Exactly 32% of the students in a school play a sport. Fifty students are randomly selected to determine the probability that, at most, 15 students play a sport. Should a binomial probability density function or cumulative distribution function be used? Explain. (4 points)

a. The function that models the situation is  F(t) = 48(1.08)ˣ

b. The price of the stock 6 years from now is $76.17

c. Find the graph in the attachment

d. I receive a dividend of $0.026.

Since the stock price increases at a rate of 8% every year, and is initially $48, it follows exponential growth.

So, the current price [tex]F(t) = A(1 + r)^{t}[/tex] where

So,  [tex]F(t) = A(1 + r)^{t}[/tex]

[tex]F(t) = 48(1 + 0.08)^{t} \\= 48(1.08)^{t}[/tex]

So, the function that models the situation is F(t) = 48(1.08)ˣ

The price of the stock 6 years from now is gotten when t = 6.

So,

[tex]F(t) = 48(1.08)^{t} \\= 48(1.08)^{6} \\= 48(1.5869)\\= 76.17[/tex]

So, the price of the stock 6 years from now is $76.17

Find the graph in the attachment

Since every quarter, the company pays a dividend of 1.5 %, the rate per year would be r = 1.5 % ÷ 1/4 year = 1.5 % × 4 = 6 % per year.

Since they pay at a rate, r = 6 % = 0.06 of the stock price, F(t) as dividend.

After n years, the dividend is D = (r)ⁿF(t)

= (0.06)ⁿF(t)

So, [tex]D = (0.06)^{t}F(t) \\= (0.06)^{t}[4.8(1.08)^{t}][/tex]

So, after 3 years when t = 3,

[tex]D = (0.06)^{t}[4.8(1.08)^{t}]\\D = (0.06)^{3}[4.8(1.08)^{3}]\\D = 0.000216 \times 48 \times 1.2597\\D = 0.013[/tex]

Since there are 3 shares, the total dividend would be D' = 3D

= 3 × 0.013

= 0.026

So, i receive a dividend of $0.026

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Answer:

Step-by-step explanation:

Comment

The first thing you ought to notice is that the original shape is a rectangle, with 2 of the y coordinates of the 4 points of 1. What that statement means is that two of the points (1,1) and (3,1) both sit on the line y = 1. they don't move. The other two points do move and they form a circular shape. So what you are going to get is a cylinder.

Answer: cylinder

Answer: 345

Step-by-step explanation: the alls

The values that are included in the random variable of the experiment that include rolling one 6-sided die and one 10-sided die are 10, 14 and 16

The experiment elements are given as:

The sample spaces of both dice are:

6-sided = {1, 2, 3...., 6}

10-sided = {1, 2, 3...., 10}

When the outcomes of both dice are added, we have:

Sample space = {2, 3, 4, 5, 6, 7, 8, 9, .............. 16}

Minimum = 2

Maximum = 16

This means that the values that are included in the random variable are in the range 2 - 16 i.e. starting from 2 and ending in 16

Hence, the values that are included in the random variable of using one 6-sided die and one 10-sided die and rolling them together are 10, 14 and 16

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The measure of the angle is 51 degrees.

If the sum of two angles is ninety levels, then we say that they may be complementary. thus, the supplement of an attitude is received by means of subtracting it from 90. as an example, the supplement of 40° is ninety° - forty° = 50°.

If two attitudes are complementary, the sum in their measure is ninety tiers. So, the measures of the 2 complementary angles are 51 degrees and 39 degrees.

While the sum of angles is equal to ninety ranges, they are known as complementary angles. For example, 30 stages and 60 stages are complementary angles.

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Answer: 1.7

Step-by-step explanation:

The rate of gallons per hour is the same as the unit rate. You want to find out how many gallons are filled in one hour, so divide 3 down to one, 3 divided by 3 is one. Then, also divide 5 by 3. 5 divided by 3 is 1.6666... and as an hour is out of 60, round it to 1.7.

I hope this helps!

It will take 16hr 30min for Mrs. Smith to catch up.

Let,

t + 3 = Time of Mr. Smith

t = Time of Mrs. Smith

v1 = 55 mph the speed of Mr. Smith

v2 = 65 mph the speed of Mrs. Smith

Formula: Distance = speed × time

v1 ( t + 3)  = v2t

55 ( t + 3 ) = 65t

65t = 55t + 165

65t - 55t = 165

10t = 165

t = 16.5 hr

t = 16 hr 0.5 × 60 min

t = 16 hr 30 min

Therefore, it will take 16hr 30min for Mrs. Smith to catch up.

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Answer:

only (0,5)

Step-by-step explanation:

(0,5) is in the shaded region on the graph, so it is a solution.

One other point is in the unshaded region so it is NOT a solution. The other two points are on the dashed line, so they are NOT solutions. If the line was solid (not dashed) they would work, but since the line is dashed they are NOT solutions.

Answer:

A. (0,5)

Step-by-step explanation:

A process that behaves the same way as a procedure so that similar results are produced is called a simulation.

In this question,

Simulations are used for finding probabilities for compound events. The probability model of a random phenomenon consists of a sample space of possible outcomes, associated events, random variables, and a probability measure that specifies probabilities of events and determines distributions of random variables.

Procedure is a method of analyzing or representing statistical data; a procedure for calculating a statistic. The goal of statistical analysis is to identify trends.

Hence we can conclude that a process that behaves the same way as a procedure so that similar results are produced is called a simulation.

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Answer:

x=6 because if you multiple 4x6 you get 24

not exactly sure but try

Answer:

it is not possible

Step-by-step explanation:

there are two different variables in one equation, so you cannot solve for one. You would need a system of equations to do that.

you can solve for x in terms of y, which is x = (24+4y)/5 but i dont think thats what the question is asking so the answer is probably just that its not possible

The recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously is f(n + 1) = f(n) + 0.75

The general recursive function is expressed as:

an+1 = d + an

where

r is the common difference

Given the sequence below

1.5, 2.25, 3.0, 3.75, ...

Common difference =  2.25 - 1.5 = 0.75

Substitute

f(n + 1) = f(n) + d

f(n + 1) = f(n) + 0.75

Hence the recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously is f(n + 1) = f(n) + 0.75

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The function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily

The function is given as:

f(x) = 86(1.08)^x

There are 7 days in a week.

This means that:

1 day = 1/7 week

So, x days is

x day = x/7 week

Substitute x/7 for x in

f(x) = 86(1.08)^(x/7)

Rewrite as:

f(x) = 86(1.08^1/7)^x

Evaluate

f(x) = 86(1.01)^x

In the above, we have:

r = 1.01 - 1

Evaluate

r = 0.01

Express as percentage

r = 1%

Hence, the function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily

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Answer: the answer is d

Step-by-step explanation:

Answer:

[tex] [/tex] [tex] [/tex] [tex] [/tex] [tex] [/tex]

Answer:

1.x=0, –10

2.x=3, 4

Step-by-step explanation:

1.

x(x+10)=0===> x=0, –10

2.

x²–3x–4x+12===> x²–7x+12=0

(x–3)(x‐4)=0====> x=3, 4

Answer:

B. 54π units ²

Step-by-step explanation:

solution:

given,

Radius (r) = 3

(l) = 15

we know that,

T.S.A. of cone = πr( r + l )

= π × 3(3 + 15)

= π × 3 × 18

= π × 54

= 54π units ²

Answer:

53.7

Step-by-step explanation:

The area of the rectangular base is 7(2.3)=16.1.

So, the total volume is (1/3)(16.1)(10), which is about 53.7

The probability that one would have selected 2 five-dollar bills is; 1/4.

It follows from the task content that the piggy bank contains; 4 one-dollar bills and 4 five-dollar bills to make a total of 8 bills.

Hence, provided the probability events are carried out with replacement, the probability to have selected 2 five-dollar bills is;

= 4/8 × 4/8

= 1/4.

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Answer:

1/4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

By the triangle inequality theorem, 5<AC<23.

So, the answer is A.

Johnny created a Tally marks chart.

A frequency distribution table displays the frequency of each data set in an organized way. It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance. The first step that a mathematician does with the collected data is to organize it in the form of a frequency distribution table. All the calculations and statistical tests and analyses come later.

Tally Marks are used to keep a track of numbers in the quickest possible way. Tally marks are used for counting and are represented as a set of five lines in which there are four vertical lines (one vertical line is made for each of the first four numbers) and the fifth number is represented by a diagonal line across the previous four numbers. It can be understood through the given figure

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There are no solutions for z³ = x³ + y³ for a right triangle

The equation is given as:

z³ = x³ + y³

By Pythagoras theorem, we have:

z² = x² + y²

Multiply both sides by z

z³ = zx² + zy²

By comparing z³ = zx² + zy² and z³ = x³ + y³, we have:

x³ + y³ = zx² + zy²

Factor out z

x³ + y³ = z(x² + y²)

Make z the subject

z = (x³ + y³)/(x² + y²)

There exist no solution for the above equation

Hence, there are no solutions for z³ = x³ + y³ for a right triangle

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The number of times that Derrick batted last season is 188 times.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to denote percentage is %.

A percentage of 25% here means that twenty five times out of hundred times, Derrick hit the ball. In order to convert a percentage to a decimal, divide the percentage by 100.

Number of times Derrick bat last season = Number of hits last season / percentage of his batting average

47 / 25%

47 / 0.25 = 188

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Answer:

7.7 km

Explanation:

Use cosine rule as here given two sides and one angle.

Cosine rule states:

a² = b² + c² - 2bc cos(A)

While solving, treat a = 7.5 km as to that opposite angle is given of 68°

then b = missing side, c = 5.2 km, A = 68°

Applying rule:

7.5² = b² + 5.2² - 2(b)(5.2) cos(68)

56.25 = b² + 27.04 - 3.8959b

56.25 - 27.04 = b² - 3.8959b

b² - 3.8959b = 29.21

b² - 3.8959b - 29.21 = 0

apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]

[tex]\sf b = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad\:when \:\ ax^2 + bx + c = 0[/tex]

[tex]\sf b = \dfrac{ -(-3.8959) \pm \sqrt{(-3.8959)^2 - 4(1)(-29.21)}}{2(1)}[/tex]

[tex]\sf b = 7.69 291 \quad or \quad b = -3.797[/tex]

[tex]\sf b = 7.7 \quad (rounded \ to \ nearest \ tenth)[/tex]

As length cannot be negative. Hence the value of b is only 7.7 km

The answer is 7.7 km.

Let's apply the Cosine Law in this situation.

a² = b² + c² - 2bc cos(A)

Now, substitute the values based on the given diagram.

Here, using the Quadratic Equation, we can solve :

Answer:

I'm assuming that it is 4:1

Step-by-step explanation:

Answer:

2.8kg

Step-by-step explanation:

There are 7 parts of meat for every 3 parts so there are 7+3=10 parts in total.

4/10=1 "part"

there are 7 parts of meat so (4/10)*7=28/10=2.8kg of meat.

(a) The city with a larger median room temperature is city B.

(b) The city having the highest noon temperature is city B.

(c) The city having the noon temperatures with a higher interquartile range is city A.

(d) The city having more noon temperatures that 81°F is city B.

In the given question, the noon temperatures for two cities, A and B, recorded over a month are shown via the box-and-whisker plots.

We are asked to use it and answer the questions:

(a) The median of data is represented by the line in the box of the box-and-whisker plot. Thus,

The median noon temperature for city A is 73°F.

The median noon temperature for city B is 76°F.

Thus, the city with a larger median room temperature is city B.

(b) The highest temperature is seen as the end point of the whiskers. Thus,

The highest temperature for city A is 85°F.

The highest temperature for city B is 92°F.

Thus, the city having the highest noon temperature is city B.

(c) The interquartile range is the difference between the end line of the box and its start line. Thus,

The interquartile range for city A is (81 - 64)°F or 17°F.

The interquartile range for city B is (81 - 68)°F or 13°F.

Thus, the city having the noon temperatures with a higher interquartile range is city A.

(d) From the given box-and-whisker plots, we can see that after 81°F, city B has a long whisker, showing more outliers.

Thus, the city having more noon temperatures that 81°F is city B.

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The inequality that represents the height that is displayed by the graph is: 10 ≤ h ≥ 50.

In an inequality graph, we the small circle at any end is shaded or full, the inequality sign used is either "less than or equal to" or "greater than or equal to" ("≤" or "≥"). If the circle is empty or not shaded, we use "less than" or "greater than" ("<" or ">").

In the graph showing Jeremy’s height above the ground at any time during the ride, we have a full circle (shaded) starting from 10, and another on the right at 50.

This implies that the range of height is from 10 to 50. Since the circle is full (shaded), then we would use "less than or equal to" and "greater than or equal to" ("≤" and "≥") in writing the inequality that represents the height.

Thus, where h is the height, the inequality would be: 10 ≤ h ≥ 50.

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Answer:

64

Step-by-step explanation:

2x-4y=3

x= (3 +4y)/2

substitute into the main equation

y= 0

x= 3/2

16^x /256^y

16^3/2 ÷ 256^0

√16^3 ÷1

= 64

Answer:

64

Step-by-step explanation:

2x - 4y = 3

2x = 4y + 3

x = 2y + 1.5

[tex] \dfrac{16^x}{256^y} = [/tex]

[tex] = \dfrac{16^{2y + 1.5}}{256^y} [/tex]

[tex] = \dfrac{16^{2y + 1.5}}{16^{2y}} [/tex]

[tex] = 16^{2y + 1.5 - 2y} [/tex]

[tex] = 16^\frac{3}{2} [/tex]

[tex] = 4^3 [/tex]

[tex] = 64 [/tex]

Answer:

7 - 10

Step-by-step explanation:

Because it is -3 and 7 - 10 = -3

Simple Random sampling

Meaning:

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected.

For example, if you randomly select 1000 people from a town with a population of 100,000 residents, each person has a 1000/100000 = 0.01 probability. That's a simple calculation requiring no additional knowledge about the population's composition. Hence, simple random sampling.

Advantage:

Simple random sample advantages include ease of use and accuracy of representation. No easier method exists to extract a research sample from a larger population than simple random sampling.

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Using a system of equations, the parts are of 14 and 20.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are x and y. The total is of 34, hence:

x + y = 34 -> y = 34 - x.

The ratios are given as follows:

[tex]\frac{4}{7}x = \frac{2}{5}y[/tex]

Then:

[tex]\frac{4}{7}x = \frac{2}{5}(34 - x)[/tex]

20x = 14(34 - x)

34x = 34 x 14

x = 14, y = 34 - 14 = 20.

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