Solve this system by substitution: y = -6x - 3 -3x

Determine the intercept of the line

Alexus [3.1K]

Step-by-step explanation:

y-intercept (0,2.5)

x-intercept (3.5,0)

4 0

3 years ago

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Multiply (2x + 8)(4x + 7)

Anuta_ua [19.1K]

Hey! (2x + 8)(4x + 7) = 2x(4x + 7) + 8(4x + 7) = 8x^2 + 14x + 32x + 56 =
8x^2 + 46x + 56 <==
Hope this helps! :)

7 0

4 years ago

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The bad debt ratio for a financial institution is defined to the dollar value of loans defaulted divided by the total dollar val

vlabodo [156]

Answer:

Step-by-step explanation:

From the information given:

Consider X to be the random variable denoting the bad debt ratios for Ohio Bank.

Then, $X \sim N ( \mu, \sigma ^2)$

Thus the null hypothesis and the alternative can be computed as:

Null hypothesis:

$H_o : \mu \leq3.5\%$

Alternative hypothesis

$H_1 : \mu > 3.5\%$

The type I and type II error is as follows:

Type I:

The mean bad debt ratio is > 3.5% when it is not

Type II:

The mean bad debt ratio is ≤ 3.5% when it is not.

The test statistics can be calculated by using the formula:

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

where;

sample size n = 7

mean = 6+8+5+9+7+5+8 = 48

sample mean $\overline x =\dfrac{48}{7}$

$\overline x$ = 6.86

sample standard deviation is :

$s = \sqrt{\dfrac{\sum( x -\overline x)^2}{n-1}}$

$s = \sqrt{\dfrac{( 6 -6.86)^2+( 8-6.86)^2+ ( 5 -6.86)^2 + ...+( 7 -6.86)^2+ ( 5 -6.86)^2+( 8 -6.86)^2 }{7-1}}$

s = 1.573

population mean $\mu = 3.5$

Therefore, the test statistics is :

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

$t = \dfrac{6.86- 3.5}{\dfrac{1.573}{\sqrt{7}}}$

$t = \dfrac{3.36}{\dfrac{1.573}{2.65}}$

$t = \dfrac{3.36\times {2.65}}{{1.573}}$

t = 5.660

At significance level of 0.01

$t_{0.01} = 3.707$

P - value = P(T > 5.66)

P - value = 1 - (T < 5.66)

P - value = 1 - 0.9993

P-value = 0.0007

Therefore, since $t_{0.01} < t$ , we reject the null hypothesis and conclude that the claim that the mean bad debt ratio for Ohio banks is higher than the mean for all financial institutions is true.

4 0

4 years ago

Find the explicit formula for the geometric sequence 2,6,18,54

xenn [34]

Answer:

the explicit formula for the geometric sequence 2,6,18,54 is $a_{n}=a_{1}.r^{n-1}$

2,6,18,54

Step-by-step explanation:

In the sequence given: 2,6,18,54

The common ration is 3 because

a₁ = 2

a₂= 2*3 =6

a₃ = (2*3)*3 = 2*3^2 = 18

a₄= (2*3*3)*3 =2*3^3 = 54

Here we see for a₂ 3 has power 1, for a₃ 3 has power 2 and so on.

So, the formula will be

$a_{n}=a_{1}.r^{n-1}$

Here aₙ is the no of term.

a₁ is the first term of the sequence

and r is the common ratio among the sequence.

8 0

4 years ago

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Sophie, Jonah, and Chase have a total of $89 in their wallets. Sophie has $6 less than Chase and Jonah has 3 times what Chase ha

Marrrta [24]

So first you need to find a formula for who has what!

Because nobody said what chase had, chase is our variable!

Chase = x
Sophie = x-6 (six less than Chase so subtraction)
Jonah = x•3 (three times the amount of Chase)

Now you will put all of this in an equation- adding everybody together! The total is 89 so that will be what’s after the equal sign!

Your equation: x+x-6+x•3=89

First you will use PEMDAS, since there are no parentheses or exponents- you’ll do multiplication first!

x+x-6+(x•3)=89
When you multiply that out, you will be left with: x+x-6+3x=89

Second you will add all common terms! Remember- the 3x means there are THREE x’s in that one spot. Take out all x’s in the equation and add them together!

x+x+3x=5x

Now you are left with:
5x-6=89

Now you will solve this like a regular equation! First, you have to move the -6 to the right so you will do the inverse operation (the opposite sign) and add 6 to both sides! 89+6 is 95 and -6+6 is 0, so the 6 on the left cancels out and isn’t there anymore!

Now you have 5x=95. To get the x by itself, you will divide both sides by 5! (Once again, doing the inverse operation! Since 5 and x are being multiplied, you have to divide.)

When you divide, you are left with x=19. In this question, the answer is:

Each person has $19.

3 0

3 years ago

Solve this system by substitution: y = -6x - 3 -3x - 8y = 24