Two standard dice are thrown. Determine the theoretical probability that the sum is
a) 4 b) 7
c) an even number d) not a 6 e) not a perfect square
Step-by-step explanation:
there are 36 (6×6) possible results and number combinations for 2 dice.
a)
to create a sum of 4 we need one of the following combinations :
1 3
2 2
3 1
so, 3 out of the overall possible 36 possibilities.
and that means the probability is 3/36 = 1/12
b)
to create a sum of 7 we need one of the following combinations :
1 6
2 5
3 4
4 3
5 2
6 1
so, 6 out of the overall possible 36 possibilities.
and that means a probability of 6/36 = 1/6
c)
since the possible outcomes in that regard are only 2 (even and uneven), with equal balance the probability is 1/2.
make it more formal ?
to get an even sum, every possible number on one die can be combined with 3 possibilities on the other.
1 can be combined with 1, 3, 5
2 with 2, 4, 6
3 with 1, 3, 5
4 with 2, 4, 6
5 with 1, 3, 5
6 with 2, 4, 6
these are 6×3 = 18 combinations of of the possible 36.
so, the probability is 18/36 = 1/2
d)
not a 6 ?
so, what does that mean ?
we are looking only at 5 possible outcomes per die.
that is 5×5 = 25 combinations out of the possible 36.
that means that probabilty is 25/36.
e)
not a perfect square ?
we have in the range of the possible sums with 2 dice (2 .. 12) only two perfect squares : 4 and 9
so, the sum must NOT be 4 AND NOT be 9.
so, here it might be easier to count the unwanted cases and then deduct the probability from 1 to express the opposite.
the combinations to get 4 we have already under a)
3 combinations with 3/36=1/12 probability.
the combinations to get 9
1 none
2 none
3 6
4 5
5 4
6 3
so, 4 combinations with a probability of 4/36 = 1/9
therefore, we have (3+4) = 7 cases out of the possible 36 we actually want to avoid.
so, the probability to get any one of the other (desired) combinations is therefore (36-7)/36 = 29/36
The probabilities are:
a) 0.083b) 0.167c) 0.5d) 0.861e) 0.806.How to get the probabilities?The probability for a given outcome is given by the quotient between the number of combinations that give that outcome and the total number of combinations.
Here each dice has 6 possible outcomes, so the total number of combinations for the two dice is:
6*6 = 36 combinations.
a) Here we need to count how many combinations add to 4, the notation I will use is:
dice 1 dice 2
1 3
3 1
2 2
There are 3 combinations that add to 4, then the probability of getting a sum equal to 4 is:
P = 3/36 = 0.083
b) Same thing as before, this time we count the combinations that add to 7.
dice 1 dice 2
1 6
6 1
5 2
2 5
4 3
3 4
There are 6 combinations that add to 7, so the probability is:
P = 6/36 = 0.167
c) The possible even numbers are: {2, 4, 6, 8, 10, 12}
A way of doing this, is:
If the first dice is even/odd, then the second also must be even/odd.
Then the probability is just 1/2 = 0.5 (because there are the same number of odd and even numbers in a dice).
d) The sum must not be equal to 6, the combinations that add up to 6 are:
dice 1 dice 2
2 4
4 2
3 3
1 5
5 1
So 5 combinations add up to 6, then there are 31 combinations that do not add up to 6, this means that the probability of not getting a sum equal to 6 is:
P = 31/36 = 0.861
e) The perfect squares are 4 and 9, we already know that 3 combinations add up to 4, now let's find the combinations that add up to 9.
dice 1 dice 2
6 3
3 6
5 4
4 5
So 4 combinations add up to 9, then there is a total of 7 combinations that give a perfect square, then there are 29 combinations that do not add to a perfect square.
The probability is:
P = 29/36 = 0.806
If you want to learn more about probability, you can read:
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Ahmed went for a walk and covered 5-kilometre distance in 25
minutes. Help him to find his speed of walking.
5/0.25 = 20km/h
or
5000/1500 = 3.33m/s
Answer:
help with this https://brainly.com/question/25211060
Step-by-step explanation:
Sidney originally had c cups of Greek yogurt. He used 1.75 cups to make a salad dressing and now he has 5.5 cups left over. Which equation can be used to determine the value of c?
A.1.75c=5.5
B. c/1.75=5.5
C.c-1.75=5.5
D. 1.75+c-5.5
please help me !!! and thank youu !
Answer:
a=-3
b=-63
c= 2
d=8
e=9
f=128
h=-21
i=24
Step-by-step explanation:
4/8 x 4/8
i want some friends
answer if you like and comment if you want to be my friend
Answer:
i will be ur friend........ with pleasure
Answer:
1/8
Step-by-step explanation:
Have a good
bye bye
answer the question no link or bot
Answer:
4^(-14)
Step-by-step explanation:
When multiplying or dividing powers of the same number, you can just add or subtract the powers.
How do you write 3.866 x 10^15 in standard form?ASAP BRAINLIST
Answer:
3866000000000000
Step-by-step explanation:
you move the decimal 15 spaces to the right
Logan and his father each have a sandwich and a drink for lunch at a restaurant. A sandwich costs $5.25 and a drink costs $1.75. Logan's father leaves a 20% tip. What is the amount of the tip?
Answer:
$1.4
Step-by-step explanation:
$5.25 + $1.75 = $7
20/100 × $7
= 20× 7 /100
= 140/100
= $1.4
What is 6(x+4) 1 hehe
Answer:
2
Step-by-step explanation:
two plus four equals six
What value of n makes the equation true -1/5+7=2
Answer:
where is the n in the equation?
Step-by-step explanation:
Charlie drove 495 miles in 9 hours. How long would it take to drive 715 miles?
Answer:
13 hours
Step-by-step explanation:
if he drives 495 miles in 9 hours, he drives 55 miles each hour. 55x13=715
Answer:
13 hours
Step-by-step explanation:
Charlie drove 495 miles in
= 9 hours
∴ Rate
= miles/hours
= 495/9
= 55 miles per hour
∴ No. of hours to travel 715 miles
= miles/miles per hour
= 715/55 hours
= 13 hours
Thus, 13 hours would it take to drive 715 miles.
Which can be used to prove that lines P and Q are parallel?
A)same-side exterior angle theorem
B)converse of the alternate interior angles theorem
C)converse of the same-side interior angles theorem
D)converse of corresponding angles postulate
Answer:
B
Step-by-step explanation:
the converse of alternate interior angles theorem states that if two lines are intersected by a transversal forming congruent alternate interior angles then the lines are parallel.
You deposit 572.30 for an account that pays 4.5% interest how much interest you earn after six years
Answer:
$154.52
Step-by-step explanation:
First, you need to know the formula for this type of question.
The formula is I = Prt. These variables are: I = Interest, P = Principle investment, r = Rate, and t = Time.
So, your equation is I = 572.30(0.045)(6), where you have to find "I".
If you multiply 0.045 and 6, you get 0.27. Then, you multiply 0.27 and 572.30, which is 154.521.
The interest you earn will be $154.521. You can round the thousandths digit based on how you have been taught to do, but I will round the answer to 154.52.
Good luck!
For each pair of functions f and g below, find S (8 (x)) and
Please help
9514 1404 393
Answer:
(a) f(g(x)) = g(f(x)) = x; functions are inverses
(b) f(g(x)) = g(f(x)) = x +4; functions are not inverses
Step-by-step explanation:
(a)f(g(x)) = f(1/(6x)) = 1/(6(1/(6x))) = 1/(6/(6x)) = 1/(1/x)
f(g(x)) = x
__
g(f(x)) is the same, because f(x) = g(x).
g(f(x)) = x
f and g are inverses of each other__
(b)f(g(x)) = f(x +2) = (x +2) +2
f(g(x)) = x +4
__
g(f(x)) is the same, because f(x) = g(x).
g(f(x)) = x+4
__
f and g are not inverses of each otherIf k = -5 find the value of -7k? Please explain step by step or show work on piece of paper to get marked.
Answer:
35
Step-by-step explanation:
Given k=-5
Substitute into the equation given
-7(-5) = 35
if a box holds 24 1/8-in cubes what is the volume
Answer:
the box volume is 34
Step-by-step explanation:
so you add then multiply 24 by 1/8 and that make 34 and sorry if it's not correct I'm bad at matg
Which best describes the value of 8 in 3.458?
Since 8 is in the thousandths place, the value of the digit is 0.008.
Since 8 is in the hundredths place, the value of the digit is 0.08.
O Since 8 is in the thousandths place, the value of the digit is 0.08.
Since 8 is in the hundredths place, the value of the digit is 0.008.
Answer:
Since 8 is in the thousandths place, the value of the digit is 0.008.
um I hope that's correct.
Which equation shows the quadratie formula used correctly to solve 7x? = 9+X for x?
Exact form niya is ung pang c
last answer(4 )
x=7x^2-x-9
HELP ME, THE MIDPOINT OF AB IS M (-4,-7). If the coordinates of A are (-7,-6) what are the coordinates of B?
Answer:
(-1,-8)
Step-by-step explanation:
Multiply each value of midpoint by 2 and take away given points coordinates
the differentiation of x^4 + y^4=0 is..?
Answer:
I am doinnnnnmngggg gggg
What is the distance between -33 and -18.5 on a number line
Step-by-step explanation:
The distance between two numbers in a number line is obtained by subtract the two numbers. The order of the subtraction starts with the number a bigger value followed by the number with the smaller value. For example,
x
and
y
are the two numbers and
x
≥
y
, then the correct order should be
x
−
y
.
Answer and Explanation:
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Given the numbers
7
and
−
11
on the number line, find the distance between the two numbers.
Solution:
Since
7
is...
Please answer this question!!!
Answer:
C: 3x (x-3)=0
Step-by-step explanation:
3x=0 or x-3=0
x=0 or x=3
Steven drove 12,060 miles in the last 12 months. On average, how many miles did Steven drive each month?
The average distance traveled by Steven in 1 month is 1,005 miles.
What is the average?In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. Scoring an average of 85 on the test means may signify a value in the middle of two extremes or the simple average.So, average miles traveled in 1 month:
Distance Steven drove is 12060 miles.Distance traveled in 12 months.So, the average distance traveled in 1 month is:
12060/12 1005 milesTherefore, the average distance traveled by Steven in 1 month is 1,005 miles.
Know more about averages here:
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Answer:
The average distance traveled by Steven in 1 month is 1,005 miles.
Step-by-step explanation:
measurements <2 and <4 are??
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Acording to given figure, The Angles 2 and 4 forms :
Alternative Exterior Angles ~Find an expression which represents the difference when (-9x +9) is subtracted
from (x + 8) in simplest terms.
Answer:
10x - 1
Step-by-step explanation:
(x + 8) - (-9x + 9) = x + 8 + 9x - 9 = (x+9x) + (8-9) = 10x -1
The equivalent Expression is (10x- 1).
What is Expression?An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.
For example, A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.
Given:
We have to find the difference when (-9x +9) is subtracted from (x + 8)
so, (x + 8) - (-9x + 9)
= x + 8 + 9x - 9
= (x+9x) + (8-9)
= 10x -1
Hence, the equivalent Expression is (10x- 1).
Learn more about Expression here:
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Help omg if so thank you.
Answer:
35
Step-by-step explanation:
49*5/7
=35
Pls help me with this question
Answer:
-1;undefined;1;0
Step-by-step explanation:
The first one (-9/9), can also be written as - 9/9 = - 1.
The second one (9/0), is undefined because every single term even 0 itself, if you divide it by 0, it'll be undefined!
The third one, we see we have division, and whenever we have division or multiplication and also 2 negative signs, they cancel each other, as you're left with 9/9=1.
The fourth one, whenever you have 0 at the numerator, no matter the denominator(only matters when it's =0, but that's undefined), the result will always be 0 !
To find the quotient of 3 1/6 multiply 3 by? A.1/6 B.3/6 C.3 or D.6?????!!!!! Hellpppppp meeeeeeeeee
Step-by-step explanation:
first, you multiply 3 by 6 and then add 1 to the answer the quotient will be 19/6
Each workbook is 3/8in thick. How many inches thick is a stack of 5 workbooks
Answer:
15/8 or 1 7/8
Step-by-step explanation:
Multiply the numerator by the number of workbooks (5)
You get 15/8.
Simplify
The length of 5 workbooks is 7 1/8 inch.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Thickness of workbook = 3/8 inch
Total workbooks = 5
So, the thickness of 5 workbooks
=5* 3/8
=15/8
=7 1/8 inch
Hence, the thickness of 5 workbooks is 7 1/8 inch.
Learn more about unitary method here:
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25² x 4² square root
Answer:
25.317977802344
Step-by-step explanation:
25x25= 625
4x4= 16
625+16= 641
The square root of 641 is 25.317977802344
n this case we are going to use the 'Babylonian Method' to get the square root of any positive number.
We must set an error for the final result. Say, smaller than 0.01. In other words, we will try to find the square root value with at least 1 correct decimal place.
Step 1:
Divide the number (641) by 2 to get the first guess for the square root.
First guess = 641/2 = 320.5.
Step 2:
Divide 641 by the previous result. d = 641/320.5 = 2.
Average this value (d) with that of step 1: (2 + 320.5)/2 = 161.25 (new guess).
Error = new guess - previous value = 320.5 - 161.25 = 159.25.
159.25 > 0.01. As error > accuracy, we repeat this step again.
Step 3:
Divide 641 by the previous result. d = 641/161.25 = 3.9751937984.
Average this value (d) with that of step 2: (3.9751937984 + 161.25)/2 = 82.6125968992 (new guess).
Error = new guess - previous value = 161.25 - 82.6125968992 = 78.6374031008.
78.6374031008 > 0.01. As error > accuracy, we repeat this step again.
Step 4:
Divide 641 by the previous result. d = 641/82.6125968992 = 7.7591072555.
Average this value (d) with that of step 3: (7.7591072555 + 82.6125968992)/2 = 45.1858520774 (new guess).
Error = new guess - previous value = 82.6125968992 - 45.1858520774 = 37.4267448218.
37.4267448218 > 0.01. As error > accuracy, we repeat this step again.
Step 5:
Divide 641 by the previous result. d = 641/45.1858520774 = 14.1858562034.
Average this value (d) with that of step 4: (14.1858562034 + 45.1858520774)/2 = 29.6858541404 (new guess).
Error = new guess - previous value = 45.1858520774 - 29.6858541404 = 15.499997937.
15.499997937 > 0.01. As error > accuracy, we repeat this step again.
Step 6:
Divide 641 by the previous result. d = 641/29.6858541404 = 21.5927760397.
Average this value (d) with that of step 5: (21.5927760397 + 29.6858541404)/2 = 25.63931509 (new guess).
Error = new guess - previous value = 29.6858541404 - 25.63931509 = 4.0465390504.
4.0465390504 > 0.01. As error > accuracy, we repeat this step again.
Step 7:
Divide 641 by the previous result. d = 641/25.63931509 = 25.0006678318.
Average this value (d) with that of step 6: (25.0006678318 + 25.63931509)/2 = 25.3199914609 (new guess).
Error = new guess - previous value = 25.63931509 - 25.3199914609 = 0.3193236291.
0.3193236291 > 0.01. As error > accuracy, we repeat this step again.
Step 8:
Divide 641 by the previous result. d = 641/25.3199914609 = 25.3159643039.
Average this value (d) with that of step 7: (25.3159643039 + 25.3199914609)/2 = 25.3179778824 (new guess).
Error = new guess - previous value = 25.3199914609 - 25.3179778824 = 0.0020135785.
0.0020135785 <= 0.01. As error <= accuracy, we stop the iterations and use 25.3179778824 as the square root.
So, we can say that the square root of 641 is 25.31 with an error smaller than 0.01 (in fact the error is 0.0020135785). this means that the first 2 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math. sqrt(641)' is 25.317977802344327.