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3 years ago

Find any 5 rational numbers between; a) -1 and 2 b) −3 8 −5 14

Mathematics

1 answer:

kap26 [50]3 years ago

4 0

Answer:

Step-by-step explanation:

Hello,

You can list the following ones which are correct for a), b) and c)

$\boxed{\sf \bf \ \ 1, \dfrac{1}{2}, \dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5} \ \ }$

Thanks

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The average demand for rental skis on winter Saturdays at a particular area is 150 pairs, which has been quite stable over time.

pentagon [3]

Answer:

a) 15.87% probability that demand will exceed this supply on any winter Saturday

b) The shop needs to have 197 pairs of skis in stock.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

$\mu = 150, \sigma = 20$

(a) The rental shop stocks 170 pairs of skis. What is the probability that demand will exceed this supply on any winter Saturday?

This probability is 1 subtracted by the pvalue of Z when X = 150. So

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

$Z = \frac{170 - 150}{20}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

1 - 0.8413 = 0.1587

15.87% probability that demand will exceed this supply on any winter Saturday

(b) How many pairs of skis in stock does the shop have to have to make the probability in question (a) less than .01?

This is X when Z has a pvalue of 0.99.

So X when Z = 2.33

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

$2.33 = \frac{X - 150}{20}$

$X - 150 = 2.33*20$

$X = 196.6$

Rounding up, since the number of pairs is a discrete number

The shop needs to have 197 pairs of skis in stock.

6 0

3 years ago

which of the following statements is true? a. the radius of a circle is twice its diameter b. to find the diameter of a circle,

Bess [88]

Answer:

Statement B, C, E are correct

Solution:

We have to find the true statements

We know that,

To find the diameter of a circle, multiply its radius by two

Thus statement E is correct

Also,

To find the diameter of a circle, divide its circumference by π

Thus statement B is correct

circumference of a circle is obtained by multiplying diameter with pi

The circumference of a circle is greater than its diameter

Thus, Statement C is correct

4 0

3 years ago

Read 2 more answers

Given the explicit expression f (n) = 5n - 2, write a set showing the sequence, and write a recursive expression.

denpristay [2]

Answer:

$f(n) = 5 + f(n - 1)$

Step-by-step explanation:

Given

$f(n) = 5n - 2$

Required

Write a recursive expression

$f(n) = 5n - 2$

When n = 1

$f(1) = 5 * 1 - 2 = 5 - 2 = 3$

$f(1) = 3$

When n = 2

$f(2) = 5 * 2 - 2 = 10 - 2 = 8$

$f(2) = 8$ can be rewritten as

$f(2) = 5 + 3$

Substitute 3 for f(1)

$f(2) = 5 + f(1)$

Express 1 as 2 - 1

$f(2) = 5 + f(2-1)$ ----- (1)

When n = 3

$f(3) = 5 * 3 - 2 = 15 - 2 = 13$

$f(3) = 13$ can be rewritten as

$f(3) = 5 + 8$

Substitute 8 for f(2)

$f(3) = 5 + f(2)$

Express 2 as 3 - 1

$f(3) = 5 + f(3 - 1)$ ------ (2)

Write out (1) and (2)

$f(2) = 5 + f(2-1)$

$f(3) = 5 + f(3 - 1)$

Replace 2 and 3 with n in both cases; This gives

$f(n) = 5 + f(n - 1)$

Hence;

The recursive is $f(n) = 5 + f(n - 1)$

7 0

3 years ago

Use the drop-down menus to complete each equation so the statement about its solution is true.

aleksklad [387]

First, let's simplify the expression: 7 - 5 + 3x - 1 ⇒ 3x + 1 (slope=3, y-intercept = 1)

Next, let's understand what they are asking for:

no solutions means same slope but different y-intercepts

Answer: 3x + _______ (the blank can be anything except 1)

one solution means different slopes

Answer: ________x + _______ (the first blank can be anything except 3, the second blank can be anything)

infinitely many solutions means same slope and same y-intercept

Answer: 3x + 1

3 0

3 years ago

Read 2 more answers

If tan 0=1/3 find cot 0.

Karolina [17]

Answer: cot 0 = 3

Cotangent is the reciprocal of tangent, so it would be 3/1, which simplified to 3.

8 0

3 years ago