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4 years ago

Evaluate this exponential expression. 3 • (5 + 4)2 – 42 =

Mathematics

2 answers:

Alecsey [184]4 years ago

4 0

Answer: $=201$

Step-by-step explanation:

Given the exponential expression $3(5 + 4)^2 - 42$ , it is necessary to follow these steps to evaluate it:

Make he addition inside the parentheses:

$3(5 + 4)^2 - 42 =3(9)^2 - 42$

The exponent 2 indicates that you must multiply 9 by itself twice, then:

$=3(9*9) - 42=3(81)-42$

Now you need to multoply 3 by 81:

$=243-42$

And finally, you must make the subtraction indicated. Then:

$=201$

REY [17]4 years ago

3 0

Answer:

Step-by-step explanation:

First,you need to do the cacul of the parenthese,second,you solve by multiply and after that,by substract the answer by 42.

The answer will be 12

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The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, al

Valentin [98]

Answer:

a) $p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 0$

Alternative hypothesis: $\mu_y -\mu_x$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679$

The next step is calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Now we can calculate the p value, since we have a left tailed test the p value is given by:

$p_v =P(t_{(9)}$

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

Now we have everything in order to replace into formula (1):

$-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469$

$-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069$

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0

3 years ago

The average speed of one airplane is 200 mph faster than that of an automobile. If the automobile starts at 3 a.m. and the airpl

Svetlanka [38]

Answer:

Distance = 500 miles

Step-by-step explanation:

Step 1: Write the data of speed, distance and time for aeroplane and automobile.

Automobile:

Speed = r

Time = 10 hours (3 am till 1 pm)

Distance = SxT

Distance = r x 10 = 10r

Aeroplane:

Speed = 200 + r (200 mph more than automobile)

Time = 2 hours ( 11 am till 1 pm)

Distance = SxT

Distance = 2x(200+r) = 400+2r

Step 2: Equate both distances to find the value of r

Distance of automobile = Distance of aeroplane

10r = 400 + 2r

8r = 400

r = 50

Step 3: Find the distance using any one equation

Distance of automobile = 10r

r = 50

Distance = 10 x 50 = 500 miles

Therefore, the plane travels 500 miles.

3 0

3 years ago

Read 2 more answers

For every 2 hours, approximately $1,302 worth of product is sold to consumers. How much money will the company make from selling

valkas [14]

Answer:

391,248 dollars

Step-by-step explanation:

8 0

3 years ago

Name all of the sets to which the real number 60 belongs

liberstina [14]

Natural, Whole, and Integers. Hopefully I helped :)

5 0

4 years ago

What us the midpoint of A(-8,2) and B(4,-2)

marusya05 [52]

Answer:

(-2 , 2)

Step-by-step explanation:

A(-8 , 2) = (x1 , y1)

B(4 , -2) = (x2 , y2)

midpoint = (x1 + x2/2 , y1 + y2/2)

=(-8 + 4/2 , 2-(-2)/2)

=(-4/2 , 2+2/2)

(-2 , 2)

(3 , 7) = (x1 , y1)

(9 , 2) = (x2 , y2)

distance of PQ = $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

= $\sqrt{(9 - 3)^2 + (2 - 7)^2}$

= $\sqrt{(6)^2 + (-5)^2}$

= $\sqrt{36 + 25}$

= $\sqrt{61}$

=7.8 unit

4 0

3 years ago