What is the height of a cone when the radius is 4 and the volume is 32

Answer:

A= 63

Step-by-step explanation:

the both sides are equal so it will be 63 and 63

angle c would be 54

Adding all the sides would give 180 as all sides equal 180

C(x) = 0.25x + 45 , Slope is .25 dollars per mile and the y intercept is 45 dollars.

Given,

The cost C(ar), where a is the number of miles driven, of renting a car for a day is $45 + $0.25 per mile.

To find the slope , y - intercept and C(a)

Now, According to the question:

A renting a car for a day is $45 plus  $0.25 per mile.

C(x) = 0.25x + 45

This is in the form y = mx + b where m is the slope and b is the y intercept

The slope is .25 dollars per mile and the y intercept is 45 dollars

Hence, C(x) = 0.25x + 45 , Slope is .25 dollars per mile and the y intercept is 45 dollars.

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The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

The intervals of each behavior of the function are given as follows:

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Using the time formula, it will take the lizard 19 days to reach the top of the well.

The time formula, using distance and speed, is as follows:

Time = Distance ÷ Speed

The depth of the well and the lizard's position = 19 feet

Daily crawling-up rate = 5 feet

Daily crawling down rate = 4 feet

Difference between crawling up and slipping down rates = 1 foot per day (5 - 4)

Therefore, the lizard's net average crawling up speed or rate = 1 foot per day

Time (in days) = Distance/Average Rate

19/1 = 19 days

Thus, for the lizard to reach the top of the well, it will take 19 days.

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Answer:

here are some websites you can use:

mathpapa .com

desmos .com (scientific calculator)

calculatorsoup .com

The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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1.) Probability of getting 1: 0.12 or 12%.

2.) Probability of getting 2: 0.16 or 16%.

3.) Probability of getting 3: 0.25 or 25%.

4.) Probability of getting 4: 0.18 or 18%.

5.) Probability of getting 5: 0.15 or 15%.

6.) Probability of getting 6: 0.14 or 14%.

To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:

Number: 1 2 3 4 5 6

Times: 12 16 25 18 15 14

To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):

Probability of getting 1 = 12 / 100 = 0.12.

Probability of getting 2 = 16 / 100 = 0.16.

Probability of getting 3 = 25 / 100 = 0.25.

Probability of getting 4 = 18 / 100 = 0.18.

Probability of getting 5 = 15 / 100 = 0.15.

Probability of getting 6 = 14 / 100 = 0.14.

Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:

1: 0.12 or 12%,

2: 0.16 or 16%,

3: 0.25 or 25%,

4: 0.18 or 18%,

5: 0.15 or 15%,

6: 0.14 or 14%.

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Here's the complete chart:

Month  Balance Interest Payment New Balance

0  $1,357.56     -            -          $1,357.56

1 $1,383.54 $23.98 $150 $1,257.52

2 $1,409.62 $26.08 $150 $1,266.06

3 $1,435.81 $27.19 $150 $1,473.61

Percent is a way of expressing a fraction or a ratio as a number out of 100. The word "percent" comes from the Latin per centum, which means "per hundred." Percentages are commonly used in many areas, including finance, economics, and statistics. For instance, interest rates, inflation rates, and stock market returns are often expressed as percentages. In addition, percentages are used to calculate discounts, markups, and taxes.

Here,

To calculate the new balance by the end of the 3rd month, we need to use the formula for the balance after n months with monthly payments:

B(n) = (1 + r)ⁿ * B(0) - (PMT/r) * [(1 + r)ⁿ-1]

where B(0) is the initial balance, r is the monthly interest rate, PMT is the monthly payment, and n is the number of months.

In this case, we have:

B(0) = $1357.56

r = 1.7% per month = 0.017

PMT = $150

n = 3 months

Plugging these values into the formula, we get:

B(3) = (1 + 0.017)³ * $1357.56 - ($150/0.017) * [(1 + 0.017)³ - 1]

= $1473.61

Therefore, the new balance by the end of the 3rd month is $1473.61.

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The standard absolute value graph has been shifted 7 units to the right and 3 units down to get this graph.  

That means we have answer B: f(x) = | x - 7 | - 3

Remember that the left-right shifts are opposite from what they would appear to be in the equation.

  | x - 7 | shifts it right 7 units.

  | x + 7 | shifts it left 7 units.

The values are given below,

Left Hand Limit i.e. lim x -> 1- f(x) = 3 ,

Right Hand Limit i.e. lim x -> 1+ f(x) = 1 ,

Function value at x = 1 i.e. f(1) = 1 ,

Left Hand Derivative lim x -> 1- f'(x)= -6 and

Right Hand Derivative lim -> 1+ f'(x) = -6.

So, the function f(x) is neither continuous nor differentiable at x = 1.

Given, a piecewise function

              3㏑(3 - 2x) + 3                for x < 1

f(x) =

                   -3x² + 4                      for x ≥ 1

Now, for lim x -> 1- f(x) we will consider the function  3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.

lim x -> 1 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3

= 3 ㏑(1) + 3

= 0 + 3

= 3

Now, for lim x -> 1+ f(x) we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.

lim x -> 1 -3x² + 4 = -3(1)² + 4

= -3 + 4

= 1

Now, for f( 1 ) we will consider the function -3x² + 4,

f(1) = -3(1)² + 4

= -3 + 4

= 1

Now, for lim x -> 1- f'(x) we will consider the derivative of the function

3㏑(3 - 2x) + 3,

lim x -> 1 -6/(3 - 2x) = -6/(3 - 2(1))

= -6

Now, for lim -> 1+ f'(x) we will consider the derivative of the function

-3x² + 4,

lim x -> 1 -6x = -6(1)

= -6

So, the function f(x) is neither continuous nor differentiable at x = 1.

Hence, lim x -> 1- f(x) = 3 , lim x -> 1+ f(x) = 1 ,  f( 1 ) = 1 , lim x -> 1- f'(x) = -6 and lim -> 1+ f'(x) = -6.

The function is neither continuous nor differentiable at x = 1.

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With 99% confidence that the true difference lies between 0.1316 and 0.2694.

A 99% confidence interval for the difference in average SAT scores between coached and uncoached students can be constructed using the data above.

The confidence interval is calculated as (mean of coached students - mean of uncoached students) +/- (2 * standard error of the difference in means).

The mean of coached students is (0.3098 + 0.3399 + 0.219 + 0.0798) / 4 = 0.2155, and the mean of uncoached students is (0.0046 + 0.0248) / 2 = 0.0147. The standard error of the difference in means can be calculated as the square root of ((0.2155(1-0.2155)/4) + (0.0147(1-0.0147)/2)).

The confidence interval is then (0.2155 - 0.0147) +/- (2 * 0.0347) = 0.201 +/- 0.0694, or (0.1316, 0.2694). This indicates that, on average, coached students gain 0.201 points more than uncoached students, with 99% confidence that the true difference lies between 0.1316 and 0.2694.

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

45

Step-by-step explanation:

Answer:

\(59\)

Step-by-step explanation:

\(--------------------------------------------\)

\(7\cdot6+12+5\) = \(?\)

\(42+12+5\) = \(?\)

\(54+5\) = \(?\)

\(59\)

\(--------------------------------------------\)

Hope this helps! <3

\(--------------------------------------------\)

良い日をお過ごしください！:D

\(--------------------------------------------\)

Answer:

Ariana is going to invest P($) in an account paying an interest rate of 3.4% compounded monthly.

After 14 years, the amount of money in Adrina's account is calculated by:

A = P x (1 + rate)^(time)

or

A = P x (1 + 3.4/12)^(14 x 12)

or

9200 = P x (1 + 3.4/12)^(14 x 12)

=> P = 9200/[(1 + 3.4/12)^(14 x 12)]

=> P = 5791.044$

Hope this helps!

:)

The value of the account to reach $9,200 in 14 years is $5,791.

Since interest rate of 3.4% compounded monthly. And, the amount is  $9,200 in 14 years

So, the value should be

\(A = P \times (1 + rate)^{(time)}\\\\A = P \times (1 + 3.4/12)^{(14 \times 12)}\\\\9200 = P \times (1 + 3.4/12)^{(14 \times 12)}\\\\ P = 9200\div [(1 + 3.4/12)^{(14 \times 12)]}\)

P = $5791

hence, The value of the account to reach $9,200 in 14 years is $5,791.

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The paralellograms have 2 pairs of parallel sides, but the trapezoids have just one pair of parallel sides

The item most likely to weigh 2 kilograms is a roast chicken.

The size, breed, and any other ingredients or stuffing used can all affect the weight of a roast chicken. Weights of roast chickens can range from petite ones weighing less than 1 kilogram to larger ones weighing more than 2 kilograms.

The other things that we have there would either weigh less than 2 Kg such as a tea bag or much more than 2 Kg such as a horse. The egg and the tea a very light and would be less than 2 Kg in weight while the bag and the horse would be above 2 Kg in weight.

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So,the value of the 30th percentile of the given data will be =P30=4

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, assessed at x, is the likelihood that X will have a value less than or equal to x in probability theory and statistics.

Using the Cumulative Distribution Function to Calculate Probabilities

F(x) is a cumulative distribution function that calculates the likelihood that the random variable X is smaller than or equal to x:

To get the cumulative probability that X is less than or equal to 1, multiply P(X=0) by P(X = 0) by (P=1):

First, we will determine the value of the cumulative probability P(X<=x):

x         f(x)       P(X<=x)

1       0.02          0.02

2       0.01          0.03

3       0.2          0.23

4       0.17           0.4

5       0.39           0.79

6       0.2           0.99

7 0.01 1

30th percentile will be the x value,

below which less than or equal to 30% of the data falls.

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Answer: y = 2x + 7

Step-by-step explanation:

Given line = -1/2

given line = y = -1/2x + 7

Perp line = y = 2x + 7

The midpoint of the line segment with endpoints (2, 6) and (10, 4) is (6, 5).

To find the midpoint of a line segment, we can use the midpoint formula, which states that the coordinates of the midpoint are the average of the coordinates of the endpoints.

Let's denote the coordinates of the first endpoint as (x1, y1) and the coordinates of the second endpoint as (x2, y2).

In this case, the first endpoint is (2, 6) with coordinates (x1, y1) = (2, 6), and the second endpoint is (10, 4) with coordinates (x2, y2) = (10, 4).

To find the midpoint, we use the midpoint formula:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Plugging in the values, we have:

Midpoint = ((2 + 10) / 2, (6 + 4) / 2)

= (12 / 2, 10 / 2)

= (6, 5)

As a result, (6, 5) is the point on the line segment where the endpoints are (2, 6) and (10, 4) respectively.

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Answer:

Susie has a cupcake shop, which opened in 2015. The amount of money her shop earns is represented by

g(x) = 12√x+1 where x is the number of years since 2015. How many years after 2015 will the shop need

to be open in order for her to earn $36?

Please show all work in writing and solving the equation.

We want to find the number of years after 2015 (let's call it "y") that Susie's cupcake shop needs to be open to earn $36. To do that, we need to solve the equation:

g(x) = 12√x+1 = 36

First, we'll simplify the right side of the equation:

12√x + 1 = 36

Next, we'll subtract 1 from both sides:

12√x = 35

Now, we'll divide both sides by 12:

√x = 35/12

Next, we'll square both sides:

x = (35/12)^2

Finally, we'll calculate the value of x:

x = (35/12)^2 = (35/12)*(35/12) = 35^2 / 12^2 = 1225 / 144 = 25/3

So, the shop needs to be open for 25/3 years after 2015 in order to earn $36. To convert this answer to a whole number of years, we can round up to 9 years.

Therefore, the shop needs to be open for 9 years after 2015 in order to earn $36

Answer:

x = 26 years

Step-by-step explanation:

For my class the problem was a little different.  It was: g(x) = \(12\sqrt[3]{x+1}\).

Susie has a cupcake shop, which opened in 2015.  The amount of money her shop earns is represented by g(x) = \(12\sqrt[3]{x+1}\) where x is the number of years since 2015.  How many years after 2015 will the shop need to be open in order for her to earn $36?

You replace g(x) with the amount of money.

36 = \(12\sqrt[3]{x+1}\)

You have to isolate the cube root.  Divide both sides by 12.

\(\frac{36}{12}\) = \(\frac{12\sqrt[3]{x+1}}{12}\)

So you're left with:

3 = \(\sqrt[3]{x+1}\)

Now you need to get rid of the cube.

3³ = (\(\sqrt[3]{x+1}\))³

3³ is the same as 3 * 3 *3 = 27

27 = x + 1

Subtract 1 from both sides.

27 - 1 = x +1 - 1

x = 26 years

Answer:

The correct answer will be "56".

Step-by-step explanation:

Use a combination of 8 things taken 3 at a time :

⇒  \(8_{C_{3}}\)

⇒  \(\frac{8!}{(3!(8 - 3)!)}\)

⇒  \(\frac{8!}{(3!5!)}\)

⇒  \(\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}\)

⇒  \(8\times 7\)

⇒  \(56\)

Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.

Using the principle of combination :

Hence, we have ;

8C3 = [8! ÷ (8 - 3)! 3!]

8C3 = [8! ÷ 5!3!]

8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)

8C3 = 8 × 7

8C3 = 56

Hence, there are 56 different possible samples.

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Answer:

14+22i

Step-by-step explanation:

We multiply and simplify (3-5i)(-2+4i)​ to get:

14 + 22i

A complex number is a number of the form a + bi, where a and b are real numbers, and i is an imaginary unit satisfying i² = -1. For example, 2 + 3i is a complex number.

Complex numbers can be multiplied using the following rules:

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

Thus, the two complex numbers can be multiplied and simplified as follow:

(3-5i)(-2+4i)​ = 3(-2+4i)​ -5i(-2+4i)​

                    = 3(-2) + 3(4i) -5i(-2) -5i(4i)

                    = -6 + 12i + 10i -20i²

                   = -6 + 22i + 20    (Note: i² = -1)

                   = -6 + 20 + 22i

                   = 14 + 22i

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Answer:

30$ sales tax, 460$ Total

Step-by-step explanation:

7% of 430 is 30.1, after rounding it’s 30, and 430 plus 30 is 460.

You’re welcome

Answer:

-9.57

Step-by-step explanation:

Solving for number 3:

Step 1. Define the function.

The original function we have is:

Step 2. To find the inverse function, the first thing we need to do is to change F(x) for y:

Step 3. Now, we are going to interchange the letters x and y (swap x and y):

Step 4. Finally, the last step is to solve for y:

change y for F-1(x), and the inverse function is:

Answer:

Answer:

Solving for number 3:

Step 1. Define the function.

The original function we have is:

Step 2. To find the inverse function, the first thing we need to do is to change F(x) for y:

Step 3. Now, we are going to interchange the letters x and y (swap x and y):

Step 4. Finally, the last step is to solve for y:

Change y for F-1(x), and the inverse function is:

Answer:

Step-by-step explanation:

This method uses a sample of the  population mean to make generalizations about the whole, but can introduce error due to not observing the whole population.

The goal of inferential statistics is to use sample statistics to make inferences about population parameters. This is done by taking a sample of the population, usually a relatively small one, and using it to draw conclusions about the entire population. This method has the benefit of being much cheaper and easier to conduct than studying an entire population, however, it leaves room for error because it does not observe every member of the population. If the sample is not representative of the population, it can lead to faulty conclusions about the population as a whole. Additionally, if the sample size is too small, it may not be able to accurately represent the population. Therefore, it is important to carefully consider the sample size, as well as the representativeness of the sample, in order to draw reliable conclusions from inferential statistics.

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