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2 years ago

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Lan make 60 cakes. he gives 1/4 of the cakes to Helen. he gives 20 of the 60 cakes to sue. what fraction of the 60 cakes does he

have left?

2 answers:

weqwewe [10]2 years ago

4 0

Answer:

5/12

Step-by-step explanation:

1/4 of the cakes is 60 divided by 4 which is 15. That goes to Helen

20 go to Sue

so far, he has given away 35 cakes out of the 60

he is left with 25 cakes

that is 25/60 which can be simplified to 5/12

tresset_1 [31]2 years ago

3 0

Answer:

5/12

Step-by-step explanation:

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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

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2 years ago

The exact circumference of a circle is 34π meters. What is the approximate area of the circle? Use 3.14 for π. Round to the near

LiRa [457]

Answer:

A = 907.46 $m^{2}$

Step-by-step explanation:

C = πd

34π = πd

d = 34

r = 17

A = $\pi r^{2}$ = 3.14( $17^{2}$ ) = 3.14(289) = 907.46 $m^{2}$

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konstantin123 [22]

Answer: B) reflection over the y-axis

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3 years ago

The cost to produce a product is modeled by the function f(x) = 5x^2 − 70x + 258, where x is the number of products produced. Co

Advocard [28]

The minimum of a quadratic function, with a positive coefficient a, is its vertex.

Let's find the x₀ coordinate.

$f(x) = 5x^2 -70x + 258\\\\x_0=\dfrac{-b}{2a}=\frac{-(-70)}{2*5} =\frac{70}{10} =7$

Now we need to find y₀ coordinate. That will be the minimum of function.

$y_0=5\times7^2-70\times7+258=13$

So, the minimum cost to produce the product is $13

Decompose 5x^2 − 70x + 258 into multipliers

$5x^2 - 70x + 258=(5x^2-70x+245)+13=5(x^2-14+49)+13=\\=5(x-7)^2+13$

Answer: 5(x − 7)^2 + 13; The minimum cost to produce the product is $13.

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