Which are the solutions of x^2 = 19x + 1?

Answer:

a) 0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes

b) 0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

Mildly obese:

Mean 376 minutes and standard deviation 67 minutes, which means that [tex]\mu = 376, \sigma = 67[/tex]

Sample of 6

This means that [tex]n = 6, s = \frac{67}{\sqrt{6}} = 27.35[/tex]

Lean

Mean 520 minutes and standard deviation 110 minutes, which means that [tex]\mu = 520, \sigma = 110[/tex]

Sample of 6

[tex]n = 6, s = \frac{110}{\sqrt{6}} = 44.91[/tex]

A) What is the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for mildly obese people. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{420 - 376}{27.35}[/tex]

[tex]Z = 1.61[/tex]

[tex]Z = 1.61[/tex] has a pvalue of 0.9463

1 - 0.9463 = 0.0537

0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes.

B) What is the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for lean people. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{420 - 520}{44.91}[/tex]

[tex]Z = -2.23[/tex]

[tex]Z = -2.23[/tex] has a pvalue of 0.0129

1 - 0.0129 = 0.9871

0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

eAnswer:

B, C, E, F

Step-by-step explanation:

[tex]9^{2}+a^{2}=15^{2} \\144=a^{2}\\a=12[/tex]

Answer:

A sample size of 21 is needed.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Using an estimated standard deviation of $11,605

This means that [tex]\sigma = 11605[/tex]

What sample size do you need to have a margin of error equal to $5000 with 95% confidence

A sample size of n is needed. n is found when M = 5000. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5000 = 1.96\frac{11605}{\sqrt{n}}[/tex]

[tex]5000\sqrt{n} = 1.96*11605[/tex]

[tex]\sqrt{n} = \frac{1.96*11605}{5000}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*11605}{5000})^2[/tex]

[tex]n = 20.69[/tex]

Rounding up,

A sample size of 21 is needed.

Answer:

f=5/8x^2+-3/2Divide both sides by two

Step-by-step explanation:

Hope that helped

Answer: is x^2 + y^2 = 100

Answer:

Option C.

Step-by-step explanation:

Suppose that we have a point (x, y)

If we do a dilation with a center in the origin of scale factor K, then the new coordinates of our point will be:

(k*x, k*y)

If k > 1, we have an elargement.

if 0 < k < 1, we have the opposite case.

Now, suppose that one random vertex of the preimage is A (a, b)

Then after we do the dilation, the new coordinate of this vertex will be:

A' = (k*a, k*b)  (this is, the original coordinates multiplied by the scale factor)

And this will happen for all points actually, so particularly the corresponding coordinates of the vertices of the image are the vertices of the preimage multiplied by the scale factor.

Then the correct option is C

Answer:

2r + 6 = 16

r = 5

Answer:

x=1, y=-5

Step-by-step explanation:

4(1)+2y=-6

2y=-10

y=-5

or

-3x-2(-5)=7

-3x=-3

x=1

Hope this helps!

Answer:

The null hypothesis will be that the average annual donor income is less or equal to $ 100,000

Step-by-step explanation:

The claim is mostly treated as alternate hypothesis .

In this question the claim is given as the average annual donor income has increased therefore it is written as

Ha: u > 100,000

The null hypothesis is reverse of the alternate hypothesis

H0: u ≤ 100,000

The null hypothesis will be that the average annual donor income is less or equal to $ 100,000

Answer:

x=-3y+12

Step-by-step explanation:

Yes.

Answer:

23 nights

Step-by-step explanation:

What does "Proportional" Mean? Proportional means that the ratio is the same throughout.

Step One: First, to set this up, we will put the 16 centimeters for the numerator and then the 8 nights on the bottom. The bottom is the independent variable because we can't physically change the number of nights. 16/8.

Step Two: Now, we have to scale this up to 46. Because the 46 is the centimeters, we have to do 46/16 to see how much we need to scale it by: 46/16= 2.875.

Step Three: Lastly, we can multiply 8 by 2.875 to see how many nights it took: 8 times 2.875 is 23 nights.  

Answer:

-9

Step-by-step explanation:

Hello! So, we need to find log_6 1/6. The definition of log is the power that you need to multiply that number by to get the next number. 1/6=6^-1, so our equation would be:

-1=x/9, so x is clearly -9.

Have a nice day.

~cloud

Answer:

You are correct

Step-by-step explanation:

[tex]log_{6} \frac{1}{6} =\frac{x}{9}[/tex]

[tex]log_{6} 6^{-1} =\frac{x}{9}[/tex]

[tex](-1)log_{6}6=\frac{x}{9}[/tex]

[tex]-1=x/9[/tex]

[tex]-9=x[/tex]

Hope that helps :)

Answer:

No, Andre is not correct.

Step-by-step explanation:

I believe Andre is not correct because each 1 on the left balances with a 1 on the right. So taking away the two 1s on the left only leaves the hanger balanced if two 1s are removed on the right. This leaves on the left and three 1s on the right, so x=3. This is like x+2=5 if you subtract 2 from the x side then you get x=3. Hope this helps!

Answer:

A

Step-by-step explanation:

Answer:

50% because there are only 2 colors

Step-by-step explanation:

Answer:50%

Step-by-step explanation:

The probability is 50% or 1/2 because there's only 2 types of jelly bean in the jar unless either one has more amount than the other's

9514 1404 393

Answer:

  $3633.96

Step-by-step explanation:

The monthly payment is given by the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

monthly payment for principal P at annual rate r for t years.

  A = $672096(0.04/12)/(1 -(1 +0.04/12)^(-12·24)) = $3633.96

The monthly payment for the mortgage is $3633.96.

Answer:

6.26 automobile registrations

Step-by-step explanation:

Given

[tex]y=0.3949x-778.7[/tex] --- [function, missing from the question]

Required

The expected number in 1988

To do this, we substitute 1988 for x in: [tex]y=0.3949x-778.7[/tex]

[tex]y = 0.3949 * 1988 - 778.8[/tex]

[tex]y = 785.0612 - 778.8[/tex]

[tex]y = 6.2612[/tex]

[tex]y \approx 6.26[/tex] --- approximated to the nearest hundredth

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Reflection across the x-axis just changes the signs of the y-coordinates. Rotation -120° about B' is difficult to do by hand. The transformation rule for that is ...

  (x, y) ⇒ (x·cos(-120°) +y·sin(-120°), -x·sin(-120°) +y·cos(-120°))

  (x, y) ⇒ ((-(x-3) +(y+2)√3)/2 +3, (-(x-3)√3 -(y+2))/2 -2)

__

It looks like your problem is presented in GeoGebra, which makes reflection and rotation easy.

Answer:

The mean absolute deviation is 2. Hope this helps

Step-by-step explanation:

7+2+8+9+9+5+6+8+1=5.5

7-5.5=1.5

5.5-2=3.5

8-5.5=2.5

9-5.5=3.5

9-5.5=3.5

5.5-5=0.5

6-5.5=1.5

8-5.5 2.5

5.5-1=4.5

1.5+3.5+2.5+3.5+3.5+0.5+1.5+2.5+4.5=2

Answer is 2.

I hope this can help!

Have a nice day :)

~Amy

Answer:

R = 3.813% per year.

Step-by-step explanation:

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

#SPJ1

Answer:

OOO

Step-by-step explanation: