An office receives a shipment of identical boxes containing office supplies. The shipment contains 6 boxes of pencils, 14 boxes of pens, and 16 boxes of paper. How many additional boxes of paper must be added to the original 36 boxes in order for the probability of randomly selecting a box of paper from this shipment to be exactly 1/2 ?
Answer:
4
Step-by-step explanation:
Given that:
There are 6 boxes of pencils, 14 boxes of pens and 16 boxes of paper.
Total number of original boxes = 6 + 14 + 16 = 36
To find:
Number of additional boxes of paper to be added so that the probability of getting a paper box while selecting a random box becomes exactly [tex]\frac{1}{2}[/tex].
Solution:
First of all, let us have a look at the formula of probability:
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, number of favorable cases will be equal to the number of paper boxes and
Total number of cases will be equal to the total number of boxes available.
Let us first calculate the original probability:
[tex]\frac{16}{36}\neq \frac{1}2[/tex]
If 1 paper box is added, then probability
[tex]\frac{17}{37}\neq \frac{1}2[/tex]
If 2 paper boxes are added, then probability
[tex]\frac{18}{38}\neq \frac{1}2[/tex]
If 3 paper boxes is added, then probability
[tex]\frac{19}{39} \neq \frac{1}2[/tex]
If 4 paper boxes is added, then probability
[tex]\frac{20}{40} = \frac{1}2[/tex]
Therefore, we need to add 4 paper boxes.
The probability of randomly selecting a box of paper from this shipment to be exactly 1/2 need to add 4 boxes.
Given that,
The shipment contains 6 boxes of pencils
And 14 boxes of pens, and 16 boxes of paper.
We have to find,
How many additional boxes of paper must be added to the original 36 boxes in order for the probability of randomly selecting a box of paper from this shipment to be exactly 1/2.
According to the question,
Total no. of original boxes = 6 + 14 + 16 = 36
Formula for probability of an event E can be observed as:
[tex]P(E) = \frac{Number \ of \ favourable \ cases}{Total \ number \ of \ cases }[/tex]
Here, number of favorable cases will be equal to the number of paper boxes,
Total number of cases will be equal to the total number of boxes available.
The probability of randomly selecting a box of paper from this shipment to be exactly 1/2 .
Let us first calculate the original probability:
[tex]\frac{16}{36} \neq \frac{1}{2}[/tex]
The probability of original paper boxes is not 1\2.
If 1 paper box is added, then probability,
[tex]\frac{17}{37} \neq \frac{1}{2}[/tex]
The probability of 1 paper boxes is not 1\2.
If 2 paper box is added, then probability,
[tex]\frac{18}{38} \neq \frac{1}{2}[/tex]
The probability of 2 paper boxes is not 1\2.
If 3 paper boxes are added, then probability,
[tex]\frac{19}{39} \neq \frac{1}{2}[/tex]
The probability of 3 paper boxes is not 1\2.
If 4 paper boxes is added, then probability,
[tex]\frac{20}{40} = \frac{1}{2}[/tex]
The probability of 4 paper boxes is 1\2.
Hence, The probability of randomly selecting a box of paper from this shipment to be exactly 1/2 need to add 4 boxes.
To know more about Probability click the link given below.
https://brainly.com/question/23044118
1. How many ways are there to arrange four
boys and three girls in a line for a photo if
the girls must be in order of height from
shortest to tallest?
Answer: it could be boy girl boy girl, or it can go boys first and girls last, or it can be girls first and boys first, so i would say 3 ways
Step-by-step explanation:
hope this helped
From the figure and statement provided, select the proper TO PROVE statement.
If two angles of a triangle are equal, the sides opposite those angles are equal.
MN = AB
AB + BC = AC
a is parallel to b
m is parallel to l
AB = BC
Answer:
I think that the answer is AB+BC=AC
2. What will happen to the current if resistance is doubled while voltage is kept
constant? State the relationship of current and resistance based on your
answer.
Answer:
deeeeeeeeeezzzzzzeeee nits
I got it wrong im stupid at this kind of stuff please help
Answer:
I think is "Became 3 times as large"
Step-by-step explanation:
I WILL GIVE BRAINLIEST!! {y=−x+3y=x+5 What is the solution for this system of equations? Enter your answer in the boxes.
Answer:
The solution is (5 , 1)
Step-by-step explanation:
Answer:
x−y=12
Step-by-step explanation:
calculate the rise and run to find the slope of each line
I need help with question 4,5 & 8
Any help would be appreciated!
Answer:
4.-7/4 . 5. 5/3 6. -4/1
7. 3/1, 8. -2/1 9. 6/1
Step-by-step explanation:
The wholesale price of a jacket is $72. If the jacket is sold in a department store for a retail price of $86.40, what is the percent markup?
Answer:
20%
Step-by-step explanation:
Subtract the selling price from the wholesale price.
86.40-72.00=14.4
Find the percentage of the difference from the wholesale price.
14.4/72.0=0.2
This means 20%.
Answer my math question I asked so many times I lost most of points by
Answer:
Step-by-step explanation:
Parabolas can be written in the form
[tex]y = a(x-h)^2+k[/tex]
The vertex is (h, k). The vertex in the graph is (5, 0).
so far, we have
[tex]y = a(x-5)^2+0\\y = a(x-5)^2[/tex]
The other points we are given are (6, 1), (7, 4), (8, 9)
[tex]9 = a(8-5)^2\\9 = a(3)^2\\9 = 9a\\a = 1\\\\4 = a(7-5)^2\\4 = a(2)^2\\4 = 4a\\a = 1\\\\1 = a(6-5)^2\\a = 1[/tex]
In vertex form
[tex]y = (x-5)^2\\y = x^2 - 10x + 25[/tex]
Solve the inequality: -8(8x – 16) < 64(2 – 2).
A) <0
x <
B) 2 <4
С
a <8
D) All real numbers
E
No solution
Answer:
The answer is D. all real numbers
Step-by-step explanation:
Frank bought 5 pounds of dog food for 8.75. At this rate how much would he pay for 8 pounds
$14
you need to set up a preportion
if 5 lbs costs 8.75 then we need to figure out how much 8 lbs cost, obviously lol.
anyways what ya finna do is make a fraction
5 8
--- = ----
8.75 x
then u cross multiply. 8 x 8.75 = 70
70 = 5x
x= $14
Two rectangular prisms are similar. The ratio of the areas of the bases is 121:49. What is the ratio of the volumes of the similar solids?
Answer:
The ratio of the volumes of the similar solids is 1331:343.
Step-by-step explanation:
Ratios
Given the ratio of two lengths is a:b. Given a two-dimensional shape is similar to another shape, the ratio of their areas is [tex](a/b)^2[/tex], and the ratio of their volumes is [tex](a/b)^3[/tex].
We know the ratio of the areas of the bases of two similar rectangular prisms is 121:49. Thus, the ratio of its dimensions is:
[tex](a/b)^2=(121/49)[/tex]
Taking the square root:
[tex]a/b = \sqrt{121/49}=11/7[/tex]
Thus, the ratio of the volumes is:
[tex](a/b)^3=(11/7)^3=1331/343[/tex]
The ratio of the volumes of the similar solids is 1331:343.
20000×50×45×0×23×5×6+229+466+7+5+8+9+1+2+3+45+6+7+8+9+10. Hope you like question don't answer if you don't want to. Have a great day
help asap do all show work
y=-x
slope for perp line = 1
2y=-x+6
y=-1/2x +3
slope for perp line = 2
15.
i don’t wanna do all sorry it’s a lot of work so i’ll tell u how to do it instead. first write it in slope intercept form which is
y-y1=m(x-x1)
it’s parallel which means it shares the same slope. if it’s perpendicular it would be opposite reciprocals so for -3/2 the perp slope would be 2/3.
the line is
y+1=3/4(x-4)
we distribute the 3/4 so it’s now
y+1=3/4x-3
then we subtract the 1
y=3/4x-4 is the equation boom done
alberto knows that all the lines and rays are congruent to each other . he reasons that all segments must therefore be congruent to each other. alberto conclude that AB CD What is his error
Answer:
Step-by-step explanation:
Alberto is correct in reasoning that all lines and rays are congruent to each other but incorrect in his reasoning about the line segments.
Line segments are equal in measure only when they are equal in length. They can have any orientation on a plane.
Since, AB = 3 units
CD = 4 units
Therefore, AB ≠ CD
Error in AB ≅ CD
Explain how you would graph the line containing a slope of -1/5 that goes through the point (1,-4).
Answer:
so.
Step-by-step explanation:
what’s the slope of (5,9) and (8,4)
Answer: -5/3
Step-by-step explanation:
Use the slope formula: [tex]\frac{y_{2}-y_1 }{x_2-x_1}[/tex]
You substitute the numbers in and subtract to get -5/3.
You are buying a digital camera that costs $375. The store lets you make a down payment. You can pay the remaining cost in 4 equal monthly payments with no interest charged. You make a down payment of $175. How much will your monthly payment be until the camera is paid off?
Answer:
$50 a month for 4 months until the camera is paid off.
Step-by-step explanation:
375- 175
200
200/4 = 50
$50 each moth
A school paid $248 for new basketballs and soccer balls. The number of basketballs purchased was 6 less than 3 times the number of soccer balls purchased. Basketballs cost $28 each and soccer balls cost $20 each. How many soccer balls did the school purchase?
Answer:
The school purchased 4 soccer balls.
Step-by-step explanation:
Total cost of basketball and soccer ball = $248
We are given: The number of basketballs purchased was 6 less than 3 times the number of soccer balls purchased.
We can write it as
x = Soccer Balls
3x-6 = Basketballs
Cost of each Soccer Ball = $20
Cost of each Basketball = $28
The equation will become
[tex]20(x)+28(3x-6)=248[/tex]
Solving the equation to find x
[tex]20(x)+28(3x-6)=248\\20x+84x-168=248\\104x=248+168\\104x=416\\x=\frac{416}{104} \\x=4[/tex]
So, Soccer balls x = 4
Basketballs = 3x-6 = 3(4)-6 = 12-6 = 6
So, the school purchased 4 soccer balls.
Leroi and Sylvia both put $100 in a savings account. Leroi decides he will put in an additional $10 each week. Sylvia decides to put in an additional 10% of the amount in the account each week.
a.) Who has more money after the first additional deposit? Explain.
b.) Who has more money after the second additional deposit? Explain.
Answer:
a.)leroi he has 100 B.) she will have more money in the long run
Step-by-step explanation:
did this lesson before
Answer:
10% of 100 is 10$. Leroi also puts in 10$. So, they put in the same amount.
A and B: It will be equal.
What is -2 2/3 • -4 3/7
Answer:
11 17/21
Step-by-step explanation:
Determine the maximum number of zeros of the polynomial function
-9x^2 + 2x + 2.
a. 3
b. 2
c. 1
d. 4
Answer:
d
Step-by-step explanation:
Answer: 2
Step-by-step explanation:
Answer my questions plz help
9514 1404 393
Answer:
a = -2/3, b = 8, c = -24y-intercept: (0, -24)x = -b/(2a) = -8/(2(-2/3)) = 8(4/3)x = 6DOWNMax: (6, 0)Vertex: (6, 0)Domain: {x | x ∈ ℝ}Range: {x | x ≤ 0}Step-by-step explanation:
To find a, b, c, compare the given function to ...
f(x) = ax² +bx +c
You will see that ...
a = -2/3b = 8c = -24The y-intercept is the function value for x=0. It is the constant term:
y-intercept = f(0) = -24
Use the above values of a, b to find the line of symmetry.
[tex]x = \dfrac{-b}{2a}=\dfrac{-8}{2\cdot\dfrac{-2}{3}}=8\cdot\dfrac{3}{4}=6[/tex]
Per the calculation, the line of symmetry is ...
x = 6
The negative leading coefficient tells you the parabola opens DOWN.
Because it opens down, the vertex at (6, 0) is a Maximum.
As with any polynomial, the domain is "all real numbers", hence any x that is an element of Reals.
The range is all values below the vertex (including the vertex), so is ...
x ≤ 0
Trapezoid PSTK is isosceles. SK = 20, SH = 12, If ST = 1 4 HK, find HK, APTSK, m∠P, and PS. Find HK, Area of pstk, HK and PS
Answer:
HK = 16
Step-by-step explanation:
12^2+x^2=20^2
x = HK
Simplify: - 5 + 2(8 - 12)
Answer:
-13
Step-by-step explanation:
-5 + 2( 8 - 12 )
Distribute;
-5 + 2 ( 8 - 12 )
-5 + 16 - 24
Simplify;
-5 + 16 - 24
11 - 24
-13
Answer:
-13
Step-by-step explanation:
Follow the Order of Operations:
1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction
Parentheses:
-5+2(-4)
Exponents:
There is no exponents so we can skip that step
Multiplication and Division:
-5-8
Addition and Subtraction:
-13
Hope this helps! Have a safe and wonderful Thanksgiving!
A turtle at the zoo weighs 145 pounds. It is two times heavier than the baby turtle. How much does the baby turtle weigh.
Answer: 72.5 lbs
Step-by-step explanation:
Create the equation:
145=2x -->where x is how much the baby turtle weighs
Solve the equation:
Divide both sides by 2 to get 72.5 lbs
Solve algebraically for x and explain each step( using mathematical vocbuary) for the following: 2(x+5)+ 3x = 30
The length of the parallel sides of a trapezoid are 15 m and 25 m. If the perpendicular distance between the parallel sides is 10 m, what is the area of the trapezoid?
Answer:
Area of trapezoid = 200 m²
Step-by-step explanation:
Parallel side1 a= 15m
Parallel side2 b= 25m
Perpendicular distance h = 10 m
We need to find area of the trapezoid.
The formula used to find area of the trapezoid is: [tex]Area \ of \ trapezoid=\frac{a+b}{2}h[/tex]
Putting values and finding area of the trapezoid:
[tex]Area \ of \ trapezoid=\frac{a+b}{2}h\\Area \ of \ trapezoid=\frac{15+25}{2}\times 10\\Area \ of \ trapezoid=40\times5\\Area \ of \ trapezoid=200 \ m^2[/tex]
So, area of trapezoid = 200 m²
Brainliest 5 stars Thanks!
Answer:
(x - 6)(x - 2)(x + 4)Step-by-step explanation:
Given function
f(x) = x³ - 4x² - 20x + 48 with one root of x = 6Finding other factors, considering (x - 6) is the factor
x³ - 4x² - 20x + 48 = x³ - 6x² + 2x² - 12x - 8x + 48 =(x - 6)(x² + 2x - 8) =(x - 6)(x² - 2x + 4x - 8) = (x - 6)(x - 2)(x + 4)Explain why you write a mixed number as a fraction before using it as a dividend or divisor.
Answer:
I think it's because it is easier to solve when put into equations.
Step-by-step explanation: