Dan and Paul share some money in the ratio 9:5.
Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.
How much did Paul originally have?
Answers
Answer:
Paul had £40 originally.
Step-by-step explanation:
Given
Let d be the money Dan has and p be the money Paul has
Then according to the given situation,
\(\frac{d}{p} = \frac{9}{5}\\d = \frac{9p}{5}\ \ \ Equation\ 1\)
Now from the statement, "Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1"
\(\frac{d-32}{p} = 1\) Eqn 2
From 2
\(d - 32 = p\\\)
Putting d = 9p/5
\(\frac{9p}{5} - 32 = p\\9p - 160 = 5p\\9p-5p = 160\\4p = 160\\\frac{4p}{4} = \frac{160}{4}\\p = 40\)
Checking
\(d = \frac{9(40)}{5} = \frac{360}{5} = 72\\\frac{d}{p} = \frac{72}{40} = \frac{9}{5}\)
Hence,
Paul had £40 originally.
Related Questions
You lease a car at $23,495 for 3 years at $429.95 a month with a $500 down payment. The interest is 30% of the payments and $4,643.46 in interest is paid over 3 years. What is the remaining balance when the lease ends? How did you arrive at $12,160.26?
Answers
Answer:
Step-by-step explanation:
total interest paid is given as $4,643.46.
total payments = $429.95 x 36 months = $15,478.20
total lease payments = total payments - total interest
total lease payments = $15,478.20 - $4,643.46 = $10,834.74
Remaining balance = Total cost of the lease - Total lease payments
$23,495 - $10,834.74 = $12,660.26
Complete the following sentence (select all that apply). The expected count of females who are not pierced is what we would expect to see in the sample if ___________________________. Group of answer choices gender and piercing were significantly related. gender and piercing are independent. the null hypothesis is true. the null hypothesis is not true.
Answers
The statement that completes the blank is (c) the null hypothesis is true.
In sampling techniques, the expected count of a variable is dependent on the null hypothesis.
This means that, if the null hypothesis is true, then the expected count is what is expected to be seen in the sample.
This in other words, means that the complete statement is:
The expected count of females who are not pierced is what we would expect to see in the sample if the null hypothesis is true.
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Jason and 4 friends went bowling. Three friends rented shoes for $2 each. The total cost to rent the shoes and the lane fees was $42. What was the cost of the lane fees for each person?
Answers
Answer: 7.20$
Step-by-step explanation:
Since there are five people over all, and three of them bought shoes for 2$, you would take 2$ Times that by 3 = 6$, now take that 6$ and subtract that by the 42$, leaving you with 36$ left. Take that 36$ and divide it among the 5 people and you get 7.20$ for a lane
lalue of a numbe
Evaluate the following.
=
X
6
=
Answers
Answer:
|-8| = 8
|12| = 12
Step-by-step explanation:
|-8| = 8
|12| = 12
Absolute values of numbers are always positive.
Hope this helps!
Which of the following represents a geometric sequence?
I 1/4,1/4,1/4,1/4
II 1/4,1/5,1/6,1/7
III 1/4,1,-4,16
IV 1/4,-4,1/4,-4
OOOO
A. I
B. II
C. III
D. IV
Next
Save and Exit
Answers
Answer:
A. I
Step-by-step explanation:
The other person is wrong and I took the test
Claire traveled 382 miles. She drove 82 miles every day. On the last day of her trip she only drove 52 miles. Write and solve an equation to find the number of days Claire traveled. Explain each step of your problem solving strategy.
Answers
An equation is a mathematical expression that shows the relationship between two variables
How to write and solve an equation to find the number of days Claire traveled.Since Claire traveled 382 miles. She drove 82 miles every day. On the last day of her trip she only drove 52 miles.
Let d represent the number of days Claire travelled.
Since Claire travelled 82 miles per day, the number of miles she travels in d days is D = 82 × d = 82d
Also, since she travels 52 miles on the last day, the total distance she travels is D' = 82d + 52
Now, since the total distance Claire travels is 382 miles, we have that
D' = 382 miles
So,
82d + 52 = 382
So, the required equation is 82d + 52 = 382
Solving the equation for d, we have
82d + 52 = 382
82d = 382 - 52
82d = 330
d = 330/82
d = 4.02 days
d ≅ 4 days
The equation for the number of days Claire travelled is 82d + 52 = 382 The number of days claire travelled is 4 daysLearn more about equation for number of days travelled here:
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(Free Points!!!)
What are quartiles?
A) Tiles that are worth 25 cents
B) Another name for quarters
C) A way to measure liquids
D) A group of number data showing 25% of the numbers
Answers
Answer:
D? (also nice pfp lol) word word
16) 56 is what percent of 40?
%
Answers
140
Step-by-step explanation:
56:40*100 =
(56*100):40 =
5600:40 = 140
What is the ratio of number of students receiving and C and the number of students receiving an A
Answers
The ratio of number of students receiving and C and the number of students receiving an A is 4 to 1.
What is ratio and proportion?When comparing two quantities of the same kind, ratio is utilised. For two numbers, a and b, the ratio formula is written as a: b or a/b. Two or more ratios are said to be in proportion if they are all equal. Fractions are the foundation of the concepts of ratio and proportion. The fundamental building blocks of numerous other mathematical notions are ratio and proportion. In many everyday situations, such as when comparing heights, weights, distances, or times, or when adding components to a recipe, ratio and proportion can be used to help us solve our difficulties.
From the table we observe that the number of students receiving C is: 12.
The number of students receiving A is 3.
The ratio of number of students receiving and C and the number of students receiving an A is:
C / A = 12 / 3 = 4 / 1
Hence, the ratio of number of students receiving and C and the number of students receiving an A is 4 to 1.
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The correct question is:
Which equations are correct?
Select each correct answer.
6a^5(6a^5)=36a^25
6b^4(−3b^4)=−18b^8
5x^4(4x^2)=20x^6
3z^7(4z^2)=12z^9
Answers
6(3x+4)+2(2x+2)+2=22x+31 solve the equation for the given variable
Answers
The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.
What is the solutuon to the given equation?Given the equation in the question:
6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31
To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.
Apply distributive property:
6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31
18x + 24 + 4x + 4 + 2 = 22x + 31
Collect and combine like terms on both sides:
22x + 30 = 22x + 31
Next, we want to isolate the variable x on one side.
22x - 22x + 30 = 22x - 22x + 31
30 = 31
However, we notice that the x terms cancel out when subtracted:
30 ≠ 31
This means that there is no solution.
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What is the value of x?
Answers
The value of x in the segment is 3
How to determine the value of x?Using the secant and segment theorem, we have:
x * (x + 21) = (x + 1) * (x + 1 + 14)
Evaluate the sum
x * (x + 21) = (x + 1) * (x + 15)
Expand
x^2 + 21x = x^2 + 15x + x + 15
Subtract x^2 from both sides
21x = 15x + x + 15
Evaluate the like terms
5x = 15
Divide both sides by 5
x = 3
Hence, the value of x is 3
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Levi borrowed $7129 at 4% simple interest for 6 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 6 months? Round answers to the nearest cent if necessary. Group of answer choices
Answers
Answer:
Interest will amount to $142.58
Total amount Levi will have to pay back at the end of 6 months=$7271.58
Step-by-step explanation:
Simple interest=principal×rate×time
Principal=$7129
Rate=4%=0.04
Time=6 month=0.5 year
Simple interest=principal×rate×time
=$7129×0.04×0.5
=$142.58
Interest will amount to $142.58
Total amount Levi will have to pay back at the end of 6 months
=principal + total interest
=$7129+$142.58
=$7271.58
Choose one of the topics below for your paragraph.
1. Write a paragraph about a trend that interests you and why it is popular. Give sentences
(Paragraph)
● For example, consider a trend in cars, food, or technology. Give sentences (Paragraph)
2. Write a paragraph about a popular TV program. Give sentences (Paragraph)
Who usually watches the program? Give sentences (Paragraph)
Why is it popular? Give sentences (Paragraph)
●
Answers
Answer:
1. A trend that gives me interest is the 1, 2 buckle my shoes 3, 4 buckle some more- The reason is why does it even exist and why did it get so popular is such a fast amount of time, and the way people get distracted on technology which we are using all over the world and it takes us away from the real world and makes us stay there.
2. Cocaine Bear it looks good and funny, I watched it with all my friends and they all enjoyed it with me.
Step-by-step explanation:
Marsha Waide borrows 56,000 and agrees to pay it back in 5 years. If the simple interest rate is 14%, find the total amount she pays back.
She pays $back. (Round to the nearest dollar as needed.)
Answers
Answer:
63840
Step-by-step explanation:
divide 56000 by 5 the answer is 11200 multiply 11200 by. .14 the answer should be 1568 then multiply by 5 that answer should be 7840 then add 7840 by 56000
Please help I am so lost thank you all
Answers
h = hours till they're 58 miles apart
Check the picture below.
so they're travelling in opposite directions, however the combined distances is 58 miles at say "h" hours, by the time that happend Hopi has been walking "h" hours and Brittany has also being walking "h" hours too.
Since the combined distance is 58 miles than if Hopi has covered "m" miles then Brittany covered the slack of "58 - m".
\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hopi&m&15&h\\ Brittany&58-m&14&h \end{array}\hspace{5em} \begin{cases} m=(15)(h)\\\\ 58-m=(14)(h) \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{substituting on the 2nd equation}}{58-(\stackrel{m}{15h})=14h}\implies 58=29h\implies \cfrac{58}{29}=h\implies \boxed{2=h}\)
marilee plants a vegetable patch measuring 12 m x 8 m .she plants carrots on half of the patch ,and potatoes on a quarter of the patch each .Calculate the area covered by each type of vegetable?
Answers
The area covered by each type of vegetables is 48 meter square and 24 meter square.
What is Area of rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
Area of rectangle = length × breadth
Total Area of rectangle = 12(8) = 96
Half area covered by carrots,
area of carrots patch = 96/2 = 48
area covered by potatoes = 96/4 = 24
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A football team played A games last year. They lost B of those games. What was their winning percentage
Answers
Answer:
(A - B)/A x 100%
Explanation:
If they played A games last year and lost B of those games, they win the rest of the games, so they win A - B games.
Then, the percentage is calculated as the number of games that they win over the total number of games multiplied by 100, so the winning percentage is
(A - B)/A x 100%
For a normal distribution with mean 0 and standard deviation 1, which of the following Python lines outputs the probability P(x<0.325)?
Question 1 options:
a)
import scipy.stats as st
print(st.norm.cdf(0.325, 0, 1))
b)
import pandas as pandas
print(st.norm.pdf(0.325, 0, 1))
c)
import scipy.stats as st
print(st.norm.sf(0.325, 0, 1))
d)
print(normal(0.325, 0, 1))
Answers
Python lines to get the output for the probability P(x<0.325) are -
a) import scipy.stats as
st print(st.norm.cdf(0.325, 0, 1))
Hence, option a is the correct answer.
The Python code -
import scipy.stats as
st print(st.norm.cdf(0.325, 0, 1))
This line of code imports the scipy.stats module as "st", and then uses the norm.cdf function to calculate the cumulative distribution function (CDF) of a normal distribution with mean 0 and standard deviation 1, evaluated at x=0.325.
The CDF gives the probability that a random variable from the normal distribution is less than or equal to a certain value, so this line of code is outputting the probability P(x<0.325).
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Hugo bought a pair of boots on sale for$52 The original price was $65 what percent was the discount
Answers
Answer:
20%
Step-by-step explanation:
\(\frac{52}{65}\)×100=80
100-80=20
Hello can anyone help me with this please?
Answers
Answer:
The product of exponents is equal to the sum of the exponents.
Step-by-step explanation:
(x^2)*(x^2)=x^4, as it can be written as x*x*x*x, which is also x^4.
(x^3)(x^3)(x^3) does NOT equal x^27
(x^3)(x^3)(x^3) equals x^9
Helppppppppppppppppp
Answers
The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is
Answers
An opportunity cost of 9 percent, is $42.
We have given that,
The present value of $100 is to be received 10 years from today,
assuming an opportunity cost of 9 percent,
present value =$100
N=10 years
I/y=9
What is the formula for the present value?PV= FV/(1+r)^n
Where FV is the future value.
Use the given values in the formula we get,
Therefore the correct answer is 42.
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The sum of two numbers is twenty-three. One number is forty-seven less than six times the other. Find the numbers.
Answers
Answer:
10, 13
Step-by-step explanation:
Lets call the other x
x + 6x - 47 = 23
7x - 47 = 23
7x = 70
x = 10
6 x 10 - 47= 60 - 47 = 13
Hope this helps!
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Question: The time is 1 o'clock. What are the next two times at which the hour and minute hands will be perpendicular?
Answers
The next two times at which the hands of the clock will be perpendicular are at 1:20 and at 1:50.
When will the hands be perpendicular?The two hands will be perpendicular when the angle between them is 90°. Remember that every 5 minutes that the minute clock moves, there is an angle of 30°.
Each hour that the hour hand moves, there is an angle of 30°.
The first time that we will have an angle of 90° between the hands is at:
1:20
Because the minute hand is at an angle of -30° with respect to the x-axis at 20 minutes, and the hour hand is at an angle of 60° at 01.
The next time will be when the minute clock moves another 30 minutes (half the circle) and this will be at 01:50.
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I need help please its urgent I need it now
1⅛ ÷ x³ × ⅝ ÷ 5x²
100 points and brainliest
Answers
Answer:
Today: Tuesday, 19th January 2021
2.20 PM
\( \tt 1\frac{1}{8} \div {x}^{3} \times \frac{5}{8} \div 5 {x}^{2} \)
\( \tt = \frac{9}{8} \div {x}^{3} \times \frac{5}{8} \div 5{x}^{2} \)
\( \tt = \frac{9}{8x^{3} } \times \frac{5}{8} \div 5 {x}^{2} \)
\( \tt = \frac{45}{64x^{3} } \div 5 {x}^{2} \)
\({\boxed{\red{ \tt = \frac{9 }{64x^{5}}}}}\)
\({\boxed{\boxed{ \tt{\red{i}}\:{\orange{hope}}\:{\green{this}}\:{\blue{help}}}}}\)
Answer:
225/64x
Step-by-step explanation:
1⅛ ÷ x³ × ⅝ ÷ 5x²
Move it around
1⅛ × ⅝ ÷ x³ ÷ 5x²
45/64/x/5
225/64x
Quadrilateral KLMN is similar to quadrilateral OPQR. Find the measure of side QR.
Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
M
21
N
R
13
K
43
0
Answers
Answer: 12.6=13
Step-by-step explanation:
Certain advertisers would like to estimate the proportion of viewers who spend the majority of their television time
watching alone. The consensus is that this percentage has been increasing over the years due to the increased
number of television sets in households.
a. Determine the sample size needed to construct a 90% confidence interval with a margin of error of no more than
6% to estimate the true proportion of viewers who watch television alone.
b. What impact would a pilot sample that showed that 44% of viewers spend the majority of their television time
watching alone have on your on results.
a. The sample size needed is
(Round up to the nearest integer.)
b. The new sample size needed would be 0
(Round up to the nearest integer.)
Answers
Answer:
Step-by-step explanation:
A polygon has the following coordinates: A(6,-7), B(1,-7), C(1,-4), D(3,-2), E(7,-2), F(7,-4). Find the length of BC. A. 5 units B. 2 units C. 4 units D. 3 units
Answers
The formula to find the distance between two points A(x₁,y₁) and B(x₂,y₂) is:
\(D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)In this case, we have:
\(\begin{gathered} B(x_1,y_1)=(1,-7) \\ C(x_2,y_2)=(1,-4) \end{gathered}\)\(\begin{gathered} D=\sqrt[]{(1-1)^2+(-4-(-7))^2} \\ D=\sqrt[]{(0)^2+(-4+7)^2} \\ D=\sqrt[]{3^2} \\ D=3 \end{gathered}\)Therefore, the length of segment BC is 3 units.
Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
Answers
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
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