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3 years ago

A theater can hold 120 giants or 144 elves. If 90 giants are already inside, how many elves can also be admitted?

Mathematics

2 answers:

EastWind [94]3 years ago

6 0

Answer:

36 elves

Step-by-step explanation:

Using proportions

We have space for 30 more giants

30 giants x elves

------------- = ----------

120 full 144 elves full

Using cross products

30*144 = x*120

Divide each side by 120

30*144/120 = 120x/120

36 = x

We can have 36 elves

navik [9.2K]3 years ago

3 0

Answer:

Step-by-step explanation:

make proportion giants to elves

120/144 = 90/x cross multiply

120x =144*90

120x =12960 divide by 120

x = 108

so if there are 90 giants in the theater there are 108 elves also

considering that total 144 elves can be in the theater subtract 144 and 108 so 36 more elves can be admitted

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Answer:

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Step-by-step explanation:

Let A be kids who have a fever, and B be kids who have a sore throat, so

Based on the given information we have

P(A) = 70%, P(B) = 40%, and P(B|A) = 30% (B|A is read as "B given A", which means probability of B happening given that A has already happened)

We are asked to find P(A|B), the probability of a kid having a fever given that we already know he has a sore throat.

Step 1: First find P(A and B), this is the probability of a kid having both a fever and a sore throat. We use the formula

P(B|A) = P(A and B)/P(A)

We have 2 of these values listed above, so we plug them in...

30% = P(A and B)/70%

This give us a value for P(A and B) which equals 21% [multiply both sides by 70% to isolate P(A and B), (30%)(70%) = 21%]

Now we flip the equation to P(A|B), which is

P(A|B) = P(A and B)/P(B)

We have 2 of the values, so we plug them in...

P(A|B) = 21%/40%

This gives us a value of 52.5% (divide 21% by 40%)

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3 years ago

A researcher at the University of Washington medical school believes that energy drink consumption may increase heart rate. Supp

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Answer:

Step-by-step explanation:

Given that:

mean μ = 70

sample size = 25

sample mean = 73

standard deviation = 7

level of significance = 0.10

The null hypothesis and the alternative hypothesis can be computed as follows:

$\mathtt{H_o : \mu = 70} \\ \\ \mathtt{H_1 : \mu > 70 }$

The z score for this statistics can be calculated by using the formula:

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

$z = \dfrac{73- 70}{\dfrac{7}{\sqrt{25}}}$

$z = \dfrac{3}{\dfrac{7}{5}}$

$z = \dfrac{3 \times 5}{{7}{}}$

z = 2.143

At level of significance of 0.10

degree of freedom = n -1

degree of freedom = 25 - 1

degree of freedom = 24

The p - value from the z score at level of significance of 0.10 and degree of freedom of 24 is:

P - value = 1 - (Z < 2.143)

P - value = 1 - 0.9839

P - value = 0.0161

Decision Rule: since P value is lesser than the level of significance, we reject the null hypothesis.

Conclusion: We conclude that energy drink consumption increases heart rate.

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3 years ago