Answer:
a) The probability of a tie is the probability of getting the same outcome in both dice.
First, we roll die A and we get a given outcome. (here the probability is 1 because there is no restriction)
Now we need to roll die B and get the same outcome, so here we have only one possible outcome out of 6, then in this case the probability is 1/6
The joint probability (the product of the individual probabilities) is: P = 1*(1/6) = 1/6
b) We want to find the probability that die A wins.
Here we need to analyze each possible outcome for die A.
Let's define:
pₙ = probability of winning given that the outcome is n.
If the outcome is a 1, die A can only lose or tie, then here:
p₁ = 0
If the outcome is a 2, then die A only wins if die B rolls a 1, (1 outcome out of 6)
Then the probability of winning is:
p₂ = 1/6
If the outcome is a 3, then die A wins if die B rolls a 1 or a 2, here we have two possible outcomes out of 6.
p₃ = 2/6
We already can see the pattern, if the outcome is a 4, we get:
p₄ = 3/6
if the outcome is a 5:
p₅ = 4/6
if the outcome is a 6:
p₆ = 5/6
The total probability is the sum of all the joint probabilities:
For each roll in dice A, the probability is 1/6 (the probability of getting a given outcome)
Then the probability that die A wins is:
P = (1/6)*p₁ + (1/6)*p₂ + ... = (1/6)*(p₁ + p₂ + p₃ + p₄ + p₅ + p₆)
P = (1/6)*(0 + 1/6 + 2/6 + 3/6 + 4/6 + 5/6)
P = (1/6)*(15/6) = 0.4167
Part B if the height of each prism is 10 Cm what is the surface area prism
Answer:
Prism A:
[tex]Area = 288cm^2[/tex]
Prism B:
[tex]Area =250cm^2[/tex]
Step-by-step explanation:
Given
See attachment for prisms
[tex]Height(h) = 10cm[/tex]
Required
Determine the surface area of both prisms
Prism A is triangular and as such, the surface area is:
[tex]Area = 2 * A_b + (a + b + c) * h[/tex]
Where
[tex]A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}[/tex]
and
[tex]s = \frac{a + b + c}{2}[/tex]
Such that a, b and c are the lengths of the triangular sides of the prism.
From the attachment;
[tex]a = 8; b =6; c =10[/tex]
So, we have:
[tex]s = \frac{a + b + c}{2}[/tex]
[tex]s = \frac{8 + 6 + 10}{2}[/tex]
[tex]s = \frac{24}{2}[/tex]
[tex]s = 12[/tex]
Also:
[tex]A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}[/tex]
[tex]A_b = \sqrt{12 * (12 - 8) * (12 - 6) * (12 - 10)}[/tex]
[tex]A_b = \sqrt{576}[/tex]
[tex]A_b = 24[/tex]
So:
[tex]Area = 2 * A_b + (a + b + c) * h[/tex]
[tex]Area = 2 * 24 + (8 + 6 + 10) * 10[/tex]
[tex]Area = 288cm^2[/tex]
Prism B is a rectangular prism. So, the area is calculated as:
[tex]Area = 2 * (ab + bh + ah)[/tex]
From the attachment
[tex]a = b = 5[/tex]
[tex]h =10[/tex]
So:
[tex]Area =2 * (5 * 5 + 5 * 10 + 5 * 10)[/tex]
[tex]Area =250cm^2[/tex]
Find the 4th term in the sequence
with the following definition:
a1 = 0
an = 2(an-1 -3)
Answer:
-42
Step-by-step explanation:
[tex]a_{1}=0\\a_{n}=2(a_{n-1}-3)\\a_{2}=2(a_{1}-3)=2(0-3)=-6\\a_{3}=2(a_{2}-3)=2(-6-3)=-18\\a_{4}=2(a_{3}-3)=2(-18-3)=-42[/tex]
Please help me with this ASAP ASAP please please help please please
Answer:
Step-by-step explanation:
For the lateral area we have to find the perimeter:
p = 2 x 8 x π
p = 16 π
now we can find it
LA = p x height
LA = 16 π x 3 = 48 π
for find the the surface area we have to find the base area
Base area = radius^2 π
base area = 8^2 π = 64 π
now can we find it
SA = 2 x base area + LA
SA = 2 x 64π + 48π = 128π + 48π = 176π
V = base area x height
V = 64π x 3 = 192 π
help plzzzzzz!!!!!!!
Answer:
just count how many shapes like the front triangle is one face
Answer:
2 triangle faces, 3 rectangle faces. Thank me later
What amount of fencing (in feet) is needed?
(b)What is the total cost (in dollars) of the fencing if it costs $1.69 per foot?
