Write an expression equivalent to 7 + 21 that shows multiplication by a common factor

The length of a rectangle exceeds its breadth by 9cm.Find the area of rectangle.

svp [43]

B. I hope this helps.

5 0

3 years ago

A 1970 comic book has appreciated 10% per year and originally sold for $0.35. What will it be worth in 2010?

madreJ [45]

1970 to 2010 = 40 years
New price = .35*(1.1)^40
New price = .35*45.26
New price = .15.84

8 0

3 years ago

If two thirds of a number decreased by 20 is 40, what is the number

oee [108]

Answer:

The unknown number is 90

Step-by-step explanation:

This question requires a good understanding so as to interprets it well

And always ensure that all symbols used in representation are well stated so as to help the examiner or anyone who will mark it to understand better

So back to the question,let the unknown number be x

And two thirds of the unknown number is 2/3x

2/3x was decreased by 20 which can be written as 2/3x-20

And this decrease gives 40

That's,2/3x-20=40

Then go ahead to solve the question

Start by finding the LCM and the LCM is 3

2x-60/3=40

Cross multiply

2x-60=40×3

2x-60=120

Collect like terms by adding 60 to both sides

2x=180

Divide both sides by 2

x=90

Therefore the final answer is 90

8 0

3 years ago

A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true

kvv77 [185]

Answer:

99.74% probability that the sample proportion will be less than 0.1

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .