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
blsea [12.9K]
3 years ago
7

In which direction will this parabola open? x=53(y+17)^2-41

Mathematics
1 answer:
navik [9.2K]3 years ago
8 0
x=53(y+17)^2-41\\
x=53(y^2+34y+289)-41\\
x=53y^2+1802y+15317-41\\
x=53y^2+1802y+15276

As a>0 so the concavity (open) of the parable is to the right.
You might be interested in
Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa
Debora [2.8K]

Answer:

a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

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 estabilishes 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.

Mean 8.7% and standard deviation 20.2%.

This means that \mu = 8.7, \sigma = 20.2

40 years:

This means that n = 40, s = \frac{20.2}{\sqrt{40}}

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

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

By the Central Limit Theorem

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

Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = 1.35

Z = 1.35 has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

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

Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = -0.22

Z = -0.22 has a pvalue of 0.4129

0.4129 = 41.29% probability that the mean return will be less than 8%

8 0
3 years ago
How to solve <img src="https://tex.z-dn.net/?f=log_%7By%7D%285y%29%20%3D%202" id="TexFormula1" title="log_{y}(5y) = 2" alt="log_
Natalija [7]

Answer:

  y = 5

Step-by-step explanation:

Expand the logarithm:

\log_y{(5)}+\log_y{(y)}=2\\\\\dfrac{\log{(5)}}{\log{(y)}}+1=2 \quad\text{change of base formula}\\\\\dfrac{\log{(5)}}{\log{(y)}}=1 \quad\text{subtract 1}\\\\\log{(5)}=\log{(y)} \quad\text{multiply by log(y)}\\\\5=y \quad\text{take the anti-log}

_____

You can also take the antilog first:

  5y = y²

  y(y -5) = 0 . . . . . subtract 5y, factor

  y = 0 or 5 . . . . . y=0 is not a viable solution, so y=5.

5 0
3 years ago
The mean game scores and standard deviations of four seasons of a football team are given below. Season Mean Standard Deviation
timurjin [86]
To find the margin of error, multiply the z-score by the standard deviation, then divide by the square root of the sample size.The z*-score for a 90% confidence level is 1.645.The margin of error is 0.20.The confidence interval is 48.3 to 48.7.48.8 is not within the confidence interval. 
7 0
3 years ago
Read 2 more answers
Sharon is buying a circular rug for her living room. The diameter of the rug is 8 feet. Which measurement is closest to the area
Vanyuwa [196]

Answer:

B) 50.24 ft^2

Step-by-step explanation:

radius =1/2 diameter = 4

area = Pi(r^2) = 3.14(4^2) = 3.14(16) = 50.24

6 0
3 years ago
The product of two consecutive numbers exceeds the square
Lyrx [107]

Answer:

20,21

Step-by-step explanation:

Let x be the first number.

Let y be the 2nd number.

Given y - x = 1 (since they are consecutive)

Rearrange it: y = x+1 (equation 1)

Also given:

xy-20=x^{2} (equation 2)

Now we can substitute y = x + 1 into equation 2.

x(x+1)-20 = x^{2} \\x^{2} +x-20 = x^{2} \\x-20=x^{2} -x^{2} \\x-20=0\\x=20

Since we know x, the smaller number is 20, we can substitute to equation 1 to find y, the larger number.

y = 20+1

= 21.

Therefore the 2 numbers are 20 and 21.

8 0
1 year ago
Other questions:
  • ather went to the front near the crank to start the motor. Father put his thumb against his palm instead of putting it around th
    6·1 answer
  • Solve the following system of equations
    7·1 answer
  • What is y - 2 = -3 [x-7] written in standard form
    10·1 answer
  • A company charges 8 a hrs what would the company charge for a lawn that takes 1 hrs 45 minutes to mow
    9·2 answers
  • Z varies jointly with x, and y, and z=7 when x= 2, y= 2<br> pleasee I need an answer now!!
    15·2 answers
  • Verify that f and g are inverses functions using composition , show your steps
    9·1 answer
  • Pls answer, will give brainliest...
    10·1 answer
  • Hi this was an accident so nevermind
    11·2 answers
  • What is the answer? Thank you I’ll mark you as the brainliest!!
    15·2 answers
  • Unit 4 Ratio, Proportions, &amp; Percent
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!