Answer:
x = 61
Step-by-step explanation:
The angle above the line n adjacent to 2x - 6 is (x + 3) alternate angle.
Adjacent angles are supplementary, thus
2x - 6 + x + 3 = 180, that is
3x - 3 = 180 ( add 3 to both sides )
3x = 183 ( divide both sides by 3 )
x = 61
Answer: 7(3m - 7n)
<u>Step-by-step explanation:</u>
Factor each term then see what value(s) they have in common:
21m - 49n
∧ ∧
3 · 7 · m 7 · 7 · n
Both terms have a 7 in common. What is left over after removing the 7?
21m: 7(3m)
49n: 7(7n)
GCF: 7 Leftovers: 3m <em>and</em> 7n
Factored form of expression is: 7(3m - 7n)
If the value of the baseball card increases by 3% per year then we can say that each year the value of the card may be multiplied by 103% = 1.03, thus:
Value after n years = original price*(1.03)^n
Value after 15 years = 75*(1.03)^15
= $116.85
Answer:
Equivalent expression of
is, 
Step-by-step explanation:
The distributive property says that:

Given the expression: 
Apply the distributive property:

Simplify:

Therefore, the equivalent expression of
is, 
Answer:
d. t distribution with df = 80
Step-by-step explanation:
Assuming this problem:
Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:
a. t distribution with df = 82.
b. t distribution with df = 81.
c. t distribution with df = 41.
d. t distribution with df = 80
Solution to the problem
When we have two independent samples from two normal distributions with equal variances we are assuming that
And the statistic is given by this formula:
Where t follows a t distribution with
degrees of freedom and the pooled variance
is given by this formula:
This last one is an unbiased estimator of the common variance
So on this case the degrees of freedom are given by:

And the best answer is:
d. t distribution with df = 80