Answer:
20.5
Step-by-step explanation:
ur welcome :D
Ave you ever tried to get out of jury duty? about 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty.†(a) if 11 people are called for jury duty, what is the probability that all 11 will be available to serve on the jury? (round your answer to three decimal places.) 0.042 correct: your answer is correct. (b) if 11 people are called for jury duty, what is the probability that 5 or more will not be available to serve on the jury? (round your answer to three decimal places.) 0.115 correct: your answer is correct. (c) find the expected number of those available to serve on the jury. what is the standard deviation? (round your answers to two decimal places.)μ = 8 incorrect: your answer is incorrect. peopleσ = 1.436 correct: your answer is correct. people
Answer:
The answers to the question are;
(a) 0.042 to three decimal places.
(b) 0.115 to three decimal places.
(c) μ = 8.25, σ = 1.44 to two decimal places.
Step-by-step explanation:
To solve the question, we note that this is a binomial distribution problem
(a) The probability that all 11 will be available is given by
P(11) = ₁₁C₁₁ × 0.75¹¹×0.25¹¹⁻¹¹ = 0.0422
(b) Probability of 6 or less success = P(6) + P(5) +P(4) +P(3) + P(2) + P(1) +P(0)
P(6) = ₁₁C₆ × 0.75⁶×0.25⁵ = 0.080299
P(5) = ₁₁C₅ × 0.75⁵×0.25⁶ = 0.026766
P(4) = ₁₁C₄ × 0.75⁴×0.25⁷ = 0.063729
P(3) = ₁₁C₃ × 0.75³×0.25⁸ = 0.001062
P(2) = ₁₁C₂ × 0.75²×0.25⁹ = 0.0001180
P(1) = ₁₁C₁ × 0.75¹×0.25¹⁰ = 0.000007867
P(0) = ₁₁C₀ × 0.75⁰×0.25¹¹ = 0.00000002384
Therefore P(6) + P(5) +P(4) +P(3) + P(2) + P(1) +P(0) = 0.11462
Which is 0.115 to three decimal places
(c) The expected number of those available to serve on the jury =
Probability of success = n·p = 11×0.75 = 8.25
μ = 8.25
The standard deviation,σ [tex]=\sqrt{npq}[/tex] =[tex]\sqrt{11*0.75*0.25}[/tex] = 1.43614 ≅ 1.44 to two decimal places
The probability of everyone being available for jury duty can be calculated by multiplying the individual probabilities. More complex probabilities, such as the chance of more than 5 not being available, can be determined using a binomial distribution or a normal approximation. The expected number and standard deviation are calculated from these probabilities.
Explanation:The probability of different outcomes for jury duty service can be calculated based on known probabilities and using principles of statistics. If 25% of those called find an excuse to avoid it, that means 75% are available. We can use that data to find the probability of all 11 individuals being available, or more than 5 being unavailable.
a) Probability that all 11 will be available: The probability would be (0.75)^11 = 0.042. Because all events are independent, we multiply the individual probabilities.
b) Probability that 5 or more will not be available: You would use a binomial distribution or a normal approximation to a binomial distribution to find this probability (0.115).
c) Expected number and standard deviation: The expected number of people available to serve would be the total people called multiplied by the probability of being available (11*0.75) = 8.25 people. The standard deviation, which is a bit more complex to compute, would be about 1.436 people.
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The freezing point of water is 0∘ C. Scientists use positive numbers to show temperatures above the freezing point of water and negative numbers to show temperatures below the freezing point of water. Snowy's Dessert Cart keeps the ice in their snow cones at a temperature of −15∘ C What does −15∘ C represent in this situation?
Answer:
The -15°C temperature of the ice in their snow cones mean that the temperature of that ice is 15° below the freezing point of water.
Step-by-step explanation:
It is explained that Celsius scale was calibrated based on water. The scientists use 0°C to represent the freezing point of water and subsequently use positive numbers to indicate temperatures above the freezing point of water and negative numbers to indicate temperatures lower than the freezing point of water.
So, a temperature of -15°C simply means that the temperature is 15° lower than the freezing point of water.
Hope this Helps!!!
Answer:
Its A
Step-by-step explanation:
Help please I'm not sure if I got it right, I'm a bit confused. 5th grade math
Answer:
check your math
Step-by-step explanation:
The first subtraction was correct:
36 -7 3/4 = 28 1/4
The second subtraction needs to be revisited.
28 1/4 -6 2/4 = 27 5/4 -6 2/4 = 21 3/4
__
You can do what you did, but you need to pay attention to the signs.
28 1/4 -6 2/4 = (28 -6) +(1/4 -2/4) = 22 - 1/4 = 21 3/4
The result of subtracting 2/4 from 1/4 is -1/4, not +1/4.
_____
The length of the first cut piece was 21 3/4 inches.
Answer:
21 ¾ inches
Step-by-step explanation:
36 - 6½ - 7¾
36 - (6½ + 7¾)
36 - (6 + 7 + ½ + ¾)
36 - (13 + [2+3]/4) lcm:4
36 - (13 + 5/4)
36 - (13 + 1 + ¼)
36 - 14 - ¼
22 - ¼
21¾ inches
You have 555 reindeer, Bloopin, Rudy, Ezekiel, Prancer, and Balthazar, and you want to have 333 fly your sleigh. You always have your reindeer fly in a single-file line.
How many different ways can you arrange your reindeer?
Answer:
60 combinations for single file.
Step-by-step explanation:
Bloopin has 12 combinations where he leads the single file line of 3 only reindeer's at a time including the reindeer that leads the file. This is not a file of five but as the question asks for 3 there are 5 reindeer's that each have a turn of 12 each, to single file 3 reindeer's, it is here we get 12 for each combination.
12 x 5 = 60 combination.
Eduardo has a recipe that uses 2/3 cup of flour for each batch .If he makes 4 batches ,how many cups of flour will he need? Write your answer as a mixed number. Use the number line to help.
Answer:
[tex]2\dfrac{2}{3}[/tex] cups of flour
Step-by-step explanation:
Each batch uses 2/3 cup of flour.
If Eduardo makes 4 batches, he is going to need [tex]4X\frac{2}{3}[/tex] cups of flour.
[tex]4 X \dfrac{2}{3}=\dfrac{8}{3}=2\dfrac{2}{3}[/tex]
Eduardo is going to need [tex]2\dfrac{2}{3}[/tex] cups of flour.
Final answer:
Eduardo will need 2 2/3 cups of flour for 4 batches.
Explanation:
To find the total cups of flour Eduardo needs for 4 batches:
Amount of flour for 1 batch: 2/3 cup
Total cups for 4 batches: (2/3 cup) x 4 = 8/3 cups = 2 2/3 cups
So, Eduardo will need 2 2/3 cups of flour for 4 batches.
Suppose the probability density function of the length of computer cables is f(x)= 0.1 from 1200 to 1210 millimeters. A) Determine the mean and standard deviation of the cable length. B) If the length specifications are 1195 < x < 1205 millimeters, what proportion of cables is within specifications?
Answer:
a) Mean = 1205
Standard Deviation = 2.89
b) P( 1195 < x < 1205) = 0.5
50% of the cables lie within the given specification.
Step-by-step explanation:
We are given the following information in the question:
[tex]f(x) = 0.1[/tex]
a = 1200, b = 1210
We are given a uniform distribution.
a) Mean:
[tex]\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{1200+1210}{2} = 1205[/tex]
Standard Deviation:
[tex]\sigma = \sqrt{\displaystyle\frac{(b-a)^2}{12}}\\\\= \sqrt{\displaystyle\frac{(1210-1200)^2}{12}} = \sqrt{8.33} = 2.89[/tex]
b) P( 1195 < x < 1205)
[tex]=\displaystyle\int_{1195}^{1205} f(x) dx\\\\=\displaystyle\int_{1200}^{1205} (0.1) dx\\\\=0.1[x]_{1200}^{1205} = (0.1)(1205-1200) = 0.5[/tex]
50% of the cables lie within the given specification.
During the summer Austin sells tomatoes at his family's produce stand . Every morning he starts with 150 tomatoes on. Sunday Austin sells 45 of the 150 tomatoes. He wants to know what percent of the tomatoes he sold.
Answer:
30%
Step-by-step explanation:
Given:
Every morning he starts with 150 tomatoes.
On Sunday Austin sells 45 of the 150 tomatoes.
Question asked:
What percent of the tomatoes he sold ?
Solution:
As Austin sells 45 tomatoes out of 150 tomatoes, we will find percent of the tomatoes he sold by using :
Percent of the tomatoes he sold = Number of tomatoes he sold divided by total number of tomatoes he starts with.
[tex]Percentage =\frac{45}{150} \times100\\[/tex]
[tex]=\frac{4500}{150} \\ = 30[/tex]
Therefore, 30% of the tomatoes he sold on Sunday.
the answer is 30%
step by step problem
Answer
You decide to invest a total of $1500 in a money market account at an annual interest rate of 3.4%.
Find the balance in the account after 8 years if it is compounded quarterly.
Find the balance in the account after 8 years if it is compounded monthly.
Find the balance in the account after 8 years if it is compounded continuously.
PLEASE SHOW WORK
Answer:
1) $1966.62
2) $1968.12
3) $1968.88
Step-by-step explanation:
1) 1500 × (1 + .034/4)³²
= 1966.618592
2) 1500 × (1 + .034/12)⁹⁶
= 1968.123402
3) 1500 × (e^(8×0.0314))
= 1968.880502
Answer:
1968.880502
Step-by-step explanation:
PLEASE Help! ASAP PLZ
Answer:
0.57 yr
Step-by-step explanation:
To find the doubling time with continuous compounding, we should look at the formula:
[tex]FV = PVe^{rt}[/tex]
FV = future value, and
PV = present value
If FV is twice the PV, we can calculate the doubling time, t
[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]
1. David's doubling time
[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.06125}\\\\& = & \textbf{11.317 yr}\\\end{array}[/tex]
2. Violet's doubling time
The formula for interest compounded periodically is
[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]
where
n = the number of payments per year
[tex]\begin{array}{rcl}9600 & = & 4800\left (1 + \dfrac{0.065}{4} \right )^{4t}\\\\2 &= & (1 + 0.01625 )^{4t}\\& = & 1.01625^{4t}\\\ln 2& = & 4 (\ln 1.01625)\times t \\& = & 0.064478t\\t& = & \dfrac{\ln 2}{0.064478}\\\\& = & \textbf{10.750 yr}\\\end{array}[/tex]
3. David's doubling time vs Violet's
11.317 - 10.750 = 0.57 yr
It would take 0.57 yr longer for David's money to double than Violet's.
Which of the following equations is written in the slope-intercept form?
y + b = m + x
x + y = 1/3m
x = mb + y
y = mx + b
Answer:
y = mx + b
Hope I helped!!! :)
~Nuha
Susie's bank account balance for January through June was -100 300-475-9200 -250 and 500 what is the range of Susie's bank account balance over the six months.
Answer:
The range is 9,100
Step-by-step explanation:
Six different figures for the account balance for the six months are given.
The range of a set of numbers is defined as the difference between the highest and the lowest of the numbers.
In this question, we have;
Highest: 9200
Lowest: 100
Range = Highest - Lowest = 9200 - 100 = 9100
Answer:
There is a typo in your question it's supposed to be 200 not 9200
Step-by-step explanation:
Osvoldo has a goal of getting at least 30% percent of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of carbohydrates, and 55 grams were from whole grains. Did Osvoldo meet his goal?
Answer: Osvoldo did not meet his goal.
Step-by-step explanation:
If he ate 220 grams of carbohydrates today and 55 grams were from whole grains, it means that the percentage of the carbohydrates he ate today that came from whole grains is
55/220 × 100 = 25%
Since he has a goal of getting at least 30% percent of his grams of carbohydrates each day from whole grains, then he did not meet his goal because 25% is lesser than 30% and he needs 30% or more
Consider the function f ( x ) = − 5 x 3 f(x)=-5x3. Determine the average rate of change (ARoC) of f f over the following intervals of x x. From x = 3 x=3 to x = 3.5 x=3.5.
The average rate of change of f over intervals of x from x = 3 to = 3.5 is - 159.
Given that the function is,
f (x) = - 5x³
Used the formula for the average rate of change of function f at interval [a, b] is,
f' (x) = [ f (b) - f (a) ] / (b - a)
Here, f (x) = - 5x³
At x = 3;
f (3) = - 5 × 3³
= - 135
At x = 3.5;
f (3.5) = - 5 × (3.5)³
= - 214.4
Hence, the average rate of change of f over intervals of x from x = 3 to = 3.5 is,
f ' (x) = [- 214.5 - (- 135)] / (3.5 - 3)
f ' (x) = [- 79.5] / 0.5
f ' (x) = - 159
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Final answer:
The average rate of change of the function f(x) = -5[tex]x^3[/tex] from x = 3 to x = 3.5 is -158.75.
Explanation:
The average rate of change (ARoC) can be determined using the formula:
ARoC = (f(x2) - f(x1)) / (x2 - x1)
In this case, the given function is f(x) = -5x^3. To find the ARoC from x = 3 to x = 3.5, substitute these values into the formula:
ARoC = (-5[tex](3.5)^3 - (-5(3)^3)[/tex]) / (3.5 - 3)
Simplifying the equation gives:
ARoC = (-5(42.875) - (-5(27))) / (0.5)
ARoC = (-214.375 + 135) / 0.5
ARoC = -79.375 / 0.5
ARoC = -158.75
Therefore, the average rate of change of f(x) from x = 3 to x = 3.5 is -158.75.
Alex has a calibrated bottle. The water level is at the 0 mL mark. When Alex places a baseball under the water, the water level rises to the 200 mL mark. What is the volume of the baseball?
Answer:
4/3*π*[tex]100^{3}[/tex]
Step-by-step explanation:
water level rises to the 200 mL mark, it means the ball diameter is 200, and the radius is: 100
So the voulume of the ball is: 4/3*π*[tex]r^{3}[/tex]
= 4/3*π*[tex]100^{3}[/tex]
Hope it will find you well.
Why is it advantageous to fill out the Budget and Cash Flow spreadsheet at the start of the simulation?
Answer:
It is likewise significant on the grounds that it causes you decide if your business has enough cash to run or to grow it in future. Thus budget and cash flow spreadsheet is an absolute necessity in a simulation to grow.
Step-by-step explanation:
Cash flow spreadsheet alludes to the announcement of planned cash inflows and outflows. Budget cash flow spreadsheet is utilized to assess the momentary cash necessity and it can likewise be utilized to distinguish where the most extreme cash is going out and from where is the greatest inflow.
Four of the seven students are from Middle Georgia State College. What is the probability that both of the interviewed students are from Middle Georgia State College? Express your answer as a reduced fraction or decimal rounded to at least four decimal places.
The probability that both of the interviewed students are from Middle Georgia State College is 2/7 or 0.2857 rounded to four decimal places.
Explanation:To calculate the probability that both interviewed students are from Middle Georgia State College, one would use the formula for conditional probability, considering the process as two sequential events. The first student being from the college and then the second one, given the first is already from the college. Since there are four students from the college out of a total of seven, the probability of picking one Middle Georgia State College student first is 4/7. After the first student from the college has been picked, there are now three remaining Middle Georgia students out of the remaining six students. Thus, the probability for the second pick is 3/6, which simplifies to 1/2. The total probability is the product of these two probabilities: (4/7) * (1/2) = 2/7, or approximately 0.2857 when rounded to four decimal places.
Given that line l and line m are parallel, if m∠1 = 34°, and m∠2 = 116°, what is m∠3?
64°
36°
63°
34°
Answer:
The answer to your question is 34°
Step-by-step explanation:
Data
m∠1 = 34°
m∠2 = 116°
m∠3 = ?
Process
1.- If lines l and m are parallel then angles 1 and 3 are interior alternate angles.
2.- Interior alternate angle measure the same.
3.- m∠1 = m∠3
4.- m∠3 = 34°
5.- Another information given is not necessary to answer this question.
Answer: 34°
Step-by-step explanation:
There may be another way to do it; angle 1 is equal to 34°, angle one and the supplement of 3(we will call it angle 4) are supplementary. So if angle 1 equals 34, angle 4 = 180-34 (which equals 146). since angles 3 and 4 are supplementary, angle 3; would equal 180 - 146 (which equals 34).
Have a nice day! Good luck with the exam.
PLZZZZZZZZZ COME HELP ME
Answer:
-2/3
Step-by-step explanation:
using rise over run from point B you go up 2 points and then to point A left 3 and since the line is going down the slope will be negative so -2/3
Pencils cost $0.24 each and pens cost 79 each mrs. Trevonne but six pencils and 5 pen how much did she pay for the pencil and pens in dollars and cents?
Answer:
5 dollars and 19 cents
Step-by-step explanation:
hsgd
Compare each common trigonometric function with its respective inverse function and explain why these comparisons make sense in the light of the definition of the inverse of a function. Also, explain why you think the domains and ranges of the inverse trigonometric functions make sense in relation to their parent functions.
Final answer:
The trigonometric functions and their inverse functions are related to each other because they undo each other's actions. Inverse trigonometric functions give the angle whose trigonometric ratio is a given value. The domains and ranges of inverse trigonometric functions are restricted to ensure that they are well-defined.
Explanation:
The trigonometric functions and their inverse functions are related to each other because they undo the actions of the other function. Let's take the sine function as an example. The sine function takes an angle as input and gives the ratio of the opposite side to the hypotenuse as output. Its inverse function, arcsine, takes a ratio as input and gives the angle whose sine is that ratio as output.
These comparisons make sense in the light of the definition of the inverse of a function because an inverse function undoes the action of the original function. In the case of trigonometric functions, they represent a ratio between the sides of a right-angled triangle, and their inverses give the corresponding angle.
The domains and ranges of the inverse trigonometric functions make sense in relation to their parent functions because they are restricted to a specific range to ensure that the inverse function is well-defined. For example, the domain of arcsine function is [-1, 1] because the output of sine function is always between -1 and 1. By restricting the domain, we can ensure that the inverse function is a one-to-one mapping and has a well-defined output for each input.
Eli is a 12.5 pounds of potatoes to make mashed potatoes. She uses one tenth as many pounds of butter as potatoes. How many pounds of butter does Ellie use
Answer:
Eli used 1.25 pounds of butter to make mashed potato.
Step-by-step explanation:
We are given the following in the question:
Amount of potato used by Eli = 12.5 pounds
Amount of butter used =
[tex]\dfrac{1}{10}(\text{Amount of potato used})[/tex]
Thus, pounds of butter used by Eli is:
[tex]\dfrac{1}{2}\times 12.5\\\\=1.25[/tex]
Thus, Eli used 1.25 pounds of butter to make mashed potato.
If an M:N relationship is mandatory on both sides, and if both relations resulting from the entities involved in the relationship each have 3 records, then the resulting bridge relation cannot have less than ________ records.
Answer:
3
Step-by-step explanation:
A mandatory relationship means that for every A there must be a B and vice versa. The excessive is saying that you have a relationship with 3 records each, therefore the bridge relation cannot have less than 3 records otherwise the mandatory aspect will be broke.
I hope you find this information useful and interetsing! Good luck!
Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is described by the formula below. C(x) = 1000 + 4x + 0.02x2 + 0.0001x3 (a) Find the marginal cost function. C'(x) =
Answer:
a) The marginal cost function is given by
C'(x) = 4 + 0.04x + 0.0003x² (in dollars)
b) C'(70) = $8.27
Step-by-step explanation:
C(x) = 1000 + 4x + 0.02x² + 0.0001x³
a) Marginal cost is usually defined as the cost of producing one extra unit of product. It expresses how much the total cost is changing with respect to number of units of product.
Mathematically,
MC = (dC/dx) = C'(x)
For this question,
C'(x) = 4 + 0.04x + 0.0003x²
b) C'(70) means the marginal cost at x = 70 units, that is, how much the total cost is changing after the production of 70 units; the cost of producing one extra unit of product after producing 70 units.
C'(x) = 4 + 0.04x + 0.0003x²
C'(70) = 4 + 0.04(70) + 0.0003(70²)
C'(70) = $8.27
Hope this helps!
A rose garden is going to be built in the city park in the shape of a parallelogram with a rectangular walkway through it. The garden region is shown below. There will not be roses in the walkway. Find the total area where roses will be planted. Show your work.
Answer: the total area where roses will be planted is 1520 feet²
Step-by-step explanation:
The formula for determining the area of a parallelogram is expressed as
Area = base × height
From the information given,
Base = 20 + 40 = 60 feet
Height = 38 feet
Area of the rose garden = 60 × 38 = 2280 feet²
The formula for determining the area of a rectangle is expressed as
Area = length × width
From the information given,
Length = 38 feet
Width = 20 feet
Area of the rectangular walkway is
20 × 38 = 760 feet²
Therefore, the total area where roses will be planted is
2280 - 760 = 1520 feet²
changle. Show all work. Round each length to the nearest tenth and each angle to the
nearest degree.
17.
AC =
mZA =
mZC =
Answer:
Part 1) [tex]BC=12.2\ units[/tex]
Part 2) [tex]m\angle A=55^o[/tex]
Part 3) [tex]m\angle C=35^o[/tex]
Step-by-step explanation:
Part 1) Find AC
we know that
In the right triangle ABC of the figure
Applying the Pythagorean Theorem
[tex]AC^2=AB^2+BC^2[/tex]
substitute the given values
[tex]AC^2=7^2+10^2[/tex]
[tex]AC^2=149\\AC=12.2\ units[/tex]
Part 2) Find the measure of angle A
we know that
In the right triangle ABC
[tex]tan(A)=\frac{BC}{AB}[/tex] ----> by TOA (opposite side divided by the adjacent side)
substitute the values
[tex]tan(A)=\frac{10}{7}[/tex]
using a calculator
[tex]m\angle A=tan^{-1}(\frac{10}{7})=55^o[/tex]
Part 3) Find the measure of angle C
we know that
In the right triangle ABC
[tex]m\angle A+m\angle C=90^o[/tex] ----> by complementary angles
substitute the given value
[tex]55^o+m\angle C=90^o[/tex]
[tex]m\angle C=90^o-55^o=35^o[/tex]
help me answer this please
Answer:
y = 4x -3
Step-by-step explanation:
The line perpendicular to the given line can be written as the same equation with the coefficients of x and y swapped, and one of them negated. The constant may be different, so we'll call it "c".
4x -y +c = 0 . . . . . line perpendicular to that given
The y-intercept of the second given line can be found by setting x=0. That gives the equation -y -3 = 0. The perpendicular line with x=0 would have equation ...
-y +c = 0
Comparing these two tells us c = -3.
So, the general form of the perpendicular line we want is ...
4x -y - 3 = 0
We can add y to put this in slope-intercept form:
y = 4x -3
A falling object travels a distance given by the formula d=4t+16t^2, where t is measured in seconds and d is measured in feet how long will it take for the object to travel 72ft
Answer:
2 seconds.
Step-by-step explanation:
Given [tex]d=4t+16t^{2}[/tex] and d = 72 ft
We need to solve [tex]72=4t+16t^{2}[/tex]
[tex]4t+16t^{2}-72=0[/tex]
[tex]4t^{2}+t-18=0[/tex]
[tex]4t^{2}+9t-8t-18=0[/tex]
[tex]t(4t+9)-2(4t+9)=0[/tex]
[tex](t-2)(4t+9)=0[/tex]
[tex]t-2=0,4t+9=0[/tex]
[tex]t=2,t=-\frac{9}{4}[/tex]
Since, time can not be negative, so the required time is t = 2 seconds.
Final answer:
To find the time it takes for the object to travel 72 feet based on the given distance formula d=4t+16t², you can solve for t by substituting the distance value of 72 feet into the formula and solving for t.
Explanation:
Distance: To find the time it takes for the object to travel 72 feet, we can set the distance formula d = 4t + 16t² equal to 72 feet and solve for t.
Step-by-step explanation:
Given: d = 4t + 16t² and d = 72 feet
Substitute d = 72 into the formula: 72 = 4t + 16t²
Rearrange the equation: 16t² + 4t - 72 = 0
Solve for t using the quadratic formula or factoring.
The solutions for t will give you the time it takes for the object to travel 72 feet.
researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% 40 % of this population prefers the color red. If 14 14 buyers are randomly selected, what is the probability that exactly 2 2 buyers would prefer red? Round your answer to four decimal places.
Answer: the probability that exactly 2 buyers would prefer red is 0.0320
Step-by-step explanation:
We would assume a binomial distribution for the color preferences of new car buyers. The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = (1 - r) represents the probability of failure.
n represents the number of trials or sample.
From the information given,
p = 40% = 40/100 = 0.4
q = 1 - p = 1 - 0.4
q = 0.6
n = 14
x = r = 2
Therefore,
P(x = 2) = 14C2 × 0.4^2 × 0.6^(14 - 2)
P(x = 2) = 91 × 0.16 × 0.0022
P(x = 2) = 0.0320
A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft. What is the greatest number of packages that can fit in the truck?
Answer:
24000 pieces.
Step-by-step explanation:
Given:
Side lengths of cube = [tex]\frac{1}{4} \ foot[/tex]
The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.
Question asked:
What is the greatest number of packages that can fit in the truck?
Solution:
First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.
[tex]Volume\ of\ cube =a^{3}[/tex]
[tex]=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot[/tex]
Length = 8 foot, Breadth = [tex]6\frac{1}{4} =\frac{25}{4} \ foot[/tex], Height =[tex]7\frac{1}{2} =\frac{15}{2} \ foot[/tex]
[tex]Volume\ of\ rectangular\ prism =length\times breadth\times height[/tex]
[tex]=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot[/tex]
The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube
The greatest number of packages that can fit in the truck = [tex]\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube[/tex]
Thus, the greatest number of packages that can fit in the truck is 24000 pieces.
label the sides opposite, adjacent, or hypotenuse, then find the missing side. Round to the nearest tenth for 25, 26, 27, 29, & 30
Answer:
Please see the attached pictures for full solution.