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2 years ago

Q#1:The volume of a cube is 46656 cubic metres.Find the length of each side?

Mathematics

1 answer:

Lady_Fox [76]2 years ago

3 0

Answer:

Step-by-step explanation:

1) To find the cube root of a number prime factorize

46656 = 2*2*2*2*2*2 * 3 * 3 * 3 * 3 * 3 * 3

$\sqrt[3]{46656}=\sqrt[3]{2*2*2*2*2*2*3*3*3*3*3*3} =2*2*3*3 = 36$

Length of each side = 36 m

Q) i) -512 = (-8) * (-8)*(-8)

-512 is a cube number

v) -17576 = (-26) * (-26)*(-26)

-17576 is cube number

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Please please please help me

Gwar [14]

A) 15/4 = 4/4+4/4+4/4+3/4= 3 3/4
B)9/2= 2/2+2/2+2/2+2/2+1/2= 4 1/2
c = 26/12 = 12/12 + 12/12 + 2/12 = 2 2/12
d) 20/6 = 6/6 + 6/6 + 6/6 + 2/6 = 3 2/6

8 0

2 years ago

Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with the dimensions shown below. Us

Eva8 [605]

The area of the base would be found using the area of a triangle formula which is 1/2 x base x height.

The base and height are the two sides perpendicular to each other, which are both 5 inches.

The area of the base = 1/2 x 5 x 5 = 12.5 square inches.

The volume of the triangular prism is the area of the base times the height, which is 4 inches.

Volume of the triangular prism is 12.5 x 4 = 50 cubic inches.

Volume of the triangular prism is 1/3 x area of base x height, which is 7:

Volume of the triangular prism = 1/3 x 12.5 x 7 = 29.17 cubic inches.

Total volume = 29.17 + 50 = 79.17 cubic inches.

3 0

2 years ago

An epidemiologic survey of roller-skating injuries in Metroville, a city with a population of 100,000 (during the midpoint of th

Ahat [919]

Answer: c. $\dfrac{90}{1800}\times100\%$

Step-by-step explanation:

As per given , we have

Total number of residents injured from roller-skating =1,800

Total number of deaths from roller-skating = 90

Formula for Mortality rate : $Mortaility\ rate= \dfrac{Deaths\ due \ to\ injury}{Tota\ injuries}$

Then, the proportional mortality ratio (%) due to roller-skating was

= $\dfrac{90}{1800}\times100\%$

= 5%

Hence, the correct answer is c. $\dfrac{90}{1800}\times100\%$

8 0

2 years ago

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For

SpyIntel [72]

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.71$

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here $n = 16$ , we want $P(X \geq 13)$ . So

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591$

$P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835$

$P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273$

$P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042$

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741$

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now $n = 160$ . So

$\mu = E(X) = np = 160*0.71 = 113.6$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74$

Using continuity correction, this is $P(X \geq 110 - 0.5) = P(X \geq 109.5)$ , which is 1 subtracted by the pvalue of Z when X = 109.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{109.5 - 113.6}{5.74}$

$Z = -0.71$

$Z = -0.71$ has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

3 0

2 years ago

What is the volume of the pyramid?

s2008m [1.1K]

Answer:

$16\sqrt{3}$ $cm^{3}$

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one. Please have a look at the attached photo,

<em>A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4StartRoot 3 EndRoot cm and an area of 12StartRoot 3 EndRoot cm2. </em>

<em>What is the volume of the pyramid?</em>

My answer:

As we know, The volume of a pyramid = $\frac{1}{3}$ base area × its height