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]
Find the value of x
Pls help
Answer:
x = 5
Step-by-step explanation:
the sum of the angles is 180
16x - 5 + 22x - 5 = 180
38x - 10 = 180
38x = 190
x = 5
Answer:
5
Step-by-step explanation:
As both angles situated in one straight line
➝There sum will be 180°
➝(16x-5)+(-5+22x)=180
➝16x-5-5+22x=180
➝16x+22x-5-5=180
➝38x-10=180
➝38x=180+10
➝38x=190
➝x=190/38
➝x=5
Please Help! I'll give thanks and best rate if its correct! (type link into another tab)
Answer:
x = 8
Step-by-step explanation:
Answer:
sorry bro I would but that link is super long
Step-by-step explanation:
thats what she said
HURRY I NEED HELPP!!
mr kabi invest k375 at a simple interest rate of 8.375 per annum what amount will his investment grow to over 4 years 8 months?
Answer:
I am not sure
Step-by-step explanation:
Sorry
The invested amount will be k 521.56 after 4 years 8 months if Mr. Kabi invests k375 at a simple interest rate of 8.375 per annum.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
It is given that:
Mr Kabi invest k375 at a simple interest rate of 8.375 per annum
The invested amount = k 375
Rate of interest = 8.375 per anum
Rate of interest = 8.375/12 per month
Rate of interest = 0.6979 per month
Number of months = 4x12 + 8 = 56
As we know, the formula for the simple interest is given by:
A = P(1 + rt)
A = 375(1 + 0.6979×56)
A = k 521.56
Thus, the invested amount will be k 521.56 after 4 years and 8 months if Mr. Kabi invests k375 at a simple interest rate of 8.375 per annum.
Learn more about the simple interest here:
brainly.com/question/22621039
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HELP !! giving the brainlest answer to whoever gives the correct answer !! HELPPP PLLSS LAST MINUTEEE
Answer:
D
Step-by-step explanation:
What is the quotient ?
Answer: A quotient is the the number resulting from the division of one number by another.
Step-by-step explanation:
24/4 the quotient (answer) is 6
Plz tell me if I am correct
Answer:
Yep good job!!!
Whoever gets this right gets brainliest note ( ITS 4 FUN ! NOT A GRADE) 2+4x7=?
a pet shop sells a 6 can multipack of dog food for £3.18 and a 15 can multipack for £7.80. which multipack is the best value for money
Answer:
the 15 multi pack
Step-by-step explanation:
6x+4=22
What is the value of x?
Answer:
x = 3
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other.
Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& roots)
Multiplication
Division
Addition
Subtraction
~
First, subtract 4 from both sides of the equation:
6x + 4 (-4) = 22 (-4)
6x = 22 - 4
6x = 18
Next, divide 6 from both sides of the equation:
(6x)/6 = (18)/6
x = 18/6
x = 3
3 is your value for x.
~
What number is 40% of 720
Answer:
288
Step-by-step explanation:
Hope it helps :>
Answer:
288
Step-by-step explanation:
Choose all of the expressions that can be used to find the volume of the rectangular prism.
Answer:
C. (6 × 5) × 2 = 60 m³
D. 5 × (6 × 2)
E. (2 × 5) × 6
Step-by-step explanation:
Volume of a rectangular prism can be given as, V = L*W*H
L = 6
W = 5
H = 2
However, whichever way we choose to use as either L, W, or H, we would still get the same value as the volume.
Thus:
✔️V = (6 × 5) × 2 = 60 m³
✔️V = 5 × (6 × 2) = 60 m³
✔️V = (2 × 5) × 6 = 60 m³
These are the three expressions that can be used to find the volume.
Find the 23rd term of the sequence: 77,65,53,41
Answer:
The 23rd term is -187
Step-by-step explanation:
U₂₃=??, a=77, d=-12, n=23
U₂₃=a+(n-1)d
U₂₃=77+(23-1)(-12)
U₂₃=77+22(-12)
U₂₃=-187
U₂₃=-187
∴U₂₃=-187
Use the distributive property to write an equivalent expression. 6(x+y+z)
Answer: To confuzing
Step-by-step explanation:
Is it right ????????
Answer:
yeah
Step-by-step explanation:
CALCULUS: Which of the following functions grows the fastest as x goes to infinity?
A. 2^x
B. ln(x)
C. sin(x)
D. x^20 (I put this my first try & got it wrong)
I believe D is the right answer, but I got it wrong. Can someone please tell me why?
Answer:
It is A. 2^x
Step-by-step explanation:
For relative rates of growth, we know: Log < Poly < Exponential.
This rules out B, C, and D quickly. Although, if you do L'Hôpital's rule, it might seem like A & D are very comparable. However, if you continually took the derivative of 2^x and x^20, eventually x^20 would equal zero, while 2^x would still be a variable. So, you would have:
[tex]\lim_{x \to \infty} \frac{2^{x}}{0} =[/tex] ∞
When the limit of x as it approaches infinity is infinity, then f(x) grows at a faster rate than g(x).
Also, by looking at the graph (which is attached), you can see that 2^x grows faster than x^20.
A principal of $2900is invested at 3.25% interest, compounded annually. How much will the investment be worth after 9years? Use the calculator provided and round your answer to the nearest dollar.
Given:
Principal = $2900
Rate of interest = 3.25% compounded annually.
Time = 9 years.
To find:
The amount of investment after 9 years.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right){nt}[/tex]
Where, P is principal, r is rate of interest, n number of times interest compounded in an year and t is the number of years.
Substitute P=2900, r=0.0325, n=1 and t=9.
[tex]A=2900\left(1+\dfrac{0.0325}{1}\right)^{1\times 9}[/tex]
[tex]A=2900\left(1+0.0325\right)^{9}[/tex]
[tex]A=2900\left(1.0325\right)^{9}[/tex]
Using calculator, we get
[tex]A=3867.306[/tex]
[tex]A\approx 3867[/tex]
Therefore, the worth of the investment after 9 years will be $3867.
Simplify the numeric expression below. Show all
work.
8-12-(6 + 4)
Answer:
negative 14 or -14
Step-by-step explanation:
8-12-10
= 8-22
= -14
Name the first three numbers in this sequence
_ _ _ 80, 160,320,640,1280
Answer:
10, 20, 40
Step-by-step explanation:
Answer and Step-by-step explanation:
The first three numbers are 10, 20 and 40.
This is because the sequence is being increased by twice the previous number.
To get from 10 to 20, you multiply by 2, to get from 20 to 40, we multiply by 2, to get from 40 to 80, we multiply by 2, to get to 80 to 160, we multiply by 2, and so on.
#teamtrees #PAW (Plant And Water)
Can somebody help me please
Step-by-step explanation:
First, find complete data.
That would be 2, 12 and 5, 30
Divide the output by the input to get the relationship/constant.
12/2 = 6 30/5 = 6
So...
1 x 6 = 6
and
48 / 6 = 8
9514 1404 393
Answer:
(b) Output 6, Input 8
Step-by-step explanation:
One of the things you can look at is the ratio of output to input. Here, it is constant, which makes things a lot easier
output/input = 12/2 = 30/5 = 66/11 = 6
Then for input 1, output is 1×6 = 6.
For unknown input, we have ...
input × 6 = 48
input = 48/6 = 8
__
The two blanks are ...
input: 8; output 6
What do I multiply to find the time and a half rate?
Answer:
Time and a half pay is 50% more than an employee's regular rate of pay. For every hour of overtime an employee works, you must give them their regular rate of pay plus half of that. To calculate an employee's overtime rate of pay, multiply their regular rate by 1.5.
Inverse of (1,3)(2,4)(6,8)
Answer:
{(3,1),(2,4),(6,8)}
Step-by-step explanation:
Since for inverse of (x,y), it's(y,x)
i.e. the forst term and second term of order pair switch their places
The graphs below have the same shape. What is the equation of the blue
graph?
F(X) = x2
G(X) = ?
A. G(X) = x2 + 4
B. G(X) = x2-4
C. G(X) = (x+4)2
D. G(x) = (x-4)2
Answer:D
Step-by-step explanation:
The blue graph is a 4 unit horizontal shift of the red graph. The correct equation of g(x) = [tex](x-4)^{2}[/tex].
What is horizontal shift?Given a function f , a new function g(x)=f(x−h) , where h is a constant, is a horizontal shift of the function f . If h is positive, the graph will shift right. If h is negative, the graph will shift left.
Thus, since, f(x) has shifted 4 units to the right horizontally, the correct equation of g(x) = [tex](x-4)^{2}[/tex].
Learn more about horizontal shift here
https://brainly.com/question/4173593
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convert .182 as a percentage
Answer:
18.2%
Step-by-step explanation:
For decimals, just move the point two times to the right.
Answer:
18.2
Step-by-step explanation:
0.182 x 100 = 18.2
Find the lengths of the missing side. Round your answer to the nearest tenth
Answer:
13.2
Step-by-step explanation:
using the Pythagorean theorem:
L² = 20² - 5²
L² = 400 - 225 = 175
L = 13.23
PLEASE HELP WILL MARK BRAINLIST
Answer:
the answer for question 2 is (D)
Angela opened a bank account with $0.50. Later in the week she deposited money and $24 in her account. How much money did she deposit?
Answer:
24 is the whole desposited. unless you are not counting the money she spent to open it. then it would be $23.50
Decide whether each statement is true or false. If a statement is true, say which of Euclid’s five postulates apply to it, then write the converse and contrapositive statements, and then decide which of these statements are true (it may help to rewrite the statements in “if-then” form). If it is false, give a counterexample or explain why.
a. A triangle can be drawn from any three points that are not on the same line.
b. A square can be drawn from any four points not on the same line.
c. When two lines intersect, the four angles they make add to 360 degrees.
d. There is only one parallel line to any given line.
Answer:
A) True
B) False
C) True
D) False
Step-by-step explanation:
A. This statement is True.
From euclid's postulates, if there are three straight lines that intersect each other another, and the sum of the interior angles formed between one of the straight lines and the other two straight lines is less than 180°, then it can be said that the other two straight lines will cross each other if they are both further extended on the same side of the figure in which the sum of the angles was less than 180° as we earlier said.
The converse statement is;
If three lines are drawn and two of the lines converge, then it means the third line can be drawn in such a way that the sum of the interior angles between this third line and the other two lines would be less than 180°.
The contrapositive statement is;
If the sum of the interior angles between the first line and the other two lines equals 180°,then it means that the other two lines will not intersect each other.
B. This statement is false.
The reason is because 4 sides of a square are always equal in length. As a result,all the 4 interior angles must be equal to 90°.
c. This statement is True.
From the first answer above, we saw that if there are three straight lines that intersect each other another, the sum of the interior angles formed between one of the straight lines and the other two straight lines is less than 180°.
Therefore, on the opposite side of the intersection, the sum of the adjacent angles would be equal to 180°
Thus;
180° + 180° = 360°
The converse statements is;
If two lines meet at a point then it means that the sum of the angles at that point equals 360°
The contrapositive statements is;
If the two lines do not meet at any point, then the sum of the angles on each straight line is 180°
d. This statement is False.
The reason is because there is not only one parallel line to any given line because a parallel line can be drawn from aso many points not even on the line in question.
WILL GIVE BRAINLIST PLS HELP Find z. Just write the number. Answer should be a whole number.
Answerz=16
Step-by-step explanation:
PLZ HELP DEW BY 5PM
This graph represents the relationship between x and y.What is an equation showing the relationship between x and y?Enter your answer in the box.
Answer:
Points I guess