explanation:

(2)4-168

8-168

-160

Answer:You should have learnt this in kindergarten yet you're in high school, the answer is 86

well, as I said a while back, Heron's Area formula works for any triangle, so long we have all sides, and in this case we do, since it's not a right-triangle SOH CAH TOA won't work, so let's plug the values in Heron's

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a = 12\\ b = 8\\ c = 6\\ s=\frac{12+8+6}{2}\\ \qquad 13 \end{cases} \\\\\\ A=\sqrt{13(13-12)(13-8)(13-6)} \implies A=\sqrt{13(1)(5)(7)} \\\\\\ A=\sqrt{455}\implies {\Large \begin{array}{llll} A\approx 21.33 \end{array}}~cm^2[/tex]

The value of all the missing angles is in the measure of m∠1 = 88°, m∠2 = 42°, and m∠3 = 113°.

We know that,

Sum of all angles of triangle = 180°.

Therefore, m∠3 + 42° + 25° = 180°.

m∠3 = 180° - 67°

m∠3 = 113°

Vertical angles: Vertical angles are the angles that are opposite to each other when two lines cross.

We know that,

Vertical or opposite angles have equal measures.

So, 42° and m∠2 are vertical or opposite angles.

Therefore, the value of m∠2 = 42°.

Similarly, for m∠3, We know that,

Sum of all angles of triangle = 180°.

∴ ∠1 + ∠2 + 50° = 180°.

=> ∠1 + 42° + 50° = 180°

=> m∠1 = 88°.

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Answer:

  11

Step-by-step explanation:

You want the ratio of the populations of city C and city A, given city C is 2 times the 2,115,000 population of city B, and city A's population is 3.7×10⁵.

The ratio of interest is ...

  2B/A = 2(2115000)/(3.7×10⁵)

A calculator provides an easy answer to the value of this expression. (See attached.)

City C is about 11 times the population of City A.

__

Additional comment

If you want to work this out "by hand", you will need to find the quotient of ...

  4230000/370000 = 423/37 = 11 17/37 ≈ 11

because 17/37 < 1/2.

The converse of the conditional statement "If the streetlights are on, then the sun has gone down" is If the sun has not gone down, then the streetlights are on and is denoted as option D.

This is referred to as the type of sentence which is formed when the hypothesis and the conclusion are interchanged.

In this scenario, "If the streetlights are on, then the sun has gone down" when interchanged will be  If the sun has not gone down, then the streetlights are on which therefore makes option D the correct choice.

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Answer:

A

288 nickels

Step-by-step explanation:

There are now 435 nickels, after he put in 147. To find the answer, we need to find what the amount of nickels was before Shawn put in the 147. So, we need to subtract 147 from 435.

435 - 147 = 288

So, there were 288 nickels in the jar at the start.

The vector that translates P to P' is (-4 , 6)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

The points are given;

[tex]{P = (3, -2)}\\{P' = (-1, 4)}[/tex]

The translation rule is calculated as:

{(x,y) = P' - P}

So, we have:

{(x,y) =(− 1, 4) - (3, − 2)}

Combine the terms;

{(x,y) = (-1 -3 , 4 + 2)}

{(x,y) = (-4 , 6)}

Express as vectors;

(x, y) = (-4 , 6)

Hence, the vector that translates P to P' is  (-4 , 6)

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