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Andreas93 [3]
2 years ago
14

Mrs. Ward want to buy a suit marked $60. She received a 25% discount, and then there is a 7% sales tax. How much does Mrs. Ward

actually spend on the suit?
Mathematics
1 answer:
RoseWind [281]2 years ago
7 0
48.15 is the answer
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USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eight people at random off
Law Incorporation [45]

Answer:

a) Figure and code attached

b) E(X)=\mu = np = 8*0.2= 1.6

Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28

Sd(X)=\sigma= \sqrt{1.28}= 1.131

c) P(X\geq 7) =0.97

And we can calculate this with the complement rule.

P(X \geq 7) = 1-P(X

So then we have:

P(X \leq 6) = 0.03

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=8, p=0.2)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

We can use the following R code to generate the histogram for this case:

> x <- seq(0,8,by = 1)

> y <- dbinom(x,8,0.2)

> plot(x,y,type = "h",main="Histogram")

And as we can see we got the result on the figure attached. And the distribution seems to be skewed to the right.

Part b

For this case the expected value is given by:

E(X)=\mu = np = 8*0.2= 1.6

The variance is given by:

Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28

And the standard deviation would be:

Sd(X)=\sigma= \sqrt{1.28}= 1.131

Part c

For this case we have the following inequality:

P(X\geq 7) =0.97

And we can calculate this with the complement rule.

P(X \geq 7) = 1-P(X

So then we have:

P(X \leq 6) = 0.03

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

5 0
3 years ago
Please Help Keep getting 6.4
elixir [45]

Answer:

r = 3

Step-by-step explanation:

x^2 + 6x + y^2 - 8y = - 16

Take half the linear term and square it.

x^2 + 6x + (3)^2 + y^2 - 8y + (-4)^2 = - 16

Add the squared amounts to the right.

x^2 + 6x + 9 + y^2 - 8y + 16 = - 16 + 9 + 16  

Combine on the right.

x^2 + 6x + 9 + y^2 - 8y + 16 = 9

Represent the 2 quadratics as perfect squares.

(x + 3)^2 + y - 4)^2 = 9

The radius is the square root of 9 which is 3

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Please help me!!! brainliest
nevsk [136]

Answer:

1, 2, 4

Step-by-step explanation:

  1. 4 1/12·2 2/3 = 49/12·11/4 = 49/12·33/12 = 1617/144 = 11 11/48 Good
  2. 2 1/5·6 1/4 = 11/5·25/4 = 44/20·125/20 = 5500/400 = 13 3/4 Good
  3. 1 1/2·3 1/5 = 3/2·16/5 = 15/10·32/10 = 480/100 = 4.8 Doesn't Work
  4. 3/4·8 1/5 = 3/4·41/5 = 15/20·164/20 = 2460/400 = 6 3/20 Good
  5. 5 1/2·5 = 11/2·5 = 55/2 = 27 1/2 Doesn't Work

(Note: Division of big numbers should be done by simplification, although not shown here.)

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2 years ago
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Which of the following arcs are congruent in the circle below?
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Answer:

C

Step-by-step explanation:

CB is congruent to AB because the both are 30 degrees

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3 years ago
A computer manufacturing company has sent a mail survey to 2,800 of its randomly selected customers that have purchased a new la
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Answer:

The 96% confidence interval for the population proportion of customers satisfied with their new computer is (0.77, 0.83).

Step-by-step explanation:

We have to calculate a 96% confidence interval for the proportion.

We consider the sample size to be the customers that responded the survey (n=800), as we can not assume the answer for the ones that did not answer.

The sample proportion is p=0.8.

p=X/n=640/800=0.8

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8*0.2}{800}}\\\\\\ \sigma_p=\sqrt{0.0002}=0.014

The critical z-value for a 96% confidence interval is z=2.054.

The margin of error (MOE) can be calculated as:

MOE=z\cdot \sigma_p=2.054 \cdot 0.014=0.03

Then, the lower and upper bounds of the confidence interval are:

LL=p-z \cdot \sigma_p = 0.8-0.03=0.77\\\\UL=p+z \cdot \sigma_p = 0.8+0.03=0.83

The 96% confidence interval for the population proportion is (0.77, 0.83).

4 0
3 years ago
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