1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marin [14]
3 years ago
6

Solve the system of equations​

Mathematics
1 answer:
Solnce55 [7]3 years ago
5 0

Hey, there!!

Given that:

y = 3x.........(i)

y =  {x}^{2}  + 3x - 16.......(ii)

Putting the value of y in equation (ii)

{3x}^{} =  {x}^{2}  + 3x - 16

{x }^{2}  - 16=0

( {x)}^{2}  -  {4}^{2}  = 0

(x + 4)(x - 4) = 0

Therefore,

Either Or

(x+4)=0 (x-4)=0

x= -4 x= 4

so, x= (+ -)4

And if you wanna get value of y, just keep value of x in equation (i).

y= 3x

y= (3×4) or (3×-4)

y= 12 or -12

{As it is the quadratic equation it has two values. }

<em><u>Hope it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

You might be interested in
PLEASE HELP!! URGANT!!
ella [17]

Answer: 100

set up equation: GHE+EHI=GHI

(x+38)+(x+104)=134

calculate

you get x= -4

put -4 into EHI

(-4)+104= 100

8 0
3 years ago
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t
skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that \mu = 273, \sigma = 100

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 30, s = \frac{100}{\sqrt{30}}

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}

Z = 0.88

Z = 0.88 has a p-value of 0.8106

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}

Z = -0.88

Z = -0.88 has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 50, s = \frac{100}{\sqrt{50}}

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}

Z = 1.13

Z = 1.13 has a p-value of 0.8708

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}

Z = -1.13

Z = -1.13 has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 100, s = \frac{100}{\sqrt{100}}

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}

Z = 1.6

Z = 1.6 has a p-value of 0.9452

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}

Z = -1.6

Z = -1.6 has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0
2 years ago
I need some help with these two questions please help!
antoniya [11.8K]

Answer:

Step-by-step explanation:

-10.6*0.5=m+11.7

-5.3=m+11.7

-5.3-11.7=m

-17=m

14.2=2(-5.8+t)

14.2=-11.6+2t

14.2+11.6=2t

25.8=2t

25.8/2=t

12.9=t

6 0
3 years ago
Evaluate: 11 + sqrt(-4 + 6×4÷3)
Murrr4er [49]

Answer:

11+\frac{2\sqrt{15}}{3}

Step-by-step explanation:

11 + \sqrt{(-4 + 6\times4\div3)} \\\\11+\sqrt{\frac{-4+6\times \:4}{3}}\\\\\sqrt{\frac{-4+6\times \:4}{3}}=\frac{2\sqrt{5}}{\sqrt{3}}\\\\=11+\frac{2\sqrt{5}}{\sqrt{3}}\\\\\frac{2\sqrt{5}}{\sqrt{3}}=\frac{2\sqrt{15}}{3}\\\\=11+\frac{2\sqrt{15}}{3}

3 0
3 years ago
The temperature is -3°F at 7:00 A.M. During the next 4 hours, the temperature increases 21°F. What is the temperature at 11:00 A
3241004551 [841]

Answer: 18°F

Step-by-step explanation: if you add 21 and -3 you get 18

4 0
3 years ago
Other questions:
  • What does ⅓ have to be multiplied by to make it a whole number? What about 2/6? How are these two fractions related?
    10·1 answer
  • The weight, in pounds, of each wrestler on the high school wrestling team at the beginning of the season is listed below.
    8·1 answer
  • What times what equals 162
    13·1 answer
  • If 3v/7 = 6then v = ? <br> I’m not sure
    5·2 answers
  • Give a ratio equivalent to 4/8
    11·2 answers
  • Im not sure how to do this <br>​
    10·2 answers
  • Need help ASAP <br> i dont understand this someone help
    12·1 answer
  • Please help me i need this right nowpleaseedcd vid,
    15·1 answer
  • Did you know it takes about 40 pounds of olives to make 3 liters of olive oil? Orchard A grew about 2000 pounds of olives. How m
    8·1 answer
  • Is this sample of the coins likely to be representative?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!