A scout troop consists of 10 boys and 10 girls. The total weight of their backpacks is 600 pounds. All the boys have to carry backpacks that weigh the same amount. All the girls, too, must carry bags of equal weight, but the girls' backpacks are 1.5 times lighter than the boys' backpacks. How heavy is one boy's backpack?

Answers

Answer 1

Answer:

36 lbs

Step-by-step explanation:

let the weight of each boy's backpack be B and the weight of each girl's backpack be G.

Given that the total weight of all (i.e 10 boys' and 10 girls') backpacks equals 600 lbs,  i.e.

10B + 10G = 600   (simplifying by dividing both sides by 10)

B + G = 60 ------- eq 1

Also given that a girl's backpack is 1.5 times LESS than a boy's backpack.

written another way, we can say that a boy's backpack is 1.5 times MORE than a girl's backpack, or:

B = 1.5G   (rearranging)

B - 1.5G = 0     ------ eq 2

We can solve eq 1 and eq 2 by elimination,

(eq 1) - (eq 2)

(B + G) - (B - 1.5G) = 60 - 0

B + G - B + 1.5G = 60

G  + 1.5G = 60

2.5G = 60   (divide both sides by 2.5)

G = 60 / 2.5

G = 24 lbs   (substitute this into equation 1)

B + G = 60

B + 24 = 60

B = 60 - 24

B = 36 lbs


Related Questions

For the function f(x) = x + 7, what is the ordered pair for the point on the graph where x = 2b? (2b, 2b + 7) (2b, x + 7) (x, x + 7) (x, 2b + 7)

Answers

Answer:

(2b, 2b + 7).

Step-by-step explanation:

y = x + 7 and x = 2b ,

therefore y = 2b + 7.

Answer:

(2b, 2b + 7)

Step-by-step explanation:

What is the slope of the line represented by the equation y
4 X - 3?
0.-
to

Answers

Answer:

The slope is 4/1

Step-by-step explanation:

for every 4 units you go up on the y-axis, you go 1 unit on the x-axis.

Solve for y.
y/-1 +-7=-11​

Answers

Answer:

y = 4

Step-by-step explanation:

Move all terms not containing  y  to the right side of the equation.

-y = -4

Multiply each term in  − y  =  − 4  by  − 1

y = 4

Hope this can help you

Simplify to create an equivalent expression. −3(2+4k)+7(2k−1)

Answers

Answer:

[tex]\huge\boxed{2k-13}[/tex]

Step-by-step explanation:

[tex]\sf -3(2+4k)+7(2k-1)\\Expanding \ brackets\\-6-12k+14k-7\\Combining \ like \ terms\\-12k+14k-6-7\\2k -13[/tex]

2k-13
First step= -3(2+4K)+7(2k-1)
Second step= -6 - (12k) + 14k- 7
Third step= -12k+14k - 6 -7= 2k-13

Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 32 feet. The distance between the birdwatcher and the second bird is 45 feet. A triangle is created from point Bird Watcher, point First Bird, and point Second Bird. Angle First Bird is a right angle, and angle Second Bird measures x degrees. What is the angle measure, or angle of depression, between this bird and the birdwatcher? Round your answer to the nearest tenth. 35.4° 44.7° 45.3° 54.6°

Answers

Answer:

Step-by-step explanation:

When you draw out that picture (and very good description, btw!) basically what you have is a right triangle that has a base of 32 and a hypotenuse of 45. The right angle is one of the base angles and x is the vertex angle. We need to find the vertex angle before we can find the angle of depression from the second bird to the watcher. The side of length 32 is opposite the angle x, and 45 is the hypotenuse, so the trig ratio we need is the only one that directly relates side opposite to hypotenuse, which is the sin ratio:

[tex]sin(x)=\frac{32}{45}[/tex] and

sin(x) = .711111111

Go to your calculator and hit the 2nd button then the sin button and on your screen you will see:

[tex]sin^{-1}([/tex]  

and after that open parenthesis enter in your decimal .711111111 and hit equals. You should get an angle of 45.325. That's angle x. But that's not the angle of depression. The angle of depression is the one complementary to angle x.

Angle of depression = 90 - angle x and

Angle of depression = 90 - 45.325 so

Angle of depression = 44.67 or 44.7 degrees.

Answer:

Its 45.3!!!

Step-by-step explanation:

-2x-7+9-2= Please can i have an answer

Answers

Answer:

-2x

Step-by-step explanation:

-2x-7+9-2

Combine like terms

-2x +0

-2x

Answer:

-2x

Step-by-step explanation:

from the question

-2x-7+9-2=

step 1

collect the like terms

we have,

-2x-7+9-2

-2x + 2 -2

-2x + 0

-2x

therefore the answer to the question -2x-7+9-2 is equal to -2x

A group of students is arranging squares into layers to create a project. The first layer has 4 squares. The second layer has 8 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?

Answers

Answer:

answer is d

Step-by-step explanation:

Study the samples below to answer questions
26 and 27.
pls brainiest

Answers

Answer:

1 st pattern 48+122 = 170

2 nd pattern 8½+3½ = 5

so, 3rd pattern 41+13= 54 (B)

41+13=54 this is the ans

Find the missing the side of the triangle A. 130−−−√ m B. 179−−−√ m C. 42–√ m D. 211−−−√ m

Answers

Answer:

The answer is option A

Step-by-step explanation:

Since the triangle is a right angled triangle we can use the Pythagoras theorem to find the missing side

Using the Pythagoras theorem

That's

[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]

From the question

x is the hypotenuse or the longest side of the triangle

Substituting the values into the above formula we have

[tex] {x}^{2} = {9}^{2} + {7}^{2} [/tex]

[tex] {x}^{2} = 81 + 49[/tex]

[tex] {x}^{2} = 130[/tex]

Find the square root of both sides

We have the final answer as

x = √130 m

Hope this helps you

Help!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

x > - 8 or x < 2

Step-by-step explanation:

Given

- 8 < 2(x + 4) or - 3x + 4 > x - 4

Solve each part separately

- 8 < 2(x + 4) ← divide both sides by 2

- 4 < x + 4 ( subtract 4 from both sides )

- 8 < x , thus

x > - 8

OR

- 3x + 4 > x - 4 ( subtract x from both sides )

- 4x + 4 > - 4 ( subtract 4 from both sides )

- 4x > - 8

Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity

x < 2

Solution is x > - 8 or x < 2

9.Find the perimeter of the triangle formed by points (0,4), (0,0) and (3,0)

(1 Point)

55


1212

1111

None of these


Answers

Answer:

              12

Step-by-step explanation:

A(0,0) ∧  B(3,0)  ⇒  AB = 3

A(0,0) ∧  C(0,4)  ⇒  AC = 4

From Pythagorean theorem:

AB² + AC² = AB²

3² + 4² = AB²

AB² = 9+16 = 25

AB = 5

Perimeter:  

               AB + AC + BC = 3 + 4 + 5 = 12

Can someone help me? Thanks!

Answers

Answer:

question 11: A

question 12: B

Step-by-step explanation:

Thanks calculator :)

Answer:

11. less than

12.less than

hope this helps

Step-by-step explanation:

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Answers

Answer:

See explanation

Step-by-step explanation:

a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes

b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes

c) 6:50 - 4:30 = 2 hours and 20 minutes

d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes

Answer:

a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes

b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes

c) 6:50 - 4:30 = 2 hours and 20 minutes

d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes

Step-by-step explanation:

Plz help me ASAP! I will mark brainliest

Answers

Answer:

x=20

<B=150°

Step-by-step explanation:

Opposite Interior Angles

8x-10=3x+90

8x-3x=90+10

5x=100

x=20

<B=3x+90

=3(20)+90

=60+90=150

Answer:

x=20

<B = 150

Step-by-step explanation:

The angles are alternate interior angles and when the lines are parallel, alternate interior angles are equal

8x-10 = 3x+90

Subtract 3x from each side

8x-10 -3x = 3x+90-3x

5x-10 = 90

Add 10 to each side

5x-10 +10 = 90+10

5x = 100

Divide by 5

5x/5 = 100/5

x = 20

<B = 3x+90

    = 3*20 +90

    = 60+90

    = 150

Find the length of the arc. A. 187π/12 ft B. 16π/3 ft C. 49π/6 ft D. 343π/12 ft

Answers

Answer:

[tex]\huge \boxed{\mathrm{Option \ C}}[/tex]

Step-by-step explanation:

Length of arc formula = θ/360 × 2[tex]\pi[/tex]r

The angle is 210 degrees.

The radius is 7 ft.

210/360 × 2[tex]\pi[/tex](7)

Simplify the expression.

210/360 × 14[tex]\pi[/tex]

2940/360[tex]\pi[/tex]

49/6[tex]\pi[/tex]

The length of the arc of circle having radius 7 feet is 49π/6 which is option C.

What is arc?

An arc is a part of circumference of a circle which is formed from two radius of the circle. The length of arc is equal to Θr in which r is radius and Θ is angle in radian form.

How to find length of arc?

We have been given the radius of the circle be 7 feet and angle be 210°.

The length of arc will be Θr in which r is the radius and Θ is the angle in radian form.

First we have to convert angle in radian form=210*π/180=7π/6.

Length of arc=7π/6*7

=49π/6

Hence the length of the arc of circle having radius 7 feet is 49π/6 which is option C.

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i need help on figuring this out and the answer plz!!

Answers

Answer:

$76

Step-by-step explanation:

The amount changed is the total amount of the whole entire thing.

Therefore, we use absolute value or simply find the difference.

21 - (-55) = 76

So the bank account changed $76 over the 2 days.

You are selling lemonade for $1.50, a bag of kettle corn for $3, and a hot dog for $2.50 at a fair. Write and simplify an expression for the amount of money you receive when p people buy one of each item

Answers

Answer:

1.5p + 3p + 2.5p

Step-by-step explanation:

This expression, 1.5p + 3p + 2.5p, will represent the amount of money received when p people buy one of each food item.

Since the price of each is the coefficient for p, this will represent how much money will be gained from each food item. All 3 terms will be added together to represent the total amount of money gained from selling all 3 items.

Please help! I’m this figure, which angles are congruent? Find the measure of all the angles if m< 2= 76 degrees

Answers

Problem 1.

Yes it is true that vertical angles are congruent, but that's not what your teacher is asking. Instead, your teacher is asking basically how the term "congruent" is defined.

Two segments are congruent if they are the same length. Two angles are congruent if they are the same measure. Two triangles are congruent if they have the same angles and sides.

So in short, "congruent" just means "same". You can think of having mirror copies.

==========================================

Problem 2.

Angles 2 and 4 are one pair of vertical angles. They are opposite one another in this X shape formed by the two lines. The other pair of vertical angles are angle 1 and angle 3.

Angle 2 is given to be 76 degrees, so this means angle 4 is this measure as well.

Angle 1 = 180 - (angle 2) = 180 - 76 = 104, which is also the measure of angle 3 as well. I'm using the idea that the adjacent angles form a straight angle. This is known as a linear pair (ie the angles form a straight line).

==========================================

Problem 3.

If all three angles are the same (all 60 degrees), then we have an equilateral triangle. We could say it's equiangular, but it's also equilateral as well meaning all 3 sides are the same length. "equi" means "equal", "angular" means what you'd expect, and "lateral" means "side".

If only two angles are equal with the third one different, then we have an isosceles triangle. An isosceles triangle is one where only two sides are the same length.

If none of the angles are the same, then we have a scalene triangle. As you probably expect, none of the sides are the same length with a scalene triangle.

----

If all three angles are less than 90 degrees, then the triangle is acute

If one angle is 90 degrees, then we have a right triangle

If one angle is over 90 degrees (but less than 180), then the triangle is obtuse

---

Often you'll see the terms of the previous two sections combined. For instance, we could have an isosceles right triangle. Or we might have an obtuse scalene triangle. Any equilateral triangle is acute (as all three angles are less than 90).

To solve this problem we have to understand what congruent angles are and then find the angles that are congruent to one other in this given question.

What are Congruent Angles?

Congruent angles are angles that are equal to one another and in the given question, we were given m<2 = 76 degrees.

Data;

m<2 = 76 degrees

If we look critically at the angles, we can use opposite angle theorem here to predict angles that are congruent to another here.

angles 2 and angle 4 are congruent to one another while angle 1 and angle 3 are congruent to one another.

This implies that

m<2 = 76°m<4 = 76°

Let's solve for other angles.

But the some of angles at a point is equal to 360°

Applying that theorem here,

[tex]m > 1=x\\m > 2 = 72^0\\m > 3 = x\\m > 4 = 72^0[/tex]

Let's substitute the values and solve.

[tex]x+ x + 72+72 = 360\\2x + 144 = 360\\2x = 360 - 144\\2x = 216\\x = \frac{216}{2} \\x = 108^0[/tex]

This can be further summarized as

m<1 = 108°m<2 = 72°m<3 = 108°m<4 = 72°

Learn more on corresponding angles here;

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Please answer it now

Answers

Answer:

1306.90≅  1307 rounded to the nearest tens

Step-by-step explanation:

r= radius = 13 cm

l is the slant height =19 cm

surface area of the cone= area of the circle + area of the curved of the cone

SA=πrl +πr²

SA=π(13)(19) +169π

SA= 247π +169π= 416π=1306.90≅  1307 rounded to the nearest tens

Two rectangles are joined together to form a single large area. The rectangles do not overlap. The first rectangle has side lengths of 333 meters and 555 meters. The second rectangle has side lengths of 777 meters and 444 meters. What is the combined area?

Answers

Answer:

Step-by-step explanation:

333 times 555=184815

777 times 444=344988

now add 184815+344988=529803

divide this decimals 5.2 divided 4

Answers

Answer:

1.3

Step-by-step explanation:

5.2/4 = 1.3

To check, 1.3 multiplied by four is 5.2.

Answer:

It’s 1.3

Step-by-step explanation:

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What is the value of the expression below when w = 3?
4w2 – 7w – 8​

Answers

Step-by-step explanation:

w=3

4w^2-7w-8

4*3^2-7*3-8

4*9-21-8

4*9-29

36-29

7

hope this helps

Answer:

7

Step-by-step explanation:

PLEASE HELP!!!! ASAPP!!!! I will name Brainliest.
A pyramid has a square base that measures 10 feet on a side. The height of each face is five feet. What is the surface area of the pyramid?

Answers

Answer:

[tex]\boxed{\sf 200 \ feet^2}[/tex]

Step-by-step explanation:

The 3D shape is a square-based pyramid.

The surface area of a square-based pyramid is given as:

[tex]\sf SA=2 \times (base \ length) \times (slant \ height) + (base \ length)^2[/tex]

Plug in the values.

[tex]\sf SA=2 \times 10 \times 5 + 10^2[/tex]

[tex]\sf SA=100 + 100[/tex]

[tex]\sf SA=200[/tex]

evaluwate 5(14-2to the third power)+8/2

Answers

Answer:

216,004

Step-by-step explanation:

so 5(14-2)third power + 8/2,

that would be

5(12)third power + 8/2

(60) third power + 4

216,000 + 4

nikhil has RS 80000 from this,he gives 30% to his wife and 20% to his father. Find the amount received by wife and father​

Answers

Answer:

Amount received by wife = RS 24000

Amount received by father = RS 16000

Step-by-step explanation:

His income is RS 80000

He gave 30% of his income to his wife

That's

[tex] \frac{30}{100} \times RS \: \: 80000[/tex]

Which is RS 24000

He gave 20% of his income to his father

That's

[tex] \frac{20}{100} \times RS \: \: 80000[/tex]

Which is RS 16000

Hope this helps you

Mother received 24000
Father received 16000

Plz thanks and mark me the branliest ans

Select the equation written in slope-intercept form that corresponds to the given slope and y-intercept. m=6 b=-2

Answers

Answer:

y = 6x - 2

Step-by-step explanation:

slope-intercept form: y = mx + b

Note that:

m = slope = 6

b = y-intercept = -2

x = (x , y)

y = (x , y)

Plug in the corresponding numbers to the corresponding variables:

y = 6x + (-2)

y  = 6x - 2

y = 6x - 2 is your answer.

~

Answer:

y = 6x-2

Step-by-step explanation:

The slope intercept equation  form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 6x-2

PLEASE HELP! WILL GIVE BRAINLIEST!

Answers

Answer:

f(1) = 45

f(n) = f(n-1)*(4/5)

Step-by-step explanation:

f(1)

= 45(4/5)^(1-1)

= 45(4/5)^(0)          use law of exponents

= 45*1

= 45

f(1) = 45

f(n) = f(n-1)*(4/5)

Convert 75 miles per hour to feet per second ​

Answers

Answer:

110 feet per second

Step-by-step explanation:

You would mutiply your speed in miles per hour by 5,280. That's the number of feet in a mile and your result is your speed in feet per hour.

75 x 5,280 = 396,000 feet per hour

Then you would divide your speed by 60 and that result is your speed in feet per minute.

396,000 / 60 = 6,600 feet per minute

Lastly, you would divide that speed by 60 and the result is your speed in feet per second.

6,600 / 60 = 110 feet per second

The conversion of 75 miles per hour to feet per second is approximately 110 feet per second.

How do we convert units from miles per hour to feet per second?

We can do this by using conversion factors that relate the two units. Specifically, we can use the fact that 1 mile equals 5,280 feet and 1 hour equals 3,600 seconds.

To convert miles per hour to feet per second, we need to multiply the value in miles per hour by a conversion factor that will cancel out the "miles" unit and replace it with "feet," and another conversion factor that will cancel out the "hours" unit and replace it with "seconds."

So, first we convert miles per hour to feet per hour by multiplying 75 miles/hour by 5,280 feet/mile.

This gives us:

= 75 miles/hour x 5,280 feet/mile

= 396,000 feet/hour

Next, we convert feet per hour to feet per second by dividing by 3,600 seconds/hour.

This gives us:

=396,000 feet/hour ÷ 3,600 seconds/hour

= 110 feet/second

Therefore, 75 miles per hour is approximately equal to 110 feet per second.

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Simplify to create an equivalent expression. 8-4(-x+5)

Answers

Answer:= -12+4x

Step-by-step explanation:

Distribute -4 through the parentheses

8+4x=20

Calculate the difference

-12+4x

The marketing department at Quality Home Improvement Center (QHIC) uses simple linear regression analysis to predict home upkeep expenditure on the basis of home value. Predictions of home upkeep expenditures are used to help determine which homes should be sent advertising brochures promoting QHIC's products and services.

Answers

Full question :

The Tasty Sub Shop Case:

A business entrepreneur uses simple linear regression analysis to predict the yearly revenue for a potential restaurant site on the basis of the number of residents living near the site. The entrepreneur then uses the prediction to assess the profitability of the potential restaurant site.

And

The QHIC Case:

The marketing department at Quality Home Improvement Center (QHIC) uses simple linear regression analysis to predict home upkeep expenditure on the basis of home value. Predictions of home upkeep expenditures are used to help determine which homes should be sent advertising brochures promoting QHIC’s products and services.

Discuss the difference in the type of prediction in both cases and provide rational of the reasons that these predictions were used.

Answer and explanation:

In the first case, The Tasty Sub Shop Case, the entrepreneur aims to utlilize the predicted values from his regression analysis in ascertaining profit of his potential business. He does this using the values from number of residents in the area(independent variables) to predict the revenue for his business(dependent variables). His predictions using the number of residents in the area are largely because the residents in the area are his target consumers and are the ones to buy food from his restaurant and increase his revenue.

