Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 247 feet and a standard deviation of 41 feet. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent. a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 216 feet

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Reason \to Frequency[/tex]

[tex]Congestive\ heart\ failure \to 990[/tex]

[tex]Coronary\ atherosclerosis\to 1400[/tex]

[tex]Heart\ attack \to 744[/tex]

[tex]Infant\ birth\to 3800[/tex]

Solving (a): Frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the frequency (on the y-axis).

See attachment

Solving (b): Relative frequency distribution

The relative frequency is calculated as:

[tex]RF = \frac{F}{Total}[/tex]

Where

[tex]Total = 990+1400+744+3800[/tex]

[tex]Total = 6934[/tex]

So, we have:

[tex]Congestive\ heart\ failure \to \frac{990}{6934} = 0.1427[/tex]

[tex]Coronary\ atherosclerosis\to \frac{1400}{6934} = 0.2019[/tex]

[tex]Heart\ attack \to \frac{744}{6934} = 0.1073[/tex]

[tex]Infant\ birth\to \frac{3800}{6934} = 0.5481[/tex]

So, the relative distribution is:

[tex]Reason \to Frequency \to Relative\ Frequency[/tex]

[tex]Congestive\ heart\ failure \to 990 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis\to 1400 \to 0.2019[/tex]

[tex]Heart\ attack \to 744 \to 0.1073[/tex]

[tex]Infant\ birth\to 3800 \to 0.5481[/tex]

Solving (c): Relative frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the relative frequency (on the y-axis).

See attachment

Solving (d): Relative frequency Pareto chart

First, calculate the cumulative relative frequency

This is done by adding up the previous relative frequency,

So, we have:

[tex]Reason \to Relative\ Frequency \to Cumulative[/tex]

[tex]Congestive\ heart\ failure \to 0.1427 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis \to 0.2019 \to 0.2019+0.1427=0.3446[/tex]

[tex]Heart\ attack \to 0.1073\to 0.3446+0.1073 = 0.4519[/tex]

[tex]Infant\ birth \to 0.5481 \to 0.5481+4519 =1[/tex]

So, we have:

[tex]Reason \to Relative\ Frequency \to Cumulative[/tex]

[tex]Congestive\ heart\ failure \to 0.1427 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis \to 0.2019 \to 0.3446[/tex]

[tex]Heart\ attack \to 0.1073\to 0.4519[/tex]

[tex]Infant\ birth \to 0.5481 \to 1[/tex]

Next, we simply plot the reasons (on the x-axis) against the cumulative relative frequency (on the right) and the left of the Pareto chart.

See attachment

Completing the square gives

[tex]x^2-2x-2=(x-1)^2-3[/tex]

and comparing to [tex]y=x^2[/tex], the graph of [tex]y=x^2-2x-2[/tex] would be a horizontal shift to the right by 1 unit, and a vertical shift down by 3 units.

Hope this help!!!

Have a nice day!!!

Answer:

C

Step-by-step explanation:

To convert milli- to kilo-, move the decimal point six places to the left

Answer:

Sorry if this is wrong, but seeing the question I think the best answer following the question would be answer B, because for A it shows that 1 hour is 35 miles when it says 70 miles in 1 hour, not C because as the time rises so does the distance, and I checked D and it's wrong.

Step-by-step explanation:

Answer: [tex]y=6x-7[/tex]

Step-by-step explanation:

We use the formula y=mx+b to put it into slope-intercept form

m=6 (slope)

b=-7 (y-intercept)

Therefore, the answer is y=6x-7

Answer:

prime factorization of 225 = 32•52.

Step-by-step explanation:

The number 225 is a composite number so, it is possible to factorize it. 225 can be divided by 1, by itself and at least by 3 and 5.

A composite number is a positive integer that has at least one positive divisor other than one or the number itself. In other words, a composite number is any integer greater than one that is not a prime number.

He used 620 gallons of gas

Answer:

[tex]P(x < 4) = \frac{9}{50}[/tex]

Step-by-step explanation:

Given

[tex]n(S) = 50[/tex]

See attachment for distribution

Required

[tex]P(x < 4)[/tex]

This is calculated as:

[tex]P(x < 4) = \frac{n(1) + n(2) + n(3)}{n(S)}[/tex]

Using the data on the frequency distribution table, we have:

[tex]P(x < 4) = \frac{4 + 2 + 3}{50}[/tex]

[tex]P(x < 4) = \frac{9}{50}[/tex]

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Answer:

  7 1/75 football fields

Step-by-step explanation:

Multiply it out. The units of feet and yards cancel, leaving football fields.

  = (2104·1·1)/(3·100) football fields ≈ 7.0133... football fields

  = 7 1/75 football fields

Answer:

x = 1/4

y = -1/2

z = 9/4

Step-by-step explanation:

Here we have a system of 3 equations with 3 variables:

4*x + 2*y + 1 = 1

2*x - y = 1

x + 3*y + z = 1

The first step to solve this, is to isolate one of the variables in one of the equations, let's isolate "y" in the second equation:

2*x - y = 1

2*x - 1 = y

Now that we have an expression equivalent to "y", we can replace this in the other two equations:

4*x + 2*(2*x - 1) + 1 = 1

x + 3*(2*x - 1) + z = 1

Now let's simplify these two equations:

8*x - 1 = 1

7*x - 3 + z = 1

Now, in the first equation we have only the variable x, so we can solve that equation to find the value of x:

8*x - 1 = 1

8*x = 1 + 1 = 2

x = 2/8 = 1/4

Now that we know the value of x, we can replace this in the other equation to find the value of z.

7*(1/4) -3 + z = 1

7/4 - 3 + z = 1

z = 1 + 3 - 7/4

z = 4 - 7/4

z = 16/4 - 7/4 = 9/4

z = 9/4

Now we can use the equation y = 2*x - 1 and the value of x to find the value of y:

y = 2*(1/4) - 1

y = 2/4 - 1

y = 1/2 - 1

y = -1/2

Then the solution is:

x = 1/4

y = -1/2

z = 9/4

Step-by-step explanation:

find the arithmetic mean of given data 12 15 18 20

Answer:

Evans would have $852.8

Step-by-step explanation:

Given

[tex]PV = \$800[/tex]

[tex]r = 3.25\%[/tex]

[tex]t = 2[/tex]

[tex]n = 1[/tex] --- annually'

Required

The future value

This is calculated using:

[tex]FV = PV*(1 + \frac{r}{n})^{nt[/tex]

So, we have:

[tex]FV = 800 * (1 + 3.25\%/1)^{2*1}[/tex]

[tex]FV = 800 * (1 + 3.25\%)^{2}[/tex]

[tex]FV = 800 * (1 + 0.0325)^{2}[/tex]

[tex]FV = 800 * (1 .0325)^2[/tex]

[tex]FV = 852.845[/tex]

[tex]FV = 852.8[/tex]

FV =

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2*x+2*3=x-4

2x+6=x-4

2x-x=-4-6

x=-10

Answer:

[tex]x = - 10[/tex]

Step-by-step explanation:

Let's solve:

[tex]2(x+3)=x−4[/tex]

Step 1: Simplify both sides of the equation.

[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]

Step 2: Subtract x from both sides.

[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]

Step 3: Subtract 6 from both sides.

[tex]x+6−6=−4−6 \\ x=−10[/tex]

Answer:

A) 0.7696

B) 0.0474

C) Yes it's unusual

D) 0.05746

E) No, it is not unusual

F) No, it is not unusual

Step-by-step explanation:

This is a binomial probability distribution question.

We are told that 92.4% of those admitted graduated.

Thus; p = 92.4% = 0.924

From binomial probability distribution, q = 1 - p

Thus;

q = 1 - 0.924

q = 0.076

Formula for binomial probability distribution is;

P(x) = nCx × p^(x) × q^(n - x)

A) At least 11 graduated out of 12.

P(x ≥ 11) = P(11) + P(12)

P(11) = 12C11 × 0.924^(11) × 0.076^(12 - 11)

P(11) = 0.3823

P(12) = 12C12 × 0.924^(12) × 0.076^(12 - 12)

P(12) = 0.3873

P(x ≥ 11) = 0.3823 + 0.3873

P(x ≥ 11) = 0.7696

B) that exactly 9 of them graduated out of 12. This is;

P(9) = 12C9 × 0.924^(9) × 0.076^(12 - 9)

P(9) = 0.0474

C) We are not given significance level here but generally when not given we adopt a significance level of α = 0.05.

Now, exactly 9 out of 12 that graduated which is P(9) = 0.0474.

We see that 0.0474 is less than the significance level of 0.05. Thus, we can say that it is unusual to randomly select 12 students from the special programs and get exactly 9 that graduate

D) that at most 9 of them out of 12 graduated.

P(x ≤ 9) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9)

This is going to be very long so I will make use of an online probability calculator to get the values of P(0) to P(8) since I already have P(9) as 0.0474.

Thus, we have;

P(0) = 0

P(1) = 0

P(2) = 0

P(3) = 0.00000001468

P(4) = 0.00000040161

P(5) = 0.00000781232

P(6) = 0.00011081163

P(7) = 0.00115477385

P(8) = 0.00877476184

Thus;

P(x ≤ 9) = 0 + 0 + 0 + 0.00000001468 + 0.00000040161 + 0.00000781232 + 0.00011081163 + 0.00115477385 + 0.00877476184 + 0.04741450256

P(x ≤ 9) = 0.05746

E) P(x ≤ 9) = 0.05746 is more than the significance level of 0.05, thus we will say it is not unusual.

F) from online binomial probability calculator, probability of getting only 9 out of 12 is more than the significance value of 0.05. Thus, we will say it is not unusual

Answer:

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

Step-by-step explanation:

The buckets are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

8 covered buckets, so N = 8.

4 buckets are selected, so n = 4.

2 contain a ball, which means that k = 2.

Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.

This is P(X = 2). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,8,4,2) = \frac{C_{2,2}*C_{6,2}}{C_{8,2}} = 0.2143[/tex]

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

Answer: the required sample size =1658944

Step-by-step explanation:

When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]

z-value for 99% confidence = 2.576

[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]

Hence, the required sample size =1658944

Step-by-step explanation:

Question 264138: How many liters of a 40% alcohol solution must be mixed with a 65% solution to obtain 20 liters of a 50% solution? x=8 gallons of 65% solution is used. 20-8=12 gallons of 40% solution is used.

please mark as brainliest

Answer:

[tex]b = 74^o[/tex] --- acute base

Step-by-step explanation:

Given

See attachment for the figure

Required

The acute base angle of the trapezoid

From the question, the isosceles triangle and the trapezoid share the same base.

Represent the base angle with b.

So:

[tex]b + b + 32^o = 180^o[/tex] --- angles in a triangle

[tex]2b = 180^o-32^o[/tex]

[tex]2b = 148^o[/tex]

Divide by 2

[tex]b = 74^o[/tex]

Answer:alternate exterior angles

Step-by-step explanation:

Since they’re on the outside of the parallel lines that makes them exterior

Answer:

1042.5

Step-by-step explanation:

Given :-

Using Unitary Method :-

→ Cost of 1 m is P 69.95

→ Cost of 15m is P ( 69.5 * 15 ) = P 1042.5

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Answer:

  B

Step-by-step explanation:

If the probability of event "A" is 'p', then the probability of the event "not A" is

  P(not A) = 1 - P(A) = 1 - p

For p=0.5, this is ...

  P(not A) = 1 -0.5 = 0.5 . . . . . matches choice B

Answer:

○B. 0.5 is the proof the outcome (not A).

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Answer:

  30 grams

Step-by-step explanation:

The time 120 seconds is 4 times the half-life of 30 seconds. That means (1/2)^4 = 1/16 of the original amount will remain. That is (480 g)(1/16) = 30 g.

  30 g of the radioactive rhodium will be left

Answer:

I searched the q and this is what I found

Step-by-step explanation:

Explanation: Number greater than 4 are 5 and 6 . So required probability is 26=13.

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Answer:

  B.  (-5, -2)

Step-by-step explanation:

That point is ...

  A + 1/5(B - A)

  = (-7, -4) + 1/5(3 -(-7), 6 -(-4)) = (-7, -4) +1/5(10, 10)

  = (-7, -4) +(2, 2) = (-5, -2)

The point (-5, -2) is 1/5 of the way from A to B.

Step-by-step explanation:

A. 2(x+4)=2x+8

=G

B. 3(2x-1)=6x-3

=I

C. 4(x+2)=4x+8

=J

D. 2(x+3)=2x+6

=K

E. 3(4x+1)=12x+3

=H

A - G

B - I

C - J

D - K

E - H

HOPE IT HELP

Answer:

Period: [tex]\pi[/tex]

Phase shift: n

Step-by-step explanation:

Tangent function:

Has the following format:

[tex]f(x) = \tan{ax - n}[/tex]

In which the period is [tex]\frac{\pi}{x}[/tex] and the phase shift is n.

In this question:

[tex]f(x) = -4\tan{(x-n)}[/tex]

[tex]a = 1[/tex], and thus, the period is [tex]\pi[/tex], with a phase shift of n.