Simplify: 6y + 5z + 8y

An amount of $700 is invested partly at 8% and partly at 10%. The yearly income from both investments is $64. The amount investe

ioda

A8% is X
10% is 700-X

X(.08)+ .10(700-X)= 64
.08x+ 70-.10X=64
-.02X+70=64
-70=-70
-.02x= -6
Divide by -.02
X= 300

Answer $300 was invested at 8%

Check 300 times .08= 24. 700-300=400 times .10 = 40 and 24+40=64

5 0

3 years ago

In a city known for many tech start-ups, 311 of 800 randomly selected college graduates with outstanding student loans currently

Allushta [10]

Answer:

Null hypothesis: $p_{1} - p_{2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)(\frac{1}{800}+\frac{1}{800})}}=-1.182$

$p_v =2*P(Z$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.

Step-by-step explanation:

1) Data given and notation

$X_{1}=311$ represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$X_{2}=334$ represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

$n_{1}=800$ sample 1

$n_{2}=800$ sample 2

$p_{1}=\frac{311}{800}=0.389$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$p_{2}=\frac{334}{800}=0.418$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

z would represent the statistic (variable of interest)

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

$\alpha=0.05$ significance level given

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference in the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} - p_{2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{311+334}{800+800}=0.403$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)(\frac{1}{800}+\frac{1}{800})}}=-1.182$

4) Statistical decision

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

$p_v =2*P(Z$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.

6 0

3 years ago

The product of 5 and y added to 3

bazaltina [42]

Write equation:-

The product of 5 and y added to 3

5 × y + 3

6 0

3 years ago

The value of the square root of -16 is not -4 because

Nady [450]

Answer:

negative numbers can't have a square root it would have to be imaginary

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers

What number should be added to both sides of the equation to complete the square?<br> x2 - 6x = 5

ikadub [295]

Answer:

First of all, it is better to note that x2 is not equal to x² .In mathematics x2 is equal to 2nd x or 2x i.e. 2 times x=2*x=x*2.

I don't know what this question means ! But if it means to just confine x2 and -6x in a square or to make them part of a square then it could be done as follows.

Assume x2 as x² as per your needs as case may be.

Now use the identity

(a² - 2a×b + b²) =(a - b )²

Here , in LHS

a appears twice as in a² and in 2a×b.

So for given expression (x2 – 6x = 5) or (x² – 6x = 5) or (x² - 6x -5 =0)

Assume x=a

Then,

6x =2*x*3 =2*a*b

=> 3 = b

Thus

(x² - 6x -5 =0)

=> x² - 2*x*3 + 3² -3² -5 =0

=> ( x² - 2*x*3 + 3² ) - 3² -5 =0

=> (x - 3)² - 3² = 5

=> (x - 3)² = 5 + 3²

=> (x - 3)² = 5 + 9 = 14 = ( ±√(14) )²

Now comparing

(x² – 6x = 5) and (x - 3)² = 5 + 9,

it can be said that number 9 should be added to both sides of (x² – 6x = 5) or (x² – 6x) = ( 5 ) to make ( x² ) and (-6x ) as the constituting parts of the square (x-3)² .

I hope it helps.

Thank you for patiently reading it.

6 0

3 years ago

Simplify: 6y + 5z + 8y – 3z