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4 years ago

Why are you allowed to move the decimal points before dividing with decimals? Explain your reasoning.

2 answers:

7 0

If you move the decimal point the same number of places in the dividend and the divisor, you are multiplying them both by the same power of 10. That does not change the quotient.

Goshia [24]4 years ago

6 0

Answer:

If you move the decimal point the same number of places in the dividend and the divisor, you are multiplying them both by the same power of 10. That does not change the quotient.

Step-by-step explanation:

it was what i got and it was right

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Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequentl

Pachacha [2.7K]

Answer:

a) 0.24356 or 24.36%

b) [102.39 , 105.61]

c) The interpretation of this confidence interval is that in samples of 427 people aged 65 years and older, there is a 99% probability that the number of people that suffers sleep apnea is between 103 and 105.

Step-by-step explanation:

This can be considered a binomial distribution (a person either has sleep apnea or not).

Based on the sample we have the probability of suffering the condition is

p = 104/427 = 0.24356

and q (the probability of not suffering the condition) is

q=1-0.24356=0.75644

So the proportion of people aged 65 years and older who have sleep apnea is 0.24356 or 24.36%

To check if we can approximate this binomial distribution with the Normal distribution we must see that

np ≥ 5 and nq ≥ 5

where n is the sample size. Since

427*0.24356 ≥ 5 and 427*0.75644 ≥ 5

we can approximate the binomial with a Normal distribution with mean

np = 427*0.24356 = 104

and standard deviation

$\large s=\sqrt{npq}=\sqrt{427*0.24356*0.75644}=8.867$

The 99% confidence interval (without the continuity correction factor) is given by the interval

$\large [\bar x-z^*\frac{s}{\sqrt n}, \bar x+z^*\frac{s}{\sqrt n}]$

where

$\large \bar x$ is the sample mean

s is the sample standard deviation

n is the sample size

$\large z^*$ is the 0.01 (99%) upper critical value for

the Normal distribution N(0;1).

The value of $\large z^*$ can be found either by using a table or a computer to find it equals to

$\large z^*=2.576$

and our 99% confidence interval (without continuity correction) is

$\large [104-2.576*\frac{8.867}{\sqrt{427}}, 104+2.576*\frac{8.867}{\sqrt {427}}]=[102.8946,105.1054]$

We can now introduce the continuity correction factor. This should be done because we are approximating a discrete distribution (Binomial) with a continuous one (Normal).

This is simply done by widening the interval in 0.5 at each end, so our final 99% confidence interval is

[102.3946 , 105.6054] = [102.39 , 105.61] rounded to 2 decimal places.

The interpretation of this confidence interval is that in samples of 427 people aged 65 years and older, there is a 99% probability that the number of people that suffers sleep apnea is between 103 and 105.

If another study found a 15% of elderly people suffered sleep apnea, that would mean that in a sample of 427 only 64 would have the condition. Since that number is less than 103 by far, that would give us a reason to doubt about the conditions that framed the study (sample size, sampling method, age of people, etc.)

4 0

3 years ago

Factors of polynomial 3xsquare +x-4

Dennis_Churaev [7]

Answer:

(3x + 4)(x - 1)

Step-by-step explanation:

3x^2 + x - 4

use middle term break method

we need two number which gives 12 when multiplied and 1 when subtracted

3x^2 + (4 - 3)x - 4

3x^2 + 4x - 3x - 4

x(3x + 4) -1(3x + 4)

(3x + 4)(x - 1)

4 0

3 years ago

Read 2 more answers

Giving 100 points.

Nitella [24]

Answer:

1. Cost per customer: 10 + x

Average number of customers: 16 - 2x

$\textsf{2.} \quad -2x^2-4x+160\geq 130$

3. $10, $11, $12 and $13

Step-by-step explanation:

Given information:

$10 = cost of buffet per customer
16 customers choose the buffet per hour
Every $1 increase in the cost of the buffet = loss of 2 customers per hour
$130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

Part 1

Cost per customer: 10 + x

Average number of customers: 16 - 2x

Part 2

The cost per customer multiplied by the number of customers needs to be at least $130. Therefore, we can use the expressions found in part 1 to write the inequality:

$(10 + x)(16 - 2x)\geq 130$

$\implies 160-20x+16x-2x^2\geq 130$

$\implies -2x^2-4x+160\geq 130$

Part 3

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

$\implies -2x^2-4x+160\geq 130$

$\implies -2x^2-4x+30\geq 0$

$\implies -2(x^2+2x-15)\geq 0$

$\implies x^2+2x-15\leq 0$

$\implies (x-3)(x+5)\leq 0$

Find the roots by equating to zero:

$\implies (x-3)(x+5)=0$

$x-3=0 \implies x=3$

$x+5=0 \implies x=-5$

Therefore, the roots are x = 3 and x = -5.

Test the roots by choosing a value between the roots and substituting it into the original inequality:

$\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144$

As 144 ≥ 130, the solution to the inequality is between the roots:

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:

$x =0 \implies 10 + 0=\$10$