Which expression is NOT equivalent to the other three?

8,000 is invested in two different accounts earning 3% and 4% interest. If the two accounts earn a total of $295 in interest, ho

lesya692 [45]

Answer:

$5,500

Step-by-step explanation:

Let A be the amount invested at 3%, B the amount at 4%.

Total value:

1.A%2BB=8000

Interest:

Multiply eq. 1 by -3 and add to eq. 2,

-3A-3B%2B3A%2B4B=-24000%2B29500

highlight%28B=5500%29

Then from eq. 1,

A%2B5500=8000

highlight%28A=2500%29

3 0

3 years ago

Read 2 more answers

A classmate simplifies the expression in exercise 1. is the expression he wrote equivalent to the original expression? explain.

AlladinOne [14]

Excercise 1:

No, this is not simplified fully. The full answer would be −7dk+14d−21k−7, not 14d - 9 - 21k - 7dk + 2. So, it is not equivalent.

Excercise 4:
7dk (2 - 3 - 1) - 7

Just multiply 7dk into (2) (-3) and (-1)
you'd get:
−14dk+−7 after simplifying it fully.

p = parameter
w = width

w+2.75

p = 2w+2(w+2.75) = 4w+5.5 = 30

Answer to the last one:

w = 6.125

4 0

3 years ago

PLEASE HELP ASAP THIS IS THE LAST QUESTION AND I AM STUCK!!

Varvara68 [4.7K]

<h3>Answer: B) 7 units</h3>

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Explanation:

The y coordinates of the two points are the same, so we can subtract the x coordinates and apply absolute value

|R - T| = |-6 - 1| = |-7| = 7

Or we can say

|T - R| = |1 - (-6)| = |1 + 6| = |7| = 7

Either way, the two points are 7 units apart.

You could use the distance formula to get the same answer, but that's definitely overkill in my opinion. The trick mentioned above also could work if the x coordinates were the same, but the y coordinates were different. In any other case, you would have to use the distance formula.

5 0

3 years ago

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and

Brums [2.3K]

Answer:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

$p_v =P(t_9>10.349)=1.34x10^{-6}$

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=51.6$ represent the sample mean

$s=1.1$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =48$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean score is higher than 48, the system of hypothesis would be:

Null hypothesis: $\mu \geq 48$

Alternative hypothesis: $\mu > 48$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

Calculate the P-value

First we find the degrees of freedom:

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

Since is a one-side upper test the p value would be:

$p_v =P(t_9>10.349)=1.34x10^{-6}$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

5 0

3 years ago

Evan runs a website that has gotten quite popular. However, its popularity seems to be decreasing and the site is now getting 7%

anyanavicka [17]

Answer:

(a-b) *(a-b) *(a-b)

=(a*a*a) -3*(a*a*b)+3*(a*b*b)-(b*b*b)

34000*(1-7%)*(1-7%)*(1-7%)

=34000*(1-0.07)*(1-0.07)*(1-0.07)

=34000*[(1*1*1)-3*(1*1*0.07)+3*(1*0.07*0.07)-(0.07*0.07*0.07)]

=34000*(1-0.21+0.0147-0.000343)

=34000*(0.804357)

=34*1000*(804.357/1000)

=34*804.357

=27348.138

=27348

4 0

3 years ago