Given the graphs of f(x) = 2x + 2 and g(x) = x - 2, find the solution to this system of equations:​

Answer:

1) 0.4096 = 40.96% of waiting times are between 8 and 10.8 minutes.

2) 0.1401 = 14.01% of waiting times are less than 6.8 minutes.

3) 0.1788 = 17.88% probability that you are late.

4) The cutoff for the top 4% of waiting times is of 14.15 minutes.

5) The waiting time for the 30th percentile is of 8.235 minutes.

Step-by-step explanation:

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Average of 9.60 minutes and a standard deviation of 2.60 minutes during peak hours.

This means that [tex]\mu = 9.6, \sigma = 2.6[/tex]

1) What proportion of waiting times are between 8 and 10.8 minutes?

This is the pvalue of Z when X = 10.8 subtracted by the pvalue of Z when X = 8. So

X = 10.8

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

[tex]Z = \frac{10.8 - 9.6}{2.6}[/tex]

[tex]Z = 0.46[/tex]

[tex]Z = 0.46[/tex] has a pvalue of 0.6772

X = 8

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

[tex]Z = \frac{8 - 9.6}{2.6}[/tex]

[tex]Z = -0.62[/tex]

[tex]Z = -0.62[/tex] has a pvalue of 0.2676

0.6772 - 0.2676 = 0.4096

0.4096 = 40.96% of waiting times are between 8 and 10.8 minutes.

2) What proportion of waiting times are less than 6.8 minutes?

This is the pvalue of Z when X = 6.8.

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

[tex]Z = \frac{6.8 - 9.6}{2.6}[/tex]

[tex]Z = -1.08[/tex]

[tex]Z = -1.08[/tex] has a pvalue of 0.1401

0.1401 = 14.01% of waiting times are less than 6.8 minutes.

3) You reach Wells Hall parking lot and your class starts in 12 minutes. What is the chance that you are late to class, that is waiting time is at least 12 minutes?

This is 1 subtracted by the pvalue of Z when X = 12. So

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

[tex]Z = \frac{12 - 9.6}{2.6}[/tex]

[tex]Z = 0.92[/tex]

[tex]Z = 0.92[/tex] has a pvalue of 0.8212

1 - 0.8212 = 0.1788

0.1788 = 17.88% probability that you are late.

4) Based on your unpleasant experiences in the past you know that your waiting time is in the top 4%. What is the cutoff for the top 4% of waiting times?

The cutoff for the top 4% of times is the 100 - 4 = 96th percentile, which is X when Z has a pvalue of 0.96. so X when Z = 1.75.

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

[tex]1.75 = \frac{X - 9.6}{2.6}[/tex]

[tex]X - 9.6 = 1.75*2.6[/tex]

[tex]X = 14.15[/tex]

The cutoff for the top 4% of waiting times is of 14.15 minutes.

5) What is the waiting time for the 30th percentile?

This is X when Z has a pvalue of 0.3. So X when Z = -0.525.

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

[tex]-0.525 = \frac{X - 9.6}{2.6}[/tex]

[tex]X - 9.6 = -0.525*2.6[/tex]

[tex]X = 8.235[/tex]

The waiting time for the 30th percentile is of 8.235 minutes.

Answer:

x = 9

Step-by-step explanation:

6x + 9x - 3 + 48 = 180

15x= 180 -45

x = 135 / 15

x = 9

i hope my answer is correct and helps a little bit.

Answer:

x=9

Step-by-step explanation:

Answer:

Its slope is

m = -1/(1/2) = -2

y = -2x + b

Get b from the given point.

-4 = -2(6) + b

b = 8

y = -2x + 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given slope (m) = -3/4

and x1 = 6

and y1 = 4

Solve for b (y2) using x2 = 0.
m = -3/4 = (y2-y1)/(x2-x1)

-3/4 = (4-y1)/(6-0)

-3/4 = (4-y1)/6

-(3/4)*6 = 4 - y1

-18/4 = 4 - y1

y1 = b = 16/4 + 18/4 = 34/4 = 8 1/2

therefore the correct answer should be:

Equation of the line:

y = -3/4x + 8 1/2

Answer:

Q1 = 40

Step-by-step explanation:

Set up numbers from least to greatest

21, 40, 52, 58, 72, 75, 96

First, find the median,

Median is: 58

Now Q1 is all numbers before the median (without counting the median)

21, 40, 52

The median here is 40

Answer:

D/40

Step-by-step explanation:

The answer is D because if you were to put them in the correct order it would be

21, 40, 52, 58, 72, 75, 96

      Q1        Q2       Q3

Q1 is quartile 1 so the answer is 40

Hope this helps!

