Four boys weighed themselves in different pairs and alone. The weights of the pairs were 110 kg, 112 kg, 113 kg, 118 kg, 121 kg, and the weight of one pair was lost. The total weight of the four boys was 230 kg. What was the lost weight?

Answers

Answer 1

The lost pair of weight can be found by subtracting the a known pair from

the total weight leaving the value of the lost pair.

The lost weight of a pair of boys is 120 kg

Reasons:

Let a, b, c, and d represent the weights of the four boys, we have;

The number of ways of selecting pairs (two boys) of boys from a group of

four is given using combination formula as follows;

[tex]_nC_r = \dfrac{n!}{r! \cdot (n - r)!}[/tex]

Which gives;

[tex]_4C_2 = \dfrac{4!}{2! \cdot (4 - 2)!} = 6[/tex]

₄C₂ = 6

Therefore, the weights of the pairs are;

a + b = 110

a + c = 112

a + d = 113

b + c = 118

b + d = 121

c + d = Lost weight

c + d = Lost weight

a + b + c + d = 230 (given)

Therefore;

The lost weight, c + d = 230 - (a + b)

Which gives;

c + d = 230 - (110) = 120

The lost weight = c + d = 120

The lost weight = 120 kg

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Answer 2

Answer:

116

Step-by-step explanation:

you can use variables

a+b=110

a+c=112

a+d=113

b+c=118

b+d=121

add up the weights and you get 574 kg (you need to find c+d)

3a+3b+2c+2d=574

a+b+c+d = 230 as given then you multiply by 3 so you can cancel out 3a and 3b and subtract 690-574 because we multiplied by 3

you are left with c+d=116

similar method to the answer previously


Related Questions

Write the following equation in the general form Ax + By + C = 0.

1/2 y - 1/3x - 1 = 0

-2x + 3y - 6 = 0
2x - 3y - 6 = 0
2x - 3y + 6 = 0

Answers

The answer is the second option.

To find the answer quickly, fist look at the signs associated with the terms. The is a negative sign with the B and C in the original equation, and the second option is the only one that follows that.

You use 6 as the C since that is a shared value when multiplying 2 and 3, so 1/2 becomes 2 and 1/3 becomes 3.

pasagot please
answer it please​

Answers

Answer:

Step-by-step explanation:

Let's start by looking at the graph of the two equations.

Since you are not looking for where the lines cross, I have chosen any 3 points for each equation almost randomly. I have not used either the x or y intercepts except once.

As a sample for the method of calculation

Let x -2y = 4

Let x = -2.             Find y and put it in the table

-2 - 2y = 4             Add 2 to both sides

-2+2-2y = 4 + 2    Combine

-2y = 6                  Divide by -2

y = 6/-2

y = - 3

Put that in the table under the first equation.

The other 5 points are done the same way.

Find the value of y to the nearest tenth.

Answers

Step-by-step explanation:

the easiest approach seems to be the law of sines :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides and the angles are always opposite of each other.

we have here a right-angled triangle, so the angle opposite of 10 is 90 degrees.

10/sin(90) = 10/1 = 10 = y/sin(37)

y = 10×sin(37) = 6.018150232 ≈ 6.0

ILLA
2. Miles makes $14 per hour but has to pay $55 for his cell
phone bill.

Answers

miles had to work 4 hours to pay his phone bills and he had 1$ left over

Answer:

i dont know

Step-by-step explanation:

what question are you asking?

if 20 articles cost $90,then the cost of 9 articles is

Answers

Answer:

$40.50

Step-by-step explanation:

90 divided by 20 is 4.5. then you multiply that times 9 and that's your answer.  

Which of the following best represents the average rate at which infants gain weight for the first six months after birth?

Answers

Step-by-step explanation:

Infants may gain 5 to 7 ounces (140 to 200 grams) of weight a week and grow 1/2 to 1 inch (1.5 to 2.5 centimeters) per month from birth to 6 months. A baby's birth weight will double by the time they turn five months old.

Algebra 2 please help

Answers

Answer:

4th option

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 4x² - 5x + 8 +2x² + x - 2 ← collect like terms

= 6x² - 4x + 6

If e
very day, Kim practices volleyball and clarinet. Each day, she practices volleyball for 2.5 hours. If after 8 days she practiced both volleyball and clarinet for a total of 36 hours, how many hours per day did Kim practice clarinet?

Answers

Answer:

2hours

Step-by-step explanation:

2.5×8

=20

36-20

=16

16/8

=2hours

The functions r and s are defined as follows.
r(x) = -x +1
s(x)=2x2-1
Find the value of r(s(4)).
numeral composition of functions

Answers

Answer:

.........................................

Which of the following is a solution to the inequality below?19 ≥ 5k + 6

Answers

Answer:

k ≥ 13/5 or k ≥ 2.6 ( same thing )

Step-by-step explanation:

symbol stays the same throughout (≥)

subtract 6 from both sides of the symbol ( 13 ≥ 5k)

divide both sides by 5 (13/5  ≥ k )

your answer can be written as k ≥ 13/5 or k ≥ 2.6

What is the first step in solving this equation?
3(2x + 6) - 4x = 2(5x - 2) + 6
Use the subtraction property of equality to subtract 6 from both sides.
Use the addition property of equality to add 4x to both sides.
Combine the like terms on each side of the equation.
O Use the distributive property on each side of the equation.

Answers

Answer: use distributive property

Step-by-step explanation:

you must always start from the numbers in the parentheses

What is the value of X?

Answers

Answer:

45 i think

if not 54

I'm pretty sure it's 45

hope this helped :)

i will give crown if answered right i just need to check my work

Answers

Answer:

9x(3x-2) (3x+2)

Step-by-step explanation:

[tex]81x^{3}-36x[/tex]

9(9x³ - 4x)

9x(9x² - 4)

Since both terms are perfect squares factor using the difference of squares formula,  a² - b² = (a + b) (a - b)

Therefore, 9x(3x-2) (3x+2)

Answer:

81z^3-36z = 9z(3z-2)(3z+2)

Step-by-step explanation:

(81z^3-36z)=9z(9z^2-4)

9z(9z^2-4)=9z(3z-2)(3z+2)

81z^3-36z=9z(3z-2)(3z+2)

81z^3-36z=9z(3z-2)(3z+2)

How do you do this, because I really do not know how to do this and plz explain how to do this

Answers

Answer:

A

Step-by-step explanation:

the leading degree(the biggest power in the function) x^4 and the leading coefficient is the number next to the highest power which is -5

so the answer should be

-5,4,x -> infinity, f(x) -> -infinity ; x -> -infinity, f(x) -> -infinity    

when you get asked questions like this look for the biggest power and the number next to it. if the power is even x will always be positive if its odd x can be either positive or negative it depends on restrictions.

for instance in this example -5 * x^4 will always give you negative because -5 will multiply with a positive number x (the power is even so its always positive)

What is the product?

(4y − 3)(2y2 + 3y − 5)

8y3 + 3y + 15
8y3 − 23y + 15
8y3 − 6y2 − 17y + 15
8y3 + 6y2 − 29y + 15

Answers

Answer:

the last one

Step-by-step explanation:

plz help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

Use DESMOS to plot both lines (attached).

If you make your own lines on the graph paper, pick two points for each line and connect them with a ruler.  Both are straight lines, so we only need two points.

Pick any two values of x and solve each equation for y.  I picked x = 1 and 3

EQ1:  y=2x-2

EQ2:  y=-x+4

Value of y    EQ1  EQ2

           x =1     0       3

           x =3    4        1

Plot the points (1,0) and (3,4) for EQ1.

Do the same for EQ2:  (1,3) and (3,1)

The attached graph shows these points.  Note that one can draw stright lines for both equations using only these two points.

