Answer:
a) 0.3 = 30% probability of drawing a white chip.
b) 0.3333 = 33.33% probability that bowl B1 had been selected, given that a white chip was drawn.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. P(W), the probability of drawing a white chip.
1/3(one white out of 3) of 0.3(from B1).
1/2(two white out of 4) of 0.2(from B2).
1/5(one white out of 5) of 0.5(from B3). So
[tex]P(W) = 0.3333*0.3 + 0.5*0.2 + 0.2*0.5 = 0.3[/tex]
0.3 = 30% probability of drawing a white chip.
b. P(B1 Given W), the conditional probability that bowl B1 had been selected, given that a white chip was drawn.
The probability of drawing a white chip from B1 is 1/3 out of 0.3, so:
[tex]P(B1 \cap W) = 0.3\frac{1}{3} = 0.1[/tex]
Then the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1}{0.3} = 0.3333[/tex]
0.3333 = 33.33% probability that bowl B1 had been selected, given that a white chip was drawn.
What’s the range of the function on the graph?
Please answer this: There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest meter, how many meters are in 158 inches?
Answer:
40 m
Step-by-step explanation:
158 · 2.54 = 401.32
401.32/100 = 40.132
40.132 ≈ 40
Which number is GREATEST?
0.27
0.046
0.297
0 0.3
Answer:
0.3
Step-by-step explanation:
Go left to right for each digit, which one is greater. They all have a decimal so for right now we can’t eliminate any. Next digit we two 2s a 0 and a 3. Whch number is greater? The three! So the greatest number is 0.3.
football team consists of 20 each freshman and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that.
a. All 4 are seniors.
b. There is 1 each: freshman, sophomore, junior, and senior.
c. There are 2 sophomores and 2 freshmen.
d. At least 1 of the students is a senior.
Answer:c
Step-by-step explanation:
c
A rancher has 600600 feet of fencing to put around a rectangular field and then subdivide the field into 33 identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
Answer:
x = 150 ft
y = y = 150 / 17 ft
Step-by-step explanation:
Area of the field is A = x*y
Let´s assume x is the larger side of the rectangle, and that we will get 33 identical smaller rectangular plots dividing x into 33 rectangles ( using 34 sides of length y ) then the quantity of fence is:
p = 2*x + 34*y ⇒ 600 = 2*x + 34*y y = ( 600 - 2*x)/34
A = x*y
A (x) = x* ( 600 - 2*x)/34
A (x) = ( 600*x - 2*x²)/34
Taking derivatives on both sides of the equation:
A´(x) = (1/34)* ( 600 - 4*x )
A´(x) = 0 (1/34)* ( 600 - 4*x ) = 0 600 - 4*x = 0
x = 600/4
x = 150 feet
And y = (1/34)( 600 - 2*150)
y = 300/34 y = 150 / 17 ft
y = 8.82 ft
How do we know that is a maximum area, we find the second derivative of A
A´´(x) = - 4/34 then A´´(x) < 0
We get a maximum of function A for the value x = 150
In ΔIJK, the measure of ∠K=90°, KJ = 65, IK = 72, and JI = 97. What is the value of the cosine of ∠J to the nearest hundredth?
Answer:
[tex]\cos(J) = 0.67[/tex]
Step-by-step explanation:
Given
[tex]\angle K = 90^o[/tex]
[tex]KJ = 65[/tex]
[tex]IK = 72[/tex]
[tex]JI = 97[/tex]
Required
[tex]\cos(J)[/tex]
The question is illustrated with the attached image.
From the image, we have:
[tex]\cos(J) = \frac{KJ}{JI}[/tex]
This gives:
[tex]\cos(J) = \frac{65}{97}[/tex]
[tex]\cos(J) = 0.67010309278[/tex]
[tex]\cos(J) = 0.67[/tex] --- approximated
Tom has a steel box that has a capacity of 5 gallons. What is the maximum amount of fluid, in quarts, that this box can hold?
A. 10 qt.
B. 15 qt.
C. 18 qt.
D. 20 qt.
Answer:
d. 20 qt.
Step-by-step explanation:
4 quarts to a gallon so 4x5= 20
Calculate the value of 3x³ -2x²- 9x+2 if x= -2
Answer: -12
Step-by-step explanation:
3(-2)^3 - 2(-2)^2 - 9(-2) + 2 = N
3(-8) - 2(4) - 9(-2) + 2 = N
-24 - 8 + 18 + 2 = N
-12 = N
The table shows how the time it takes a train to travel between two cities depends on its average speed. The table shows how the time it takes a train to travel between two cities depends on its average speed Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour? What does the number 160 represent in the rational function that models the situation? distance, in miles, between the cities amount of fuel, in gallons, used by the train time, in minutes, needed to travel between the cities
Answer:
Step-by-step explanation:
Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour?
✔ y = 160/x
What does the number 160 represent in the rational function that models the situation?
✔distance, in miles, between the cities
amount of fuel, in gallons, used by the train
time, in minutes, needed to travel between the cities
Answer: NOTE Pictures Are not in order! Make sure you check page number.
Step-by-step explanation:
On page 6 the answers are ”C” and ”5lbs”
On page 7 the answers are “C”, “$ 418”, “ The cat”, and then “ $960”.
On page 8 the answers are : < Just copy paste this below.>
“Based on the calculation, they should purchase the second television as the cost is cheaper.
Based on the information given in the question, the cost of the first television will be:
= $330 + ($14 × 8)
= $330 + $102
= $442
The cost of the second television will be:
= $369 + ($9 × 8)
= $369 + $72
= $441
Therefore, the second television is cheaper.”
^
<Just copy paste this. > [Then check. “A,B,C,”.]
On page 9 the answer is “ D “.
Select the points that are solutions to the system of inequalities. Select all that apply A. (-12, 0) B. (1, 2) C. (0, 0) D. (-10, 1)
Answer:
B. (1, 2)
D. (-10, 1)
Step-by-step explanation:
Both points land in the highlighted area.
Hope this helps! :)
Answer:
The correct answer would be
A. (–12, 0) & D. (–10, 1)
It took Fred 12 hours to travel over pack ice from one town to another town 360 miles away. During the return journey it took him 15 minutes
Step-by-step explanation:
what is your question please
Determine if the triangles are congruent. If they are, state how you know. NO LINKS!!!!
Part 1c. Show your work please.
Answers:
Each pair of triangles are congruent. The congruence reasoning is shown below.
ASASSSHA======================================
Further Explanation:
ASA is where we have the marked side between two marked angles. This is slightly different from AAS or SAA. The order is important. The diagram shows how the angles pair up (eg: the double arc angles are the same measure). Using ASA is enough to prove the triangles congruent.SSS is used here because we have three pairs of congruent sides. The unmarked sides overlap perfectly, so we consider this a shared side. They are congruent to each other (because of the reflexive property). So we have enough info to show that the triangles are congruent.HA stands for hypotenuse angle. It's probably not that often used. It only applies to right triangles. The two overlapped segments are the hypotenuse of each right triangle, so that takes care of the "H" of "HA". The A part refers to the congruent acute angles (not the right angles). Therefore, the triangles are congruent by the HA theorem.Abbreviations:
ASA = angle side angle
SSS = side side side
HA = hypotenuse angle
A man invests K8 000 for 5 years at 10%p.a. compound interest.
Calculate the investment value at the end of 5 years.
Answer:
Step-by-step explanation:
Compoud interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. the formula is:
[tex]c_n=c_o(1+i)^n\\\\c_o->initial~invesment\\i->interest\\n->number~of~ intervals[/tex]
[tex]c_5=8000(1+\frac{10}{100})^5\\c_5=12848.88[/tex]
If the diameter of a circle is 50 yds, the radius is
Answer:
r = 25 yds
Step-by-step explanation:
The radius is 1/2 of the diameter
r =1/2d
r =1/2( 50 yds)
r = 25 yds
need help asap! The graphs below have the same shape. what is the equation of the red graph?
no links
Answer:
B. [tex]g(x) = x^{3} - 5[/tex]
Step-by-step explanation:
The graph of f(x) is the graph of g(x) translated 5 units downwards.
abb
9. Hãy đặt các phán đoán đơn và biểu thị thành phán đoán hợp câu
sau đây: "Nếu bị đau đầu hoặc sốt thì có thể uống thuốc Panadol,
Nếu bị cảm cúm hoặc đau đầu thì có thể uống thuốc Tiffy. Thơm
bị cảm cúm và đau đầu. Do đó Thơm có thể uống thuốc Panadol
hoặc thuốc Tiffy". Hãy xác định giá trị của phán đoán hợp trên.
Answer:i took the test
Step-by-step explanation: 76879686
Find the value of y
A) 9.850
B) 18.610
C) 65.825
D) 125.365
Answer:
B) 18.610
Step-by-step explanation:
Using SOHCAHTOA (trig ratios), the tangent of 28° is the ratio of its opposite length to its adjacent.
in this scenario, the side opposite to 28°, and the side adjacent to it is 35°
tan 28° = y/35
Using inverse operations, multiply both sides by 35
y = 35 * tan 28
Solve your answer using your calculator.
I attached a picture that can help you later to recognize what function to use depending on the sides given.
A force of 50 pounds acts on an object at an angle of 45 degrees. A second force of 75 pounds acts on the object at an angle of -30 degrees. Find the direction and magnitude of the resultant force.
Answer:
The magnitude of the resultant force is:
[tex]R=100.3 \:pound[/tex]
The direction is:
[tex]\theta=1.2^{\circ}[/tex]
Step-by-step explanation:
Let's find the components of each vector is x and y-directions first.
Sum of x-component vector forces.
[tex]F_{tot-x}=F_{1}cos(45)+F_{2}cos(30)[/tex]
[tex]F_{tot-x}=50cos(45)+75cos(30)[/tex]
[tex]F_{tot-x}=100.3 \: pound[/tex]
Sum of y-component vector forces.
[tex]F_{tot-y}=-F_{1}sin(45)+F_{2}sin(30)[/tex]
[tex]F_{tot-y}=-50sin(45)+75sin(30)[/tex]
[tex]F_{tot-y}=2.1 \: pound[/tex]
The magnitude of the resultant force is:
[tex]R=\sqrt{100.3^{2}+2.1^{2}}[/tex]
[tex]R=100.3 \:pound[/tex]
The direction is:
[tex]tan(\theta)=\frac{2.1}{100.3}[/tex]
[tex]\theta=arctan(\frac{2.1}{100.3})[/tex]
[tex]\theta=1.2^{\circ}[/tex]
I hope it helps you!
A label printer prints 9 pages of labels in 2.0 seconds. How long will it take to print 396 pages of labels?
Answer:
88 or 1 minute and 28 seconds
Step-by-step explanation:
396/9= 44 times the two seconds it takes to print is 88
Answer:
1782
Step-by-step explanation:
9 divided by 2.0
=4.5
4.5×396
=1782
A coin is flipped 60 times and lands on heads 36 times. Based on the experimental probability, how many heads would you predict for 200 flips of the coin?
Answer:
108
Step-by-step explanation:
200 divided by 60 equals 3 then 36 times 3 equals 108
Answer:
120 heads
Step-by-step explanation:
The Experimental probability for heads is 36/60. now we have to find the experimental probability for 200 flips. so 36/60 = ?/200. We have to find a number that 60 multiplies by to get 200. That number is 200/60 = 20/6 = 3 1/3. So multiply 36 by 3 1/3: 36 * 3 = 108. 36 * 1/3 = 12. 108 + 12 = 120. So it is 120 heads
Help plz so close to being done
Answer:
20 is the answer I got
salma is 1.45 meters tall. at 3p.m she measures the length of a tree's shadow to 29.35 meters. she stands 24.3 meters away from the tree, so that the tip of her shadow meets the tip of the treels shadow. find the height of the tree to the nearest hundreth of a meter.
Answer:
23.67
Step-by-step explanation:
Answer:
kimjnuhbygvtcfrdxe
Step-by-step explanation:
Shannon was born on 12/21/1982. How many eight digit codes could she make using the digits in her birthday?
============================================================
Explanation:
Ignoring the slashes, there are 8 digits here. If we could tell those '1's and '2's apart, then we'd have 8! = 40,320 different codes. The exclamation mark indicates a factorial.
However, the '1's and '2's are indistinguishable. We have to divide by a!*b! = 3!*3! = 6*6 = 36 to account for this.
The a! = 3! = 6 is from the fact we have 3 copies of '1'.
The b! = 3! = 6 is from the fact we have 3 copies of '2'
Dividing by 36 gets us (40,320)/36 = 1120
solve the equation
x + -18 = 3x + 54
Answer:
-36
Step-by-step explanation:
See image below:)
Answer:
x = -36
Step-by-step explanation:
subtract 'x' from each side to get:
-18 = 2x + 54
subtract 54 from each side to get:
-72 = 2x
x = -72/2
x = -36
A spinner is divided into 4 equal sections numbered 1 through 4. It is spun twice, and the numbers from each spin are added.
What is the probability that the sum is less than 6?
Answer:
4equal to plus 5 eul is to be 9
Substitute the isolated variable into the second equation. I need help with this, i don’t understand.
Answer:
Step-by-step explanation:
Substitute the value for y or x into the equation thats listed with it.
For the first one, substitute 3 in place of y.
3x + 6 y = 60 turns into
3x + 6 * 3 = 60
3x + 18 = 60
3x = 60-18
3x = 42
x = 42/3
x = 14
Apply the same to the other equations
10x + 4y = 70 turns into
10 * 5 + 4y = 70
Then solve for y
Gary has four times as many points as Frank. Evan has five times as many as Frank. Dave is two times as many as Frank. altogether they have a total of 1,260 points
Answer:
the answer to this would be 114 i think sorry is im wrong
Step-by-step explanation:
Under the translation (X +3, y - 1) the point (3,4) will become (0.5)
True or False
9514 1404 393
Answer:
False
Step-by-step explanation:
Point (3, 4) will become (3+3, 4-1) = (6, 3), not (0, 5). The statement is False.
_____
Additional comment
The point (0, 5) would be translated to (3, 4). That is not what the question is asking.
Madison and Aidan roll two number cubes. Which of the following rules will make the game fair?
Madison wins if a total of 5 is rolled. Aidan wins if a total of 10 is rolled.
Madison wins if a total of 8 is rolled. Aidan wins if a total of 6 is rolled.
Madison wins if a total of 9 is rolled. Aidan wins if a total of 7 is rolled.
Madison wins if a total of 2 is rolled. Aidan wins if a total of 11 is rolled.
Answer:
If I understand this right I think it would be 8 and 6?
Step-by-step explanation:
Sorry if this is wrong I'm really bad at math, please tell me if this is right.
I need help with #3. Please help. I have to show all work so please explain
Answer:
a = 2
Step-by-step explanation:
Use Pythagorean Theorem:
[tex]a^2+b^2=c^2\\a^2+2.1^2=2.9^2\\a^2+4.41=8.41\\a^2=4\\\sqrt{a^2}=\sqrt{4}\\a=2[/tex]
Therefore, a is 2 meters.
