Answer:
[tex]P(E_1 or E_2) = \frac{7}{12}[/tex]
Step-by-step explanation:
Given
Two cubes of side 1 - 6
Required
Probability that the outcome of the roll is an odd sum or a sum that is a multiple of 5
First, the sample space needs to be listed;
Let [tex]C_r[/tex] represent the Red cube
[tex]C_b[/tex] represent the Blue cube
S represent the sample space
[tex]C_r = (1,2,3,4,5,6)\\C_b = (1,2,3,4,5,6)\\S = (2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12)[/tex]S is gotten by getting the sum of [tex]C_r[/tex] and [tex]C_b[/tex]
[tex]n(S) = 36[/tex]
Calculating the Probability
Let [tex]E_1[/tex] represent the event that an outcome is an odd sum
[tex]E_1 = (3,5,7,3,5,7,5,7,9,5,7,9,7,9,11,7,9,11)[/tex]
[tex]n(E_1) = 18[/tex]
[tex]P(E_1) = \frac{n(E_1)}{n(S)}[/tex]
[tex]P(E_1) = \frac{18}{36}[/tex]
Let [tex]E_2[/tex] represent the event that an outcome is a multiple of 5
[tex]E_2 = (5,5,5,5,10,10,10)[/tex]
[tex]n(E_2) = 7[/tex]
[tex]P(E_2) = \frac{n(E_2)}{n(S)}[/tex]
[tex]P(E_2) = \frac{7}{36}[/tex]
Let [tex]E_3[/tex] represent the event that an outcome is an odd sum and a multiple of 5
[tex]E_3 = E_1 and E_2[/tex]
[tex]E_3 = (5,5,5,5)[/tex]
[tex]n(E_3) = 4[/tex]
[tex]P(E_3) = \frac{n(E_3)}{n(S)}[/tex]
[tex]P(E_3) = \frac{4}{36}[/tex]
Calculating [tex]P(E_1 or E_2)[/tex]
[tex]P(E_1 or E_2) = P(E_1) + P(E_2) - P(E_1 and E_2)[/tex]
[tex]P(E_1 or E_2) = P(E_1) + P(E_2) - P(E_3)[/tex]
[tex]P(E_1 or E_2) = \frac{18}{36} + \frac{7}{36} - \frac{4}{36}[/tex]
[tex]P(E_1 or E_2) = \frac{18 + 7 - 4}{36}[/tex]
[tex]P(E_1 or E_2) = \frac{21}{36}[/tex]
[tex]P(E_1 or E_2) = \frac{7}{12}[/tex]
Hence, the probability that the outcome of the roll is an odd sum or a sum that is a multiple of 5 is [tex]\frac{7}{12}[/tex]
Answer:
P=(E1 or E2) 7/12
Step-by-step explanation:
determine the length of each side using the distance formula. (0,3),(3,0),(0,-3),(-3,0)
Answer: 3
Step-by-step explanation:
HELP ME PLEASE 10 POINTS ON IT PLEASE HELP ME
Answer:
4, 12, 16 (respectively)
Step-by-step explanation:
if you need one just comment and ill add one
[tex]answer = \\ red = 4 \\ blue = 12 \\ green = 16 \\ solution \: \\ let \: the \: ratios \: be \: x \: 3x \: 4x \\ x \ + 3x + 4x = 32 \\ or \: 8x = 32 \\ or \: x = \frac{32}{8} \\ x = 4 \\ replacing \: value \\ 3x \\ = 3 \times 4 \\ = 12 \\ 4x \\ = 4 \times \: 4 \\ = 16 \\ hope \: it \: helps...[/tex]
Gregory drinks 6 liters of water over 2 days. In how many days would he consume another 12 liters?
Answer:
12 liter in 4 days
Step-by-step explanation:
twice as many days, twice as many liters
Answer:
6 days
Step-by-step explanation:
"another 12 liters" => 12liters + 6 liters = 18 liters
6 liters - 2days
18 liters - x
6x = 18 * 2
x = 6 days
Please help with this question
Answer:
for x=i
Step-by-step explanation:
For
1+x²=0 => x²= -1 => x=√-1 => x= i
the given equation is not true
Points P and Q belong to AB. If AB = a and AP = 2PQ = 2QB, find the distance between: the midpoints of AP and QB.
NO explanation needed. I need this fast
Answer:
The distance between midpoint of AP and QB is [tex]\frac{5a}{8}[/tex].
Step-by-step explanation:
Given that: AB = a
AP = 2PQ = 2QB
Thus,
PQ = QB = [tex]\frac{a}{4}[/tex]
PQ + QB = [tex]\frac{a}{4}[/tex]+ [tex]\frac{a}{4}[/tex]
= [tex]\frac{a}{2}[/tex]
AP = [tex]\frac{1}{2}[/tex] a = [tex]\frac{a}{2}[/tex]
The distance between midpoint of AP and QB can be determined as;
[tex]\frac{AP}{2}[/tex] + PQ + [tex]\frac{QB}{2}[/tex]
= [tex]\frac{a}{4}[/tex] + [tex]\frac{a}{4}[/tex] + [tex]\frac{a}{8}[/tex]
= [tex]\frac{2a+2a+a}{8}[/tex]
= [tex]\frac{5a}{8}[/tex]
Therefore, the distance between midpoint of AP and QB is [tex]\frac{5a}{8}[/tex].
Use the method of completing the square for F(x)=x^2 - 8x + C, to
determine the value of F(2)
Answer:
[tex]F(2)=C-12[/tex]
Step-by-step explanation:
Given: [tex]F(x)=x^2-8x+C[/tex]
To find: value of [tex]F(2)[/tex]
Solution:
[tex]F(x)=x^2 - 8x + C\\=x^2-2(4)x+C[/tex]
Add and subtract [tex]4^2[/tex] in the left side of the equation
[tex]F(x)=x^2-2(4)x+4^2-4^2+C[/tex]
Use formula: [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]F(x)=(x-4)^2-4^2+C\\=(x-4)^2+C-16[/tex]
Put [tex]x=2[/tex]
[tex]F(x)=(x-4)^2+C-16\\F(2)=(2-4)^2+C-16\\=4+C-16\\=C-12[/tex]
Melissa made three batches of oatmeal cookies. Her recipe calls for amounts of sugar (in cups) and flour (in cups) in the following ratios.
What is the unit rate of change of flour (y) with respect to sugar (x)? That is, how much flour corresponds to one cup of sugar?
The unit rate of change is?
Graph the proportional relationship described above, with the x-coordinate representing cups of sugar, and the Y-coordinate representing cups of flour.
PLEASEEEEEE
the answer is 11/4
The unit rate of change between variables is the quotient between the difference between y-values and the difference between x-values
The unit rate of change is y = 2.25x
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the values of x be set A = { 2 , 3 , 4 }
Let the values of y be set B = { 4 1/2 , 6 3/4 , 9 }
So , the unit rate of change can be calculated by slope and linear equation of line
So , Slope m is
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 6 3/4 - 4 1/2 ) / ( 3 - 2 )
m = 2.25
So , the equation will be y = mx
y = 2.25x
Therefore , the unit rate of change is y = 2.25x
Hence ,
The unit rate of change is y = 2.25x and the graph is shown below
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geometry and perimeter help plz :(
Answer:
11) 1.9ft
12) 8.7mi
13) 7ft
14) 6ft
15) 9mi
Answer:
11) ? = 7.6/4 = 1.9 ft.
12) ? = 52.2/6 = 8.7 mi.
13) ? = 21/7 = 3 ft.
14) ? = 57/9.5 = 6 ft.
15) ? = 63/7 = 9 mi.
Phone company A conducted a study that showed 97% customer satisfaction, with a standard deviation of 1%. The sample included 25 people who appear in one of their commercials during the past three years
phone company B conducted a study to show 94% customer satisfaction with a standard deviation of 4% a random sample consisting of 100 customers
which of the company claims is more believable and why? 
A.Phone Company A because the time span was longer
B. Phone company B bc the sample was not biased
C. Company A bc the standard deviation is smaller
D.Company B because the standard deviation is larger
Answer:
B. Phone company B because the sample was not biased.
Step-by-step explanation:
While Phone company A had a higher satisfaction rate, 25 people that conducted this poll were in at least 1 commerical of the phone company's in the past 3 years. This means that their reflection of the company is biased (typically higher) and not completely based off of their performance but instead how cool it was to be in a commerical or how much they were paid. If the poll was a more random sample of just customers, it would be more believable data. On the other hand, while phone company B had a lower satisfaction rate and higher deviation, their statistics are more believable due to the random sampling of customers.
Answer:
B
Step-by-step explanation:
How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 60% antifreeze? Simply your answer
Answer:
0.67 gallon of water
Look at the diagram.
Which angle is supplementary to
can u maybe write the full question?
What is the difference between -5 and positive three
Answer: -8
Explanation: -5-3=-8
really need help yall life's depend on it plz help!!!!!!! How many numbers are 10 units from 0 on the number line?
Answer:
Step-by-step explanation:
2 numbers : 10 and -10
The functions f(x) and g(x) are shown on the graph.
Ax) = 1x
What is g(x)?
10
f(x) = x1
g(x) = ?
10
10
-5
A. g(x) = [x - 51
O B. g(x):= [X1 - 5
O.C. g(x) = 1x1 + 5
D. g(x) = (x + 51
Answer: i thini its 2
Step-by-step explanation:
The function g(x) is:
g(x) = Ix - 5I.
Therefore, the option A in the given question is correct.
What is transformation on the graphs?When a function is transformed, the graph's curve either "moves to the left, right, up, or down," "expands or compresses," "reflects," or all three.
The function is made possible by the fundamental function f(x) and the constant
g(x) = f(x - k),
horizontally moving, the f(x) k unit coordinates may be drawn.
The shift's direction depends on the value of k. Specifically,
If k > 0, the basis graph shifts right by k units.
If k < 0, the base graph shifts k units to the left.
Given that the parent function is f(x) = IxI.
From the definition,
the transformed function is moved horizontally to 5 units to the right.
So, the function is g(x) = Ix - 5I.
Therefore, g(x) = Ix - 5I.
Learn more about the transformation on the graphs here:
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Your question is incomplete; most probably, your complete question is this:
For f (x) = 2x+1 and g(x) = x+14, find (fog)(x).
A. 2x+29
B. 2x2 - 6
C. 4x2 + 4x -6
D. 2x3 + x2 -14x -7
Answer:
(fog)(x)=2x+29 (A)
Step-by-step explanation:
You put g(x) into f(x) for x and solve.
ASAP please, find x
Answer:
60
Step-by-step explanation:
Find the value of x. Leave your answer in simplest radical form. The chord measures 14, the diameter measures 18. Hint: use pythagorean theorem
Answer:
x = 4√2
Step-by-step explanation:
Find the value of x. Leave your answer in simplest radical form. The chord measures 14, the diameter measures 18. Hint: use pythagorean theorem
To solve, we will follow the steps below:
using Pythagoras theorem
opposite² + adjacent² = hypotenuse²
14² + y² = 18²
196 + y² = 324
subtract 196 from both-side of the equation
196 -196 + y² = 324-196
y² =128
Take the square root of both-side
√y² = √128
y =√128
y = √64×2
y =√64×√2
y = 8√2
x = half of y
x = y/2
x = 8√2 ÷ 2
x = 4√2
what is the slope of the line shown below?
Answer:
D. [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Use [tex]m = \frac{y2-y1}{x2-x1}[/tex] to find slope. The m in y = mx + b is always your slope.
Please. Answer Giving Brainliest!! (05.07) The net of a pyramid is shown below: The net of a square based pyramid, with base edges labeled 5 inches and the height of the triangle labeled 10 inches. The surface area of the solid is ____ square inches.
Answer: Area= square
A=5×5= 25
A=triangle 1 & 3
5×10= 50÷2= 25 25+25=50
A=triangle 2&4
10×5=50÷2=25×2=50
Area of 1-4= 25+50+50= 125
A= 125
I hope u get what ur looking for and I wish u give me brainlist But I know u won't cuz everyone say that . But thank you so much if u put for me and It would be a very appreciated from you and again thank you so much
What is 146 to the nearest square foot
Answer:
1.0138
Step-by-step explanation:
This conversion of 146 square inches to square feet has been calculated by multiplying 146 square inches by 0.0069 and the result is 1.0138 square feet.
4) Members of the school band are buying bouquets of flowers to sell at the fundraiser.
They plan on buying 120 bouquets of flowers. The ratio of the number of bouquets of roses to the number of bouquets of sunflowers will be 5/3. How many bouquets of flowers did they buy?
Bouquet of Roses?
Bouquet of Sunflowers?
Answer: Roses= 75, Sunflowers= 45
Step-by-step explanation:
Add the ratios- 5 + 3 = 8
Divide the total by the sum = 120 ÷ 8 = 15
Multiply the ratios- 5 x 15 = 75 and 5 x 3 = 45
∴ 5:3 = 75 , 45
What is the best definition of an exterior angle ?
Answer:
A
Step-by-step explanation:
The Exterior Angle is the angle between any side of a shape, and a line extended from the next side. Another example: When we add up the Interior Angle and Exterior Angle we get a straight line 180°. They are "Supplementary Angles".
Please complete the attached proof. Thanks.
Answer:
Step-by-step explanation:
A car rental company charges customers based on the equation C(m) = .25m + 30, where C(m) represents
the total cost, and m represents the number of miles driven by the customer. Explain what the numbers .25
and 30 mean in the context of the problem.
PLEASE HELP
Perform the indicated operation. Simplify answer
Subtract 3x-7 from 9x+5.
Answer:
(9x +5)-(3x-7)
6x +12
Step-by-step explanation:
PLEASE HELP MEE ILL GIVE THANKS AND BRANLIEST! Delilah has 150 microphones and each day he gives 10 away to his friends. The number of microphones left, s, if given a function of b, s = 150 - 10b. Solve the equation and determine how many are left.
Answer:
-10b+150
Step-by-step explanation:
Answer:
-(s-150)/10
Step-by-step explanation:
In 1867, the United States purchased the Alaska territory from Russia for $7.2 x 10^6. The total area was about 6 x 10^5 sq miles. What was the price per square mile?
Answer:
the two parties agreed that the United States would pay Russia $7.2 million for the territory of Alaska. For less that 2 cents an acre, the United States acquired nearly 600,000 square m
Step-by-step explanation:
the two parties agreed that the United States would pay Russia $7.2 million for the territory of Alaska. For less that 2 cents an acre, the United States acquired nearly 600,000 square m
If AB = CA and m1 = 45°, what is m3?
A.
47°
B.
45°
C.
43°
D.
90°
Answer:
B 45 degrees
Step-by-step explanation:
if AB and CA are = the M2 = 90 degrees
in an right triangle ware one angle is 90 degrees and one is 45 degrees the outer one will be 45 degrees
the total of the angles in a triangle is 180 degrees so 180 - 90 = 90
90 - 45 = 45
so the remaining angle is 45.
f(n)=64+6n
complete the recursive formula of f(n).
f(1)=?
f(n)=f(n-1)+?
Answer:
f(n) = f(n - 1) + 6
Step-by-step explanation:
Help and hurry please
Answer:
D.
Step-by-step explanation:
First try to eliminate answers.
You have to work between 30 and 40 hours to get 1565.
It's not A or B.
Now, you can see that the choices are 31, and 35
1565 is only 15 more than 1550.
It's 31.