Consider the volume of the region shown below, which shows a right circular cone with a top radius of 3 cm and height 9cm

Equation of the parabola is [tex]y=\frac{1}{8} (x-7)^2[/tex] with a focus at [tex](7,2)[/tex] and a directrix at [tex]y=-2[/tex]

How to find the equation of parabola with focus and directrix ?

We know that focus of the parabola [tex](h,k+p)=(7,2)[/tex]

So [tex]k+p=2[/tex]......(a)

And directrix of the parabola

[tex]y=k-p\\=-2[/tex]

[tex]k-p=-2[/tex]........(b)

So add the equation (a) AND (b)

[tex]k+p=2\\k-p=-2\\------------\\2k=0\\k=0\\p=2[/tex]

Equation of the parabola with directrix and focus

[tex]y-k=\frac{1}{4p} (x-h)^2[/tex]

Substitute all the values

[tex]y-0=\frac{1}{4(2)} (x-7)^2\\y=\frac{1}{8} (x-7)^2[/tex]

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These series show convergence of series which are

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction

sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

According to the statement

we have given the some series and we have to find that the out of these series which series is convergent.

So, For this purpose we have to check the convergence of series.

So,

we know that the for the convergent of series there is a one condition and if those condition will satisfy on the series then the series is convergent and if not then series is divergent.

So, the condition for convergent is a series converges if the absolute value of the sum of any finite number of sequential terms can become arbitrary small by starting the addition from a term which is far enough. So, if this condition is not satisfied the series diverges.

When we apply this condition on all given series then only 2 series satisfy this condition which is

So, These series show convergence of series  which are

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction

sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

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Answer:

B. The series converges because it has a sum of 2/3

Here are the answers for the rest of the assignment:

C.

B.

C and D

A and C

B and D

C.

B. 0.31 and A. 0.0025

B. 1.0317 and C. 1.9683

(please read below)

Step-by-step explanation:

Had the assignment and these are the correct answers, enjoy :)

p.s Take a break here for a second, this was your last assignment before the unit test and finals, pre-calc is a very hard subject to master and calc is going to be even harder so I just want to say that I am proud of you, you have done a great job this year.

I have also taken the course(and many others) and answered countless questions for brainly (you have probably seen some of them if you took pre-calc) and this is my final answer for edge(might do one or 2 more for the finals) and it has been my greatest pleasure to bring you guys edge answers for 3 years strait but sadly this is where my road ends, I have tried my hardest to make your lives easier with my answers as others have for me. I hope some of y'all continue on my legacy and continue bringing good to the world 1 answer at a time.

So long fellows, thank you for taking the time to listen I hope y'all do well in life :)

Triangles ABC and DEF are similar. The scale factor for the pair is: 1/6.

The ratios of the corresponding sides of similar triangles are equal, because they are proportional.

If triangles ABC and DEF are similar triangles, then:

AB/DE = BC/EF = AC/DF

Plug in the given values

2/12 = 5/30 = 6/36 = 1/6

This means that the triangles are certianly similar. The scale factor for the pair is: 1/6.

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Answer:

78.5 inches square is the answer

Step-by-step explanation:

area-3.14*(5)^2

Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..

Lets try to solve out the problem,

Length = 3x-1

Width = x+1

Perimeter = 2(l+b)

Area = l*b

Perimeter= 2 (3x-1 + x+1)

P= 8x

Area = (3x-1) (x+1)

=> 3x(x+1) -1 (x+1)

=> 3x^2 + 3x -x -1

=> 3x^2 + 2x -1.

Hence Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..

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Answer:

probability of choosing two women over people in a community=⅔

The possible values for the width is w≥10.

Given that the length of a rectangle is 4 times the width and perimeter is to be less than or equal to 100 meters.

The perimeter of a rectangle is the total distance of its four outer boundaries. The perimeter of the object is twice the length and width of the object. This calculation is made using the formula:

perimeter = 2(length + width).

Here Perimeter=100 and length=4w

Substituting these values in the formula to find width, and we get

100≤2(4w+w)

100≤2(5w)

Divide both sides by 2, and we get

100/2≤(2(5w))/2

50≤5w

Divide both sides by 5, and we get

50/5≤5w/5

10≤w

Hence, the possible value for width when the length of a rectangle is 4 times the width is w≥10.

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Refractory period brief time-out of the heart's electrical impulse that allows for sufficient time for ventricular filling between beats.

End-diastolic pressure is at its resting level (end-diastolic pressure) and ventricular volumes are at their maximum value when the heart muscle is relaxed (end-diastolic volume).

What is the state of the heart during systole?

What are the 4 phases of cardiac cycle?

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Out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style. This can be obtained by using formula of probability and multiplying the total number of pizzas.

The formula for Expected value:

EV = P(X) × n

where EV is the expected value and P(X) is the probability of X and n is the total number.

In the question it is given that,

First we have to find the probability of stuffed crust or pan style,

P( stuffed crust or pan style) = P(stuffed crust) + P(pan style)

The number of stuffed crust and pan style = 161 + 191 = 352

The total number of crusts sold are ⇒ 307 + 224 + 161 + 191 = 883

⇒ P( stuffed crust or pan style) = 161/883 + 191/883

                                                   = 352/883

The expected value of stuffed crust or pan style,

n = 2000, P(X) = 352/883

EV = P(X) × n = (352/883) × 2000 = 797.28 ≈ 797

Hence out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style.

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The additive inverse is:

(a) 4   (b) 18   (c) -620  (d) -60  (e) 244  (f) 8921

The additive inverse of a number x is the number that, when added to x  yields zero.

It is shown as [tex]x+(-x)=0[/tex]

To find the additive inverse of a number we just change the sign of the given number which means positive changes to negative and vice versa.

The additive inverse of the given numbers are:

(a) 4

(b) 18

(c) -620

(d)-60

(e) 244

(f) 8921

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For Part A the probability is 0.0095 and for Part B the probability is

0.0043.

Probability of defect is perhaps the most important indicator of a manufacturing process's quality. It's a statistical technique used to indicate how often a product will fail during its lifespan, which in turn allows you to estimate the likelihood that an item will result in customer dissatisfaction.

Part A:

The number of rivets=22 rivets

Probability that no rivet is defective= [tex](1-p)^{22}[/tex]

The probability that at least one rivet is defective=1-[tex](1-p)^{22}[/tex]

For 19% of all seams need reworking, probability that a rivet is defective is given by

1-[tex](1-p)^{22}[/tex] = 0.19

[tex](1-p)^{22} = 1-0.19\\(1-p)^{22} = 0.81\\ p=1-\sqrt[22]{0.81} \\p=0.0095[/tex]

Part B:

For 9% of all seams need reworking, probability of a defective rivet is:

1-[tex](1-p)^{22}[/tex] = 0.09

[tex](1-p)^{22} = 1-0.09\\(1-p)^{22} = 0.91\\ p=1-\sqrt[22]{0.91} \\p=0.0043[/tex]

Hence, For Part A the probability is 0.0095 and for Part B the probability is 0.0043.

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the answer is infact c!

The number of cards which must be drawn from the standard deck is 12.

Given a standard deck of cards.

We have to find the number of  cards to be drawn so that we will get atleast 3 cards from each suit. Because they have used atleast in the question so the cards can be more also so we have to reach at minimum level of cards to be drawn to guarantee atleast 3 cards of the same suit.

Number of suits in a  standard deck= 4 (Clubs, Hearts, Diamond,  Spades)

Cards in 1 suit=13

We need atleast 3 cards of the  same suit so we need atleast 3*4=12 cards. (3 from each suit)

Hence the minimum cards which must be drawn to get atleast 3 cards of the same suit is 12.

