The cost of each 1 pound candy is $30, 1 box of cookies is $5 and 1 can of popcorn is $10.
We have the church youth group is selling snacks to raise money to attend their convention.
We have to determine the cost of each item they sold.
Write the following statement in the form of a mathematical equation - Steve bought 2 toffees each of $x and 5 chocolates each of $y. The total cost is $50.The mathematical equation representing the above statement is -
2x + 5y = 50
According to question -
Assume that the cost of :
1 pound candy = $x
1 box of cookies = $y
1 can of popcorn = $z
Now, write down the mathematical equation representing their total sales -
Amy - 2x + 3y + z = 85
Brian - 4x + 4y + 3z = 170
Paulina - 8x + 8y + 5z = 330
We will use the Cramer's rule to solve these equations -
The 3 x 3 coefficient matrix is -
[tex]\left[\begin{array}{ccc}2&3&1\\4&4&3\\8&8&5\end{array}\right][/tex]
Find its determinant -
D = 2(4 x 5 - 3 x 8) - 3(4 x 5 - 8 x 3) + 1(4 x 8 - 4 x 8) = 4
Create the X- matrix (X - matrix is formed by replacing the x-column values with the answer-column values) as follows -
[tex]\left[\begin{array}{ccc}85&3&1\\170&4&3\\330&8&5\end{array}\right][/tex]
Find th determinant of this X - matrix same as done above -
D(X) = 120
Similarly create a Y - matrix and Z - matrix and find their respective determinants. On solving you will get -
D(Y) = 20
D(Z) = 40
According to the Cramer's rule -
[tex]$x = \frac{D_{x} }{D}[/tex]
[tex]$y = \frac{D_{y} }{D}[/tex]
[tex]$z = \frac{D_{z} }{D}[/tex]
Therefore -
x = 120/4 = 30
y = 20/4 = 5
z = 40/4 = 10
Hence, the cost of each 1 pound candy is $30, 1 box of cookies is $5 and 1 can of popcorn is $10.
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DUE TODAY HELP!!
NO TIME FOR LINKS
I NEED THE EXPLANATION
Answer:
oh its 6 digit
Step-by-step explanation:
trust me
x2+16x+
Help me guys
Evaluate 4 x^3 + 4x when x = 3
Answer:120
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
Given information:
• 4x³ + 4x
• x = 3
To evaluate the expression further, plug in the given variable and simplify:
4x³ + 4x Replace x with 3.
4(3)³ + 4(3) PEMDAS - put 3 to the 3rd power.
4(27) + 4(3) Use the distributive property to get rid of the parentheses.
108 + 12 Add the two values.
120
The simplification of 4x³ + 4x when x = 3 is 120.
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Part 1: Graph a function when give the following Domain and Range:
Answer:
Step-by-step explanation:
This is basically the same thing as the last question.
The domain goes from - 8 to 5. The 5 has an open circle for it's endpoint < does not include the end point
the range is a little tricky. It goes from - 6 to 9. The -6 is has a circle (because it is not included in the answer). I'm not sure how you show that on a graph.
I think the best answer is this: if either the domain or range is separated by < then you must change the one that uses ≤ into < so the endpoints of the domain are in agreement. You cannot have the domain using < when the range uses ≤. They both must be the same. I think the best choice is<
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The function can have virtually any shape between the ends of the domain and range. The function can have any value in the range at x = -8, and can have any value in the domain at y = 9.
The attachment shows two different functions having the required characteristics.
What is the answer to this question?
Answer:
the answer is option 3rd
What is the probability of rolling a sum of 2 on a standard pair of six-sided dice? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary
How many solutions does this equation have?
9m + 8 - 3m = 4(m + 5)
Answer:
yyyg h ug guy Judy bg
Step-by-step explanation:
by HGTV byf g gu o
Exactly 1 solution
I took the test in k12 and this is the correct answer.
Good luck
2x 32 10 10 find x please help ASAP
Please help me!!! -Tom saved up $250 to spend on vacation. If he spends 843 a week for four weeks, how much money
does he have left?
Answer:
Step-by-step explanation: first multiply 843 by 4 and you get 3372 then subtract 250 by 3372 and you get $- 3122
A washer and a dryer cost $959 combined. The washer costs $59 more than the dryer. What is the cost of the dryer?
