Answer:
a) P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = [tex]\frac{1}{9}[/tex]
b) P( the sum of both dice adding up to 4) = [tex]\frac{5}{54}[/tex]
Step-by-step explanation:
Given - You roll two six-sided dice. Die 1 is fair. Die 2 is unfair such that the probability of rolling an odd number is [tex]\frac{2}{3}[/tex] and the probability of rolling an even number is [tex]\frac{1}{3}[/tex] , though the probability rolling of each odd number is the same, and the probability of rolling each even number is the same.
To find - What is the probability of:
a) rolling a number less than 4 on Die 1 and rolling a 5 on Die 2.
b) the sum of both dice adding up to 4.
Proof -
The sample space , S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }
Now,
Given that , Dice 1 is fair
⇒P₁(1) = P₁(2) = P₁(3) = P₁(4) = P₁(5) = P₁(6) = [tex]\frac{1}{6}[/tex]
Also, Given Dice 2 is unfair
⇒P₂(1) = P₂(3) = P₂(5) = [tex]\frac{2}{3}.\frac{1}{3} = \frac{2}{9}[/tex]
P₂(2) = P₂(4) = P₂(6) = [tex]\frac{1}{3}.\frac{1}{3} = \frac{1}{9}[/tex]
Now,
a)
P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = P₁(1)P₂(5) + P₁(2)P₂(5) + P₁(3)P₂(5)
= P₂(5) [ P₁(1) + P₁(2) + P₁(3) ]
= [tex]\frac{2}{9}[/tex] [ [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] ] = [tex]\frac{2}{9}[ \frac{3}{6}]\\[/tex] = [tex]\frac{1}{9}[/tex]
⇒P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = [tex]\frac{1}{9}[/tex]
b)
P( the sum of both dice adding up to 4) = P₁(1)P₂(3) + P₁(2)P₂(2) + P₁(3)P₂(1)
= [tex]\frac{1}{6}[/tex] × [tex]\frac{2}{9}[/tex] + [tex]\frac{1}{6}[/tex] × [tex]\frac{1}{9}[/tex] + [tex]\frac{1}{6}[/tex] ×[tex]\frac{2}{9}[/tex] = [tex]\frac{5}{54}[/tex]
⇒P( the sum of both dice adding up to 4) = [tex]\frac{5}{54}[/tex]
Q13. Mavi Jeans has two retail outlets: Dallas and Phoenix. The Dallas store does 65 percent of the total sales in a year. Further analysis indicates that if a sale is made in Dallas, there is 0.5 probability this is a sale of belts, while if a sale is made at the Phoenix store this probability is 0.3. If Mavi Jeans knows that a belt has been sold, what is the probability this sale has occurred in Dallas
Answer:
0.7558 = 75.58% probability this sale has occurred in Dallas
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.
In this question:
Event A: Belt sold
Event B: Sold in Dallas.
Probability of belt being sold:
50% of 65%(made in Dallas)
30% of 100 - 65 = 35%(made in Phoenix). So
[tex]P(A) = 0.5*0.65 + 0.3*0.35 = 0.43[/tex]
Sold in Dallas:
50% of 65%. So
[tex]P(A \cap B) = 0.5*0.65 = 0.325[/tex]
What is the probability this sale has occurred in Dallas?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.325}{0.43} = 0.7558[/tex]
0.7558 = 75.58% probability this sale has occurred in Dallas
Pls help! The question is in the picture down below!
Answer:
Let me know if there is anything you don't get
∠3 = 102 because ∠1 and ∠3 are supplementary and 102 + 78 = 180
∠4 = 102 because ∠1 and ∠4 are consecutive interior angles
∠5 = 78 because ∠1 and ∠5 are corresponding angles
∠6 = 133 because ∠2 and ∠6 are supplementary angles
∠7 = 47 because ∠2 and ∠7 are vertical angles
∠8 = 47 because ∠2 and ∠8 are opposite interior angles
∠9 = 133 because ∠8 and ∠9 are supplementary, and we just saw ∠2=∠8
∠10 = 102 because ∠1 and ∠10 are supplementary
You could have used a whole bunch of different relations, but I wanted to focus on ∠1 and ∠2 since those were told to us
Step-by-step explanation:
For this question you need to know several parts of geometry. Let me know if anything doesn't make sense.
First, parallel lines are two or more lines which are angles in such a way that no matter how long they are they will not cross. In other words they are slanted at the same angle. you can see this with lines a and b in this picture.
Second, a transversal is a line that crosses through two or more parallel lines. A transversal creates a number of angles that have special properties. I would like you to look specifically at line c as I describe these angles. line c is a transversal to Ines a and b. Also line d is also a transversal.
There are seven special angles to know.
The easiest is supplementary angles. This you don't need parallel lines, but if any two lines ever cross this creates 4 angles. you can actually look at where lines c and b intersect in your problem. Angles 2. 6 and 7 are labeled but there is one more unlabeled one. Now, 180 degrees is a straight line. With angles you can see angles 6 and 7 add together to be a straight line. Similarly 2 and 6 do as well. These are two sets of supplementary angles.
To list off the supplementary angles here 9 and 8 are supplementary, as are 2 and 6, 6 and 7, 1 and 3, 1 and 10, and finally 4 and 5.
From supplementary angles comes vertical angles. Again, if you look at angles 2, 6 and 7 we already know ∠2 + ∠6 = 180 and ∠6 + ∠7 = 180. Well lets say ∠6 = 133. Well then, we could use algebra to see that both ∠2 AND ∠7 are 47 degrees. This is the property of vertical angles. if you have two lines intersecting, any two angles that have a third in between the are called vertical angles, and are equal.
some examples of vertical angles are ∠2 and ∠7as well as ∠3 and ∠10,
Finally we go into parallel line specific angles. If you have two or more parallel lines with a transversal, so in particular look at a and b as the parallel lines and c as the transversal. The transversal creates some special angles. in particular, the transversal crosses a and b at the same angle, so angles 8 and 7 have the same value. These are known as corresponding angles, since they correspond tot he same position with a transversal crossing through parallel lines.
the corresponding angles in the picture are ∠8 and ∠7, ∠3 and ∠4 and finally ∠1 and ∠5. the last two using line d as a transversal.
After corresponding angles opposite interior angles I think are the next logically to look at. Opposite means they are on two different parallel lines and on different sides of the transversal, while interior means they are between the parallel lines. so if you look at the parallel lines a and b there are angles 8 and 2 that are interior angles. Since 8 is against line a and 2 is against line b, and ∠8 is above transversal c while ∠2 is below it, they are opposite angles. so 8 and 2 are opposite interior angles. Now, if you look at ∠8 and ∠7 you know these are corresponding angles, then ∠7 and ∠2 are vertical angles. This means opposite interior angles are equal.
A list of opposite interior angles are ∠8 and ∠2, and ∠10 and ∠4.
Alongside opposite interior, there are opposite exterior angles. opposite means on different parallel Ines and on opposite sides of the transversal, while this time exterior means not between the parallel lines. Now just like we figured with opposite interior angles
The only labeled pair of opposite exterior angles are ∠9 and ∠6. Now just like we figured with opposite interior angles, let's start with ∠8 and ∠9, which are supplementary. then ∠8 and ∠7 are corresponding angles so ∠9 and ∠7 are supplementary. We can also see ∠7 and ∠6 are supplementary. well, since ∠9 + ∠7 = 180 = ∠6 + ∠7 then ∠9 = 180 - ∠7 = ∠6 so ∠9 = ∠6. This shows opposite exterior angles are equal.
So we did two kinds of opposite angles, it might make sense there are non opposite angles. And there are. these are called consecutive angles. There are consecutive exterior and consecutive interior angles. An example of each are ∠1 and ∠4 for consecutive interior, consecutive because they are on the same side of the transversal, and interior because they are between the two parallel lines. ∠3 and ∠5 are consecutive exterior angles.
You can use similar reasoning we have been so far to conclude all consecutive angles are supplementary
Find the area of the smallest side of the right triangle.
A. 313 ft
B. 5 ft.
C. 25 ft.
D. 13 ft
Answer:
c
Step-by-step explanation:
A line with a slope of 0 passes through the point (9,5). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
if the slope is 0, it is horizontal. and remember, m is the slope. (0)
Step-by-step explanation:
x is 9, y is 5.
slope intercept form is y=mx+b, so you plug in the numbers.
5= 0*9+5
or, 5=5
100 points and BRAINLESS pless help
Answer: 50 square units
Step-by-step explanation:
Create a probability model for the outcome of flipping a coin 3 times. what is the probability of landing on heads at least once
a. 2/3
b. 1/2
c. 7/8
d. 1/8
Answer:
it is A.2/3
Step-by-step explanation:
The variable y varies directly as x. When x = 20, y = 12. What is the value of y when x = 15?
A. 7
B. 9
C. 18
D. 25
The value of y when x = 15 is 9
VariationIf the variable y varies directly as x, this is expressed as;
y = kx
where k is the constant of proportionality
If x = 20 when y = 12, then;
k = y/x
k = 12/20
If x = 15, then the value of y is;
y = 12/20*15
y = 9
Hence the value of y when x = 15 is 9
Learn more on variation here: https://brainly.com/question/6499629
#SPJ1
Name and find the measure of each angle in the figure.
HELP PLEASE
In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, answered "none," said "one," said "two," said "three," and responded with four or more. A survey respondent is selected at random. Find the probability that his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05.
P(four or more cell phones)
(Round to three decimal places as needed.)
Can you help me here is the image
Answer:
C. y= 1.5x
Step-by-step explanation:
Everytime multiply the first number 1.5 (y) by the X variables it gives you another Y variable. For example, 1.5 times 2 = 3. 1.5 times 3 = 4.5. And 1.5 times 4 = 6!
Plzzz someone help me
100
400 people were surveyed
about their eye color. 8% of
the people surveyed have
green eyes. How many
people had green eyes?
Answer:
32 people
Step-by-step explanation: If there are 400 people and there is 8% of that, then first convert 8% to a decimal so its easier to work with. The multiply with 400:
0.08 * 400 = 32
Answer: 32 people have green eyes
Which is the graph of the line given below? *
y=2/3x-5
To make this graph the first step is to look at the slope-intercept form
- we see that 2/3 is the slope and -5 is the y-intercept (the point on the y-axis)
So, now you can find the y-intercept on the graph (-5) and make a dot there
Next, move right 3 and up 2 and repeat until you have enough points to make a line :)
graph below- hope this helps :)
whats 100 times 63 times 23 divided by 20 times 30 times 0 times 5 times 50 times 10
Answer:
0
Step-by-step explanation:
100 × 63 × 23 ÷ 20 × 30 × 0 × 5 × 50 × 10
You see the bold " × 0"; this means whatever happened before the " × 0" means nothing. You are left with "× 0 × 5 × 50 × 10". Any number times 0 or 0 times any number = 0. Your answer is 0.
Mrs jones uses 1/2 of a block of cheese to make packed lunches each day. how many days will 3 blocks of cheese last for?
Answer:
6 days
Step-by-step explanation:
Answer:
6 days
Step-by-step explanation:
1 day=1/2
2 day=1
3 day=1 and 1/2
4 day=2
5 day=2 and 1/2
6 day=3
hope this helps :)
giving the brainliest answer to who ever can help me out!!! AND has the correct answer need help asap!?!!
Answer:
caca water
pee water
Step-by-step explanation:
Y= 5x -8 function rule
Answer:
Step-by-step explanation:
Are these equivalent the the expression on the top right
Answer:
No
Yes
No
Yes
(choice 3 is a no)
If 60 minutes equals one hour, which expression would you use to find the number of
hours in 240 minutes?
imeter, Area, Dimensions - Real World Hacice estions Notes/Examples 1. A triangular garden has sides measuring 14 feet, 17 feet, and 28 feet. If Cody is laying a brick ETER border around the garden, how many feet of brick will he laya uchs Hihe rectangular path
If 9% of a number equals 10, find 90% of that number.
36/81 × 10/50 simplest form
Answer:
36/81 x 10/50 is 29/45. Since 29 is a prime number and 45 is not divisible by 29, 29/45 would be the simplest form.
Hope this helps! Brainliest?
Math Which expressions represent 9 divided by the sum of 1 and 2? Check all that are true. 09/(1+2) 9+1+2 I (9 - 1) + 2 (1 + 2) = 9 09+ (1 + 2)
Answer: 9/(1+2)
Hope it helps :)
what is the value of x when h(x) x-3
Answer:
-1
Step-by-step explanation:
I did it in my review
Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is. Andre wrote:
228=2⋅28=56
Elena said, “No, exponents mean repeated multiplication. It should be 28⋅28, which works out to be 784.” Do you agree with either of them? Explain your reasoning.
Answer:
no, exponents are how many times the base is used, it would be 2x2x2... so on until there are 28 2s
Step-by-step explanation:
what is the volume of a rectangular prism wi the the dimensions3 base 5/8 cm, height 2/3 cm, and length 3/4 cm?
Answer:
5/16 cm³Step-by-step explanation:
Given that the:
Width (W) = 5/8 cmHeight (H) = 2/3 cmLength (L) = 3/4 cmFind the volume of the cuboid!
Volume equation =
W × H × L =
5/8 × 2/3 × 3/4 =
(5×2×3)/(8×3×4) =
30/96 =
5/16 cm³The volume = 5/16 cubic centimetres
____________________
#IndonesianPride - kexcvi
Which expression is equivalent to 4(-2c) - c
-6c
8c - 1
-9c
7c + 1
I'm not good at this stuff -_-
Answer:
none of those?
Step-by-step explanation:
4(-2c) = -8c
Answer: -9c
Step-by-step explanation:
4(-2c) - c
= -8c - c
= -9c
-9c is the answer
Gribbles are small, pale white, marine worms that bore through wood. While sometimes considered a pest since they can wreck wooden docks and piers, they are now being studied to determine whether the enzyme they secrete will allow us to turn inedible wood and plant waste into biofuel.1 A sample of 50 gribbles finds an average length of 3.1 mm with a standard deviation of 0.72. Give a best estimate for the length of gribbles, a margin of error for this estimate (with 95% confidence), and a 95% confidence interval.
Answer:
The best estimate for the length of gribbles is of 3.1 mm.
The margin of error for this estimate, with 95% confidence, is of 0.2 mm.
The 95% confidence interval is between 2.9 mm and 3.3 mm.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
Best estimate for the length of gribbles
The best estimate is the sample mean, that is 3.1 mm.
Margin of error:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.01
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.01\frac{0.72}{\sqrt{50}} = 0.2[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error for this estimate, with 95% confidence, is of 0.2 mm.
Confidence interval:
The lower end of the interval is the sample mean subtracted by M. So it is 3.1 mm - 0.2 mm = 2.9 mm
The upper end of the interval is the sample mean added to M. So it is 3.1 mm + 0.2 mm = 3.3 mm
The 95% confidence interval is between 2.9 mm and 3.3 mm.
(7-9i)(4-2i)multiply and simplify
Answer: -32-126i
Step-by-step explanation:
If Brittany walks 4 miles in 50 minutes, then Brittany will walk how far in 90 minutes if she walks at the same speed the whole time? If necessary round your answer to the nearest tenth of a mile
Answer:
Wrong Anewer, I can't delete my answer so I just edited this in
Answer: try calculating it this is very easy that’s why you just have to times it
ing
Step-by-step explanation: