If two fair dice are rolled, find the probability that the sum of the dice is 9, given that the sum is greater than 5.
The probability is
Answers
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Explanation:
Refer to the dice chart below. It represents all possible ways to roll two dice and sum up the face values.
According to the table, there are...
A = 1 copy of the sum "2"B = 2 copies of the sum "3"C = 3 copies of the sum "4"D = 4 copies of the sum "5"There are A+B+C+D = 1+2+3+4 = 10 instances where we get a sum between 2 and 5. The table shows 6*6 = 36 sums total. This means there are 36-10 = 26 sums where they are between 6 and 12, aka "the sum being greater than 5".
Those 26 sums are what we focus on. Out of those 26 items, four of them are sums of "9".
The probability we want is therefore 4/26 = 2/13
The probability that the sum of the dice is 9, given that the sum is greater than 5 is 0.154
See attachment for the sample space of a roll of two dice.
From the attached sample space,
The number of sum greater than 5 is: 26The number of sum greater than 5 that is 9 is: 6Represent the events that a sum is greater than 5 with A, and a sum is greater than 5 is 9 with B.
So, we have:
[tex]n(A) = 26[/tex]
[tex]n(A\ n\ B) = 4[/tex]
The probability that the sum of the dice is 9, given that the sum is greater than 5 is then calculated using:
[tex]Pr = \frac{n(A\ n\ B)}{n(A)}[/tex]
This gives
[tex]Pr = \frac{4}{26}[/tex]
[tex]Pr = 0.154[/tex]
Hence, the probability is 0.154
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Related Questions
Regina ate 25 grapes and 15 cashews. Simplify the ratio of grapes to cashews that she ate.
Answers
Answer:
The ratio would be 5 to 3
Step-by-step explanation:
I know this because you would divide the amount of grapes and the amount of cashews by 3 which would equal 5 to 3
The ratio of grapes to cashews that she ate is 5:3.
What is ratio?A ratio is the comparison of two quantities and that can be the comparisons of parts to parts, parts to wholes, and wholes to parts are all examples of ratios.
Given that, Regina ate 25 grapes and 15 cashews.
We need to simplify the ratio of grapes to cashews that she ate.
The ratio = 25/15
= 5/3
Hence the ratio of grapes to cashews that she ate is 5:3.
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a square has an area of 64 square units. if it’s side were only half as long, what would it’s area be??
Answers
Answer:
16
Step-by-step explanation:
8x8 is 64, so half of 8 is 4 so 4x4 is 16
Give the two missing numbers in the following sequences.8,9,11,14,?,23,?
Answers
Answer:
18 and 29
Step-by-step explanation:
8+0=8
8+1=9
9+2=11
11+3=14
14+4=18
18+5=23
23+6=29
As you can see, the number that you add to the previous number in the sequence is increased by 1 as the sequence grows in length. The number added goes from 0 to 1 to 2 to 3 and so on. :-)
Use the drop-down menus to complete each statement to show why 5sqrt(7) is between 10 and 15.
Answers
Answer:
First drop down: √4 and √9
Second drop down: 2 and 3
Third drop down: 10 and 15
Step-by-step explanation:
the root of four is 2
the root of nine is 3
thus √ 7 is between 2 and 3
5√7 is between 10 and 15 because 2x5 is 10 and 3x5 is 15.
hallar una ecuacion de la parabola cuyo foco es (-2,2) y cuya directriz es = -8
Answers
The equation of the parabola whose focus is (-2,2) and whose directrix is x= -8 is [tex](y+2)^2=-20(x+5)[/tex]
The standard formula for finding an equation of a parabola is expressed as [tex]y^2=4ax[/tex]
If the curve is shifted to the left and down, the equation becomes [tex](y-k)^2=4a(x-h)[/tex] where:
(h, k) is the vertex of the parabola
If the focus is at (-2, 2) and the directrix is at x = -8, the equivalent vertex of the parabola will be at (-5, -2) and the midpoint between the vertex and directrix is at a = -5
Substitute these values into the formula of the parabola.
[tex](y-k)^2=4a(x-h)\\(y-(-2))^2=4(-5)(x-(-5))\\(y+2)^2=-20(x+5)\\[/tex]
Hence the equation of the parabola whose focus is (-2,2) and whose directrix is x = -8 is [tex](y+2)^2=-20(x+5)[/tex]
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The area of a rectangle is 50 ft, and the length of the rectangle is 5 ft less than three times the width. Find the dimensions of the rectangle.
Answers
Answer:
L - 10 . W - 5
Step-by-step explanation:
Length = 3*width - 5
area = length * width
50 = (3w-5)* w
50 = 3w^2-5w
0 = 3w^2 - 5w -50
0= (3w+10)(w-5)
w = 5 , w can't equal -10/3 because width can't be negative
width is 5
Length = 3 * 5 - 5
Length = 10 , width = 5
Answer:
first lets say w is the width
50(area)=w(idth)+3(w-5)
50=w+3w+15
50=4w+15
35=4w
8.75=w
w equals 8 3/4
Hope This Helps!!!
Classify the quadrilateral, Explain your reasoning. Thank you!!
Answers
Answer: y=7, x=2
Step-by-step explanation:
∠Q+∠P=180° (∠s between 2 // lines)
97°+(12y-1)°=180°
12y-1=83°
12y=84
y=7
5x+6=8x (Iso triangle)
x=2
Can someone help plz
Answers
Problem 1
The price for one super skateboard is £75.00 which is found in cell C8. When it comes to excel spreadsheets, we always read across the top first before reading the left hand side. So the format is columnRow which may seem strange if you're used to reading the row first.
Right next to cell C8 is D8 and that's the number of super skateboards sold (26 of them). Multiply the unit price by the number of units sold to get the revenue for this particular type of item.
75*26 = 1950
Now the question is: what if the company sells more than 26 skateboards? Let's say there was an error and 30 boards were sold. To quickly recompute the correct answer, we can rely on references rather than hardcoded values.
Typing out [tex]=C8*D8[/tex] will compute the multiplication of items C8 and D8. The equal sign out front is very important. It tells the spreadsheet program that you want to do this type of operation (rather than just write out plain text). If you were to simply type in C8*D8 without the equal sign, then the result is exactly C8*D8 without filling in the variables.
Answer is =C8*D8Don't forget about the equal sign out front
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Problem 2
Like before, we'll have an equal sign as the first thing we type in. Then we'll type in Sum(E5:E14) to sum of the values from E5 to E14. You could type in Sum(E5,E6,E7,E8,E9,E10,E11,E12,E13,E14) or you could type in E5+E6+E7+E8+E9+E10+E11+E12+E13+E14; however, that would be a tedious approach prone to error. The spreadsheet program interprets the colon as a way to fill in the gap from start to end. We start at E5 and end at E14, and add up everything in between.
Note that all the cells referenced are the various revenues for each type of item. Each of these cells is computed by multiplying the C and D column items.
Answer is =Sum(E5:E14)Don't forget about the equal sign out front
===========================================================
Problem 3
There are a few other alternatives, but your teacher might be talking about adding each item one at a time. Refer to problem 2 for more info.
Answer is =Sum(E5,E6,E7,E8,E9,E10,E11,E12,E13,E14)Or
Answer is =E5+E6+E7+E8+E9+E10+E11+E12+E13+E14Don't forget about the equal sign out front
===========================================================
Problem 4
Answer: 96 poundsExplanation: Simply pick out the smallest item. The excel command is "min" and you provide it a list of values to pick from. In this case, that list being E5:E14 to represent E5,E6,...,E13,E14. So you'll type in =Min(E5:E14) similar to what you did for the "sum" command.
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Problem 5
Answer: 1950 poundsExplanation: As you can probably guess, the "max" function is used here. It picks out the largest value of a list. The command is =Max(E5:E14)
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Below I've attached two images. Figure 1 shows the commands to type in, while figure 2 shows the result of each command. In other words, it's the before and after. I used LibreOffice spreadsheet, but this applies to any spreadsheet program as they all tend to follow the same idea.
9. Machine Trades Find the width X of the V-thread shown. (Round to the
nearest thousandth.)
Answers
Answer:
X would be 1,000
Step-by-step explanation:
Prove that y = arcsinx on the root of 1 x squared satisfies the equality (1 - x squared)y' - xy = 1
Answers
Answer:
Step-by-step explanation:
The first part is a computation, combining the chain and quotient rules. We know that the derivative of f(x)=arcsin(x) is 1/sqrt(1-x2), and we need to differentiate the denominator. We use the chain rule: let u=1-x^2, and v=sqrt(u). Then du/dx=-2x, and dv/du = 1/(2 sqrt(u)). Combining, dv/dx=-x/sqrt(1-x2). Now, we put everything together using the quotient rules: y' = (f'v-v'f)/v2. Multiplying by (1-x2)=v2, we obtain (1-x2)y'= sqrt(1-x2)/sqrt(1-x2) +xarcsin(x)/sqrt(1-x2), which we can rewrite as 1+xy, as desired. Let's call this equation ().
We prove the second part by induction on n. To do this, we need two things: a base case, that is, proving the case n=0, and an inductive step, where we prove case n+1 from case n. To do the base case, we differentiate both sides of equation (*) that we proved above: d/dx ((1-x2 )y') = d/dx (xy+1 ). On the left-hand side, we get -2xy'+(1-x2 )y'', using the product rule, and on the right-hand side, we get xy'+y, similarly. Rearranging, we've proven the case n=0 of the desired statement. The inductive step is similar: we differentiate the equation from case n using the chain rule. Each of the first two terms splits into two: respectively, -2xy(n+2)+(1-x2)y(n+3), and (2n+3)y(n+1)+(2n+3)xy(n+2). If we combine the terms with the same numbers of derivatives on y, we get (1-x2)y(n+3)-(2n+5)xy(n+2)-((n+1)2+2n+3)y(n+1)=0 -which is what we wanted to prove, since ((n+1)2+2n+3) simplifies to (n+2)2.
Which graph represents a proportional relationship?
Answers
Answer: The first graph
Step-by-step explanation:
A proportional graph always goes through the origin
Answer:
The first graph
Step-by-step explanation:
Find the slope and y-Intercept of the line in the graph. Drag and drop each number into the correct box
to complete the statement.
7
(0,5)
4 3
2
1
0
(3,-1)
-1
-2
3
TO
de
8 7
0 1 2
55
The slope is m
and they-intercept is b =
Answers
Answer:
slope = - 2, y- intercept = 5
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line
m = [tex]\frac{-1-5}{3-0}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
The y- intercept is the point on the y- axis where the line crosses
The y- intercept = 5
Evaluate the expression 16+1+2
Answers
fred bags groceries at Wegman's. on average he fills 21 bags for every three customers what IS FREDS AVERAGE RATE OF CHANGE
Answers
Answer:
The rate of change will be the number of bags Fred fills for 1 customer.
Write a ratio.
21 : 3
x : 1
To solve for x, cross multiply.
3x : 21
Divide both sides by 3.
x = 7
Fred’s average rate of change is 7 bags.
:)
ents
2 in
2 in
What is the area of the given figure? Enter your answer as a single number. Round to the
nearest tenths place. Use 3.14 as an approximation for pi. Your answer will be in the units of
inches squared
15
Answers
Answer:
"given figure"
No figure was given.
Step-by-step explanation:
d = 10.2 ft, r = 0.5 ft/h
Answers
Answer:
20.4
Step-by-step explanation:
If you are using D = r × t
10.2 = 0.5(t)
10.2/0.5 = t
20.4 = t
Answer:
20.4
Step-by-step explanation:
Addison plays 6 songs in of an hr. How many
songs can she play for 4 hours?
Answers
Answer:
24
Step-by-step explanation:
4x6=12or 2x6=12so then 12+12=24
Answer:
6 songs per hour, so multiply that with the number asked which is four
so four times six is24
so she can play 24 songs in four hours!
~ ...
~ !
~ !
Write the ratio as a fraction: 630kilometers in 5hours. Simplify your answer.
___ km/hour
Answers
Answer:
126/1=126
Step-by-step explanation:
630:5 as a fraction would be 630/5.
630/5 simplified would be 126/1.
Hope this helps :)
Answer:
630:5 would be 126:1
Step-by-step explanation:
To solve this we would divide 630 by five giving us 126, and divide 5 by 5 giving us one
Now we have 126:1, or 126 km/hour
plz help asap plzz plllzzzzz
Answers
A furniture store receive
order for 456 chairs. They
can fit 9 chairs in a large
shipping box. How many
shipping boxes will they
need to ship all of the
chairs?
Answers
Which figure is NEVER a parallelogram?
triangle
rectangle
rhombus
square
Answers
Answer:
Triangle
Step-by-step explanation:
A parallelogram have four sides
Question 9 of 10 What is the approximate value of x in the diagram below? (Hint: You will need to use one of the trigonometric ratios given in the table.) 54 sin 36 A 0.588 oos 36 x 0.809 ta 369 0.727 23 36° he A. 18.61 B. 13.52 C. 16.72 D. 28.43 E. 31.64 O F. 39.12
Answers
9514 1404 393
Answer:
E. 31.64
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between the legs of a right triangle:
Tan = Opposite/Adjacent
You are given trig values for 36°. That means ...
tan(36°) = 23/x
x = 23/0.727 ≈ 31.64
PLS HELP ME
what party was against a strong central government, government promotion of trade and industry?
A: Federalist
B: Democrat-republicans
C: Whigs
D: Democrats
I need it now pls it's a k-12 test
Answers
Answer:
the answer is a federalist and your welcome
Step-by-step explanation:
The Federalists, led by Secretary of Treasury Alexander Hamilton, wanted a strong central government, while the Anti-Federalists, led by Secretary of State Thomas Jefferson, advocated states' rights instead of centralized power.
Find set A′ ∩ B′
U={a, b, c, d, e, f, g}
A={b, c, e, g}
Answers
Answer:
i dont know
Step-by-step explanation:
i dont know
A company charges $60 per day plus $0.50 per mile for truck rentals. If Greg rents a truck for 3 days and drives 150 miles, how much will the company charge?
Answers
Answer:
$255
Step-by-step explanation:
Equation would be
60x+0.5y= $ charged
x= days
y = per mile
60 * 3 + 0.5 * 150 = $
180+75=
=255
Greg would have to pay $255
Hope this helps!
(Pls mark brainiest)
Thanks!
Write the equation of the line that passes through (-2, 4) and is perpendicular to x = 3.
Answers
Check the picture below.
Find the volume of a cylinder either enter. An exact answer in terms of pie or 3.14 please help me
Answers
To find the area of a cylinder, we multiply the area of the base times it’s height. For a cylinder the base is a circle so we use
pi r^2 to find it. In this problem the radius or r = 4 so the area of the base equals 16 pi. The height is 8. So we multiply these two to get the answer of 128 pi
Twelve pounds of the element plutonium is released in a nuclear accident. The amount of plutonium P that is present after t months is given by P(t)=12e^-0.1507t. What amount of plutonium remains after 36 months? Round to two decimal places.
Answers
The amount of Plutonium that remains after 36 months is 0.05
The equation for the amount of Plutonium after t months is
[tex]\mathbf{P(t) = 12e^{-0.1507t}}[/tex]
After 36 months; we have: t = 36.
Substitute 36 for t in P(t).
So, we have:
[tex]\mathbf{P(36) = 12e^{-0.1507 \times 36}}[/tex]
Simplify the exponent
[tex]\mathbf{P(36) = 12e^{-5.4252}}[/tex]
Evaluate the exponent
[tex]\mathbf{P(36) = 12 \times 0.004404}[/tex]
Multiply
[tex]\mathbf{P(36) = 0.052848}[/tex]
Approximate to 2 decimal places
[tex]\mathbf{P(36) = 0.05}[/tex]
Hence, the amount that remains is 0.05
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what is the reason for line 3??
Answers
Answer:
SAS similarity
Step-by-step explanation:
LO and LP are proportional to LN and LM, as shown by:
[tex]\frac{LO}{LN} =\frac{LP}{LM}[/tex]
Because these are equal, both pairs of corresponding lines have the same scale factor and are proportional as a result. The angle between them is congruent due to the reflexive property as given, and with 2 pairs of proportional sides including the angle, ΔLMN is similar to ΔLPO by the SAS similarity postulate
HEEEEELP!!!!! what are 5 expressions that are equivelent to 8x+16
Answers
Answer:
8x + 16 = 2(4x + 8) = 4(2x + 4) = 8(x + 2) = 16((1/2)x + 1) = -8(-x - 2)
Step-by-step explanation: