Answer:
14 rows.
Step-by-step explanation:
We have been given that Jess is planting rows of squash. To plant a row of squash Jess needs 6/7 square feet. There are 12 square feet in Jess's backyard.
To find number of rows that Jess can plant, we will divide total area of backyard by area needed to plant each row as:
[tex]\text{Number of rows that Jess can plant}=12\div\frac{6}{7}[/tex]
[tex]\text{Number of rows that Jess can plant}=\frac{12}{1}\div\frac{6}{7}[/tex]
Convert into multiplication problem by flipping the 2nd fraction:
[tex]\text{Number of rows that Jess can plant}=\frac{12}{1}\times \frac{7}{6}[/tex]
[tex]\text{Number of rows that Jess can plant}=\frac{2}{1}\times \frac{7}{1}[/tex]
[tex]\text{Number of rows that Jess can plant}=14[/tex]
Therefore, Jess can plant 14 rows of squash in her backyard.
Please help me with this!
Answer:
-540
Step-by-step explanation:
The coefficient of the k-th term of (a+b)^n is nCk. (k = 0, 1, 2, ..., n)
Here, we want the coefficient of a^3b^3 for n=6, so k=3 and the coefficient is ...
6C3 = 6!/(3!(6-3)!) = 5·4 = 20
So for a=3x and b=-y, we want ...
20a^3b^3 = 20(3x)^3(-y)^3 = -540x^3y^2
The coefficient you're looking for is -540.
Use the order of operations to evaluate the expression below.
20+7 • (5-3) = (8-6) - 4
Answer:
34 = -2
Step-by-step explanation:
20 = 7 x (5-3) = 34
(8-6) - 4 = -2
So the answer is 34 = -2
The equation 20+7 • (5-3) = (8-6) - 4, when evaluated using the order of operations, gives the result 34 = -2, which indicates that the original equation is not balanced.
Explanation:Let's evaluate the expression 20+7 • (5-3) = (8-6) - 4 using the order of operations, which can be remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
First, we solve the expressions in parentheses: 7 • (5-3) = 7 • 2 = 14 and (8-6) - 4 = 2 - 4 = -2.
Then we perform the addition: 20 + 14 = 34. At this point, we have 34 = -2, which is not correct. Therefore, the original equation is not balanced.
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Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 496 and standard deviation 115. You choose an SRS of 100 students and average their SAT reading scores. If you do this many times, the mean of the average scores will be close to:_______. A. 115.
B. 115 / square root of 100 = 1.15.
C. 115 / square of 100 = 11.5.
Answer:
496
Step-by-step explanation:
I am assuming that there are options lacking. The average score, due to the Law Of Big Numbers, using a big enough sample will be close to the mean of the random variable. Thus the mean of the average scores will be close to 496 if the process is done many times.
The mean of the average scores will be close to the population mean of 496.
Explanation:The mean of the average scores will be close to the population mean, which is 496. The Central Limit Theorem states that as the sample size increases, the sample mean approaches the population mean. In this case, since we are choosing an SRS of 100 students, the mean of the average scores will be close to the population mean of 496.
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One maid can clean the house in 2 hours. Another maid can do the job in 8 hours. How long will it take them to do the job working together?
A 16/6 hr
B 8/5 hr
C 1/10 hr
D 1/16 hr
Answer: B 8/5 hr
Step-by-step explanation:
One maid can clean the house in 2 hours. This means that the rate at which she cleans the house per hour is 1/2
Another maid can do the job in 8 hours. This means that the rate at which the other maid cleans the house per hour is 1/8
If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be
1/2 + 1/8 = 5/8
Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,
5/8 = 1/t
t = 8/5 hour
Option B is correct. Working together, the two maids can clean the house in 8/5 hours.
Explanation:Let's assume that the combined rate of both maids working together is x house cleaned per hour. We can set up the equation:
1 maid's rate + another maid's rate = combined rate
1/2 + 1/8 = x
Solving for x:
4/8 + 1/8 = x
5/8 = x
The combined rate of the maids working together is 5/8 house cleaned per hour. To find how long it will take them to clean the house together, we can set up the equation:
(5/8) house per hour = 1 house
Let t be the time it takes them to clean the house together. We can write the equation:
(5/8) * t = 1
Solving for t:
t = 1 / (5/8)
t = 8/5 hours.