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The time taken for Jenny to run the same distance at 10% faster is 13.05 seconds

Time taken by Jenny = 14.5 - (10% × 14.5)

= 14.5 - (0.1 × 14.5)

= 14.5 - (1.45)

= 13.05 seconds

Therefore, the time taken for Jenny to run the same distance is 13.05 seconds

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The examples and solutions to the functions are illustrated below based on the information given.

1st example: The cost of a bag of rice is $100 and subsequent bags cost $95. Illustrate. the function to calculate the cost for p bags of rice.

The function will be:

C = 100 + (95 × p)

C = 100 + 95p

2nd example: The cost of a pen is $5. Find the cost of s pens.

The function will be:

C = 5 × p

C = 5p

3rd example: Calculate the total amount for m tickets if each ticket is $20.

The function will be;

C = 20 × m

C = 20m

4th example: Bon bought g mangoes at $2 each and d oranges at $3.40 each. Calculate the total cost.

C = (2 × g) + (3.40 × d)

C = 2g + 3.4d

5th example: The average age of k number of boys is 7. Find their total age.

The function will be:

a = (7 × k)

a = 7k

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Question 1: Akira sells lemonade at 50 cents a glass. Let m be the amount of money they make in total for g glasses. Akira only has enough lemonade for 20 glasses.

A) Write a function m(g) to represent the total money (in dollars) they make from lemonade sales.

B) What is the domain of the function? Why?

Answer:

A) m(g) = 0.5g

This is since she makes 0.5 dollars per glass

B) The domain is [tex]0 \leq g \leq 20[/tex] where g is an integer. This is since it's impossible to make less than 0 glasses and they cannot make more than 20.

Question 2: Danyon sells CD's at $20 per CD. He has only 15 CD's left.

A) Write a function m(c) to represent the total money he makes from selling c CD's.

B) What is the domain of the function? Why?

Answer:

A) m(c) = 20c, as he makes 20 dollars per CD.

B) The domain is [tex]0 \leq c \leq 15[/tex] where c is an integer, as he can't make less than 0 CD's, and he has only 15 left.

Question 3: A factory is capable of making 60 units per hour. The factory can only run for 24 hours before cool down, and 150 units have already been made.

A) Write a function u(h) to represent the number of units after h hours.

B) What is the domain of the function? Why?

Answer:

A) u(h) = 60h + 150 as it makes 60 units per hour and 150 are already made.

B) The domain is [tex]0 \leq h \leq 24[/tex] as the factory can't run for negative hours and has to cool down after 24 hours.

Question 4: Alazne sells sunglasses at $7 per pair. She has only 30 left before she needs to re-stock.

A) Write a function m(s) which calculates the amount of money she makes after selling s sunglasses.

B) What is the domain of the function? Why?

Answer:

A) m(s) = 7s, as she gets $7 per pair of sunglasses

B) [tex]0 \leq s \leq 30[/tex] where s is an integer, one cannot have a fraction of a pair and she only has 30. She also cannot sell negative sunglasses.

Question 5: Lincoln works at a burger joint in the summer. He makes $3 from every burger he makes. He already has $22 saved. He cannot make more than 10 burgers a day.

A) Write a function m(b) which calculates how much money he gets after making b burgers.

B) What is an appropriate domain for this function?

Answer:

A) m(b) = 3b + 22, as he already has 22 dollars and makes 3 more for every burger.

B) [tex]0\leq b\leq10[/tex], where b is an integer. This is since he cannot make a fraction of a burger, negative burgers, or more than 10 burgers.

Answer: 9,-9

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

9x9=81

Based on the function, the range of f(x) = 2(3)^x can best be described as y > 0.

When a number is raised to a power, the result will always be positive even if the number is raised to a negative number.

This means that 3^x will always be positive which means that 2(3)^x will also be positive. y will therefore always be greater than 0.

Full question is:

Which best describes the range of the function f(x) = 2(3)^x?

y > 0

y ≥ 0

y > 2

y ≥ 2

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Answer:

98

Step-by-step explanation:

96+100=196

196÷2=98

Answer:

97.

Step-by-step explanation:

86 96 100 98

Place them in order:

86 96 98 100

The median is the middle value of an ascending sequence of numbers.

As there is an even number of values the median is the mean of the 2 middle ones:

So here it is (96 + 98) / 2

= 97.

Answer:

14 years ago

Explanation:

Let Mario's age be m, Jonas age be j.

From, Mario is 63 years older than Jonas

Equation 1: m = j + 63

From, Mario's age is four times Jonas age

Equation 2: m = 4j

Solve them by substitution:

m = j + 63

4j = j + 63

4j - j = 63

3j = 63

j = 21

Find Mario's age:

m = j + 63

m = 21 + 63

m = 84

Follow this steps:

m - y = 10(j - y)

84 - y = 10(21 - y)

84 - y = 210 - 10y

-y + 10y = 210 - 84

9y = 126

y = 14

The answer is 14 years ago.

Let Mario's age be M, and Jonas' age be J.

The formed equations :

To find their current ages, substitute the 2nd equation in the 1st equation.

4J = J + 63

3J = 63

J = 21

M = 4(21)

M = 84

For Mario to be 10 times Jonas' age, he has to be an age that is a multiple of 10.

Case (1) : Mario's age = 80

Subtract 4 from both their ages.

Mario : 84 - 4 = 80

Jonas : 21 - 4 = 17

17 × 10 ≠ 80

Case (2) : Mario's age = 70

Subtract 14 from both their ages.

Mario : 84 - 14 = 70

Jonas : 21 - 14 = 7

7 × 10 = 70

Answer: the answer is c.

Step-by-step explanation:

The equation which represents exponential decay is y=[tex]6(1/3)^{x}[/tex]

Given four equations : 1)y=[tex]3^{x} -4[/tex], 2) y=[tex]2(4)^{x}[/tex], 3) y=[tex]3^{x}/2[/tex], 4) y=[tex]6(1/3)^{x}[/tex].

Equation is relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Exponential equation look like [tex]a^{x}[/tex].

Decay means when x value increases ,the y value decreases.

We haveto put 3 values for x in the equations to check.

1)y=[tex]3^{x} -4[/tex]

put x=0,y=-3

put x=1, y=-1

put x=2, y=5

No,itdoes not represents exponential decay.

2) y=2[tex]4^{x}[/tex]

put x=0,y=2

put x=1, y=8

put x=2, y=32

No,it does not represents exponential decay.

3) y=[tex]3^{x}/2[/tex]

put x=0,y=0.5

put x=1, y=1.5

put x=2, y=4.5

No,it does not represents exponential decay.

4)y=6[tex](1/3)^{x}[/tex]

put x=0,y=6

put x=1, y=2

put x=2, y=0.67

Yes ,it represents exponential decay.

Hence the equation which represents exponential decay is y=6[tex](1/3)^{x}[/tex].

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The inverse of the function f(x)= 2x/7 + 4 is y = 7x/2 - 14.

Given the function; f(x)= 2x/7 + 4

First. we write the function as an equation then interchange the variables.

y = 2x/7 + 4

x = 2y/7 + 4

We solve for y.

2y/7 = x - 4

2y = 7x - 28

y = 7x/2 - 28/2

y = 7x/2 - 14

Therefore, the inverse of the function f(x)= 2x/7 + 4 is y = 7x/2 - 14.

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Answer:

D.

Step-by-step explanation:

Standard deviation tells us the dispersion of data/scores around the mean.

We can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.

A standard deviation (or σ) is a measure of how widely distributed the data is about the mean (μ). A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. A standard deviation around 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.

We use the following formula to compute the standard deviation:

[tex]\sigma = \sqrt\frac{{\sum_{i=1}^{N}\left | x_i - \mu \right | }^2}{N}[/tex]

In this formula, σ is the standard deviation, [tex]x_i[/tex] is the data point in the set we are solving for, μ is the mean, and N is the total number of data points.

In the question, we are asked to tell what standard deviations tell us from the given options.

From the above discussion, we can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.

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Answer:

36

Step-by-step explanation:

Hello!

Area of a Parallelogram: [tex]A = b*h[/tex]

Given our shape:

Don't forget, the height is the altitude to the base, which means it forms a perpendicular intersection. The height is not the slant height of the parallelogram.

The area is 36 un².

Answer:

[tex]\sqrt{\frac{15}{2} }[/tex] or 2.738

Step-by-step explanation:

Let’s just look at the triangle on the top with the [tex]\sqrt{10}[/tex] on the top and x on the bottom. (Basically the top half to the equilateral triangle)

There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]

We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b=[tex]\frac{1}{2}(\sqrt{10})[/tex] or [tex]\frac{\sqrt{10} }{2}[/tex]

Plugging these values into the equation:

x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}

[tex]x^{2}=\sqrt{10} ^{2}-\frac{\sqrt{10} }{2} ^{2}[/tex]

[tex]x^{2} =10-\frac{10}{4}[/tex]

[tex]x^{2} =\frac{15}{2}[/tex]

[tex]x=\sqrt{\frac{15}{2} }[/tex]

This approximately equals 2.738

Answer:

[tex]x=\sqrt{\frac{15}{2} }[/tex]. Another form of this answer is [tex]x=\frac{\sqrt{15} }{\sqrt{2} }[/tex](it's the same thing)

Step-by-step explanation:

Because the triangle is equilateral, all other sides of the triangle are also [tex]\sqrt{10}[/tex]. Also, x is the altitude of this triangle as it forms a right angle with the base and is therefore perpendicular. We know that this triangle is equilateral and in any triangle that has at least two sides that are equal(in other words isosceles), the altitude is also the median and angle bisector. A median would cut the side it reaches into half. So, x would cut the base into two equal parts. Since the base is [tex]\sqrt{10}[/tex], divide it by two and both halves are [tex]\frac{\sqrt{10}}{2}[/tex]. What we are left with is two right triangles, both with legs [tex]\frac{\sqrt{10} }{2}[/tex] and x. Using the Pythagorean Theorem, we know that [tex]a^{2}+b^{2}=c^{2}[/tex], with [tex]a[/tex] and [tex]b[/tex] being the legs and [tex]c[/tex] being the hypotenuse. So, we plug in the values and get [tex]\frac{\sqrt{10} }{2} ^{2}[/tex][tex]+x^{2}=\sqrt{10}^{2}[/tex]. Squaring, we get [tex]\frac{10}{4}+x^{2}=10[/tex]. This becomes [tex]x^{2}=10-\frac{10}{4}[/tex] which equals [tex]x^{2}=\frac{40}{4}-\frac{10}{4}[/tex]. Finally, [tex]x^{2}=\frac{30}{4}[/tex]. This is [tex]x^{2}=\frac{15}{2}[/tex]. Square rooting this we get [tex]x=\sqrt{\frac{15}{2} }[/tex]. Another form of this answer is [tex]x=\frac{\sqrt{15} }{\sqrt{2} }[/tex]

Answer:

75%

Step-by-step explanation:

The 95 percent confidence interval for the mean is (266.76,426.24).

A confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.

The formula of Confidence Interval =  Mean ±   [tex]t\frac{Standard Deviation}{\sqrt{number of observations} }[/tex]

where t is a constant

Given:

Mean = 346.5

Standard Deviation = 170.378

t-critical value for 95% Confidence interval with degrees of freedom(df)=n-1= 19 is 2.093

∴ Substituting values in formula we get

E = [tex]2.093 X170.378/\sqrt{20}[/tex] = 2.0931.96 x 38.0976=79.74

95% Confidence interval : (346.5-79.74,346.5+79.74)

95% Confidence interval : (266.76,426.24)

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Answer:

70 degrees.

Step-by-step explanation:

As AB is a diameter M < C = 90 degrees.

Therefore m < B = 90 - 20 = 70.