The width of a rectangle is 4 units less than the length. The area of the rectangle is 32 units. What is the width, in units, of the rectangle?

The c has only one number  is c = 81/4 that satisfy the conclusion of rolle's theorem.

The three hypotheses of Rolle's theorem are:

(a) f(x) is continuous on [a,b]

(b) f(x) is differentiable on (a,b)

(c) f(a) = f(b)

i) If you graph f(x), you can see that it is continuous that is no breaks on the interval [0,81]

ii) f(x) is differentiable on (0,81)

f '(x) = 1/(2√x) - 1/9  which exists on the open interval (0,81)

iii) f(0) = f(81) = √81 - 81/9 = 9-9 = 0

Rolle's Conclusion:

f'(c) = 0

f'(c) = 1/(2√c) -1/9 = 0

(9 - 2√c)/(18√c) = 0

√c = 9/2

c = 81/4

There is one number c = 81/4, which satisfies f '(c) = 0.

Therefore the c has only one number  is c = 81/4 that satisfy the conclusion of rolle's theorem.

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Full question:

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)

f(x) =x − 1/9 x, [0, 81].

Answer:

x = ± 9

Step-by-step explanation:

x² = 81 ( take square root of both sides )

x = ± [tex]\sqrt{81}[/tex] = ± 9

[tex]{ \red{ \boxed{ \pink{ \sf{x = 9}}}}}[/tex]

Step-by-step explanation:

Here, the question is,

[tex]{ \green{ \sf{ {x}^{2} = 81}}}[/tex]

Apply square root on both the sides then,

[tex]{ \green{ \sf{ \cancel { \sqrt{x} }^{ \cancel2}}}} \: = { \green{ \sf{ \sqrt{81}}}} [/tex]

Now,

[tex]{ \green{ \sf{x = \sqrt{81}}}} [/tex]

We got √81 as answer but what is the perfect square number of 81? That is 9. Same number when multiplied twice to get the resultant number makes a perfect square number. i.e. 9×9 = 81. So, the answer is

[tex]{ \green{ \boxed{ \red{ \tt{x = 9}}}}}[/tex]

The equation of the perpendicular line that passes through the point (- 3, - 1) is y = 2 · x + 5.

In this question we must determine the equation of a line that is perpendicular to another line and pass through a given point. Mathematically speaking, lines are represented by the following equation:

y = m · x + b

Where:

And the slopes of two lines perpendicular to each other satisfy the following relationship:

m · m' = - 1

Where:

First, determine the slope of the perpendicular line by means of the slope relationship:

m = - 1 / 2

m' = - 1 / m

m' = - 1 / (- 1 / 2)

m' = 2

Second, find the intercept of the perpendicular line by the equation of the line:

b = y - m · x

b = - 1 - 2 · (- 3)

b = - 1 + 6

b = 5

Third, write the equation of resulting line:

y = 2 · x + 5

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The volume of the cylinder is 18149.2 yards³.

It is important to note that the volume of a cylinder is calculated as:

Volume = πr²h

Radius = 17

Height = 20

Therefore, the volume will be:

Volume = πr²h

Volume = 3.14 × 17² × 20

Volume = 18149.2

The volume is 18149.2 yards³.

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The value of an integer or any letter associated with a variable is known as its coefficient. In the expression 2x + 3y, for instance, the variable x has a coefficient of 2 and the variable y has a coefficient of 3.

There are 842 buttons in 36 shirts and 42 jackets if the number of buttons in each is equal to x.

Additionally, the collection of six shirts and seven jackets has 137 buttons.

It can be expressed using the following equations:

36 x + 42 y = 842 ------(1);

6 x + 7 y = 137 ------(2);

6 x + 36 x + 42 y = 822 ------(3).

Although the constant term on one side of equation is different, the x and y coefficients are the same in both of these equations. This indicates that neither equation has a solution.

I.e →a1/a2=b1/b2≠c1/c2

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Answer: The answer will be 74.07 percent.

According to the question, let the number be x

Then, x*54/100 = 40

x = 40 × 100 / 54

x = 74.07 (approx)

Using the confidence interval, the margin of error is 0.02.

In the given equation we have to find the margin of error.

The resulting confidence interval for the proportion of students applying for college is (0.65,0.69).

Let p = population proportion of students applying for college

P = Sample proportion of students applying for college

ME = margin of error

So the confidence interval

CI = (P-ME, P+ME)

From the given question;

(P-ME, P+ME) = (0.65,0.69)

So lower bound= P-ME = 0.65............................(1)

Upper Bound = P+ME = 0.69............................(2)

Simplifying the Equation 1 and 2

Add equation 1 and 2 we get

2P = 1.34

Divide by 2 on both side we get

P = 0.67

Putting the value of P in the equation 2

P+ME = 0.69

0.67+ME=0.69

Subtract 0.67 on both side we get

ME = 0.02

Hence, the margin of error is 0.02.

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Answer: 4 reds

Step-by-step explanation:

Answer:

Re-arrange the terms and combine the like terms.

2

3

y

−

1

3

y

−

3

−

4

=

1

3

y

−

7

Step-by-step explanation:

Answer:

According to sources on googIe, the average price of a hot dog would be $5.22.

If a shopper needs 48 hot dogs, they would need a total of $250.56 dollars to pay.

Step-by-step explanation:

48 x 5.22 = 250.56

The equation in slope intercept form that represent the situation is y = 50x - 99050.

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Neil charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount.

Using the table that shows the amount he charged for tutoring each year. we can find the rate of change.

The rate of change is the slope.

Therefore, (2005, 1200)(2008, 1350)

m = slope = 1350 - 1200 / 3

slope = 150 / 3

slope = 50

Therefore, let's represent the equation in slope intercept form. We will have to find the y-intercept of the equation.

Hence, using (2005, 1200)

y = 50x + b

1200 = 50(2005) + b

b = 1200 - 100250

b = - 99050

Hence, the equation is y = 50x - 99050.

where

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Using graphing calculator, the solution to the inequality is attached

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.

If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.

Using a graphing calculator;

Kindly find the attached graph as solution to the inequality

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Answer:

no, because 3 + 5 < 9

Step-by-step explanation:

given three sides of a triangle

For the sides to form a triangle the sum of any 2 must be greater than the third.

given sides 3, 5 and 9 , then

3 + 9 = 12 > 5

5 + 9 = 14 > 3

3 + 5 = 8 < 9

the 3 sides do not form a triangle since 3 + 5 < 9

Answer:

y=-1(-3)+2

Step-by-step explanation:

on my test

Answer: 6

Step-by-step explanation:

      If the domain is {-3 ≤ x ≤ 0}, then we will decide which of the given values is not in the range.

     6 is not between, including the values of, -3 and 0, so the number not in the range is 6.

Answer:

65

Step-by-step explanation:

Answer:

No, it doesn't have all lines of symmetry

Step-by-step explanation:

If you can see, the triangle's line of symmetry is from a vertex to the center of another line. So, draw a line from the bottom left vertex (corner) to the center of the right side/line. And then, draw another from the right corner to left center line.

The speed of the football in the air is 7.1 yards per second

From the question, the given parameters are:

Distance = 60 yards

Time to cover this distance = 8,5 seconds

The speed of the football in the air is calculated as

Speed = Distance/Time to cover this distance

Substitute the known values in the above equation

So, we have the following equation

Speed = 60/8.5

Evaluating the quotient in the above equation, we have

Speed = 7.1

Hence, the ball's speed in air is 7.1 yards per second

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The error that Travon makes is
(C) Tavon forgot to take the square root to find the final answer. The correct answer is about 6.99

What is a root in mathematics?
In mathematics, a number's "root" is a number that, when multiplied by itself, equals the original number; alternatively, a number's "root" can also be an equation's solution, which is typically presented as a number or an algebraic formula.

For instance, since 7*7=49, the square root of 49 is 7. In this instance, 7 is referred to as the square root of 49 since it must be multiplied twice to produce the number. 3 because 3*3*3=27 is the cube root of 27. Since 27 is obtained by multiplying 3 by three, we refer to this as a cube root, so 3 is the cube root of 27.

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The set of side measurements that could be used to form a triangle is 8, 9 and 15

If a, b and c are the sides of the triangle

Then a + b > c

b + c > a

c + a> b

The first set of sides are

4, 6, 12

4 + 6 > 12

10 < 12

It will not form a triangle

The second set of sides are

5, 19 and 24

5 + 19 > 24

24 = 24

It will not form a triangle

The third set of sides are

6, 10 and 17

6 + 10 > 17

16 <17

It will not form a triangle

The fourth set of sides are

8, 9 and 15

8 +9 > 15

17 > 15

8+15 > 9

23 > 9

9 + 15 > 8

24 > 8

It will from a triangle

Hence, the set of side measurements that could be used to form a triangle is 8, 9 and 15

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The option that explains Sarita's mistake is Sarita’s solution is correct. She made an error in her verification.

