Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains red pieces of candy out of pieces of candy total.
Answer:
Dependent event
[tex]P(Red = 2) = \frac{5}{588}[/tex]
Step-by-step explanation:
Given
[tex]Total = 49[/tex]
[tex]Red = 5[/tex]
Solving (a): Are the events dependent?
Yes, they are.
When the first red candy is selected and eaten, the total number of candies reduced to 48 and the number of red candies also reduced to 4.
So, the probability of selecting a 2nd candy is dependent on the first candy selected.
Solving (b): P(Red = 2)
This is calculated as:
[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]
The first selection has the following probability:
[tex]P(Red) = \frac{Red}{Total}[/tex]
[tex]P(Red) = \frac{5}{49}[/tex]
The second selection has the following probability:
[tex]P(Red|Red) = \frac{Red - 1}{Total - 1}[/tex]
[tex]P(Red|Red) = \frac{5 - 1}{49 - 1}[/tex]
[tex]P(Red|Red) = \frac{4}{48}[/tex]
So, we have:
[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]
[tex]P(Red = 2) = \frac{5}{49} * \frac{4}{48}[/tex]
Reduce fraction
[tex]P(Red = 2) = \frac{5}{49} * \frac{1}{12}[/tex]
Multiply
[tex]P(Red = 2) = \frac{5}{588}[/tex]
Sets L and M are defined as follows.
L={-1,1,4,5,7,8)
M={1,2,7)
Answer each part below. Write your answer in roster form or as Ø.
(a) Find the union of L and M.
(b) Find the intersection of L and M
Answer:
the union of l and m is minus 1,1,2,4,5,7,8.....and the intersection of l and m is 1.......
A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.07 cents per square centimeter. Find the dimensions for the can that will minimize production cost.
9514 1404 393
Answer:
radius: 3.685 cmheight: 12.896 cmStep-by-step explanation:
The cost of the ends of the can will be ...
c1 = 0.07(2πr²)
The cost of the side of the can will be ...
c2 = 0.04(2πrh)
The volume of the can will be ...
v = πr²h
We want the derivative of the total cost to be zero, and we want the volume to be 550 cm³. We can take the derivatives of both equations to find a relation between r and h.
d(c1 +c2) = 0.28πr·dr +0.08π(h·dr +r·dh) = 0
d(v) = 2πrh·dr +πr²·dh = 0
Solving the first equation for dh/dr gives ...
dh/dr = -π(0.28r +0.08h)/(π(0.08r)) = -(7r+2h)/(2r)
Solving the second equation for dh/dr gives ...
dh/dr = -2πrh/(πr²) = -2h/r
Equating these expressions, we get ...
-(7r +2h)/(2r) = -2h/r
7r +2h = 4h . . . . . . . multiply by -2r
h = 7/2r . . . . . . . . . . subtract 2h, divide by 2
__
Now, we can find the can dimensions from the volume equation.
550 = πr²(7/2r)
r³ = 1100/(7π)
r ≈ ∛50.02 ≈ 3.685 . . . . . cm
h = 7/2(3.685 cm) = 12.896 cm
The can cost will be a minimum when the radius is 3.685 cm and the height is 12.896 cm.
_____
Additional comment
You may notice that the ratio of height to diameter is the same as the ratio of end cost to side cost: 7/4. This is the generic solution to this sort of problem.
Solve for x . 7 - (2 x + 11) + 3(3 - x ) = 20
A.7/5
B.-3
C.-4
Answer:
the answer to the question is a:-3
Solve for x
X-8 = -10
A) X = 2
B) X = -2
C) X = 18
D) X = -18
Answer:
x=–2
Step-by-step explanation:
x-8=-10
x=-10-8
x=–2
Answer:
-8= -10
, = -10+8
, = -2
A toy car costs $60. It is reduced to 10% in a sale. How much does it cost in a sale ?
Answer:
$54
Step-by-step explanation:
10% of $60 is $6
$60-$6=$54
A. 270
B. 180
C. 90
D. 360
Answer:
B 180
Step-by-step explanation:
The period is the interval it takes to repeat
The bottom of the first curve to where it repeats is 180
To make a batch of salad dressing, combine 9 tablespoons of oil with 18 tablespoons of vinegar. How many tablespoons of vinegar are needed for every tablespoon of oil?
Answer:
18 divided by nine is two. so for every one table spoon of oil there's two table spoons of vinegar. Please give brainliest
Answer:
2
Step-by-step explanation:
Make a ratio:
Oil : Vinegar
9 : 18
1 : 2
For each tablespoon of oil, 2 tablespoons of vinegar is needed.
