Make r the subject.
Q=4πr^2+1/3πr^2h


​

Using a system of equations, it is found that the number of votes that he received for each place is given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

He received 892 total votes, hence:

x + y + z = 892.

Total of 2029 points, hence:

3x + 2y + z = 2029.

He had 4 fewer than twice as many second-place votes as first-place votes, hence:

x = 2y - 4.

Replacing in each of the first two equations:

x + y + z = 892.

2y - 4 + y + z = 892

3y + z = 896.

3x + 2y + z = 2029

3(2y - 4) + 2y + z = 2029

8y + z = 2041.

Multiplying the first equation by -1, and subtracting the second equation from the first, we have that:

5y = 1145

y = 1145/5

y = 229.

The other amounts are given as follows:

Hence the number of votes that he received for each place is given as follows:

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Given that a rectangle ABCD, where AB = 4, side BC that AP 3 and P lies on diagonal AC such 3/2. We have to find the distance PB.Solution:In the given rectangle ABCD,AB = 4Therefore,

AD = BC = 4 [because opposite sides of a rectangle are equal]P lies on diagonal AC and AP = 3We have to find PBWe will use the Pythagorean theorem and properties of similar triangles to find the distance PB.From triangle APD,

Using Pythagorean theorem,PD2 = AD2 + AP2 = 42 + 32 = 16 + 9 = 25PD = √25 = 5From triangle ABC,Using Pythagorean theorem,AC2 = AB2 + BC2 = 42 + BC2BC2 = AC2 - AB2= (3/2)2 - 42= 9/4 - 16= - 55/4 [As, the value inside the square root can't be negative, Therefore PB can't exist, and we can say that PB is imaginary or it doesn't exist]Hence, the distance PB is imaginary or it doesn't exist.

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The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.

To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:

z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906

z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849

Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.

To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:

P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.

As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.

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Answer:

A. They are now a significant part of communication

Step-by-step explanation:

take care

It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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Answer:

x>2

Step-by-step explanation:

Answer:

I used Desmos to graph your requirements, and i took a screenshot of the graph. Credit to Desmos for the great graphing system.

Step-by-step explanation:

Answer:

see image

Step-by-step explanation:

Anytime you see f(x) that just means y.

So f(x)=5 just means

y = 5

Anytime you have an equation to graph that is in the format

"y= anumber", that is a Horizontal line. So the first piece of your graph is the horizontal line thru 5. But also that's only for x>=3. It includes the 3 with the "or=to" underline. So the point must be a solid filled-in point. (Some weird books or teachers use a [ square bracket.) Same logic works for the second piece of the function. f(x) = -6 is the same as y= -6 and is a horizontal line thru -6. But the point at (3, -6) is an Open dot! See image.

Answer:

5563.85 But round the nearest whole number is 5564

Step-by-step explanation:

Formule is P=Ie^(r)(t)

If, In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded continuously,  then 5563.85 is the population in 2022.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

In 2010 the Network Club membership was 2,500.

Annual growth rate of approximately 8%

8% is converted to decimal value by dividing 8 with 100

8/100=0.08

\(P=Ie^{rt}\)

p is the final population

I is the initial population

\(p=Ie^{0.08(10)}\)

\(p=2500e^{0.8}\)

p=5563.85

Hence, 5563.85 is the population in 2020.

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The sample proportion of the defective garments from the given random sample size is equal to 20%.

Total number of random sample size of garments = 200

Total number of defective garments = 40

Sample proportion

= (number of defective garments)/ (total number of random sample size)

Substitute the value we get,

⇒ Sample proportion = ( 40 / 200 )

⇒ Sample proportion = ( 0.2 )

In percentage form

⇒ Sample proportion = 0.2 × 100

⇒ Sample proportion = 20%

Therefore, the shape of the sampling proportion of the given sampling distribution when out of random samples size of 200 garments 40 are defective is equal to 20%.

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The above question is incomplete , the complete question is:

what is the shape of the sampling distribution of the sample proportion of 40 defective garments for random samples of size 200? justify your answer.

Answer:

12π or 37.7 cm

Step-by-step explanation:

The formula for the circumference of a circle is 2πr or πd. In this case, r represents the radius, a segment from the center of the circle to any point on the circle. The d stands for diameter, a line running through two endpoints on the circle with the center point in the middle. This means that the diameter is twice the radius (imagine a line cutting across half a pizza and then a line cutting across only a quarter, this is diameter and radius at work!).

To solve for the circumference, I will use both formulas (although πd is easier since the diameter is already given)

2πr

2π(12/2)

2π(6)

12π ≈ 37.7 cm

πd

π(12)

12π ≈ 37.7 cm

Answer:

23 there will be 100 paperclips leftover

The fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.

So, (A) The fraction of the animals is chickens: 52/80

Simplest form: 13/20

(B) In decimal form: 0.65

Therefore, the fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.

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Answer:

MAD = 2

Step-by-step explanation:

First We'll find the mean of data

Mean = \(\frac{20}{5}\)

Mean = 4

Then, we'll find absolute deviation

=> |4-3| = 1

=> |4-2| = 2

=> |4-1| = 3

=> |4-1| = 3

=> |4-3| = 1

Now, taking the mean of these absolute deviations:

MAD = \(\frac{1+3+3+2+1}{5}\)

MAD = \(\frac{10}{5}\)

MAD = 2

Answer:

Step-by-step explanation:

Equation A:

-3(x + 7) = 24

=> -3x -21 = 24

=> -3x = 45

=> x = -15

Equation B:

x + 7 = -8

=> x = -15

Answer:

10 cm

Step-by-step explanation:

The total number of tires in the parking lot, is (13×2)+(98×4)=t.

There are 13 bikes and each bike has 2 tires,

so the number of bike tires = number of bikes × number of tires

Thus,  number of bike tires = 13×2.

There are 98 cars and each car has 4 tires,

so the number of car tires = number of cars × number of tires

Thus,  number of car tires = 98×4.

To find the total number of tires (t),

add the number of bike tires and car tires together: (13×2)+(98×4)

Thus, t = (13×2)+(98×4)

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Answer:

I'm not sure if you mean 5 x 105 which = 525. Or 5 x 10^5 which = 500,000

Step-by-step explanation:

The answer to the first one. is easy, you just have to multiply it first. The second one is pretty simple too. You would have move or shift the decimal point 5 times to the right.

Step-by-step explanation:

it will

5 shirts for $20

hope it helps

Answer:

30/3=10

so every bucket gets 10 liters

Step-by-step explanation:

If the sample of bacteria is growing at an hourly rate of 15% continuously and the  bacteria began with 11 bacteria then there will be 244.178 samples bacteria after 21 hours.

Given growth of bacteria 15% ,bacteria at beginning 11.

We have to find the number of sample of bacteria after 21 hours.

We have to first form exponential function which shows the growth of bacteria in variable t.

Exponential function which shows the sum is y=P\(e^{rt}\)

where P is initial amount ,

r is rate and

y is the sum

So in our problem P=11 and r=0.15

y=11*\(e^{0.15t}\)

To find the  samples after 21 hours we have to put t=21.

y=11\(e^{0.15*21}\)

y=11*\(e^{3.1}\)

y=11*22.198  (\(e^{3.1}\)=22.198 from e table)

y=244.178

Hence the samples after 21 hours will be 244 approximately.

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Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

We have,

To find the mean and variance of the return series, we can substitute the given model into the equation and calculate:

Mean of rt:

E(rt) = E(0.02 + 0.5rt-2 + et)

= 0.02 + 0.5E(rt-2) + E(et)

= 0.02 + 0.5 * 0 + 0

= 0.02

The variance of rt:

Var(rt) = Var(0.02 + 0.5rt-2 + et)

= Var(et) (since the term 0.5rt-2 does not contribute to the variance)

= 0.02

The mean of the return series rt is 0.02, and the variance is 0.02.

To compute the lag-1 and lag-2 autocorrelations of rt, we need to determine the correlation between rt and rt-1, and between rt and rt-2:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

Since we are given r100 = -0.01 and r99 = 0.02, we can substitute these values into the equations:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

= Cov(r100, r99) / (σ(r100) * σ(r99))

= Cov(-0.01, 0.02) / (σ(r100) * σ(r99))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

= Cov(r100, r98) / (σ(r100) * σ(r98))

To compute the 1- and 2-step-ahead forecasts of the return series at

t = 100, we use the given model:

1-step ahead forecast:

E(rt+1 | r100, r99) = E(0.02 + 0.5rt-1 + et+1 | r100, r99)

= 0.02 + 0.5r100

2-step ahead forecast:

E(rt+2 | r100, r99) = E(0.02 + 0.5rt | r100, r99)

= 0.02 + 0.5E(rt | r100, r99)

= 0.02 + 0.5(0.02 + 0.5r100)

The associated standard deviation of the forecast errors can be calculated as the square root of the variance of the return series, which is given as 0.02.

Thus,

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer: $217.26

Step-by-step explanation:

13.79 x 6 = 82.74

300 - 82.74 = 217.26

Ms. Gregory has $217.26 left.

1) This is a question in which we need to evaluate x when x=6.

2) So, we can plug x=6 into that rational equation to figure out the value:

So, that is the answer

The probability of drawing a second black bead, given that the first bead is black, is 1/3 or 0.33.

The probability of drawing two black beads from a bag without replacement is given as 335. The probability of drawing one black bead is also given as 310. To calculate the probability of drawing a second black bead, given that the first bead is black, we can use the formula P(B2|B1) = P(B1 and B2) / P(B1). The probability of drawing one black bead is P(B1) = 310. The probability of drawing the two black beads is P(B1 and B2) = 335. Therefore, P(B2|B1) = 335 / 310 = 1/3 = 0.33.

The probability of drawing two black beads from a bag without replacement is given as P(B1 and B2) = 335. This means that, out of all the possible combinations of beads in the bag, 335 of them contain two black beads. The probability of drawing one black bead is given as P(B1) = 310. This means that, out of all the possible combinations of beads in the bag, 310 of them contain one black bead. To calculate the probability of drawing a second black bead, given that the first bead is black, we can use the formula P(B2|B1) = P(B1 and B2) / P(B1). The probability of drawing one black bead is P(B1) = 310. The probability of drawing two black beads is P(B1 and B2) = 335. Therefore, P(B2|B1) = 335 / 310 = 1/3 = 0.33. This means that the probability of drawing a second black bead, given that the first bead is black, is 1/3 or 0.33.

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Answer:

không

Step-by-step explanation:

Answer:

(a + b)(a - b) = a² - b²

Step-by-step explanation:

(a + b)(a - b) = a (a - b ) + b (a - b )

                 = a²  - ab + ba  - b²             [ ab = ba ]

                 = a² - ab + ab - b²               [ ab - ab = 0 ]

                 = a² - b²

The correct expression to find the volume of a rectangular prism is D. (3 × 6) × 15 = 270 in.3.

Expression is a word, phrase, or gesture that conveys an idea, thought, or feeling. It is an outward representation of an emotion, attitude, or opinion. Expressions can be verbal, physical, or written. They can also take the form of art, music, or dance. Expression is used to communicate and express emotions, thoughts, and ideas. It can be a powerful tool to create a connection with others and build relationships.

The correct expression to find the volume of a rectangular prism is D. (3 × 6) × 15 = 270 in.3. This expression involves multiplying the length, width, and height of the rectangular prism in order to calculate the total volume. In this case, the length is 3, the width is 6, and the height is 15. If these values are multiplied together, the result is 270 in.3, which is the total volume of the rectangular prism.

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1. The finance charge on June 11 is $1.98.

2. The new card balance on June 12th is $341.30

To calculate the finance charge and new card balance, we first need to calculate the average daily balance for the billing cycle.

May 13 Charge toys: $129.79 (balance: $129.79)

May 15 Payment $50 (balance: $79.79)

June 1 Charge clothing $135.95 (balance: $215.74)

June 8 Charge Housewares $37.63 (balance: $253.37)

Billing cycle: May 13 to June 11 (30 days)

Average daily balance:

=  (129.79 x 18) + (79.79 x 16) + (215.74 x 10) + (253.37 x 6) / 30

= $152.49

The Finance charge is computed as:

= Average daily balance * Monthly periodic rate.

= 152.49 x (1.3/100)

= $1.98.

To calculate the new card balance on June 12th, we need to add the finance charge and any new charges to the previous balance and subtract any payments made.

Previous balance (as of June 1st) = $215.74

New charges (since June 1st) = $135.95 + $37.63 = $173.58

Payments made (since May 15th) = $50

The New card balance on June 12th will be:

= $215.74 + $173.58 + $1.98 - $50

= $341.30

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The amount of juice the cup can hold given that the cup has diameter of 8 centimeters and a height of 12 centimeters is 602.88 cm³

To know the amount of juice the cup can hold, we shall obtain the volume of the cup.

We shall use the formula for obtaining volume of cylinder to obtain the volume of the cup. Details below:

Volume = πr²h

Volume = 3.14 × 4² × 12

Volume = 3.14 × 16 × 12

Volume = 602.88 cm³

Thus, we can conclude from the above calculation that the amount of juice the cup can hold is 602.88 cm³

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