The height of a cone is twice the radius of its base.
What expression represents the volume of the cone, in
cubic units?
A. 2/3 pi x 3
B. 4/3 pi x 2
C. 2 pi x 3
D. 4 pi x 3

The circumference of the circle is 10π cm, and the area is 25π cm².

The formulas for the circumference (C) and area (A) of a circle in terms of

the radius (r) are:

Circumference (C) = 2πr

Area (A) = πr²

Given that the radius (r) is 5 cm, we can substitute this value into the formulas:

Circumference (C) = 2π(5) = 10π cm

Area (A) = π(5)² = 25π cm²

So, the circumference of the circle is 10π cm, and the area is 25π cm².

Final answer:

To find the measure of angle 2, which is complementary to angle 1 with a measure of 56°, subtract 56° from 90°, resulting in angle 2 measuring 34°.

Explanation:

If angles 1 and 2 are complementary, it means that the sum of their measures is 90 degrees. Since the measure of ∠1 is given as 56°, we can find the measure of ∠2 by subtracting the measure of ∠1 from 90 degrees:

Measure of ∠2 = 90° - Measure of ∠1

Measure of ∠2 = 90° - 56°

Measure of ∠2 = 34°

Therefore, the measure of ∠2 is 34 degrees.

Answer:

Okay, so 2 years later, here's your answer.

472 adult tickets and 868 student tickets were sold.

Step-by-step explanation:

Let x be the number of adult tickets sold.

Let y be the number of student tickets sold.

Your Equations:

x + y = 1340 tickets

5x + (1)y = $3228

Isolate the y variable:

y = 1340 - x

y = 3228 - 5x

Substitute:

1340 - x = 3228 - 5x

Solve:

1340 - x = 3228 - 5x

Add 5x on both sides

1340 + 4x = 3228

Subtract 1340 on both sides

4x = 1888

Divide 4 on both sides

x = 472

Plug in x into an equation:

472 + y = 1340

Subtract 472 on both sides

y = 868

472 adult tickets were sold

868 student tickets were sold.

Voted myself a 1-star XD

Answer:

618 birds.

Step-by-step explanation:

Let the estimated number of birds=x

Out of x birds, he tied a belt around the legs of 40 birds.

When he observed 520 birds, 34 of which had belts.

Expressing each as a ratio

[tex]\frac{x}{40}=\frac{520}{34}[/tex]

Cross Multiply

34x=520X40

x=520X40÷34=611.7≈618

There are an estimated 618 birds.

Answer:

The best estimate for the bird population is 613 birds

Step-by-step explanation:

Let x be the total of number of estimated bird

From x, 40 birds are with belt

he observed 520 birds, 34 of which had belts.

Then taking reciprocal of both statements

x/40 = 520/34

34x = 520*40 = 20800

x = 20800/34

x = 613The total of number of estimated birds is 613 birds

The total of number of estimated birds is 613 birds

You can use the Pythagorean Theorem to find missing lengths in objects that are right triangles.

The Pythagorean Theorem is a mathematical principle that relates to right triangles. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

You can use the Pythagorean Theorem to find missing lengths in objects that are right triangles.

The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

By rearranging the formula, you can solve for the missing length when given the lengths of the other two sides.

This can be applied to real-world problems involving measurements of objects or distances, such as determining the length of a ladder needed to reach a certain height on a wall or calculating the distance between two points on a map.

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Answer:

For the one on the left:

Center: (-15,-7)

Radius: 1.73

For the one on the right:

Center:(3,-11)

Radius: 6

Step-by-step explanation:

I used the desmos graph and it calculated when the circle was, And i counted where these items were

Answer:

area is 6.9cm2

Step-by-step explanation:

you just multiply it out and divide by 2

Answer:

[tex]\frac{17}{96}[/tex]

Step-by-step explanation:

Given  m = - [tex]\frac{96}{17}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{96}{17} }[/tex] = [tex]\frac{17}{96}[/tex]

Answer:

D. 100.

Step-by-step explanation:

-m + 0.02 + 2.1m = -1.45 -4.81m

Multiply by 100:

-100m + 2 + 210m = -145 - 481m

​

Answer:

B. 74 degrees

Step-by-step explanation:

sorry im not good at writing math explantions I hope this drawing helps.

The measure of angle ABC is 74 degrees.

Given:

Find:

Solution:

As we know that BAD is forming a triangle that will have 180 degrees if all the angles of the triangles are summed together.

So, ABDA=180 degrees.

Now, ADB=180-(ABD+DAB)=180-(90+37)=180-127=53 degrees.

So, 90+37=127 degrees and 90+53=143 degrees.

Now, we will subtract them to get CBD,

CBD=143-127=37 degrees.

Therefore, ABC= CBD+ABD=37+37=74 degrees.

Hence, the measure of angle ABC is 74 degrees.

Therefore, option (B) is the correct answer.

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Answer:

The answer is D.

Step-by-step explanation:

Distributive Property

4x3=12

4x7=28

28+12=40

Answer:

32.15 = (3 x 10) + (2 x 1) + (1/10) + (5/100)

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is Arithmetic sequence

a = first term= 4;

d= difference =second term - first term = 7 - 4 = 3

n= position

nth term = a + (n-1)*d

1st term = 4 + (1-1)*3 = 4 + 0 = 4

2nd term = 4 + (2-1)*3 = 4 + 1*3 = 4+3 = 7

5th term = 4 + (5-1)*3 = 4 + 4*3 = 4 + 12 = 16

6th term = 4 + (6-1)*3 = 4 + 5*3 = 4 + 15 = 19

or

To get the next term add the difference [3] to the previous term.

5th term = 13 +3 = 16

6th term = 16 + 3= 19

Answer:

The correct answers are Option 4 55(108/100)  and Option 1 55(1.08)

Step-by-step explanation:

To begin, we must analyze the information we have and establish the result, in order to compare it with the results of the operations that the answers offer.

We know that the total Charlie pays for his cell phone plan is $ 55 + 8% tax.

One of the possible ways in which you can calculate a percentage would be in this case:

(55.8) : 100

440 : 100 = 4.40

This indicates that the tax was 4.4 added to 55, giving us a total of 59.4.

Now we just have to check that options 4 and 1 are correct. Let's see:

55 (108/100) =

55 (1.08) = 59.94

This last section is exactly the same as option 1, which also makes it a correct answer.

The value of the laptop in 2011 will be $29920

Step-by-step explanation:

Cost of the laptop = $34000

Rate of decrease in value per year = 4%

Total time = 3 years

The Value decrease in 2011 = (34000 x 4 x 3) /100

= $4080

The value of the laptop in 2011 = 34000-4080

= $29920

The value of the laptop in 2011 will be $29920

Answer:

Step-by-step explanation:

what you need to do is look at the question again it say 10 feet above sea level and the other one is 7 feet below sea level. now read your question again hope you find the answer good luck

Answer:D

Step-by-step explanation: -7 is greater than -10 -10 is lower

Answer:

(Male White Rabbits Count: 14) (Male Black Rabbits Count: 18) (Female White Rabbits Count: 0) (Female Black Rabbits Count: 9)

Step-by-step explanation:

In order to get this answer you have 9 rabbits that are black and 0 white rabbits. Then there is 32 male rabbits and 14 of them are white so you subtract 14 from 32 and the rest is black rabbits which is 18. Now you have all of your answers.

Answer:

for b) the answer is 7/48

this wasn't included in the last answer so here it is.

Step-by-step explanation:

white female rabbit number/the overall total

Answer:

1875 cm>3 i think

Step-by-step explanation:

Answer:

4^2 + 4x= 1

Step-by-step explanation:

4x^2 - 4x - 5= 8x +6

4x^2- 4x+8x =6-5

4x^2 + 4x =1

Answer:

36 students

Step-by-step explanation:

right on edge

The total number of students bought their lunch from cafeteria is 36.

Given data:

The total number of girls is 35 and the total number of boys is 50.

Probability of boys bought their lunch from cafeteria = 0.44

Since total no. of boys =50

So, number of boys bought their lunch from cafeteria P ( B ) = 50*0.44

And, the value of P ( B ) = 22

Probability of girls bought their lunch from cafeteria = 0.4

Since total no. of girls =35

So, number of girls bought their lunch from cafeteria P ( G ) = 35*0.4

So, the value of P ( G ) = 14

The total number of students , n = P ( B ) + P ( G )

So, n = 22 + 14

n = 36

Hence , the number of students is 36

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The complete question is attached below:

35 total girls and 50 total boys were surveyed. How many students bought their lunch from the cafeteria? Round to the nearest whole number.

Answer:

Step-by-step explanation:

You know these ordered pairs are considered a function, because the x intercepts do not repeat themselves. In other words, each input numbers are different. If these ordered pairs were not a function, the x intercept would be repeating. For example,  22 is already a x intercept, (22,4), if 22 was put in as another x intercept like,(22,1) these ordered pairs would not be a function.

Answer:

22

Step-by-step explanation:

No coffin will be opened at the end of 500th man .

Given,

500 coffins and 500 hundred men

Here,

First man opens all the coffins, but the second man closes every second coffin, which means that the odd-numbered coffins are closed again.

Then, the third man goes to every third coffin and closes it, which means that the coffins that are multiples of 3 are closed again.

This pattern continues with each subsequent man, so by the time the 500th man goes to the coffins, all of them will be closed.

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Answer:

88,88,888

Step-by-step explanation:

Answer:

Input functions is called Domain Output functions is called Range

Step-by-step explanation:

Answer:

A- 462.86

Step-by-step explanation:

Answer:

P 81 = 73.5

Step-by-step explanation:

This is a normal distribution problem with a mean of 63.2 and standard deviation of 11.7.

Let the number that separates the bottom 81% from the top 19% be x' and let it's z-score be z'.

P(x ≤ x') = P(z ≤ z') = 0.81

Using the normal distribution table,

z' = 0.878

But note that the z-score for any value is that value minus the mean divided by standard deviation.

z' = (x' - μ)/σ

0.878 = (x' - 63.2)/11.7

x' = 73.4726 = 73.5 to 1 d.p

Hope this Helps!!!

Final answer:

To find the value that separates the bottom 81% from the top 19%, you can use the z-score formula and the given mean and standard deviation to calculate the desired value.

Explanation:

To find the value that separates the bottom 81% from the top 19%, we need to find the z-score corresponding to the 81st percentile.

Using the formula Z = (X - μ) / σ where X is the given value, μ is the mean, and σ is the standard deviation, we can rearrange it to solve for X as:

X = Z * σ + μ

Since we know the mean is 63.2 and the standard deviation is 11.7, we can calculate the z-score corresponding to the 81st percentile (0.81) using the standard normal distribution table or a calculator.

Once we have the z-score, we can substitute it into the formula to find the corresponding value.

The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 1574 + 3t - 2t².

Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :

G = 674 + 3t – 2t² + 5t + 60

I = 314 - 31 + 512 - 5t + 45

where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.

A new model {A} for the total number of new green tea and fruit juice sales can be written as -

{A} = {G} + {I}

{A} = 674 + 3t – 2t² + 5t + 60 + 314 - 31 + 512 - 5t + 45

{A} = (674 + 60 + 314 - 31 + 512 + 45) + (3t + 5t - 5t) - 2t²

{A} = 1574 + 3t - 2t²

Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 1574 + 3t - 2t².

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Final answer:

To create a new model for the total sales of green tea and fruit juice, the sales equations for both products are added together and simplified, resulting in the model A = 3t² + 1093, representing combined sales in billions as a function of time in years.

Explanation:

To find a new model A for the total number of new green tea and fruit juice sales, we need to combine the models given for G (green tea sales) and J (fruit juice sales). The models provided had some errors, but they should be:

G = 674 + 3t – 2t² + 5t + 60

and

J = 314 – 3t + 5t² – 5t + 45

Combining these models to form A (total sales), we add G and J together:

A = G + J

= (674 + 3t – 2t² + 5t + 60) + (314 – 3t + 5t² – 5t + 45)

Now, we simplify the equation by combining like terms:

A = (674 + 314) + (3t – 3t) + (5t – 5t) – 2t² + 5t² + (60 + 45)

A = 988 + 0t + 0t + 3t² + 105

A = 988 + 3t² + 105

A = 3t² + 1093

Therefore, the new model A for the total sales is A = 3t² + 1093. This model represents the combined sales of green tea and fruit juice in billions of dollars during the 20-year period as a function of time t in years.

Jane is correct because Jane correctly simplified the expression to [tex]\(3x\)[/tex].

Let's carefully simplify the expression [tex]\((2x^2 + x) + 2(-x^2 + x)\)[/tex] step-by-step to determine who is correct, Jane or Jill.

Starting with the given expression:

[tex]\[(2x^2 + x) + 2(-x^2 + x)\][/tex]

We first distribute the [tex]\(2\)[/tex] in [tex]\(2(-x^2 + x)\):[/tex]

[tex]\[(2x^2 + x) + (-2x^2 + 2x)\][/tex]

Next, we combine like terms. We combine the \(x^2\) terms and the \(x\) terms separately:

[tex]\[(2x^2 - 2x^2) + (x + 2x)\][/tex]

Simplify each group of like terms:

[tex]\[0x^2 + 3x\][/tex]

This simplifies to:

[tex]\[3x\][/tex]

Therefore, the correct simplification of the expression [tex]\((2x^2 + x) + 2(-x^2 + x)\) is \(3x\)[/tex].

Jane’s solution is:

[tex]\[\begin{aligned}& = (2x^2 + x) + 2(-x^2 + x) \\& = (2x^2 + x) + (-x^2 + x) + (-x^2 + x) \\& = (2x^2 - x^2 - x^2) + (x + x + x) \\& = 3x\end{aligned}\][/tex]

Jill’s solution is:

[tex]\[\begin{aligned}& = (2x^2 + x) + 2(-x^2 + x) \\& = (2x^2 + x) - 2x^2 + 2x \\& = 2x\end{aligned}\][/tex]

Jane correctly simplified the expression to [tex]\(3x\)[/tex], while Jill made an error by not correctly distributing the [tex]\(2\)[/tex] in the term [tex]\(2(-x^2 + x)\)[/tex].

The complete question is

Jane and jill were simplifying the expression (2x²+x) +2(-x²+x) and obtained different answers. Who is right and why?​

Jane                                                

[tex]$$\begin{aligned}& =\left(2 x^2+x\right)+2\left(-x^2+x\right) \\& =\left(2 x^2+x\right)+\left(-x^2+x\right)+\left(-x^2+x\right) \\& =\left(2 x^2-x^2-x^2\right)+(x+x+x) \\& =3 x\end{aligned}$$[/tex]

Jill

[tex]\begin{aligned}& =\left(2 x^2+x\right)+2\left(-x^2+x\right) \\& =\left(2 x^2+x\right)-2 x^2+x \\& =2 x\end{aligned}[/tex]

Answer:

The answer is C

Step-by-step explanation: