Find the volume of the cone.
either enter an exact answer in terms of it or use 3.14 for i and round your final answer to the nearest
hundredth.

Answer:

Step-by-step explanation:

.2

The given expression is equivalent to option A.

Given expression

\(a^{1/5}\)

We know the \(\sqrt{2} = a ^{1/2}\)

For option A. \(\sqrt[5]{a} = a^{1/5}\)

For option B. \(\sqrt[1/5]{a} = a^{\frac{1}{1/5} }= a^5\)

For option C. \(\frac{1}{(\sqrt{a} )^5} = \frac{1}{a^{1/2\times5}} = a^{5/2}\)

For option D. \(\frac{1}{\sqrt[5]{a} } = a^{-1/5}\)

Therefore, the given expression is equivalent to \(\sqrt[5]{a}\)

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Answer:

x = 7.5

Step-by-step explanation:

\( \frac{6}{15} = \frac{3}{x} \)

cross multiply expressions

6x = 45 divide both sides by 6

x = 7.5

Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

Answer:

20.25

Step-by-step explanation:

Answer:

20.25

Step-by-step explanation:

Use the “ %/100 = is/of ” method

45          ?

__    =     __

100          45

cross mutilps 45(45) = 2,025

then divide 2,025 by 100 = 20.25

Answer:

6.77 pounds or 6 7/9 pounds

Step-by-step explanation:

10 ≥ 4.99 + 0.74x

1. Swap sides

4.99 + 0.74x ≤ 10

2. Subtract 4.99 on both sides

(4.99 - 4.99) + 0.74x ≤ 10 - 4.99 = 0.74x ≤ 10 - 4.99

3. Subtract 4.99 from 10

0.74x ≤ 5.01

4. Divide both sides by 0.74

(0.74x/0.74) ≤ (5.01/0.74) = x ≤ 5.01/0.74

5. Solve

x ≤ 5.01/0.74 =

x ≤ 501/74 ≈

6.77

Answer:

Step-by-step explanation:

People who ride the tram = 7

People who don't ride the tram = 6

Total people at the zoological garden = People who ride the tram + People who don't ride the tram

= 7 + 6

= 13

Total people at the zoological garden = 13

Ratio of people who ride the tram to all people in three ways.

Below is how to write ratio in three ways

7 : 13

7 to 13

7/13

Ratio of all people to people who​ don't ride the tram in three ways

13 : 6

13 to 6

13/6

Answer:

3/32-pound cheese in 1 serving

Step-by-step explanation:

(3/8)/4=3/32 or 0.09375 lbs

Answer:

0 it went minus 2 minus 3 minus and so forth

The  required general solution for the given equation is

y(x) = \(e^{(-x/2)(C1 sin(\sqrt{(7/2)x} )}\) + C2 cos(√(7/2)x)) + \(e^{(-x/2)(C3 sin(\sqrt{(21/2)x }\)+ C4 cos(√(21/2)x))

here

C1, C2, C3 and C4 = constants determined by initial conditions.

It is given to us

y = sin(x) is a solution of y⁴ + 2y"' + 11y" +2y' + 10y = 0, by the method of undetermined coefficient we can calculate the general solution.

we evaluate the differential equation by considering that

y = \(e\sqrt{(rx)}\). We get r⁴ + 2r³ + 11r² + 2r + 10 = 0.

After factorizing the equation as

(r² + r + 2)(r² + r + 5) = 0.

The  evaluated roots of this equation are

r = -1/2 ± i√(7/2) and r = -1/2 ± i√(21/2).

We know that sin(x) is a solution of the differential equation,

Therefore, y = A sin(x) + B cos(x) is also a solution.

Now implementing the roots that we have derived, the general solution is

y(x) = \(e ^{(-x/2)(C1 sin(\sqrt{(7/2)x\)+ C2 cos(√(7/2)x)) + \(e ^{(-x/2)(C3 sin\sqrt{((21/2)x)} }\)+ C4 cos(√(21/2)x))

The  required general solution for the given equation is

y(x) = \(e^{(-x/2)(C1 sin(\sqrt{(7/2)x} )}\) + C2 cos(√(7/2)x)) + \(e^{(-x/2)(C3 sin(\sqrt{(21/2)x }\)+ C4 cos(√(21/2)x))

here

C1, C2, C3 and C4 = constants determined by initial conditions.

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Let x be the full price of each Mighty Mare toy pony.

During the holiday sale, Pamela purchased each toy at $3 less than its full price. Therefore, the price she paid during the sale was:

x - $3

Since she bought 4 of these toys, her total cost during the sale was:

4(x - $3)

We also know that Pamela paid a total of $52 during the sale. Therefore, we can set up an equation:

4(x - $3) = $52

Simplifying this equation, we get:

4x - $12 = $52

Adding $12 to both sides, we get:

4x = $64

Dividing both sides by 4, we get:

x = $16

Therefore, each Mighty Mare toy pony costs $16 at full price.

Let's assume that the full price of each Mighty Mare toy pony is x dollars. Since Pamela purchased 4 Mighty Mare toy ponies, each at $3 less than its full price, the cost of each toy pony during the sale would be (x - 3) dollars.

To find the equation that represents this situation, we can set up the equation based on the given information:

4 * (x - 3) = 52

In this equation, 4 represents the number of Mighty Mare toy ponies purchased, (x - 3) represents the cost of each toy pony during the sale, and 52 represents the total amount paid by Pamela.

By solving this equation, we can determine the value of x, which represents the full price of each Mighty Mare toy pony.

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Have a GREAT day!!!

Answer:

$17.5 differnce

Step-by-step explanation:

20% tip on is $57.49

20% tip off is $39.99

tip on vs off when a tip is on means its

Based on the relationship between the number of orders served by Mary, Joe, and Deandre, the number of orders they each served was:

Assuming that the number of orders served by Mary was x, the formula for the total orders served would be:

Deandre's orders + Mary's orders + Joe's orders = 95
3x + x + (x - 10) = 95

Solving for Mary's orders gives:

3x + x + x - 10 = 95

5x - 10 = 95

5x = 95 + 10

x = 105 / 5

x = 21

Number of orders by Deandre:

= 21 x 3

= 63 orders

Orders by Joe:

= 21 - 10

= 11 orders

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Answer: 4) 3x²-14x+14

Explanation:

Use the binomial theorem (a−b)² = a² - 2ab + b² to expand (x-2)².

Use the distributive property to multiply 3 by x²-4x+4.

Use the distributive property to multiply −2 by x−1.

Combine −12x and −2x to get −14x.

Add 12 and 2 to get 14.

It is 3x²+14x+14, the trinomial equivalent to 3(x-2)²-2(x-1). OPTION 4.

Answer: That is false

Step-by-step explanation: 9 is odd but not prime

The statement "If an odd number is less than 15, then it is prime" is false because the number 9 is not prime.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

If an odd number is less than 15, then it is prime.

As we know,

The prime number is the number that has factors only 1 and itself the number.

The odd number is less than 15.

The odd number is less than 15 = {13, 11, 9, 7, 5, 3}

The statement "If an odd number is less than 15, then it is prime" is false

Because the number 9 is not prime.

Thus, the statement "If an odd number is less than 15, then it is prime" is false because the number 9 is not prime.

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The miles per gallon does the car get on the trip is 6.3 miles per hour and the number of gallons required for the car to travel 549 miles is 87.14 gallons

The rate of a function is also known as its slope. According to the question, if an automobile travels 305 miles on 16 2/3 gallons of gasoline, the unit rate is calculated as;

Unit rate = 305/16(2/3)

Convert mixed fraction to improper

Unit rate = 305/(50/3)
Unit rate = 105 * 3/50
Unit rate = 6.3 miles per hour

Hence the miles per gallon does the car get on the trip is 6.3 miles per hour.

To determine how many gallons would be required for the car to travel 549 miles, this is expressed as;

Number of gallons = 549/6.3
Number of gallons = 87.14gallons

Hence the number of gallons required for the car to travel 549 miles is 87.14 gallons

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Answer:

B i believe is the answer

Step-by-step explanation:

P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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Answer:

d

Step-by-step explanation:

because

The probability that the two given players play each other at any point in the tournament is 1/105.

It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

In probability theory, we use probability to quantify the uncertainty associated with a particular event or outcome. For example, if we toss a fair coin, the probability of getting heads is 0.5, because there are two possible outcomes (heads or tails) and each outcome has an equal chance of occurring.

Let's assume the two given players are player A and player B.

In the first round, player A has to be paired with one of the 15 remaining players. The probability of this happening is 1/15.

Assuming player A wins their first match, they will be paired with one of the 7 remaining players in the second round. The probability of player B being matched up with player A at this point is 1/7.

So the probability of player A and player B playing each other in the tournament is the product of the probabilities of these two events occurring:

P(A and B play each other) = P(A and B are paired in the first round) × P(B is paired with A in the second round, assuming A wins the first round)

= (1/15) × (1/7)

= 1/105

Therefore, the probability that the two given players play each other at any point in the tournament is 1/105.

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Answer:

85.5 reals

Step-by-step explanation:

Aqui, usando a função de análise, queremos saber a quantidade de dinheiro que deve ser investido para fornecer o número de visualizações.

A maneira como podemos resolver isso é através da substituição. Precisamos apenas substituir F (x) na equação e resolver x, o que nos dará a idéia da quantidade de dinheiro a ser investido.

matematicamente

F (x) = 40x + 80

3500 = 40x + 80

40x = 3500-80 40x = 3420 x = 3420/40

x = 85,5 reais

98% confidence interval for the mean of repeated measurements of the weight is (10.216, 10.244).

We need to average at least 460 measurements to get a margin of error of 0.005 with 98% confidence.

(a) To find a 98% confidence interval for the mean of repeated measurements of the weight, we can use the formula:

CI = X ± Zα/2 * (σ/√n)

where X is the sample mean, Zα/2 is the critical value from the standard normal distribution for a 98% confidence level (which is 2.33), σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

CI = 10.230 ± 2.33 * (0.020/√40)

CI = 10.230 ± 0.014

The 98% confidence interval for the mean of repeated measurements of the weight is (10.216, 10.244).

(b) To find out how many measurements must be averaged to get a margin of error of 0.005 with 98% confidence, we can rearrange the formula for the confidence interval:

n = (Zα/2 * σ / E)²

where E is the margin of error and the other variables have the same meaning as before.

Substituting the given values, we get:

n = (2.33 * 0.020 / 0.005)²

n = 459.524

We round up to the nearest whole number because we cannot have a fractional sample size. Therefore, we need to average at least 460 measurements to get a margin of error of 0.005 with 98% confidence.

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Answer:

yo i only got number 4 for you but here it goes.......: 0.70x+18y-5

Step-by-step explanation:

(0.75x  -  12y) + (-5  +  6y  -  0.5x)

regroup to the variables : (0.70x-0.5x) + (12y+ 6y-5)

put it together: (0.70x)+(18y-5)

you cant add unlike terms so you remove the parenthesies and your done.

x - number of minutes;

f ( x ) - the distance from the finish line.

  x :        0     2      4      6

f ( x ) :    3      2      1     0

f ( x ) = 3 - x/2

Answer: B ) f ( x ) = -1/2 x + 3

Answer:

Here you go hope it helps

We fail to reject the hospital's claim that the proportion of full-term babies born in the community that weigh more than 7 pounds is 41% at the 0.10 level of significance.

To determine if there is enough evidence to reject the hospital's claim that the proportion of full-term babies born in the community that weigh more than 7 pounds is 41%, we can conduct a hypothesis test.

Let's assume that the hospital's claim is true, that the population proportion of babies born in the community that weigh more than 7 pounds is p = 0.41. Then the null hypothesis would be

H0: p = 0.41

The alternative hypothesis would be that the proportion is different from 0.41, i.e., a two-tailed test

Ha: p ≠ 0.41

The significance level of the test is α = 0.10.

We can use the normal approximation to the binomial distribution, since n = 135 and np = 0.41 × 135 ≈ 55 and n(1 − p) = 80 are both greater than 10.

The test statistic is calculated as:

z = (x − np) / sqrt(np(1 − p))

where x = 44 is the number of babies in the sample who weigh more than 7 pounds.

Substituting the values, we get

z = (44 − 0.41 × 135) / sqrt(0.41 × 135 × 0.59) = 1.53

Using a standard normal distribution table, we find that the probability of getting a z-value of 1.53 or more extreme under the null hypothesis is 0.064.

Since this probability is greater than the significance level of 0.10, we fail to reject the null hypothesis. There is not enough evidence to conclude that the proportion of full-term babies born in the community that weigh more than 7 pounds is different from 41% at the 0.10 level of significance.

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Answer:

Step-by-step explanation:

"The size of the tank a fish collector needs depends on how many fish he has."

Dependent variable is the size of the tank.

Independent variable is how many fish a fish collector has.

Answer:

It's Right, I took the test. =)

Step-by-step explanation:

Answer:

1a. 0 pounds of grapes costs 0 dollars.

1b. 1 pound of grapes costs 3 dollars.

2a. There are 0 batteries in 0 packs of batteries.

2b. There are 10 batteries in 1 pack of batteries.