What is the volume of a cylinder with a height of 8 in, and a diameter of 6 in.? Provide the
exact answer.

Answer:

[tex]17.4\ years[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=?\ years\\ P=\$3,000\\ r=0.04\\n=12\\ A=\$6,000[/tex]  

substitute in the formula above  

[tex]\$6,000=\$3,000(1+\frac{0.04}{12})^{12t}[/tex]  

[tex]2=(\frac{12.04}{12})^{12t}[/tex]  

Applying log both sides

[tex]log(2)=log[(\frac{12.04}{12})^{12t}][/tex]  

[tex]log(2)=(12t)log[(\frac{12.04}{12})][/tex]  

[tex]t=log(2)/[(12)log(\frac{12.04}{12})]=17.4\ years[/tex]  

.25 is the answer for you

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=23.9\\ h=100 \end{cases}\implies V=\cfrac{\pi (23.9)^2(100)}{3} \\\\\\ V=\cfrac{57121\pi }{3}\implies V\approx 59816.97\implies \stackrel{\textit{rounded up}}{V=59817} \\\\[-0.35em] ~\dotfill[/tex]

now, for the second one, we know the diameter is 10, thus its radius is half that or 5.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ V=225 \end{cases}\implies 225=\cfrac{\pi (5)^2 h}{3}\implies 225=\cfrac{25\pi h}{3} \\\\\\ \cfrac{225}{25\pi }=\cfrac{h}{3}\implies \cfrac{9}{\pi }=\cfrac{h}{3}\implies \cfrac{27}{\pi }=h\implies 8.59\approx h\implies \stackrel{\textit{rounded up}}{8.6=h}[/tex]

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

According to the data we have two points through which the line passes, then we can find the slope:

[tex](x1, y1) = (0,3)\\(x2, y2) = (7,0)[/tex]

[tex]m = \frac {0-3} {7-0} = - \frac {3} {7}[/tex]

Then, the equation is given by:

[tex]y = - \frac {3} {7} x + b[/tex]

We substitute a point to find "b":

[tex]3 = - \frac {3} {7} (0) + b\\b = 3[/tex]

Finally, the equation is:

[tex]y = - \frac {3} {7} x + 3[/tex]

Answer:

[tex]y = - \frac {3} {7} x + 3[/tex]

ANSWER

(-2,4] and [7,∞).

EXPLANATION

The domain refers to the interval on which the function is defined.

In the case of the graph, the domain refers to all the x-values for which the graph exists.

The graph is defined for x-values greater than 2 but less than or equal to 4 and

x-values greater than or equal to 7.

In interval notation, we have:

(-2,4] and [7,∞).

The second choice is correct:

Answer:

(-2,4] and [7, infinity)

Step-by-step explanation:

Answer:

A triangle

Step-by-step explanation:

If you slice open all of these shapes you will see a circle except the triangle.

Answer:

A triangle because the other shapes are to do with circles.

Answer A.

Step-by-step explanation:

v= 1/2x1 3/7

v= 7/8 units 3

Answer:

-1/2

Step-by-step explanation:

The slope of a line is given by

m = (y2-y1)/(x2-x1)

    = (1-2)/(3-1)

    = -1/2

The slope is -1/2

Answer:

The slope is -1/2.

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle \frac{1-2}{3-1}=\frac{2}{-1}=-\frac{1}{2}[/tex]

[tex]\Large\textnormal{Therefore, the slope is -1/2.}[/tex]

Let D = difference between mean and median of data.

Mean = (22 + 8 + 10 + 18 + 12 + 20)/6

Mean = 90/6

Mean = 15

Let m = median

m = 8, 10, 12, 18, 20, 22

m = (12 + 18)/2

m = 30/2

m = 15

D = M - m

D = 15n- 15

D = 0

Answer:

Step-by-step explanation:

I am very good at Pythagorean theorem I did it this year. So A=85 E=73 S=37 L=66.5 (or 65) T=82 P=53 D=10 O=89 C=17

To do this it is actually like the easiest thing to do in math. The formula is A²+B²=C². To do this it is easier with a scientific calculator. If you don't have one you can use this online calculator: desmos.com/scientific

Step 1. get the two number and square (²) them ( multiply that number by it) For Example 30 multiplied by 30. Or on the calculator I gave you just do 30²+40²

Step 2. After that you will get 2500. Then on the calculator get this symbol √ and but the number 2500 in front of it. it should look like this. √2500.

Step 3. After that you will get 50 which is your answer. And that is how you do Pythagorean theorem.

I hope that helped you. If you don't have a scientific calculator you can use the link I provided above. If you can't use it I reccomend buying one.

