How would you
describe the
following events, of
randomly rolling 2
dice and having a
sum that is EVEN OR
GREATER THAN 9?
Answers
The probability of the given event randomly rolling two dice and having a sum that is even or greater than 9 is 2/3.
As given,
Let us assume X is the event of the sum of two dice is even
Therefore
P(X) = The probability of having an even sum of two dice
Since all events are given in the question image, then
n(S) = Sample space = 36
X = {(1,1) , (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)}
n(X) = 18
Since
P(X) = n(A)/n(S)
P(X) = 18/36
P(X) = 1/2
Let us assume Y is the event of the sum of two dice is greater than 9, then
Y = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}
n(Y) 6
P(Y) = n(Y)/n(S)
P(Y) = 6/36
P(Y) = 1/6
P(X∪Y) = P(A) + P(B)
= 1/2 + 1/6
= 4/6
= 2/3
Therefore, probability of the given event randomly rolling two dice and having a sum that is even or greater than 9 is 2/3.
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Related Questions
in the rhombus shown below AC and BD are 6 and 4in respectively determine the area of the figure in square inches
Answers
The area of a rhombus is computed as follows:
A = p*q*1/2
where p and q are the diagonals of the rhombus.
In this case:
A = AC*BD*1/2
A = 6*4*1/2
A = 12 square inches
Find the values of x and y
Answers
Check the picture below.
[tex]13y=20x+3y\implies 10y=20x\implies y=\cfrac{20x}{10}\implies y=2x \\\\[-0.35em] ~\dotfill\\\\ 13y+(8x+y)=180\implies 14y+8x=180\implies \stackrel{\textit{substituting}}{14(\underset{y}{2x})+8x=180} \\\\\\ 28x+8x=180\implies 36x=180\implies x=\cfrac{180}{36}\implies \boxed{x=5}~\hfill \boxed{\stackrel{y = 2(5)}{y = 10}}[/tex]
In the year 2003, a person bought a new car for $12500. For each consecutive year after that, the value of the car depreciated by 7%. How much would the car be worth in the year 2005, to the nearest hundred dollars?
Answers
Answer + Explanation:
13500x0.07 = 945
945 x 2 = 1890
13500 - 1890 = 11610
To the nearest hundred dollars: 11,600
ANSWER: 11,600
The table shows the cost of shampoo at a discount store Cost $ 2.95 $4.50 $6.05 Number of bottles 1 2 3is the cost of the shampoo bottles proportional to the amount of bottles ?
Answers
Answer:
Not proportional
Explanation:
First, we determine the unit rate for each of the pairs of points.
[tex]\begin{gathered} UnitRate=\frac{\text{Cost}}{\text{Number of bottles}} \\ \frac{2.95}{1}=\$2.95\text{ per bottle} \\ \frac{4.50}{2}=\$2.25\text{ per bottle} \\ \frac{6.05}{3}=\$2.02\text{ per bottle} \end{gathered}[/tex]We see that the unit rates are not the same.
Therefore, the cost of the shampoo bottles IS NOT proportional to the number of bottles
Could I get help with this problem I have in algebra?
Answers
Answer
Explanation
Cost of a lower deck ticket = 42 dollars
Cost of an upper deck ticket = 75%
solve for y 10x+8y=4
Answers
Solve the equation.
[tex]\begin{gathered} 10x+8y=4 \\ 8y=-10x+4 \\ y=-\frac{10}{8}x+\frac{4}{8} \\ =-\frac{5}{4}x+\frac{1}{2} \end{gathered}[/tex]So y = -5/4 x +1/2.
Solve using the fractions 5/8 and 1 2/7
Answers
107/56 is the solution of fractions .
What do math fractions mean?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.The given fractions are 5/8 and 1 2/7.
We need to find the sum of given fractions.
Now, we can write 1 2/7 as 9/7.
So, 5/8 + 9/7
Here, LCM of 8 and 7 is 56
Then, 35/56 + 72/56
=(35+72)/56
=107/56
Therefore, the sum of the two given fractions is 107/56.
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The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 2". Find P(A). Outcome Probability 1 0.2 2 0.1 3 0.3 4 0.03 5 0.03 6 0.04 7 0.06 0.14 8 0.03 9 0.07 10
Answers
Solution
From the info given the numbers divisible by 2 are:
2,4,6,8,10
And the respective probabilities are:
P(2)= 0.1
P(4) =0.03
P(6)= 0.04
P(8) = 0,14
P(10)= 0.07
And addinf all the values we got:
P(A)= 0.1+0.03+ 0.04+ 0.14 +0.07= 0.38
The value of y is directly proportional to the value of x.If y=12 when x=9, what is the value of x when y=80
Answers
Step 1:
Write the formula connecting y and x.
[tex]\begin{gathered} y\text{ }\propto\text{ x} \\ y\text{ = kx} \\ k\text{ = }\frac{y}{x} \end{gathered}[/tex]Step 2:
Find the value of k when y = 12 and x = 9
[tex]\begin{gathered} k\text{ = }\frac{y}{x}\text{ = }\frac{12}{9}\text{ = }\frac{4}{3} \\ \text{Therefore} \\ y\text{ = }\frac{4}{3}x \end{gathered}[/tex]Step 3
You can find x when y = 80.
[tex]\begin{gathered} \text{Frpm y = }\frac{4}{3} \\ \text{When y = 80} \\ 80\text{ = }\frac{4x}{3} \\ \text{Cross multiply} \\ 4x\text{ = 80}\times3 \\ 4x\text{ = 240 Divide both sides of the equation by 4} \\ x\text{ = }\frac{240}{4} \\ x\text{ = 60} \end{gathered}[/tex]Final answer
x = 60
can you help me to answer 2736×2
Answers
Answer
[tex]\begin{gathered} 2\text{ 7 3 6} \\ \times\text{ 2} \\ =5\text{ 4 7 2} \end{gathered}[/tex]2 7 3 6
x 2
------------------
5
hi i need help as i try with old answer and its wrong
Answers
SOLUTION
The exercise has no question
Adalyn uses 1/5 cup of blue paint for every 2/5 cup of red paint to make purple paint. Enter the number of cups of blue paint Adalyn uses for 1 cup of red paint.
Answers
Given that;
Adalyn uses 1/5 cup of blue paint for every 2/5 cup of red paint to make purple paint.
[tex]\frac{1}{5}\text{ cups of blue paint }\rightarrow\frac{2}{5}\text{ cups of red paint}[/tex]For 1 cup of red paint, the amount of blue paints Adalyn will use is;
[tex]\frac{1}{5}\text{ cups of blue paint }\rightarrow\frac{2}{5}\text{ cups of red paint}[/tex]After 4 months of a new nutrition program rashid has lost 16% of his original weight he lost 36lb what was rashids original weight?
Answers
Rashids original weight based on the information illustrated is 225lb.
What was the original weight?From the information given, after the nutrition program rashid has lost 16% of his original weight he lost 36lb.
Let the original weight be given as x.
Therefore, 16% × x = 36
0.16x = 36
Divide through by 0.16
0.16x / 0.16 = 36 / 16
x = 36/0.16
x = 225lb
The weight is 225lb.
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Is the following relation a function? Justify your answer.
y
X
6
-1.
4
2
-1
3
O No, because there is an input value with more than one output value
O No, because there is an output value with more than one input value
Yes, because each input value has only one output value
Yes, because each output value has only one input value
Answers
No, because there is an input values with more than one output value is the following relation a function.
Based on the given function is,
x y
6 2
-1 -1
4 3
What is the Function :A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
So,
We can write,
One input value has more than output values.
In this function we have,
-1 is mapped to both -2 and -1
In this case,
-1 input value is mapped to both output values of -2 and -1.
Therefore,
No, because there is an input values with more than one output value is the following relation a function.
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at a batting cage, each set of baseballs the machine pictures cost $2.50 which inequality represents n, the number of sets of baseballs machine will pitch for no more than $15. 00?
Answers
We have that each set of baseballs cost $2.50, and for the inequality, notice that we cannot spend more than $15. Since each set cost 2.50, then the inequality to represent this situation is:
[tex]5.50n\le15[/tex]I need help on this one! Please and thank you!
Answers
Given:
[tex]\cos \theta\text{ =- }\frac{1}{8}[/tex]Solving for the angle measure:
[tex]\begin{gathered} \theta\text{ = }\cos ^{-1}(-\frac{1}{8}) \\ =\text{ }97.181 \end{gathered}[/tex]Hence, we can find the exact value of sin theta:
[tex]\begin{gathered} But\text{ }\theta\text{ is in the third quadrant.} \\ \sin (97.181\text{ -180) = sin(-82.8190}) \\ =\text{ -0.992} \end{gathered}[/tex]Hence, the exact value of sin theta is -0.992
On the first day a man did 3/8 of a job on the next day he completed another 2/5of the job what fraction the job was left undone?
Answers
Step-by-step explanation:
3/8+2/5
L.C.M=40
15+16/40=31/40
1/1-31/40
40-31/40
9/40
Instructions: Identify the type of sequence and write the explicit rule.
Answers
SOLUTION:
Case: Sequences
Method:
3, 12, 48, 192,...
Step1:
The sequence is increasing exponentially
Type: Geometric/Exponential Sequence
Step 2:
The Explicit rule is gotten from the formula:
[tex]a_n=ar^{n-1}[/tex]a= 3,
r= (12/3)
r= 4.
The rule, therefore:
[tex]a_n=3(4)^{n-1}[/tex]Final answer:
Type: Geometric sequence
Explicit rule
[tex]a_n=3(4)^{n-1}[/tex]Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Students in Mrs. McGee's third grade class are working on times tables, and they demonstrate mastery by passing tests. Rebecca has passed 12 tests so far. Her classmate, Marie, has passed 3 tests of them. From now on, Rebecca plans to take and pass 2 tests per week. Meanwhile, Marie plans to do 5 per week. At some point, Rebecca will catch up to Marie. How long will it take? How many tests will each child have passed? In weeks, the children will each have passed tests.
Answers
Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the unknown terms
Let x represents the number of weeks
Let y represents the total number of test passed
STEP 2: Interpret the statements
For Rebecca
[tex]y=2x+12[/tex]For Marie
[tex]y=5x+3[/tex]STEP 2: Find the number of weeks they will pass the same amount of test.
This means that y will be equal to y
[tex]\begin{gathered} y=y \\ 2x+12=5x+3 \\ 2x-5x=3-12 \\ -3x=-9 \\ x=\frac{-9}{-3}=3\text{ weeks} \end{gathered}[/tex]Hence, they will both pass the same number of tests in 3 weeks
STEP 3: Find the amount of tests passed
For Rebecca
[tex]\begin{gathered} 2x+12 \\ x=3 \\ y=2(3)+12=6+12=18 \end{gathered}[/tex]For Marie
[tex]\begin{gathered} y=5x+3 \\ x=3 \\ y=5(3)+3=15+3=18 \end{gathered}[/tex]Both will pass 18 tests in 3 weeks
ANSWER:
In 3 weeks, the children will each have passed 18 tests.
Salim sells fax machines that come in Standard and Enhanced models. The Standard model sells for $325 and the Enhanced model sells for $385. If Salim sold a total of 45 units and took in $15,525, how many of the Enhanced model did he sell?
Answers
fractions and geometry studying for a win test workeys
Answers
Given that the pharmacist can fill 250 prescriptions in 40 hours.
Consider the following,
[tex]\begin{gathered} 1\text{ hour}=60\text{ minutes} \\ 40\text{ hour}=40\times60=2400\text{ minutes} \end{gathered}[/tex]So it can be understood that the pharmacist can fill 250 prescriptions in 2400 minutes.
Then the time taken to fill 1 prescription is calculated as,
[tex]\begin{gathered} 250\text{ prescriptions}\equiv2400\text{ minutes} \\ \Rightarrow1\text{ prescription}\equiv\frac{2400}{250}=9.6\text{ minutes} \end{gathered}[/tex]Thus, it will take 9.6 minutes to fill 1 prescription.
Therefore, option (E) is the correct choice.
The ratio of 8 books to 20 books isA) 2:5B) 5:2C) 4:5D) 5:4
Answers
the ratio of 8 books to 20 books is:
[tex]8\colon20[/tex]now we can divide by the same number so:
[tex]\begin{gathered} \frac{8}{2}\colon\frac{20}{2} \\ \frac{4}{2}\colon\frac{10}{2} \\ 2\colon5 \end{gathered}[/tex]SO is option A)
Determine the x-intercept from the given Coordinate Pairs. * {(-1,8), (0.6). (5:5).(3,0). 1.5.-17)} O r= 3 b = 6 x = ? = -2
Answers
The x interception is when y = 0
the fouth point is (3,0), in that point y is 0 and x is 3
So the x interception is at x = 3
The answer is the first option x = 3
what is the midpoint of the segment that would be created between points L and N on the graph
Answers
Given:
The figure KLMN on graph.
Required:
what is the midpoint of the segment that would be created between points L and N .
Explanation:
We know the mid point formula
[tex]LN=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]We have L(-2, 3) and N(6, 3)
and
[tex]\begin{gathered} LN=(\frac{-2+6}{2},\frac{3+3}{2}) \\ =(\frac{4}{2},\frac{6}{2}) \\ =(2,3) \end{gathered}[/tex]Answer:
Midpoint is (2,3).
Find the area of this circle. Use3.14 for i.7 AtThe area of the circle is aboutfta.(Round to the nearest hundredth as needed.)
Answers
153.86 ft²
Explanation:[tex]\text{Area of a circle = }\pi r^{2}[/tex][tex]\begin{gathered} r\text{ = radius = 7 ft} \\ \pi\text{ = 3.14} \\ In\text{serting into the formula:} \\ \text{Area of the circle = 3.14 }\times7^2 \end{gathered}[/tex][tex]\text{Area of the circle = 153.86 ft}^2[/tex]To the nearest hundredth, Area of the circle = 153.86 ft²
Find the value of x in the triangle shown below.227ASCAssChoose 1 answer:MY= 45Col= 9MY= 5ProProD2 = 53Tea
Answers
The given triangle is a right triangle as shown by the square symbol inside. With this, we can solve the length "x" of this triangle using the Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]where c = length of the hypotenuse and "a" and "b" are any of the remaining sides.
In our triangle, we have 7 as our hypotenuse and 2 as the length of the one side. Let's apply these values in the formula above.
[tex]\begin{gathered} 7^2=2^2+b^2 \\ 49=4+b^2 \\ 49-4=4+b^2-4 \\ 45=b^2 \\ \sqrt[]{45}=\sqrt[]{b^2} \\ \sqrt[]{45}=b \\ 3\sqrt[]{5}=b \end{gathered}[/tex]Therefore, the value of x is √45.
Sort the sequences into categories. Determine which sequences are arithmetic and which are geometric. Drag each label to the correct location on the table. Each label can be used more than once. Arithmetic Sequence Geometric Sequence (90, 87, 84, 81, 78, ...) (4, 12, 36, 108, 324, ...) (8,1,1/8,1/64,1/512,...) (3, 10, 17, 24, 31,...) (1,1.4,1.8, 2.2, 2.6, ...) (3,1.5, 0.75, 0.375,...)
Answers
Given the sequences we are asked to identify whether they are geometric or arithmeti. This can be seen below.
Explanation
For an arithmetic sequence
[tex]T_2-T_1=T_3-T_2^[/tex]For a geometric sequence
[tex]\frac{T_2}{T_1}=\frac{T_3}{T_2}[/tex]Therefore;
Answer:
[tex]\begin{gathered} Arithmetic\text{ sequence}\Rightarrow90,87,84,81,78,.. \\ Geometric\text{ sequence}\Rightarrow4,12,36,108,324,... \\ Geometric\text{ sequence}\Rightarrow8,1,1/8,1/64,1/512,... \\ Arithmetic\text{ sequence}\Rightarrow3,10,17,24,31..... \\ Arithmetic\text{ sequence}\Rightarrow1,1.4,1.8,2.2,2.6.... \\ Geometric\text{ sequence}\Rightarrow3,1.5,0.75,0.375,... \end{gathered}[/tex]In this example, the rapper wants to divide a recipe in half to make a cake for 5 people instead of 10. Explain why he multiplies the first ingredient, ⅔ of a cup sugar, by ½.
Answers
Answer:1 889 - 1927 = 1889 - 1927 =9
Step-by-step explanation:
The price of a local newspaper increases from 80p to £1.
Find the percentage increase
Answers
Answer:
25%Step-by-step explanation:
The price of a local newspaper increases from 80p to £1.
Find the percentage increase
increase = Increase ÷ Original Number × 100
increase = 1 : 0.8 x 100
increase = 125
so the percentage increase is
125 - 100 =
25%
Is 4 over 14 simplified and is 15 over 20 simplified and is 21 over 35 simplified
Answers
Solution
For this case we have the following:
[tex]\frac{4}{14}=\frac{2}{7}[/tex]Then the answer is:
2/7
