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2 years ago

Acone has a height of 7 ft and a radius of 4 ft. Which equation can find the volume of the cone?

Mathematics

1 answer:

Marina86 [1]2 years ago

3 0

Answer:

Volume of the cone = $117.06\,feet^3$

Step-by-step explanation:

Height of the cone = $7\,feet$

Radius of the cone = $4\,feet$

Volume of a cone is:

$\pi \times r^2\times \dfrac{h}{3}$

As, $\pi =\dfrac{22}{7} =3.14$

Volume is:

$=3.14\times(4\times 4)\times \dfrac{7}{3}\\\\ =3.14\times 16 \times 2.33\\\\=3.14\times 37.28\\\\=117.06\,feet^3$

The volume of the cone is: $117.06\,feet^3$

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The data given below consists of the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 1

Mice21 [21]

Answer:

z -score = 0.0459

Step-by-step explanation:

Given that:

the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12.

The objective is to find the z- score , but before we can do that , we need to determine the mean and the standard deviation of the sample.

Mean = sum of the sample/ total number of the sample

Mean = (3+9+ 5+ 5+ 14+ 10+ 5+ 11+ 9+ 6+ 1+ 8+ 10+ 7+ 9+13+ 18+ 9+ 8+11+ 9+ 7+ 6+ 14+ 12)/25

Mean = 219/25

Mean = 8.76

Standard deviation = $\sqrt{\dfrac {\sum (x_i - \mu)^2}{N}}$

Mean (in order )= 1, 3,5,5,5,6,6,7,7,8,8,9,9,9,9,9,10,10,11,11,12,13,14,14,18)

Standard deviation = $\sqrt{\dfrac { (8.76 - 1)^2}{25} + \dfrac { (8.76 - 3)^2}{25} +\dfrac { (8.76 - 5)^2}{25} +...+ \dfrac { (8.76 - 18)^2}{25} }$

Standard deviation = 5.2174

The standard z score formula is:

$z = \dfrac{X- \mu}{\sigma}$

where X = median (13th observation ) = 9

$z = \dfrac{9- 8.76}{5.2174}$

$z = \dfrac{0.24}{5.2174}$

z -score = 0.0459

4 0

2 years ago

you invest $4,100 in an account that pays an interest rate of 8.5%, compound continuously. Calculate the balance of your account

Yanka [14]

Answer:

16400$

Step-by-step explanation:

Persent invest value= 4100$

Compound intrest rate=8.5% or 0. 085 (annual)

Time period =17 years

According to compound interest formula

Future valve (fv) =persent value(pv) (1+r)^n

Substitute all values

Fv=4100$(1+0.085)^17

Fv=4100$(1.085)^17

Fv=4100 * 4.00

Fv= 16400 $ answer

7 0

3 years ago

In a survey of 500 voters 430 said they would vote the same candidate again. What percent of the voters would vote the same way

aksik [14]

Answer:

86%

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

An object is thrown straight up from the top of a 100-foot platform at a velocity of 48 feet per second. The height h(t) of the

julsineya [31]

Answer:

The maximum height is 136 ft

The time it takes to achieve this height is 1.5 s.

Explanation:

1. Function for the height (given):

$h(t)=-16t^2+48t+100$

2. Type of function

That is a quadatic function, whose graph is a parabola that opens downward.

The maximum of the function, i.e. the maximum height, is the vertex of the parabola.

The vertex of a parabola with the genral equation $y=ax^2+bx+c$ is at the x-coordinate

$x=-b/(2a)$

3. Time to achieve the maximum height

Substitute b with 48 and a with - 16:

$t=-48/(2(-16))=48/32=3/2=1.5$

Then, time when the object achieves the maximum height it 1.5s

4. Maximum height:

Replace t with 1.5 in the equation, to find the maximum height, h(1.5)

$h(1.5)=-16(1.5)^2+48(1.5)+100=136$

Then, the maximum height is 136 ft

3 0

3 years ago

Plz help me, URGENT!! 20 points!

Evgen [1.6K]

Answer:

The answer to your question is 37.5

4 0

3 years ago