A shopkeeper packed two bags of sugar each 120 Kg into 3 Kg and 2 Kg packets respectively. There were half as many 2 Kg packets as 3 Kg packets. How many 3 Kg packets did he obtain?
Answer:
60
Step-by-step explanation:
Since both bags of sugar were 120 kg, there is a total of 240 kg of sugar to be distributed into the packs. Let x represent the number of 2 kg packets and y represent the number of 3 kg packets. We know that all the sugar was packed into these two kinds of packets, so:
[tex]2x+3y=240[/tex]
And we know that there were half as many 2 kg packets as 3 kg packets, so:
[tex]x=\frac{1}{2} y[/tex]
Now, we have a system of equations!
[tex]\left \{ {{2x+3y=240} \atop {x=\frac{1}{2}y }} \right.[/tex]
Let's put the second equation equal to y, since that removes the fraction:
[tex]x=\frac{1}{2}y\\ 2x=y[/tex]
Now substitute y into the first equation:
[tex]2x+3y=240\\2x+3(2x)=240[/tex]
Now simplify to find x:
[tex]2x+3(2x)=240\\2x+6x=240\\8x=240\\x=30\\[/tex]
There are 30 of the 2 kg packets! Now, we can use x to find y, the number of 3 kg packets!
[tex]2x=y\\2(30)=y\\60=y[/tex]
There are 60 of the 3 kg packets!
Answer each question to solve the equation. **Remember to state the units in your answer** Jennifer saved some money from her birthday. During the summer, she worked part time at McDonalds. She was paid $15 an hour. The equation 50+15h=1250 represents the amount of money she has. 1. What could the 1250 represent in this situation? A. The amount of money she had saved before B. The amount of money she had at the end of the summer C. The amount of money she earned per hour D. The amount of money she earned per week 2. George said that 10 could not be the solution to the equation. Explain why he is correct (Hint: put 10 in the place of h). 3. Find the solution to the equation. Show your work.
The 1250 represents option B in the situation, George is correct, the solution to the linear equation is h = 80$.
What is a linear equation?
A linear equation has only one or two variables. No variable in a linear equation is raised to a power greater than one or used as the denominator of a fraction. When two values satisfying a linear equation are found and shown, all of the points on a coordinate grid fall on the same line.
Given that,
Jennifer was paid $15 per hour.
Given equation is 50+15h=1250
1)Here 1250 represent B.
Her financial situation towards the end of the summer.
Because as mentioned in the equation 50+15h=1250
Here, 50 is the money already there with her, and 15h was the amount paid to her,
So, by adding those both the amount 1250 will be the amount with Jennifer at the end of the summer.
2)Given equation is 50+15h=1250
By putting 10 in place of h (h=10)
50+15(10)=1250,
50+150=1250,
200=1250$.
Since, LHS is not equal to RHS.
Therefore, George is correct, 10 could not be the solution to the linear equation.
3) Given equation 50+15h=1250
15h=1250-50,
15h=1200,
h=1200/15,
h=80$.
Therefore, the solution for the equation h is 80$.
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Use the number line below to show 10 + (–6). What is the sum of 10 + (–6)?
Answer:
4
Step-by-step explanation:
when you add a positive number to a negative number you subtract the two instead!
so, rephrase your math problem to
10-6=?
well 4
using the image you go back 6 places and you get 4
Evaluate the expression 8p2−2s3÷m + 58p^2-2s^3\div m\ +\ 58p
2
−2s
3
÷m + 5, when ppp =3, sss =2, and mmm =4
The solution for the expression ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5)) is 196.72
Given,
The expression: ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5))
Where,
Value of p is given as 3
Value of s is given as 2
Value of m is given as 4
Then,
((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5))
= (8 x 3² - 2 x 2³) / 4 + (58 x 3² - 2 x 2³) / 4 + (58 x 3² - 2 x 2³) / 4 + 5
= (8 x 9 - 2 x 8) / 4 + (58 x 9 - 2 x 8) / 4 + (58 x 9 - 2 x 8) / 9
= (72 - 16) / 4 + (522 - 16) / 4 + (522 - 16) / 9
= 56 / 4 + 506 / 4 + 506 / 9
= 14 + 126.5 + 56.22
= 196.22
Therefore, the solution for the expression ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5)) is 196.72
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Evaluate the sum of the finite geometric series. 3+6+12+24+48+ . . . +768
The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term. The sum of the finite geometric series 3 + 6 + 12 + 24 + 48 + . . . + 768 is 1533.
What is geometric series?The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.
The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.
Let the finite geometric series be
3 + 6 + 12 + 24 + 48 +. . . + 768
Where, the first term, a = 3
common difference, r = 6/3 = 2
n = 9
The equation be Sn = a(1 - [tex]$$r^{n}[/tex])/(1 - r)
substitute the values in the above equation, we get
S9 = 3(1 - [tex]$$2^{9}[/tex]))/(1 - 2)
simplifying the above equation, we get
= 3(1- 512)/(-1)
= 3(-511))/(-1)
= 3(511) = 1533
Therefore, the sum of the finite geometric series 3 + 6 + 12 + 24 + 48 + . . . + 768 is 1533.
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In a recent year the populations of china was 1.3x10^9According to the census data the population of the us was about 308,745,538 about how many times greater was the population of china than the population of the us step by step pleas
According to the census data, the population of China is more than the population of US by a factor 4.2
How to find how many times greater was the population of China over US populationGiven data
population of China = 1.3x10^9
population of US = 308,745,538
population of china = 1.3x10^9. can be rewritten as = 1,300,000,000
comparing the both figures representing population. we divide the population of China by the population of US
let the number of times the population of china is greater than population of US be x, such that
308,745,538 * x = 1,300,000,000
308,745,538x = 1,300,000,000
x = 1,300,000,000 / 308,745,538
x = 4.2106
x ≅ 4.2
We therefore say that the population of china is more than the population of US by a factor 4.2
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The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Work out the cost of a) 1 kg of turnips. b) 1 kg of mushrooms. check image
If the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.
Given that the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.
We are required to find the cost of 1 kg of mushrooms and the cost of 1 kg of turnips.
Cost is basically the expenditure that we do in order to buy or produce a product.
Suppose the cost of 1 kg of mushrooms be x and the cost of 1 kg of turnips be y. The equations will be as under:
2x+2.5y=8.55------1
3x+4y=13.10-------2
Equation1 *3 and Equation2 *2.
6x+7.5y=25.65-----3
6x+8y=26.20-------4
Subtract 4 from 3.
6x+7.5y-6x-8y=25.65-26.20
-0.5y=-0.55
y=1.1
Put the value of y in 1.
2x+2.5*1.1=8.55
2x+2.75=8.55
2x=8.55-2.75
2x=5.80
x=2.9
Hence if the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.
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At the end of December, the Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Type the answer in the box to represent the Cookie Shop's profit at the end of January.
The Cookie Shop's profit at the end of January will be $12000.
The profit earned by the shop at the end of December = $15000
The profit decreased by 20% at the end of January
Therefore decrease percentage, which is used to determine the percentage decrease of two values (final value and initial value)
[tex]Decrease percentage = \frac{Final value - Initial Value}{Final Value} * 100[/tex]
According to the formula, the initial value is subtracted from the final value. The resulting value is divided by the initial value and multiplied by 100 to obtain the decreased percentage
Decrease Percentage 20%
Final value = $15000
[tex]20 = \frac{15000 - Initial Value}{15000} * 100[/tex]
[tex]\frac{20}{100} = \frac{15000 - Initial Value}{15000}[/tex]
[tex]\frac{20}{100} * 15000 ={15000 - Initial Value}[/tex]
20 * 150 = 15000 - Initial Value
3000 = 15000 - Initial Value
Initial value = 15000 - 3000
Initial value = $12000
The profit earned by the Cookie Shop at the end of January will be $12000.
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Help!!
The number of yards Kyle travels on in-line skates, y, varies directly with the amount of time spent skating, t. When Kyle skates for 1.5 min, he can travel 351 yd.
Which equation shows this direct linear variation?
y = 526.5t
Y = 234t
y = 175.5t
y = 352.5t
Answer:
y = 234t
Step-by-step explanation:
Divide the equation by t on both sides. See image.
find the perimeter of the new similar triangle to the triangle below with a ratio of 3:5, old to new triangle
A. 24.17
B. 8.7
C. 14.5
D. 24
E. 9
Answer:
A. 24.17.
Step-by-step explanation:
Perimeter of given triangle
= 4 + 4.5 + 6
= 14.5.
3:5 = 14.5 : P where P is perimeter of new triangle
3/5 = 14.5/P
3P = 5*14.5
P = 14.5 * 5 / 3
= 24,166667
= 24.17.
the price of a scooter and a cycle are in the ratio 5:2 if the scooter costs ruppes 4,200 more than the cycle ,whats the price of the cycle
The price of the cycle is 2800 and the price of the scooter is 2800+ 4200=7000
Let the price of the cycle be x
Then the price of the scooter will become X + 4200
As the price of a scooter and the price of a cycle are in the ratio of 5:2
So, it can be written as
x+4200: x:: 5:2
which implies
x= 2a and x+4200= 5a
a= x/2 and x+4200/5
equating both the equations, we get
x/2=(x+4200)/5
in order to solve this linear equation, we need to move 2 from the left-hand side to the right-hand side which would result in the change of sign from division to multiplication and we need to move 5 from the right-hand side to the left-hand side which would result in the change of sign from division to multiplication
5x=2x+8400
3x= 8400
X= 8400/3
X= 2800
So, the price of the cycle is 2800 and the price of the scooter is 2800+ 4200=7000
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Match each equation with the correct solution.
PLEASE HELP!! 30 POINTS!!
Answer:
Step-by-step explanation:
You just have to distribute all the equations. Start with the parenthesis. I'll do one for you. 2(x-5) +7 = x+8. Distribute 2(x-5) and you gest 2x-10+7=x+8. subtract x from the right and you get x-10+7=8. Combine like terms so you get x-3=8. Then add 3 on both sides and you get x=11.
394.82−55.75 helppppppppppp
Answer: 339.07
Step-by-step explanation:
Answer:
339.07.
Step-by-step explanation:
I've attached an image to help break down this problem. (credit to cymath.com)
Hope this helps! :)
what is the value of the 5 in 3,152,308.
Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624. Find the amount of his tax.
Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624 the amount paid as tax is $ 3,765.
Given details in the question are as follows:
Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624,
By using the given tax table on the screenshot we are calculating the tax paid by Jim.
if your taxable income is greater than the $23,600 but lesser than the $23,624 and you fill separate tax return, the amount will be paid as tax is
$ 3,765.
what is a separate tax return?Married filing separately is a tax status for married couples who choose to record their respective incomes, exemptions, and deductions on separate tax returns.
The alternative to married filing separately is married filing jointly. Usually, it makes sense financially for married couples to file jointly. However, when one spouse has significant medical expenses or miscellaneous itemized deductions, or when both spouses have about the same amount of income, it might be wiser to file separately.
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Write the equation of the line that passes through the points (6,-3) and (1,7) in the form y = mx + b.
m=
b=
How many different 4-digit PIN codes are there that only include the digits 2, 3, 4, 6, 7, 8 and 9
if each of those digits is only allowed to be used once?
The number of different 4-digit PIN codes if each of those digits is only allowed to be used once is 840
How to determine the number of different 4-digit PIN codes if each of those digits is only allowed to be used once?The digits are given as:
2, 3, 4, 6, 7, 8 and 9
There are 7 digits represented in the above list
If each of those digits is only allowed to be used once, then we have the following possibilities
First character: Any of the 7 digits
Second character: Any of the remaining 6 digits
Third character: Any of the remaining 5 digits
Fourth character: Any of the remaining 4 digits
The number of 4-digit PIN codes is
Number = 7 * 6 * 5 * 4
Evaluate
Number = 840
Hence, the number of different 4-digit PIN codes if each of those digits is only allowed to be used once is 840
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Ty plays football at his neighborhood park with his friends. He can make field goals and touchdowns. Field goals are worth 1 point each and touchdowns are worth 6 points each. Ty can no more than 18 points before his neighborhood buddies kick him out of the game for dominating too much.
Write an inequality to describe the constraints.
Use "f" for field goal and "t" for touchdown.
***THE PICTURE IS PART 2***
The inequality that describes the constraints is f + 6t ≤ 18
If Ty has 4 field goals and 3 touchdowns, he cannot remain on the team.
What is the inequality that describes the constraints?Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≤ because Ty's score has to be at most 18 points.
The from of the inequality that describes the constraints is:
(point of a touchdown x number of touchdowns) + (point of field goals x number of field goals) ≤ maximum points
(1 x f) + (6 x t) ≤ 18
f + 6t ≤ 18
Ty's total score when he has 3 touch downs and 4 field goals
(1 x 4) + (6 x 3) ≤ 18
4 + 18 ≤ 18
22 ≤ 18
Ty cannot remain on the team because his score exceeds 18. (i.e. 22 > 18).
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solve for x with explanatory proccess
Answer:
x = -6.8
Step-by-step explanation:
2.4x - 9.1x + 12.5x = -39.44
combine all like terms
5.8x = -39.44
÷5.8 ÷5.8
x = -6.8
I hope this helps!
Please help me asap !
Answer:
a = 71°
Step-by-step explanation:
This looks like a supplementary angle
109 + a = 180
-109 -109
a = 71°
I hope this helps!
Answer:
a = 71°
Step-by-step explanation:
Hello!
The sum of angles on a line is 180°. That means, 109° and a have to add up to 180°.
Angles that add up to 180° are called supplementary angles.
Solve for a180° - 109° = a71° = aa is 71°.
(-4)² = -(4)² True Or False
Help Quick Please!
Answer: True
Step-by-step explanation: Because Im A Top G
HELP ASP SHOW WORK YOULL GET BRAINILEST
Answer:Ill try my best.
The answer is
3rd one
Step-by-step explanation:
subtract 70 from both sides of the equation
Determine whether each list is a sequence or a series and finite or infinite. 1,2,4,8,16,32, . . . . . .
From the list of numbers presented:
12481632we can determine that this is a infinite serie.
What are sequences?A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.
A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:
1, 2, 4, 8, 16, 32
2ⁿ⁻¹2⁰ = 12¹ = 22² = 42³ = 82⁴ = 162⁵ = 322ⁿ⁻¹
In this series we have the initial value of the same, but we do not know the final value, although we know its behavior, we can say that this series has no end, it is an infinite serie.
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Which choice could you use to find the distance (d) between the points shown on the number line?
Answer:
d = 380 units
Step-by-step explanation:
Find the absolute value of the difference of the 2 numbers, that is
d = | - 235 - 145 | = | - 380 | = | 380 | = 380
or
d = | 145 - (- 235) | = | 145 + 235 | = | 380 | = 380
PLEASE!!!!If DEF =110 then what are FEG and HEG?
Answer:
FEG: 70 degrees
HEG: 110 degrees
Step-by-step explanation:
vertical angles are the same, and for supplementary angles you subtract 180, so likes for FEG you subtract 110 from 180, and for HEG its just the same thing
HELP ASP SHOW UR WORK WILL GET BRAINILEST AND 10 points
Answer:
7 baskets
Step-by-step explanation:
in the first game, he shot 6 baskets so
34 - 6 = 28
she shot the same number for each of the 4 games,
so divide 28 and 4.
the answer is 7
hope this helps
a. Write 64√2 in the form 2^n
We get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.
An expression is a way in which numbers are written.
It can be variables, constants or a combination of both.
We are given an expression:
64 √2
We know that:
64 = 2 × 2 × 2 × 2 × 2 × 2
64 = 2⁶
Also, we can write √2 as
√2 = 2⁰°⁵
We get that:
2⁶ × 2⁰°⁵
simplifying the expression, we get that:
= 2⁶⁺⁰°⁵
= 2⁶°⁵
Therefore, we get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.
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How do I find (rs)(4)=?
How do i also find (r/s)(3)=?
The functions are express as follows:
(rs)(4) = 8(r / s)(3) = 2How to solve composite functions?A composite functions is gotten from the combination of two or more functions.
Therefore,
(rs)(4) = r(4) × s(4)
r(x) = 2√x
s(x) = √x
Hence,
r(4) = 2√4 = 2 × 2 = 4
s(4) = √4 = 2
Therefore,
(rs)(4) = r(4) × s(4) = 4 × 2 = 8
(r / s) (3) = r(3) / s(3)
r(3) = 2√3
s(3) = √3
Hence,
(r / s) (3) = r(3) / s(3) = 2√3 / √3 = 2
Therefore, the functions are express as follows:
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50 pts if you can solve this correctly
Answer:
C.
Step-by-step explanation:
c^2-a^2
will give you b
Answer:
The Answer is C
Step-by-step explanation:
Hope this helps!!!
f (x) = - |x + 9| find x
Answer:
source?
Step-by-step explanation:
wiyhout one I cannot help you, best of luck!