Helene paid back $100 in the Month 1 of her loan. In each month after
that, Helene paid back $50. The graph shows the sequence. Write an
explicit rule, using function notation, to model the situation.
a car travels 60km in 36minutes.At the same average speed, how far will it travel in 1 hour 12 minutes
Answer:
120km
Step-by-step explanation:
1hr 12 min is double 36 minutes
so just double 60
In ALJK, k = 480 cm, j = 420 cm and LJ=43°. Find all possible values of ZK, to the
nearest 10th of a degree.
Answer:
[tex]K \approx 51.2^\circ[/tex]
[tex]K \approx 128.8^\circ[/tex]
Step-by-step explanation:
Given
[tex]k = 480[/tex]
[tex]j = 420[/tex]
[tex]\angle J = 43^\circ[/tex]
Required
Find the measure of K
The value of K ranges from: [tex]0^\circ \le K \le 180^\circ[/tex]
To do this, we apply sine rule;
[tex]\frac{j}{\sin J} = \frac{k}{\sin K}[/tex]
So, we have:
[tex]\frac{420}{\sin 43} = \frac{480}{\sin K}[/tex]
Cross multiply
[tex]\sin K * 420 = \sin 43 * 480[/tex]
Make sin K the subject
[tex]\sin K= \frac{\sin 43 * 480}{420}[/tex]
[tex]\sin K= \frac{0.6820 * 480}{420}[/tex]
[tex]\sin K= 0.7794[/tex]
Take arc sin of both sides
[tex]K = sin^{-1}(0.7794)[/tex]
[tex]K \approx 51.2^\circ[/tex]
Recall that: [tex]0^\circ \le K \le 180^\circ[/tex]
The other possible value of K is:
[tex]K \approx 180 - 51.2[/tex]
[tex]K \approx 128.8^\circ[/tex]
Miguel is posting photos on a school website. He has 48 photos, and he is allowed to
use 12 pages. He wants to put the same number of photos, p, on each page.
1) Which equation represents the situation?
Answer:
12p=48
Step-by-step explanation:
PLEASE HELP THIS IS VERY IMPORTANT I WILL GIVE YOU BRAIN THING IF ITS CORRECT (you can use a calculator if you want)
9514 1404 393
Answer:
BA, EDStep-by-step explanation:
Yes, it is very important. The idea here is that the decimal point in division problems like these can be moved the same number of places in the same direction in each number without changing the result.
__
1. Without a calculator, this is about 8/5, which you know to be more than 1 and less than 4. The only suitable answer choice is the correct one:
B 1.645 ft.
__
2. Moving the decimal point 1 place to the left in both numbers, we have ...
(892×10) ÷ (8×10) = 8290 ÷ 80 . . . . matches A
Moving the decimal point 3 places to the left in both numbers, we have ...
(892×0.001) ÷ (8×0.001) = 0.892 ÷ 0.008 . . . . matches E
The other choices did something other than move the decimal point the same number of places. (Your calculator can verify this.)
__
3. Moving the decimal point 3 places to the right, we have ...
(4367×1000) ÷ (0.004×1000) = 4,367,000 ÷ 4 ≈ 1,000,000
_____
Additional comment
For numbers like the ones in problem 3 that differ substantially in magnitude, it can work well to adjust the decimal points in both numbers so the divisor is between 1 and 10. This lets you easily estimate the position of the decimal point in the quotient.
Of course, if you're doing long division by hand, you always adjust the decimal points so the divisor is an integer (possibly with no trailing zeros).
Find the x in each triangle
HELP NOW!!!! PLSSS
Answer:
8 CM
Step-by-step explanation:
(Hypotenuse)²=(Base)²+(Height)²
10²=X+6².
100=X+36
100-36=X ( by transposition method )
√64=X
8=X
Simplify:
12(5 + 5)2 - 17 +3
Answer:
My first answer: 5 + 5 = 10 x 12 = 120 x 2 = 240 - 17 = 223 + 3 = 226
If not then,
12 x 5 + 12 x 5 = 120 x 2 = 240, 17 + 3 = 20, 240 - 20 = 220
Step-by-step explanation:
Numbers in parenthesis are evaluated first.
Answer:
1186 --- Sorry if I'm wrong -_-
Step-by-step explanation:
Add: 5 + 5 = 10
Exponentiation: the result of step No. 1 ^ 2 = 10 ^ 2 = 100
Multiple: 12 * the result of step No. 2 = 12 * 100 = 1200
Subtract: the result of step No. 3 - 17 = 1200 - 17 = 1183
Add: the result of step No. 4 + 3 = 1183 + 3 = 1186
Plz help me in math problem Its easy I just want to know how to solve this equation.
Polydactyl cats are cats with extra toes. A researcher believes that the proportion of the population of polydactyl cats in region A is greater than the proportion in region B. Let pB represent the population proportion of polydactyl cats in region A, and let pB represent the population proportion of polydactyl cats in region B. Which of the following are the appropriate hypotheses to test the researchers belief?
A. H0 : PA - PB = 0
Ha : PA is not equal to 0.
B. H0 : PA - PB = 0
Ha : PA - P > = 0
C. H0 : PA - PB = 0
Ha : PA - 0 < 0
D. H0 : P^a - P^b = 0
Ha : P^a - P^b is not equal to 0
E. H0 : P^a - P^b = 0
Ha : P^a - P^b > = 0
Answer:
The answer is "Option B".
Step-by-step explanation:
The null hypothesis relates to either the initial reality in which no significant statistically meaningful evidence stays; else the equal variances which would be the reverse of the zero become preferred rather than the zero. From the above case, that scientist claimed that 'the proportion of main coon cats' community in region A surpassed these in region B.' The alternate theory is Ha: PA - PB > = 0 whereas the Null is from the idea that Polydactyl cats were the same as in areas A and B.
Evaluate the math problem
Answer:
b. 25
Step-by-step explanation:
The square root cancels out
and you divide only 100 and 4
Answer:
5 or 25
Step-by-step explanation:
I first got the 25 but when I tried a different formula to make sure it's correct I got 5.
On the Navajo Reservation, a random sample of 218 permanent dwellings in the Fort Defiance region showed that 60 were traditional Navajo hogans. In the Indian Wells region, a random sample of 139 permanent dwellings showed that 19 were traditional hogans. Let p1 be the population proportion of all traditional hogans in the Fort Defiance region, and let p2 be the population proportion of all traditional hogans in the Indian Wells region.
(a) Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)
lower limit
upper limit
(b) Examine the confidence interval and comment on its meaning. Does it include numbers that are all positive? all negative? mixed? What if it is hypothesized that Navajo who follow the traditional culture of their people tend to occupy hogans? Comment on the confidence interval for p1 – p2 in this context.
Because the interval contains only positive numbers, we can say that there is a higher proportion of hogans in the Fort Defiance region.Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of hogans in the Fort Defiance region. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that there is a higher proportion of hogans in the Indian Wells region.
Answer:
Step-by-step explanation:
On the Navajo Reservation, a random sample of 218 permanent dwellings in the Fort Defiance region showed that 60 were traditional Navajo hogans. In the Indian Wells region, a random sample of 139 permanent dwellings showed that 19 were traditional hogans. Let p1 be the population proportion of all traditional hogans in the Fort Defiance region, and let p2 be the population proportion of all traditional hogans in the Indian Wells region.
(a) Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)
lower limit
upper limit
(b) Examine the confidence interval and comment on its meaning. Does it include numbers that are all positive? all negative? mixed? What if it is hypothesized that Navajo who follow the traditional culture of their people tend to occupy hogans? Comment on the confidence interval for p1 – p2 in this context.
Because the interval contains only positive numbers, we can say that there is a higher proportion of hogans in the Fort Defiance region.Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of hogans in the Fort Defiance region. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that there is a higher proportion of hogans in the Indian Wells region.
what's the range of 7,5,7,8,6
Answer:
3
Step-by-step explanation:
Define the range of a list of numbers.
I'm not %100 percent certain because I learned that a long time ago.
Answer: 3
Step-by-step explanation:
The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number.- source
SOO the first thing we have to do is find the smallest and largest numbers : 5 (smallest), 8 (largest).
Then we have to substract5 from 8 (8-5= 3)
The range is 3!
If you need extra help you can go to the site khanacademy as they give educational videos and practice on how to do the standards. Ever since I started using it I have become an A students.
I hope this helps and may God bless you! Have a nice day, bye!
Help quick pleaseee.........
Answer:
a) 341
b) 7243
c) 11018
d) 33000
FOR BRAINLIST!!
While building the White House model for the
iconic movie Independence day the movie makers
had to use a scale drawing in which the height of
the scale was 2 feet and the actual height of the
White house was 70 feet. If the actual length of the
white house is 168 feet, what is the length of the
scale model in feet?
А.
4.8 ft
B.
1.2 ft
5 ft
58.8 ft
Answer:
4.8
Step-by-step explanation:
Since the scale is 2 feet and the real is 70 to find the cale factor you do 70/2. Since the answer to that is 35 the scale factor is 35. SO to find tha drawing scale factor in feet you do 168/35 to get 4.8,
What is the slope of the terminal ray?
Answer:
-1.52
-0.990 radians
No
2.15 radians
Step-by-step explanation:
The slope is equal to the y-coordinate/x-coordinate = -32/21 = -1.52
Then, tan^-1(m)=tan^-1(-32/21)=-0.990 radians
This does not give the correct value of theta, however.
The correct value of theta is tan^-1(-32/21)+pi=2.15 radians
order of operations problem please help
Answer:
36 .......................
Answer:
1/2
Step-by-step explanation:
What is the value of the expression -3(3+2)
Answer:
-15
Step-by-step explanation:
8 - 6 ÷ 3 + 11 =
what is the answer
Answer:
17
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
You would use pemdas to solve this so since there is no parentheses, exponents, or multiplication you would do the division first and then the subtractions then addition because the subtraction comes first in this equation. 6 divided by 3 is 2 then 8 - 2 = 6 and then 6 + 11 = 17
How much work is needed to move a 40 pound box a distance of 2 feet?
????-foot pounds
Answer:
80-foot pounds
Step-by-step explanation:
As per the given data, the work needed to move the 40 pound box a distance of 2 feet is 79.86 foot-pounds.
What is work done?In physics, work is defined as the product of force and displacement, where force is the applied force and displacement is the distance moved by the object in the direction of the applied force.
To calculate the work needed to move a 40 pound box a distance of 2 feet, we need to use the formula:
Work = Force x Distance x Cos(theta)
where Force is the amount of force applied to move the box, Distance is the distance moved, and Cos(theta) is the cosine of the angle between the force vector and the direction of motion.
Assuming that the force is applied in the same direction as the motion, the angle between the force vector and the direction of motion is 0, and thus Cos(0) = 1. Therefore, the formula simplifies to:
Work = Force x Distance
We are given that the box has a weight of 40 pounds. Since weight is a type of force, we can use the formula:
Force = Mass x Acceleration due to gravity
where Mass is the mass of the box and Acceleration due to gravity is the gravitational acceleration constant, which is approximately 32.2 feet per second squared.
Converting the weight of the box from pounds to slugs (the unit of mass in the English system of units) gives:
Mass = Weight / Acceleration due to gravity = 40 pounds / 32.2 feet per second squared = 1.24 slugs
Therefore, the force required to move the box is:
Force = Mass x Acceleration due to gravity = 1.24 slugs x 32.2 feet per second squared = 39.93 pounds-force
Finally, we can calculate the work needed to move the box a distance of 2 feet as:
Work = Force x Distance = 39.93 pounds-force x 2 feet = 79.86 foot-pounds
Therefore, the work needed to move the 40 pound box a distance of 2 feet is 79.86 foot-pounds.
For more details regarding work done, visit:
https://brainly.com/question/13662169
#SPJ3
Write linear equations in slope intercept form using the graph...
Answer:
Y = - x + 4
Step-by-step explanation:
What is the equation of a circle with center (2, 3) that passes through the point (5, 3)
Answer:
(x−2)^2+(y+1)^2=26
Step-by-step explanation:
https://socratic.org/answers/456712
Question 4:
QA: once is the depth of each diver for three minutes from now
QB: in how many minutes will the assistant be 33.3 m below the surface
QC: according to the algebraic model, in how many minutes will the divers be at the same depth
Answer:
a. Jacques will be 46.4m below the surface and his assistant will be 78.1m below the surface.
b. 10 minutes
c. 6 minutes
Step-by-step explanation:
Let the equation for Justin's motion be J(x)=-13.9-7.5x (where J(x) is his distance from the surface in metres and x is time in minutes), because he starts off 13.9m below the surface and descends 7.5m every minutes.
Let the equation for the assistant be a(x)=-97.3=+6.4x (where a(x) is his distance from the surface in metres and x is time in minutes), because he starts off 97.3m below the surface and ascends 6.4m every minutes.
a.
J(x)=-13.9-7.5x
J(3)=-13.9-7.5(3)=-13.9-22.5=-36.4
a(x)=-97.3=+6.4x
a(3)=-97.3+6.4(3)=-97.3+19.2=-78.1
b.
a(x)=-97.3=+6.4x
-33.3=-97.3=+6.4x
64=6.4x
x=10
c.
when divers are at the same depth, J(x)=a(x)
J(x)=a(x)
-13.9-7.5x=-97.3=+6.4x
83.4=13.9x
x=6
Write the word sentence as an equation. Then solve the equation.
A number k increased by 7 is 34.
An equation that represents this word sentence is
.
The solution is k=
.
Answer:
27
Step-by-step explanation:
Here's the complete question:
Write the word sentence as an equation. Then solve the equation. A number k increased by 7 is 34.
An increase in k simply means that there's an addition. This will be:
k + 7 = 34
k = 34 - 7
k = 27
Therefore, the value of k is 27
Step-by-step explanation:
Answer:
k = 34 - 7
k = 27
Step-by-step explanation:
increased by 7 = 34 which is means,
this number was 27
The solution is Equation: k = 34 - 7
Solution: k = 27
please tell me please
Answer: H
Step-by-step explanation: H. Its H
Sorry, Here watch this
|l
|l \
|l (( \
|l / |
|l
Answer:
44
Step-by-step explanation: