Answer:
0.2288
Step-by-step explanation:
This is straightforward.
What we need to do is to divide the number of defective semiconductor chips over the total number of semiconductor chips.
Initially, the total number of semi conductor chips is 119 and the total number of defective semiconductor chips is 28.
After the first selections , we can infer that the total number of semiconductor chips is 118 while the number of defective ones is 27.
Hence on the second drawing, the probability that he will
Select a defective one is 27/118
Camilo estimates the weight of the dog . The veterinarian says that the dog weighs 84 pounds . The percent error in Camillo's estimate is less than 10%
Answer:
The estimated weight is in the range:
75.6 pounds [tex]\leq[/tex] Weight [tex]\leq[/tex] 92.4 pounds
Step-by-step explanation:
Since, the maximum error is 10%.
Therefore, the maximum and minimum vales will be 10% more and 10% less than 84 pounds, respectively.
For Maximum Limit:
[tex]Weight_{max}[/tex] = (1.1)(84 pounds)
[tex]Weight_{max}[/tex] = 92.4 pounds
For Minimum Limit:
[tex]Weight_{min}[/tex] = (0.9)(84 pounds)
[tex]Weight_{min}[/tex] = 75.6 pounds
Hence, the estimated weight is in the range:
75.6 pounds [tex]\leq[/tex] Weight [tex]\leq[/tex] 92.4 pounds
For a birthday party Mr. Perkins or do you eat chocolate chip cookies and 16 sugar cookies each cookie is the same price he also picks up a cupcake for himself which cost two dollars and $75 the total bill is $44.03 what is the cause of a cookie
Question is not proper, Proper question is given below;
For a birthday party, Mr. Perkins orders 8 chocolate chip cookies and 16 sugar cookies. Each cookie is the same price. He also picks up a cupcake for himself, which costs $2.75. The total bill is $44.03. What is the cost of a cookie?
Answer:
The Cost of the cookie will be $1.72.
Step-by-step explanation:
Given:
Mr Perkins orders 8 chocolate chip cookies and 16 sugar cookies.
Since cost of both the cookies are same then Let us assume the cost of cookies be 'x'.
Total cost of the cookies = [tex](8 + 16)x = 24x[/tex]
Cost of Cup cakes = $2.75.
Total bill he pays = $44.03
We need to find the cost of each cookies.
Now we know that Total bill he pays is equal to sum of Cost of cookies and Cost of Cup cakes he bought.
Framing in equation form we get;
[tex]44.03 = 24x + 2.75[/tex]
Now Subtracting both side by 2.75 using Subtraction property we get;
[tex]2.75+24x-2.75 = 44.03 - 2.75\\\\24x = 41.28[/tex]
Now Dividing both side by 24 using Division property we get;
[tex]\frac{24x}{24} = \frac{41.28}{24}\\\\x=1.72[/tex]
Hence The Cost of the cookie will be $1.72.
I NEED THE ANSWERS TO THIS QUESTION AS SOON AS POSSIBLE CHECKING UP ON BEHIND SCHOOL WORK THANK YOU
Answer:
See all four answers with their explanation below and the graph attached.The green arrow on the number line is the solution of the inequality.Explanation:
a). Description of what Brian did wrong.
Brian did not solve the inequality correctly. It seems he made several wrong steps:
He added up 2 and 3 to get 5, which is wrong because 2 and 3 are in opposite sides of the inequalityHe use the symbol <, which is wrong because there is a negative sing in front of the varialbe (x) which changes the symbol to >.b). Your work solving the inequality:
Subtract 2 from both sides:- x < 3 - 2
-x < 1
Muliply both sides by - 1, which changes the symbol < to >:x > - 1
Then the solution of the inequality is all the real numbers greater than - 1.
c). The correct solution graphed on a number line
Since the number - 1 is not included in the solution set of the inequality you must use an oper circle around the number - 1 on the number line.Since the solution set is all the numbers greater than - 1 you draw an arrow pointing to the right of the number - 1 on the number line.See the correct graph in the diagram attached. The green line on the number line is the solution to the inequality.d). The correct solution in set notation.
Three valid forms indicating the solution in set notation are:
{x: > - 1}, which is read x such that x is greater than - 1{x | x > - 1}, which is read x such that x is greater than - 1{x ∈ R | x > - 1}, which is read, x belonging to real numbers, such that x is greater than - 1.Both the colon (:) and the straight bar (|) mean "such that".
The Williams family wants to cover one wall in their living room with 1-foot square mirror tiles. The wall measures 8 feet by 10 feet. How many mirror tiles will they need to cover the wall?
Answer:80 mirror tiles will be needed to cover the wall is 80
Step-by-step explanation:
The dimension of one wall in living room is 8 feet by 10 feet. The wall is rectangular in shape. The area of a rectangle is expressed as
Length × width. The area of one wall in the living room would be
8 × 10 = 80 feet^2
The Williams family wants to cover one wall in their living room with 1-foot square mirror tiles.
The number of mirror tiles that they will need to cover the wall would be
80/1 = 80 mirror tiles.
The Williams family will need 80 mirror tiles to cover the wall.
The Williams family wants to cover one wall in their living room with 1-foot square mirror tiles. The wall measures 8 feet by 10 feet. To find out how many mirror tiles are needed, we calculate the area of the wall using the formula for area:
Area = length × width
Substituting the given measurements:
Area = 8 feet × 10 feet = 80 square feet
Since each mirror tile covers 1 square foot, the number of mirror tiles required is equal to the area of the wall:
Number of mirror tiles = 80
Therefore, the Williams family will need 80 mirror tiles to cover the wall.
A farmer grows 196 pounds of potatoes. He sells them to a grocer who divides them into 5 pound and 2-pound bags. If the grocer uses the same number of 5 and 2-pound bags, how many bags of each did he use?
Answer:The number of the 2- pound bags is 56 and the number of the 5- pound bags is 140
Step-by-step explanation:
Let the number of the 2- pound bags and the 5- pound bags be n since they used the same number.
5n + 2n = 196
7n=196
n= 196/7
n= 28
Therefore the number of the 2- pound bags is 2× 28= 56
and the number if the 5- pound bags is 5×28= 140
How many positive integers less than 10,000 are such that the product of their digits is 210?A. 24
B. 30
C. 48
D. 54
E. 72
Answer:
correct option is D. 54
Step-by-step explanation:
given data
product of digits = 210
integers = 10000
to find out
How many positive integers less than 10,000
solution
we know product of digits 210 are = 1 × 2× 3×5×7
210 = 1 × 6 × 5 × 7
here 2 × 3 = 6 ( only single digit )
here 4 digit numbers with combinations of the digits are = {1,6,5,7} and {2,3,5,7}
3 digit numbers with combinations of digits are = {6,5,7}
and product of their digits = 210
so combination will be
combinations of {1,6,5,7} is 4! = 4 × 3 × 2 × 1 = 24
combinations of {2,3,5,7} is 4! = 4 × 3 × 2 × 1 = 24
combinations of {6,5,7} is 3! = 3 × 2 × 1 = 6
so total is = 24 + 24 + 6
total is = 54
so correct option is D. 54
Purchasing a movie combo pack of one popcorn and two drinks from $14 saves $4 compared to purchasing the items individually. If a drink is $5' what is the individual cost of a popcorn
Answer:
the individual price of a popcorn is $8.
Step-by-step explanation:
p+2d=14 is the price with deal
p+2d=14+4 if there was no deal
plug 5 into the equation as d
2(5)+p=18
solve for p.
p=8
YOU GUYS GET NO MOM GET MO DAD GET MO GRANDMA GET NO GRANDPA GET NO CAR GET MO HOUSE…..your mom
NEED HELP NOW 30 POINTS. Which number is closest to square root of 57? 7.8 7.5 8.5 6.7
√57 = 7.549
Round to 7.5
Answer:
7.5
Step-by-step explanation:
7.549
A person rolls a standard six-sided die 9 times. In how many ways can he get 3 fours, 5 sixes, and 1 two?
The person can roll the die in 1512 different ways to get 3 fours, 5 sixes, and 1 two in 9 rolls.
Explanation:When rolling a standard six-sided die, there are 6 possible outcomes for each roll. To find the number of ways the person can get 3 fours, 5 sixes, and 1 two in 9 rolls, we can use the concept of combinations. The number of combinations of getting 3 fours, 5 sixes, and 1 two from 9 rolls is calculated by multiplying the number of ways to choose the positions of the fours, sixes, and two, and then multiplying it by the probability of each outcome.
To calculate this, we can use the formula for combinations:
C(n, r) = n! / ((n - r)! x r!)
Using this formula, we can find the number of ways to choose the positions of the fours, sixes, and two:
Number of ways to choose the positions of the fours: C(9, 3) = 9! / ((9 - 3)! x3!) = 84Number of ways to choose the positions of the sixes: C(6, 5) = 6! / ((6 - 5)! x 5!) = 6Number of ways to choose the positions of the two: C(3, 1) = 3! / ((3 - 1)! x 1!) = 3Finally, we can multiply these numbers together to find the total number of ways:
Total number of ways = 84 x 6 x 3 = 1512
Learn more about Combinations here:https://brainly.com/question/24703398
#SPJ3
Kelly drove north for 9 miles and then east for 12 miles at an average rate of 42 miles per hour to arrive at the town of Prime. Brenda left from the same location, at the same time, and drove along a straight road to Prime at an average rate of 45 miles per hour. How many minutes earlier than Kelly did Brenda arrive?
Answer:
Step-by-step explanation:
This is one of the more interesting motion problems I've seen. I like it! If Kelly is driving north (straight up) for 9 miles, then turns east (right) and drives for 12 miles, what we have there are 2 sides of a right triangle. The hypotenuse is created by Brenda's trip, which originated from the same starting point as Kelly and went straight to the destination, no turns. We need the distance formula to solve this problem, so that means we need to find the distance that Brenda drove. Using Pythagorean's Theorem:
[tex]9^2+12^2=c^2[/tex] and
[tex]81+144=c^2[/tex] and
[tex]225=c^2[/tex] so
c = 15.
Brenda drove 15 miles. Now we can fill in a table with the info:
d = r x t
Kelly 12+9 42 t
Brenda 15 45 t
Because they both left at the same time, t represents that same time, whatever that time is. That's our unknown.
If d = rt, then for Kelly:
21 = 42t
For Brenda
15 = 45t
Solve Kelly's equation for t to get
t = 1/2 hr or 30 minutes
Solve Brenda's equations for t to get
t = 1/3 hr or 20 minutes
That means that Brenda arrived at the destination 10 minutes sooner than Kelly.
Need help with two questions please
Answer:
Question 1
since triangles are similar
angle B = angle D
8x + 16 = 120
x = 13
Question 2
Ttiangles are similar
therefore, sides are in ratio
AB ÷ XY = BC ÷ YZ = AC ÷ XZ
substituting all values we get
BC = 22
BC = 22AC = 16
There are black, blue, and white marbles in a bag. The probability of choosing a black marble is 0.36. The probability of choosing a black and then a white marble is 0.27. To the nearest hundredth, what is the probability of the second marble being white if the first marble chosen is black?
a) 0.27
b) 0.39
c) 0.75
d) 0.86
Answer: c) 0.75
Step-by-step explanation:
Given : The probability of choosing a black marble is P(Black)= 0.36.
The probability of choosing a black and then a white marble is P( Black and white) = 0.27.
Then by conditional probability ,
The probability of the second marble being white if the first marble chosen is black = [tex]P(\text{white }|\text{Black})=\dfrac{\text{P( Black and white)}}{\text{P(Black}}[/tex]
[tex]=\dfrac{0.27}{0.36}=\dfrac{27}{36}=0.75[/tex]
Therefore , the probability of the second marble being white if the first marble chosen is black = 0.75
Final answer:
The probability of the second marble being white given that the first marble is black is calculated using conditional probability. By dividing the joint probability of choosing a black and then a white marble (0.27) by the probability of choosing a black marble (0.36), we find that the probability is 0.75.
Explanation:
The question asks to find the probability of the second marble being white given that the first marble chosen is black. The probability of choosing a black marble is given as 0.36, and the probability of choosing a black and then a white marble is 0.27. To find the probability of choosing a white marble after a black one, we use the concept of conditional probability, given by:
P(White | Black) = P(Black and White) / P(Black)
Here P(White | Black) is the probability of the second marble being white given that the first marble is black, P(Black and White) is the probability of choosing a black marble and then a white marble, and P(Black) is the probability of choosing a black marble. Substituting the given values:
P(White | Black) = 0.27 / 0.36 = 0.75
This means that the probability of the second marble being white, given that the first marble chosen is black, is 0.75, which corresponds to option (c) in the provided selections.
A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement. a) What is the probability that both balls are white? (Answer may be left as a fraction or as a three-place decimal.) b) What is the probability that both balls are the same color? (Answer may be left as a fraction or as a three-place decimal.)
The probabilities are (a) the probability that both balls are white is 0.058 and (b) the probability that both balls are the same color is 1.904.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement.
Total number of balls : 6+4+3 +1 = 13
(a)
Out of 13 balls,
3 are white, so probability of getting first white ball is,
P(first white) = 3/13
After that 12 balls remaining out of which 3 are white so
P(second white| first white) = 3/12
So required probability is
P(both white) = P(Second white| first white)P(first white) = (3/13) x (3/12) = 0.0576 = 0.058
(b)
Since there is only one green ball, so both balls cannot be same. Therefore,
P(both of same color) = P(both blue)+P(both red)+P(both white) = 0.923+ 0.923+ 0.058= 1.904
The probability that both balls of same color is
P(both of same colors) = 1.904
Therefore, the probabilities are (a) 0.058 and (b) 1.904
To learn more about the probability;
brainly.com/question/11234923
#SPJ5
Kanna Kamui let her DS charge for 108 minutes from 05%. What percent charge is Kanna's DS.
Note: A Nintendo DS takes 4 hours to charge fully.
Answer:
The percent charge of Kanna's DS is 50%
Step-by-step explanation:
we know that
A Nintendo DS takes 4 hours to charge fully (100%)
4 hours is the same that 240 minutes
using proportion
Find out what percentage represent 108 minutes
[tex]\frac{100}{240}\ \frac{\%}{min} =\frac{x}{108}\ \frac{\%}{min}\\\\x=100(108)/240\\\\x=45\%[/tex]
Remember that
Kanna Kamui charge her DS from 5%
so
[tex]5\%+45\%=50\%[/tex]
therefore
The percent charge of Kanna's DS is 50%
To figure out the charge percentage of Kanna's DS, we need to know the time it takes for a full charge and the time Kanna's DS was charged. The calculation (108 minutes charged / 240 minutes for a full charge) x 100 gives approximately 45%.
Explanation:The question is asking about the percentage charge of Kanna's DS after being charged for a specific period. First, we need to know how long it takes for a DS to become fully charged, which is 4 hours (equivalent to 240 minutes). Now, Kanna let her DS charge for 108 minutes, and the proportion of time spent charging to the total time needed to fully charge the DS represents the percentage of charge.
So, to calculate this, we would divide the time spent charging (108 minutes) by the total time needed for a full charge (240 minutes) and multiply by 100 to get the percentage.
Therefore, the calculation would be: (108/240) x 100 = 45% (rounding to the nearest whole number).
Learn more about Percentage Calculation here:https://brainly.com/question/32197511
#SPJ12
A truck carries apples, grapes, and blackberries in the ratio of 4:3:4 if the apples weigh 160 pounds, how much the the truckload of fruit weigh in total
Answer:the truck load of fruit weigh 440 pounces
Step-by-step explanation:
Let the total weight of the truck load of fruit weigh x pounds.
The truck carries apples, grapes, and blackberries in the ratio of 4:3:4
The total ratio is the sum of the proportions of apples, grapes, and blackberries. It becomes 4+3+4 = 11
if the apples weigh 160 pounds, it means that
4/11 × x = 160
4x/11 = 160
4x = 160×11 = 1760
x = 1760/4
x = 440
Which of the following is the balance for a single $3,200 deposit in an account with an APR of 2.6% that compounds interest quarterly and is invested for 6 years?
First, convert the APR to the periodic interest rate by dividing it by the number of compounds in a year. Then, determine the number of periods by multiplying the number of years by the number of compounds per year. Finally, use these values in the compound interest formula to find the balance.
Explanation:To solve this, we first need to switch from Annual Percentage Rate (APR) to the periodic interest rate. APR is an annual measure, but interest is compounded quarterly in this case. The periodic interest rate is the APR divided by the number of compounds in a year. So 2.6% APR converted to a periodic interest rate is 0.026/4 = 0.0065.
Next we determine the total number of periods. Since we have 6 years and interest is compounded quarterly, we have 4 compounds/year * 6 years = 24 periods.
Now we can use the compound interest formula: A=P(1+r/n)^(nt), where:
P is the principal, which is $3,200r is the annual interest rate in decimal, which is 0.026 here n is the number of compounds per year, which is 4 heret is the time the money is invested for in years, which is 6 hereSubstitute these values into the formula, we get: A = 3200(1 + 0.0065)^(24), calculate this to get the balance.
Learn more about Compound Interest here:https://brainly.com/question/14295570
#SPJ12
A fishing barge leaves from a dock and travels upstream (against the current) for 4 hours until it reaches its destination 12 miles away. On the return trip the barge travels the same distance downstream (with the current) in 2 hours. Find the speed of the barge in still water.
Answer:
v(b) = 4,5 mil/h speed of the barge in still water
Step-by-step explanation:
d = v*t barge going upstream 12 miles and 4 hours trip
barge returning back 12 miles and 2 hours trip
let call v(b) barge velocity and
v(w) water velocity
d = 12 (Mil) = 4 (h)* [(v(b) - v(w)]
3 = v(b) - v(w) (1)
d = 12 (mil) = 2 (h) * [ (v(b) + v(w)]
6 = v(b) + v(w) (2)
Equations (1) and (2) is a two system equation. Solving
from equation (1) v(w) = v(b) - 3
By subtitution in equation (2)
6 = v(b) + v(b) - 3
9 = 2v(b)
v(b) = 9/2 ⇒ v(b) = 4,5 mil/h
Two sides of a triangle have the following measures: 15 and 39. What is the range of possible measures for the third side?
A) 15 < x < 24
B) 24 < x < 39
C) 24 < x < 54
D) 39 < x < 54
Answer:
A) 15 < x < 24
Step-by-step explanation:
According to the law of the triangle, we know that the lengths of any two sides of a triangle are more significant than the length of the 3rd side. Here A is the answer because 15 is the length of the first side, and 39 is the length of the third side. So the length of the 2nd side is (39-15) = 24. It means that the length of the 2nd side is included between 15<x<24.
Which of the following are steps in the process in solving application problems using the two-order system?
1. Assign two variables for the unknowns.
2. Make a guess for the value of the variables.
3. Write two equations using the assigned variables.
4. Make another guess, based on the results of the first guess. Solve the pair of equations.
Answer:
1 and 3
Step-by-step explanation:
For resolving an application problems using the two - order system, the following steps must be taken:
First assign two variables for the unknowns.
Second write two equations using the assigned variables.
Third solve the pair of equations.
Then, only 1 and 3 are steps in the process in solving application problems, using the two-order system
PLLLZZZZ!!! HELP!!! WILL GIVE BRAINLIEST!!!!
Given a polynomial f(x), if (x − 6) is a factor, what else must be true?
A. f(0) = −6
B. f(0) = 6
C. f(−6) = 0
D. f(6) = 0
Answer:
D because x is what you subtract/add to get zero in (x − 6). x - 6 + 6 = 0
That is how the class taught me.
If y is a differentiable function of x, then the slope of the curve of xy^2 - 2y + 4y^3 = 6 at the point where y=1 is
(Show work!)
a -1/18
b -1/26
c 5/18
d -11/18
e 0
Answer:
a. -1/18
Step-by-step explanation:
Differentiating implicitly, you have ...
y^2 +2xyy' -2y' +12y^2y' = 0
Solving for y', we get ...
y'(2xy -2 +12y^2) = -y^2
y' = -y^2/(2xy -2 +12y^2)
To make use of this, we need to know the value of x at y=1. Filling in y=1 into the given equation, we have ...
x -2 +4 = 6
x = 4 . . . . . . . . subtract 2
So, at the point (x, y) = (4, 1), the slope is ...
y' = -1/(8 -2 +12)
y' = -1/18
_____
The attached graph shows that the line with slope -1/18 appears to be tangent to the curve at (4, 1).
What would be the difference at the end of one year between the simple interest earned on a deposit of $450 at 4.5% and the compound interest earned on $450 at 4.5% compounded annually?
$22.50
$22.25
$0
$20.25
Answer: $0
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 1 year
P = $450
R = 4.5%
Therefore
I = (450 × 4.5 × 1)/100
I = 2025/100
I = 20.25
For compound interest,
Initial amount deposited into the account is $450 This means that the principal,
P = 450
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 4.5%. So
r = 4.5/100 = 0.045
It was compounded for just a year. So
t = 1
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 450 (1+0.045/1)^1×1
A = 450(1.045) = $470.25
Compound interest = 470.25 - 450 = 20.25
The difference is 20.25 - 20.25 = 0
Answer:
$0
Step-by-step explanation:
There is no difference between the simple interest and compound interest at the end of one year.
At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?A. 6 to 1B. 3 to 2C. 2 to 3D. 1 to 5E. 1 to 6
Answer:
The correct answer is B. 3 to 2.
Step-by-step explanation:
To solve this problem let suppose
English = E
History = H
Maths = M
so
E = H* 2 (there are twice as many English majors as history majors)
E = M* 3 (three times as many English majors as mathematics majors)
lets suppose E=6 then,
H = 3 and M =2
So
H to M = 3/2.
Using algebra, we establish that if the number of mathematics majors is x, then the number of English majors is 3x and history majors would be 3x/2. The ratio of history majors to mathematics majors simplifies to 3:2.
To determine the ratio of the number of history majors to the number of mathematics majors given the provided relationships among different majors, we must set up the problem with algebra. Let's assume the number of mathematics majors is x. According to the problem, there are three times as many English majors as mathematics majors, so the number of English majors is 3x. It is also stated that there are twice as many English majors as history majors. Since the number of English majors is 3x, the number of history majors must be 3x/2.
Now, we establish the ratio of history majors to mathematics majors using the numbers we have. Since we have 3x/2 for history majors and x for mathematics majors, we can write the ratio as (3x/2):x which simplifies to 3:2 since x cancels out in the ratio.
Therefore, the correct answer is B. 3 to 2.
Four items are on sale at a local store. A shirt was originally $9.50 and now is $7.60. A pair of jeans were $25.00, and now they are priced $20.00. A pair of boots were $55.00, and they are on sale for $44.00. Do these regular and sale prices represent a proportional relationship
Answer:YES
Step-by-step explanation:
Answer : Yes, regular and sale prices represent a proportional relationship.
Step-by-step explanation :
We have to determine the ratio of regular and sale prices of shirt, jeans and boots .
A shirt was originally $9.50 and now is $7.60.
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 9.50}{\$ 7.60}[/tex]
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]
A pair of jeans were $25.00, and now they are priced $20.00.
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 25.00}{\$ 20.00}[/tex]
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]
A pair of boots were $55.00, and they are on sale for $44.00.
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 55.00}{\$ 44.00}[/tex]
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]
From this we conclude that, all the items are in same ratio that means the regular and sale prices represent a proportional relationship.
Hence, yes, regular and sale prices represent a proportional relationship.
According to a recent Census Bureau report, 12.7% of Americans live below the poverty level. Suppose you plan to sample at random 100 Americans and count the number of people who live below the poverty level. a. What is the probability that you count exactly 10 in poverty? b. What is the probability that you start taking the random sample and you find
Answer:
a) [tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]
b) [tex]P(X \leq 10) = 0.2614[/tex]
c) [tex] (1-0.127)^7 (0.127) =0.0491[/tex]
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=100, p=0.127)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
a. What is the probability that you count exactly 10 in poverty?
For this case we want this probability P(X=10)
[tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]
b. What is the probability that you count 10 or less in poverty? .2614
For this case we want this probability [tex]P(X=\leq10)[/tex]
[tex]P(X\leq10)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)[/tex]
And we can find the individual probabilities like this:
[tex]P(X=0)=(100C0)(0.127)^{0} (1-0.127)^{100-0}=1.263x10^{-6}[/tex]
[tex]P(X=1)=(100C1)(0.127)^{1} (1-0.127)^{100-1}=1.837x10^{-5}[/tex]
[tex]P(X=2)=(100C2)(0.127)^{2} (1-0.127)^{100-2}=0.000132[/tex]
[tex]P(X=3)=(100C3)(0.127)^{3} (1-0.127)^{100-3}=0.000629[/tex]
[tex]P(X=4)=(100C4)(0.127)^{4} (1-0.127)^{100-4}=0.00222[/tex]
[tex]P(X=5)=(100C5)(0.127)^{5} (1-0.127)^{100-5}=0.00620[/tex]
[tex]P(X=6)=(100C6)(0.127)^{6} (1-0.127)^{100-6}=0.0143[/tex]
[tex]P(X=7)=(100C7)(0.127)^{7} (1-0.127)^{100-7}=0.0279[/tex]
[tex]P(X=8)=(100C8)(0.127)^{8} (1-0.127)^{100-8}=0.0471[/tex]
[tex]P(X=9)=(100C9)(0.127)^{9} (1-0.127)^{100-9}=0.0701[/tex]
[tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]
And then repplacing we got:
[tex]P(X \leq 10) = 0.2614[/tex]
c. What is the probability that you start taking the random sample and you find the first person in poverty on the 8th person selected? .0491
For this case we need after 7 people , 1 in poverty so we can find this probability like this:
[tex] (1-0.127)^7 (0.127) =0.0491[/tex]
To calculate the probabilities, we can use the binomial probability formula. For part (a), the probability of counting exactly 10 people below the poverty level can be found by substituting the values into the formula. For part (b), the question is incomplete, so a specific answer cannot be provided.
Explanation:To calculate the probabilities, we can use the binomial probability formula:
P(X=k) = C(n,k) * p^k * q^(n-k)
where:
- P(X=k) is the probability of getting exactly k successes
- C(n,k) is the number of ways to choose k items from a set of n items (combination)
- p is the probability of success
- q is the probability of failure (1-p)
In this case, we're interested in finding the probability of counting exactly 10 people living below the poverty level from a sample of 100 Americans, assuming the poverty rate is 12.7%.
To find the probability that exactly 10 people live below the poverty level, we have:
P(X=10) = C(100,10) * (0.127)^10 * (1-0.127)^(100-10)
Using a calculator or combinatorial calculator, we can find that C(100,10) = 17310309456440.
Substituting the values, we have:
P(X=10) = 17310309456440 * (0.127)^10 * (0.873)^90
Calculating this expression gives us the probability of counting exactly 10 people in poverty.
The question appears to be incomplete as it ends with 'you find'. Please provide the complete question for a more accurate answer.
Benjamin & Associates, a real estate developer, recently built 195 condominiums in McCall, Idaho. The condos were either two-bedroom units or three-bedroom units. If the total number of bedrooms in the entire complex is 497, how many two-bedroom units are there? How many three-bedroom units are there?
To find the number of two-bedroom and three-bedroom units in the complex, we can set up a system of equations and solve them using substitution or elimination.
Explanation:To solve this problem, we need to set up a system of equations. Let x represent the number of two-bedroom units and y represent the number of three-bedroom units. From the problem, we know that there are a total of 195 condos. So, we have the equation: x + y = 195. We also know that the total number of bedrooms is 497, which can be expressed as: 2x + 3y = 497. We can now solve this system of equations using substitution or elimination to find the values of x and y. When solved, we find that there are 112 two-bedroom units and 83 three-bedroom units in the complex.
Learn more about Number of two-bedroom and three-bedroom units in a complex here:https://brainly.com/question/33894917
#SPJ12
Write an equation that can be used to solve the problem. Then answer the question asked. A group of college students are volunteering for Habitat for Humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Dale Horton can paint a certain room in 3 hours. Kathy Garcia can paint the same room in 9 hours. How long will it take them working together to paint the room?
Answer:
Required equation : [tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]
Together they can paint the same room in 2.25 hours or 2 hours 15 minutes.
Step-by-step explanation:
It is given that Dale Horton can paint a certain room in 3 hours.
One hour woks of Dale Horton = 1/3
Kathy Garcia can paint the same room in 9 hours.
One hour woks of Kathy Garcia = 1/9
Let together they can paint the same room in t hours.
One hour woks of both = 1/t
[tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]
[tex]\frac{1}{t}=\frac{3+1}{9}[/tex]
[tex]\frac{1}{t}=\frac{4}{9}[/tex]
After reciprocal we get
[tex]\frac{t}{1}=\frac{9}{4}[/tex]
[tex]t=2.25[/tex]
1 hour = 60 minutes.
0.25 hour = 15 minutes.
Therefore, together they can paint the same room in 2.25 hours or 2 hours 15 minutes.
Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?
A. 22(2/9)%B. 16(2/3)%C. 11(1/9)%D. 10%E. 5%
Answer:
option D
Step-by-step explanation:
Assume number of bulb in the hostel be 100
number of bulb on at 8 p.m.
= 80 % of total bulb
= 0.8 x 100 = 80 bulb
Let L be the number of light on and 100 - L be the light that are off
now,
Light on = 40 % of (100 - L) + 90 % of L
80 = 40 - 0.4 L + 0.9 L
40 = 0.5 L
L = 80 bulb
number of bulbs which were off = 100-80 = 20 bulb
number of bulbs that are on are supposed to be off = 40 % of 20
= 0.4 x 20 = 8 bulbs
percentage = [tex]\dfrac{8}{80}}\times 100[/tex]
= 10 %
Hence, the correct answer is option D
\begin{aligned} &y=2x -1 \\\\ &5x-4y=1 \end{aligned} y=2x−1 5x−4y=1 Is (1,1)(1,1)left parenthesis, 1, comma, 1, right parenthesis a solution of the system?
Answer:
Therefore, ( 1 , 1 ) is the Solution to the Given Equations
[tex]y=2x-1[/tex]
[tex]5x-4y=1[/tex]
Step-by-step explanation:
Given:
[tex]y=2x-1[/tex] ..............Equation ( 1 )
[tex]5x-4y=1[/tex] ..............Equation ( 2 )
To Find:
x = ?
y = ?
Solution:
[tex]y=2x-1[/tex] ..............Equation ( 1 )
[tex]5x-4y=1[/tex] ..............Equation ( 2 )
Substituting equation 1 in equation 2 we get
[tex]5x-4(2x-1)=1\\applying\ distributive\ property\ we\ get\\5x-8x+4=1\\\\-3x=1-4=-3\\\\x=\frac{-3}{-3}=1\\ \therefore x = 1\\[/tex]
Substituting 'x' in Equation ( 1 ) we get
[tex]y=2\times 1-1\\\\y=1\\\\\therefore y =1\\[/tex]
Therefore, ( 1 , 1 ) is the Solution to the Given Equations
[tex]y=2x-1[/tex]
[tex]5x-4y=1[/tex]
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also, assume that the probabilities of the individual parts working are P(A) = P(B) = 0.93, P(C) = 0.95, and P(D) = 0.92. Find the probability that the machine works properly.
Answer:
0.756
Step-by-step explanation:
It is given that a machine has four components, A, B, C, and D.
[tex]P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92[/tex]
If these components set up in such a manner that all four parts must work for the machine to work properly.
We need to find the probability that the machine works properly. It means we have to find the value of [tex]P(A\cap B\cap C\cap D)[/tex].
If two events X and Y are independent, then
[tex]P(X\cap Y)=P(X)\times P(Y)[/tex]
Assume the probability of one part working does not depend on the functionality of any of the other parts.
[tex]P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)[/tex]
Substitute the given values.
[tex]P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92[/tex]
[tex]P(A\cap B\cap C\cap D)=0.7559226[/tex]
[tex]P(A\cap B\cap C\cap D)\approx 0.756[/tex]
Therefore, the probability that the machine works properly is 0.756.
Final answer:
The probability that the machine works properly is found by multiplying the probabilities of all four components working: P(A) * P(B) * P(C) * P(D) = 0.93 * 0.93 * 0.95 * 0.92 = 0.7513, or 75.13%.
Explanation:
To find the probability that the machine works properly, we need to calculate the probability that all four components, A, B, C, and D, are working. Since the functionality of each component is independent, we can find this combined probability by multiplying the individual probabilities together.
The probability of A working is P(A) = 0.93, B working is P(B) = 0.93, C working is P(C) = 0.95, and D working is P(D) = 0.92. So the probability of the machine working is:
P(Machine works) = P(A) * P(B) * P(C) * P(D) = 0.93 * 0.93 * 0.95 * 0.92 = 0.7513
Therefore, the probability that the machine works properly is 0.7513, which is 75.13%.