Answer:
A dryer costs $450.
A washer costs $509.
Step-by-step explanation:
Let:
"washer" = x
"dryer" = y
Set the equations:
x + y = 959
x = y + 59
First, plug in y + 59 for x in the first equation for x:
x + y = 959
(y + 59) + y = 959
Simplify, combine like terms:
y + y + 59 = 959
2y + 59 = 959
Next, isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis, Exponents (& Roots), Multiplications, Divisions, Additions, Subtractions.
First, subtract 59 from both sides of the equation:
2y + 59 (-59) = 959 (-59)
2y = 959 - 59
2y = 900
Next, divide 2 from both sides of the equation:
(2y)/2 = (900)/2
y = 900/2
y = 450
Next, plug in 450 for y in one of the equations:
x = y + 59
x = (450) + 59
x = 509
Check:
x + y = 959
450 + 509 = 959
959 = 959 (True).
~
Answer:
$450
Step-by-step explanation:
1. First, let's make a system of equations:
[tex]y+59=x,x+y=959[/tex] (y = dryer, x = washer)2. (Solving)
Solve y + 59 = x for y:
[tex]y + 59 = x[/tex] [tex]y + 59-59=x-59[/tex] (Subtract 59 from both sides)[tex]y = x-59[/tex]Substitute x - 59 for y in x + y = 959
[tex]x + y = 959[/tex] [tex]x+x-59=959[/tex] [tex]2x - 59 = 959[/tex] [tex]2x - 59 + 59 = 959 + 59[/tex] (Add 59 to both sides)[tex]2x = 1018[/tex] [tex]\frac{2x}{2} = \frac{1018}{2}[/tex] (divide both sides by 2)[tex]x = 509[/tex]Substitute 509 for x in y = x - 59
[tex]y = x - 59[/tex] [tex]y = 509-59[/tex] [tex]y = 450[/tex]Therefore, the dryer costs $450. (The washer costs $509).
Which of the following represents this statement? 4x-7>3
Answer:
b
.................................
Answer:
Step-by-step explanation:
The answer is actually a. Hope this helps :)
Jasmine is a receptionist at a doctors office. She books 36 appointments each day . Four out of every 24 appointments are cancelled. How many appointments are cancelled each day?
If Jasmine books 36 appointments each day, 6 appointments will be canceled.
Number of appointments booked each day = 36 appointments
Since four out of every 24 appointments are canceled. This means the fraction of appointments that are canceled will be:
= 4/24 = 1/6
Now, since three are 36 appointments each day, the number of appointments that are canceled will be:
= 1/6 × 36
= 6 appointments
In conclusion, 6 appointments will be canceled each day.
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Hello everyone, I hope you had a great day, I need help on this please, thanks.
Answer:
A
Step-by-step explanation:
A. is the only correct solution to this question because you can also see that if we take 8 and divide this by 32 we get 1/4, so we know it is true.
A box of 6 nail polishes cost $10. How much is each nail polish?
Answer:
1.66Step-by-step explanation:
You should divide 10 by 6 hope it HELPED
In a lottery game, a player picks 9 numbers from 1 to 46. If 8 of the 9 numbers match those drawn, the player wins second prize. What is the probability of winning this prize? Be sure to leave your answer as a reduced fraction in order to earn credit.
There is a _____
probability of winning second prize.
Answer: [tex]\frac{37}{1,101,716,330}\\\\[/tex]
This is the same as writing 37/1101716330
======================================================
Explanation:
Let's say the nine winning numbers are: 1,2,3,4,5,6,7,8,9
Let's further say that if we matched everything from 1 to 8, then we'll win second prize. That ninth value can be anything but 9. So we could have something like one of these examples
1,2,3,4,5,6,7,8,101,2,3,4,5,6,7,8,111,2,3,4,5,6,7,8,12As you can see, there are 46-9 = 37 different choices we can have for that last slot. In other words, there are 37 items in the set {10,11,12,...,45,46} we can pick for that last ninth slot. Note that 46-10+1 = 37. This value will form the numerator of the answer.
------------------------------------------
Now to calculate how many ways there are to select the nine values regardless if we win or lose.
Since order doesn't matter, we use the nCr combination formula.
