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3 years ago

I have to simplify each expression and justify each step

Mathematics

1 answer:

algol [13]3 years ago

8 0

Ok, so according to BODMAS (which stands for brackets, orders, division, multiplication, addition and subtraction), we have to solve the expression inside the bracket first, then solve the division and multiplication. So in this case we have,

3x times (7 times x)
= 3x times (7x) --> we have multiplied 7 and x)
= 21x^2 (^2 means squared)

Hope this helps!

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A researcher wants to check the claim that convicted burglars spend less than 18.7 months in jail, on average. She takes a rando

vivado [14]

Answer:

a. No, there is not enough evidence to support the claim using a level of significance of 1%.

b. Null Hypothesis, $H_0$ : $\mu \geq$ 18.7 months

c. Alternate Hypothesis, $H_A$ : $\mu$ < 18.7 months

d. P-value of hypothesis test = 0.0199 or 1.99%

e. We conclude that the convicted burglars spend more than or equal to 18.7 months in jail, on average.

Step-by-step explanation:

We are given that a researcher wants to check the claim that convicted burglars spend less than 18.7 months in jail, on average.

She takes a random sample of 67 such cases from court files and finds that the mean is 16.8 months with a standard deviation of 7.3 months.

Let $\mu$ = true mean time convicted burglars spend in jail.

SO, Null Hypothesis, $H_0$ : $\mu \geq$ 18.7 months {means that the convicted burglars spend more than or equal to 18.7 months in jail, on average}

Alternate Hypothesis, $H_A$ : $\mu$ < 18.7 months {means that the convicted burglars spend less than 18.7 months in jail, on average}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean time spent in jail = 16.8 months

s = sample standard deviation = 7.3 months

n = sample of cases = 67

So, test statistics = $\frac{16.8-18.7}{\frac{7.3}{\sqrt{67} } }$ ~ $t_6_6$

= -2.13

Hence, the value of test statistics is -2.13.

Now, P-value of the test statistics is given by;

P-value = P( $t_6_6$ < -2.13) = 0.0199 or 1.99%

If the P-value of test statistics is more than the level of significance, then we will not reject our null hypothesis as it will not fall in the rejection region.

If the P-value of test statistics is less than the level of significance, then we will reject our null hypothesis as it will fall in the rejection region.

Now, here the P-value is 0.0199 or 1.99% which is clearly higher than the level of significance of 1%, so we will not reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the convicted burglars spend more than or equal to 18.7 months in jail, on average.

6 0

3 years ago

PLEASE HELP!! i'm struggling sm :/

Bogdan [553]

Answer:

Check boxes 3, 4, 6, and 8.

Step-by-step explanation:

We have the equation:

$y=-3x+2$

And we want to select all equations that are perpendicular to the above equation.

Remember that perpendicular lines have slopes who are negative reciprocals of each other.

Therefore, the slope of our equations must be the negative reciprocal of -3.

The negative reciprocal of -3 is 1/3. We flipped -3 to -1/3, and then multiplied by a negative.

Therefore, any equation with a slope of 1/3 is perpendicular to our original line.

Therefore, we will check boxes 3, 4, 6, and 8.

5 0

3 years ago

Can someone solve this for me with their explanation please?

Lana71 [14]

First you want to subtract 36

so it looks like this $\sqrt[4] {(4x+164)^3}=64$

Then you want to cancel out the square root 4 by raising that to the 4th power (you must do this to both sides)

${(4x+164)^3}=64^4$ which is equal to ${(4x+164)^3}=16777216$

Then you take the cube root to both sides [tex]\sqrt[3]{(4x+164)^3}=\sqrt[3]{16777216}[tex]

Then you end up with the equation 4x+164=256

Then subtract 164 to both sides

4x=92

then divide 92 by 4

Then you get x=23

7 0

4 years ago

Slope of (5,3) (-4,13)

Ira Lisetskai [31]

Answer:

m= -10/9

...........

5 0

3 years ago

Explain how you know that 7/12 is greater than 1/3 but less than 2/3

velikii [3]

Well, it's greater than 1/3 because 1/3 of 12 is 4, and it's more than 4/12.
It's less than 2/3 because 2/3 of 12 is 8, and 7/12 is not 8/12.

4 0

3 years ago