Two number cubes are rolled for two separate events: Event A is the event that the sum of numbers on both cubes is less than 10. Event B is the event that the sum of numbers on both cubes is a multiple of 3. Complete the conditional-probability formula for event B given that event A occurs first by writing A and B in the blanks: P_________( a0 | _________ a1) = P_______( a2 ∩ _____________a3) P(__________________ a4) If someone could please comment cant figure this question out
Final answer:
The conditional probability formula for event B given event A is represented as P(B|A), which is calculated using P(A and B) / P(A). Using dice as an example, the events are described and demonstrated to be neither mutually exclusive nor independent due to overlapping outcomes and interdependence.
Explanation:
The conditional probability of event B given that event A has occurred is represented as P(B|A). To fill in the blanks in the provided formula, it would be P(B | A) = P(B ∩ A) / P(A). Using the provided scenarios, we need to calculate P(A), which is the probability that the sum of numbers on both cubes is less than 10, P(B), which is the probability that the sum of numbers on both cubes is a multiple of 3, and P(A and B), which is the probability that both events occur simultaneously. Finally, we use the formula P(A|B) = P(A and B) / P(B) to calculate the conditional probability.
For example, event A could be rolling a 3 or 4 first, followed by any even number, and event B could be rolling a sum at most 7 on two dice. These events are not mutually exclusive since they can both occur simultaneously, nor are they independent since the occurrence of one affects the likelihood of the other happening.
The completed conditional-probability formula is: P(B|A) = P(A ∩ B) / P(A)
To complete the conditional-probability formula for event B given that event A occurs first, we need to fill in the blanks with the appropriate terms:
P(B|A) = P(A ∩ B) / P(A)
Let's break down each term:
a0: Event A occurs
a1: Event B occurs
a2: Event A and B occur simultaneously (intersection of A and B)
a3: Event A occurs
a4: Event B occurs
Therefore, the completed conditional-probability formula is:
P(B|A) = P(A ∩ B) / P(A)
deshawn is covering a 4 yard by 1 3/4 yard section of his bedroom wall with decorative tiles. The tiles are 1/4 by 1/4 yard. How many tiles will it take to cover 1 square yard?
It will take 16 tiles to cover 1 square yard.
Explanation:To find out how many tiles it will take to cover 1 square yard, we need to calculate the area of one tile.
The tiles are 1/4 by 1/4 yard, so the area of one tile is (1/4) * (1/4) = 1/16 square yard.
To cover 1 square yard, we need to divide the total area by the area of one tile:
1 square yard / (1/16 square yard) = 1 * (16/1) = 16 tiles.
You can spend up to $35 on a shopping trip.
a. You want to buy a shirt that costs $14. Identify an inequality that represents the amount of money, x (in dollars), you will have left if you buy the shirt.
x+14≥35
x+14≤35
x−35≥14
x−35≤14
Question 2
Solve the inequality.
The solution is .
Question 3
b. You notice that the shirt is on sale for 30% off. Identify the new inequality.
x+9.8≥35
x+35≤9.8
x+9.8≤35
x+9.8≤24.5
Question 4
c. Do you have enough money to buy the shirt that is on sale and a pair of pants that costs $23? Which best explains your answer?
no; The cost of the shirt and the pants is $37, which is more than $35.
yes; The cost of the shirt and the pants is $32.80, which is less than $35.
no; The cost of the shirt and the pants is $32.80, which is more than $21.
yes; The cost of the shirt and the pants is $21, which is less than $23.
the answer to this question is 21 dollars are left
Miles has 24 baseball cards he wants to display the cards in even rows and columns.draw two different arrays to show how miles could display his cards.label your drawings with a multiplication equation
Answer:
Total number of cards which have to arrange in even rows and Columns=24
So, Even arrays are
=6 rows and 4 columns
=4 rows and 6 columns
=12 rows and 2 columns
=2 rows and 12 columns
The two different arrays to show how miles could display his cards will be (2, 12) and (4, 6).
What are permutation and combination?A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
Miles has 24 baseball cards he wants to display the cards in even rows and columns.
The factor of the number 24 will be
24 = 2 x 2 x 2 x 3
Then the number of the combination will be given below.
Number of combination = 4 {(2, 12), (12, 2), (6, 4), (4, 6)}
The two different arrays to show how miles could display his cards will be (2, 12) and (4, 6).
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Paloma decided to divide 1,292 by 31 using partial quotients. She uses 30 as her first partial quotient. Which are the partial quotients Paloma should show in her work?
A) 30,10
B) 30,10,1
C) 10,10,10,1
D) 10,10,10,10,1
Answer:Partial quotients Paloma should show in her work are B) 30,10,1.
Step-by-step explanation:
Given : Paloma dividing 1292 (dividend) by 31 (divisor) using partial quotients.
so the easy multiples of 31 are as 31×2=62 ,31×3=93,31×10=310....so on
if she uses 30 as her first partial quotient then 31×30=930, so after subtracting 930 from 1292 we get 362 as new dividend then 31×10=310 is the easiest multiple of 31 so that 362-310=52 as new dividend ,then 31×1=31 subtracting this from 52 gives 52-31=21 which is the remainder.
Therefore, Partial quotients Paloma should show in her work are 30,10 and 1.
Write an equation that illustrates the identity property of multiplication and the zero property of multiplication
5*0 = 0*5 I think this works for both. Take this answer with a grain of salt and double check it, just in case.
Jeremy is recording the weights, in ounces, of different rock samples in a lab. The weights of seven rocks are listed below.
11, 13, 14, 6, 10, 9, 10
The eighth rock that he weighed was 5 ounces. How would the interquartile range of the data be affected if Jeremy includes the weight of the eighth rock?
Jeremy is recording the weights, in ounces, of different rock samples in a lab. The weights of seven rocks are listed below.
11, 13, 14, 6, 10, 9, 10
The eighth rock that he weighed was 5 ounces. How would the interquartile range of the data be affected if Jeremy includes the weight of the eighth rock?
Answer:
The value of the (RIC) will increase from 4 to 5.75, that is, 44%
Step-by-step explanation:
To answer this question you have to know the definition of Rank well.
The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin
The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.
Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%
Answer:
Hence the interquartile range increased by 3(7-4) when we included the eight weight.
Step-by-step explanation:
The weight of the seven rocks is given as:
11 13 14 6 10 9 10
on arranging the data in the ascending order we get the observation as:
6 9 10 10 11 13 14
we divide our data into 3 sets:
the median of data([tex]Q_2[/tex]) is: 10 (as it is the middle value among the data)
The lower set of data is:
6 9 10
[tex]Q_1=9[/tex] ( as it is the middle value)
The upper set of data is:
11 13 14
[tex]Q_3=13[/tex] ( as it is the middle value in the upper set of data)
Hence, the interquartile range is: [tex]Q_3-Q_1=13-9=4[/tex]
The weight of eight rocks is given as:
11 13 14 6 10 9 10 5
On arranging the data in ascending order we get:
5 6 9 10 10 11 13 14
The median of the data is denoted by [tex]Q_2[/tex] which is the middle value of the given data.
Hence the median here is between 10, 10.
so, the median is given by:
[tex]\dfrac{10+10}{2}=10[/tex]
thus [tex]Q_2=10[/tex]
also the lower set of data is:
5 6 9
Thus [tex]Q_1=6[/tex] (as it is the middle value in the lower set of data)
the upper set of data is:
11 13 14
Thus [tex]Q_3=13[/tex]
Hence, the interquartile range is:
[tex]Q_3-Q_1=13-6=7[/tex]
So when we were having seven weights the interquartile range was: 4
and when we included the eight weight the interquartile range becomes: 7
Hence the interquartile range increased by 3(7-4) when we included the eight weight.
A motorboat traveling a distance of 225 miles in 5 hours while traveling with the current. Against the current, the same trip took 9 hours. Find the rate of the boat in calm water and rate of the current.
Rate of boat in mph and rate of current in mph
boat= 35mph
current=10mph
Could someone tell me the answer pls Thankss alot
374/ 15= about 24.9 miles
mr. kork sold his car for 8,400. this was 200 more than two fifths of what he had paid for the car originally
If your question is, "how much had Mr. Kork paid for the car?"
(8,400-200)/.4=$20,500
Achristensen's answer is correct. Just want to add a little more explanation how to arrive at the result.
let x be the original price.
Rewrite the verbal question as an equation using x:
8400 = 200 + 2/5 * x
solve for x:
8400-200 = 2/5*x
5/2*8200 = x
x = 20500
The original price was $20,500
Which construction might this image result from?
A.
construction to copy a line segment
B.
construction of a perpendicular bisector
C.
construction of a perpendicular to a line through a given point on the line
D.
construction of a line parallel to an existing line
E.
construction of a perpendicular to a line through a given external point
Answer:
E
Step-by-step explanation:
Construction of a perpendicular to a line through a given point on the line might this image result from. Correct option is C.
A. Construction to copy a line segment: This construction involves using a straightedge and compass to create an identical copy of a given line segment.
B. Construction of a perpendicular bisector: This construction involves finding the perpendicular bisector of a given line segment, which is a line that intersects the segment at its midpoint and forms right angles with it.
C. Construction of a perpendicular to a line through a given point on the line: This construction involves drawing a line perpendicular to a given line through a specific point on that line.
D. Construction of a line parallel to an existing line: This construction involves drawing a line that is parallel to a given line and passes through a specific point not on the given line.
E. Construction of a perpendicular to a line through a given external point: This construction involves drawing a line perpendicular to a given line and passing through a point located outside the given line.
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Ben made a four digit number with the numbers 7,4,3,9. The number was smaller than 4 and bigger than 1. The 7 cannot go in the tenths place, and 9 must go to any place value to the right of the seven. What is the number?
3.479 is the answer
A truck driver is 2 hours into 1,346-Mile drive and has driven 125 Miles s far. Which of the following is the number of miles the truck driver still must cover to reach th halfway point to the trip ?
what percent of 1620 dinner rolls is 85 dinner rolls
Answer:
it is 1905.88%
Step-by-step explanation:
We have,85%x X=1620
Or 85/100*x=1620
multiplying both sides by 100 and dividing both sides by 85
we have x = 1620 * 100/85
x=1905.88
if you are using a calculator ,simply enter 1620x100÷85,which will give you the answer
85 dinner rolls represent approximately 5.25% of 1620 dinner rolls. The calculation is done by dividing 85 by 1620 and then multiplying by 100.
To find what percent of 1620 dinner rolls is 85 dinner rolls, we use the basic formula of (part/whole) x 100. In this case, the 'part' is the 85 rolls, and the 'whole' is the 1620 rolls. So we calculate the percentage as follows:
(85 / 1620) x 100 = (0.05247) x 100 [10pt] [10pt]= 5.247%
Thus, 85 dinner rolls are approximately 5.25% of 1620 dinner rolls.
Graph y - 5 = - 2/3 (x + 9) using the point and slope given in the equation.
Please help FAST!!!!
Answer:
Please find the attachment.
Step-by-step explanation:
We are asked to graph the equation [tex]y-5=-\frac{2}{3}(x+9)[/tex].
We know that point-slope form of an equation is in form [tex]y-y_1=m(x-x_1)[/tex], where, m represents slope of line and [tex](x_1,y_1)[/tex] is a point on the line.
We can see that slope of the line is [tex]-\frac{2}{3}[/tex], so line will be a decreasing line.
We can represent the given equation as [tex]y-5=-\frac{2}{3}(x-(-9))[/tex].
The line will pass through the point [tex](-9,5)[/tex].
The graph of the linear equation can be seen in the image at the end.
How to graph the linear equation?To graph any line, we just need to identify two points in the line, and then we can connect them with a line.
Here the equation is:
y - 5 = (-2/3)*(x + 9)
We can see that this equation contains the point (-9, 5) (both sides of the equation become zero in that point)
5 - 5 = (-2/3)*(-9 + 9)
0 = 0
And evaluating in x = 0 we get:
y - 5 = (-2/3)*(0 + 9)
y = 5 + (-2/3)*9
y = 5 - 6
y = -1
So we have the point (0, -1)
Just graphing these two points and conecting them with a line we will get the following graph:
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If e pieces of candy cost $2.10, how much would 4 pieces cost?
Answer:
$8.40
Step-by-step explanation:
Multiply 2.10 and 4. You get 8.4
4 pieces of candy would cost $8.40.
Explanation: It would cost $8.40, because $2.10 x 4 = $8.40.
A car drives 80 mph if you add 760 how much is the total
what 1000×2099 math is really hard
Answer:
2,099,000
Step-by-step explanation:
the answer is 2,099,000
Rob spent 25%, percent more time on his research project than he had planned. He spent an extra h
hours on the project.
Which of the following expressions could represent the number of hours Rob actually spent on the project?
Rob spent 25% extra percent on his project than the had planned.
Let us assume total number of hours spent x hours.
Given that he spent an extra h hours on the project
So, we could say 25% of x is h.
0.25 x = h.
Dividing both sides by 0.25.
We get 0.25h/0.25 = h/0.25.
x = h/0.25.
Let us convert 0.25 into fractions.
0.25 = 25/100 = 1/4.
Therefore,
x = h/1/4 = 4h.
Therefore, Rob planned 4h hours.
He spent h hours extra.
So, he spent total 4h+h = 5h hours total.
Therefore, 5h expressions could represent the number of hours Rob actually spent on the project.3/2(b + 1) = 3..........
b = - [tex]\frac{1}{2}[/tex]
multiply both sides by 2(b + 1) to eliminate the fraction
3 = 3× 2(b + 1)
3 = 6(b + 1) = 6b + 6 ( subtract 6 from both sides )
- 3 = 6b ( divide both sides by 6 )
b = - [tex]\frac{3}{6}[/tex] = - [tex]\frac{1}{2}[/tex]
If mADC and mBDC have a sum of 180, name the straight angle.
i am pretty sure it is mADC
Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0. Parallel lines are numbered up to pi/2 to the north and to the south. If we assume Earth is spherical, the length of any parallel of latitude is equal to the circumference of a great circle of Earth times the cosine of the latitude angle.
a. The radius of earth is about 6400 kilometers. Find the circumference of a great circle.
b. Write an equation for the circumference of any latitude circle with angle 0
c. Which latitude circle has a circumference of about 3593 kilometers?
d. What is the circumference of the equator?
Answer:
a) circumference of great circle=40212.4km
b) circumference of latutude circle=40212.4cos[tex]\theta[/tex] kilometers
c)The latitude circle is at an angle of 84.9°
d)Circumference of equator=40212.4km
Step-by-step explanation:
Refer to the figure shown below, we are given that earth has been charted with vertical and horizontal line and horizontal lines are called latitude lines.
So every horizontal line corresponds to a circle.
So the great circle will have radius equal to earth radius.
a)we are given with earth radius=6400km.
Hence circumference of a great circle= 2πX6400=40212.4km
b)At a latitude with angle x=[tex]\theta[/tex], the circumference of latitude circle = [tex]40212.4cos\theta[/tex]
c)If a latitude circle has a circumference of about 3593km,
then [tex]40212.4cos\theta=3593[/tex]
[tex]cos\theta=\frac{3593}{40212.4} =0.0894[/tex]
[tex]\theta=cos^{-1}(0.0894)[/tex]=84.9°
Hence the latitude circle is at an angle of 84.9°
d) At equator angle is 0.
Hence circumference of equator=40212.4cos(0)=40212.4km
4(b-6)+19 simplify the expression
Step 1. Expand
4b - 24 + 19
Step 2. Collect like terms
4b + (-24 + 19)
Step 3. Simplify
4b - 5
The answer is 4b - 5 :)
At 7:00 a.m the temperature was 8 C what was the temperature at midnight if the temp was 10 lower?
(18x-44 )(8x-10) (13y-38) geometry
Simplifying
18x + -44 = 13y + -38
Reorder the terms:
-44 + 18x = 13y + -38
Reorder the terms:
-44 + 18x = -38 + 13y
Solving
-44 + 18x = -38 + 13y
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '44' to each side of the equation.
-44 + 44 + 18x = -38 + 44 + 13y
Combine like terms: -44 + 44 = 0
0 + 18x = -38 + 44 + 13y
18x = -38 + 44 + 13y
Combine like terms: -38 + 44 = 6
18x = 6 + 13y
Divide each side by '18'.
x = 0.3333333333 + 0.7222222222y
Simplifying
x = 0.3333333333 + 0.7222222222y
The provided expressions (18x-44)(8x-10)(13y-38) are polynomials in mathematics. However, without further context, it's challenging to give a useful solution or explanation.
Explanation:Unfortunately, the question provided isn't clear and seems to be a collection of disconnected parts. The primary elements, (18x-44)(8x-10)(13y-38), represent three polynomials in mathematics. These polynomials might be part of equation to be solved, but the information provided is not sufficient for a conclusive answer.
Main Point
The expressions given above are polynomials grouped together. Polynomials are expressions comprising variables and coefficients, connected by the + or - operations. They can be included in various mathematical problems, from solving equations to geometry.
More about PolynomialsA polynomial of degree one is a linear polynomial, of degree two is a quadratic, degree three is a cubic, and so forth.
Though the given expression includes x and y variables, without further information or context, it's impossible to provide a detailed solution or explanation.
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help mee plsss & thank youu
For this case, we have the following polynomial:
[tex]3x ^ 6yz + x ^ 4y ^ 2 + 2xz ^ 5-6x ^ 2y ^ 3-7y\\[/tex]
A term of the polynomial composed by:
[tex]3x ^ 6yz[/tex], where:
3: Represents the coefficient of the term
x, y, z: Represent the associated variables
6: Represents the exponent associated with the variable x. (y, z have exponent 1)
Thus, using the previous definition, it is observed that the expression has 5 terms.
Answer:
Option c
What is an equation of the line in slope intercept form m=2/7 and the y intercept is (0,-12).
The equation is y=mx+b
so it would be y=2/7(x)-12
Beach cruises prints brochures and fliers to advertise their dolphin watching tours. To print, the brochure requires three pages while the flier requires two. They are limited to 500 sheets of paper, but need to print at least 80 brochures and 100 fliers. Each brochure cost .10 to print and each flier costs .06 to print. How many of each should their print to minimize their cost?
Let x the number of brochures and y the number of fliers.
Optimizing function⇒ f(x,y) = 0.1 x + 0.06 y
Constraints:
x ≥ 80
y ≥ 100
3x + 2y ≤ 500
See the attached figure which represents the constraints.
From the attached figure:
The vertices of the feasible region are (80, 100), (80, 130) and (100, 100).
Substitute the points (80, 100), (80, 130) and (100, 100). in the function
f(x,y) = 0.1 x + 0.06 y
If (x,y) = (80, 100) ⇒ f(x,y) = 14
If (x,y) = (80, 130) ⇒ f(x,y) = 15.8
If (x,y) = (100, 100) ⇒ f(x,y) = 16
The minimum value 14 at (80, 100).
To minimize the cost, she would print 80 brochures and 100 fliers.
This is an optimization problem in mathematics that can be solved by linear programming. The constraints of the problem can be represented by inequalities, and the objective function (cost of printing) can be minimized by finding the optimal number of brochures and fliers to print.
Explanation:This question is a type of optimization problem in mathematics, specifically a type of problem often found in linear programming. The objective is to minimize the cost of printing brochures and fliers.
First, set up the inequalities based on the constraints. Let x be the number of brochures and y be the number of fliers.
Since each brochure uses 3 sheets and each flier uses 2, and there are only 500 sheets available, the inequality is 3x + 2y <= 500.As they need to print at least 80 brochures and 100 fliers, we have two more inequalities: x >= 80 and y >= 100.Then, we need to find the number of brochures and fliers to minimize the cost, which is 0.10x + 0.06y. You can solve this problem using methods of linear programming, such as graphing the feasible region and finding the minimum point.
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Complete the point-slope equation of the line (6,4) and (7,2).
y-2=________
y - 2 = - 2(x - 7)
the equation of a line in ' point- slope form ' is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
to calculate m use the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (6, 4 ) and (x₂, y₂ ) = (7, 2)
m = [tex]\frac{2-4}{7-6}[/tex] = -2
using m = - 2 and (a, b) = (7, 2)
y - 2 = - 2(x - 7 ) ← in point-slope form
Over the last 4 years, James has earned $56 interest on a deposit of $280 that he made to his savings account. What is the simple annual interest rate for James' savings account?
Answer:
5.6%
Step-by-step explanation: