Answers
\Omega=\{1;\ 2;\ 3;\ 4;\ 5;\ 6;\ 7;\ 8;\ 9;\ 10\}\\\\|\Omega|=10\\\\A=\{1;\ 3;\ 6;\ 7\};\ B=\{2;\ 3\}\\\\A\ \cup\ B=\{1;\ 2;\ 3;\ 6;\ 7\}\\\\|A\ \cup\ B|=5\\\\P(A\ \cup\ B)=\dfrac{|A\ \cup\ B|}{|\Omega|}\to P(A\ \cup\ B)=\dfrac{5}{10}=\dfrac{1}{2}=0.5=0.50
Related Questions
In a car how many miles do you go per day? How many days until you hit 10,000 miles?
Answers
divide the number of miles per day by the total miles to find how long it will take:
10,000 miles / 25 miles per day = 400 days
Find the point on the line 4x+4y+5=0 which is closest to the point (−2,−3).
Answers
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) will be located on the line perpendicular to the given line and will go through the given point
step 1
the slopes of two perpendicular lines
are
m1*m2=-1
given line
4x+4y+5=0------> 4y=-4x-5----> y=-x-1.25
m1=-1
so
m2=1
step 2
find the equation of the line with m2=1 and point (−2,−3)
y-y1=m*(x-x1)-----> y+3=(1)*(x+2)----> y=x+2-3-----> y=x-1
step 3
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) is the intersection of the line y=-x-1.25 and the line y=x-1
using a graph tool
see the attached figure
the solution is the point (-0.125,-1.125)
A recipe for cookies calls for 2⁄3 of a cup of chocolate chips and 4 cups of flour. If you want to make a bigger batch, using 6 cups of flour, how many cups of chocolate chips will you need?
Answers
how many cups of chocolate if using 6 cups of flour
= (6 x 2/3) / 4
= 4/4
=1
answer
1 cup of chocolate if using 6 cups of flour
Simplify 11/12 - 6/4
Answers
Short answer: -7/12
Why?
So, here are the steps on how to solve this. It takes a bit of work. (First step: 6/4 can be simplified down to 3/2, so do that.) - (Second step: Find the least common denominator. The least common denominator is 12. Convert 3/2 to a 12 denominator by multiplying both sides by 6. {3 * 6} / {2 * 6} ==> 18/12) - (Third step: Subtract the numerators. {11}/12 - {18}/12 ==> -7/12
Hope this helped you! ♥
A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5
1/8hours in the afternoon, how many hours does she work in the evening?
Answers
Answer:
She worked [tex]6\frac{7}{8}[/tex] hours in evening.
Step-by-step explanation:
Suppose, x be the hours waitress worked in evening,
Given,
She works 1.75 hours less in the afternoon than in the evening.
Thus, the number of hours she worked in afternoon = x - 1.75,
According to the question,
[tex]x-1.75 = 5\frac{1}{8}[/tex]
[tex]x-\frac{175}{100}=\frac{41}{8}[/tex]
[tex]x-\frac{7}{4}=\frac{41}{8}[/tex]
[tex]x=\frac{41}{8}+\frac{7}{4}[/tex]
[tex]x=\frac{41+14}{8}[/tex]
[tex]x=\frac{55}{8}=6\frac{7}{8}[/tex]
Therefore, she worked [tex]6\frac{7}{8}[/tex] hours in evening.
Solve ax - by = f for x
Answers
[tex]ax - by = f [/tex]
We must clear the value of x in the expression.
For this, we must follow the following steps:
1) add by on both sides of the equation:
[tex]ax - by + by = f + by ax = f + by[/tex]
2) multiply both sides by 1 / a:
[tex](1 / a) * ax = (1 / a) f + (1 / a) by x = (1 / a) f + (1 / a) by[/tex]
3) Common factor 1 / a:
[tex]x = (1 / a) * (f + by)[/tex]
Answer:
[tex]x = (1 / a) * (f + by)[/tex]
help needed please.
Answers
The explanation is shown below:
1. To solve the exercise you must apply the following proccedure:
2. You have that He wants it to be 2 parts compost to 10 parts potting soil and he wants to end up with 10 grams of mix. Therefore:
=(2/12)x12 kilograms
=0.166x12 kilograms
=2 kilograms
The sum of three consecutive integers is 162. what is the smallest og these integers?
Answers
Becky is 18 and would like to buy a house when she is 36. What is the discount factor for today's prices if the housing values increase 6% per year?
Answers
Yearly increase of house value (i) = 6% = 0.06
After 18 years,
The house value = (1+i)^n = (1+0.06)^18 = 2.85 the current value.
Additionally,
Increase in rate = (2.85-1)/2.85 = 0.6491 ≈ 0.65 = 65%. This is the discount rate for today's price. In other words, if the house is bought today, it will be paid for 65% less the price after 18 years.
Answer: 35.0%
Step-by-step explanation:
A box has a volume of 135 feet3. The length is same as the height, and the width is 5 times the length. What are the dimensions of the box?
Answers
thus the volume will be:
volume=length*width*height
thus
135=x×x×5x
135=5x³
solving for x we get:
27=x³
getting the cube root of both sides:
∛27=x³
x=3 ft
thus
length=3 ft, height=3ft, width=3×5=15 ft
The dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.
Explanation:This is a classic problem of volume where we need to consider the volume formula of a box, which is length × width × height. The question states that the box has a volume of 135 cubic feet, with the length being the same as the height, and the width being 5 times the length.
To find the dimensions of the box, we can set up the equation: length × 5 ×length × length = 135. Simplifying, we get that the length is the cube root of 135/5, which equals to 3. Thus, the dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.
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In FGH, mF = 65, mG = 55, and mH = 60. Which side of FGH is the shortest?
Answers
FH is the shortest side
Explanation:
In any triangle, the length of any side is proportional to the measure of its opposite interior angle.
This means that:
The shortest side is the side opposite to the smallest interior angle in the triangle
The longest side is the side opposite to the largest interior angle in the triangle
Now, in the given triangle we have:
measure angle F = 65°
measure angle G = 55°
measure angle H = 60°
We can note that angle G is the smallest angle.
Based on the above, the shortest side would be the one opposite to angle G which is side FH.
Hope this helps :)
Answer: Fh is the shortest
a what helps people in developing countries obtain minimal funding to start small businesses
Answers
People in developing countries can find minimal funding through small-business grants to start small businesses. Grants are basically free money. Unlike loans, they are financial awards that don't have to be paid back.
What is the solution to the equation 7(a – 10) = 13 – 2(2a + 3)
Answers
Hope this Helps!!
Answer:
[tex]a=7[/tex]
Step-by-step explanation:
we have
[tex]7(a-10)=13-2(2a+3)[/tex]
Solve for a
[tex]7a-70=13-4a-6[/tex]
Group terms that contain the same variable and move the constants to the other side
[tex]7a+4a=13-6+70[/tex]
Combine like terms
[tex]11a=77[/tex]
Divide by [tex]11[/tex] both sides
[tex]a=7[/tex]
Can someone help with number 3
Answers
201 , 218, 242, 257, 265, 275 , 301
find the midpoint ( there are 7 numbers so the mid point would be the middle number 257)
look at the numbers below the mid point ( 201, 218, 242)
the first quartile is the mid point of those numbers: 218
answer is 218
An ice cream cone has a diameter of 2 inches and a height of 5 inches. What is the volume of the ice cream cone? Round your answer to the nearest hundredth. (Use 3.14 for π.) 10.47 in.3 20.93 in.3 5.23 in.3 15.7 in.3
Answers
to find the volume, you multiply radius squared by pi. the result of that is multiplied by the height divided by 3. [tex]V= 3.14* r^{2} \frac{h}{3} [/tex]
Answer:
The answer 5.23
Step-by-step explanation:
10,14 and 18 can someone answer Pls pls
Answers
Answer:
10) 35
14) x = 1/2
18) 10 cm
Explanation:
For question 10, we can set up a proportional equation, cross-multiply and solve for the missing number:
[tex]\frac{x}{14} = \frac{5}{2}[/tex]
2x = 14(5)
2x = 70
2x / 2 = 70 / 2
x = 35
The missing number is 35
For question 14, we isolate variables on one side of the equation and constants on the other by performing whatever operations are necessary and then solve for the variable:
14x + 2 = 9
14x + 2 - 2 = 9 - 2
14x + 0 = 7
14x = 7
14x / 14 = 7 / 14
x = 7 / 14
x = 1/2
x = [tex]\frac{1}{2}[/tex]
For question 18, there are 10 millimeters (mm) in 1 centimeter (cm) so we can use this relationship so set up a conversion factor and cross-multiply to find the missing value like we did in question 10:
[tex]\frac{10}{1} = \frac{100}{x}[/tex]
10x = 100(1)
10x = 100
10x / 10 = 100 / 10
x = 10
There are 10 cm in 100 mm.
If the sample size gets smaller, how does that affect the shape of the smapling distribution of sample means
Answers
what is the side length of a square with area 16 cm
Answers
Length² = 16
Length = √16
Length = 4
Answer: Length = 4cm
The perimeter of a rectangular field is 242 yards if the width of the field is 54 yards what is the lenght
Answers
242 = 2 (L +W)
121= L+W
121= L + 54
L = 121-54
L= 67 Yards
Which situation involves descriptive statistics?
A. The survey shows that 1 in 3 moviegoers would attend a midnight showing.
B. A recent survey of the cost of new homes in the United States shows that the median price of a new home is up $15,000 since last year.
C. A reporter surveys some commuters in a city to estimate what percent of city’s commuters spend 45 minutes or more getting to work.
D. Eighty percent of the recipes in a cookbook require salt.
Answers
All options involve descriptive statistics, but option B is a classic example as it involves computation of a median, an important tool in descriptive statistics.
Explanation:Descriptive statistics is used to describe, show or summarize data in a meaningful way. All the options given indicate the use of descriptive statistics because they all describe a given population or set of data using numerical measures. However, the most classical use of descriptive statistics is found in option B: 'A recent survey of the cost of new homes in the United States shows that the median price of a new home is up $15,000 since last year.' This situation involves the computation of a median, a common measure in descriptive statistics, to summarize property price data.
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To the nearest tenth, what is the area of the shaded segment when AG = 6 ft?
10.3 ft2
21.1 ft2
1.7 ft2
28.3 ft2
Answers
Answer:
Option A is correct.
Step-by-step explanation:
Given:
AG = 6 ft ⇒ Radius of the circle , r = 6 ft
⇒ GB = AG = 6 ft
To find: Area of shaded Segment.
Area of Shaded Segment = Area of Sector AGBA - Area of Δ AGB
Sector AGBA forming 90° angle at center. [tex]\implies\,\theta=90^{\circ}[/tex]
Area of Sector = [tex]\frac{\theta}{360}\times\pi r^2[/tex]
Area of Sector AGBA = [tex]\frac{90}{360}\times3.14\times6^2[/tex]
= [tex]\frac{1}{4}\times3.14\times36[/tex]
= [tex]28.26\:ft^2[/tex]
ΔAGB is a right angled triangle.
So, Area of ΔAGB = [tex]\frac{1}{2}\times AG\times GB[/tex]
= [tex]\frac{1}{2}\times6\times6[/tex]
= [tex]6\times3[/tex]
= [tex]18\:ft^2[/tex]
Area of Shaded Segment = 28.26 - 18 = 10.26 ≈ 10.3 ft²
Therefore, Option A is correct.
Assuming a truck container holds 24 cases, how many cases would 6 truck containers hold?
Answers
multiply 6 by 24
Answer:
6 truck containers can hold 144 cases
Step-by-step explanation:
A truck container holds 24 cases and we have to find number of cases would 6 truck container will hold.
We will solve this question by unitary method.
∵ One truck container holds cases = 24
∴ 6 truck containers will hold cases = 24×6 = 144
Therefore 144 cases is the answer.
(09.01 LC) Look at the figure below: A circle is shown with the center O. OP is a segment joining center O to a point P on the circle. MN is a line touching the cir Which is the tangent to the circle? (6 points) Segment OP Line ST Line MN Segment QR
Answers
Answer:
Line MN is the answer
Step-by-step explanation:
The amount of money in Nadia’s savings account is represented by the recursive formula mc010-1.jpg. If mc010-2.jpg, what are the first two numbers in the sequence? $25.36, $75.99 $50.00, $101.25 $101.25, $153.78 $75.99, $127.89
Answers
Answer:
a is correct
Step-by-step explanation:
How do you factor the expression #2x^2+ 5x + 3#?
Answers
a = 2; b = 5; c = 3.
-5 plus or minus sqrt( 25-4(2)(3) )
Then x = ----------------------------------------------
2(2)
-5 plus or minus sqrt (1) -5 plus or minus 1
= -------------------------------------- = --------------------------
4 4
-1 is one root, so x+1 is one factor. Can you find the other root and factor?
How many different soccer teams consisting of 11 players can be formed from 18 players?
Answers
18 c 11
Combination = n!/(n-r)!r!
18!/(7! * 11!)
There are 31,824 possible teams
if a tree diagram were drawn to determine the number of possible outcomes when choosing one of 5 salads, one of 6 entrees, and one of 9 desserts, how many leaves would there be?
Answers
Answer:
270
Step-by-step explanation:
Just multiply.
5*6*9=270
Answer: There would be 270 leaves of a tree diagram.
Step-by-step explanation:
Since we have given that
Number of salads = 5
Number of entrees = 6
Number of desserts = 9
If we draw a tree diagram, we need to find the number of leaves there would be :
So, the number of leaves there would be is given by
[tex]5\times 6\times 9\\\\=270[/tex]
Hence, there would be 270 leaves of a tree diagram.
A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area (A=lw), how long is the rectangle? a. 21 inches b. 340 inches c. 20 inches d. 15 inches
Answers
The rectangle that has an area of 357 square inches(a=357) is 17 inches wide(w=17). You are asked how long the length of the rectangle is. Then, you just need to put the number into the equation provided.
a=lw
area= length * width
357=length * 17
length= 357/17=21 inches
Answer:
a - 21 inches
Step-by-step explanation:
Following the formula [tex]Area = l*w[/tex], we can find the length of the rectangle by plugging in values into the formula, then solving for [tex]l[/tex].
[tex]357=l*17[/tex]
[tex]\frac{357}{17} =\frac{l*17}{17} \\\\21=l\\l=21[/tex]
The function is defined below. find all values of that are not in the domain of . if there is more than one value, separate them with commas.
Answers
The number of nails of a given length is normally distributed with a mean length of 5.00 in. and a standard deviation of 0.03 in. Find the number of nails in a bag of 120 that are less than 4.94 in. long.
Answers
P(x<4.94)=P(z<Z)
Z=(x-μ)/σ
where:
x=4.94 in
μ=5 in
σ=0.03
thus
Z=(4.94-5)/0.03
Z=-2
thus
P(x<4.94)=P(z<-2)=0.0228
Thus the number of nails that are less than 4.94 will be:
0.0228×200=4.56~5 nails
About 3 nails is correct on grad point