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suter [353]
3 years ago
13

A cylindrical jar of jam has a diameter of 6cm and a height of 8cm if the jar is 70% full how many cubic centimeters of jam is i

n the jar?
Mathematics
1 answer:
VikaD [51]3 years ago
5 0

Answer:

158.256 \:  {cm}^{3}

Step-by-step explanation:

For cylindrical jar:

Diameter = 6 cm

Radius (r) = 6/2 = 3 cm

Height (h) = 8 cm

V_{cylindrical \: jar}  = \pi {r}^{2} h \\  \\  = 3.14 \times  {(3)}^{2}  \times 8 \\  \\  = 3.14 \times 72 \\  \\  = 226.08 \:  {cm}^{3}  \\  \\  \because \: jar \: is \: filled \: upto \: 70 \% \\  \\   \therefore \: V_{jam} = 70 \% \: of \: V_{cylindrical \: jar}  \\  \\  \therefore V_{jam} = 0.70 \times 226.08 \\  \\   \therefore V_{jam} = 158.256 \:  {cm}^{3}

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Factor of 32 other factor is 4 what number am i
mrs_skeptik [129]
I think the answer is 8. After solving i got 8

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3 years ago
You spin a spinner and flip a coin find the probability of the compound event the probability of spinning an even number and fli
Anastaziya [24]

Answer: their is 50 percent that it will land on heads

Step-by-step explanation: it will have a completely random chance no matter how many times you flip a coin on tails it will always have a fifty percent chance even if you flipped the coin 1000000 and it landed on tails all those times it would still have the fifty fifty probability of landing on heads hope this has helped and good question  

3 0
3 years ago
Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with
Alexxandr [17]

Answer:

Step-by-step explanation:

Hello!

The SAT math scores have a normal distribution with mean μ= 540 and standard deviation σ= 119

Eleonor scored 680 on the math part.

X: score obtained in the SAT math test

*-*

The ACT Assessment math test has a normal distribution with mean μ= 18.2 and standard deviation σ= 3.6

Gerald took the test and scored 27.

X: score obtained in the ACT math test

a.

To standardize the values you have to use the following formula:

Z= (X-μ)/σ ~N(0;1)

For each score, you have to subtract its population mean and divide it by the standard deviation.

Eleonor score:

Z= (680-540)/119= 1.176 ≅ 1.18

Gerald Score

Z= (27-18.2)/3.6= 2.44

b.

Since both variables are very different you cannot compare the "raw" scores to know which one is higher but once both of them were standardized, you can make a valid comparison.

In this case, Eleonor's score is 1.18σ away from the mean, while Gerald's score is 2.44σ away, i.e. Gerald's score is further away from the mean score than Eleonor's so his score is higher.

c.

In this item, you are asked to find the value that divides the top 10% of the population from the bottom 90%.

Symbolically you can express it as:

P(Z>c)=0.1

or

P(Z≤c)= 0.9

The tables of standard normal distribution show accumulative probabilities of P(Z<Z₁₋α), sois best to use the second expression.

In the body of the distribution table, you have to look for a probability of 0.90 and then reach the corresponding Z value looking at the table margins. The first column shows the integer and first decimal digit, the first row shows the second decimal digit. So the corresponding value of Z is 1.28

Now you have to reverse the standardization to know the corresponding scores for each test.

SAT test score:

Z= (c-μ)/σ

Z*σ = c-μ

c = (Z*σ ) + μ

c= (1.28*119)+540

c= 692.32

The student should score 692.32 in his SAT math test to be in the top 10% of the population.

ACT test score

Z= (c-μ)/σ

Z*σ = c-μ

c = (Z*σ ) + μ

c= (1.28*3.6)+18.2

c= 22.808 ≅ 22.81

The student should score 22.81 in his ACT math test to be in the top 10% of the population.

d.

In this item, their vas a sample of students that took the ACT taken and you need to calculate the probability of the sample mean being greater than 25.

If you were to take a 100 random samples of ACT scores of 100 students and calculate the mean of all of them, you will get that the sample mean is a random variable with the same kind of distribution as the original variable but it's variance will be influenced by the sample size. In this case, the original variable is:

X: score obtained in the ACT math test

This variable has a normal distribution X~N(μ;δ²), then it's the sample mean will also have a normal distribution with the following parameters X[bar]~N(μ;δ²/n)

Remember when you standardize a value of the variable of interest you subtract its "mean" and divide it by its "standard deviation" in this case the mean is μ and the standard deviation will be √(δ²/n) ⇒ δ/√n and the formula of the standard normal is:

Z= (X[bar]-μ)/(δ/√n)~N(0;1)

with n=100

μ= 18.2

δ= 3.6

P(X[bar]>25)= 1 - P(X[bar]≤25)

1 - P(Z≤(25-18.2)/(6.3/√100))= 1 - P(Z≤10.79)= 1 - 1 = 0

The probability of the mean ACT score for a random sample of 100 students being more than 25 is zero.

I hope it helps!

4 0
3 years ago
Next door to me lives a man with his son. They both work in the same factory. I watch them going to work through my window. The
kirza4 [7]

9514 1404 393

Answer:

  k = 5

Step-by-step explanation:

Suppose the distance to the factory is 1 unit. Then the speed the father walks is ...

  speed = distance/time = 1 / 30 . . . . units per minute

When the father leaves 10 minutes earlier than the son, his position t minutes after the son starts walking is ...

  d = 1/30(t +10)

Similarly, when the father starts 5 minutes earlier than the son, his position t minutes after the son starts walking is ...

  d = (1/30)(t +5)

We want that to be the same as the distance the son covers t minutes after he starts walking. The son's progress is ...

  d = 1/20t

To find the value of k such that the distance covered is the same 2k minutes after the son starts, we will use t=2k and d=d, so ...

  (1/30)(2k +5) = (1/20)(2k)

  4k +10 = 6k . . . . . multiply by 60

  10 = 2k . . . . . . . . . subtract 4k

  5 = k . . . . . . . . . . . divide by 2

__

The attached graph shows the different scenarios, where the blue line is the son's progress. When the father starts 5 minutes earlier, the son meets him half-way to the factory after 10 minutes, so k = 10/2 = 5.

5 0
2 years ago
How do you find the lateral area of the prism
Lina20 [59]
Hi there!

The lateral area is the area of the figures connecting the bases. We have rectangles here. We'll need to find the area of each figure and add them together to find the lateral area.

WORK:
(2.8 x 12) + (8.1 x 12) + 2(4 x 12)
33.6 + 97.2 + 96
LA = 226.8 units^2

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
7 0
3 years ago
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