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Maria received 55% of the vote in a student council election. What decimal and fraction, written in its simplest form, are equivalent to the percentage of the vote maria received
Answer:
The decimal and fraction equivalent to the percentage of the vote maria received is 0.55 and [tex]\frac{11}{20}[/tex] .
Step-by-step explanation:
Given:
Maria received 55% of the vote in a student council election.
Now, to find the decimal and fraction of the percentage of the vote maria received.
Percentage of vote Maria received = 55%.
So, the fraction and decimal of the percentage in its simplest form:
[tex]\frac{55}{100}[/tex]
On simplifying it:
[tex]=\frac{11}{20}[/tex].
Thus, the fraction is [tex]\frac{11}{20} .[/tex]
[tex]\frac{11}{20}[/tex]
[tex]=0.55.[/tex]
Hence in the decimal is [tex]0.55.[/tex]
Therefore, the decimal and fraction equivalent to the percentage of the vote maria received is 0.55 and [tex]\frac{11}{20}[/tex] .
To estimate the average annual expenses of students on books and class materials a sample of size 36 is taken. The sample mean is $850 and the sample standard deviation is $54. A 99% confidence interval for the population mean is:_______.A) $823.72 to $876.28.
B) $832.36 to $867.64.
C) $826.82 to $873.18.
D) $825.48 to $874.52.
Answer:
its C i think
Step-by-step explanation:
Biking at 10 mph, it takes Kristen 1/2 hour to reach the train station to go to work. Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 28 mph. How far does Kristen travel to work
Answer: 38 mph
Step-by-step explanation:
Add. 10 plis 28 is 38.
Answer: 19 miles
Step-by-step explanation:
Distance = speed × time
Biking at 10 mph, it takes Kristen 1/2 hour to reach the train station to go to work. This means that the distance covered on her way to the train station is
0.5 × 10 = 5 miles
Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 28 mph. Distance covered by the train is
0.5 × 28 = 14 miles
Therefore, the distance that Kristen travels to work is
14 + 5 = 19 miles
You invest $3,200 in an account that pays an interest rate of 8.5%, compounded continuously.
Calculate the balance of your account after 6 years. Round your answer to the nearest hundredth.
Answer: the balance is $5328.95
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 3200
r = 8.5% = 8.5/100 = 0.085
t = 6 years
Therefore,
A = 3200 x 2.7183^(0.085 x 6)
A = 3200 x 2.7183^(0.51)
A = $5328.95 to the nearest hundredth
Answer:
FOR PLATO/EDMENTUM USER THE right answer is: 5328.93
Step-by-step explanation:
The sum of the differences must be zero for any distribution consisting of n observations.
A. True
B. False
Answer:
false
Step-by-step explanation:
Sin * (x - y) , if sin x = 8/17 cos y = 12/37
Answer:
-429/629
Step-by-step explanation:
Use angle difference formula:
sin(x − y) = sin x cos y − sin y cos x
Assuming x and y are in the first quadrant:
sin(x − y) = sin x cos y − √(1 − cos²y)√(1 − sin²x)
Plugging in values:
sin(x − y) = (8/17) (12/37) − √(1 − (12/37)²)√(1 − (8/17)²)
sin(x − y) = (8/17) (12/37) − (35/37)(15/17)
sin(x − y) = -429/629
What is the distance between m, a negative number, and 0 on a number line?
Answer:
It depends on what negative number it is. For example -23 is 23 units or whatever to 0.
Step-by-step explanation:
Find the missing length QG. Round answer to nearest tenth.
Answer:
The answer to your question is QG = 55.8 ft
Step-by-step explanation:
Data
QG = x
Process
1.- Find T
The sum of the internal angles in a triangle equals 180°
G + Q + T = 180
-Solve for T
T = 180 - G - Q
- Substitution
T = 180 - 41 - 67
-Simplification
T = 72°
2.- Use the law of sines to find QG
QG / sin T = GT / sin Q
-Solve for QG
QG = GT sinT / sin Q
-Substitution
QG = 54 sin 72 / sin 67
- Simplification
QG = 54 (0.951)/0.921
-Result
QG = 55.8 ft
Answer:
Step-by-step explanation:
Considering the given triangle QGT, to determine QG, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes
QG/SinT = GT/SinQ = QT/SinG
The sum of the angles in a triangle is 180°. It means that
T = 180 - (41 + 67) = 72°
Therefore
QG/Sin72 = 54/Sin 67
Cross multiplying, it becomes
QGSin67 = 54Sin72
0.921QG = 54 × 0.951
0.921QG = 51.354
QG = 51.354/0.921
QG = 55.8 ft
Mr. Burk traveled 240 miles last weekend. His average rate of speed for the trip was 70 miles per hour. Since he did not stop, about how many hours long was his trip?
Answer:
about 3 1/2 hours long
Step-by-step explanation:
70 goes into 240 evenly 3 times, and 70×3 equals 210. that leaves 30 miles remaining. since he is moving at an average rate of 70mph, 3/7 would be the remaining time. to decimal that equals a total of about 3 hours and 25 minutes, which, rounded up, equals 3 and 1 half hours.
Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the width and length by the same amount. What will be the length (longer dimension) of the new garden? Enter your answer in the box.
Answer:
Step-by-step explanation:
Let x represent the constant amount by which the length and width of the garden is increased.
Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the width and length by the same amount. This means that the new length of the garden would be (13 + 2x) cm and the new width of the garden would be (10 + 2x) cm. Therefore,
(13 + 2x)(10 + 2x) = 208
130 + 26x + 20x + 4x² -208 = 0
4x² + 46x - 208 - 130 = 0
4x² + 46x - 78 = 0
Dividing through by 2, it becomes
2x² + 23x - 39 = 0
2x² + 26x - 3x - 39 = 0
2x(x + 13) - 3(x + 13) = 0
2x - 3 = 0 or x + 13 = 0
x = 3/2 or x = - 13
Since the value of x cannot be negative, then
x = 3/2 = 1.5 m
The length of the new garden is
13 + 1.5 = 14.5 m
Mt. Vesuvius has an altitude of 3000 feet. A person stands 120 feet away from the base of the volcano. What is the angle of elevation from the person on the ground to the top of the volcano?
Answer: the angle of elevation from the person on the ground to the top of the volcano is 87.7°
Step-by-step explanation:
The person, his angle of elevation and his distance from the foot of the mountain forms a right angle triangle.
The altitude of the mountain represents the opposite side of the right angle triangle.
The distance of the person from the base of the volcano represents the opposite side of the right angle triangle.
To determine the angle of elevation from the person on the ground to the top of the volcano, we would apply the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan θ = 3000/120 = 25
θ = Tan^-1(25)
θ = 87.7° to the nearest tenth.
A palindrome is a string whose reverse is identical to the original string. Give examples of bit strings of length 5 and 6 that are palindromes. How many bit string palindromes of length n are there? How many ternary string palindromes of length n are there?
Answer:
The answers to the question are as follows
a). Please see the examples of bit strings of length 5 and 6 that are palindromes in the following explanation.
b). The number of even length palindromes is [tex]26^{\frac{n}{2} }[/tex]
The number of odd length palindromes is [tex]26^{\frac{n+1}{2} }[/tex]
c). The number of ternary string palindromes of length n is 702.
Step-by-step explanation:
a). Examples of bit strings of length 5 and 6 that are palindromes are
Bit strings of length 5 Bit strings of length 6
Kayak Hannah
Level Redder
Civic Terret
Madam Kakkak
Solos degged
Tenet
Rotor
Minim
Radar
Refer
Terret
b). When n is even, we have a choice of any of the 26 characters for the first letter, similarly, we can choose any character for the second, and so on up till the n/2 th position after which subsequent letters depend on the letter chosen before the half point following the definition of a palindrome.
Therefore we have n/2 independent choices with repetition therefore we have [tex]26^{\frac{n}{2} }[/tex] palindromes of even length with or without meaning in the alphabet
On the other hand, when n is odd, we are free to chose any letter up to the middle letter as before this means we have [tex]\frac{n-1}{2} +1 = \frac{n+1}{2}[/tex] free choices
Therefore the number of odd length palindromes are [tex]26^{\frac{n+1}{2} }[/tex]
c). For a ternary string palindrome, we have 26 letters for the first position, and also 26 for the second, while the third is the same as the first which is one option.
Where n = 2 we have 26 ways of selecting the first and second letters which are equal
Therefore the number of ternary string palindromes of length n are 26×26 + 26 = 702
Bit string palindromes of length 5 and 6 are strings that are the same forward and backward, like '10101' or '100001'. The number of palindromic bit strings of length n is 2 raised to the floor of n/2, and the number of ternary string palindromes of length n is 3 raised to the floor of n/2.
Explanation:A palindrome is a string that remains the same when reversed. Examples of bit string palindromes of length 5 include '10001', '01110', '10101', '01010'. For length 6, examples could be '100001', '011110', '101101', '010010'.
In general, to calculate the number of palindromic bit strings for any given length, the first half of the string can be anything (2 ⌊n/2⌋ possibilities), and the second half must mirror the first. Thus there are 2 ⌊n/2⌋ bit string palindromes of length n.
For ternary palindromes (strings composed of the digits 0, 1, and 2), use the same logic but switch the base to 3. Thus there are 3 ⌊n/2⌋ ternary string palindromes of length n.
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Write the quadratic function in standard form.
y=2(x - 3)² +9
Answer:
y = 2x^2 - 12x + 27
Step-by-step explanation:
Step 1: Distribute the power
y = 2(x - 3)² + 9
y = 2(x^2 - 6x + 9) + 9
y = 2x^2 - 12x + 18 + 9
y = 2x^2 - 12x + 27
Answer: y = 2x^2 - 12x + 27
please help me with this question
Answer:
Step-by-step explanation:
Haven't seen a related rates problem in a while! These are fun! Not too bad when you keep your stuff organized. First, label what you've been given. If the radius is decreasing, then we have
[tex]\frac{dr}{dt}=-.2[/tex]
We are told to find [tex]\frac{dV}{dt}[/tex] when r = 9.
Now we have to find the derivative of the volume of a sphere using implicit differentiation. The derivative is
[tex]\frac{dV}{dt}=\frac{4}{3}\pi3r^2\frac{dr}{dt}[/tex]
It looks like we have everything we need to solve for the unknown. The derivative is even already set up to solve for the change in volume. All we have to do now is plug in the values.
[tex]\frac{dV}{dt}=\frac{4}{3}\pi3(81)(-.2)[/tex]
This does give us a negative number, -203.575 to be exact, but if you answer it without the negative, you say that the volume is decreasing at the rate of 203.575 cm/min cubed
Compute the amount of interest earned in the following simple interest problem A deposit of $1,295 at 7% for 180 days
Answer: the amount of interest earned is $44.7
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount deposited.
P represents the principal or amount deposited.
R represents interest rate
T represents the duration in years.
From the information given,
P = $1295
R = 7%
T = 180 day. Assuming there are 365 days in a year. Converting 180 days to years, it becomes
180/365 = 0.49315 year
Therefore,
I = (1295 × 7 × 0.49315)/100 = $840,
I = $44.7
Twin brothers, Billy and Bobby, kid mother grandparents lawn together for 60 minutes. Billy could mow the lawn by himself in 20 minutes less time then it would take Bobby. How long will it take Bobby to mow the lawn by himself
Answer:
Bobby around 131 minutes and Billy around 111 minutes
Step-by-step explanation:
To solve the problem it is important to raise equations regarding what happens.
They tell us that Billy (Bi) and Bobby (Bo) can mow the lawn in 60 minutes. That is to say that what they prune in a minute is giving as follows:
1 / Bo + 1 / Bi = 1/60 (1)
They say Billy could mow the lawn only in 20 minutes less than it would take Bobby, therefore
1 / Bi = 1 / (Bo-20) (2)
Replacing (2) in (1) we have:
1 / Bo + 1 / (Bo-20) = 1/60
Resolving
(Bo - 20 + B0) / (Bo * (Bo-20) = 1/60
120 * Bo - 1200 = Bo ^ 2 - 20Bo
Rearranging:
Bo ^ 2 - 140Bo -1200 = 0
Now applying the general equation
Bo = 130.82 or Bo = 9.17, this last value cannot be because Billy took 20 minutes less and neither can he prune faster than the two together, therefore Bobby only takes around 131 minutes and Billy around 111 minutes
Checking with equation 1:
1/131 +1/111 = ~ 1/60
Final answer:
Bobby would take 120 minutes to mow the lawn by himself.
Explanation:
The question asks us to calculate how long it will take Bobby to mow the lawn by himself if it takes his twin brother Billy 20 minutes less to do the job on his own, and they can mow the lawn together in 60 minutes. To solve this, we can use the concept of work rate and the idea that the combined work rate of Billy and Bobby equals the reciprocal of the time they take to work together.
Let's assume Bobby takes x minutes to mow the lawn by himself. Thus, Billy would take x - 20 minutes. We can express their work rates as:
Bobby's work rate: 1/x lawn/minuteBilly's work rate: 1/(x - 20) lawn/minuteThe combined work rate when they mow together is the sum of their individual work rates, which is equal to 1/60 since they take 60 minutes together. So, we have:
1/x + 1/(x - 20) = 1/60
By solving this equation for x, we find the time it takes Bobby to mow the lawn by himself.
Multiply through by 60x(x - 20) to clear the denominators:60(x - 20) + 60x = x(x - 20)60x - 1200 + 60x = x^2 - 20xCombine like terms:x^2 - 140x + 1200 = 0Solve for x using the quadratic formula or by factoring:(x - 120)(x - 10) = 0Therefore, x = 120 or x = 10. Since x has to be greater than 20, x = 120 is the correct solution.Hence, Bobby will take 120 minutes to mow the lawn by himself.
Find the value of each variable in the parallelogram
pls help:)
Answer:
Step-by-step explanation:
In a parallelogram, the opposite sides are equal and parallel.
Also, consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.
Angle 2m and angle n are supplementary angles. Therefore,
2m + n = 180 - - - - - - - - - - - -1
Also, the opposite angle in a parallelogram are equal. This means that
2m = 70
m = 70/2
m = 35 degrees
Substituting m = 35 into equation 1, it becomes
2 × 35 + n = 180
70 + n = 180
n = 180 - 70
n = 110 degrees
The value of m and n are 35 and 110 respectively.
We are given that one of the angles of the parallelogram is [tex]70^\circ[/tex].
Since opposite angles in a parallelogram are supplementary, the angle directly opposite the 70° angle must be [tex]180^\circ -70^\circ = 110^\circ[/tex].
We are also given that one of the non-consecutive interior angles has a measure of 2m°.
Since consecutive interior angles in a parallelogram add up to 180°, the angle next to the 2m° angle must have a measure of 180°- 2m°.
The opposite sides of a parallelogram are congruent.
This means that n° must be congruent to 110°. So, n = 110.
We can now solve for 'm'.
Since the angle next to the 2m° angle must have a measure of 180°−2m° and this angle is also congruent to 110°.
We have the equation: [tex]110^\circ = 180^\circ - 2m^\circ[/tex]
[tex]2m^\circ = 70^\circ[/tex]
[tex]m=35[/tex]
The gas tank of Alberto's car holds a total of 42 liters of gas. At the beginning of the week, Alberto's car has 35.8 liters of gasoline in its tank. He uses 28.6 liters of gasoline during the week. Then he completely fills the tank with gas. How many liters of gas does Alberto buy?
Answer:
34.8 liters
Step-by-step explanation:
He has 35.8 liters.
He uses 28.6 liters.
Now that tanks has 35.8 liters - 28.6 liters = 7.2 liters
The capacity of the tank is 42 liters, and he has only 7.2 liters.
The fill up will be 42 liters - 7.2 liters = 34.8 liters
Answer: he bought 34.8 liters of gas.
Step-by-step explanation:
Let x represent the number of liters of gas that Alberto bought.
At the beginning of the week, Alberto's car has 35.8 liters of gasoline in its tank. He uses 28.6 liters of gasoline during the week. This means that the number of liters of gas left would be
35.8 - 28.6 = 7.2
Then he completely fills the tank with gas. If the gas tank of Alberto's car holds a total of 42 liters of gas., it means that
x + 7.2 = 42
x = 42 - 7.2
x = 34.8 liters
Suppose parametric equations for the line segment between (6,9) and (0,0) have the form: x = a+bt y = c+dt If the parametric curve starts at (6,9) when t=0 and ends at (0,0) at t=1, then find: a = b = c = d =
What is 0.05 Equal to 0.5.
Jerry says I've got my money in a great account that compounds interest monthly. The equation y=388 (1.008) represents how much money I have at the end of the month. What is Jerry 's monthly interest rate? What is his annual interest rate? Write an equation to represent your total money if you invest $500 in an account with the same rate of return .Let m represent the number of months the money has been invested
Answer:
(a)His monthly Interest Rate=0.8%
(b)Annual Interest Rate = 9.6%
(c)[tex]500(1.008)^m[/tex]
Step-by-step explanation:
For a Principal P invested at a yearly rate r, compounded m times in t years
Amount at Compound Interest= [tex]P(1+\frac{r}{m})^{mt}[/tex]
Comparing with Jerry's equation y=388 (1.008)
(a)His monthly Interest Rate= 0.008=0.8%
(b)Annual Interest Rate= Monthly Interest Rate X 12 =0.8 X 12 = 9.6%
(c)If I invest $500 at the same rate of return,
Total Money after m months
= [tex]P(1+\frac{r}{m})^{mt}[/tex][tex]=500(1+0.008)^{m}[/tex][tex]=500(1.008)^m[/tex]
Final answer:
Jerry's monthly interest rate is 0.8%, and his annual interest rate is approximately 9.96%. An investment of $500 in the same account would grow according to the equation [tex]y = 500(1.008)^{m}[/tex], where m represents the months invested.
Explanation:
Jerry says he's got his money in a great account that compounds interest monthly. The equation [tex]y=388(1.008)^{m}[/tex] represents how much money he has at the end of the month. The monthly interest rate is found in the equation inside the parentheses, 1.008, which means the monthly interest rate is 0.8% (since 1.008 is equal to 1 plus 0.008 or 1 + 0.8/100). To find the annual interest rate, we need to use the compounding formula, which for monthly compounding can be simplified to [tex](1 + monthly interest rate)^{12} - 1[/tex]. so, [tex](1.008)^{12}- 1[/tex] gives an annual rate of approximately 9.96%.
To write an equation representing your total money if you invest $500 in an account with the same rate of return, we use the formula [tex]y = P(1 + r)^{m}[/tex], where P is the principal amount ($500), r is the monthly interest rate (0.008), and m represents the number of months the money has been invested. Therefore, the equation is [tex]y = 500(1.008)^{m}[/tex].
A sports survey taken at THS shows that 48% of the respondents liked soccer, 66% liked basketball and 38% liked hockey. Also,30% liked soccer and basketball, 22% liked basketball and hockey, 28% liked soccer and hockey. finally, 12% liked all three sports. A. Draw a. venn diagram to represent the given information. B. What is the probability that a randomly selected student likes basketball or hockey? Solve this by also using an appropriate formula. C. What is the probability that a randomly selected student does not like any of these sports?
Answer:
a) The Venn diagram is presented in the attached image to this answer.
b) 0.82
c) 0.16
Step-by-step explanation:
a) The Venn diagram is presented in the attached image to this answer.
n(U) = 100%
n(S) = 48%
n(B) = 66%
n(H) = 38%
n(S n B) = 30%
n(B n H) = 22%
n(S n H) = 28%
n(S n B n H) = 12%
The specific breakdowns for each subgroup is calculated on the Venn diagram attached.
b) The probability that a randomly selected student likes basketball or hockey.
P(B U H)
From the Venn diagram,
n(B U H) = n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) = 26 + 10 + 18 + 12 + 16 + 0 = 82%
P(B U H) = 82/100 = 0.82
c) The probability that a randomly selected student does not like any of these sports.
P(S' n B' n H')
n(S' n B' n H') = n(U) - [n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) + n(S n B' n H')]
n(S' n B' n H') = 100 - (26 + 10 + 18 + 12 + 16 + 0 + 2) = 100 - 84 = 16%
P(S' n B' n H') = 16/100 = 0.16
Faculty members at Lowell Place High School want to determine whether there are enough students to have a Valentine's Day Formal. Eighty-eight of the 200 students said they would attend the Valentine's Day Formal. Construct and interpret a 90% confidence interval for p.
Answer:
The 90% confidence interval is (0.383,0.497)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 200
Number of children that would attend Valentine's Day Forma, x = 88
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{88}{200} = 0.44[/tex]
90% Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = \pm 1.64[/tex]
Putting the values, we get:
[tex]0.44\pm 1.64(\sqrt{\dfrac{0.44(1-0.44)}{200}}) = 0.44\pm 0.057\\\\=(0.383,0.497)[/tex]
Interpretation:
The 90% confidence interval is (0.383,0.497). We are 90% confident that the proportion of children attending Valentine's Day Formal is between 38.3% and 49.7%
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.3 and a standard deviation of 2.5. Answer parts (a)dash(d) below. (a) Find the probability that a randomly selected study participant's response was less than 4. The probability that a randomly selected study participant's response was less than 4 is nothing. (Round to four decimal places as needed.)
Answer:
P ( X < 4 ) = 0.3015
Step-by-step explanation:
Given:
- The ratings for current lives on a scale 0 - 10 were normally distributed with parameters mean (u) and standard deviation (s).
u = 5.3
s = 2.5
Find:
Find the probability that a randomly selected study participant's response was less than 4.
Solution:
- Declare a random variable X that follows a normally distribution with parameters u and s, mean and standard deviation respectively.
X~N( 5.3 , 2.5 )
- To determine the probability of the rating to be less than 4 for a randomly selected study participant's response we have:
P ( X < 4 )
- Compute the Z-score value for the limit given:
P ( Z < (4 - 5.3) / 2.5 )
P ( Z < -0.52 )
- Use the Z-Table to calculate the above probability as follows:
P ( Z < -0.52 ) = 0.3015
- Hence, the required probability is equivalent to Z-score value probability:
P ( X < 4 ) = P ( Z < -0.52 ) = 0.3015
The probability that a randomly selected study participant's response was less than 4 is 0.3015.
To find the probability that a randomly selected study participant's response was less than 4, we can use the properties of the normal distribution. Given that the mean is 5.3 and the standard deviation is 2.5, we can standardize the value 4 using the z-score formula: z = (X - µ) / σ, where X is the value of interest, µ is the mean, and σ is the standard deviation. Once we find the z-score, we look up this value in the standard normal distribution table (Z-table) or use a calculator to find the probability.
Step-by-step calculation:Calculate the z-score for X = 4: z = (4 - 5.3) / 2.5 = -0.52.Look up the z-score in the Z-table or use a calculator to find the probability that Z < -0.52.For a z-score of -0.52, the probability is approximately 0.3015 (found from Z-table or through calculator).The probability that a randomly selected study participant's response was less than 4 is therefore 0.3015, or 30.15% when converted into percentage form.
The equation Upper A left parenthesis t right parenthesis equals 2000 e Superscript 0.055 t gives the balance after t years of an initial investment of 2000 dollars which pays 5.50% compounded continuously. a. Find a formula for StartFraction dA Over dt EndFraction b. Find and interpret Upper A prime left parenthesis 8 right parenthesis. Include appropriate units. c. Compare the approximation of $171 to the actual change. Report your answer to two decimal places.
Answer:
a) Rate of change of amount
[tex]A'(t) =110e^{0.055t}[/tex]
b) &170.79
c) 0.21
Step-by-step explanation:
We are given the following in the question:
The balance is given by the equation:
[tex]A(t) =- 2000e^{0.055t}[/tex]
where t is the time in years and the initial investment is $2000 when compounded continuously.
a) Rate of change of amount
[tex]\dfrac{d(A(t))}{dt} = \dfrac{d}{dt}(2000e^{0.055t})\\\\\dfrac{d(A(t))}{dt} = 2000e^{0.055t}\times 0.055\\\\\dfrac{d(A(t))}{dt} =110e^{0.055t}[/tex]
b) We have to find the value of A'(8)
[tex]A'(t) =110e^{0.055t}\\A'(8) = 110e^{0.055(8)} = 170.79[/tex]
Interpretation:
The future value of 9 year investment of $2000 will be $170.79 more than the future value of 8 year investment.
c) Comparison
Approximation = $171
Actual change = $170.79
Difference =
[tex]\text{Approximation - Actual change}\\=171 - 170.79\\=0.21[/tex]
Thus, the error is 0.21
The formula for dA/dt is 2000(0.055)e^(0.055t). A'(8) is found by substituting t=8 into dA/dt. To compare the approximation of $171 to the actual change, subtract the initial investment from the new balance after 8 years.
Explanation:a. To find the formula for dA/dt, we differentiate the equation A(t) = 2000e^(0.055t) with respect to t. Using the chain rule, we have dA/dt = 2000(0.055)e^(0.055t).
b. To find A'(8), we substitute t = 8 into the expression for dA/dt. Plugging in the values, we get A'(8) = 2000(0.055)e^(0.055(8)). This will give us the rate of change of the balance after 8 years.
c. To compare the approximation of $171 to the actual change, we subtract the initial investment of $2000 from the new balance after 8 years. The approximation is $171, so the actual change is A(8) - 2000. Plugging in the values, we get A(8) - 2000 = 2000e^(0.055(8)) - 2000.
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There is 7/8 quarts of orange juice. Mrs. Mathewson would like to serve her guests 3/16 quarts orange juice. How many guests can she serve orange juice?
Mrs. Mathewson can serve orange juice to 4 guests. The solution was found by first converting the fractions to the same denominator, then dividing the total orange juice by the amount per guest, and taking into account that you can't serve fractions of a guest.
Explanation:The problem presented here is a basic division problem that requires you to divide the total amount of orange juice by the amount served to each guest. Mrs. Mathewson has 7/8 quarts of orange juice and she would like to serve each guest 3/16 quarts of orange juice.
Firstly, we'll convert both fractions to the same denominator for simplicity. As 8 is a multiple of 16, we can leave the second fraction as it is (3/16) and change the first fraction to 14/16 (which is the same as 7/8). Now, we divide 14 by 3 which gives us roughly 4.6.
This result means Mrs. Mathewson can serve orange juice to 4 guests with a bit left over. As we can't serve a fraction of a guest, it means she can only serve 4 whole guests.
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Mrs. Mathewson can serve orange juice to 14 guests.
Explanation:
To determine how many guests Mrs. Mathewson can serve orange juice, we need to find the quotient of the total amount of orange juice and the amount per guest. Given that there are 7/8 quarts of orange juice and Mrs. Mathewson wants to serve 3/16 quarts per guest, we divide the total amount by the amount per guest: (7/8) ÷ (3/16) = (7/8) × (16/3) = 14 guests.
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Linda Johnson, a broker, sold a home for $85,000. The home had been listed with another real estate firm for a 7% commission. The commission split between Johnson's principal broker and the other principal broker was 50/50. The commission split between Johnson and her principal broker was 65% to the broker, 35% to the principal broker. What was Johnson's commission from the sale of the home
Answer:
Linda's share was $ 1933.75
Step-by-step explanation:
We first need to calculate the comission that was paid to the other real state firm wich is 7% of the sales price, so we can use the following equation:
Comission = 85000 * (7/100) = 85000*0.07 = 5950 $
Since this comission was split in half between Johnson's broker and the other broker we have 5950/2 = 2975 for each of them. From that value 65% should stay with the broker wich is Linda in this case so:
Linda's share = 2975*(65/100) = 2975*(0.65) = 1933.75 $.
Given Information:
Sale Amount = $85,000
Commission rate = 7%
Linda Johnson commission rate = 65% of 50% of commission amount
Required Information:
Linda Johnson share in the sale = ?
Answer:
Linda Johnson share in the sale = $1933.75
Step-by-step explanation:
Linda Johnson share in the sale is
Linda's share = 65% of 50% of commission amount
Where commission amount is
commission amount = 7% of sale amount
commission amount = 0.07*85,000
commission amount = $5,950
Linda's share = 0.65*0.50*5,950
Linda's share = $1933.75