Two numbers are such that the ratio between them is 3:5. If each is increased by 5 , the ratio becomes 2:3. Find the original numbers
Answers
The ratio of two numbers is 3:5. If each is increased by 5 , the ratio becomes 2:3. The original numbers are 15 and 25.
To find the original numbers, we need to use the given ratios and set up a system of equations. Let x be the first number and y be the second number.
From the first ratio, we have:
3/5 = x/y
From the second ratio, we have:
2/3 = (x + 5)/(y + 5)
Cross-multiplying and simplifying each equation gives us:
5x = 3y
3x + 15 = 2y + 10
Rearranging and subtracting the first equation from the second equation gives us:
3x - 5x = 2y - 3y - 5
-2x = -y - 5
Solving for y gives us:
y = 2x - 5
Substituting this value of y into the first equation gives us:
5x = 3(2x - 5)
5x = 6x - 15
x = 15
Substituting this value of x back into the equation for y gives us:
y = 2(15) - 5 = 25
Therefore, the original numbers are 15 and 25.
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Related Questions
One side of square ABCD has a length of 12 meters. A certain rectangle whose area is equal to the area of ABCD has a width of 8 meters. What is the length, in meters, of the rectangle
Answers
Answer:
width = 18 m
Step-by-step explanation:
Area of square and area of rectangle are equal.
Square:side = 12 m
Area = side *side
= 12 * 12
= 144 m²
Rectangle:length = 8 m
Area of rectangle = length * width
= 8 *width
Area of rectangle = area of square
8* width= 144
width = 144 ÷ 8
\(\boxed{\bf width = 18 \ m}\)
Suppose $726.56 is deposited at the end of every six months into an account earning 6.45% compounded semi-annually. If the balance in the account four years after the last deposit is to be $31 300.00, how many deposits are needed? (This question asks for 'n')
Answers
We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.
To solve this problem, we can use the formula for the future value of an annuity:
\(FV = P * ((1 + r)^n - 1) / r\)
Where:
FV is the future value of the annuity
P is the periodic payment or deposit amount
r is the interest rate per period
n is the number of periods
In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).
We can rearrange the formula and solve for n:
n = log((FV * r) / (P * r + FV)) / log(1 + r)
Substituting the given values:
n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)
Using a calculator or software, we find that n ≈ 9.989.
Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.
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8(y-1)-3y=6(2y-6) help plsss
Answers
Answer:
y = 4
Step-by-step explanation:
First, distribute 8 through the parentheses
8y - 8 - 3y = 6(2y - 6)
Then, distribute 6 through the parentheses
8y - 8 - 3y = 12y - 36
Collect like terms (8y - 3y)
5y - 8 = 12y - 36
Move the variable (12y) to the left hand side and change its sign
5y - 12y - 8 = -36
Move the constant (-8) to the right hand side and change its sign
5y - 12y = -36 + 8
Collect like terms
-7y = -36 + 8
Calculate the sum
-7y = -28
Divide both sides of the equation by -7
y = 4
*Select TWO answers* Name the first step that could be used to solve
this equation: -7(x-12) = 42*
Distribute the -7 to both the x and the -12
Subtract 12 from both sides of the equation.
Divide both sides of the equation by - 7
Divide both sides of the equation by 42
Multiply both sides of the equation by -7
Add 12 to both sides of the equation
Answers
Answer:
Distribute the -7 to both the x and the -12
Step-by-step explanation:
The first step taken would be to distribute the -7 to the x and the -12 to get rid of the ()
-7(x-12) = 42*
\/
-7x + 84 = 42*
Please Help!!!!
2) ____S + ___O2 → ____SO3
1- How many moles of sulfur must be burned to give 0.567 moles of SO3?
2-How many moles of SO3 can be produced from 65.2 moles of O2?
3)____NaOH + _____Al →_____ Na3AlO3 +_____H2
1-How many moles of aluminum are required to produce 0.58 moles of hydrogen gas?
2- How many moles of Na3AlO3 can be formed from 7.24 moles of NaOH?
3-How many moles of NaOH are required to produce 3.5 moles of hydrogen gas?
Answers
Answer: What is the balanced equation for so2 O2 SO3?
2SO2 + O2 → 2SO3.
Step-by-step explanation:
WILL MARK BRAINLIEST!!Find the solution of the system of equations.
2x – 9y = 38
4x + 5y = –16
Answers
Answer:
answer 9x
Step-by-step explanation:
Y=-38/9 or 4.2
That is solution
an urn contains 6 blue balls and 4 red balls. 6 balls are chosen at random and without replacement from the urn. if x is the number of red balls chosen, find the standard deviation of x.
Answers
The standard deviation of the number of red balls chosen, x, is 1.2.
In probability theory, the standard deviation is a measure of the amount of variation or dispersion in a set of values. It helps us understand how spread out the values are from the mean. In this scenario, we have an urn containing blue and red balls, and we are randomly selecting 6 balls without replacement. We want to determine the standard deviation of the number of red balls chosen, denoted by x.
To find the standard deviation of x, we need to calculate the variance first. The variance represents the average of the squared differences between each value and the mean. The standard deviation is then the square root of the variance.
Step 1: Finding the probability of selecting a red ball
In the given urn, there are a total of 6 blue balls and 4 red balls. To determine the probability of selecting a red ball, we divide the number of red balls by the total number of balls:
P(red) = 4 / (6 + 4)
= 0.4
Step 2: Calculating the mean of x
The mean of x, denoted as μx, represents the expected value or average number of red balls chosen. Since the probability of selecting a red ball is 0.4, we can calculate the mean as follows:
μₓ = (Number of trials) × P(red)
= 6 × 0.4
= 2.4
Step 3: Determining the variance of x
The variance, denoted as Var(x), is calculated by finding the average of the squared differences between each value of x and the mean:
Var(x) = (Number of trials) × P(red) × P(blue)
= 6 × 0.4 × 0.6
= 1.44
Step 4: Finding the standard deviation of x
Finally, the standard deviation, denoted as σx, is the square root of the variance:
σₓ = √Var(x)
= √1.44
= 1.2
Therefore, the standard deviation of the number of red balls chosen, x, is 1.2.
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help
4. Which list shows the integers in order from least to greatest?
A) -8, -5, 0, 2, 6
B) 0, 2, -5, 6, -8
C) -5, -8, 0, 2, 6
D) 0, -3, -5, 2, 6
Answers
Simplify the following expression by combining like terms:
9ab + 2b - 3a + 2b - ab + 3a
Answers
Answer:
8ab+4b
Step-by-step explanation:
9ab-ab=8ab
2b+2b=4b
-3a+3a=0
Answer:
8ab+4b
Step-by-step explanation:
Can someone pls help meeeeeee!!!
Answers
Answer:
For question 2, Ethan needs 3 cups of milk to make the batter for 3 times as many cakes.
For question 3, Isabella needs 5/4 of a gallon of the food to make 5 gallons of the mixture.
Malcolm buys a 5/6- pound bag of black beans and a 3/4- pound bag of pinto beans. how many pounds of beans does Malcolm buy in all?
Answers
Answer:
5/6 + 3/4 = 19/12
Simplified answer would be 1 7/12
Step-by-step explanation:
The members of a school club are selling tickets for a fundraiser. The goal for the fundraiser is to earn $50.00 each day from ticket sales. The list below shows the percent of the goal reached each day. On the first day, the members earned 90% of their daily goal. On the second day, the members earned 6% more than their daily goal. On the third day, the members earned 14% less than their daily goal. How much money, in dollars, did the members earn from ticket sales on all three days?
Answers
On the first day, the members earned 90% of their daily goal of $50.00 which is equal to $45.00 (0.9 x $50.00 = $45.00).
On the second day, the members earned 6% more than their daily goal of $50.00 which is equal to $53.00 ($50.00 + 0.06 x $50.00 = $53.00).
On the third day, the members earned 14% less than their daily goal of $50.00 which is equal to $43.00 ($50.00 - 0.14 x $50.00 = $43.00).
Therefore, the members earned a total of $45.00 + $53.00 + $43.00 = $141.00 from ticket sales on all three days.
The members of the school club earned $141.00 from ticket sales over the three days.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find out how much money the members of the school club earned from ticket sales on all three days
Let us calculate the amount of money earned each day and then add them together.
On the first day, the members earned 90% of their daily goal, which is:
0.9 x $50.00 = $45.00
On the second day, they earned 6% more than their daily goal, which is:
$50.00 + 0.06 x $50.00 = $53.00
On the third day, they earned 14% less than their daily goal, which is:
$50.00 - 0.14 x $50.00 = $43.00
To find the total amount of money earned over the three days, we simply add the amounts earned on each day:
$45.00 + $53.00 + $43.00 = $141.00
Therefore, the members of the school club earned $141.00 from ticket sales over the three days.
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Rate my friend. He nice
Answers
Answer:
6/10
Step-by-step explanation:
because, yes.
Juan paid 13.46 for a 3.47-pound bag of shrimp at one store. the following week, he paid 18.75 for a 5.15-pound bag at another store. find the unit price for each bag is the better buy based on the unit price. round the answers to the nearest cent.
Answers
The unit price for a 5.15 pound bag is the better buy for Juan
Juan paid $13.36 for a 3.47 pound bag of shrimp:
So, cost of one pound bag of shrimp= \(\frac{1*13.46}{3.47}\)
=$3.88
Hence, unit price for the 3.47 pound bag=$3.88
Following week, Juan paid $18.75 for a 5.15 pound bag at another store:
So, cost of one pound bag of another store= \(\frac{1*18.75}{5.15}\)
=$3.64
Hence, unit price for the 5.15 pound bag at another store=$3.64
It is clear from the above result that second buy (5.15-pound bag at another store) is the better buy for Juan because it cost less per pound.
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Ali, Carrie and Bryan received a sum of money. Bryan's money was 3/5 as much as Ali's money. The ratio of Ali's money to Carrie's money was 4:1. Ali had $160 more than Bryan. How much was the sum of money.
Answers
Answer:
The sum of money received by Ali, Carrie and Bryan is $ 740.
Step-by-step explanation:
At first we translate mathematically each sentence:
(i) Ali, Carrie and Bryan received a sum of money.
\(a\) - Ali's money.
\(b\) - Bryan's money.
\(c\) - Carrie's money.
(ii) Bryan's money was \(\frac{3}{5}\) of Ali's money.
\(b = \frac{3}{5}\cdot a\) (1)
(iii) The ratio of Ali's money to Carrie's money was 4 : 1.
\(\frac{a}{c} = 4\) (2)
(iv) Ali had $ 160 more than Bryan.
\(a = b + 160\) (3)
After some algebraic handling, we have the following system of linear equations:
\(3\cdot a - 5 \cdot b = 0\) (1b)
\(a - 4\cdot c = 0\) (2b)
\(a - b = 160\) (3b)
The solution of the system is: \(a = 400\), \(b = 240\), \(c = 100\)
The sum of money is:
\(s = a + b + c\)
\(s = 740\)
The sum of money received by Ali, Carrie and Bryan is $ 740.
Simplify 22 – 5(2x + 4).
Answers
Answer:
-10x+2
Step-by-step explanation:
22-5(2x+4)
22-10x-20
2-10x
-10x+2
Answer:
-10x+2
hope this help plz if you need something ask me if youll like stay safe :)
What is the coefficient in the following expression?
5a to the 2 power subtracted by 7
a)7
d)2
c)5
b)a
Answers
Answer:
c)5
Step-by-step explanation:
Coefficient is always the numerical value before the variable
I hope this helped and have a good rest of your day!
\The following data represent the time, in min- utes, that a patient has to wait during 12 visits to a doctor's office before being seen by the doctor: 17 15 20 20 32 28 12 26 25 25 35 24 Use the sign test at the 0.05 level of significance to test. the doctor's claim that the median waiting time for her patients is not more than 20 minutes before being admitted to the examination room. Analyze the data by using the signed-rank test.
Answers
Let's solve the problem using the signed-rank test:
Step 1: The null hypothesis (H₀) is that the median waiting time is 20 minutes or less, and the alternative hypothesis (H₁) is that the median waiting time is more than 20 minutes.
Step 2: Calculate the differences between each observation and the hypothesized median of 20 minutes, and assign ranks to the absolute values of the differences:
Observation: 17 15 20 20 32 28 12 26 25 25 35 24
Difference: -3 -5 0 0 12 8 -8 6 5 5 15 4
Rank: 3 4 5 5 8 6 2 7 9 9 12 1
Step 3: Calculate the sum of positive ranks (W⁺) and the sum of negative ranks (W⁻):
W⁺ = 8 + 6 + 7 + 9 + 9 + 12 = 51
W⁻ = 3 + 4 + 5 + 5 + 8 + 2 = 27
Step 4: Determine the test statistic (T) as the smaller of W⁺ and W⁻:
T = min(W⁺, W⁻) = min(51, 27) = 27
Step 5: Find the critical value or calculate the p-value based on the significance level (0.05) and test statistic (T):
For a sample size of 12 and a significance level of 0.05, we can consult a signed-rank test table to find the critical value. In this case, the critical value is 8. Since T (27) is greater than the critical value (8), we reject the null hypothesis.
Step 6: Make a decision: We have sufficient evidence to conclude that the median waiting time for the patients is more than 20 minutes.
In summary, based on the signed-rank test, we reject the doctor's claim that the median waiting time for her patients is not more than 20 minutes before being admitted to the examination room.
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I NEED HELP ASAPPPP‼️‼️‼️
SOMEONE PLEASE HELP ME WITH THIS QUESTION‼️‼️‼️
AND I PROMISE YOU I WILL AWARD YOUR ANSWER AS BRAINLIEST ANSWER❤️❤️‼️‼️
Answers
Answer:
40 degrees
Step-by-step explanation:
Mark me as brainliest
Answer:
First find the angle next to 110 °
110+?=180 (linear pair)
? = 180-110
? = 70
Since the triangle is isosceles, the bottom two angles are 70 °.
Now, to find x....
All interior angles of a triangle equals 180°.
180 = 70+70+x
180 = 140+x
x = 180-140
x = 40
3. Disney on Ice is traveling to Chicago to perform. The revenue from their ticketsales is a function of the ticket price, x, and can be modeled with (x - 3)(450 – 3x).What are the ticket prices at which Disney on Ice would make no money at all?Type Here:Explain or show your reasoning.Type Here:
Answers
They would not earn money when the function is equal or less to 0
then we equal 0
\((x-3)(450-3x)\leq0\text{ }\)we will have two answers when clear x
\(\begin{gathered} (x_1-3)\leq0 \\ x_1\leq3 \\ (450-3x_2)\text{ }\leq\text{0} \\ 450\leq3x_2 \\ x_2\ge\frac{450}{3} \\ x_2\ge150 \end{gathered}\)they won't make money when the ticket price is equal or less than 3 or when the ticket price is equal or greater than 150
the correct expression for not making money is :
\((-\infty,3\rbrack\text{ }\lbrack150,\infty)\)A certain lottery has 39 numbers. In how many different ways can 6 of the numbers be selected?
Answers
Answer:
6.3
Step-by-step explanation:
please help thank you
Please help me! image is below
If PR is 4, WQ is 8, and QR is 5, SP = ___ units
Answers
Answer:
From the attached graphic, we can see:
(SP + PR) * PR = (WQ + QR) * QR
SP * PR + PR^2 = WQ * QR + QR^2
4 SP + 4*4 = 8 * 5 + 25
4 SP + 16 = 65
4 SP = 49
SP = 49 / 4
SP = 12.25
Step-by-step explanation:
Graph the equation.
y= - 2x + 4
Answers
a point on the y-axis at positive 4
for the rest of the points go right 1 down 2
and left 1 up 2
(60 + 10)
130
Solve for a
Answers
Answer:
Step-by-step explanation:
here you go mate'
step 1
(60 + 10)130 equation
step 2
(60 + 10)130 simplify with the brackets
step 3
130(70) multiply the numbers
answer
9100
Find the value of x
………..
Answers
Answer:
135°
Step-by-step explanation:
In a hexagon, sum of all angles = 720
x + x + x + x + 90 + 90 = 720
4x + 180 = 720
4x = 720 - 180
4x = 540
x = 135°
Kindly help for number 57 :)
Answers
Answer:
.....................
Toilet rolls come in a pack of 4 and 9 the 4-pack is priced at £2.04 and the 9- pack is priced at £4.68 . By calculating the price per roll, determine which pack is better value
Answers
4pack price plus 9pack price
so it implies that 2.o4+4.68=6.72
3456 cubic inches to cubic ft
The lesson is Multiple unit multipliers.
Answers
Answer:
Step-by-step explanation:
1 cubic foot is 12 * 12 * 12 cubic inches.
1 cubic foot = 1728 cubic inches.
1 cubic foot = 1728 cubic inches
x cubic feet = 3456 Cross multiply
1728 x = 3456 * 1 Divide by 1728
x = 3456/1728
x = 2 cubic feet.
The other way to do this is
3456 cu inches [1 cubic Foot/1728 cubic inches] note that the units cancel and you are left with 1 division problem.
The question still comes to 2.
The vertices of a parallelogram PQRS are P(4, 7), Q(8, 7),
R(6, 1), and S(2, 1).
Complete the statements about the parallelogram. For each
box, select the letter before the correct option.
Answers
The midpoint of diagonal PR is: B. (5, 4).
The midpoint of diagonal QS is: D. (5, 4).
The midpoint of the diagonals: E. coincide.
This implies that the diagonals of the parallelogram PQRS G. are equal to each other.
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) end points, we would add each end point together and then divide by two (2):
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
For line segment PR, we have:
Midpoint of PR = [(4 + 6)/2, (7 + 1)/2]
Midpoint of PR = [10/2, 8/2]
Midpoint of PR = [5, 4].
For line segment QS, we have:
Midpoint of QS = [(8 + 2)/2, (7 + 1)/2]
Midpoint of QS = [10/2, 8/2]
Midpoint of QS = [5, 4].
In conclusion, we can reasonably infer and logically deduce that the midpoint coincides and the diagonals of parallelogram PQRS are equal to each other.
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Problem 13. (1 point) Find the rank and nulity of the matrix [1 0 2]
A = [0 1 1]
[1 2 1] • Rank (number of leading ones in its RREF) = • Nulity (number of columns without leading ones in its RREF) = Note: You can earn partial credit on this problem. 1 with entries in Z3.
Answers
The rank of the matrix A is 2, and the nulity is 1.
To find the rank and nulity of the matrix A, we need to determine the number of leading ones in its row reduced echelon form (RREF) and the number of columns without leading ones in its RREF, respectively.
The RREF of matrix A is:
[1 0 2]
[0 1 1]
[0 0 0]
In the RREF, there are two leading ones, one in the first row and one in the second row. Therefore, the rank of matrix A is 2.
The nulity is the number of columns without leading ones in the RREF. In this case, there is one column without a leading one, which is the third column. Thus, the nulity of matrix A is 1.
In summary, the rank of matrix A is 2, indicating that there are two linearly independent rows or columns. The nulity is 1, meaning that there is one special solution in the nullspace of the matrix.
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