Ask question

Ask question

All categories

3 years ago

5

the difference of two numbers is 5. the sum of three times the larger number and twice the smaller number is 30. what is the sma

ller number

1 answer:

Ganezh [65]3 years ago

5 0

Answer:

smallest number=3

Step-by-step explanation:

let the numbers be x & y and x>y

x-y=5

multiply by 2

2x-2y=10

and 3x+2y=30

adding

5x=40

x=40/5=8

8-y=5

y=8-5=3

You might be interested in

Lydia has half of her investments in stock paying an 11% dividend and the other half in a stock paying 14% interest. If her tota

SVETLANKA909090 [29]

Based on the calculations, the amount of money she invested is equal to $3,520.

<h3>How to determine the amount invested?</h3>

First of all, we would assign variables to the amount of money that he invested at different interest rates as follows:

Let x be the amount of money she invested at 11%.

Let y be the amount of money she invested at 14%.

Since Lydia invested the same amount of money in both stocks, we have:

x = y ....equation 1.

At the two interest rates, the total amount Lydia gets is given by:

0.11x + 0.14y = 440 ....equation 2.

Solving the equations simultaneously, we have:

0.11y + 0.14y = 440

0.25y = 440

y = 440/0.25

y = $1,760.

Thus, the total investment is given by:

Total investment = 1760 + 1760

Total investment = $3,520.

Read more on interest rates here: brainly.com/question/16793428

#SPJ1

8 0

2 years ago

Logx(8x-3)-logx 4=2<br> please help ill give you everything i have !!

Gelneren [198K]

Logx (8x-3) - logx 4 = 2
logx [(8x-3)/4] = 2
x^2=(8x-3)/4
4x^2=4(8x-3)/4
4x^2=8x-3
4x^2-8x+3=8x-3-8x+3
4x^2-8x+3=0
4(4x^2-8x+3=0)
(4^2)(x^2)-8(4x)+12=0
(4x)^2-8(4x)+12=0
(4x-2)(4x-6)=0
2(4x/2-2/2)2(4x/2-6/2)=0
4(2x-1)(2x-3)=0
4(2x-1)(2x-3)/4=0/4
(2x-1)(2x-3)=0
Two options:
1) 2x-1=0
2x-1+1=0+1
2x=1
2x/2=1/2
x=1/2

2) 2x-3=0
2x-3+3=0+3
2x=3
2x/2=3/2
x=3/2

Answer: Two solutions: x=1/2 and x=3/2

6 0

3 years ago

2.06. In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nucle

DaniilM [7]

Answer:

$z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795$

$p_v =2*P(Z>2.795)= 0.005$

So if we compare the p value and using any significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=74$ represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

$X_{2}=70$ represent the number of people suburban residents are in favor

$n_{1}=100$ sample 1 selected

$n_{2}=125$ sample 2 selected

$p_{1}=\frac{74}{100}=0.74$ represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

$p_{2}=\frac{70}{125}=0.56$ represent the proportion of suburban residents are in favor

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportions are different, the system of hypothesis would be:

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

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

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 $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{74+70}{100+125}=0.64$

Calculate the statistic

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

$z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795$

Statistical decision

The significance level provided is $\alpha=0.05$ ,and we can calculate the p value for this test.

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

$p_v =2*P(Z>2.795)= 0.005$

So if we compare the p value and using any significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.

5 0

3 years ago

Which of the following is an example of a rational function?

stellarik [79]

Answer:

(Second Option) = g of x equals the quantity x squared minus 5x plus 7 end quantity divided by the quantity x minus 3 end quantity

Step-by-step explanation:

A rational function contains a polynomial in both the numerator and the denominator. This answer fits that requirement.

5 0

2 years ago

(5x4 - 4x³ - 2x² + x − 19) − (x4 + 5x³ + 8x² + x + 5) evaluate !!

MAXImum [283]

Answer:

$p(x) = 4x^4-9x^3-10x^2-24$

Step-by-step explanation:

I'm going to assume that your equation is $(5x^4-4x^3-2x^2+x-19) - (x^4+5x^3+8x^2+x+5)$
So to evaluate it we need to simplify it. Find like terms and perform addition/subtraction on them.

$p(x) = (5-1)x^4 + (-4-5)x^3+(-2-8)x^2+(1-1)x+(-19-5) \\ \to p(x) = 4x^4-9x^3-10x^2-24$

7 0

2 years ago