James has x merit points.
Sarah has three times as many merit points than James.
Robert has 61 fewer merit points than James.
Each merit point is worth 3 pence.
All three of the students have a total of £15.72
Work out how many merit points each student has.
Answers
James has 117 merit points, Sarah has 351 merit points, and Robert has 56 merit points.
Let's break down the given information and solve the problem step by step.
Let's assume James has x merit points.
According to the given information, Sarah has three times as many merit points as James. Therefore, Sarah has 3x merit points.
Robert has 61 fewer merit points than James. So, Robert has (x - 61) merit points.
Now, we can calculate the total value of the merit points in pence. Since each merit point is worth 3 pence, we can express the total value in pence as:
Value in pence = (x * 3) + (3x * 3) + ((x - 61) * 3)
Next, we need to convert the total value from pence to pounds. Since there are 100 pence in 1 pound, we divide the total value in pence by 100 to get the value in pounds:
Value in pounds = Value in pence / 100
According to the problem, the total value is £15.72. So we can set up the equation:
Value in pounds = 15.72
Now we can substitute the expression for the value in pounds into the equation:
((x * 3) + (3x * 3) + ((x - 61) * 3)) / 100 = 15.72
Simplifying the equation:
(3x + 9x + 3x - 183) / 100 = 15.72
Combining like terms:
15x - 183 / 100 = 15.72
Multiplying both sides of the equation by 100 to eliminate the fraction:
15x - 183 = 1572
Adding 183 to both sides:
15x = 1755
Dividing both sides by 15:
x = 117
Now we have the value of x, which represents the number of merit points James has. Plugging this value into the expressions we obtained earlier, we can find the number of merit points for each student:
James: x = 117 merit points
Sarah: 3x = 3 * 117 = 351 merit points
Robert: (x - 61) = 117 - 61 = 56 merit points
Therefore, James has 117 merit points, Sarah has 351 merit points, and Robert has 56 merit points.
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Related Questions
difference of 85 and 45
Answers
The difference of 85 and 45 is 40
Hareem takes a medicine to control his blood pressure. he takes a 25 mg pill in the morning. suppose that 60% of the medicine is processed by hareem's body by the time he takes a second 25 mg pill in the evening. what is the recursive definition for the amount of the blood pressure medicine in hareem bloodstream after n hours?
a. a1=25, an= 0.40an-1 + 25
b. a1=25, an = 0.60n-1 +25
c. a1=40, an=0.60n-1 +25
d. a1 = 0.60, an = 0.40an-1
Answers
The recursive definition for the amount of the blood pressure medicine in Hareem's bloodstream after n hours can be defined as :
a. a1=25, an= 0.40an-1 + 25
Base Case:
The initial amount of medicine in Hareem's bloodstream after 0 hours is 25 mg.
Recursive Step:
The amount of medicine in Hareem's bloodstream after n hours can be calculated by taking 60% of the amount of medicine in his bloodstream after (n-1) hours, and then adding 25 mg.
To write this recursive definition in mathematical notation:
M(n) = 25 mg, if n = 1
M(n) = 40 mg, if n = 6
M(n) = M(n-1) + (60% * M(n-1)), if n > 6
This recursive definition represents the amount of the blood pressure medicine in Hareem's bloodstream after n hours. The base case sets the initial amount of medicine, and the recursive step calculates the amount of medicine at each hour by taking 60% of the previous amount and adding 25 mg.
The correct option is a. a1=25, an= 0.40an-1 + 25
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jacks mom purchased a savings bond for jack. the value of the savings bond increases by 5% each year. one year after it was purchased, the value of the savings bond was $210. find the value of the bond when jacks mom purchased it.
Answers
Answer:
Step-by-step explanation:
A retail grocer bought a case of 12 packages of coffee for $52.32.
How much did the retailer pay for each package of coffee?
The retailer sold each package for $12.59.
What is the difference between the retailer’s cost and the selling price for each package of coffee?
Answers
Answer:
4.36
8.23
Step-by-step explanation:
Answer:
4.36
Step-by-step explanation:
PLEASE HELP!!!
Solve.
-2x+3y-z=-2
3x + y = 4
-2y+2z=4
Enter your answer, in the form (x, y, z), in the boxes in simplest terms.
Answers
Step-by-step explanation:
the second equation gives us right away
y = 4 - 3x
we can use that now in the 3rd equation :
-2(4 - 3x) + 2z = 4
-8 + 6x + 2z = 4
6x + 2z = 12
3x + z = 6
z = 6 - 3x
now we use both in the 1st equation :
-2x + 3(4 - 3x) - (6 - 3x) = -2
-2x + 12 - 9x - 6 + 3x = -2
-8x + 6 = -2
-8x = -8
x = 1
y = 4 - 3x = 4 - 3×1 = 4 - 3 = 1
z = 6 - 3x = 6 - 3×1 = 6 - 3 = 3
so,
(1, 1, 3)
Write an equation for the description.
Felix sold 35 fewer raffle tickets than Helene. How many tickets F did Felix sell if Helene sold H tickets?
Answers
Answer:
H = F + 35
Step-by-step explanation:
If Felix has 35 less than Helen, then adding 35 to Felix's amount should equal Helen's amount
A cooler contains nine bottles of sports drink: 4 lemon-lime flavored, 3 orange flavored, and 2
fruit punch flavored. Your friend randomly selects a drink and drinks it. 10 minutes later, you
randomly select a drink and drink it. What is the probability that your friend got a drink flavored
fruit punch and you got a drink flavored orange?
Answers
Answer:
The probability that out of the nine drinks in the cooler, one of the two friends selects a drink flavored fruit punch after which the next of the two friends selects a drink flavored orange is \(0.08 \overline 3\)
Step-by-step explanation:
The given parameters for the content of the cooler are;
The total number of bottles of sports drink in the cooler, n = 9 bottles
The number of lemon-lime flavored bottles of sports drink in the cooler, L = 4 bottles
The number of orange flavored bottles of sports drink in the cooler in the cooler, O = 3 bottles
The number of fruit punch flavored bottles of sports drink in the cooler, F = 2 bottles
The probability of selecting a drink flavored fruit punch, \(P_F\) = F/n = 2/9
The probability of selecting a drink flavored orange given that a drink flavored fruit punch has already been selected is \(P_{O(n_1)}\) = O/(n₁)
Where;
n₁ = n - 1 = 9 - 1 = 8
∴ \(P_{O(n_1)}\) = O/(n₁) = O/(n - 1) = 3/(9 - 1) = 3/8
Therefore, the probability that the first of two friends to select a drink got a drink flavored fruit punch and the second of the two friends got a drink flavored orange is, P = \(P_F\) × \(P_{O(n_1)}\)
∴ P = 2/9
\(P = \dfrac{2}{9} \times \dfrac{3}{8} = \dfrac{6}{72} = \dfrac{1}{12}\)
The probability that one of two friends selects a drink flavored fruit punch and the next of the two friends selected a drink flavored orange is P = 1/12 = 0.08\(\overline 3\).
You save 4000 in a bank account that pays 3. 25% annual interest. Calculate the amount in the account 5 years later when the interest is compounded quarterly and daily
Answers
The amount in the account after 5 years when compounded quarterly is $4702.7 , when compounded daily is $4705.8 .
The principle amount in bank account is $4000,
The annual rate of interest is = 3.25%,
If the interest is compounded quarterly:
The interest rate per quarter is = 3.25%/4 = 0.8125%
After 5 years, the number of quarters will be = 5 × 4 = 20 quarters,
The balance in the account will be:
⇒ 4000 × (1 + 0.008125)²⁰ = 4702.7
So, the amount in the account after 5 years with quarterly compounding will be $4702.7.
If the interest is compounded daily,
The interest rate per day is = 3.25%/365 = 0.00890411%
After 5 years, the number of days will be = 5 × 365 = 1825 days,
The balance in the account will be:
⇒ 4000 × (1 + 0.0000890411)¹⁸²⁵ = $4705.8
Therefore, the amount in the account after 5 years with daily compounding will be $4705.8.
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If You have this information about return of stock in 3
periods:
-12%, 20% and 25%.
calculate:
a. The arithmetic average.
b. The geometric average.
Answers
Answer:
✔ ∅ a. The arithmetic average.Step-by-step explanation:
If You have this information about return of stock in 3
periods:
-12%, 20% and 25%.
calculate:
✔ ∅ a. The arithmetic average.
✘ O b. The geometric average.
What is the greatest common factor of 12 and 8?
Answers
Answer:
4
Step-by-step explanation:
12/4=3
8/4=2
Answer:
4
Step-by-step explanation:
Determine what type of statistical inference should be used to answer each of the questions below. (You will only use each response one time.)
Answer choices are: Two dependent means, proportions from dependent samples, two independent means, one proportion, one mean, means from dependent samples
1. You want to estimate the typical salary for women working in the nursing field.
2. You want to estimate the proportion of nurses that quit after working for only one year.
3. You want to estimate the difference in the number of men and women that quit the nursing field after only one year.
4. You want to estimate the difference in the salaries of men and women working in the nursing field.
5. The same one hundred people were asked in 2000 and in 2006 how much they had spent on medical bills. Has there been in increase in medical cost?
6. The same one hundred people were asked in the year 2000 and again in the year 2006 if they trusted their local hospitals. Has there been a change in people's trust?
Answers
1. One mean 2. One proportion 3. Proportions from dependent samples 4. Two independent means 5. Means from dependent samples 6. Proportions from dependent samples
1. You want to estimate the typical salary for women working in the nursing field.
Answer: One mean
2. You want to estimate the proportion of nurses that quit after working for only one year.
Answer: One proportion
3. You want to estimate the difference in the number of men and women that quit the nursing field after only one year.
Answer: Two independent means
4. You want to estimate the difference in the salaries of men and women working in the nursing field.
Answer: Two independent means
5. The same one hundred people were asked in 2000 and in 2006 how much they had spent on medical bills. Has there been an increase in medical cost?
Answer: Means from dependent samples
6. The same one hundred people were asked in the year 2000 and again in the year 2006 if they trusted their local hospitals. Has there been a change in people's trust?
Answer: Proportions from dependent samples
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The top-notch middle school had athletes from all the grades playing on a sports team. 6th grade 7th grade 8th grade basketball 2 4 7 baseball 1 6 5 soccer 7 4 4 football 8 15 10 explain what the ratio 5:73 represents. the ratio 5:73 represents the ratio of 8th grade baseball players to total athletes. the ratio 5:73 represents the ratio of 7th grade football players to total athletes. the ratio 5:73 represents the ratio of total athletes to 7th grade football players. the ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
Answers
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
What is ratio?In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.
Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10
= 73
Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.
There are on one event is where 5 athletes are, that is 8th grade baseball players.
So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
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(HELP ASAP 12 POINTS!!) Which point is located at (-3, 4)? A)point B B)point A C)point D D)point C
Answers
Answer:
A
Step-by-step explanation:
A is located at -3,4
Answer:
A
Step-by-step explanation:
Brainliest! Fast answer! Correct answer!
Answers
Answer:
It would be C i believe
Step-by-step explanation:
Two small charged objects are located as shown in the diagram. In the diagram each square represents 10
−2
m.Q
1
=3nC and Q
2
= −6nC. Remember that 1nC (nanocoulomb) is 10
−9
coulombs. You will calculate the net electric field at location
A
=<−0.07,−0.04,0> m. Before doing any calculations, on a copy of the diagram, draw two arrows representing the electric field at the observation location due to each of the charged particles. Use your diagram to answer the following questions: Now calculate these quantities: What is the electric field at
A
due to Q
1
?
E
1
=κ Attempts: 3 of 10 used Part 4 What is the electric field at
A
due to Q
2
?
E
2
=ε >N/C Attempts: 0 of 10 used What is the net electric field at
A
?
E
n→1
=ε >N/C Attempts: 0 of 10 used
Answers
Electric field due to Q1 is 27/10 N/C, electric field due to Q2 is -54/10 N/C and electric field at A due to Q1 is 2.32454 N/C.
Given,
Q1 = 3nCQ2
= -6nC
The distance between them is 0.1 m. (10^2m)
The electric field due to a charge is given by κQ/r^2
Where Q is the charge,
r is the distance,
and κ is a constant.κ = 9 x 10^9 Nm^2/C^2
Electric field due to Q1 =κQ1/r^2
=9 x 10^9 x 3 x 10^-9/ (0.1)^2
= 27/10 N/C
At point A due to E1 = Electric field at point A due to Q1 = E1x i + E1y j + E1z k.
Since the point A is (-0.07, -0.04, 0), so we have to calculate the electric field at point A due to Q1 on the x-axis, y-axis and z-axis respectively.
Therefore, E1x = E1cosθ, E1y = E1sinθ, E1z = 0
Where θ is the angle that E1 makes with the x-axis.
Tanθ= 0.04/0.07
= 0.5714θ
= 30.9638°
Now, E1x = E1cosθ
= 27/10 x cos30.9638°
= 23.2454/10 N/C
And E1y = E1sinθ
= 27/10 x sin30.9638°
= 13.3935/10 N/C
So, E1 = E1x i + E1y j + E1z k
= 23.2454/10 i + 13.3935/10 j + 0 k
= (2.32454, 1.33935, 0) N/C, at point A due to Q1.
Electric field due to Q2 = κQ2/r^2
= 9 x 10^9 x (-6 x 10^-9)/ (0.1)^2
= -54/10 N/C, at point A due to Q2.
E2 = Electric field at point A due to Q2= E2x i + E2y j + E2z k
Since the point A is (-0.07, -0.04, 0), so we have to calculate the electric field at point A due to Q2 on the x-axis, y-axis and z-axis respectively.
Therefore, E2x = E2cosθ, E2y = E2sinθ, E2z = 0
Where θ is the angle that E2 makes with the x-axis.
Tanθ = 0.04/0.07
= 0.5714θ
= 30.9638°
Now, E2x = E2cosθ
= -54/10 x cos30.9638°
= -46.491/10 N/C
And E2y = E2sinθ
= -54/10 x sin30.9638°
= -26.7872/10 N/C
So, E2 = E2x i + E2y j + E2z k
= -46.491/10 i - 26.7872/10 j + 0 k
= (-4.6491, -2.67872, 0) N/C, at point A due to Q2.
Net Electric field at point A,En→1 = E1+E2
= (2.32454, 1.33935, 0) + (-4.6491, -2.67872, 0)
= (-2.32456, -1.33937, 0) N/C, at point A.
The electric field at A due to Q1 is 2.32454 N/C.
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help with the function and equations question below
Answers
The total charge (in dollars) for a rental that includes insurance is C = 0.85M + 22.65.
The given equations are S = 0.60M+17.75 and I = 0.25M+4.90.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let C be the total charge (in dollars) for a rental that includes insurance.
Total charge = Standard charge + Insurance charge
That is, C = S + I
Total charge = C = 0.60M + 17.75 + 0.25M + 4.90
= (0.60M + 0.25M) + 17.75 + 4.90
= 0.85M + 22.65
Therefore, the total charge (in dollars) for a rental that includes insurance is C = 0.85M + 22.65.
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What is the measure if Angle JKL?
Answers
The measure of the angle JKL as per the attached diagram is equal to 97 degrees.
As per in the question,
Diagram is attached.
Angle JKL is linear pair angle with given angle of measure 83 degrees.
Sum of the pair of linear pair is always equal to 180 degrees.
Let 'x' be the measure of angle JKL, we get,
83° + m ∠JKL = 180°
Subtract 83° from both the side of the equation we get,
⇒ 83° - 83° + m ∠JKL = 180° - 83°
⇒ m ∠JKL = 97°
Therefore, the measure of the angle JKL as per the attached diagram is equal to 97 degrees.
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Which number should go in the shaded overlap factors if 30 -and factors if 20
Answers
Answer:
1,2,5,10
Step-by-step explanation:
hope this helps
A cold drink initially at F warms to F in 4 min while sitting in a room temperature F. How warm will the drink be in degrees Farenheit if left out for 30 min
Answers
The drink will be F + 7.5 degrees Fahrenheit warm if left out for 30 minutes.
Let us first find the rate at which the drink is warming up.
We can use the formula,
T = T0 + k.t
where T is the temperature of the drink after time t,
T0 is the initial temperature, `
k is the rate of warming and t is the time.
Since the drink goes from F to F in 4 minutes,
we have F = F + 4k or k = 1/4.
Therefore, after 30 minutes, we have T = F + (1/4) * 30 = F + 7.5`.
Hence, the drink will be F + 7.5 degrees Fahrenheit warm if left out for 30 minutes.
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On Sunday, the owners of the Mildletown Café are giving away muffins. The owners budgeted $75 to spend on muffins for the event, and each muffin costs $0.82. The inequality 75 > 0.82m, where m is the number of muffins, represents the situation. How many customers could possibly get a muffin? Select all that apply.
A 89 customers
B 90 customers
C 91customers
D 92 customers
E 93 customers
Answers
A,B, and C
Explanation:
75/.82 = 91.463…
A person can only be represented by whole numbers, therefore 91 customers are able to get a muffin.
And also this one please very important please
Answers
Answer:
B. x = 5 +i√5 and x = 5 - i√5
Step-by-step explanation:
Find the area of the shaded region. Round to the nearest hundredth where necessary.
Answers
Answer: See explanation
Step-by-step explanation:
7. 300-117= 183 square inches
8. 346.185-153.86= 192.325 square inches
10. 100.46-64=36.46 square inches
a beam having a circular cross-section of diameter, D, is designed to resist a maximum bending moment of 80kNm. the maximum allowable bending stress is 500MPa what is the minimum required diameter, D, of the cross section of the beam?
Answers
To determine the minimum required diameter (D) of the cross-section of the beam, we need to consider the maximum bending moment and the maximum allowable bending stress.
The bending stress in a beam is given by the formula:
σ = (M * c) / I
Where σ is the bending stress, M is the maximum bending moment, c is the distance from the neutral axis to the outermost fiber (which is equal to half of the diameter for a circular cross-section), and I is the moment of inertia of the cross-section.
Rearranging the formula, we have:
D = (2 * M) / (σ * π)
Substituting the given values, with M = 80 kNm (converted to Nm) and σ = 500 MPa (converted to N/m²), we can calculate the minimum required diameter (D):
D = (2 * 80,000 Nm) / (500,000,000 N/m² * π)
D ≈ 0.255 meters or 255 mm
Therefore, the minimum required diameter of the cross-section of the beam is approximately 0.255 meters or 255 mm to resist the maximum bending moment of 80 kNm within the allowable bending stress of 500 MPa.
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Mary needs to order pizza for 18 students. Each student should get 4/7 of a pizza. How many pizzas should Mary order? How much pizza will be leftover?
Answers
Answer:
11 pizzas, 5/7 left
Step-by-step explanation:
to find out how much pizza is needed, multiply 4/7 by 18 to get 72/7. round up to get 77/7 or 11 pizzas. 77/7 - 72/7= 5/7 so there will be 5/7 left over
Answer:
12
Step-by-step explanation:
4 x 18
6 x 1 = 72 /6
72/6 = 12
6/6 = 1
12 /1
12
COMPARING METHODS In Exercises 27-32, tell whether you would use the Law of Sines, the Law of Cosines, or the Pythagorean Theorem (Theorem 9.1) and trigonometric ratios to solve the triangle with the given information. Explain your reasoning. Then solve the triangle.
Answers
A sphere is inscribed in a cube with edge length 9 inches. Then a smaller cube is inscribed in the sphere. How many cubic inches are in the volume of the inscribed cube
Answers
To find the volume of the inscribed cube, we need to determine the edge length of the cube first. Let's denote the edge length of the inscribed cube as "x".
In a cube inscribed in a sphere, the diameter of the sphere is equal to the diagonal of the cube. Therefore, the diameter of the sphere is equal to the space diagonal of the large cube, which is given as 9 inches.
The space diagonal of a cube with edge length "a" can be found using the Pythagorean theorem:
Diagonal² = a² + a² + a²
Diagonal² = 3a²
Since the diameter of the sphere is 9 inches, we can write:
3a² = 9²
3a² = 81
a² = 81 / 3
a² = 27
a = √27
a = 3√3
Now we know the edge length of the large cube, which is 3√3 inches. The volume of a cube is given by V = a³, where "a" is the edge length.
Volume of the inscribed cube:
V = (3√3)³
V = 3³ * (√3)³
V = 27 * 3
V = 81 cubic inches
Therefore, the volume of the inscribed cube is 81 cubic inches.
The volume of the cube inscribed in the sphere, given the sphere is inscribed in a cube with an edge length of 9 inches, is 81 cubic inches.
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Please hurry man I feel bad for asking but sometimes you gotta do what you gotta do. The conditional statement is if i am not in "Maine" then i am not in the north. determine the truth value of the inverse. Is it true or false???????????
Answers
Answer: false
N entry level technical writer's annual pay is $55,068 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its technical writers. If the firm cuts the work year to 51 weeks but keeps the same rate of pay, how much should the technical writer expect his annual pay to decrease? Round your answer to the nearest dollar.
Answers
Answer:
The technical writer should expect his annual pay to decrease by $1,059
Step-by-step explanation:
52 weeks = $55,068
51 weeks =
Cross Multiply
51 weeks × $55,068/52 weeks
= $54009
The writer will be paid $54009 for 51 weeks
His pay reduced by:
$55,068 - $54,009
= $1,059
true or false.
y +2<8; y = 3
Answers
Answer:
false
Step-by-step explanation:
Alex has a bucket in the shape of a cylinder. The diameter of the bucket is 12 inches and its height is 11.25 inches. How many buckets would it take ot fill an empty aquarium with 65 gallons of water? Show your work.
Answers
There would be 11 cylindrical buckets required to fill the empty aquarium with 65 gallons.
What is cylinder?A cylinder is three dimension solid, which has two circular base and which are connected by a curved surface.
Given that,
The diameter of cylindrical bucket d is 12 inches
so radius r=6 inches
And the height of bucket is 11.25 inches.
Volume of cylinder=π×r^2×h
Let n buckets are required to fill 65 gallons.
Since, 1 gallon = 231 inches,
65×231=n×22/7×6×6×11.25
15015×7=n×22×36×11.25
n=11.79
n=11 (approx.)
11 buckets will be required.
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