Answer:

a) the probability that the next ream out- lasts the present one by more than 2 days is 0.0787

b) the number of reams that must be purchased is 19

Step-by-step explanation:

Given the data in the question;

Lets X₁ and X₂ be the two random variables that represents the first and second ream lasts

given that both random variables follow normal distribution with mean 4 and standard deviation 1.

a)

Find the probability that the next ream out- lasts the present one by more than 2 days.

P( X₂  - X₁ > 2 ) = P( [(X₂  - X₁ - E(X₂  - X₁)) / √(V(X₂  - X₁)] > [ (2-E(X₂  - X₁))/√(V(X₂  - X₁) ]

= 1 - P( Z ≤ [2-(μ₂  - μ₁)] / [√( V(X₂) + V(X₁) ) ] )

= 1 - P( Z ≤ [2-(4  - 4)] / [√( 1 + 1 )] )

= 1 - P = ( Z ≤ 2 / √2 )

= 1 - p( Z ≤ 1.4142 )

from excel; p( Z ≤ 1.41 ) = 0.9213

P( X₂  - X₁ > 2 ) = 1 - 0.9213

P( X₂  - X₁ > 2 ) = 0.0787

Therefore, the probability that the next ream out- lasts the present one by more than 2 days is 0.0787

b)

How many reams must be purchased if they are to last at least 60 days with probability at least 80%

total value is 4n

standard deviation is nσ

so

P(nX ≥ 60 ) = 0.80

P( nX-nμ /nσ  ≥  60-nμ/nσ) = 0.80

P( Z ≥  60-4n/n) = 0.80

1 - P( Z ≥  60-4n/n) = 0.80

P( Z < z ) = 0.20

now since z = 60-4n/n

from standard normal table

critical value of z corresponding to cumulative area of 0.20 is -0.841

so

z = - 0.841

60-4n/n =  -0.841

60 - 4n =  -0.841n

60 = -0.841n + 4n

60 = 3.159n

n = 60 / 3.159

n = 18.99 ≈ 19

Therefore, the number of reams that must be purchased is 19

Answer:

A. 91 ft

Step-by-step explanation:

The path is 2ft wide and the pool's radius is 12.5ft (radius is half diameter, diameter is 25ft). This means that the radius of the circle created by the path is 14.5ft (2+12.5).

Knowing the radius, we can find the circumference.

Circumference = 2πr

Circumference = 2π(14.5) = 91.10618695ft ≈ 91ft

Answer:

A. 25.7°

Step-by-step explanation:

the sum of straight angle is 180°.

so, i subtract 154.3 from 180.

i get 25.7 °

Answer:

-25-5x-5y

Step-by-step explanation:

Answer: 10 miles

Step-by-step explanation:

Mile 1: 3.00

Mile 2: 3.50

Mile 3: 4.00

Mile 4: 4.50

Mile 5: 5.00

Mile 6: 5.50

Mile 7: 6.00

Mile 8: 6.50

Mile 9: 7.00

Mile 10: 7.50

Answer:

Step-by-step explanation:

[tex]\text{Maximize p = 5X1 + 4X2 + 3X3 subject to;} \\ \\ 1X1 + 7X2 + 4X3 <= 90[/tex]

[tex]2X1 + 1X2 + 7X3 <= 96[/tex]

[tex]8X1 + 4X2 + 1X3 <= 90[/tex]

[tex]X1 > = 0[/tex]

[tex]X2 >= 0[/tex]

[tex]X3 >=0[/tex]

[tex]\text{USing LP software, The Optimal Solution: Maximum Contribution} = 90.547;}\\ \\ x1 = 7.07692, \\ \\ x2 = 5.62393, \\ \\ x3 = 10.8889[/tex]

Answer: The answer is 20  3/16

Step-by-step explanation:.

Its B.

Answer:

The median resistance of the wire is not small than 0,15 Ω at 0,05 of level of significance

Step-by-step explanation:

From data we get    x ( sample mean ) s  ( sample standard deviation) and n size of the sample

0.148 0.147 0.151 0.146 0.151 0.148 0.147 0.152

0.151 0.148 0.149 0.147 0.146 0.149 0.151 0.147

n = 16

x ≈ 0,1487

s = 0,00193

Test Hypothesis

1.-Null Hypothesis               H₀                x  =  μ₀  = 0,15

Alternative Hypothesis  Hₐ                 x < 0,15

We assume data follows normal distribution

as n = 16 we should use a t-student table

As the question is : "Is the median resistance less than 0,15 0hm " we must use  one-tail-test ( to the left)

Then:

2.-Significance level  α = 5 %      α = 0,05

degree of freedom   n = 16     df = n - 1    df = 15

From t-table we find t(c) = 1,7531      at the left is t(c) = - 1,7531

3.-t(s) = ( x - 0,15 ) / s / √n

t(s) = 0,1487 - 0,15 / 0,00193/√16

t(s) = - 0,0013 * 4 / 0,00193

t(s) = - 2,69

4.- Comparing t(s) and t(c)  

|t(s) | > |t(c)|       2,69 > 1,753

Then t(s) is in the rejection region

5.- We reject H₀  . At 95 % of confidence Interval

Answer:

Tiger shows you, step by step, how to solve YOUR Quadratic Equations 3x^2-x-11=0 by Completing the Square, Quadratic formula or, ...

Answer:

557152

Step-by-step explanation:

You first multiply the 8 in 308 to the 9 in 1809, then the 0, then the 9, then finally the 1 in 1809. For the tens place, don't forget to put a zero under the ones place because that's not where you start. So for 0 everything is 0 so just put a line of 5 zeros in the second row. Lastly, the 3 multiplies to 9, 0, 8, and the 1 in 1809. In the 3rd row, put 2 zeros because you're multiplying to get the hundreds place. Line and add them all up to get 557152. Hope this helps!

Answer:

1809 x 308 eqauls 557,172

if you click the image it will show you how to solve the equation step by step. I hope this helps you.

Answer:

Around 54% is what I would say.

Step-by-step explanation:

Answer:

8^(7), which is 2097152

Step-by-step explanation:

8^(4) × 8^(3)

= 8^(4+3)

= 8^(7)

= 2097152

Answer:

The answer is 2097152.

Step-by-step explanation:

1) Use the product rule: x^a x^b = x^ a + b.

[tex] {8}^{7} [/tex]

2) Simplify.

[tex]2097152[/tex]

Thus, the answer will be 2097152.

Answer:

16:6

Step-by-step explanation:

96:36

Highest common factor is 6

divide both sides by 6

16:6

Answer:

BD = 4

Step-by-step explanation:

∆BAD is congruent to ∆CAD based on the AAS Congruence Theorem.

Therefore:

BD = CD

3x + 1 = 5x - 1 (substitution)

Collect like terms

3x - 5x = -1 - 1

-2x = -2

Divide both sides by -2

x = -2/-2

x = 1

✔️BD = 3x + 1

Plug in the value of x

BD = 3(1) + 1

BD = 3 + 1

BD = 4

Answer:

x = -4/5

Step-by-step explanation:

Divide 5 on both sides to isolate x on one side. You get x = -4/5

Answer:

x=-4/5 hope this helps you out math is always hard

Answer:

Please edit the question I can't see it completely

Answer:

The diameter is in the 77th percentile.

Step-by-step explanation:

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

25.14 mm and standard deviation 0.08 mm.

This means that [tex]\mu = 25.14, \sigma = 0.08[/tex]

A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on?

This is the pvalue of Z when X = 25.2. So

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

[tex]Z = \frac{25.2 - 25.14}{0.08}[/tex]

[tex]Z = 0.75[/tex]

[tex]Z = 0.75[/tex] has a pvalue of 0.77.

The diameter is in the 77th percentile.

Answer: A=bh to find the area of parallelograms.

Step-by-step explanation:

Answer:

lol

Step-by-step explanation:

lol

Answer:

pzie6zkezkzorzozirusultaluspuar

Answer:

m<PQR = 82°

Step-by-step explanation:

In a Rhombus, the diagonals bisect its angles. This means that they divide each the four angles into two equal parts.

Therefore:

(4x - 27)° = (2x + 7)°

Solve for x

4x - 27 = 2x + 7

Collect like terms

4x - 2x = 27 + 7

2x = 34

Divide both sides by 2

2x/2 = 34/2

x = 17

✔️m<PQR = (4x - 27) + (2x + 7)

Plug in the value of x

m<PQR = (4*17 - 27) + (2*17 + 7)

m<PQR = 41 + 41

m<PQR = 82°