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Answer:

a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 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 establishes 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.

Mean of 8.9 minutes and a standard deviation of 2.9 minutes.

This means that [tex]\mu = 8.9, \sigma = 2.9[/tex]

Sample of 37:

This means that [tex]n = 37, s = \frac{2.9}{\sqrt{37}}[/tex]

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

320/37 = 8.64865

Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]

[tex]Z = -0.53[/tex]

[tex]Z = -0.53[/tex] has a p-value of 0.2981

0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

275/37 = 7.4324

Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So

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

[tex]Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]

[tex]Z = -3.08[/tex]

[tex]Z = -3.08[/tex] has a p-value of 0.001

1 - 0.001 = 0.999

0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So

0.2981 - 0.0010 = 0.2971

0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

The linear equation that could be used to find her monthly pay rate will be y = 12x + 50.

It is referred to as the relationship between two variables, and a straight line is produced when the linear equation's graph is shown. The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.

It is given that, Esther is employed by a marketing firm. She makes $12 per hour and receives a $50 monthly travel reimbursement.

Suppose x be the number of months,

The linear equation could be used to find her monthly pay rate is,

Total amount = Amount per hour×number of hour+ travel allowance

y = 12x + 50

Thus, the obtained linear equation for a given condition will be y = 12x + 50.

Learn more about the linear equation here:

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A n B = { 1 , 0 , - 1 }

A n C = { - 1 , 0 , 2 , 3 }

_________________________________

A n ( B U C ) =

( A n B ) U ( A n C ) =

{ - 1 , 0 , 1 } U { - 1 , 0 , 2 , 3 } =

{ - 1 , 0 , 1 , 2 , 3 }

Answer:

2 doctors to 9 patients

Step-by-step explanation:

Divide each by 3. They cant be simplified more.

Answer:

Approximately 10.5, or 10.5095541.

Step-by-step explanation:

To find the radius given the circumference of a circle, we first have to divide the circumference by pi, or an estimation of 3.14. This will give us the diameter.

Since we know that the radius of a circle is simply half the diameter, we divide the number we got from the problem above by 2. This will give you your answer!

Answer:

r = 10.50

Step-by-step explanation:

Circumference =

[tex]2\pi \: r[/tex]

[tex] 66 = 2\pi \: r[/tex]

[tex] \frac{66}{2\pi} = r[/tex]

r = 10.5

Answer:

2630 g

Step-by-step explanation:

From the given information:

Given that:

mean (μ) = 3750 g

Standard deviation (σ) = 500

Suppose the hospital officials demand special treatment with a percentage of  lightest 3% (0.03) for newborn babies;

Then, the weight of birth that differentiates the babies that needed special treatment from those that do not can be computed as follows;

P(Z < z₁) = 0.03

Using the Excel Formula; =NORMSINV(0.03) = -1.88

z₁ = - 1.88

Using the test statistics z₁ formula:

[tex]z_1 = \dfrac{X-\mu}{\sigma}[/tex]

[tex]-1.88 = \dfrac{X-3570}{500}[/tex]

By cross multiply, we have:

-1.88 × 500 = X - 3570

-940 = X - 3570

-X = -3570 + 940

-X = -2630

X = 2630 g

Hence, 2630 g is the required weight of birth   that differentiates the babies that needed special treatment from those that do not

Answer:

x=11

Step-by-step explanation:

22*y=32

y=16/11

So,

x*16/11=16

x=11

Answer:A

Step-by-step explanation:

Answer:

-4 and 1

Step-by-step explanation:

-4 times 1 equals -4 and then -4 plus 1 equals 3

The two numbers that satisfy the given conditions are 4 and -1. They multiply to -4 and add up to 3.

To find two numbers that satisfy the given conditions, we can set up a system of equations.

Let's assume the two numbers are represented by 'x' and 'y'. We know that their product is -4 and their sum is 3, so we can write the following equations:

xy = -4 (Equation 1)

x + y = 3 (Equation 2)

To solve this system of equations, we can use the substitution or elimination method. Let's use the substitution method.

From Equation 2, we can express y in terms of x: y = 3 - x.

Substituting this into Equation 1, we get:

x(3 - x) = -4

Expanding and rearranging the equation, we have:

3x - x² = -4

Rearranging again, we get a quadratic equation:

x² - 3x - 4 = 0

We can factor this equation:

(x - 4)(x + 1) = 0

Setting each factor to zero, we find two possible solutions for x:

x - 4 = 0 --> x = 4

x + 1 = 0 --> x = -1

Now, we can substitute these values of x back into Equation 2 to find the corresponding values of y:

For x = 4: y = 3 - 4 = -1

For x = -1: y = 3 - (-1) = 4

Therefore, the two numbers that satisfy the given conditions are 4 and -1. They multiply to -4 and add up to 3.

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Answer: 1) V≈1244.07 in             2) V≈54286.72 ft         3) V≈23816.41 yd

Step-by-step explanation:

Answer:80^w2−48

Step-by-step explanation:

Answer:

If You Factor it it will be (w+8) (5w2-3)

Step-by-step explanation:

Answer:  -157,464

Step-by-step explanation:

an=a^1*r^n-1

a10=8*-3^10-1

a10=8*-3^9

a10=8*-19683

a10=-157464

Answer:

a10 = -157,464

Step-by-step explanation:

a1 = 8

a2 = -24

r = a2/a1 = -3

an = a1 × r^(n - 1)

a10 = a1 × (-3)^(10 - 1)

a10 = 8 × (-3)^(9)

a10 = -157,464

Answer:

[tex]a:b = 8:3[/tex]

Step-by-step explanation:

To find the ration, we want to get in equation in the form [tex]\frac{a}{b} =\frac{x}{y}[/tex].

We can start by dividing by b on both sides:

3a = 8b

÷b     ÷b

[tex]\frac{3a}{b} = 8[/tex]

Now, we can divide by 3 on both sides to get:

[tex]\frac{a}{b} = \frac{8}{3}[/tex]

We can change the format into a ratio:

[tex]a:b = 8:3[/tex]

Answer:

2.542

Step-by-step explanation:

Given the data :

Customer Pre-training Survey, x1 __Post-training Survey, x2 __ difference, d = (x2-x1)

A 6 8 2

B 5 5 0

C 10 10 0

D 7 10 3

E 6 8 2

F 5 6 1

G 2 8 6

This is a paired test as each subject has two different data values :

Difference in score, d :

dbar = Σd / n

dbar = (2+0+0+3+2+1+6) /

dbar = 14 / 7

dbar = 2

Standard deviation of d ; Sd = √[Σ(d - dbar)²/n-1]

Using calculator ; Sd = 2.082

Test statistic = dbar ÷ (Sd/√n)

Test statistic = 2 ÷ (2.082 / 7)

Test statistic = 2 ÷ 0.7869220

The statistic = 2.5415

Answer: Her highest score is on turn two because she used a negative number over a positive and a positive is more than a negative.

Step-by-step explanation:

10>-16

Answer:

13 =x

Step-by-step explanation:

The width is x

The length is 2 times the width or 2x

A = length * width

A = 2x* x

338 = 2x^2

Divide by 2

338/3 = 2x^2/2

169 = x^2

Taking the square root of each side

sqrt(169) = sqrt(x^2)

13 =x

Answer:

It's Cos.

Hope this helps

Answer:

$1,298.12

Step-by-step explanation:

there are 1564 hundreds in 156,400

so 1564 x .83 = 1298.12

Answer:

4x+5=2x-3 1-5

4x-2x=-3+1-5-5

2x=-2

[tex] \frac{2x}{2} = \frac{ - 2}{2} [/tex]

x=

[tex]x = \frac{ - 2}{2} [/tex]

Answer:

20 ways

Step-by-step explanation:

by using combination rule :

6C3 = 6! /(3! × 3!)

= 6×5×4×3! / 3! × 3×2×1

= 20 ways

==========================================================

Explanation:

Order matters because we want to distinguish between first place, second place, and third place winners. So something like ABC is different from BCA.

We have 6 ways to pick a first place winner, then 5 for second place, then 4 for third place. Overall, there are 6*5*4 = 30*4 = 120 permutations

You could use the nPr formula with n = 6 and r = 3 as an alternative method

[tex]_n P _r = \frac{n!}{(n-r)!}[/tex]

The exclamation marks indicate a factorial.

Answer:

SAS. ( side, angle, side)

in option 2nd

Answer:

False

SAS = This stands for Side Angle Side congruency theorem

Step-by-step explanation:

Question 1.)

If any of the 2 angles of any triangle is congruent to any of the 2 angles of the other triangle, then this would be true. Let's find the measure of ∠R and ∠G:

=> ∠G = 180 - (98 + 30)

∠G = 52

=> ∠R = 180 - (98 + 26)

∠R = 56

Now we know that Angles of ΔHIG are 30, 98, and 52, and Angles of ΔSQR are 26, 98, and 56. 2 angles of 1 triangle are not congruent 2 angles of the other triangle, therefore the triangles aren't congruent.

Question 2.)

SAS congruency is used since an angle and it's 2 adjacent sides are given for each triangle.

Hope this helps!

Answer:

A) 48

Step-by-step explanation:

Given:

b = 16

c = 20

Pythagorean thm:

a² + b² = c²

a² + 16² = 20²

a² + 256 = 400

a² = 144

a = 12

To find perimeter:

P = a + b + c

P = 12 + 16 + 20

P = 48

Answer:

total number of people on Friday = 285

total number of people on Saturday = 355

total increment = 355-285 = 70

total increase percentage = 70÷285*100

= 24.56%

hope it helps!

Answer:

B. 36 yd

Step-by-step explanation:

I calculated it logically

Answer:

x = 5

Step-by-step explanation:

I didn't quite understand what you were asking but x should equal 5

Answer: 1 is the answer because nothing time _ will equal 5 but 1 times anything equal that number So its 1

Answer:

88 in

Step-by-step explanation:

we have to find the circumference of the circle which is ;

C = pie d

= 22/7 x 28

= 88 in

Answer:

14/100*1800

25200/100

252

Step-by-step explanation:

therefore vat=252

Answer:

D.6,600 ft

Step-by-step explanation:

I hope it helps