Answer:
2.143
Step-by-step explanation:
An urn contains 8 black and;
6 pink balls.
5 balls are randomly drawn from the urn in succession, with replacement.
What is the probability that all the 5 balls drawn from the urn are pink?
The probability of drawing a pink ball in the first draw is 6/14The probability of drawing a pink ball in the second draw is 6/14The probability of drawing a pink ball in the third draw is 6/14The probability of drawing a pink ball in the fourth draw is 6/14The probability of drawing a pink ball in the fifth draw is 6/14The probability that all the 5 balls drawn is pink is 5 × 6/14 = 30/14 = 2.143 (rounded off to 3 decimal places)
The probability of drawing 5 pink balls is 0.271
Since the balls are replaced after each draw, the probability of drawing a pink ball each time is always
6/14
=3/7
Since we are drawing 5 balls, the probability of drawing 5 pink balls with replacement is
[tex](3/7)^{5}[/tex]
≈0.2706
Rounding to 3 decimal places, the probability is 0.271
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Complete the equation of the line through (−10,3), (−10,3) and (−8,−8) ,(−8,−8).
Answer:
(y + 8) = -5.5(x + 8)
or
y = -5.5x - 52
Step-by-step explanation:
So find the slope first:
[tex]\frac{-8-3}{-8+10}=\frac{-11}{2} =-5.5[/tex]
Point - Slope Form: (y + 8) = -5.5(x + 8)
Slope - Intercept Form: y = -5.5x + b
-8 = 44 + b
b = -52
y = -5.5x - 52
Jose purchased 4/9 pound of peanut and 7/11 pounds of raisins find the total weight of his purchase
Answer:
The total weight of his purchase is 1.08 pounds
Step-by-step explanation:
To find the total weight of his purchase, we sum the weight of each of his purchases.
He purchased:
4/9 pound of peanut.
7/11 pounds of raisins
Total:
The least common multiple between 9 and 11 is 99.
Then
[tex]\frac{4}{9} + \frac{7}{11} = \frac{11*4 + 9*7}{99} = \frac{107}{99} = 1.08[/tex]
The total weight of his purchase is 1.08 pounds
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket , to the nearest 100th of a foot. y=-16x^2+230x+112
Answer:
The maximum height reached by the rocket is of 938.56 feet.
Step-by-step explanation:
The height y, after x seconds, is given by a equation in the following format:
[tex]y(x) = ax^{2} + bx + c[/tex]
If a is negative, the maximum height is:
[tex]y(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
In this question:
[tex]y(x) = -16x^{2} + 230x + 112[/tex]
So
[tex]a = -16, b = 230, c = 112[/tex]
Then
[tex]x_{v} = -\frac{230}{2*(-16)} = 7.1875[/tex]
[tex]y(7.1835) = -16*(7.1835)^{2} + 230*7.1835 + 112 = 938.56[/tex]
The maximum height reached by the rocket is of 938.56 feet.
Ania kupiła w księgarni dwie książki i zapłaciła 37,20, a jurek za swoje zapłacił trzy razy więcej. Ile zapłacił jurek
Answer:
111.60
Question:
Ania bought two books in a bookstore and paid 37.20, and Jurek paid three times more for his. How much did Jurek pay?
Step-by-step explanation:
This is a question on multiplying decimals by natural numbers.
Number if books bought by Ania = 2
Cost for the two books = 37.20
Jurek paid = 3 times the amount Ania paid
Amount Jurek paid = 3×37.20
To multiply decimals with whole numbers, first multiply without the decimals
3×3720 = 11160
3 has no decimal place
37.20 has 2 decimal place
Therefore the answer would be in two decimal place = 111.60
So 3× 37.2= 111.60
Help asap giving branlist!!!
Answer:
D.
Step-by-step explanation:
So you know you have to have $62 as the base fee.
If you exceed 2 gigabytes, you subtract that by 2 because you want to find how many gigabytes you're going over. You then multiply it by 30 to find the cost.
You get C = 62 + 30(g - 2)
Answer:
anwser is d because it is write.
Step-by-step explanation:
Ralph is 3 times as old as Sara. In 4 years, Ralph will be only tice as old as Sara will be then.
If x represents Sara's age now, which of the following expressions represents Ralph's age in four years?
A. 3x
B. 2x+4
C. 3x+4
Answer:
In 6 years, Ralph will be only twice as old as Sara
Step-by-step explanation:
Answer:
The answer is C, 3x+4
Step-by-step explanation:
The “in four years” part translates to +4. The 3x translates to 3 times his current age. Hope this helped :)
Which of the following measurements is more precise?
4.69 m or 8.99 m
Answer:
The measures represent the same precisionWhen we talk about precision in measurements, we need to mention the significant figures, because that determines the precision.
Specifically, the more significant figures there are, more precise will be the number.
In this case, you can observe that both numbers have the same number of significant figures, which is 3, which means both numbers are equal in precision.
at a coffee shop, the first 100 customers’ orders were as follows
Answer:
81%
Step-by-step explanation:
22+5=27
22/27
1. Ryan budgets $35 a week for lunch for 5 days. What
is his average lunch expense each day?
Answer: $7
Step-by-step explanation:
35/ 5 = 7
Answer:
$7
Step-by-step explanation:
Bc/ 35/5=7
??!!!?!?
.....
....
...
Answer:
A) (3,2)
Step-by-step explanation:
Conditions:
x+y ≤ 6x ≥ 0y ≥ 0A) (3,2)
yes, as all 3 conditions are met3+2≤6, 3≥0, 2≥0B) (0,7)
no, as the first condition is not met0+7 > 6Use the 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values. A bell-shaped distribution with mean 1050 and standard deviation 7.
The interval is to:_______.
Answer:
Intervals = (1,064) , (1,036)
Step-by-step explanation:
Given:
Use 95% method
Mean = 1,050
Standard deviation = 7
Find:
Intervals.
Computation:
95% method.
⇒ Intervals = Mean ± 2(Standard deviation)
⇒ Intervals = 1,050 ± 2(7)
⇒Intervals = 1,050 ± 14
⇒ Intervals = (1,050 + 14) , (1,050 - 14)
⇒ Intervals = (1,064) , (1,036)
The Intervals = (1,064) , (1,036)
Given that:
Use 95% methodMean = 1,050Standard deviation = 7Based on the above information, the calculation is as follows:
Intervals = Mean ± 2(Standard deviation)
Intervals = 1,050 ± 2(7)
Intervals = 1,050 ± 14
Intervals = (1,050 + 14) , (1,050 - 14)
Intervals = (1,064) , (1,036)
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3(5 − 2 x) = −2(6 – 3 x) − 10 x
Answer:
15-6x= -12-4x
15-2x= -12
-2x= -27
x= -13.5
Step-by-step explanation:
What is the volume of a rectangular prism with a length of 12ft, a width of 10ft, and a height of 18ft?
Answer:
2160ft³
Step-by-step explanation:
V=whl=10·18·12=2160ft³
A farmer planted corn in two different fields. He planted 500 seeds of regular corn in Field A and 500 seeds of experimental corn in Field B. At
harvest time, more ears of corn had grown in Field A than in Field B. The farmer concluded that more corn grew in Field A because of the type
of corn planted.
Choose two other possible variables that could have caused more corn to grow in Field A.
Answer:
1. More pollination process in the regular corn planted in field A than that of field B.
2. Low pest and insect attack on corn planted in field A compared to that of B.
Step-by-step explanation:
1. Pollination is the process in which a plant becomes fertilized, so as to produced seeds. The process requires some agent which could be; air, human, wind etc.
Therefore more pollination of the corn planted in field A than those in B would lead to more yield (ears of corn harvested) than that of B.
2. Pests and insects are agents which could reduce the yield of the corn after harvest. Comparing the two fields A and B, if the corn planted in field A were not affected by pests or insects, while those planted in B were affected, then more ears of corn would be harvested in field A.
Answer:
a,c, And gg gamer
Step-by-step explanation:
Solve 4x+5≥-23. show your work
Answer:
x≥-7
Step-by-step explanation:
4x+5≥-23
Subtract 5 from each side
4x+5-5≥-23-5
4x≥-28
Divide each side by 4
4x/4≥-28/4
x≥-7
Answer:
X≥-7
Step-by-step explanation:
Step 1: Subtract 5 from both sides.
4x+5-5≥-23-5
4x ≥-28
Step 2: Divide both sides by 4.
4x/4 ≥-28/4
X ≥-7
Anyone know the answer ?
Answer:
A. SASD. LLStep-by-step explanation:
Two sides and the angle between are marked as congruent. That immediately tells you that the Side-Angle-Side (SAS) theorem of congruence applies.
The angle is a right angle, which makes the adjacent sides be "legs" of the right triangle. Then the Leg-Leg (LL) theorem of congruence for a right triangle also applies.
Appropriate choices are ...
SAS, LL
Write an equation of the line containing the point (2,1) and perpendicular to the line 5x – 2y = 3.
So first, you want to isolate your Y. To do this, you must get it alone on ONE SIDE of the equation.
5x - 2y = 3
-5x -5x
[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{3-5x}{-2}[/tex]
ANSWER: y = \frac{3-5x}{-2}
Please answer this correctly
Answer:
Pennies: 20%
Nickels: 36%
Dimes: 18%
Quarters: 21%
Step-by-step explanation:
Pennies: [tex]\frac{125}{125+180+90+105} =\frac{125}{500} =\frac{25}{100}[/tex] or 20%
Nickels: [tex]\frac{180}{125+180+90+105} =\frac{180}{500} =\frac{36}{100}[/tex] or 36%
Dimes: [tex]\frac{90}{125+180+90+105} =\frac{90}{500} =\frac{18}{100}[/tex] or 18%
Quarters: [tex]\frac{105}{125+180+90+105} =\frac{105}{500} =\frac{21}{100}[/tex] or 21%
On a recent trip, Lamar's distance varied directly with the number of hours he drove. He traveled 288 miles in 6 hours. Which equation shows Lamar's distance, d, based on the number of hours, h, he drove?
(A) d = 6h
(B) d = 50h
(C) d = 48h
(D) d = 288h
Answer:
d = 48 h
Step-by-step explanation:
Lamar's distance traveled is directly proportional to the number of hours be drove.
So distance (d) ∝ hours (h)
Lamar traveled 288 miles in 6 hours
Since d ∝ h
then d = kh [ where k is the proportionality constant ]
if 288 = k × 6
k = =288/48
Therefore, equation will be d = 48 h will be the equation
simplify 2x+x+x+2y times 3y times y
Answer:
12 x y² + 6 y³
Step-by-step explanation:
Step(i):-
Given ( 2 x + x + x + 2 y ) times 3 y times y
( 2 x + x + x + 2 y ) × 3 y × y = ( 4 x + 2 y) × 3 y × y = ( 4 x + 2 y) 3 y²
By applying Distributive property
( a + b ) c = a . c + b . c
= 4 x . 3 y² + 2 y . 3 y²
= 12 x y² + 6 y³
Final answer:-
( 2 x + x + x + 2 y ) times 3 y times y = 12 x y² + 6 y³
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positive positive that is the probability that the bureau finds a match given that the lead at the crime scene and the lead in the possession of the suspect are actually from two differant melts or sources. To estimate the false positive rate the bureau collected 1851 bullets that the agency was confident all came from differant melts. The using its established ctireria the bureau examined every possible pair of bullets and found 658 matches. Use this info to to compute the chance of a false positive.
Answer:
Step-by-step explanation:
Given that, we have 1851 bullets that we KNOW are NOT MATCHES of one another. One by one they examine two bullets at a time.
So, there are 1851 bullets but each time we choose 2.
We have, N choose K = N! / K! (N-k)!
Here, N = 1851 and K = 2
Therefore, 1851 choose 2 = 1851! / 2! (1851-2)!
= 1851! / 2! * 1849!
= 1712175 Possible Combinations
Out of these 653 are false positive.
The chance of getting false positive is = 658 / 1712175
= 0.000384
= 0.0384 %
Therefore, The correct option is
The chance of false positive is 0.0384% Because this probability is sufficiently small (< or = 1%) There is high confidence in the agency's forensic evidence.
For 120 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degree.Round your answer to 4 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.Sample size is .Number of samples is .When constructing a x-bar chart:The center line should be .ESD(x-bar) equals .The upper control limit (UCL) should be .The lower control limit (LCL) should be .
Answer:
Center line = 46
UCL = 46.84852
LCL = 45.15148
Step-by-step explanation:
Given:
Standard deviation = 0.8
Mean, u = 46
Sample size, n= 8
First calculate the estimated standard deviation:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{0.8}{\sqrt{8}} = 0.282843[/tex]
a) The center line, X', would be the average across all components. Here the average across all 960 bottles is 46
Therefore,
[tex] X' = 46 [/tex]
b) The upper control limit, UCL:
UCL = u + 3s
= 46 + 3(0.28284)
= 46 + 0.84852
= 46.84852
c) The upper control limit, LCL:
LCL = u + 3s
= 46 - 3(0.28284)
= 46 - 0.84853
= 45.15148
Does this graph represent a function? Why or why not?
10+
8+
6-
110884
-8
O
A. No, because it is not a straight line.
B. Yes, because it passes the horizontal line test.
Ο Ο Ο
C. Yes, because it passes the vertical line test.
D. No, because it fails the vertical line test.
Answer:
Option (C).
Step-by-step explanation:
In the graph attached,
An absolute function has been given.
To check a graph whether it's a relation or a function, vertical line test is a trusted tool.
In vertical line test a vertical line (parallel to y-axis) is drawn passing through the graph.
If the vertical line cuts the graph at only one point then the graph is said to be a function.
The given graph passes the vertical test.
Therefore, it's a function.
Option C. will be the answer.
Yes, this graph represents a function, because it passes the vertical line test. Option C is correct
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
An absolute function is shown in the graph that is attached. The vertical line test is a reliable method for determining if a graph represents a relation or a function.
In the vertical line test, a vertical line that is parallel to the y-axis and cuts through the graph is created. The graph is considered to be a function if the vertical line only intersects it once.
The vertical test is passed by the shown graph. It serves a purpose as a result.
Hence option C is correct.
To learn more about the function, refer to:
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Which is required for sexual reproduction?
Answer:
2 parents are required
Step-by-step explanation:
Answer:
semen.............
Un prestigioso empresario decide repartir su herencia de S/ 176 000 entre sus tres hermanos Roberto, Luis y Armando, de manera DP al número de sus hijos e IP al monto de sus deudas. ¿Cuánto le corresponde a cada hermano?
Roberto :N° hijos 4,Monto de deudas (S/) : 2 000
Luis: N° hijos 3, Monto de deudas (S/): 6 000
Armando:N° hijos 5, Monto de deudas (S/): 8 000
Answer:
Amount received per brother based on number of children plus debt is given as
Roberto, S/ 55,333.33
Luis, S/ 46,000
Armando, S/ 74,666.67
Step-by-step explanation:
English Translation
A prestigious businessman decides to distribute his inheritance of S / 176,000 among his three brothers Roberto, Luis and Armando, DP to the number of his children and IP to the amount of his debts. How much corresponds to each brother?
Roberto: No of children 4, Amount of debts (S /): 2 000
Luis: No. of children 3, Amount of debts (S /): 6,000
Armando: No of children 5, Amount of debts (S /): 8,000
Solution
The man shares the inheritance according to the number of children per person and according to each brother's debts.
Assuming the debts are first settled,
The total debts = 2000 + 6000 + 8000 = S/ 16,000
We assume that each brother receives the respective debt amounts first, then the remaining cash is divided amongst the 3 brothers according to the number of their children.
Total amount available = S/ 176,000
total debt = S/ 16,000
Amount available less debts = 176,000 - 16,000 = S/ 160,000
There are 4, 3 and 5 children respectively for the 3 brothers.
Total number of children = 4+3+5 = 12.
Amount corresponding based on a per child basis =( S/ 160,000/12) = S/ 13,333.33
Meaning that each brother receives the following amount based on their children's sake
Roberto, 4 × S/ 13,333 = S/ 53,333.33
Luis, 3 × S/ 13,333.33 = S/ 40,000
Armando, 5 × S/ 13,333 = S/ 66,666.67
Total amount each brother then receives when the amount received due to debts are added
Roberto, 53,333.33 + 2,000 = S/ 55,333.33
Luis, 40,000 + 6,000 = S/ 46,000
Armando, 66,666.67 + 8,000 = S/ 74,666.67
To check, 55,333.33 + 46,000 + 74,666.67 = 176,000 (total inheritance!)
Hope this Helps!!!
Queremos ver como se reparte una dada suma entre 3 hermanos, siendo que tenemos unas dadas restricciones, donde debemos trabajar con relaciones directamente proporcionales e inversamente proporcionales.
Veremos que:
Roberto recibe: $112,640
Luis recibe: $28,160
Armando recibe: $35,200
Sabemos que lo que se reparte es directamente proporcional al número de hijos de cada hermano, e inversamente proporcional a las deudas de cada hijo.
Entonces, definamos las variables:
R = lo que recibe Roberto.
L = Lo que recibe Luis
A = lo que recibe Armando.
Tendremos que:
R + L + A = $176,000
directamente proporcional significa: y = k*xInversamente proporcional significa: y = k/zEntonces como lo que recibe cada hermano es directamente proporcional al número de hijos (x) e inversamente proporcional a la deuda (z) lo que cada hermano recibe será:
R = k*4/2,000L = k*3/6,000A = k*5/8,000Entonces podemos escribir:
R + L + A = $176,000
k*4/2,000 + k*3/6,000 + k*5/8,000 = $176,000
k*(4/2,000 + 3/6,000 + 5/8,000) = $176,000
k*(0.003125) = $176,000
k = $176,000/(0.003125) = $56,320,000
Ahora que conocemos el valor de k, podemos calcular lo que cada hermano recibe:
R = $56,320,000*(4/2,000) = $112,640
L = $56,320,000*(3/6,000) = $28,160
A = $56,320,000*(5/8,000) = $35,200
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A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
Answer:
The probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds is P(X<368)=0.011.
Step-by-step explanation:
We have a normal distribution with mean 460 and standard deviation 40 to describe the time for the mile run in its secondary-school fitness test.
We have to calculate the probabiltiy that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
To calculate this, we have to calculate the z-score for X=368:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{368-460}{40}=\dfrac{-92}{40}=-2.3[/tex]
Then, we can calculate the probability:
[tex]P(X<368)=P(z<-2.3)=0.011[/tex]
An AP news service story, printed in the Gainesville Sun on May 20, 1979, states the following with regard to debris from Skylab striking someone on the ground: "The odds are 1 in 150 that a piece of Skylab will hit someone. But 4 billion people ... live in the zone in which pieces could fall. So any one person’s chances of being struck are one in 150 times 4 billion—or one in 600 billion." Do you see any inaccuracies in this reasoning?
Answer:
The odds are one in approximately 27 million.Not one in 600 billionStep-by-step explanation:
From the news story, we are told that:
The odds are 1 in 150 that a piece of Skylab will hit someone.
However, 4 billion people live in the zone in which pieces could fall.
Therefore, any one person’s chances of being struck are:
[tex]=\dfrac{1}{150} \times 4$ billion\\=\dfrac{1}{37.5}$ billion\\\\=26,666,667 million[/tex]
Therefore, the odds are one in approximately 27 million.
The inaccuracy presented in this reasoning was that the odds are one in 600 billion.
Let A be an n # n matrix, b be a nonzero vector, and x0 be a solution vector of the system Ax D b. Show that x is a solution of the nonhomogeneous system Ax D b if and only if y D x!x0 is a solution of the homogeneous system Ay D 0.
Complete Question
Let A be an n x n matrix, b be a nonzero vector, and x_0 be a solution vector of the system Ax = b. Show that x is a solution of the non-homogeneous system Ax = b if and only if y = x - x_0 is a solution of the homogeneous system Ay = 0.
Answer:
Step-by-step explanation:
From the question we are told that
A is an n × n matrix
b is a zero vector
[tex]x_o[/tex] us the solution vector of [tex]Ax = b[/tex]
Which implies that
[tex]Ax_o = b[/tex]
So first we show that
if [tex]x[/tex] is the solution matrix of [tex]Ax = b[/tex]
and [tex]y= x-x_o[/tex] is the solution of [tex]Ay = 0[/tex]
Then
[tex]A(x-x_o) = 0[/tex]
=> [tex]Ax -Ax_o = 0[/tex]
=> [tex]b-b = 0[/tex]
Secondly to show that
if [tex]y= x-x_o[/tex] is the solution of [tex]Ay =0[/tex]
then x is the solution of the non-homogeneous system
[tex]Ax = b[/tex]
Now we know that [tex]y = x-x_o[/tex] is the solution of [tex]Ay =0[/tex]
So
[tex]Ay = 0[/tex]
=> [tex]A(x- x_o) = 0[/tex]
=> [tex]Ax - Ax_o = 0[/tex]
=> [tex]Ax - b = 0[/tex]
=> [tex]Ax = b[/tex]
Thus this has been proved
Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $26,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $292,000 in revenues, how many sections of each course should it offer?
Finite Math section(s)
Applied Calculus section(s)
Computer Methods section(s)
Answer:
meh
Step-by-step explanation:
What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation.
Answer:
4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-(-2))/(3-1)
m=8/2
m=4
