Answer:
C. 9
Step-by-step explanation:
it's multiple choice so plug each value in
A = -26
B = -34
C = 22
D = 46
so the answer is c
A fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?
(a) 0.25
(b) 1.00
(c) (41)(0.25)1(0.75)3
(d) (41)(0.25)3(0.75)1
(e) (0.75)3(0.25)1
Answer:
(c) [tex]\left\ ({{4} \atop {1}} )\right.[/tex] [tex]0.25^{1} 0.75^{3}[/tex]
Step-by-step explanation:
As given in the statement, we have:
Out of 4 games pieces, 1 is winner.
Probability to win =p= [tex]\frac{1}{4}[/tex]
Jeff has game pieces = n = sample size = 4
As we need to find the probability that he wins exactly 1 prize, we will use binomial probability here :
[tex]P (X = k) = \left\ ({{n} \atop {k}} )\right. p^{k} (1-p)^{n-k} \\[/tex]
Evaluating at k=1, (k=1 as we need to find probability for exactly 1 prize won)
put n = 4, p =[tex]\frac{1}{4}[/tex]
P (X = 1) =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (1-0.25)^{4-1}[/tex]
P =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (0.75)^{3}[/tex]
Which is the probability that he wins exactly 1 prize and is option c.
Probability (Jeff wins 1 price in 4 game pieces) = C] [tex](4 c 1)(0.25)^1(0.75)^3[/tex]
Important Information : Probability (Winning a price) = 1 / 4 = 0.25
Probability (Not winning price) = 1 - Pr (Winning Price) = 1 - 0.25 = 0.75
Using Binomial Probability : Pr (X = r) = [tex]N c r . P^r . Q^(n-r)[/tex] .
Here N = number of trials (4 game pieces here) , P = Probability of Success (of winning price = 0.25) , R = Number of Success (1 price) , Q = Probability of failure (of not winning price = 0.75) ,
So, Probability = [tex]4 c 1 (0.25)^1 (0.75)^3[/tex]
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The probability of meeting a random person who has the same birthday as you is 1/365 , which is approximately 0.27%. What is the probability that it takes meeting more than 40 people before you meet someone who has the same birthday as you?
Answer:
89.6%
Step-by-step explanation:
The probability a random person shares your birthday is 1/365, or 0.27%. That means the probability that they don't share your birthday is 364/365, or 99.73%.
So the probability that you meet 40 people who don't share your birthday is:
P = (364/365)^40
P = 89.6%
The probability that it takes meeting more than 40 people before you meet someone who shares the same birthday as you is roughly 10.13% given that the probability of meeting a random person who has the same birthday as you is approximately 0.27%. This is calculated as the complement of the probability that we don't encounter a matching birthday in 40 people.
Explanation:The probability of meeting a random person who shares the same birthday as us is 1/365, approximately a 0.27% chance. Now, to calculate the probability that it requires meeting more than 40 people before finding someone who has the same birthday is essentially the complement of the probability that we find someone with the same birthday in 40 people or less.
We can start by calculating the probability of not meeting someone with the same birthday in one encounter which is 364/365 (approximately 0.9973). The probability that we don’t encounter a matching birthday in 40 people is (364/365)^40 (approximately 0.8987). Subsequently, The probability that it takes meeting more than 40 people before you meet someone who has the same birthday is the complement of this probability, which is 1 - 0.8987 = 0.1013 or approximately a 10.13% chance.
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A savings account is started with an initial deposit of $600. The account earns 2.1 % interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
Answer: it will take 14 years
Step-by-step explanation:
A savings account is started with an initial deposit of $600. This means that the principal P is
P = 600
It was compounded annually. This means that it was compounded once in a year. Therefore,
n = 1
The rate at which the principal was compounded is 2.1%. So
r = 2.1/100 = 0.021
The duration of time that for which the money stayed in the account is t years. So
Time = t
The formula for compound interest is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years. Therefore,
a) the equation to represent the amount of money in the account as a function of time in years would be
A = 600 (1+0.021/1)^1×t
A = 600 (1.021)^t
b) the amount of time it takes for the account balance to reach $800 would be
800 = 600 (1.021)^t
Dividing both sides of the equation by 600, it becomes
1.33 = (1.021)^t
t = 14
Lily and Elsa are both college students.Before mom gave them this months allowance lily had $750 and Elsa had &215.After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa.How much did mom give to each girl .
After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa. Thus mom gave $ 320 to each girl
Solution:
Given that Lily and Elsa are both college students
Before mom gave them this months allowance lily had $750 and Elsa had &215
Amount (in dollars) with Lily and Elsa already is given as:
amount with Lily = $ 750
amount with Elsa = $ 215
After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa
Let "x" be the equal amount of money which mom gave to Lily and Elsa
Now amount with Lily and Elsa after mom gave equal amount is:
amount with Lily = amount with Lily already + x
amount with Lily = 750 + x
amount with Elsa = amount with Elsa already + x
amount with Elsa = 215 + x
Given that lily had twice as much money as Elsa
Amount with lily = 2(amount with elsa)
750 + x = 2(215 + x)
750 + x = 430 + 2ax
2x - x = 750 - 430
x = 320
Therefore mom gave $ 320 to each girl
A bicycle store costs $1750 per month to operate. The store pays an average of $65 per bike. The average selling price of each bicycle is $115. How many bicycles must the store sell each month to break even?
Answer:
The store must sell 35 bikes to break even.
Step-by-step explanation:
115-65 = 50. 1750 divided by 50 = 35.
Answer:you must sell 35 bikes each month to break even
Step-by-step explanation:
The point at which you break even is the point when there is neither profit nor loss. It mean that
Revenue - cost = 0
Revenue = cost
The cost of operating the bicycle per month is $1750
The store pays an average of $65 per bike. Let x represent the number of bikes that the store gets in a month. The total cost of x bikes would be
1750 + 65x
The average selling price of each bicycle is $115. Total revenue from x bikes would be
115 × x = 115x
Therefore, to break even,
1750 + 65x = 115x
115x - 65x = 1750
50x = 1750
x = 1750/50 = 35
The quadratic equation 8x²+12x-14 has two real roots. What is the sum of the squares of these roots?
Answer:
The real roots are
[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]
The sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]
Step-by-step explanation:
The given quadratic equation is [tex]8x^2+12x-14[/tex] has two real roots.
To find the roots .
[tex]8x^2+12x-14=0[/tex]
Dividing the above equation by 2
[tex]\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}[/tex]
[tex]4x^2+6x-7=0[/tex]
For quadratic equation [tex]ax^2+bx+c=0[/tex] the solution is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Where a and b are coefficents of [tex]x^2[/tex] and x respectively, c is a constant.
For given quadratic equation
a=4, b=6, c=-7
[tex]x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}[/tex]
[tex]=\frac{-6\pm\sqrt{36+112}}{8}[/tex]
[tex]=\frac{-6\pm\sqrt{148}}{8}[/tex]
[tex]=\frac{-6\pm\sqrt{37\times 4}}{8}[/tex]
[tex]=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}[/tex]
[tex]=\frac{-6\pm\sqrt{37}\times 2}{8}[/tex]
[tex]=2\frac{(-3\pm\sqrt{37})}{8}[/tex]
[tex]=\frac{-3\pm\sqrt{37}}{4}[/tex]
[tex]x=\frac{(-3\pm\sqrt{37})}{4}[/tex]
The real roots are
[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]
Now to find the sum of the squares of these roots
[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}[/tex]
[tex]=\frac{-6}{4}[/tex]
[tex]=\frac{-3}{2}[/tex]
[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}[/tex]
Therefore the sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]
Liam uses 2 quarts of yellow paint and adds 3 1/4 Jars of blue paint.Evan uses 1/2 quarts of yellow paint and adds 5 1/2 of red paint.They end up with the same volume of paint.write an equation to show it.
Answer:
2 + (13/4)x = 1/2 + (11/2)y
Step-by-step explanation:
Let each jar of paint used by Liam be x
Let each jar of paint used by Evan be y.
Liam uses 2 quarts of yellow paints and adds 3 1/4 jars of blue paint. so we have
2 + 3 1/4x
= 2 + (13/4)x
Since Evan also uses 1/2 quarts of yellow paints and add 5 1/2 jar of red paint, we have
1/2 + 5 1/2y
= 1/2 + (11/2)y
Since they end up with the same volume of paint, we have
2 + (13/4)x = 1/2 + (11/2)y
Final answer:
The equation to show that Liam and Evan end up with the same volume of paint, considering all quantities are in quarts, is 2 + 3.25 = 0.5 + 5.5.
Explanation:
To solve the problem where Liam and Evan end up with the same volume of paint, we can write an equation that sets the total volume of paint used by each person equal to each other. Since Liam uses 2 quarts of yellow paint and adds 3 1/4 (which is equivalent to 3.25) jars of blue paint and Evan uses 1/2 quart of yellow paint and adds 5 1/2 (equal to 5.5) jars of red paint, the equation comparing their total amounts of paint in quarts can be written as:
2 + 3.25 = 0.5 + 5.5
Before writing this equation, we need to ensure that both expressions represent quantities in the same unit. We confirm that all the amounts are given in quarts, so there is no need to convert units in this case. The equation illustrates that the total volume of paint used by Liam and Evan is equal.
Johnny has 7 different colored marbles in his bag. In how many ways can he choose three different marbles from his bag to play a game?
Answer:
35
Step-by-step explanation:
Use the combination formula:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
Substitute known values:
[tex]C(7,3)=\frac{7!}{3!(7-3)!}=35[/tex]
We don't use the permutation formula since the order of the drawn marbles does not matter.
Answer: 35
Step-by-step explanation:
He can choose 3 marbles from 7 distinct marbles in (7/3) ways
C(7/3) = 7!/(3!-(7-3)!)
= 7*6*5*4/4*3*2
= 35
Say you flip a coin seven times. What is the probability the number of heads will be even?
Answer:
The probability the number of heads will be even is 0.4922.
Step-by-step explanation:
Consider the provided information.
It is given that coin flip seven times.
Thus, the total number of possible outcomes are: [tex]2^7[/tex]
We want heads will be even.
Even numbers are 2, 4, 6.....
Thus, the possible case are: 2 heads, 4 heads or 6 heads.
The required probability is:
[tex](^7C_2+^7C_4+^7C_6)\times\frac{1}{2^7}=\left(\frac{7!}{2!5!}+\frac{7!}{4!3!}+\frac{7!}{6!1!}\right)\frac{1}{128}\approx 0.4922[/tex]
Hence, the probability the number of heads will be even is 0.4922.
There are 42 boys in the six grade the number of girls in the six grade is 56 Emma says the ratio of boys to the number of girls in the six grade is 5:6 is Emma correct
Answer:
no
Step-by-step explanation:
The ratio is ...
boys : girls = 42 : 56 = (14·3) : (14·4) = 3 : 4 . . . . not 5:6
Emma is not correct.
The length of a rectangle is 3 m less than the diagonal and the width is 8 m less than the diagonal. If the area is 74 m^2, how long is the diagonal in meters? Round your answer to the nearest tenth.
Answer:
14.5 m
Step-by-step explanation:
Let x represent the length of the diagonal. Then the length of the rectangle is (x-3) and its width is (x-8). The area is the product of these, so is ...
(x -3)(x -8) = 74
x^2 -11x +24 = 74 . . . . eliminate parentheses
x^2 -11x = 50 . . . . . . . .subtract 24
x^2 -11x +30.25 = 80.25 . . . . add 30.25 to complete the square
(x -5.5)^2 = 80.25 . . . . . . write as square
x - 5.5 = √80.25 ≈ 8.958 . . . . take the square root
x = 8.958 + 5.5 = 14.458 . . . . .add 5.5
The length of the diagonal is about 14.5 meters.
Answer:
Step-by-step explanation:
The diagram of the rectangle, ABCD is shown in the attached photo. The diagonal of the rectangle forms a triangle, ABC
Applying Pythagoras theorem,
d^2 = (d - 8)^2 + (d - 3 )^2
d^2 = d^2 - 16d + 64 + d^2 - 6d + 9
d^2 = 2d^2 - 22d + 73
d^2 - 22d + 73 = 0
d^2 = 22d - 73 - - - - - - 1
If the area is 74 m^2, it means that
(d- 8)(d- 3) = 74
d^2 - 11d + 24 = 74
d^2 = 74 - 24 + 11d
d^2 = 50 + 11d - - - - - - - -2
Equating equation 1 and 2, it becomes
22d - 73 = 50 + 11d
22d - 11d = 50 + 73
11d = 123
d = 123/11 = 11.182
diagonal = 11.2 m to the nearest tenth.
What would be added to the price of a $22,500 car if the DMV fees for title and license were 1.5%?
A. $3,375
B. $337.50
C. $450
D. $22,837.50
Answer:
B. $337.50
Step-by-step explanation:
1.5% of $22,500 is 337.5
Answer:
B. $337.50
Step-by-step explanation:
The amount of fluid excreted as urine each day averages approximately less than how many liters?
Answer: Averages less than 2litres per day
Step-by-step explanation:
The normal range of urine excreted per day is between 1 to 2 litres, but the kidney must produce a minimum urine volume of 500mL per day, to get rid of body waste, anything below that is abnormal, and not good for the body
The researcher has limited resources. He sends 9 emails from a Latino name, and 14 emails from a non-Latino name. For the Latino names, the mean response time was 421 minutes (standard deviation of 82 minutes). For the non-Latino names, it was 366 minutes (standard deviation of 101 minutes). Calculate the standard error for the difference in means.
Answer: 38.41 minutes
Step-by-step explanation:
The standard error for the difference in means is given by :-
[tex]SE.=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma^2_2}{n_2}}[/tex]
where , [tex]\sigma_1[/tex] = Standard deviation for sample 1.
[tex]n_1[/tex]= Size of sample 1.
[tex]\sigma_2[/tex] = Standard deviation for sample 2.
[tex]n_2[/tex]= Size of sample 2.
Let the sample of Latino name is first and non -Latino is second.
As per given , we have
[tex]\sigma_1=82[/tex]
[tex]n_1=9[/tex]
[tex]\sigma_2=101[/tex]
[tex]n_2=14[/tex]
The standard error for the difference in means will be :
[tex]SE.=\sqrt{\dfrac{(82)^2}{9}+\dfrac{(101)^2}{14}}[/tex]
[tex]SE.=\sqrt{\dfrac{6724}{9}+\dfrac{10201}{14}}[/tex]
[tex]SE.=\sqrt{747.111111111+728.642857143}[/tex]
[tex]SE.=\sqrt{1475.75396825}=38.4155433158\approx38.41[/tex]
Hence, the standard error for the difference in means =38.41 minutes
A virus takes 8 days to double its original population (A=2A0). How long will it take to quadruple its population? Round to the nearest tenth.
Answer:
It takes 16 days to quadruple its population.
Step-by-step explanation:
The population of the virus can be represented by the following exponential function.
[tex]A(t) = A_{0}e^{rt}[/tex]
In which A(t) is the population after t days, [tex]A_{0}[/tex] is the initial population and r is the growth rate.
In this problem, we have that:
[tex]A(8) = 2A_{0}[/tex]
So, we use this to find the value of r.
[tex]A(t) = A_{0}e^{rt}[/tex]
[tex]2A_{0} = A_{0}e^{8r}[/tex]
[tex]e^{8r} = 2[/tex]
Applying ln to both sides
[tex]8r = 0.6931[/tex]
[tex]r = 0.0867[/tex]
How long will it take to quadruple its population?
This is t when [tex]A(t) = 4A_{0}[/tex]
[tex]A(t) = A_{0}e^{rt}[/tex]
[tex]4A_{0} = A_{0}e^{0.0867t}[/tex]
[tex]e^{0.0867t} = 4[/tex]
Again we apply ln to both sides.
[tex]0.0867t = 1.39[/tex]
[tex]t = 16[/tex]
It takes 16 days to quadruple its population.
The number of days it takes to quadruple it's population is; 16days
According to the question;
The virus takes 8 days to double it's original population.Therefore;
8days = 2A.
We are required to determine how long it will take to quadruple it's population;
Let no. of days required = x days.
8days =======2A x days =======4ABy cross multiplication; we have;
2Ax = 32ABy dividing through by 2A; we have;
x = 16 days.Read more:
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If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?(1) |x| = y = 10(2) x = |y| = 10
Answer:
[tex]10|y|[/tex]
Step-by-step explanation:
We have been given that the vertices of a triangle are A (5, 0), B (x, y) and C (25, 0). We are asked to find the area of the given triangle.
We will use area formula for triangle with vertices A, B and C as given below:
[tex]|\frac{A_x(B_y-C_y)+B_x(C_y-A_y)+C_x(A_y-B_y)}{2}|[/tex]
Upon substituting the given coordinates of points A, B and C in above formula, we will get:
[tex]|\frac{5(y-0)+x(0-0)+25(0-y)}{2}|[/tex]
[tex]|\frac{5(y)+x(0)+25(-y)}{2}|[/tex]
[tex]|\frac{5y+0-25y}{2}|[/tex]
[tex]|\frac{-20y}{2}|[/tex]
[tex]|-10y|[/tex]
[tex]10|y|[/tex]
Therefore, the area of the given triangle would be [tex]10|y|[/tex].
You purchase 26 parking hours that you can use the next month to park your food truck at the fair. Weekday hours park $2 per hour and weekend hours cost $10 per hour. You spend a total of $220. How many week day hours did you purchase.
Answer:
Number of week day hours purchased is 5
Step-by-step explanation:
Total number of Parking hours purchased = 26 parking hours
Parking cost on weekdays = $2 per hour
Parking costs on weekends = $10 per hour
Total amount spent on parking = $220.
To Find:
Number of week days purchased = ?
Solution:
Let
The number of week days purchased be x
The number of weekends purchased be y
We know that the total hours purchased is 26
So,
x+y = 26
y = 26-x------------------------------------------------------(1)
Now the total cost is 220
(Total number of weekdays X cost per weekday ) +(Total number of weekends + cost per weekend) =220
Substituting the values
=>[tex]x\times 2 + y \times 10[/tex] = 220
=>[tex]x \times 2 + (26-x) \times 10 =220[/tex]
=>2x + 260 -10x =220
=>260 -8x = 220
=>260 -220 =8x
=>40 = 8x
=>x=[tex]\frac{40}{8}[/tex]
x= 5-------------------------------------------(2)
Now substituting (2) in (1) we get
y= 26-5
y= 21
First two need to be answered and last two need to be checked. (If you don’t see the attachments wait..)
Answer:
∠PQR measures 40°x = 7They form concentric circlesYes, according to the triangle inequalityStep-by-step explanation:
1. ∠PQR is an alternate interior angle with the one marked 40°, so it has the measure 40°.
∠PRQ is an alternate interior angle with the one marked 60°, so it has the measure 60°.
Among the answer choices, the one describing ∠PQR as 40° is the only correct one.
__
2. ∠BAD = 2×∠BAE
130 = 2(9x + 2) . . . substitute the given expressions
65 = 9x + 2 . . . . . divide by 2
63 = 9x . . . . . . . . .subtract 2
7 = x . . . . . . . . . . . .divide by 9
__
3. Think again. Anything being rotated follows a circular path. Circular paths with different radii and the same center are concentric circles.
Straight lines connecting the pre-image and image points will be parallel (and different lengths), but the question is concerned with paths, not endpoints.
Why the path is described as "concentric circles," we're not sure. The path for a 90° rotation will be a 90° arc. It is perfectly reasonable to describe the paths of the two points as concentric arcs, rather than concentric circles. See the attachment.
__
4. Correct. The triangle inequality requires the sum of the two shortest side lengths exceed the longest side length. Here, that means 2+5 > 5 (true). The "toothpicks" meet the requirements of the triangle inequality, so will make a triangle.
The "triangle sum theorem" has to do with angles, not side lengths.
A football team plays in a large stadium. With a ticket price of $19, the average attendance at recent games has been 50 comma 000. A market survey indicates that for each $1 increase in the ticket price, attendance decreases by 300. a. Express the number of spectators at a football game, N, as a function of the ticket price, x. b. Express the revenue from a football game, R, as a function of the ticket price, x.
Answer:
Part 1: N(x) = 50,000 - 300(x-19)
Part 2: R(x) =-300x² + 55700x
Step-by-step explanation:
Given,
The original price of each ticket = $ 19,
The original attendance = 50,000
Part 1 :
∵ For the each $1 increase in the ticket price, attendance decreases by 300.
Let x represents the price of each ticket after increment,
Thus, if price increment = (x-19) dollars,
New attendance, N(x) = 50,000 - 300(x-19)
Part 2 :
Since, revenue = price of each ticket × attendance
Thus, the revenue from the football game,
R(x) = x(50,000 - 300(x-19))
R(x) = 50000x - 300x²+ 5700x
⇒ R(x) =-300x² + 55700x
A vegetable garden and it's around a pasta shaped like a square that together are 12 ft wide. A path is 1 feet wide. If one bag of gravel covers 9 square feet, how many bags are needed to cover the path? Round your answers to the nearest tenth.
The overall width of the path and garden is 12 feet.
The area of the entire garden and path is 12 x 12 = 144 square feet.
The path is 1 foot wide, so the garden would be 12 - 2 = 20 feet wide.
The area of the garden only would be 10 x 10 = 100 square feet.
The area of the path only = 144 - 100 = 44 square feet.
1 bag covers 9 square feet:
44 / 9 = 4.88
You would need 5 bags.
A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he takes from a container of orange juice, he pours one cup of water back into the container. If he completes this process three times on the same container of juice, the resulting mixture will be exactly 50% water and 50% juice. How many cups of orange juice were originally in the container. (P.S ITS NOT 6)
Answer:
x=4.8473 cups
Step-by-step explanation:
Concentration of Liquids
It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by
[tex]\displaystyle C=\frac{x}{y}[/tex]
It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.
Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is
x-1 cups of juice.
The new concentration is
[tex]\displaystyle \frac{x-1}{x}[/tex]
The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is
[tex]\displaystyle x-1-\frac{x-1}{x}[/tex] cups of juice.
Simplifying, the cups of juice are
[tex]\displaystyle \frac{\left (x-1\right)^2}{x}[/tex]
The new concentration is
[tex]\displaystyle \frac{\left (x-1\right)^2}{x^2}[/tex]
For the third time, we now have
[tex]\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2}[/tex] cups of juice.
Simplifying, the final amount of juice is
[tex]\displaystyle \frac{\left (x-1\right)^3}{x^2}[/tex]
And the final concentration is
[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}[/tex]
According to the conditions of the question, this must be equal to 50% (0.5)
[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5[/tex]
Taking cubic roots
[tex]\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}[/tex]
[tex]\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}[/tex]
Operating and joining like terms
[tex]\displaystyle x-\sqrt[3]{0.5}\ x=1[/tex]
Solving for x
[tex]\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}[/tex]
[tex]x=4.8473\ cups[/tex]
Let's test our result
Final concentration:
[tex]\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5[/tex]
A certain drug dosage calls for 460 mg per kg per day and is divided into four doses (1 every 6 hours). If a person weighs 229 pounds, how many milligrams of the drug should he receive every 6 hours?
Final answer:
For a 229-pound individual, they should receive approximately 11947 mg of the drug every 6 hours.
Explanation:
The student is asking how to calculate the appropriate dosage of a medication based on a person's weight. Specifically, the problem is determining how many milligrams of a drug should be administered every 6 hours when the dosage calls for 460 mg per kg per day and the person weighs 229 pounds.
First, we convert the person's weight from pounds to kilograms, knowing that 1 pound is approximately 0.453592 kg. So, 229 pounds is equal to 229 × 0.453592 kg = 103.890648 kg.
Next, we calculate the daily dosage in milligrams using the provided dosage requirement of 460 mg per kg per day:
103.890648 kg × 460 mg/kg = 47789.09808 mg per day.
Since the medication is divided into four doses, we divide the daily total by 4 to find the amount per dose:
47789.09808 mg ÷ 4 = 11947.27452 mg per dose.
Therefore, the individual should receive approximately 11947 mg of the drug every 6 hours.
A manufacturing process produces a critical part of average length 120 millimeters, with a standard deviation of 3 millimeters. All parts deviating by more than 5 millimeters from the mean must be rejected. What percentage of the parts must be rejected, on average? Assume a normal distribution.
Answer:
9.692%
Step-by-step explanation:
We have been given that a manufacturing process produces a critical part of average length 120 millimeters, with a standard deviation of 3 millimeters. All parts deviating by more than 5 millimeters from the mean must be rejected.
5 millimeters below mean would be [tex]115[/tex] and 5 millimeters above mean would be [tex]125[/tex].
Corresponding z values for 115 and 125 would be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{115-120}{3}[/tex]
[tex]z=\frac{-5}{3}[/tex]
[tex]z=-\frac{5}{3}[/tex]
[tex]z=\frac{125-120}{3}[/tex]
[tex]z=\frac{5}{3}[/tex]
Now, we need to find [tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})[/tex] using normal distribution table.
[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=P(z<-1.66)+P(z>1.66)[/tex]
We know that [tex]P(z>1.66)=1-P(z<1.66)[/tex].
[tex]P(z>1.66)=1-0.95154 [/tex]
[tex]P(z>1.66)=0.04846[/tex]
[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=0.04846+0.04846[/tex]
[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=0.09692[/tex]
Now, we need to convert 0.09692 into percentage as:
[tex]0.09692\times 100\%=9.692\%[/tex]
Therefore, 9.692% of parts must be rejected on average.
About 0% of the parts would be rejected, on average.
Z scoreThe z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ) / σ
where μ is the mean, x = raw score and σ is the standard deviation.
Given μ = 120, σ = 3. For z > 5:
P(z > 5) = 1 - P(z < -38.3) = 1 - 1 = 1 = 0%
About 0% of the parts would be rejected, on average.
Find out more on Z score at: https://brainly.com/question/25638875
If [x] denotes the least integer greater than or equal to x and [x/2] = 0, which of the following could be the value of x?A. -2B. -3/2C. 1/2D. 1E. 2
Answer:
B) -3/2
Step-by-step explanation:
If [x/2]=0 then x/2 is a number such that the least integer greater than or equal to x/2 is 0. We can rewrite this as the inequality x/2≤0. Then, the value of x in C, D and E is wrong because they are positive numbers, then x/2 would be a positive number which contradicts this inequality.
Now, 0 is the least integer that satisfies this inequality, therefore we cannot have that x/2≤-1 since -1 is an integer and -1<0. Then x/2>-1. This discards A as wrong, because for x=-2, x/2=-1, contrary to x/2>-1.
Thus B is the right answer. To verify, if x=-3/2, then x/2=-3/4 and we have that -1<-3/4≤0 as required.
In Mathopolis, an adult is a person 21 years of age or older and a child is a person under 21 years of age. Exactly half of the adults in Mathopolis are female, and exactly half of the female adults have exactly one biological child. Nobody else has a child, and there are no other children. What percent of the people of Mathopolis are children?
Answer:
20%
Step-by-step explanation:
If there are 4 adults, 2 are female, and 1 of those has 1 child. Then the population is 4 adults and 1 child. The children make up 1/5 = 20% of the population.
Answer
20%
Step-by-step explanation:
Aops Question
The formula to determine energy is uppercase E = one-half m v squared. What is the formula solved for v?
Answer:
Step-by-step explanation:
[tex]E=\frac{1}{2}mv^2[/tex]
All the variables on the right are being multiplied together then the whole mess is being divided by 2. Let's get rid of the 2 first. The undoing of division is multiplication, so we will begin by multiplying both sides by 2 to get
[tex]2E=mv^2[/tex]
Next we will move the m. The undoing of multiplication is division. So we divide both sides by m to get
[tex]\frac{2E}{m}=v^2[/tex]
The undoing of a square is to take the square root, so we will do that to both sides giving us, finally
[tex]\sqrt{\frac{2E}{m} }=v[/tex]
Answer:
d
Step-by-step explanation:
A collection of dimes and quarters is worth $9.55. If the quarters were dimes and the dimes were quarters, the total value would be 7.60. Find the number of each coin.
Number of dimes are 18 and number of quarters are 31
Solution:
Let "d" be the number of dimes
Let "q" be the number of quarters
value of 1 dime = $ 0.10
value of 1 quarter = $ 0.25
A collection of dimes and quarters is worth $9.55
value of 1 dime x number of dimes + value of 1 dime x number of quarters = 9.55
0.10d + 0.25q = 9.55 ---------- eqn 1
If the quarters were dimes and the dimes were quarters, the total value would be 7.60
quarters were dimes means , q = d
dimes were quarters means d = q
0.25d + 0.10q = 7.60 ----- eqn 2
Let us solve eqn 1 and eqn 2 to find "d" and "q"
Multiply eqn 1 by 2.5
0.25d + 0.625q = 23.875 ---- eqn 3
Subtract eqn 2 from eqn 3
0.25d + 0.625q = 23.875
0.25d + 0.10q = 7.60
( - ) ----------------------
0.525q = 16.275
q = 31
Substitute q = 31 in eqn 1
0.10d + 0.25q = 9.55
0.10d + 0.25(31) = 9.55
0.10d + 7.75 = 9.55
0.10d = 1.8
d = 18
Thus dimes are 18 and number of quarters are 31
Answer:
i needed the answer to this too!! have a good life
Find the area of the shaded region of the circle. Round to the nearest hundredth.
160.78
615.75
547.62
454.97
Answer:Area of shaded region is 454.97
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area of circle = πr^2
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
r = 14
Area of the circle = 3.14 × 14^2 = 615.44
The shaded area is a sector
Area of a sector is expressed as
Area = #/360 × πr^2
Where
# = 94 = central angle
Area of sector = 94/360 × 3.14 × 14
= 160.68
Area of shaded region would be
615.44 - 160.68
= 454.97
Answer:
454.97 unit^2.
Step-by-step explanation:
The area of the whole circle = pi r^2
= 14^2 pi.
As there are 360 degrees in a circle the area of the shaded region , by proportion = [ (360 - 94) / 360 ] * 14^2 pi
= 454.972 unit^2.
There is a 0.9991 probability that a randomly selected 31-year-old male lives through the year. A life insurance company charges $166 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $90 comma 000 as a death benefit. Complete parts (a) through (c) below.
a. From the perspective of the 31-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If the 31-year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why?
Answer:
a) Monetary values corresponding to the two events are:
-In case of surviving the year = -166$
-In case of a death in the year = 89834$
b) Expected value of the purchasing the insurance is -85 $
c) Yes, insurance company can make a profit with this policy.
Step-by-step explanation:
a) The man need to pay 166$ first to enroll the insurance policy. If he survives within a year, he will lose 166$. Otherwise, if he dies within a year he will profit 89834$.
b) Expected value of the purchasing the insurance as following:
-In case of surviving the year:
Value: -166$
Probability: 0,9991
-In case of death in a year
Value: 89834$
Probability: 0,0009
Expected value is E(x) = -166×0,9991 + 89834×0,0009 = -85 $
c) Lets consider that 10000 different 31 year old man enrolled to this insurance policy. According to probability of death, 9 out of 10000 man expected to be dead within the year. Therefore, company need to pay 9*90000 = 810000$ to their costumers. But, company will collect 10000*166=1660000$ from their costumers in the beginning of the year
So, it is expected that company is going to profit 1660000-810000=850000$ per year.
The monetary values corresponding to surviving or not surviving for a 31-year-old male are $166 and $90,000 respectively. The expected value for the male purchasing the policy is $83.75. The insurance company can expect to make a profit from many such policies.
Explanation:a. From the perspective of the 31-year-old male, the monetary value of surviving the year is $166 (the cost of the insurance). The monetary value of not surviving is $90,000 (the death benefit).
b. To find the expected value, we multiply the probability of each outcome by its corresponding monetary value and sum them. The expected value is calculated as: (0.9991 * $166) + (0.0009 * (-$90,000)) = $164.75 + (-$81) = $83.75.
c. The insurance company can expect to make a profit from many such policies. This is because the expected value for the 31-year-old male is positive ($83.75), meaning that on average the insurance company will earn more in premiums than it pays out in benefits.
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Which of the following inequalities matches the graph below?
(A) The correct inequality is not listed.
(B) 5x + y ≥ 1
(C) 5x + y ≤ 1
(D) 5x − y ≥ 1
Answer:
The answer to your question is letter A
Step-by-step explanation:
Process
1.- Find two points of the line
A (1, 4) B ( -1, 5)
2.- Find the slope of the line
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{-5 - 4}{-1 - 1}[/tex]
[tex]m = \frac{-9}{-2} = \frac{9}{2}[/tex]
3.- Find the equation of the line
y - y1 = m(x - x1)
y - 4 = 9/2(x - 1)
2y - 8 = 9x - 9
9x - 2y = - 9 + 8
9x - 2y = - 1
4.- Convert the equation to a inequality,
9x - 2y ≤ -1