[tex]_{n} C _{r} = \frac{n!}{r!*(n-r)!}\\\\_{46} C _{9} = \frac{46!}{9!*(46-9)!}\\\\_{46} C _{9} = \frac{46!}{9!*37!}\\\\_{46} C _{9} = \frac{46*45*44*43*42*41*40*39*38*37!}{9!*37!}\\\\[/tex]
[tex]_{46} C _{9} = \frac{46*45*44*43*42*41*40*39*38}{9!} \ \text{ ... the ``37!'' terms cancel}\\\\_{46} C _{9} = \frac{46*45*44*43*42*41*40*39*38}{9*8*7*6*5*4*3*2*1}\\\\_{46} C _{9} = \frac{399,790,821,830,400}{362,880}\\\\_{46} C _{9} = 1,101,716,330\\\\[/tex]
There are slightly over 1 billion ways to select the nine values.
This large value is the denominator of our answer which is [tex]\frac{37}{1,101,716,330}\\\\[/tex]
The 37 up top represents the number of ways to win the second prize we're after, while the massive number in the denominator represents how many ways there are to play the game.
------------------------------------------
Notice that in the jump from step 4 to step 5, shown in the section above, we had the "37!" terms cancel out. What this means is that the prime number 37 is nowhere to be found anywhere in the factorization of 1,101,716,330
Why is this important? Because it tells us that the fraction [tex]\frac{37}{1,101,716,330}\\\\[/tex] cannot be reduced.
Side note: That fraction converts to the decimal form 0.00000003358397 approximately and that converts to the percentage form 0.000003358397%; both of which are very very small numbers. We can see that the odds are definitely stacked against the player.
What is the value of 6(2b-4) when b=5?
Answer:
36
Step-by-step explanation:
6[(2×5)-4]
6(10-4)
6(6)
=36
Answer:
36
Step-by-step explanation:
6(2b-4) where b=5
= 6(2(5)-4)
= 6(10-4)
= 6(6)
= 36
Please answer the following questions. D Question 1 Morgan won $2,315 at a work raffle. They deposited $1898.30 into their savir What percent of their winnings did they deposit into their savings account? D Question 2
Please see attached. Thank you for the help
Answer:
5 <= x <= 8
Step-by-step explanation:
x/5 (*5) >= 1 (*5)
x >= 5
x-1 (+1) <= 7 (+1)
x <=8
How many QUADRANT do we have in mathematics.
Answer:
4 quadrants
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
There are four Quadrants in Mathematics. Counting from the right to left, to left, then right, we can tell which quadrant we are in.
What is the relationship between the standard deviation of the sample mean and the population standard deviation?
The mean of the sample mean ˉX that we have just computed is exactly the mean of the population. The standard deviation of the sample mean ˉX that we have just computed is the standard deviation of the population divided by the square root of the sample size: √10=√20/√2.
Answer:
Step-by-step explanation:
The mean of the sample mean ˉX that we have just computed is exactly the mean of the population. The standard deviation of the sample mean ˉX that we have just computed is the standard deviation of the population divided by the square root of the sample size: √10=√20/√2.
PLEASE HELP REALLY QUICK I WILL REWARD BRAINLIEST PUT FULL EXPLANATION AND ANSWER TO THE QUESTION BELOW!!!!!!!!
Answer:
[tex]x = 27[/tex]
Step-by-step explanation:
[tex]36 + 90 + 2x = 180 \\ 126 + 2x = 180 \\ 2x = 180 - 126 \\ 2x = 54 \\ \\ x = \frac{54}{2} \\ \\ x = 27[/tex]
I hope I helped you^_^
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
Let's evaluate value of x ~
[tex]\qquad \tt \dashrightarrow \:36 + 90 + 2x = 180[/tex]
[ by linear pair property of straight line ]
[tex]\qquad \tt \dashrightarrow \:2x + 126 = 180[/tex]
[tex]\qquad \tt \dashrightarrow \:2x = 180 - 126[/tex]
[tex]\qquad \tt \dashrightarrow \:2x = 54[/tex]
[tex]\qquad \tt \dashrightarrow \:x = 54 \div 2[/tex]
[tex]\qquad \tt \dashrightarrow \:x = 27 \degree[/tex]
I hope it's easy to understand ~
I need help please ty
Answer:
1no=61
2no=53
Step-by-step explanation:
May this help you
When making the first set a bracelet Rachel used 35% of the yarn the length of the yarn
used was 70 feet how much yarn was there to start
Answer:
i think you should ask the brain
Step-by-step explanation:
Answer:
200 feetStep-by-step explanation:
Let the initial length of the yarn was x.
35% of x is 70 feet
0.35x = 70x = 70/0.35x = 200I need help with number 5
Answer:
5
Step-by-step explanation:
-3a+24-9=0
-3a = -15
a = 5
Answer:
Step-by-step explanation:
solve the equation then plug in the to numbers
Apply the order of operations to simplify each expression.
5.5+23 x 2 =
21
17
50
13
Answer:
50
Step-y-step explanation:
Answer:
21
Step-by-step explanation:
5 + 2³ × 2 = 5 + 2⁴
=5 + 16
= 21
Samuel was preparing for the triathlon. He did 3 activities every morning: Ran for 30 minutes, covering 4.5 miles. Swam for 20 minutes, covering 2/3 mi. biked for 45 min, covering 9 miles. What was Samuel's average speed during his morning training?
PLEASE HELP!!!
Answer:
≈ 0.15 miles per minuteStep-by-step explanation:
Speed = distance / time
Let's find total distance and time
Distance
4.5 + 2/3 + 9 = 45/10 + 2/3 + 9 = 9/2 + 2/3 + 9 = (27 + 4 + 54)/6 = 85/6Time
30 min + 20 min + 45 min = 95 minAverage speed
85/ 6 ÷ 95 = 85/6*1/95 = 17/114 ≈ 0.15 miles per minuteAnswer:
8.9474
Step-by-step explanation:
just trust me please i swear to god it is 8.9474
Please help me solve this!!
Answer:
its B
Step-by-step explanation:
beacuse i searched it it helps
What is the total distance in meters of a car that travels due west at 50 m/hr west between 12:00 and 4:00 pm?
Answer:
A train leaves the station at 9:00 pm traveling east at 36 miles per hour. A second train leaves the station at 10:00 pm traveling west at 42 miles per hour. At what time will both trains have traveled the same distance?
------
Let t equal the time that passed right after 10 PM.
42t = 36 (t + 1)
42t = 36t +36
6t = 36
t = 6 hours
Answer: 4 AM ✅
Step-by-step explanation:
The car traveled 200 m distance with a speed of 50 m / hr in 4 hr.
Given that,
To determine the total distance in meters of a car that travels due west at 50 m/hr west between 12:00 and 4:00 pm.
Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
What is Distance?Distance is defined as the object traveling at a particular speed in time from one point to another.
Here, the car travels due west at 50 m/hr west between 12:00 and 4:00 pm
Time = 12:00 - 4:00 = 4 hours
Speed = 50 m / hr
Distance = 50 * 4
= 200 m
Thus, the car traveled 200 m distance with a speed of 50 m / hr in 4 hr.
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The perimeter of a rectangle is 280 meters. The width is 26 meters less than the length. Find the length and width.
Answer:
The length is 83 and the width is 57
Step-by-step explanation:
The width is 26 meters less than the length, so we'll represent the width with: L-26. Since there are 2 widths to account for, we'll multiply this by 2.
Equation looks like this so far: 2(L-26)
Then, add the 2 lengths and set the expression equal to 280.
Equation: 2(L-26)+2L=280
Distribute the 2 in the first term, making the equation look like:
2L-52+2L=280
Add the 52 to both sides of the equation
4L=332
Divide by 4 on both sides
L=332/4=83
L=83
Width is 26 meters less, so 83-26=57
W=57
Which of the following is the equation for the graph shown?
9514 1404 393
Answer:
D y²/5 -x²/4 = 1
Step-by-step explanation:
The y-intercept is about 2.2, or √5. This point (0, √5) only satisfies the equation of the last choice:
y²/5 -x²/4 = 1
__
Additional comment
The second attachment tells you the foci are located at (0, ±(a²+b²)), where a² and b² are the denominators in the above equation. That is the foci are ...
(0, ±√(4+5)) = (0, ±3) . . . . as shown in the graph
This confirms the equation denominators are rightly 5 and 4, with 5 being the denominator of y².
The second attachment has the equation for a hyperbola that opens along the x-axis. Interchange the variables x and y to get the hyperbola shown in this problem statement.