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6) The sum of three consecutive even numbers is 96.<br> What is the smallest of the three numbers ?

Neko [114]

Answer:

30

Step-by-step explanation:

Consecutive even numbers can be written as X,X+2,X+4,X+6, and so forth. You only have three consecutive even numbers that equal 96, so write the following equation:

X+X+2+X+4=96

1) Combine alike terms:

3X+6=96

2) Subtract 6 from both sides:

3X=90

3) Divide both sides by 3:

X=30

Now plug in 30 for each of the consecutive even numbers' equations:

X=30

X+2=32

X+4=34

The smallest of these three numbers is 30, therefore the answer is 30!

6 0

3 years ago

The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a la

stira [4]

<h2>Answer with explanation:-</h2>

Let $\mu$ be the population mean .

By observing the given information, we have :-

$H_0:\mu=7450\\\\H_a:\mu\neq7450$

Since the alternative hypotheses is two tailed so the test is a two-tailed test.

We assume that the life of a large shipment of CFLs is normally distributed.

(a) Given : Sample size : n=81 , since n>30 so we use z-test.

Sample mean : $\overline{x}=7240$

Standard deviation : $\sigma=1350$

Test statistic for population mean :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$\Rightarrow\ z=\dfrac{7240-7450}{\dfrac{1350}{\sqrt{81}}}\\\\\Rightarrow\ z=-1.4$

The critical value (two-tailed) corresponds to the given significance level :-

$z_{\alpha/2}=z_{0.025}=1.96$

Since the observed value of z (-1.4) is less than the critical value (1.96) , so we do not reject the null hypothesis.

Hence, we conclude that we have enough evidence to accept that the mean life is different from 7450 hours .

(b) The p-value : $2P(z>-1.4)=0.1615$ , it means that the probability that the life of CFLs less than 7240 and greater than 7240 is 0.1615.

(c) The confidence interval for population mean is given by :-

$\overline{x} \pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=7240\pm(1.96)\dfrac{1350}{\sqrt{81}}\\\\=7240\pm294\\\\=(6946,7534)$

,

8 0

3 years ago

At a store, apples cost $0.80 $0.80 each and oranges cost $0.95 $0.95 each. Harry buys some apples and oranges and spends $9.55

gregori [183]

Answer:

Harry buys 6 apples and 5 oranges at the store.

Step-by-step explanation:

Given:

Cost of each apples = $0.8

Cost of each oranges = $0.95

Total money spend =$9.55

Number of fruits bought= 11

We need to find the number of apples bought and number of oranges were bought.

Solution:

Let the number of apples bought be 'a'.

Let the number of oranges were bought be 'o'.

Number of fruits bought= 11

So we can say that;

Number of fruits bought is equal to sum number of apples bought and number of oranges were bought.

framing in equation form we get;

$a+o=11$ ⇒ equation 1

Now we can say that;

Total money spend is equal to number of apples bought multiplied by Cost of each apples plus number of oranges were bought multiplied by Cost of each oranges.

framing in equation form we get;

$0.8a+0.95o=9.55$ ⇒ equation 2

Now Multiplying equation 1 by 0.8 we get;

$0.8(a+o)=0.8\times11$

$0.8a+0.8o=8.8$ ⇒ equation 3

Subtracting equation 3 from equation 2 we get;

$0.8a+0.95o-(0.8a+0.8o)=9.55-8.8\\\\0.8a+0.95o-0.8a-0.8o=0.75\\\\0.15o=0.75$

Dividing both side by 0.15 we get;

$\frac{0.15o}{0.15}=\frac{0.75}{0.15}\\\\o=5$

Substituting the value of o in equation 1 we get;

$a+o=11\\\\a+5=11\\\\a=11-5=6$

Hence Harry buys 6 apples and 5 oranges at the store.

3 0

3 years ago

If the sin of angle x is 4 over 5 and the triangle was dilated to be two times as big as the original, what would be the value o

beks73 [17]

Answer:

Sin of x does not change

Step-by-step explanation:

Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.

From trigonometry,

Sin(x)=opposite/hypotenose

Where x=4/5

Sin(4/5)= opposite/hypotenose

But we were given the scale factor of 2 which means the dilation is to two times big.

Then we have

Sin(x)=(2×opposite)/(2×hypotenose)

Then,if we divide by 2 the numerator and denominator we still have

Sin(x)=opposite/hypotenose

Which means the two in numerator and denominator is cancelled out.

Then we still have the same sin of x. as sin(4/5)

Hence,Sin of x does not change

4 0

2 years ago

Which statement describes an advantage to using equations?

Arte-miy333 [17]

Answer:

Equations make complicated math procedures easier to accomplish and simpler to understand.

Step-by-step explanation:

6 0

3 years ago

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