Write the standard form of the equation of each line given the slope and y- intercept

padilas [110]

(a).
The product of two binomials is sometimes called FOIL.
It stands for ...

   the product of the First terms (3j x 3j)
plus
   the product of the Outside terms (3j x 5)
plus
   the product of the Inside terms (-5 x 3j)
plus
   the product of the Last terms (-5 x 5)

FOIL works for multiplying ANY two binomials (quantities with 2 terms).

Here's another tool that you can use for this particular problem (a).
It'll also be helpful when you get to part-c .

Notice that the terms are the same in both quantities ... 3j and 5 .
The only difference is they're added in the first one, and subtracted
in the other one.

Whenever you have

      (the sum of two things) x (the difference of the same things)

the product is going to be

   (the first thing)² minus (the second thing)² .

So in (a), that'll be (3j)² - (5)² = 9j² - 25 .

You could find the product with FOIL, or with this easier tool.
______________________________

(b).
This is the square of a binomial ... multiplying it by itself. So it's
another product of 2 binomials, that both happen to be the same:

(4h + 5) x (4h + 5) .

You can do the product with FOIL, or use another little tool:

The square of a binomial (4h + 5)² is ...

   the square of the first term    (4h)²
plus
   the square of the last term       (5)²
plus
   double the product of the terms 2 · (4h · 5)
________________________________

(c).
Use the tool I gave you in part-a . . . twice .

The product of the first 2 binomials is    (g² - 4) .

The product of the last 2 binomials is also (g² - 4) .

Now you can multiply these with FOIL,
or use the squaring tool I gave you in part-b .

5 0

3 years ago

Read 2 more answers

Monica’s checkbook register balance is $456.98. She has written checks in the amounts of $10.00, $14.95, $6.07, and $109.10. She

Setler79 [48]

456.98-10-14.95-6.07-109.10-30=<span>286.86

So her new </span>checkbook balance is $286.86

5 0

3 years ago

The national mean annual salary for a school administrator is $90,00 a year (The Cincinnati Enquirer, April 7, 2012). A school o

timurjin [86]

Answer:

a) Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

b) $p_v =2*P(t_{(24)}$

c) If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

Step-by-step explanation:

1) Data given and notation

77600 ,76000 ,90700 ,97200 ,90700 ,101800 ,78700 ,81300 ,84200 ,97600 ,

77500 ,75700 ,89400 ,84300 ,78700 ,84600 ,87700 ,103400 ,83800 ,101300

94700 ,69200 ,95400 ,61500 ,68800

We can calculate the sample mean and deviation with the following formulas:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

The values obtained are:

$\bar X=85272$ represent the mean annual salary for the sample

$s=11039.23$ represent the sample standard deviation for the sample

$n=25$ sample size

$\mu_o =90000$ 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)

Part a: State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean salary differs from 90000, the system of hypothesis would be:

Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (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".

Part b: Calculate the statistic

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

$t=\frac{85272-90000}{\frac{11039.23}{\sqrt{25}}}=-2.141$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=25-1=24$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(24)}$

Part c: Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

6 0

3 years ago

Apply the distributive property to create an equivalent expression. 1/2 ( 10 x + 20 y + 10 z )=

Sergio [31]

Answer:

5x+10y+5z

Step-by-step explanation:

Distributive Property means you multiply each component by the value you are distributing in this case: (1/2)(10x) + (1/2)(20y) + (1/2)(10z) which will yield 5x+10y+5z

6 0

2 years ago

Hospital A has treated 156 cases of E. coli infection in the past year. Hospital B has treated 51 fewer cases. How many cases di

solniwko [45]

Answer:

105 Cases

Step-by-step explanation:

Subtract 156-51

Fewer shows subtraction

6 0

2 years ago