Answer:

Step-by-step explanation:

i) Recursive rule is

[tex]a_{n+1} =a_n-10[/tex]

2) Explicit rule for the sequence is

this is arithmetic sequence with a = -1 and d = 15

Hence

[tex]a_n=-1+15(n-1)\\a_n=15n-16[/tex]

3) [tex]P(A and B) = \frac{2}{25} (\frac{5}{6} )\\=\frac{1}{15}[/tex]

4) Sample men = total/no of entries

=[tex]\frac{409}{10} =40.9[/tex]

=41

Answer:

Answer is D 82.4%  

Step-by-step explanation:

Got it right on the test :)

The probability of on-time arrival in class given that the subject is biology is 82.4%

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

From the definition, the probability is the ratio of total favourable outcome to total outcome.

From the data table, the probability of on-time arrival in class given that the subject is biology:

= 82.4%

Thus, the probability of on-time arrival in class given that the subject is biology is 82.4%

Learn more about the probability here:

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Answer:

you bought a large cheese pizza

with 2 additional toppings on your pizza

Step-by-step explanation:

large cheese pizza = $13.99

Large pizza total = $16.49

each additional topping = $1.25

subtract $13.99 from $16.49

which equals $2.50

now subtract $1.25 from $2.50

which equals $1.25

now if you subtract $1.25 from $1.25

it equals 0

this shows you bought a large cheese pizza

with 2 additional toppings on your pizza

1 and 5 are the same angle, so if added together equal 100, then each angle is 50 degrees.

Angle 1 and angle 2 make a straight line which means they need to equal 180 degrees.

Angle 2 = 180 - 50 = 130 degrees.

Answer:

angle 2= 130

Step-by-step explanation:

180-50=130

Answer:

x = 16

y = 11

Step-by-step explanation:

Let the larger number = x

Let the smaller number = y

x  - y = 5

x = 2*y - 6

Put the second equation into the first. Substitute for x

2y - 6 - y = 5                          

combine

y - 6 = 5

and 6 to both sides.

y - 6 + 6 = 5 + 6

Combine

y = 11

=======================

Find x

x - y = 5           Substitute for y

x - 11  = 5          Add 11 to both sides.

x - 11+11=5+11

x = 16

Answer: He can predict 16 balls

Step-by-step explanation:

Answer:

16 balls; c

Step-by-step explanation:

The focus point of the parabola is (2,-2).

ANSWER

[tex](2,- 1)[/tex]

EXPLANATION

The given parabola is

[tex]y = \frac{1}{4} {x}^{2} - x - 1[/tex]

We need to write this parabola in the vertex form by completing the square,

[tex]y = \frac{1}{4} ( {x}^{2} - 4x) - 1[/tex]

[tex]y = \frac{1}{4} ( {x}^{2} - 4x + 4) - \frac{1}{4} \times 4 - 1[/tex]

[tex]y = \frac{1}{4} (x - 2 )^{2} - 2[/tex]

[tex] {(x - 2)}^{2} = 4(y + 2)[/tex]

The vertex is

(2,-2)

The focal length is

[tex]p = 1[/tex]

The focus is

[tex](2,-2 + 1)[/tex]

[tex](2,- 1)[/tex]

Answer:

A sphere

Step-by-step explanation:

A sphere is a round three dimensional object with no sharp corners or vertexes.  Since a basketball fits this criteria, it is a sphere.

Answer:

Eric's weekly salary is $680.77

Step-by-step explanation:

$35,400 divided by the number of weeks in a year, Which is 52. 52/35,400=680.77

Answer:

4.3

Step-by-step explanation:

210. she has 210 ways to choose 6 friends from the list of 10 to sit at the table closest to the head table no matter the order.

This is a problem of combinations and can be solved using the equation [tex]nC_{k}=\frac{n!}{k!(n-k)!}[/tex], where n! and k! is the factorial of a number. The factorial is defined in principle as the product of all positive integers from 1 (ie, natural numbers) to n.

She has a list of 10 friends and we want to know in how many ways she can choose 6 friends.

Using the combinations equation, with n = 10 and k = 6:

[tex]10C_{6}=\frac{10!}{6!(10-6)!}=\frac{10!}{6!(4!)}=\frac{10.9.8.7}{4.3.2.1}=\frac{5040}{24} =210[/tex]

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio, hence

[tex]a_{8}[/tex] = 6 × [tex](-1/3)^{7}[/tex] = 6 × - [tex]\frac{1}{3^{7} }[/tex] = 6 × - [tex]\frac{1}{2187}[/tex] = - [tex]\frac{2}{729}[/tex]

To determine how long it will take for $10,000 to triple with a continuous compounded interest rate of 5.5%, we use the continuous compound interest formula. Solve the equation for t by taking the natural logarithm of both sides and dividing by the interest rate, which yields t = ln(3) / 0.055.

