A shop has jars of strawberry jam and raspberry jam in the ratio 3:1
Two customers come into the shop and randomly select a jar of jam
to purchase.
The probability that both customers select strawberry jam is 11/20
a) How many jars of jam does the shop have initially?
b) Given that the customers both chose the same type of jam, work
out the probability that they both chose strawberry.
Answers
The shop initially has 0.884 jars of jam
The probability that both customers chose strawberry jam, is 0.25.
a) Let's assume the number of jars of strawberry jam is 3x and the number of jars of raspberry jam is x.
So, the total number of jars of jam in the shop is 3x + x = 4x.
According to the given information, the probability that both customers select strawberry jam is 11/20.
So, the probability of the first customer selecting a jar of strawberry jam = (3x/4x) = 3/4,
and the probability of the second customer
= ((3x-1)/(4x-1)).
Now, (3/4) ((3x-1)/(4x-1)) = 11/20
(3/4) ((3x-1)/(4x-1)) = 11/20
20(3/4) ((3x-1)/(4x-1)) = 11
15 (3x-1) = 44 (4x-1)
45x - 15 = 176x - 44
176x - 45x = 44 - 15
131x = 29
x ≈ 29/131
Therefore, the value of x is 0.221
To find the initial number of jars of jam in the shop, we can substitute this value of x into the equation:
4x = 0.884
b) The probability of the first customer selecting strawberry jam is
= (3x)/(4x)
= 3/4.
Therefore, the probability that both customers chose strawberry jam is:
= (3/4) x ((3x-1)/(4x-1))
= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))
= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))
≈ 0.25
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Related Questions
PLEASE HELP!!!!!!!!!
Answers
According to the information we can infer that the scale drawing of the football field will have dimensions of 2.5cm by 4.5cm.
How to create the scale drawing?To create the scale drawing, we need to convert the real-life dimensions of the football field into centimeters and then apply the scale of 1:2000.
Real-life dimensions:
Length: 50mWidth: 90mConverting to centimeters:
Length: 50m * 100cm/m = 5000cmWidth: 90m * 100cm/m = 9000cmApplying the scale of 1:2000:
Length on the drawing: 5000cm / 2000 = 2.5cmWidth on the drawing: 9000cm / 2000 = 4.5cmAccording to the above, the scale drawing of the football field will have dimensions of 2.5cm by 4.5cm.
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ERGENT! DUE TODAY! What is the equation in point-slope form of the line that passes through the point (3,-2) and has a slope of 2/3?
(look at image)
Answers
Answer:
y = 2/3x - 4
Step-by-step explanation:
A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $128,000.00 for 25 years at a 5.3% annual interest rate, with interest compounded monthly, and will make monthly payments of $770.82. (Round all answers to 2 decimal places.)
Create an amortization table to answer the following:
a) What is the unpaid balance after 9 months? $
b) Over the 9 months in part (a), how much total interest did she pay?
Answers
Answer:
(a) After 9 months, the unpaid balance is $125,874.09.
(b) Over the 9 months, she paid a total of $4,918.56 in interest.
To create the amortization table, we can use the formula for calculating the monthly payment of a loan:
P = (r * A) / (1 - (1 + r)^(-n))
where:
P = monthly payment
r = monthly interest rate
A = loan amount
n = total number of payments
In this case, we have:
A = $128,000.00
n = 25 years * 12 months/year = 300 months
r = 5.3% / 12 = 0.00441666667
Using the formula, we can calculate the monthly payment:
P = (0.00441666667 * $128,000.00) / (1 - (1 + 0.00441666667)^(-300))
P = $770.82
Now, we can create the amortization table:
Please help i need it!!!!!
A 6 N crate is lifted 2 meters. How much work is done?
A) 12 N/m
B) 4 N/m
C) 8 N/m
D) 3 N/m
Answers
The amount of work done is Option A) 12 N/m
What is work done?Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.
It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.
Work done on a body is equivalent to the increase in the energy of the body, because it transfers energy to the body.
The formula for work done is;
W = fd
Where, 'f' is the applied force and d is the distance
Substitute the values
Work done = 6(2)
Work done = 12 N/m
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Please help! I don't understand! :(
Directions:Turn the following expressions in radical form into exponential expressions in fractional form. You do not need to evaluate any of the expressions, just put them in simplest form.
Answers
\(\bold{Hello!}\\\bold{Your~Answer~Is~Below!}\)
______________________________
\(\bold{Solution~Steps:}\)
\(1.)~Simplify~\sqrt[14]{y} :\)
\(\bold{Use~\sqrt[n]{a^x}=a\frac{x}{n}~to~rewrite~\sqrt[14]{y}~in~exponential~fraction~form.}\)\(\bold{\sqrt[14]{y}=y\frac{1}{14} }\)\(2.)~Simplify~\sqrt[y]{5^4} :\)
\(\bold{Use~\sqrt[n]{a^x}=a\frac{x}{n}~to~rewrite~\sqrt[y]{5^4}~in~exponential~fraction~form.}\)\(\bold{\sqrt[y]{5^4}=5\frac{4}{y}}\)\(3.~Simplify~\sqrt{9^3}:\)
\(\bold{Use~\sqrt[n]{a^x}=a\frac{x}{n}~to~rewrite~\sqrt{9^3} ~in~exponential~fraction~form.}\)\(\bold{\sqrt{9^3}=9\frac{3}{2}}\)\(4.)~Simplify~\sqrt[n]{m}\)°\(:\)
\(\bold{Use~\sqrt[n]{a^x}=a\frac{x}{n}~to~rewrite~\sqrt[n]{m}}\)° \(\bold{~in~exponential~fraction~form.}\)\(\bold{\sqrt[n]{m}}\)°\(\bold{=\frac{m}{n}}\)°\(5.)~Simplify~\sqrt{y^2}:\)
\(\bold{Use~\sqrt[n]{a^x}=a\frac{x}{n}~to~rewrite~\sqrt{y^2} ~in~exponential~fraction~form.}\)\(\bold{\sqrt{y^2}=y}\)______________________________
\(\bold{Answers:}\)
\(\bold{1~is~y\frac{1}{14}.}\)\(\bold{2~is~5\frac{4}{y}.}\)\(\bold{3~is~9\frac{3}{2}.}\)\(\bold{4~is~\frac{m}{n}}\)°\(\bold{.}\)\(\bold{5~is~y.}\)______________________________
\(\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~-TotallyNotTrillex}\)
The brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. Use the
given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or
significantly high. For such data, would a brain volume of 1386.4 cm³ be significantly high?
Answers
If the brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. For such data: it is significantly low for a brain because 1386.4 cm³ is less than the upper limit.
How to find the lower and upper limits?Mean = 1085.2 cm³
Standard deviation = 125.6 cm³
Hence,
Lower limit = Mean - 2 x Standard deviation
Lower limit =1085.2 - 2 x 125.6
Lower limit =1161.2 - 251.2
Lower limit =910
Upper Limit = Mean + 2 x Standard deviation
Upper Limit = 1161.2 + 2 x 125.6
Upper Limit =1161.2 +251.2
Upper Limit =1412.4
The limit of values is from 910 to 1412.4.
A value below 910 will be is considered low and a value above 1412.4 will be considered high
Therefore 1386.4 cm³ is less than the upper limit. Thus it is significantly low for a brain.
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An employee receives a salary increase of 8% at the end of each full year working with a company. If the employee receives an initial salary of $35,400, which equation represents the employee’s salary, S, after t years since the employee began working with the company?
Answers
The equation that represents the employee’s salary, S, after t years since the employee began working with the company is S(t) = 35400 * (1.08)^t
How to determine the equation that represents the employee’s salaryFrom the question, we have the following parameters that can be used in our computation:
Initial salary = 35400
Raise = 8%
Number of years = t
The equation that represents the employee’s salary is calculated as
Salary = Initial salary * (1 + raise)^Number of years
Substitute the known values in the above equation, so, we have the following representation
Salary = 35400 * (1 + 8%)^t
So, we have
S(t) = 35400 * (1.08)^t
Hence, the equation is S(t) = 35400 * (1.08)^t
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Determine if the measurements below will create a triangle. Then, explain your thinking.
55°, 80°, 55°
Answers
Answer:
No, the measurements given cannot be used to create a triangle.
Explanation:
The sum of all the angles of a triangle should be 180°.
Here,
55°+80°+55°=190°
which is not equal to 180°.
So, the traingle cannot be formed using the given measurements.
what means ratio with explanation
Answers
PLEASE HELP ITS FOR MATH
Answers
The answer is b. none. This is because the lines are parallel and therefore do not intersect at a point, meaning that there are no solutions.
please I need this in 15 min so please could u send it asap
Answers
Answer:
11. a) P = 27t³/8
b) 27
c) t = \(\sqrt[3]{\frac{64}{81} }\)
12. a) V = 2x³
c) A = 10x²
Step-by-step explanation:
P = a * t³
1 = a * (2/3)³
a = 27/8
P = 27t³/8
--------
P = 27(2)³/8 = 27
--------
8/3 = 27t³/8
t = \(\sqrt[3]{\frac{64}{81} }\)
--------
V = x * x * 2x = 2x³
--------
A = 2(x * x) + 2(x * 2x) + 2(x * 2x) = 2x² + 4x² + 4x² = 10x²
Ryan works at the hotel 5 days a week. He spends $2.50 each
day on a roundtrip bus ticket to get to work. How much
money does Ryan earn each week after paying this expense?
Answers
Answer:
His weekly expense is $12.50. You did not mention how much he earned but you would subtract the 12.50 to find out how much he earned after his expense.
Step-by-step explanation:
If f(x)=x^(2 )+4 then verify (fof^(-1))(x)=(f^(-1) of)(x)=x. (Consider the positive values only)
Answers
Answer:
Step-by-step explanation:
If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved
What is a function?A relation is a function if it has only One y-value for each x-value.
Composite functions are when the output of one function is used as the input of another.
If f(x)=x²+4
Then we have to prove f⁻¹of(x)=f⁻¹(f(x)
Let us consider fof⁻¹(x)
f(f⁻¹(x))
x
So (fof⁻¹(x))=x
Now f⁻¹of(x)=f⁻¹(f(x)
=x
Hence, If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved
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A set of twins purchase a small, oddly shaped plot of land for their retirement. They want to divide the parcel along the grid lines into two identical plots. Can they do it and how?
Answers
The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.
To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.
For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.
If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.
However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.
To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.
If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.
the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.
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Note the full question may be :
To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.
Beth Hazelton purchased a compact vehicle with an $18,240.00. MSRP including the delivery and title fee. She selected a leather interior which costs 5 times the upgraded stereo system. If the total cost of the vehicle, including a 7% sales tax, was $21,365.20 find the cost of the (a) stereo system and (b) leather interior. Use the example in the book to help you with solving this problem.
Answers
Answer:
price of leather thingy= $2906.62
price of stereo system = $581.33
Step-by-step explanation:
final cost minus cost of total before adding the leather.
21,365.20
- 18,240.00
= $3125.2
to find the exact price of the leather since the 7% tax was included in the price we mulitply by .93
3125.2 x .93 = 2906.62
we know the stereo is 1/5 of the price of the leather so we divide by 5 2906.63 ÷ 5 = 581.33
there u go! pls give brainliest :D
Micheal records the number of miles he runs each week for nine weeks.
6,11,13,8,15,9,11,5,9
Which box plot represents the data?
Answers
Answer:
... c
Step-by-step explanation:
Which of the following is the maximum value of the function y=–2x2 + 5?
Answers
Answer:
( 1. 6 )
Step-by-step explanation:
Use the formula:
x = - b/2a
to find the maximum and minimum.
Answer: (1, 6 )
Step-by-step explanation:
This should help:
x = - b/2a
Please help I am so so confused thank you all
Answers
y-(-9) = -6(x-(-4)), y = -6x-33
HELPPPP I NEED HELP PLEASE IT'S MATH
Answers
Answer:
b. 5, 11, 6
Step-by-step explanation:
Let the sides of a triangle be a, b, and c, where a < b < c. Then, we know that a + b > c. If we use this identity to solve this problem, then we can find that answer choice b does not satisfy it. Thus, b does NOT have the lengths of a triangle.
I need help solving this please. Image is below.
Answers
The volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.
To find the volume of the solid obtained by rotating the region enclosed by the given graphs about the y-axis, we can use the method of cylindrical shells.
First, let's sketch the region to visualize it better.
The region is enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0.
Let's find the intersection points of these curves by setting them equal to each other:
18 - x = 3x - 6
Simplifying the equation, we have:
4x = 24
x = 6
So, the intersection point is (6, 12).
Now, we can integrate to find the volume of the solid.
The radius of each cylindrical shell is the distance from the y-axis to the curve y = 18 - x.
This can be expressed as x.
The height of each cylindrical shell is the difference between the two curves, which is (18 - x) - (3x - 6).
The volume of each cylindrical shell is given by the formula:
V = 2πrhΔx, where r is the radius, h is the height, and Δx is the width of each shell.
Integrating from x = 0 to x = 6, we can find the total volume:
V = ∫[0,6] 2πx[(18 - x) - (3x - 6)] dx
V = ∫[0,6] 2πx(24 - 4x) dx
V = 2π ∫[0,6] (24x - 4x²) dx
V = 2π [12x² - (4/3)x³] | [0,6]
V = 2π [(12(6)² - (4/3)(6)³) - (12(0)^2 - (4/3)(0)^3)]
V = 2π [(12(36) - (4/3)(216)) - (0 - 0)]
V = 2π [(432 - 288) - (0 - 0)]
V = 2π (432 - 288)
V = 2π (144)
V = 288π
Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.
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A rectangular room is 1.3 times as long as it is wide, and its perimeter is 27 meters. Find the dimension of the room.
Answers
The dimensions of the room are approximately 5.87 meters by 7.63 meters.
Let's assume the width of the room is "x" meters.
According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.
Perimeter = 2(length + width)
Substituting the values we know:
27 = 2(1.3x + x)
Simplifying:
27 = 2(2.3x)
27 = 4.6x
Dividing both sides by 4.6:
x = 27 / 4.6
x ≈ 5.87
The width of the room is approximately 5.87 meters.
To find the length, we can multiply the width by 1.3:
Length = 1.3 * 5.87 ≈ 7.63
The length of the room is approximately 7.63 meters.
Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.
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2. A(n) is NOT an example of an agreement. (1 point)
O lease
O month-to-month
O annual
O fine print
Answers
An Annual is not an example of an agreement.
Please can someone help me with this? Of 100 students, 27 are taking caculus,26 are taking french, and 13 are taking both calculus and french. If a student is picked at random what is the probability that the student is taking calculus OR french ? Answer needs to be in decimal form rounded to two decimal places. Look up what two decimal places is if you don't know.
Answers
Answer:
Rounded to two decimal places, the probability that a randomly chosen student is taking Calculus or French is 0.40.
Step-by-step explanation:
Probability = (Number of students taking Calculus + Number of students taking French - Number of students taking both) / Total number of students
Given:
Total number of students (n) = 100
Number of students taking Calculus (C) = 27
Number of students taking French (F) = 26
Number of students taking both Calculus and French = 13
Using the formula:
Probability = (C + F - Both) / n
Probability = (27 + 26 - 13) / 100
Probability = 40 / 100
Probability = 0.40
4 11/18-x= 1 31/16 what is x
Answers
Answer: x=241/144
Step-by-step explanation:......
Answer:
x= 2.88194 or x= 2 127/144
Step-by-step explanation:
I put your question into a math calculator and got this for the answer. Good luck!
How long would it take for an investment to at least double its original amount at 3.62% compounded semi annually
Answers
Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.
When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.
This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.
To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:
Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years
To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.
The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years
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Need answer please help
Answers
Answer: X=45
Step-by-step explanation:
Find the interest earned given the following: Amount needed: $9,350Time in years: 4Interest: 5%Compounded: semiannually
Answers
From the question
Invested Amount: $9,350
Time in years: 4
Interest: 5%
Compounded: semiannual
The formula for compound interest is
\(A=P(1+\frac{r}{100n})^{nt}\)From the given information
P = $9,350
t = 4
r = 5
Since the amount was compounded semiannually then
n = 2
Substitute these values into the equation
\(A=9350(1+\frac{5}{100\times2})^{2\times4}\)Simplify and solve for A
\(\begin{gathered} A=9350(1+\frac{5}{200})^8 \\ A=9350(1+0.025)^8 \\ A=9350(1.025)^8 \\ A=11392.07 \end{gathered}\)Interest is given as
\(I=A-P\)Hence,
\(\begin{gathered} I=11392.07-9350 \\ I=2042.07 \end{gathered}\)Therefore, the interest is $2,042.07
As an event organizer, you are to host 120guests in a room of dimensions 18m long and 12m wide. You have rectangular tables which are 2m long and 0.75m wide. The number of guests allocated for the top table is 12 and the rest of the guests are on 3springs. NB: cover space is 0.6m i) Sketch the table plan arrangement. ii) Calculate the number of tables required for the top table. iii) Calculate the number of covers on each spring. iv) calculate the number of tables required for each spring. v) What is the purpose of leaving a gangway when arranging tables and chairs for an event?
Answers
length of the table=2m cover space for a guests=0.6m so cover space for top table is 12=12×0•6=7•3(4×2)=8
Step-by-step explanation:
The room, the tables and the guests are illustrations of rectangles and areas.
How many tables are required for the top table?This is calculated using:
Tables = Guest ÷ Guest per top table
So, we have:
Tables = 120 ÷ 12
Evaluate
Tables = 10
Hence, 10 tables are required for the top table
How many covers are on each spring?This is calculated using:
Covers = Number of spring ÷ Cover space
So, we have:
Covers = 3 ÷ 0.6
Evaluate
Covers = 5
Hence, 5 covers are required for each spring
How many tables are required for each spring?This is calculated using:
Tables = Tables for top table ÷ Spring
So, we have:
Tables = 10 ÷ 3
Evaluate
Tables = 3.33
Remove decimal
Tables = 3
Hence, 3 tables are required for each spring
What is the purpose of leaving a gangway when arranging tables and chairs for an event?This is done to allow passage for walkway
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Meera needs 2 3/4 cups of flour for a batch of cookies and 3 1/3 flour for a dozen muffins. How many cups of flour does Meera need altogether?
Show work out please ( for brainliest )
Answers
Answer:
6 cups.
2 3/4 X 3 1/3
Step-by-step explanation:
PLEASE ANSWER FAST
If n
A
-3, which expression has the least value?
n²no
n8n-5
nn
-nnn-4
B