Alex has a bag of marbles. Each marble is red, blue, or yellow , and the ratio of the red to blue to yellow marbles is 6:10:15. After Alex adds 10 red marbles and removes 25 yellow marbles form the bag, the ratio of red to blue to yellow is 2:3:4. How many blue marbles are in Alex's bag

Answers

Answer 1

Answer:

There are 150 blue marbles in Alex's bag.

Step-by-step explanation:

Let [tex]x[/tex], [tex]y[/tex], [tex]z[/tex] be the quantities of red, blue and yellow marbles, respectively. From statement we derive three rational equations for initial and final ratios:

Initial ratio

[tex]\frac{x}{y} = \frac{6}{10}[/tex] (1)

[tex]\frac{y}{z} = \frac{10}{15}[/tex] (2)

Final ratio

[tex]\frac{x + 10}{z - 25} = \frac{1}{2}[/tex] (3)

After some algebraic handling we get the following system of linear equations:

[tex]x - \frac{3}{5}\cdot y = 0[/tex] (1)

[tex]y - \frac{2}{3}\cdot z = 0[/tex] (2)

[tex]2\cdot (x + 10) = z - 25[/tex]

[tex]2\cdot x +20 = z - 25[/tex]

[tex]2\cdot x - z = -45[/tex] (3)

The solution of the system of linear equations is:

[tex]x = 90[/tex], [tex]y = 150[/tex], [tex]z = 225[/tex]

There are 150 blue marbles in Alex's bag.


Related Questions

for one week 2 car dealerships keep track of the number of cars they sell each day

Answers

Answer:

Dealership A

Step-by-step explanation:

Dealership A: 0 + 4 + 4 + 6 + 6 + 7 + 8 / 7 = 5 mean sales

Dealership B: 1 + 2 + 2 + 4 + 5 + 7 + 7 / 7 = 4 mean sales

What is the surface area of the square pyramid?

Answers

Answer:

S.A= B + 1/2 Pl

     = (2*2) + 1/2 [(2+2+2+2)(3)]

     = (4) + 1/2 (24)

     = 4 + 12

     = 16 m^2

Step-by-step explanation:

The endpoints of PQ are (-2,8) and (6,12). What are the coordinates of the
midpoint of PQ.
A.4,10
B.4,4
C.2,10
D.5,7

Answers

Answer:

C. (2,10)

Step-by-step explanation:

i used desmos to get the answer :/

find the direction angle of -12i - 35j

Answers

Answer:

[tex]\theta=71.07^{\circ}[/tex]

Step-by-step explanation:

The given vector is :

v = -12i - 35j

We need to find the angle direction of v.

The general vector is given by :

v = xi+yj

The direction angle is :

[tex]\theta=\tan^{-1}(\dfrac{y}{x})[/tex]

We have, x = -12 and y = -35

So,

[tex]\theta=\tan^{-1}(\dfrac{-35}{-12})\\\\\theta=71.07^{\circ}[/tex]

So, the required direction angle is [tex]71.07^{\circ}[/tex].

Why can't we factor x^2+25?

Answers

Answer:

Explanation: Notice that if x is Real then x2≥0 , so x2+25 has no linear factors with Real coefficients

Determine the scale factor of Triangle KJL to Triangle QPR.
Help ASAP I need a good grade!

Answers

Answer:

scale factor = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, that is

[tex]\frac{QP}{KJ}[/tex] = [tex]\frac{8}{16}[/tex] = [tex]\frac{1}{2}[/tex]

Find the volume of a cone with a height of 9 in the base of 6 in used pie and do not round your answer

Answers

Answer:

84.823 in.³

Step-by-step explanation:

V = πr²[tex]\frac{h}{3}[/tex]

84.823 in.³

James scored the following points per game in the last five basketball
games he played: 31, 20, 27, 19, 28. Find the mean absolute deviation of the
number of points scored. *
A. 4.4
B. 6.2
C. 25
D. 125

Answers

The answer is C, you add them all up and divide by 5

The mean absolute deviation of the number of points scored is 4.4.

What is Mean Deviation?

The mean deviation is used to calculate how far the values fall from the mean of the data set.

Here, Given data is 31, 20, 27, 19, 28

Mean = Sum of all data / number of terms

         = (31 + 20 + 27 + 19 + 28)/5

         = 125/5

         = 25

Then, the deviation will be 6, 5, 2, 6, 3

Mean Deviation = Sum of Deviation / Total number of deviation

                          = ( 6 + 5 + 2 + 6 + 3) / 5

                          = 22 / 5

                          = 4.4

Thus, the mean absolute deviation of the number of points scored is 4.4.

Learn more about Mean Deviation from:

https://brainly.com/question/10528201

#SPJ2

find the value of x. round to the nearest tenth

Answers

Answer:

using Pythagoras theorem x=32.7

Answer:

21.7

Step-by-step explanation:

In order to solve this problem, we can use trig functions. We are given the side adjacent to the 37° given and we are looking for the hypotenuse. This means that cosine function is the most suitable. Cosine is written as:

cos(θ°) = adjacent / hypotenuse

We can substitute the values we have:

cos(37°) = 17.3 / x

And rewrite the expression:

x = 17.3 / cos(37°)

Then, use a calculator to evaluate:

x = 21.66194689

This can be rounded to 21.7

I didn’t understand so I need a help

Answers

Answer:

y is 107° and z is 36°

Step-by-step explanation:

73° and y are supplementary angles so they add up to 180°

Answer:

y = 107

z = 36

Step-by-step explanation:

We are given that line o is parallel to line m, and we can notice line k is a transversal through them both. Using same side interior angles, we can say that:

y + 73 = 180

and

y = 107

Next, using vertical angles, we can say that:

5z - 73 = y

We already have y = 107, so we can substitute that in:

5z - 73 = 107

5z = 180

z = 36

What is 3n at n = 11

Answers

Answer:

33

Step-by-step explanation:

3n but n is 11 means 3x11

Answer:

3n = 33 when n = 11

Step-by-step explanation:

n = 11

therefore

3(11)

which means 3 times 11

Answer = 33

Hope this helps!

Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, 6) and (-3,3)

Answers

The distance is 4.24 units and if you round it, it would be 4 units

A 16 oz package of brown rice costs 79 cents and a 32 oz package of white rice costs $3.49. Which package is a better deal?

Answers

Answer:

the brown rice is cheaper by the ounce than the white.

Step-by-step explanation:

Find the unit cost in each case.

Brown rice:

 79 cents

----------------- = $0.049/oz

  16 ounces

White rice:

 $3.49

----------------- = $0.109/oz

32 ounces

The brown rice, at 4.9 cents/oz, is the better deal against the competition, 10.9 cents/oz.

Marty cuts 2.05 ounces of cheese from a 4.6 ounce block of cheddar cheese. How many ounces of cheddar cheese are left in the block

Answers

Answer:Amount of cheese  left=2.55ounce

Step-by-step explanation:

Total amount of cheddar cheese =4.6ounce

Amount of cheese cut out =2.05 ounces

Amount left =Total amount of cheddar cheese-Amount of cheese cut out

=4.6ounce-2.05 ounces=2.55ounce

Can someone help me pls? Surface area of rectangular prism.

Answers

Answer: picture see the picture

Step-by-step explanation:

PLEASE HELP WILL GIVE BRAINLIEST AND I WILL LOVE YOU FOREVER

Answers

Answer:

Step-by-step explanation:

I NEED HELP!! ITS IMPORTANT

Answers

Answer:

2/10 .02

Step-by-step explanation:

justin wants to measure the thickness of a paper towel roll but his ruler is not the proper measuring device.using a full roll he takes the measurements

Answers

Answer:

Vernier caliper

Step-by-step explanation:

The paper towel is circular in shape, should he use the ruler he may come up with a value but the value may not be accurate.

Hence the measuring instrument Justin should use is a vernier caliper, which is a measuring device that can be used to measure the external diameter of the roll of paper

I need help with question number 4

Answers

Answer: x = -3

Step-by-step explanation:

Find the value of a by using law of sines.

Answers

See the picture below

Jackie surveyed the first 20 students in the lunch line.

Is this a random sample of the students in the school?

Yes or No

Answers

Answer:

Yes

Step-by-step explanation:

It is a random sample of students because they are just random people that Jackie is asking, its not only people in on grade, or only people on the basketball team.

The answer to this is yes

Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.

Answers

Answer:

2(x - 9.46)(x + 2.54)

Step-by-step explanation:

2(x² - 12x + 24)

since there are no factors that multiply to 24 and add to -12 then i used the quadratic formula to get:

6+2[tex]\sqrt{3}[/tex], 6-2[tex]\sqrt{3}[/tex]

Please help!-

For the following set of data, find the population standard deviation, to the nearest
hundredth.


Answers

Answer:

can you zoom in the picture a little?

Step-by-step explanation:

in the diagram below, which expression represents x, the degree measure of the exterior angle. a. a +b b. a-b c. a +c d. b + c

Answers

Answer: A) a+b

Step-by-step explanation:

Solve for x please help !!!!!!!

Answers

Answer:

x ≈ 20.31

Step-by-step explanation:

By applying tangent rule in the given right triangle,

tan(55°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

Measure of the opposite side = 29 units

Measure of the adjacent side = x

Substitute these values in the expression,

tan(55) = [tex]\frac{29}{x}[/tex]

x = [tex]\frac{29}{tan(55)}[/tex]

x = 20.306

x ≈ 20.31

ANYONE PLS HELP ASAP!!!

Answers

If Elijah has half a bag of candy and 1 whole bag weighs 5 pounds.
Part A answer- 2.5
Work: 5 divided by 2 which is just 2.5 which is your answer
Part B answer - 12.5
Work- 2 bags = 10 pounds (5x2=10)
We already know half a bag is 2.5 so just add 10+2.5= 12.5
I don’t know I am sorry

Help help help help help

Answers

It should be option 1

Answer:

OPTION A

SEE IMAGE FOR SOLUTION

Hope it helps

Have a great day

if 1 inch represents 10 miles how many inches will 900 miles​

Answers

Answer:

90 inches

Step-by-step explanation:

900 divided by 10 = 90

1. Which three lengths could be the lengths
of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm
B. 10 cm, 15 cm, 24 cm
C. 9 cm, 22 cm, 11 cm
D. 21 cm, 7 cm, 6 cm
(Maneuvering the middle)

Answers

Answer:

B.

Step-by-step explanation:

A- 12 + 5 = 17 (Cannot be the same)

B- 10 + 15 = 25 (More than the 3rd side) ✅

C- 9 + 11 = 20 (Cannot be less than the 3rd side)

D- 7 + 6 = 13 (Cannot be less than the 3rd side)

Pls help fast
No scam!! ​

Answers

Focus on triangle QAC. We're given that CQ = CA, which in turn means the angles opposite these sides (angles A and Q in that order) are congruent. This is one property of isosceles triangles. Let's make x equal to each of these angles.

With inscribed angle QAC = x, it doubles to 2x which is the measure of minor arc BC (inscribed angle theorem). Minor arc AB is also 2x, since we're told these two arcs have the same measure.

If minor arc BC = 2x, then cutting this in half leads to x again, which points to inscribed angle BDC equal to x. Notice how inscribed angles QAC and BDC subtend the same minor arc BC. Through similar logic, inscribed angle BDA is also x.

In short: angle BDC = angle BDA = x. This leads to angle ADC = 2x. We'll use this later.

-------------------

Let's go back to triangle QAC. The angles A and Q are both x each. The missing angle C is...

Q+A+C = 180

x+x+C = 180

2x+C = 180

C = 180-2x

Making angle QCA equal to 180-2x

Angle ACD is supplementary to this.

So,

angle ACD = 180-(angle QCA) = 180-(180-2x) = 2x. We'll use this later as well.

---------------------

The first section concluded with angle ADC = 2x, while the second section concluded with angle ACD = 2x

For triangle ACD, the bottom angles C and D are both 2x. This is sufficient evidence to show that triangle ACD is isosceles. Furthermore, it means AC = AD, which are the sides opposite angles D and C respectively.

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