The subject at hand deals with Continuous Compound Interest. The formula used to calculate this is A = Pe^(rt), where A is the final amount, P is the initial principal, r is the yearly interest rate and t is the time in years.

In this case, the initial principal P is $10,000, the final amount (A) we want is $30,000 (because we want to triple the money), and the rate r is 5.5% or 0.055 as a decimal. We want to find t.

Plugging into the formula, we get 30000 = 10000 * e^(0.055t). Dividing both sides by 10000 yields 3 = e^(0.055t). If we take the natural log (ln) of both sides, the equation simplifies to ln(3) = 0.055t. Finally, solving for t, we get t = ln(3) / 0.055.

This will give you the number of years it'll take for the money to triple at an interest rate of 5.5% compounded continuously.

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Answer:

Final answer is [tex]\frac{5}{36}[/tex].

Step-by-step explanation:

Given that two 6-sided number cubes are rolled. Now we need to find about what is the possibility of rolling a sum of 8​.

From the sample space, you can see that there are total 36 possible outcomes.

out of those outcomes, there are only 5 outcomes that has sum = 8

which are {(2,6), (3,5), (4,4), (5,3), (6,2)}.

Hence probability of rolling a sum of 8 [tex]=\frac{5}{36}[/tex].

Hence final answer is [tex]\frac{5}{36}[/tex].

Answer:

y³ - 3y² + 1/y+3

Step-by-step explanation:

y² - 9 = (y - 3) ( y + 3)

y-3/(y-3)(y+3) = 1/y+3

Answer:

y^2+1/y^2+3

Step-by-step explanation:

About 2 and a half hours

the figure is four sided so it a heptagon

for a heptagon, the sum of all interior angles is 900°

i.e. x+(x+50°)+(x+50°)+(x+50°)+×+×+(x+50°)=900°

or, 7x+200°=900°

or, 7x=700°

or, x= 100°

Answer:

The value of x = 100 ⇒ answer B

Step-by-step explanation:

* Lets study how to find the sum of the interior angles of any polygon

- We can find the sum of the measures of the interior angles of any

 polygon using the rule (n - 2) × 180°, where n is the number of its

 sides or its angles

* Now lets solve the problem

- The polygon has 7 sides and 7 angles

- The measure of three angles of them is x°

- The measure of four angles of them is (x + 50)°

∵ The sum of the interior angles = (n - 2) × 180°

∵ n = 7

∴ The sum of the interior angles = (7 - 2) × 180° = 5 × 180° = 900°

∵ Three angles each measured x°

∵ Four angles each measured (x + 50)°

∴ 3(x°) + 4(x + 50)° = 900° ⇒ simplify it

∴ 3x + 4(x) + 4(50) = 900 ⇒ add the like terms

∴ 3x + 4x + 200 = 900 ⇒ add the like terms

∴ 7x + 200 = 900 ⇒ subtract 200 from both sides

∴ 7x = 700 ⇒ divide both side by 7

∴ x = 100

* The value of x = 100

The answer is c.4a4

To determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum of a data set, you need to follow these steps:

1. Order the Data Set: Arrange the data set in ascending order.

2. Minimum and Maximum: Identify the smallest and largest values in the ordered data set.

3. Median (Q2): This is the middle value of the data set. If there is an odd number of observations, it is the middle one. If there is an even number of observations, it is the average of the two middle values.

4. First Quartile (Q1): This is the median of the first half of the data (the lower 50%). If the number of observations is odd, do not include the median in this half.

5. Third Quartile (Q3): This is the median of the second half of the data (the upper 50%). If the number of observations is odd, do not include the median in this half.

Let's consider an example data set to illustrate these steps:

Example Data Set: 3, 7, 8, 5, 12, 14, 21, 13, 18

1. Order the Data Set: 3, 5, 7, 8, 12, 13, 14, 18, 21

2. Minimum and Maximum:

  - Minimum = 3

  - Maximum = 21

3. Median (Q2):

  - Since there are 9 data points (odd number), the median is the 5th value.

  - Median = 12

4. First Quartile (Q1):

  - The lower half of the data (excluding the median) is: 3, 5, 7, 8

  - Median of this lower half = (5 + 7) / 2 = 6

5. Third Quartile (Q3):

  - The upper half of the data (excluding the median) is: 13, 14, 18, 21

  - Median of this upper half = (14 + 18) / 2 = 16

So, the five-number summary for the example data set is:

- Minimum = 3

- First Quartile (Q1) = 6

- Median (Q2) = 12

- Third Quartile (Q3) = 16

- Maximum = 21

Answer is provided in the image attached.