Probability of getting a 1 on the blue die, P(E) = 1/6
Given,
Two fair dice, one being blue and the other red.
E is the event of getting a 1 on the blue die.
F is the event of all the numbers being equal.
To find,
Probability of event E occurring, that is, the probability of getting a 1 on the blue die, P(E)
Probability (Event) = (Number of favourable outcomes) / (Total possible outcomes)
No of favourable outcomes = 6C1 = 6!/(5! x 1!) = 6
No of total possible outcomes = 36
Probability of event E occurring, that is, the probability of getting a 1 on the blue die, P(E) = 6/36 = 1/6
Therefore, by using two fair dice, one blue and one red, the probability of getting a 1 on the blue die is 1/6.
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Sets B and D are subsets of the universal set U.
These sets are defined as follows.
U= {f, k, q, s, x, y, z)
B={k, q, x, y)
D = {f.q, x, y, z)
Find the following sets.
Write your answer in roster form or as Ø.
(a) BnD' = [
(b) (BUD)' = [
Answer:
(a) B ∩ D' = {k}
(b) (B ∪ D)' = {s}
Step-by-step explanation:
Set Notation
[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]
Given sets:
U (universal) = {f, k, q, s, x, y, z}B = {k, q, x, y}D = {f, q, x, y, z}Part (a)
[tex]\begin{aligned}\sf B \cap D' & = \sf B \cap \left( \text{U}-D\right)\\ &= \sf \{k, q, x, y \} \cap \left(\{f, k, q, s, x, y, z \} - \{f, q, x, y, z \}\right)\\& = \sf \{k, q, x, y \} \cap \{ k, s \}\\ & = \sf \{k \}\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}\sf \left(B \cup D\right)' & = \sf \text{U}-\left(B \cup D\right)\\& = \sf \{f, k, q, s, x, y, z \}-\left(\{k, q, x, y\} \cup \{f, q, x, y, z\}\right)\\& = \sf \{f, k, q, s, x, y, z \}-\{ f, k, q, x, y, z\}\\& = \sf \{s\}\\\end{aligned}[/tex]
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Now we have to find,
→ B ∩ D'
→ (B ∪ D)'
Let's solve for the following sets,
a) B ∩ D' = ?
→ B ∩ D'
→ {k, q, x, y} ∩ ({f, k, q, s, x, y, z} - {f, q, x,y,z})
→ {k, q, x, y} ∩ {k, s} = {k}
Hence, the required set is {k}.
b) (B ∪ D)' = ?
→ B' ∩ D'
→ ({f, k, q, s, x, y, z} - {k, q, x, y}) ∩ ({f, k, q, s, x, y, z} - {f, q, x, y, z})
→ {f, s, z} ∩ {k, s} = {s}
Hence, the required set is {s}.
PLEASE HELP
1. A car rental company charges $260 per week plus $0.29 per mile to rent a car. How many miles can you travel in one week for $419.5?
a. the equation is ______
b.you can travel _____ miles in one week for $419.5
Find the coordinates of the point 7/10 of the way from A to B. The points given are A(-3,-6) , B(10,5)
why the grade tent truck fico duck session duck duck drink dunno rbi Thu to ft ft ft ft tho
A length of a rope is stretched between the top edge of a building
Answer:
what am i supposed to be answering..?
Step-by-step explanation:
La temperatura en la mañana fue de 5°F sobre cero. A mediodía, la
temperatura fue de 21°F bajo cero. ¿Por cuánto cambió la temperatura?
right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you 2have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the
Susan has 4 cup of raisins and she is dividing them into 3/8 cup
servings. How many servings will she have?
Answer:
32/3 servings
Step-by-step explanation:
4 / (3/8) =
(4/1) x (8/3) =
32/3
HELP ME OUT PLEASE!!!
Answer:
x=30
Step-by-step explanation:
8x - 3(2x-4) = 3(x-6)
first let's get rid of the brackets:
8x- 3·2x + 3·4 = 3x - 3·6
8x - 6x + 12 = 3x - 18
now group all the x terms and number terms
8x - 6x - 3x = -18 - 12
-x = -30
x = 30
how to explain how you know the midpoint of line segment
Answerits the point that divides the segment into two congruent segments
Step-by-step explanation:
ex. D————-o————-G
The midpoint would be the O. Mid:means Middle
hehehe hope this helps
struggling hard with probability questions, if anyone could help would be greatly appreciated, will give brainiest
The value of the probability is P(Large or Blue) = 7/10
How to evaluate the probability?The given parameters are represented on the table
Using the table parameters, we have
P(Large or Blue) = [(Large) + (Blue) - (Large and Blue)]/Total
This gives
P(Large or Blue) = ((17 + 8) + (17 +3) - 17)/(17 + 3 + 8 + 12)
This gives
P(Large or Blue) = 28/40
Simplify
P(Large or Blue) = 7/10
Hence, the value of the probability is P(Large or Blue) = 7/10
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Lily begins soving the equation 4(x -1) -x =3(x + 5) -
11. Her work is shown bekow.
How can her partial solution be interpreted?
O The equation has one solution: x =0.
O The equation has one solution: x=8.
O The equation has no solution.
O The equation has infinite solutions.
4(x-1) -X= 3(x + 5) -11
4x–4-X=3x + 15-11
3x-4= 3x + 4
PLEASE HURRY
Answer:4(x - 1) - x = 3(x + 5) - 11
Step-by-step explanation:
Lily's work:
4(x – 1) – x = 3(x + 5) – 11
4x – 4 – x = 3x + 15 – 11
3x – 4 = 3x + 4
Her partial solution, 3x - 4 = 3x + 4, can be interpreted as a FALSE statement because 3x - 4 does NOT equal 3x + 4.
Since it is a false statement, the equation has no solution.
The number of the solution will be infinity. Then the correct option is D.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
4(x – 1) – x = 3(x + 5) – 11
Simplify the equation, we have
4x – 4 – x = 3x + 15 – 11
3x - 3x = 8
The variable x is eliminated.
Then the number of the solution will be infinity.
Then the correct option is D.
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help pleasee :)
In the 1936 Olympics, Jesse Owens won a gold medal for running the 100-meter dash in 10.3 seconds. What was Owens' speed in meters per second, rounded to the nearest tenth?
Jesse Owen speed is 9.71 meters per seconds.
How to find speed?Speed is a scalar quantity that refers to "how fast an object is moving.
In other words, speed is the distance travelled per unit of time.
Therefore, it can be represented mathematically as follows:
speed = distance / time
Jesse Owen covers 100 meters dash for 10.3 seconds. Therefore, the speed he used for the race can be calculated as follows:
speed = distance / time
distance = 100 meters
time = 10.3 seconds
Hence,
speed = 100 / 10.3
speed = 9.70873786408
speed = 9.71 meters per seconds
Therefore, Jesse Owen speed is 9.71 meters per seconds.
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A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground.
The angle made by the ladder with the ground is
degrees, and the length of the ladder is
inches.
The length of the ladder is 58.31 inches and the angle made by the ladder with the ground is θ = 59.04°.
The distance between the ladder and the wall is 30 inches.
The height at which the ladder touches the wall is 50 inches from the ground.
Let x be the slant height when the ladder touches the wall.
Then, by using a Pythagorean theorem:
(Base)² + (Altitude)² = (Hypotenuse)²
(30)² + (50)² = x²
x² = 900 + 2500
x² = 3400 inches²
x = √[ 3400 inches²]
x = 10√34 inches
x = 58.31 inches
Then the angle made by the ladder with gound is :
tan (θ) = opposite / adjacent
tan (θ) = 50/30
tan (θ) = 5/3
θ = tan⁻¹ ( 5/3 )
θ = 59.04°
Therefore, the ladder is 58.31 inches long and the angle between the ground and the ladder is 59.04°.
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Solve the system by the elimination method:
-6x + 5y = -11
6x - 11y = -19
A (6,5)
B (-6,-5)
C (5,6)
D (-5, -6)
Answer:
x = 6, y = 5
Step-by-step explanation:
Solve the following system:
{5 y - 6 x = -11 | (equation 1)
{-11 y + 6 x = -19 | (equation 2)
Add equation 1 to equation 2:
{-(6 x) + 5 y = -11 | (equation 1)
{0 x - 6 y = -30 | (equation 2)
Divide equation 2 by -6:
{-(6 x) + 5 y = -11 | (equation 1)
{0 x + y = 5 | (equation 2)
Subtract 5 × (equation 2) from equation 1:
{-(6 x) + 0 y = -36 | (equation 1)
{0 x + y = 5 | (equation 2)
Divide equation 1 by -6:
{x + 0 y = 6 | (equation 1)
{0 x + y = 5 | (equation 2)
Collect results:
Answer: {x = 6, y = 5
convert into power notation 81/49
two step inequalities
please help
-1/2 (8+1/3 )
1. -4-1/6
2.-4-1/3
3.-5+1/3
4. -5+1/6
Answer:4.16667
Step-by-step explanation: 1
Simplify —
3
Equation
0 - (— • (8 + —))
2 3
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
8 8 • 3
8 = — = —————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
8 • 3 + 1 25
————————— = ——
3 3
Equation at the end of step
2
:
1 25
0 - (— • ——)
2 3
STEP
3
:
1
Simplify —
2
Equation at the end of step
3
:
1 25
0 - (— • ——)
2 3
STEP
4
:
Final result :
-25
——— = -4.16667
6
Terms and topics
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A swimming pool has a volume of 32,100 gal. Use the table of conversion facts to find out how many cubic yards of water it would take to completely fill the swimming pool. Round your answer to two decimal places.
158.93 yd³ water it would take to completely fill the swimming pool.
Given that, a swimming pool has a volume of 32,100 gal and we have to find out that how many cubic yards of water it would take to completely fill the swimming pool.
1 cubic yard (yd³) ≈ 201.97 gallon (gal)
So, by using the conversion given above we can simply find the water in cubic yards that it would take to completely fill the swimming pool.
Volume of the swimming pool = 32,100 gal
and we know that, 1 cubic yard (yd³) ≈ 201.97 gallon (gal)
Now, we get
water needed in cubic yards to completely fill the swimming pool
= 32,100/201.97
= 158.93 yd³
Hence, 158.93 yd³ water it would take to completely fill the swimming pool.
Therefore, 158.93 yd³ is the required answer.
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Question 7 of 10
Describe the nature of the roots for this equation. x²+3x-7=0
A. One real, double root
B. Two real, irrational roots
C. Two real, rational roots
D. Two complex roots
Answer:
B
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then the discriminant is
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real irrational roots
• If b² - 4ac > 0 and a perfect square then 2 real rational roots
• If b² - 4ac = 0 then 1 real double root
• If b² - 4ac < 0 then 2 complex roots
Given
x² + 3x - 7 = 0 ← in standard form
with a = 1, b = 3, c = - 7 , then
b² - 4ac
= 3² - (4 × 1 × - 7) = 9 + 28 = 37
Since b² - 4ac > 0 then 2 real irrational roots
PLEASE IM LITERALLY SO CONFUSED
One-stray Problem Solving
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POSSIBLE POINTS: 5.88
A population of bacteria is growing at an hourly rate of r so that at the end of each hour the population of the sample is multiplied by the growth factor of
z = 1+r. The beginning population is 800 bacteria, an additional 300 are present after 1 hour, and an additional 400 are present after the following
hour.
Write an expression for the population at the end of three hours in terms of the growth factor.
Answer:
1500z
Step-by-step explanation:
Given a bacteria population that is multiplied by z every hour, and the population after 2 hours is 1500, you want the population after 3 hours in terms of z.
ApplicationThe problem statement tells you the population is multiplied by z every hour. After 2 hours, the population is 800 +300 +400 = 1500. After 3 hours, that value will be multiplied by z:
1500z . . . . . population after 3 hours
__
Additional comment
The given values of population tell us z = 1100/800 = 1.375 for the first hour, and z = 1500/1100 ≈ 1.364 for the second hour. The average value of z for the two-hour period is √(15/8) ≈ 1.369. The desired expression could be any of ...
800z³ . . . . . . . population 3 hours after the beginning1100z² . . . . . . . population 2 hours after the first hour1500z . . . . . . . population 1 hour after the second hourPresumably z would have different values in each case, and we hesitate to predict what those values might be. Perhaps the population is being rounded to the nearest 10 or 100.
An exponential regression calculation models the population as ...
p = 801.945×1.36812^t . . . . . . . z ≈ 1.36812
Using this formula, we get the given population numbers by rounding to the nearest 10.
(7y-8y)2+14=2 solve for x
Answer:
y = 6
Step-by-step explanation:
(7y-8y)2+14=2
First, simplify the left side
7y - 8y = -y
2*-y = -2y
Now solve the equation
-2y + 14 = 2
Subtract 14 from both sides
-2y = -12
Take away the negative signs since both sides are negative
2y = 12
Divide both sides by 2
y = 6
(If the variable was x instead of y the variable would still equal 6)
Larry recorded his time as he ran. What was his average speed from hour 2 to hour 4?
Answer:
4-2=2
Step-by-step explanation:
Answer:
7 mph
Step-by-step explanation:
i took the same test on edg
Guess what sport I do and I'll give you brainly :)
Answer:
Gymnastics
Step-by-step explanation:
expand and simplify root5(root10+root2)
Compute the probability of flipping a coin once and getting heads, given that the previous flip was tails.
Answer:
the probability to flip a head is 50%
Step-by-step explanation:
I think.
evaluate the expression when c=2
c^2-8c-3
Answer:
-15
Step-by-step explanation:
Replace c with 2,
(2)^2 -8(2) -3 =
4 - 16 -3 + -12
= -15
The Awsome Bowl Factory makes two kinds of bowls. they produce a basic bowl every 6 minutes and a gigantic bowl every 15 minutes. They start at 8:00 a.m. how many minutes after they start will both bowls be produced together?
Answer:
21 minutes or 8:21 a.m
Step-by-step explanation:
6+15=21
please answer this correctly i'll give u 50 points and brainliest
Answer:
Step-by-step explanation:
Since lines 1 and 2 are parallel, <2=<6 because corresponding angles of parallel lines are congruent. <8 is the vertical angle of <6 meaning it's equal to <6. <8=115 degrees. <7 is the supplement of <6 and therefore 180-<6=<7. 180-115=65.
John bought a used car that costs $13,500. If the sales tax on the car is 8%, how much sales tax did he pay?
Answer:
1,080
Step-by-step explanation:
QUICK MATH
A toy store is having a sale. A video game system has an original price of $99. If it is on sale for 40% off the original price. Find the sale price of the game system. Round to the nearest CENT.