Madison went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 500 mg of sodium and each frozen dinner has 700 mg of sodium. Madison purchased 2 more frozen dinners than cans of soup and they all collectively contain 7400 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
Madison purchased 5 cans of soup and 7 frozen dinners.
Step-by-step explanation:
Given,
Quantity of sodium in each soup can = 500 mg
Quantity of sodium in each frozen dinner = 700 mg
Total quantity = 7400
Let,
Number of soup cans purchased = x
Number of frozen dinners purchased = y
According to given statement;
500x+700y=7400 Eqn 1
y = x+2 Eqn 2
Putting value of y from Eqn 2 in Eqn 1
[tex]500x+700(x+2)=7400\\500x+700x+1400=7400\\1200x=7400-1400\\1200x=6000[/tex]
Dividing both sides by 1200
[tex]\frac{1200x}{1200}=\frac{6000}{1200}\\x=5[/tex]
Putting x=5 in Eqn 2
[tex]y=5+2\\y=7[/tex]
Madison purchased 5 cans of soup and 7 frozen dinners.
Keywords: linear equation, substitution method
Learn more about substitution method at:
brainly.com/question/10710410brainly.com/question/10717746#LearnwithBrainly
Answer:
Madison purchased 5 cans of soup and 7 frozen dinners
Step-by-step explanation:
Please help with probability
Step-by-step explanation:
2. The total number of calculators is 6 + 9 + 2 = 17.
When she hands out the first calculator, the probability that it is blue is 2/17.
When she hands out the second calculator, there is one less calculator total, so the probability that it is yellow is 9/16.
The probability of both is therefore:
P = 2/17 × 9/16
P = 9/136
3. There are 13 clubs in a standard deck of 52 cards.
The probability that the first card is clubs is 13/52 = 1/4.
Since you replace the card, there are still 52 cards in the deck. So the probability that the second card is clubs is 13/52 = 1/4.
The probability that both cards are clubs is:
P = 1/4 × 1/4
P = 1/16
4. The total number of pieces of gum is 6 + 9 + 5 = 20.
When you pick the first piece, the probability that it is grape is 6/20.
When you pick the second piece, there's one less piece of gum, and one less grape flavor, so the probability is 5/19.
The probability that both pieces are grape is:
P = 6/20 × 5/19
P = 3/38
5. The total number of drinks is 6 + 3 + 4 = 13.
Since the coach replaces the first drink, the second selection will be independent of the first. So the probability is still P = 6/13.
6. A die has six sides. They are numbered 1 through 6. Three of the numbers are even. Each roll is independent, so the probability of a previous roll does not affect the probability of future rolls.
The probability that you get 3 even numbers, followed by a one, is:
P = (3/6) (3/6) (3/6) (1/6)
P = 1/48
solve y= 2/3x +7 and 3y= 2x -3
Answer:
The system has no solution
Step-by-step explanation:
we have
[tex]y=\frac{2}{3}x+7[/tex] ----> equation A
[tex]3y=2x-3[/tex]
Isolate the variable y
Divide by 3 both sides
[tex]y=\frac{2}{3}x-1[/tex] ------> equation B
Compare equation A and equation B
Both lines have the same slope and different y-intercept
so
Line A and Line B are parallel lines
The lines do not intersect
therefore
The system has no solution, because both lines are parallel
see the attached figure to better understand the problem
What is the slope of the line with the equation 0 = -15x + 6y
Answer:
15/6
Step-by-step explanation:
if ax^2+bc+c=0 is given equation then slope of this equation will be
m=-a/b
Find an equation for the line with the given properties.
Parallel to the line x = -5; containing the point (6, 2)
m×n, when m=13 and n=12
Answer:
156
Step-by-step explanation:
13 × 12
13
×
12
=
26
130
=
156
Answer:
Step-by-step explanation:
m*n
m=13
n=12
13 * 12
156
A cabin has a room for 7 campers and 2 counselors. How many cabins are needed for a total of 49 campers and 14 counselors?
Answer:
7 cabins
Step-by-step explanation:
So with division, we can find out
49 campers / 7 per cabin = 7
14 counselors / 2 per cabin = 7
As we can see, both problems equal 7, which lets us see that the camp needs 7 cabins to hold all the campers and counselors
claire%20deposited%20$2,500%20into%20an%20account%20that%20accrues%20interest%20monthly.%20she%20made%20no%20additional%20deposits%20or%20withdrawals.%20after%202%20years,%20claire%20had%20$2,762.35%20in%20the%20account.%20what%20is%20the%20annual%20interest%20rate%20of%20the%20account?%20compound%20interest%20formula:%20t%20=%20years%20since%20initial%20deposit%20n%20=%20number%20of%20times%20compounded%20per%20year%20r%20=%20annual%20interest%20rate%20(as%20a%20decimal)%20p%20=%20initial%20(principal)%20investment%20v(t)%20=%20value%20of%20investment%20after%20t%20years%205%%2011%%2026%%2031%
Check your spelling or try different keywords
Ref A: 30CF20CCD29B40FCB21BC206F16E8CD0 Ref B: ATAEDGE1016 Ref C: 2020-02-06T21:47:16Z
Answer:
The annual interest rate is 5.247%.
Step-by-step explanation:
Question
Claire deposited $2,500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had $2,762.35 in the account. what is the annual interest rate of the account?
Subtract $2,500.00 from $2,762.35 and you get 262.35- the 2-year interest. To get the annual interest, divide 262.35 by 2, which equals 131.75. Then, divide 131.75 by 2,500 (original amount) and you get 0.05247. Lastly, multiply 0.05247 by 100 to get the answer (5.247%).
To find the annual interest rate, use the compound interest formula and set it equal to the final amount in the account. After performing the necessary computations, 'r' comes out to approximately 5%.
Explanation:To find the annual interest rate of Claire's account, you'll need to use the compound interest formula: v(t) = p * (1 + r/n)^(nt), where:
'p' is the initial (principal) investment, in this case $2,500;'r' is the annual interest rate, which is what we're solving for;'n' is the number of times the interest is compounded per year, which, since it's compounded monthly, is 12; and't' is the number of years since the initial deposit, which is 2 in this case.Claire's account had $2,762.35 in it after 2 years. Therefore, you would set $2,762.35 equal to the formula and solve for 'r'.
Doing so yields $2,762.35 = $2,500 * (1 + r/12)^(12*2) which simplifies, after some mathematical computations, to an annual interest rate (r) of roughly 5%.
Learn more about Compound Interest Calculation here:https://brainly.com/question/31477844
#SPJ3
The measures of two angles in a triangle are 48° and 71°. What is the measure of the third angle?
The sum of the 3 angles needs to be 180.
To find the third angle subtract to the known angles from 180.
180 - 48 - 71 = 61
The third angle is 61 degrees.
Make a math problem for the problem 4 divided by 1/2= 8
Answer:
if Jara has [tex]\$4[/tex] and she wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex].
How many pens she can buy.
Step-by-step explanation:
If Jara has [tex]\$4[/tex] and she wants to buy pen the wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex] .
How many pen she can buy.
[tex]Let\ Jara\ can\ buy=x\ pens\\\\each\ pen\ cost=\$\frac{1}{2}\\\\Then\ Jara\ can\ buy\ pens=\$\frac{1}{2}x\\\\\frac{1}{2}x=4\\x=8\\Jara\ can\ buy\ =8\ pens[/tex]
Raymond has a set of 57 toy cars and decides to sell 19 of them to Joey. About how many toy cars does Raymond have left
Answer:
raymond has about 38 cars left
Step-by-step explanation:
Because raymond started off with 57 cars and he got rid of( take away) 19 you must use subtraction. 57 - 19 =38
If a^2 + b^2=c^2 then the triangle is a right triangle.
A triangle with side lengths of 15m, 30m and 34m is a right triangle.
True or False
***Important... Even though the question says 15m, the question owner says he meant to put 16m***
[tex]a^2+b^2=c^2\\\\16^2+30^2=34^2\\\\256+900=1156\\\\1156=1156[/tex]
True!
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
It takes Esther 12 minutes to ride a roller
coaster four times. Write an equation to represent
the proportional relationship between the number
of rides and the total amount of time.
Final answer:
The proportional relationship between the number of rides and time is represented by the equation t = 3n where t is the total time in minutes and n is the number of rides.
Explanation:
Since it takes Esther 12 minutes to ride a roller coaster four times, we can find the time taken for one ride by dividing the total time by the number of rides.
Time for one ride = Total Time / Number of Rides = 12 minutes / 4 rides = 3 minutes per ride.
The proportional relationship between the number of rides (n) and the total amount of time (t) can be represented by the equation t = 3n. This indicates that for every ride, 3 minutes are added to the total time.
what does x equal in the function: f(-11)=5x+1
Final answer:
In the equation f(-11)=5x+1, solving for x yields x = -2.4.
Explanation:
To find what x equals in the function f(-11)=5x+1, we start by understanding that the function f(x) identifies the relation between x and f(x). In this case, f(-11) has been given the value of 5x+1. Therefore, we solve for x by setting the expression equal to f(-11).
We have the equation 5x + 1 = f(-11). Since f(-11) is given as a constant, we substitute and solve for x:
5x = -12
x = -2.4
Hence, x equals -2.4 in the function f(-11)=5x+1.
If a prison deceased by 372 prisoners each month over one year what the monthy decrease
Answer:
31 deaths per month
Step-by-step explanation:
12 months in a year
372 / 12 = 31
A company provides bus trips to various events for a adults and c children. The company charges $18 for each adult and $8 for each child for a trip to an upcoming play. The bus has a maximum capacity of 40 people and the school can only spend $400 dollars on the trip. Write and solve a system of equations to determine the maximum number of adults and children that can attend the play that will satisfy these constraints.
Final answer:
To determine the maximum number of adults and children that can attend the play without exceeding the bus capacity of 40 people and the $400 budget, set up and solve a system of equations representing the capacity and budget constraints. The solution is 8 adults and 32 children.
Explanation:
We are given a situation where a company charges $18 for each adult (a) and $8 for each child (c) for a bus trip to an upcoming play, with the constraints that the bus holds a maximum of 40 people and the available budget is $400. To find the maximum number of adults and children that can attend under these constraints, we need to set up a system of equations:
For the capacity constraint: a + c = 40
For the budget constraint: 18a + 8c = 400
We can solve this system using substitution or elimination. Let's use elimination. Multiply the first equation by -8 and add it to the second equation to eliminate c:
-8a - 8c = -320
18a + 8c = 400
Adding these two equations together gives us:
10a = 80
Thus, a = 8. Plugging a = 8 back into the first equation, we get c = 32.
The maximum number of adults and children that can attend the play is 8 adults and 32 children.
Fully answer BOTH questions a and b below.
On a recent survey, 60% of those surveyed indicated that they preferred walking to running.
a. If 540 people preferred walking, how many people were surveyed?
b. How many people preferred running?
Answer:
a. Number of people surveyed were 900.
b. 360 people preferred running.
Step-by-step explanation:
Given:
On a recent survey, 60% of those surveyed indicated that they preferred walking to running.
If 540 people preferred walking.
Now, to find a. number of people were surveyed. b. number of people preferred running.
a.
Number of people preferred walking = 540.
Percentage of people preferred walking = 60%.
Let the total number of people surveyed be [tex]x.[/tex]
Now, to get the number of people surveyed:
60% of x = 540.
[tex]\frac{60}{100} \times x=540[/tex]
[tex]0.60\times x=540[/tex]
[tex]0.60x=540[/tex]
Dividing both sides by 0.60 we get:
[tex]x=900.[/tex]
Thus, number of people surveyed = 900.
b.
Total number of people surveyed = 900.
People preferred walking = 540.
Now, to get the people preferred running we subtract people preferred walking from total number of people surveyed:
[tex]900-540[/tex]
[tex]=360.[/tex]
Thus, people preferred running = 360.
Therefore, a. Number of people surveyed were 900.
b. 360 people preferred running.
6. Rectangle GHIJ is enlarged to form
rectangle KLMN.
G 5cm H
2.5 cm
20 cm
10cml
Scale Factor:
Answer:
Scale Factor=2
Step-by-step explanation:
As the rectangle is enlarging from GHIJ to KLMN
then
Sacle Factor = Larger length / Smaller Length
Scale Factor = 5 cm / 2 cm = 2
Scale Factor = 20 cm / 10 cm = 2
HELP! I put the formula but I don’t know the radius
Answer:
C. 8,624
Step-by-step explanation:
recall that the formula for circumference is
Circumference = 2πr ( = given as 85 meters)
hence,
85 = 2πr
r = 85/(2π)
given h = 15m
volume of cylinder
= πr²h
= π (85/2π)² 15 (using calculator and assuming π = 3.14)
= 8628.58
Comparing with the choices, the closest choice (within rounding error) is C. 8,624
carter needs to wrap 7 presents. he lays the ribbon out flat and says ,if i nake 6 equally spaced cuts i'll have just enough pieces i can use 1 piece for each packages and i won't have any pieces left over .does he have enough pieces to wrap all the presents
2x + 3 for x = 3
evaluate each expression for the given value of x
Answer: 9
Step-by-step explanation:
2x + 3 when x = 3
2(3) + 3
2 * 3 = 6
6 + 3 = 9
To evaluate the mathematical expression 2x + 3 for x = 3, substitute x = 3 into the equation to get 2(3) + 3 = 6 + 3, and then add the numbers to get 9.
Explanation:
To evaluate the expression 2x + 3 for x = 3, you would replace x with 3 in the expression, then follow the order of operations (PEMDAS/BODMAS) to solve the expression.
Here is the step-by-step breakdown:
Substitute x = 3 into the expression, this makes the expression: 2(3) + 3 = 6 + 3 Then, you add the numbers together to get: 9
So, when x = 3, the value of the expression 2x + 3 is 9.
Learn more about Substitution in Expressions here:https://brainly.com/question/31279690
#SPJ2
Marcy has $20 she wants to buy a book that is marked down 30% from its original price of $28. If the sales tax is 2.5 does she have enough money
Answer:
no
Step-by-step explanation:
thirty percent of $28 is $8.4, so you would subtract the two leaving you with $19.6
2.5 sales tax of $19.6 is $0.49
Adding those two, the total comes to 20.09 which is just over budget
The amount of the book is more than $20. Then she does not have enough money.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Let 'x' be the markdown price. Then the equation is given as,
30% = [(28 - x) / 28] × 100
0.30 = [(28 - x) / 28]
8.4 = 28 - x
x = $19.6
Then the amount of book after tax is given as,
⇒ $19.6 x 1.025
⇒ $20.09
The amount of the book is more than $20. Then she does not have enough money.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
A triangle has sides with lengths of 58 feet, 62 feet, and 84 feet. Is it a right triangle
Answer:
NO
Step-by-step explanation:
84*84=7056
62*62= 3844
58*58=3364
3844+3364=7208
7208 is not equal to 7056
3.14*16.8*16.8*16.9
Find answer then round to the nearest hundredths
[Mark Brainliest if correct]
Answer: 3.14 *16.8*16.8*16.9=14977.3478
14977.3478= 14,977.35
solve 1/8 + 6a/5 = 3/8 + 2a/5 + 7/8
Answer:
no6666//7
Step-by-step explanation:
88../6
The sales tax rate is 8.25%. If Sheila bought a sweater for $35, a pair of jeans for $89, and a handbag for $55, find her total cost including the sates tax. Round your answer to the nearest cent.
Answer:185,422.61
Step-by-step explanation:8.25%/100=0.0825 but since it a sale tax you add a 1 so it would be 1.0825•35=37.88•89= 337.32•55=185,422.61
what is the value of c so that -12 and 12 are both solutions of x^2-c=108?
Answer:
c=36
Step-by-step explanation:
Because [tex]x^2-c=108[/tex] can be rewritten as [tex]x^2-c-108=0[/tex], finding the value of c so that x=(+-)12 solves this equation it means to find the value of c so that [tex](+-)12^2-c-108=0[/tex].Because [tex]12^2=(-12)^2=144[/tex], we must find c so that [tex]144-c-108=0[/tex].Because [tex]144-108=36[/tex], c=36.To check, replace c=36 in the initial equation, and check it is a solution for x=(+-)12.11/4 + 2 1/8 = solve this?
Answer:
4.875
Step-by-step explanation:
A triangle has side lengths of 3 feet and 9 feet.which is the greatest possible perimeter of the triangle
If 5(3x-5) = 20, then
what is 6x -8?
Answer:
10
Step-by-step explanation:
5(3x-5)=20
3x-5=20/5
3x-5=4
3x=4+5
3x=9
x=9/3
x=3
6x-8=6(3)-8=18-8=10