The given equation is: 5(x - 3) + 7(x + 4) = 73

In order to determine the value of x, take the following steps:

1. Apply the Distributive property:

5x - 15 + 7x + 28 = 73

2. Add similar terms together:

12x  + 13 = 73

3. Combine similar terms:

12x = 73 - 13

4. Add similar terms

12x = 60

5. Divide both sides of the equation by 12

x = 60 / 12

x = 5

In order to verify the answer, substitute for x in the given equation :

5(5 - 3) + 7(5 + 4) = 73

5(2) + 7(9) = 73

10 + 63 = 73

73 = 73

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Answer:

x^4 times q^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

this looks tough, but just remember that powers can be rewritten like this

[tex]\sqrt{x^{4} x^{2} q^{4} }[/tex]

then just break up the square root sign, which is another property of square roots

[tex]\sqrt{x^{4} }[/tex]*[tex]\sqrt{x^{2} }[/tex]*[tex]\sqrt{q^{4} }[/tex]

you could break the [tex]x^{4}[/tex] into two  [tex]x^{2}[/tex] but I think you can see that it will just be [tex]x^{2}[/tex] once it's pulled out of the square root

[tex]x^{2} *x*q^{2}[/tex]

[tex]x^{3}[/tex]*[tex]q^{2}[/tex]

Does this all make sense?

Answer:

Basically Mate you gotta make a perpendicular line from the letter your told make a line from and then thats for the 2 pages basically they want you to do the same thing that is done but you do it for the letter.

PLEASE GIVE BRAINLIEST THANK YOU!!!

Z-score of age of airline passenger is 2.571

Age of airline passenger when x = 85 , μ = 49 and σ = 14 .Find standardized z-score ?

Z- Score give an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , x = 85

mean = 49

standard deviation = 14

z-score = x- μ / σ

putting all the values ,

z-score = 85 - 49 / 14

= 36 / 14

= 2.571

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The probability of selecting at least one experienced IPV is 0.598 and at least one did not experience IPV is 0.866.

In the given question we have to find the probability of selecting at least one experienced IPV and at least one did not experience IPV

From the given table

Probability of experiencing IPV

P(Experienced IPV) = 366 / 1000 = 0.366

Probability of not experiencing IPV

Q(Not-experienced IPV) = 634 / 1000 = 0.634

Now when n samples are chosen from the population, the binomial probabilty distribution follows (P + Q)^n.

Here, n = 2,

So, (p +q)^2 = p^2 + 2pq + q^2

p^2 = Both experienced IPV

2pq = One has experienced IPV and other hasn’t

q^2 = None have experienced IPV.

A. Finding the probability of at least one experienced IPV.

P(At least one has experienced IPV) = P^2 + 2PQ

                                                         = (0.366)^2 + 2(0.366)(0.634)

                                                         =0.1339+0.4641

                                                         = 0.598

B. Finding the probability of at least one did not experienced IPV.

Q(At least one did not experienced IPV) = Q^2 + 2PQ

                                                                   = (0.634)^2 + 2(0.366)(0.634)

                                                                   =0.4019+0.4641

                                                                   = 0.866

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The total amount of money Riley needs to save to buy the new scooter is $200.

Percentage is the number or ratio which is expressed as "100". It is denoted by "%". It indicates the hundredth parts of any quantity.

It is calculated by dividing the value by total value and multiplied by 100.

Formula for percentage is (Value/total value)*100

For given information,

Riley saved $60 which is 30% of the total amount.

For 1% it will be $2

So, the total amount will be $200

Thus, the total amount of money Riley needs to save to buy the new scooter is $200.

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Answer:

  7.07 cm/min

Step-by-step explanation:

You want the rate of change of water level in a conical tank 16 m high with radius 4 m when the level is 12 m and the water is draining at 2 m³/min.

The level of water in the tank is 12/16 = 3/4 of the height of the tank, so the radius of its surface is (3/4)(4 m) = 3 m. The surface area is ...

  A = πr²

  A = π(3 m)² = 9π m² ≈ 28.3 m²

The rate of change of level is the rate of change of volume divided by the surface area:

  V'/A = (-2 m³/min)/(9π m²) = -2/(9π) m/min ≈ -0.07074 m/min

The water level is falling at about 7.07 cm/min.