In a math class with 26 students, a test was given the same day that an assignment
was due. There were 17 students who passed the test and 18 students who completed
the assignment. There were 15 students who passed the test and also completed the
assignment. What is the probability that a student who failed the test completed the
homework?

Answers

Answer:

n a math class with 26 students, a test was given the same day that an assignment

was due. There were 17 students who passed the test and 18 students who completed

the assignment. There were 15 students who passed the test and also completed the

Answer:

3/26

Step-by-step explanation:

Form a venn diagram. You can see that there are 3 students who failed the test but completed the homework.

Plz mark as brainliest

-15 < x - 8 < -4

SOLVE COMPUND INEQUALITY​

Answers

[tex] \sf \: -15 < x - 8 < -4 [/tex]

Add 8 to all parts

[tex]\sf \longmapsto−15+8<x−8+8<−4+8[/tex]

[tex]\sf \longmapsto−7<x<4[/tex]

[tex] \boxed{\sf−7<x<4 }[/tex]

Graph attached

i forgot how to turn fractions into decimals pls help me

3/5 = 0.6 but how do u get 0.6

pls show the work

Answers

Answer:

A fraction is essentially division, so 3/5 is the same as 3 ÷ 5

3÷5 = 0.6

[tex]5\sqrt{3\\[/tex]

(imagine the square root is the divsion thing)

5 cannot go into 3 so the answer is a decimal

then add a zero at the end of 3 to make 30

   0.

[tex]5\sqrt{30[/tex]

and 5 can go into 30, 6 times so you add a 6 to make 0.6

    0.6

[tex]5\sqrt{30[/tex]



Maricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks,

bonds, and CDs. CDs pay 4 % Interest, bonds pay 5.3 % interest, and stocks pay 6.2 % interest.

Maricopa Success Invests $ 15000 more in bonds than in CDs. If the annual income from the

Investments is $ 6220, how much was invested in each account?

Maricopa Success invested $

in stocks.

Maricopa Success invested $

in bonds.

Maricopa Success invested $

in CDs.

Answers

Answer:

  $50,000 in stocks

  $40,000 in bonds

  $25,000 in CDs

Step-by-step explanation:

Let c represent the amount invested in CDs. Then the amount invested in bonds is (c+15000) and the amount invested in stocks is (115000 -c -(c+15000)) = (100000 -2c). The total interest earned is ...

  0.04c +0.053(c +15000) +0.062(100,000 -2c) = 6220

  -0.031c +795 +6200 = 6220

  -0.031c = -775 . . . . . . . . . . . . . . . subtract the left-side constants

  c = 25000 . . . . . . . . . . divide by the coefficient of c

  c+15000 = 40000 . . . . bonds

  100000 -2c = 50000 . . . . . stocks

Maricopa Success invested ...

  $50,000 in stocks

  $40,000 in bonds

  $25,000 in CDs

PLEASE HELP ME PLEASE ​

Answers

The answer to your problem is 2

Sam practiced his long jump in P. E. On his first attempt, he jumped 1 meter 47 centimeters. On his second attempt, he jumped 98 centimeters. How much farther did Sam jump on his first attempt than his second?.

Answers

Answer:

51

Step-by-step explanation:

98-47= 51

im bo.red so there ya go

0.1 x 0.01 x 0.001
ans ???

Answers

>> Answer

________

[tex] \: [/tex]

[tex]0.1 \times 0.01 \times 0.001 = ...[/tex]

[tex] = \frac{1}{10} \times \frac{1}{100} \times \frac{1}{1.000} [/tex]

[tex] = \frac{1}{10 \times 100 \times 1.000} [/tex]

[tex] = \bold{ \frac{1}{1.000.000}} [/tex]

Answer:

[tex]0.1 \times 0.01 \times 0.001 = 0.000001 \\ \\ \\ \\ i \: hope \: it \: is \: helpfull[/tex]

The height of a tree is 8.2 meters.
What is the tree's height in centimeters?

Answers

Answer:

820 centimeter :3

Step-by-step explanation:

8.2 meters

move the decimal back twice because of KiloHecaDecaBase (m,l,g)DeciCentiMilli

As we know 1 meter is equal to 100 centimeters so the height of the tree 8.2 meters is equal to 820 meters

What is unit conversion?

The same attribute is expressed using a unit conversion but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

Measurements are frequently offered in one set of units, like feet, but are required in another set, like chains.

A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.

Given, The height of a tree is 8.2 meters, now we know 1 meter is equal to 100cm so to convert some quantity from meters to centimeters we multiply by 100.

∴ 8.2 meters is equal to (8.2×100) = 820 centimeters.

learn more about unit conversion here :

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#SPJ5

3x^3 -5x^2 -x+3 when x=4 help I'm stuck on this

Answers

The value of the expression [tex]3x^3-5x^2-x+3[/tex] when x = 4 is 110

The given equation is:

[tex]3x^3-5x^2-x+3[/tex]

To find the value of [tex]3x^3-5x^2-x+3[/tex] when x = 4, substitute x = 4 into the expression [tex]3x^3-5x^2-x+3[/tex]

When x = 4:

[tex]3x^3-5x^2-x+3 = 3(4^3)-5(4^2)-5+3\\\\3x^3-5x^2-x+3 =3(64)-5(16)-2\\\\3x^3-5x^2-x+3 =192-80-2\\\\3x^3-5x^2-x+3 =110[/tex]

Therefore, the value of the expression [tex]3x^3-5x^2-x+3[/tex] when x = 4 is 110

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Please help meeeeeeeeeeeeee

Answers

Answer:

-47

Step-by-step explanation:

First term in the sequence is given as 30. The common difference (difference between first term and next term) is -7. Since we are looking for the 12th term we can do 30 - (11 * -7) = -47. It's 11 * -7 because we already are given one term in the problem statement.

Solve the math problem

Answers

Answer:

2) a.   slope = 4/3

2) b.   slope = -4

Step-by-step explanation:

The slope of the line that passes through points

[tex] (x_1, y_1) [/tex]  and  [tex] (x_2, y_2) [/tex]

is m, given by the slope formula below:

[tex] m = \dfrac{y_1 - y_2}{x_2 - x_1} [/tex]

2) a. (30, 32) and (18, 16)

[tex] m = \dfrac{y_1 - y_2}{x_2 - x_1} [/tex]

[tex] m = \dfrac{32 - 16}{30 - 18} [/tex]

[tex] m = \dfrac{16}{12} [/tex]

[tex] m = \dfrac{4}{3} [/tex]

2) b. (4, -26) and (10, -50)

[tex] m = \dfrac{y_1 - y_2}{x_2 - x_1} [/tex]

[tex] m = \dfrac{-50 - (-26)}{10 - 4} [/tex]

[tex] m = \dfrac{-24}{6} [/tex]

[tex] m = -4 [/tex]

Solve the equation: [tex]x^{2} +5x+6=0[/tex]
I know [tex]x^{2} +5x+6=(x+3)(x+2)[/tex] (that was part a) but I don't know where to go from here!

Answers

Step-by-step explanation:

but then you did already the most work.

because just think : when is the expression

(x+3)(x+2) equal to 0 ?

only, if at least one factor of the multiplication is equal to 0.

you know, for example, 5×0 = 0, or 0×3 = 0.

that means either (x+3) or (x+2) must be 0.

x + 3 = 0

x = -3

and

x + 2 = 0

x = -2

and there you have it.

a quadratic equation (with the highest x exponent is 2) has 2 solutions for being 0.

and this one here has the 2 solutions

x = -3 and

x = -2

again, by finding the factors you did already the biggest and most difficult part yourself. congratulations !

Yo help 20 points plssssssssssssss

Answers

Answer:

Up up up up up up up up up up

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120.

a. Find some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers.

Answers

Answer:

5 points for what

Step-by-step explanation:

HeY

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