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BartSMP [9]
4 years ago
14

a cup was filled at a constant rate. it started empty. after 2 seconds, it held 70 cm cubes of water. the radius is 4 and te hei

ght is 7. find the percent of the cup that is filled with water after 3 seconds. this is a cone
Mathematics
1 answer:
Viktor [21]4 years ago
8 0

Answer:

89.51%

Step-by-step explanation:

Assuming given units are in cm

Tge rate of filling the cup is 70/2= 35 cm3/s

Volume of the cup is \pi r^{2}\frac {h}{3} and replacing r with 4 cm and h with 7 cm then the volume is equivalent to

\pi*4^{2}*\frac {7}{3}= 117.3 cm^{3}

Volume filled after 3 seconds will be 3*35=105 cm3

Percentage filled is \frac {105}{117.3}\times 100\approx 89.51

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tatiyna
Irrational numbers are numbers that have decimals and the decimals randomly keep going on. Remember, a repeating decimal is not necessarily an irrational number. (pi, sqrt(2), etc)
An integer is a whole number. (1, 2, 3, 4, etc) it could also be negative.
4 0
3 years ago
Read 2 more answers
Consider the function f(x) = 3.x2 + 7x + 2.<br> what is the value of the discriminat?
Vika [28.1K]

Answer:

The Discriminant is 25

Step-by-step explanation:

For this case, the discriminant will be given by

b ^ 2 - 4 * a * c

Where

b = 7

a = 3

c = 2

substituting

b ^ 2 - 4 * a * c = (7) ^ 2 - 4 * (3) * (2) = 25

Therefore the value of the discriminant is 25.

How many x-intercepts does this function have?

It has two intercepts with the x axis and can be found by equaling the function to zero. That is to say,

3x2 + 7x + 2 = 0

The results will be the interceptions with x.

What are the number of zeros for this function?

The number of zeros for this function is

two real number solutions

Because it is a quadratic function.

3 0
3 years ago
Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a
spin [16.1K]

Answer:

Mean = 68.9

s^2 =18.1 --- Variance

Step-by-step explanation:

Given

\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5

For 59 - 66

x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5

For 67 - 74

x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5

For 75 - 82

x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5

For 83 - 90

x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5

So, the table becomes:

\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}

The mean is then calculated as:

Mean = \frac{\sum fx}{\sum f}

Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}

Mean = \frac{2547.5}{37}

Mean = 68.9 -- approximated

Solving (b): The sample variance:

This is calculated as:

s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}

So, we have:

s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}

s^2 =\frac{652.8}{36}

s^2 =18.1 -- approximated

5 0
3 years ago
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Answer:

it equals to 1032000

Step-by-step explanation:

because 3000 x 344 = 1032000

3 0
3 years ago
The current temperature is 48°F. It is expected to drop 1.5°F each hour.
Lostsunrise [7]

Answer:

B

Step-by-step explanation:

5 0
2 years ago
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