Hope this helped.
.......... is a factor of every even number.
Answer:
2 is the factor of every even number hope this help you
What is the five-number summary for this data set? 22, 29, 33, 38, 44, 47, 51, 56, 64, 69 Assume the numbers in each answer choice are listed in this order: min, Q1, median, Q3, max.
A. 22, 33, 45.5, 56, 69
B. 22, 38, 45.5, 51, 69
C. 22, 38, 41, 51, 69
D. 22, 33, 41, 56, 69
Answer: A: 22, 33, 45.5, 56, 59
Step-by-step explanation:
The minimum is the lowest number in the data, in this case, it was 22.
Q1 is the median of the lower quartile range, anything below the median of the overall data.
Median, the middle number in the overall data. You first need to put them from lowest to highest (numerical order). After that, I find it a lot easier to cross one from each side until I'm either left with one or two. If I'm left with one, then that is my median for the overall data set. If I'm left with two, then I simply need to add both the numbers together and divide it by 2. Typically if it is a whole number, and the numbers are 1 number value away from each other, it is usually just 0.5 more of the lower value of the two. (For example, the two numbers I come down to is 10 and 11. The median would be 10.5).
Q3 is the exact same principle as Q1 just on the upper quartile range. Just repeat what you did in Q1 but for the numbers above the overall median of the data set.
Maximum is the highest number in the data set, in this case, it was 69.
Hope this helps!
Convert 2 1/3 into improper fraction: *
7/3
O 7/6
O 6/3
O 3/6
Answer:
7/3 is the answer
Step-by-step explanation:
Use the function f(x) to answer the questions:
f(x) = 2x2 − x − 10
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Answer:
x=(-2,0) and x=(5/2,0)
Step-by-step explanation:
To find x-intercepts you set f(x), or y, to 0 and then solve.
[tex]0=2x^2-x-10\\Factor!\\0=(x+2)(2x-5)\\x+2=0\\x=2\\2x-5=0\\2x=5\\x=\frac{5}{2}[/tex]
The x-intercepts of the graph of f(x) is (-2, 0) and (5/2, 0).
The function is given as:
[tex]f(x) = 2x^2 - x - 10[/tex]
We need to find the points at which the given function crosses the x-axis.
What is the x-intercept of a function?It is the point at which the given function crosses the x-axis.
The x-intercept is found by setting y = 0 or f(x) = 0.
Given function,
[tex]f(x) = 2x^2 - x - 10[/tex]
Let's set f(x) = 0.
[tex]2x^2 - x - 10 = 0[/tex]
Solve the equation for x.
[tex]2x^2 - x - 10\\2x^2 - (5 - 4)x - 10\\2x^2 - 5x + 4x - 10\\x(2x-5) +2(2x - 5)\\(x+2)(2x-5)[/tex]
Now we have,
x+2 = 0 and 2x - 5 = 0
x = -2 and x = 5 / 2
We already know that y = 0 so the points at which the function intercepts with the x-axis are:
(-2, 0) and (5/2, 0).
The x-intercepts of the graph of f(x) is (-2, 0) and (5/2, 0).
Learn more about x-intercepts of a function here:
https://brainly.com/question/28019177
#SPJ2
Find the length of DM
Answer:
67
Step-by-step explanation:
DM=JM-JD=84-17=67
Answer:
Step-by-step explanation:
Near the beginning of Lesson 5.3, a strategy for factoring trinomials of the form x^2+ bx+c was
developed by exploring the product of the binomials (x+p) and (x+q).
Explain how the development of this factoring strategy is an example of working backwards
to solve a problem.
Answer:
Step-by-step explanation:
there are function that "invert" each other..
subtraction inverts addition...
3+2 = 5 ... 5-2 = 3
division inverts multiplication
5*2 = 10 ... 10/2 = 5
Using that concept, "factoring" is basically the inverse of multiplication
3x^2 + 9x can be factored to 3x(x+3)
if you multiply that out it reverts back to the original equation
so x^2 + 5x + 6 factors to (x+3)(x+2)
if you multiply that out (foil it)
you get x^2 + 5x + 6
The length AB of a rectangle ABCD is 8cm and its diagonal BD and measures 10 cm Find its breadth BC
What is the surface area of a cylinder that has a radius of 7 m and a height of 18 m?
879.65 m2
1099.56 m2
615.75 m2
395.84 m2
1099.56m² is the surface area of a cylinder that has a radius of 7 m and a height of 18 m.
Solve for x then measure to find A
Answer:
[tex]125 \: \: degrees[/tex]
Step-by-step explanation:
As the 2 lines are parallel
<A = <B ( Alternative Angles)
[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = 20[/tex]
[tex]<A = 6x + 5 \\ = 6 \times 20 + 5 \\ = 120 + 5 \\ = 125[/tex]
<A=6x+5
=6×20+5
=120+5
=125
<B=4x+45
=4×20+45
=80+45
=125
it is alternate angle they are equal each other
<A = < B
[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = \frac{40}{2} \\ x = 20 \\ \\ [/tex]
A company produces 2 types of computers; desktops and laptops
Answer:
?
Step-by-step explanation:
|x| = - |x| What can I write
A math class has a total of 31 students. The number of females is seven less than the number of meals. How many miles and how many females are in the class?
Answer:
Male-19&Female-13
Step-by-step explanation:
See the image for solution
Hope it helps
Have a great day
Find the area bounded by the curves x = 2y2 and x = 1 - y. Your work must include an integral in one variable.
Please help!!
Answer:
Hello,
in order to simplify, i have taken the inverses functions
Step-by-step explanation:
[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]
In a scatter plot, each ____. Group of answer choices individual is represented by a single point group mean is represented by a single point individual is represented by two data points group mean is represented by two data points
Answer:
Individual is represented by a single point
Step-by-step explanation:
helppp outt plss....
============================================================
Explanation:
For any cyclic quadrilateral (aka inscribed quadrilateral), the opposite angles are always supplementary.
One pair of such angles is A and C
A+C = 180
x+y = 180 is one equation to form
The other pair of supplementary angles is B and D
B+D = 180
y-45+2x+15 = 180
2x+y-30 = 180
2x+y = 180+30
2x+y = 210 is the other equation to form
--------------
So the system of equations we have is
[tex]\begin{cases}x+y = 180\\2x+y = 210\end{cases}[/tex]
Both equations involve 'y', with the same coefficient, so we can subtract straight down to eliminate this variable.
The x terms subtract to x-2x = -xThe y terms subtract to y-y = 0y = 0, so the y terms go awayThe right hand sides subtract to 180-210 = -30We end up with -x = -30 which solves to x = 30
--------------
Once we know x, we can determine y by plugging it into any equation involving x,y and solving for y
Let's say we picked on the first equation
x+y = 180
30+y = 180
y = 180-30
y = 150
Or we could pick on the second equation
2x+y = 210
2(30) + y = 210
60+y = 210
y = 210-60
y = 150
Only one equation is needed. However, doing both like this shows that we get the same y value, and it helps confirm the answers.
In a random sample of seven aerospace engineers, the sample mean monthly income is $6824 and the sample standard deviation is $340. Construct a 95% confidence interval for the population mean. Assume that the monthly incomes are normally distributed.
Answer:
The 95% confidence interval for the population mean is ($6510, $7138).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 7 - 1 = 6
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{340}{\sqrt{7}} = 314[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 6824 - 314 = $6510.
The upper end of the interval is the sample mean added to M. So it is 6824 + 314 = $7138.
The 95% confidence interval for the population mean is ($6510, $7138).
Find the missing side round your answer to the nearest tenth
Answer: 15
Step-by-step explanation:
find the values of x and y for the following matrix equations
Answer:
Step-by-step explanation:
Rectangle TUVW is dilated by a scale factor of 3
3 to form rectangle T'U'V'W'. Side U'V' measures 93
93. What is the measure of side UV?
Answer:
31
Step-by-step explanation:
93/3=31
So UV is equal to 31
Answer:
31
Step-by-step explanation:
What is 3 times 10^9
Answer:
3 times 10 ^ 9
Step-by-step explanation:
3 × 10 ^ 9 = 3000000000
4. Write 3x(x + 4)(x - 1) in standard form.
3x3 + 9x2 - 12x
3x3
- 12x + 9x2
3x3 + 9x2 - 12x + 1
1 - 12x + 9x2 + 3x3
Answer:
i thank the ans id 450
Step-by-step explanation:
I need help with this please if anyone know I will appreciate it
Answer:
290.44
Step-by-step explanation:
The whole figure area can be calculated by assuming that the whole floor is a complete square of 18.2 x 18.2 and subtracting the area of the rectangular cutout which is 10.2 x 4
Area of the the flooring=18.2 x 18.2 - (10.2*4)=290.44
