A gumball machine has just been filled with 50 black, 150 white, 100 red, and 100 yellow gumballs that have been thoroughly mixed. sue and jim each purchase one gumball. what is the likelihood that both sue and jim will get red gumballs?

Answers

Answer 1

33/532 or approximately 6.2% that both Sue and Jim will get red gumballs. For the purpose of this problem, going to group the gumballs into 2 sets. Red and anything else. The number of non-red gumballs is 50 + 150 + 100 = 300 The number of red gumballs is 100. So what's the probability of 2 random picks both being a red gumball. For the 1st pick, it's a simple matter of 100/400 = 1/4. For the second pick it's slightly more complicated since there's now only 99 red gumballs. So it's 99/399 = 33/133 To get the combined probability, just multiply them together. 33/133 * 1/4 = 33/532 which is approximately 6.2%

Answer 2

Final answer:

To calculate the likelihood of both Sue and Jim getting red gumballs, we multiply the probability of each event occurring sequentially. After Sue gets a red gumball, the chances are 1/4, and then 99/399 for Jim. The final probability of both getting red gumballs is 99/1596 or about 6.203%.

Explanation:

The likelihood that both Sue and Jim will get red gumballs from the gumball machine can be calculated using basic probability principles. First, we need to determine the total number of gumballs in the machine. This is the sum of black, white, red, and yellow gumballs, which are 50, 150, 100, and 100 respectively, making a total of 400 gumballs.

The probability that Sue gets a red gumball is the number of red gumballs divided by the total number of gumballs in the machine, which is 100/400, simplifying to 1/4. When Sue takes a gumball, assuming she gets a red one, there are now 399 gumballs left with 99 being red. Therefore, the probability that Jim also gets a red gumball is 99/399. To find the likelihood of both events occurring, we multiply these probabilities:

P(Both Sue and Jim get red gumballs) = P(Sue gets a red gumball) × P(Jim gets a red gumball after Sue) = (1/4) × (99/399).

Now we simplify and multiply these fractions to get the final probability. After simplifying, the final probability is 99/1596, which is approximately 0.06203 or 6.203% chance that both Sue and Jim will get red gumballs.

Related Questions

40 students are going on a field trip to the aquarium. Every student needs to be in a group, and all groups must have the same number of students. If there is 1 group, there will be students in the group. If there are groups, there will be 20 students in each group. If there are 4 groups, there will be students in each group.

Answers

10 is the answer because 40/1 = 40, 40/2= 20 and 40/= 10

If there is 1 group there will be 40 students in the group. There will be 20 students in each group if there are 2 groups. If there are 4 groups, there will be 10 students in each group.

What is Division?

Division is one of the four basic operations of mathematics.

On performing the operation division, a number is divided into some number of equal parts.

The number which is being divided is called the dividend, the number which divides the dividend is called divisor and the number got when division is performed is called the quotient and the remaining number which has not divided is called the remainder.

Total number of students = 40

If there is 1 group, number of students in the group = 40/1 = 40

If there are 20 students in each group, then the number of groups = 40/20 = 2.

If there are 4 groups, then number of students in each group = 40/4 = 10.

Hence there will be 40 students in the group if there is 1 group. There are 2 groups if there will be 20 students in each group. There will be 10 students in each group if there are 4 groups.

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Is 0 prime odd or even prime or composite?

Answers

0 is a unique case. It is neither prime nor composite, and is neither odd nor even. Zero is an absence of value case which is not made from other numbers...and didn't appear in numbering systems until the past couple of thousand years...it's a weird concept!

Answer:

0 is nor prime or composite

Step-by-step explanation:

The definition of a prime number is a positive integer that has exactly two positive divisors. Therefore, the simplest reason why 0 is not prime is that 0 is not a positive integer, and the axiom says that all whole numbers greater than 1 are either prime or composite.

Steven investigates the amount of damage to the head gaskets on the trucks in his fleet and finds that the damage index depends on the ambient temperature. He develops the equation y = - 2 3 x + 14 to model the relationship. If the temperature increases 1 degree, what happens to the damage index for the head gasket?

Answers

It's D because it decreases by 2/3 of a point

Answer:

Step-by-step explanation:

With regard to mathematics, what is an accepted statement of fact that is used to prove other statements

Answers

In mathematics, a proof is a deductive agruement for a mathematical statement.In the argument,other prevoiusly establised statements, such as theroms, an be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference.

six times the reciprocal of a number equals 2 times the reciprocal of 6. find the number.

Answers

Equation:
6(1/x) = 2(1/7)
-----
6/x = 2/7
-----
2x = 42
x = 21

6(1/x) = 2(1/6)

6/x = 1/3

6/x*1/6 = 1/3*1/6

x= 1/18

the number is 18

The quotient of 4 and the difference of an integer and 3 is the same as two-thirds. Find the integer.

Answers

To find the integer, you must cross multiply, group the same terms, then divide both side by 2:

Solution:
4/(x-3)= 2/3
12 = 2x-6
18=2x
x= 9

Solve the following problem for the roots by completing the square

3x^2 -12x = 9

Answers

3(x^2+3) is the answer you are looking for. :)

3x^2 - 12x = 9
Divide both sides by 3
x^2 - 4x = 3
To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2. So add 4 to both sides.
x^2 - 4x + 4 = 7
(x-2)^2 = 7
x - 2 = (square root) of 7
x = 2 (+/-) (square root) of 7.
x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

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The quotient of a number and five increased by four is sixteen answer

Answers

The problem would be written out like this: n/5 + 4 = 16. We would have to subtract 4 from both sides to get n/5 = 12. Then, we multiply both sides by 5 and after that step, you get 60. n = 60.

Answer: [tex]\dfrac{x}{5}+4=16\\\\and\\\\x=60[/tex]

Step-by-step explanation:

Since we have given that

The quotient of a number and five increased by four is sixteen a

Let the number be 'x'.

The quotient of a number and five is written as

[tex]\dfrac{x}{5}[/tex]

And it is increased by 4 is written as

[tex]\dfrac{x}{5}+4[/tex]

And the equation is equal to 16.

[tex]\dfrac{x}{5}+4=16[/tex]

And the solution would be

[tex]\dfrac{x}{5}+4=16\\\\\dfrac{x}{5}=16-4=12\\\\x=12\times 5\\\\x=60[/tex]

Hence, [tex]\dfrac{x}{5}+4=16\\\\and\\\\x=60[/tex]

Can someone help me with these maths questions? I totally don't get them.

Do the following coordinates lie on the following graphs?

1) y=2x+4 (7,20)
2) y=4x-14 (-1,-18)
3) y=5x-1 (0.5,2.5)
4) y=-2x+6 (0.8,5.4)
[tex] 5) y=\frac{1}{2}x+2 (0.7,1.6) [/tex]

Answers

1. 2(7) +4 = 18, does not = 20, does not lie on graph

2. 4(-1) -14 = -18, equals -18, does lie on the graph

3. 5(.5)-1 = 1.5, does not = 2.5, does not lie on the graph

4. -2(0.8)+6 = 4.4, does not = 5.4 does not lie on graph

5. 1/2(0.7) +2 = 2.35, does not = 1.6, does not lie on graph

Y = -27x + 577, where x represents the number of weeks and y represents the amount of money left in her account. After how many weeks will Alma have $145 left in her account?

Answers

To solve this problem, plugin 145 where the y is located and then solve for x
y = -27x +577
145 = -27x +577
145 -577 = -27x
-432 = -27x
-432/-27 = -27x/-27
16 = x
x = 16
After 16 weeks she will have $145 dollars in her account.

Patty is, right now, 3 times as her brother Terry. in 10 years, the sum of their age will be 36. how old are they right now? show your work.

Answers

Patty at year x will be 3 times the age of his brother

In 10 years (year z) the sum of their age will be 36

36-20=16
(Twenty being ten years gained for each of them)

16 is now the sum of their age in year x

The following are options for the ages they could possibly be
1-15 (1*3 does not equal 15)
2-14(2*3 does not equal 14)
3-13(3*3 does not equal 13)
4-12(4*3 equals 12)!!!!
5-11(5*3 does not equal 11)
6-10(6*3 does not equal 10)
7-9 (7*3 does not equal 9)
8-8(8*3 does not equal 8)

Therefore the answer would be:
Patty is 22 and his brother is 14

Patty is 12 years old, and Terry is 4 years old. After setting up an equation based on their ages now and in 10 years, we determine that Terry is 4, and since Patty is three times as old, she is 12.

The problem presented is a typical age-related algebraic question. To solve it, we can set up equations based on the information given. Let's define Patty's current age as 3T, where T represents Terry's current age. In 10 years, Patty will be 3T + 10 and Terry will be T + 10. According to the problem, the sum of their ages in 10 years will be 36. So, we can write the following equation:

3T + 10 + T + 10 = 36

Solving this equation:

Combine like terms: 4T + 20 = 36Subtract 20 from both sides of the equation: 4T = 16Divide both sides by 4 to find Terry's age: T = 4

With Terry's age being 4, Patty's current age is 3 times Terry's age, which means Patty is 3 × 4 = 12 years old. So, Patty is 12 and Terry is 4 years old right now.

The circumference of a circular field is 295.16 yards what is the radius of the field use 3.14 for pi and do not round your answer

Answers

Circumference = 2 x 3.14 x radius

295.16 = 6.28 x radius

295.16 / 6.28 = radius

47 = radius

The radius of circle is 47 yards.

What is Circumference of circle?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle. It is typically expressed in units like cm or unit m.

The radius of the circle is considered when applying the formula to determine the circumference of the circle. Therefore, in order to calculate the circle's perimeter, we need to know the radius or diameter value.

Given:

Circumference of circle= 295.16 yards

Now,

circumference of circle= 2πr

295.16= 2 x 3.14 x r

295.16 = 6.28 x r

r = 295.16/ 6.28

r = 47 yards.

Hence, the radius of circle is 47 yards.

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Given f(x) = x − 7 and g(x) = x2 . Find g(f(4)). g(f(4)) =

Answers

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~

To solve this we will first find out what f(x) equals at the given point of 4, and than substitute that answer it for g(f(4))...

f(x) = x - 7

f(4) = 4 - 7 = -3

g(f(4)) = (x - 7)^2 > -3^2 = 9

So...

The answer is: g(f(4)) = 9

Answer: 9

Step-by-step explanation:

Explain how the energy of a toy car is transformed as it slides down a ramp. Give evidence that the energy of the car remains the same at all points on the ramp.

Answers

At the top of a ramp, all of the energy of the car is potential: that is, it has yet to be moved but has the ability to move. As the car is sliding down the ramp, the potential energy is being transformed into kinetic energy, which reaches a maximum at halfway down the ramp. After this point, the kinetic energy begins to lessen and the potential energy begins to increase, until the car comes to a full stop, at which point kinetic energy is at zero and the potential energy is again at a maximum.

Answer:

as the car slides down the ramp it is in kinetic energy and when it is on the top of the ramp it is on potential energy we see that the energy is being transferred

Determine if f is a linear or nonlinear function and if f is a constant function.

Answers

hello :
function is linear when are the form : y = ax +b
function is linear constant are the form : y = b

How to solve 3d+8=2d-17

Answers

3d + 8 = 2d - 17
d + 8 = - 17
d = - 25

The value of d for the expression 3d + 8 = 2d - 17 is -25.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

3x = 4 is an equation.

2x = 4 is an equation.

We have,

3d + 8 = 2d - 17

3d and 2d are like terms.

So,

keep like terms on one side.

3 - 2d = -17 - 8

d = -25

Thus,

The value of d is -25.

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A painter charges an initial fee of $50 and $30 for each hour of labor. Write a linear function to determine the total cost. How much will it cost if the painter takes 4.5 hours to paint?

Answers

The initial fee of $50 is essentially the y intercept because this is the value when x = 0 (x is the number of labor-hours). So b = 50.

The slope is m = 30 because each increase of 1 hour leads to the cost bumping up by 30 dollars. In other words, slope = rise/run = (change in cost)/(change in hours) = 30/1

So we plug m = 30 and b = 50 into the y = mx+b formula to get y = 30x+50

Replace y with f(x) to get f(x) = 30x+50

The linear function for the cost is f(x) = 30x+50

Note: Some books may use other letters (instead of x and f(x)), but the idea is still the same

Once you know the cost function, you replace x with 4.5 to find the amount it will cost to have a painter work for 4.5 hours.

f(x) = 30x+50
f(4.5) = 30*4.5+50
f(4.5) = 135+50
f(4.5) = 185

It will cost 185 dollars to have the painter work for 4.5 hours

What value of c makes the trinomial below a perfect square x2 + 10x + c?

Answers

hello :
x² + 10x + c
calculate the discriminant Δ = b²-4ac a = 1 b = 10 c = c
Δ = 10²-4c
the trinomial below a perfect square when : Δ = 0
10² -4c = 0
4c = 10²
c= 25
x²+10x+25 = x² +2(5)x+5² = (x+5)²

A kennel owner needs 4 1/2 feet of wall space for each crate. How many crates can she fit along a 27 foot wall?

Answers

6 /////////////////////////////////////

A given cube has a volume of 1728 cubic inches. Find the length of an edge, area of one side, surface area, and surface area in square feet.

Answers

for a cube
v=s³
SA=6s²
area of 1 side=s²
s=length of 1 edge

so

1728=s³
cube root both sides
12=s

length of an edge is 12in

the area of one side is 12² or 144 in²

surface area is 6s² or 6(144) or 864 in²

A given cube with a volume of 1728 cubic inches:

Find the length of an edge:
The edge length (s) can be found using the formula for the volume of a cube: s³ = 1728. Therefore, s = 12 inches.Find the area of one side:
Each face of the cube is a square, so area of one face = s² = 12² = 144 square inches.Find the surface area:
Total surface area = 6 * (area of one face) = 6 * 144 = 864 square inches.Find the surface area in square feet:
To convert square inches to square feet, divide by 144 (since 1 square foot = 144 square inches). Therefore, surface area in square feet = 864 / 144 = 6 square feet.

235+374= use rounding or compatible numbers to estimate the sum

Answers

round to tens: 240 + 370 = 610
round to hundreds: 200 + 400 = 600

hope this helps

one dozen eggs cost 1.98$. How much does 1 egg cost? ( round to the nearest cent )

Answers

If 1 dozen eggs (12 eggs) cost $1.98, then you need to divide $1.98 by 12 to find how much 1 egg costs.
So, $1.98 divided by 12 = .165 There is a 5 so you would round it up to 17 cents.

The cost of one egg is $0.165.

Given that, one dozen eggs cost 1.98$.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Now, cost of 1 egg = Cost of one dozen eggs ÷ 12

= 1.98/12

=0.165

Therefore, the cost of one egg is $0.165.

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NEED HELP BADLY PLEASEEEE WILL GIVE BRAINLY

List the next three terms in the following sequence:
1, 2, 4, 8, 16, 32,...

a. 48, 80, 128
b. 64, 96, 160
c. 64, 128, 256
d. 46, 92, 184

Answers

Its C because it multiplies by 2

The first number multiplied by two is 2. Two multiplied by two is four. Four multiplied by two is eight. Eight multiplied by two is 16....and so on. So in this case, the answer would be C because 32*2=64, 64*2=128, 128*2=256.

What is the 100th term in the following arithmetic number pattern: 2,7,12

Answers

So the change in between terms is 5 so you would put 5x, then for the first term, which is 2, 5*1(x)(because it's first term) then the difference between 5-2(because it's the 2nd term) So you would plug 100 in for x so 5(100)-3=497. Hope this helped!

Express the volume v of the box as a function of the length x of the sidfe of the square cut from each corner

Answers

i dont know what the word sidfe

what property is illustrated by this problem 2(3 + 4) = 2x 3 +2 x 4

Answers

Distributive Property

It snowed 4 times during October. The snowfall amounts were 0.75 inches, 1.93 inches, 4.73 inches, and 2.33 inches. What was the total snowfall for October?

Answers

9.74 inches i did this problem yesterday

The total snowfall for October was 9.74 inches. Adding the snowfall amounts of 0.75, 1.93, 4.73, and 2.33 inches resulted in this sum.

Let's break down the calculation step-by-step:

Identify the given snowfall amounts for October:

The snowfall amounts are 0.75 inches, 1.93 inches, 4.73 inches, and 2.33 inches.

Add up the snowfall amounts to find the total:

Total snowfall = 0.75 inches + 1.93 inches + 4.73 inches + 2.33 inches.

Perform the addition

Total snowfall = 9.74 inches.

The total snowfall for October was 9.74 inches. This result is obtained by adding all four individual snowfall amounts together.

So, the calculation in step-by-step form is as follows:

0.75 + 1.93 + 4.73 + 2.33 = 9.74 inches.

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16 pound turkey cost $14.24 what is the price per pound

Answers

$.89 per pound is the answer

The answer would be $0.89,
$14.24 divided by 16

Explain why the following statement are equivalent 4(x+y)=4x+4y

Answers

They are equivalent because they are showing the Distributive Property....The Distributive Property shows that you can Distribute one number into another one, and still get the same answer.....So, you would have to do 4x+4y!!! I hope this helps!!!

The equation 4(x+y)=4x+4y represents the same value after solving.

What is Distributive Property?

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Given:

We have 4(x+y)=4x+4y.

We have the Distributive Property

a x ( b+ c )= a x b + a x c

let x= 2 and y = 5

So, 4 (x+ y) = 4 (2+ 5)= 4(7) = 28

and, 4x+ 4y= 4(2)+ 4(5) = 8+ 20 = 28

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Question 1 (3 points) study the Proof Given.

List the reasons for Items 2,3, & 4.

Right the number and then the answer.
Question 2 (3 points
)Study the Proof: Give the reasons for the missing reason. List the number and then state the reason.

Answers

Question 1
2. Definition of midpoint
3. Given
4. Transitive Property

Question 2
1. Given
2. Addition Property of Equality
3. Segment Postulate Property.

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