Find the volume when the region bounded by the parabola y = 7 − x ^2 and the line y = 4 is rotated about the x axis.
Volume =

______________________________

______________________________

To find the upper-tail p-value, we need to find the probability of getting a t-value equal to or greater than the observed test statistic of t = 0.833, given the degrees of freedom df = 27.

Using a t-table or calculator, we find that the probability of getting a t-value greater than 0.833 with 27 degrees of freedom is 0.206. Therefore, the upper-tail p-value for the test statistic is 0.206.

So, the answer is (b) 0.206.

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Answi tride so hard i dont know but i wish you luck

Step-by-step explanation:

Step-by-step explanation:

Answer:

36 Cups

Step-by-step explanation:

You need to find how much punch Leon has. First, find how much grape juice he adds.

Leon adds 2 bottles of grape juice. Each bottle has 64 fluid ounces of juice.

2×64=128

Leon adds 128 fluid ounces of grape juice, but the problem asks about cups. So, find how many cups are equal to 128 fluid ounces. There are 8 ounces in a cup, so divide by 8.

128÷8=16

Leon adds 16 cups of grape juice.

Now, add to find how much punch Leon has in all. He uses 20 cups of ginger ale and 16 cups of grape juice.

20+16=36

Victor has 36 cups of punch in all.

The required cups of punch Leon will have is 36.

He pours 20 cups of ginger ale into his punch bowl. Then, he adds two 64-fluid-ounce bottles of grape juice.
To determine how many cups of punch Leon has.

In calculation, it deals with the numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
In the punch, there is  20 cups of ginger ale
he adds two 64-fluid-ounce bottles of grape juice,
= 64 * 2 = 128
= 128
Now, in 1 cup = 8 ounces. So,
number of cups in 128 ounces,

= 128 / 8 = 16
Now , total cups = 16 + 20 = 36

Thus, the required cups of punch Leon will have is 36.

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Answer: t≈8.93 units

Step-by-step explanation:

The cosine of an angle (cos) is the ratio of the adjoining leg of a right triangle to the hypotenuse

Hence,

\(\displaystyle\\cos56^0 =\frac{5}{t} \\\)

Multiply both parts of the equation by t(t≠0):

\(\displaystyle\\cos56^0(t)=\frac{5}{t} (t)\\\\t(cos56^0)=5\)

Divide both parts of the equation by cos56°:

\(\displaystyle\\t=\frac{5}{cos56^0} \\\\t\approx\frac{5}{0,56} \\\\t\approx8,93\ units\)

The cost of the calculator before the total is $24.95

From the question, we have the following parameters that can be used in our computation:

Total cost = $28.19

Tax = 13%

Using the above as a guide, we have the following:

Total cost = Initial cost * (1 + Tax)

substitute the known values in the above equation, so, we have the following representation

Initial cost  * (1 + 13%) = 28.19

So, we have

Initial cost   = 28.19/(1.13)

Evaluate

Initial cost = 24.95

Hence, the cost of the calculator before the total is $24.95

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Answer:

D

Step-by-step explanation:

In 2 hours they wash 8 cars total so...

8

16

24

The extra time is 15 mins for 2 cars

Question

Suppose the following facts to be true: The probability of a random kindergartener having chicken pox at any given time is 2%. Among kindergarteners who have chicken pox, 75% have red spots. Among kindergarteners who do not have chicken pox, 1% have red spots. Given that Sanjay, a kindergartener, has red spots, what is the probability that Sanjay has chicken pox? Enter your answer as a fraction in simplified form.

Answer:

75/124

Step-by-step explanation:

This is a question based on conditional Probability

We would solve this using Bayes's Theorem of Conditional Probability

From the above question, we have the following information:

The probability of a random kindergartener having chicken pox at any given time is 2%.

Hence, the probability that a kindergartner would not have chicken pox

= 100% - 2%

= 98%

Kindergarteners who have chicken pox, 75% have red spots.

Kindergarteners who do not have chicken pox, 1% have red spots.

The Sanjay, a kindergartener, has red spots, the probability that Sanjay has chicken pox is calculated as:

= (Probability of a random kindergartener having chicken pox at any given time ⋂ Probability of kindergarteners who have chicken pox, and have red spots)/ [(Probability of a random kindergartener having chicken pox at any given time ⋂ Probability of kindergarteners who have chicken pox, and have red spots) + (Probability Kindergarteners who do not have chicken pox and have red spots ⋂ Probability that a kindergartner would not have chicken pox)

= (2% × 75%)/[(2% × 75%) +( 1% × 98%)]

= 150/150 + 98

= 150/248

= 75/124

Answer:

13: 7x 3y

14: 37

15: 60

16: 23

I'm sorry but my vision is too bad, I can't read 17.

:(

Answer:

14.) 2/3

15.) 1/9

16.) 1/4

17.) 1

Step-by-step explanation:

Sorry I couldn't help you with number 18, it's not in the picture.

Hope this helps!

The cumulative probability of having x or fewer successes is 0.157.

To calculate the probability of 11 or fewer successes in 12 trials with a probability of success of 0.4, we can use the cumulative distribution function (CDF) of the binomial distribution. The CDF gives the cumulative probability of having x or fewer successes in n trials.

In this case, the cumulative probability of 11 or fewer successes in 12 trials is given by:

P(X <= 11) = ∑(12 choose i) * (0.4)^i * (0.6)^(12-i)

for i = 0, 1, 2, ..., 11

Where (12 choose i) is the number of ways to choose i successes out of 12 trials, and can be calculated as

12! / (i! * (12-i)!).

This can be calculated using a binomial cumulative distribution function calculator. The result should be approximately 0.157.

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The architect's new design for the room increased the volume by 40 ft³ or 50%.

Length is a term used to describe the magnitude of a line segment, arc, or other geometric figure. It is measured in linear units, such as inches, feet, meters, and centimeters. Length is a one-dimensional measurement; it does not include width, height, or depth. Length is also used to describe the amount of time it takes to complete a task, such as a movie's length or the length of a school day.

Original Length: 10 ft
Original Width: 8 ft
Original Volume: 80 ft³

New Length: 12 ft
New Width: 10 ft
New Volume: 120 ft³

Increase in Volume: 40 ft³

The architect's new design added 2 feet to the length and width of the room, which increased the volume by 40 ft³. This increase in volume was calculated by taking the difference between the original volume (80 ft^3) and the new volume (120 ft³). This change in design resulted in a 50% increase in the room's volume.

In conclusion, the architect's new design for the room increased the volume by 40 ft³ or 50%.

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In this scenario, we have two parallelograms, ghlj and gstu. The given information states that gstu is inside of ghlj. We are then asked to determine why angle ∠l is congruent to angle ∠t.

To understand why ∠l is congruent to ∠t, we need to look at the properties of parallelograms. In a parallelogram, opposite angles are congruent. In other words, if two sides of a parallelogram are parallel, then the opposite angles formed by these sides will be equal.

Looking at parallelogram ghlj, we see that side gh is parallel to side sj (given information). This means that angle ∠l and angle ∠t are opposite angles and therefore congruent.

In conclusion, the reason why ∠l is congruent to ∠t is due to the property of parallelograms. Since gstu is inside ghlj, side gh is parallel to side sj. This parallelism leads to the congruence of the opposite angles ∠l and ∠t.

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Answer:

x = (59/16)

y = (-65/32)

Step-by-step explanation:

2x + 12y = −17

3x + 2y = 7

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

(2x + 12y = −17) × 3

6x + 36y = -51

(3x + 2y = 7) × -2

-6x - 4y = -14

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

6x + 36y = -51

-6x - 4y = -14

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

32y = -65

÷32 ÷32

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

y = (-65/32)

3x + 2y = 7

3x + 2(-65/32) = 7

3x - (65/16) = 7

+(65/16) +(65/16)

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

3x = (177/16)

÷3 ÷3

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

x = (59/16)

I hope this helps!

Daniel's purchasing power will decrease because the interest rate is lower than the historical rate of inflation.

Purchasing power can be portrayed as the quantity of labor and products that a unit of cash or an amount of cash can buy. The connection between financing cost and inflation rate influences the buying force of a saving record.

At the point when the loan cost is higher than the inflation rate, purchasing power increments. Yet, when the interest rate is lower than the expansion rate, buying power falls. For example, In the United States for the 12 months ending April 2022, the annual inflation rate was 8.3%. Since the 0.5% annual interest rate being earned by Daniel is lower than the 8.3% annual inflation rate, the most likely thing to happen to the purchasing power of his savings over time is to fall.

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The total rate charged per hour by each mechanic was $155.

We can divide this amount by the total number of hours worked to determine the rate per hour for each mechanic.

The first mechanic worked for 5 hours and the second mechanic worked for 20 hours. This means that the total number of hours worked was 25.

$155 divided by 25 = $6.20

Therefore, the rate charged per hour by each mechanic was $6.20.

If the sum of the two rates was $15 per hour, then the rate for each mechanic was $7.50 per hour. This means that the two mechanics would have charged $7.50 per hour for the first 5 hours and $7.50 per hour for the last 20 hours, resulting in a total of $155.

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The products of the given monomials are

i. 90a⁵b⁵c⁹

ii. x⁴y⁴

iii. 50x¹¹y³z

iv. 80b⁴c⁴

v. 30m⁵n⁷

From the question, we are to determine the products of each of the three monomials

i. 9ab²c⁵, 2a³b²c² and 5abc²

9ab²c⁵ × 2a³b²c² × 5abc²

= 9 × 2 × 5 × a × a³ × a × b² × b² × b × c⁵ × c² × c²

= 90 × a⁵ × b⁵ × c⁹

= 90a⁵b⁵c⁹

ii. xy², x²y and xy

xy² × x²y × xy

= x × x² × x × y² × y × y

= x⁴ × y⁴

= x⁴y⁴

iii. 5x⁵, y²x⁵ and 10xyz

5x⁵ × y²x⁵ × 10xyz

= 5 × 10 × x⁵ × x⁵ × x × y²  × y × z

= 50 × x¹¹ × y³ × z

= 50x¹¹y³z

iv. (-4b²c), (-2bc) and 10c²b

(-4b²c) × (-2bc) × 10c²b

= -4b²c × -2bc × 10c²b

= -4 × b² × c × -2 × b × c × 10 × c² × b

= -4 × -2 × 10 × b² × b × b × c  × c × c²

= 80 × b⁴ × c⁴

= 80b⁴c⁴

v. Multiply (-5m²n²) by (-6m³n⁵)

(-5m²n²) × (-6m³n⁵)

= -5m²n² × -6m³n⁵

= -5 × m² × n² × -6 × m³ × n⁵

= -5 × -6 × m² × m³ × n² × n⁵

= 30 × m⁵ × n⁷

= 30m⁵n⁷

Hence, the products of the given monomials are

i. 90a⁵b⁵c⁹

ii. x⁴y⁴

iii. 50x¹¹y³z

iv. 80b⁴c⁴

v. 30m⁵n⁷

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Given that the square region has been partitioned into 5 identical rectangular regions, and the perimeter of each rectangular region is 30. We are to find the perimeter of the square region.

As we know that the perimeter of a rectangle is given by P= 2 (l + b)
Let's say the length of the rectangle is 'l' and the breadth of the rectangle is 'b'. Since the five rectangular regions are identical, all of them will have the same length and breadth. Let's take the length and breadth of each rectangular region as x and y respectively. So, the perimeter of each rectangular region is given by P = 2(x + y) = 30Given P = 30, we get2(x + y) = 302x + 2y = 30x + y = 15... equation (1)
We know that the square region is partitioned into 5 identical rectangular regions. Therefore, the length of the square region will be 5 times the length of the rectangular region and the breadth of the square region will be the same as the breadth of the rectangular region. So, length of the square region = 5x, and breadth of the square region = y.
The perimeter of the square region = 2(5x + y) = 10x + 2yAs we know that x + y = 15 (from equation 1)So, 10x + 2y = 10(x + y) + 8y= 10(15) + 8y= 150 + 8y. Therefore, the perimeter of the square region is 150 + 8y.

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Thus, the two positive whole numbers that are greater than one multiply to 576 and share only the number one in common is 5.

One of the categories that mathematicians have created for numbers is titled whole numbers, and it contains all of the numbers from 0 to infinity.

The specific class or collection of numbers known as whole numbers includes:

Two positive whole numbers greater than 1 are 2 and 3.

2 and 3 does not have any common factor except 1.

sum of 2 and 3 = 5

Thus, the two positive whole integers that are greater than one multiply to 576 and share only the number one in common is 5.

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Answer:

please anyone answer my latest math questoin on my profile in need urgent help right now

The equation of the tangent line to the curve are  \(y=x-1 , y=\frac{xe-e^{2}+8 }{e}\).

It is required to find the solution.

A tangent is a line that touches the edge of a curve or circle at one point, but does not cross it. The tangent line to a curve at a point is that straight line that best approximates (or “clings to”) the curve near that point.

Given:

\(y=8\frac{lnx}{x} \\\\y'=8(\frac{1/x*x-lnx*1}{x^{2} } \\\\y'=\frac{1-lnx}{x^{2} }\)

Now, we find the slope of the tangent by inserting the point (1,0) into the derivative.

\(m_{tangent}=\frac{1-ln1}{1^{2} }\\\\m_{tangent}=1-0/1\\\\m_{tangent} =1\)

We can now find the equation, because we know the slope and a point (1, 0).

\(y-y_{1} =m(x-x_{1} )\\\)

y-0=1(x-1)

y=x-1

We can now find the equation, because we know the slope and a point (e, 8/e).

\(y-y_{1} =m(x-x_{1} )\\\\y-8/e=1(x-e)\\\\y=\frac{xe-e^{2}+8 }{e}\)

Therefore, the equation of the tangent line to the curve are  \(y=x-1 , y=\frac{xe-e^{2}+8 }{e}\).

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The doubling time for the bacteria population is approximately 2.08 hours.

The formula for exponential growth

n = \(n_0\) × 2^(t/d)

where \(n_0\) is the initial number of bacteria (at t=0)

d is the doubling time

2^(t/d) is the factor by which the population has grown since t=0.

After 12 hours, there are 2 million bacteria

Substitute the values

24,691.4 =  \(n_0\) × 2^(12/d)

24,691.4/  \(n_0\) = 2^(12/d)

ln(24,691.4/ \(n_0\)) = ln(2^(12/d))

ln(24,691.4/  \(n_0\)) = (12/d) × ln(2)

d = 12 / (ln(24,691.4/  \(n_0\))/ln(2))

Estimate that the initial number of bacteria

\(n_0\) = 2000000 / 81

= 24691.4

Substitute this into our equation for d,

d = 12 / (ln(3)/ln(2))

d ≈ 2.08 hours

Therefore, the doubling time is approximately 2.08 hours.

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If there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

each slice of the 12-inch thin-crust cheese pizza would have an equal distribution of sauce and toppings. This means that each slice would have the same amount of sauce and toppings spread evenly across its surface.

Since the pizza is cut equally into eight slices, each slice would represent 1/8th of the total pizza. Therefore, each slice would have an equal portion of the sauce and toppings.

It's important to note that the exact amount of sauce and toppings on each slice would depend on the original distribution applied to the pizza before it was sliced. If the pizza was prepared with a uniform distribution of sauce and toppings across the entire pizza, then each slice would indeed have an equal amount. However, if there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

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Answer:

I think

Step-by-step explanation:

That it is 2.3435

Answer: B

Step-by-step explanation: Its like that beacuse you are decreasing by 9 leaters the 9 is negtive anyways you start with 500 and lose 9 leters per minute

Answer:

b

Step-by-step explanation:

Answer:

I would say 4 inches

Step-by-step explanation:

Answer:

210

Step-by-step explanation:

There are 7 * 6 * 5 ways to finish. This is because we have 3 slots:

For 1st place, there are 7 people that could take that place, so we have 7

For 2nd place, there are 6 people, because one person already took 1st, so they cant be second as well.

For 3rd place, there are 5 people, because 2 people already took first and second place, and neither of them can be third then.

So we have:

7*6*5 = 210

Answer:

210 ways

Step-by-step explanation:

For 1 st place there are 7 different runners

Now there are only 6 options

For 2nd place there are 6 different runners

Now there are only 5 options

For 3rd place there are 5 different runners

7*6*5

Answer:

area = 693

Step-by-step explanation:

The area of a quadrilateral can be found using the formula; base * height

It is given that the height is 33, the base is 21;

Multiply the two

21 *33 = 693

Answer:

4 + b² = 104

Hope this helps. :)

Answer:

b^{2}  + 4 = 104.

Step-by-step explanation:

The sum of 4 and the second power of b basically means 4 + b^2.

b^2 + 4 = 104

\(b^{2} + 4 = 104\)

b^2 = 100

b = plus or minus 10.

Hope this helps!

There were 671 liars living on the island initially out of 2013 people living on the island.

Let's assume the number of truthtellers is x and the number of liars is y.

According to the given information, each day one person says that when they leave the island, the number of truthtellers will be equal to the number of liars.

This implies that the person speaking must be a liar.

On the first day, if the person speaking is a liar, then the number of liars on the island will increase by one (y+1) and the number of truthtellers will remain the same (x).

The equation can be written as:

x = y + 1

On the second day, if the second person speaking is also a liar, the number of liars will increase by one again (y+2) and the number of truthtellers will remain the same (x).

The equation becomes:

x = y + 2

We can generalize this pattern for each day:

x = y + k

After 2013 days, there is no one left on the island, so x + y = 0.

Substituting this into the equation, we get:

(y + k) + y = 0

Simplifying, we find:

2y + k = 0

Since y represents the number of liars, we want to find a value of y that satisfies this equation.

To do that, we need to find a value of k such that 2013 + k is divisible by 2.

By observing that 2013 is odd, we can conclude that k must be an odd number.

The smallest odd number that satisfies this condition is k = 1.

Substituting k = 1 into the equation, we get:

2y + 1 = 0

Solving for y, we find:

y = -1/2

However, the number of liars cannot be negative, so we can disregard this solution.

Therefore, there were 671 liars living on the island initially.

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