Find four consecutive integers such that 8 times the sum of the first and the third is 40

Simpify the expression.<br>5+4z-2z<br><br>Simpilfied expression

Dafna11 [192]

Answer:

2z + 5

Step-by-step explanation:

you have to combine like terms

subtract 4z - 2z and you get 2z

the number with the variable next to it goes first not the constant

2z + 5

the variable is z and the constant is 5 because it doesn't have variable next to it

hope this makes sense and helps :)

tell me if you have any questions

4 0

2 years ago

Read 2 more answers

The American Psychological Associated conducted a survey in 2003 of psychologists to estimate the average incomes for psychologi

Alex Ar [27]

This question is incomplete, the complete question;

The American Psychological Associated conducted a survey in 2003 of psychologists to estimate the average incomes for psychologists based on their academic degree and years of experience. 36 psychologists responded who had a just received their masters degree in 2003. The average was $48,800 with a standard deviation of $16,800.

The 95% Confidence Interval is ($, $ )

Answer:

at 95%, confidence interval is ( $43312, $54288 )

Step-by-step explanation:

Given the data in the question;

sample size n = 36

mean x' = 48,800

standard deviation σ = 16,800

at 95% confidence level;

∝ = 1 - 95% = 1 - 0.95 = 0.05

∝/2 = 0.05 / 2 = 0.025

z critical value, $Z_{\alpha/2$ = 1.96

now, confidence interval for population mean is given by the formula

x' ± $Z_{\alpha/2$ ( σ/√n )

so we substitute

⇒ 48800 ± 1.96( 16800/√36 )

⇒ 48800 ± 1.96( 2800 )

⇒ 48800 ± 5488

⇒ 48800 - 5488, 48800 + 5488

⇒ ( 43312, 54288 )

Therefore, at 95%, confidence interval is ( $43312, $54288 )

6 0

3 years ago

if we increased one side of a square by 5 units and decreased the other by 3 units the area of the resulting rectangle would be

zvonat [6]

Answer:

18 units

Step-by-step explanation:

So let's list out the sides.

for the first square let's just call them x

for the second square then they would be x+5 and x-3

So let's write out their areas we will cal the area of the first one z

x*x = z

(x+5)*(x-3) = z+21

since z = x^2 we can set up the second equation as a quadratic.

(x+5)*(x-3) = x^2 + 21

x^2 - 3x + 5x - 15 = x^2 + 21

But look, the x^2s cancel out

2x - 15 = 21

2x = 36

x = 18

Test it out and see if it fits the description, And if you don't understand anything just let me know so I can explain more.

3 0

3 years ago

What is the rate of change of y with respect to x for this function? How do I solve problems like this?

Vesnalui [34]

If i am doing this correct.

pick to points and use the distance formula\
Y2 - Y1
divided by
X2 - X1

so i picked the points
-2, 12
0, 3

this would mean
12-3
0-(-2)
which would be

9
2

so 9/2 it isn't possible so it would stay as 9/2 which is your answer.. C

Hope this helps.!!!!

7 0

3 years ago

Find the focus and directrix of parabola xsquared= 2y

Akimi4 [234]

Answer:

directrix: y = -1/2; focus = (0,1/2)

Step-by-step explanation:

rewrite in standard form:

2y = x^2

factor 4

4 * (y/2) = x^2

rewrite as

4 * 1/2 ( y - 0 ) = (x - 0 )^2

therefore

(h,k) = (0,0) , p = 1/2

directrix is line || to x-axis, distance - p from the center (0,0) y-coordinate (of the parabola)

y = 0 - p

y = 0 - 1/2

y = -1/2

now for the focus!

the focus is distance p from center (0,0) along y-axis --> (0, 0+p)

therefore

(0,0+1/2)

(0,1/2) is the focus!

5 0

3 years ago