In the other case, the marketing department in QHIC utilizes the predicted values in determining their customers who need to be aware of their products. They get the predicted values(home upkeep expenditure and dependent variable) by plotting their relationship with home value(independent variable) and then use predicted values of home upkeep expenditures in determining their customers who they will market their products to. They do this because predicting home upkeep expenditures will enable them determine what homes can afford or will need their products and services.

one utilizes his predictions at ascertaining profit while the other uses his predictions in determining potential customer base to market products to. The first case is making a revenue/ profitability prediction while the other is making a market prediction

Other Questions
You are certain to get a red card when selecting 27 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusiv solve the following problem (1+5^2)-16(1/2)^3 HELP PLEASE ASAP Which statement best explains why John Deans testimony was so important during the Watergate investigations? Dean was a member of CREEP and created the plan to reelect Nixon. Dean was a lawyer who could clearly describe how the Nixon administration broke the law. Dean was able to testify to dozens of conversations with Nixon about the break-in and cover-up. Dean was not involved in the Watergate break-in, so he was able to have an impartial perspective. The Triangle shown below has an area of 12 Units^2.Find X106 a(n) = -5 + 6(n - 1)a(n)=5+6(n1)a, left parenthesis, n, right parenthesis, equals, minus, 5, plus, 6, left parenthesis, n, minus, 1, right parenthesisFind the 12^\text{th}12 th 12, start superscript, start text, t, h, end text, end superscript term in the sequence. what is the answer for 6x-4=-26+5x Find an angle such that is 4 times its complement equals 200 If the degree measures of the angles of a triangle are in the ratio 3 : 3 : 4, what is the degree measure of the largest angle of the triangle? (Sum of all three angles is 180) According to Aristotle, which two elements of Greek tragedy occur at the climax? A. peripeteia and catastrophe B. peripeteia and anagnorisis C. catastrophe and anagnorisis D. catastrophe and katharsis Please select the best answer from the choices provided A B C D what is the key to the recognition of a trait whose expression is determined by the effects of two or more genes Fill in the blank in the following sentence with the appropriate preterite verbbelow.Yoa la playa con mi familia el verano pasado.O A. voy B. fuiO C. fueO D. soy In determining whether a company's financial condition is improving or deteriorating over time, horizontal analysis of financial statement data would be more useful than vertical analysis.a. True b. False PLEASE PLEASE PLEASE HELP ME ANSWER THIS QUESTION QUICK!! The picture of the question is down below. To find relative location, first find a reference point. Question 4 options: True False what is the name pf a sculpture or photo of someone A shopkeeper sells a DVD player at a price RM 2,500. If the cost price of the DVD player was RM 3,500, find the profit/loss in which the shopkeeper is. Also, find the percent for the same. Three guests check into a hotel room. The manager says the bill is $30, so each guest pays $10. Later the manager realizes the bill should only have been $25. To rectify this, he gives the bellhop $5 as five one-dollar bills to return to the guests.On the way to the guests' room to refund the money, the bellhop realizes that he cannot equally divide the five one-dollar bills among the three guests. As the guests aren't aware of the total of the revised bill, the bellhop decides to just give each guest $1 back and keep $2 as a tip for himself, and proceeds to do so.As each guest got $1 back, each guest only paid $9, bringing the total paid to $27. The bellhop kept $2, which when added to the $27, comes to $29. So if the guests originally handed over $30, what happened to the remaining $1? Which option is correct and how would one solve for it? Read the passage from Animal Farm.By the late summer the news of what had happened on Animal Farm had spread across half the county. Every day Snowball and Napoleon sent out flights of pigeons whose instructions were to mingle with the animals on neighbouring farms, tell them the story of the Rebellion, and teach them the tune of "Beasts of England."Which social insight does Orwell develop in the passage?Corrupt leaders use propaganda to push their agendas.Oppression over many people can be devastating.Dystopian societies live by specific modes of conduct.Educated people will not give in to totalitarianism. Unlike direct materials, the sum of all the direct labor variances is always equal to the flexible budget variance.A. TrueB. False