By definition of conditional probability,
P(B | A) = P(A ∩ B) / P(A)
==> P(A) = P(A ∩ B) / P(B | A) = 0.15/0.75 = 0.2
By definition of complement,
P(B') = 1 - P(B)
==> P(B) = 1 - P(B') = 1 - 0.7 = 0.3
Now by the inclusion/exlcusion principle, we have
P(A U B) = P(A) + P(B) - P(A ∩ B)
==> P(A U B) = 0.2 + 0.3 - 0.15 = 0.35
3x (x - 2) = x^2 - 4
Answer:
x = 1, x = 2
Step-by-step explanation:
Given
3x(x - 2) = x² - 4 ← distribute parenthesis on left side
3x² - 6x = x² - 4 ( subtract x² - 4 from both sides )
2x² - 6x + 4 = 0 ( divide through by 2
x² - 3x + 2 = 0 ← in standard form
Consider the factors of the constant term (+ 2) which sum to give the coefficient of the x- term (- 3)
The factors are - 1 and - 2 , since
- 1 × - 2 = + 2 and - 1 - 2 = - 3 , then
(x - 1)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
WILL GIVE BRAINLIEST
How many integers n between 1 and 100 inclusive are there, such that n^2 + n is divisible by 99
Answer:
It is 121
Step-by-step explanation:
Which function can be used to find r, the total amount the teacher pays in dollars when
z scissors are ordered?
A teacher is ordering scissors for her classroom.
• the teacher pays a one-time fee of $8.
• the teacher also pays $2 for each pair of scissors ordered.
show that the the product of the first two numbers 28,48 of that stem is equal to the product of their LCM and HCF
Answer:
HCF is 4
LCM is 336
Step-by-step explanation:
2/28 , 48
2/14 , 24
2/7 , 12
2/7 , 6
3/7 , 3
7/7 , 1
1 , 1
HCF is 2 × 2 =4
LCM is 2 × 2 × 2 × 2 × 3 × 7 = 336
Please help I don’t understand math
Answer:
x = 12
Step-by-step explanation:
The sum of the two smaller angles is 140
80+5x = 140
Subtract 80 from each side
80+5x-80 =140-80
5x = 60
Divide each side by 5
5x/5 = 60/5
x = 12
Use the function below to find F(-4).
F(x) = 2^x
Answer:
Step-by-step explanation:
F(x)=2^x
[tex]F(-2)=2^{-2} =\frac{1}{2^2} =\frac{1}{4}[/tex]
please help asap, see attached photo!!
answer please it's urgent
Answer:
HOPE IT HELP YOU . Plz tell me if it is write or wrong .
Find X
Round to the nearest tenth
Answer:
x=437.3 ft
Step-by-step explanation:
cos(29)=B/H, cos(29)=x/500. x=437.3 ft
if the area is 1 then what is the side length of a square?
Answer:
1
Step-by-step explanation:
Since we are taking the area of a square, you can take the square root of its area to find the side lengths.
√1 = 1
When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown?
Answer:
The Polynominal is not shown. So how can i answer???
Step-by-step explanation:
Thank You! Hope it helps! Please Mark me brainliest!
A man walks at the rate of 88 paces to the minute if the average length of his paces is 0.875m, find the time take to walk 2.31km.
Answer:
30 minutes
Step-by-step explanation:
Walk rate = 88 paces/ minute
Average length of pace = 0.875 m
Time taken to walk 2.31 km ;
The distance in metres :
1000 m = 1 km
2.31 km = (1000 * 2.31) = 2310 m
Recall :
Time taken = distance / speed
Distance walked in a minute = 88 * 0.875 = 77 m
Time taken = 2310 / 77
Time taken = 30 minutes
Verify that –(-x) is the same as x , for x = −4/5
Answer:
Step-by-step explanation:
-(--4,5)= -(4,5)= -4,5
To earn $60 for the skateboard, Waheeda decides to run a lemonade stand. If she sells each glass of lemonade for $1.50, how many glasses of lemonade will she need to sell? Write and solve an equation to find the answer.
Cost of skateboard : $60
Cost of each lemonade = $1.50
Total glasses of lemonade to be sold = 60/1.5
= 60/15×10
= 4×10
= 40
Therefore she has to sell 40 glasses of lemonade
Must click thanks and mark brainliest
BRAINLIST!! 20 POINTS! PLEASE HELP ILL FAIL IF I DONT PASS THIS TEST!!!
What type of counting problem is this?
How many different sums of money exist if we can choose 4 coins from any number of pennies, nickels, dimes, and quarters?
Combination without repetition
Permutation with repetition
Combination with repetition
Permutation without repetition
Answer:
the third one: Combination with repetition
Step-by-step explanation:
it says there are any number of pennies, nickels, dimes, and quarters, so there is repetition. the order doesn't matter because it asks for the different sums, so it's a combination with repetition
"How many different sums of money exist if we can choose 4 coins from any number of pennies, nickels, dimes, and quarters?" is a Combination with repetition problem.
What is combination with repetition?A combination with repetition involves a multiset. A multiset allows elements to be repeated unlike an ordinary set.
Number of ways to select r things from n possibilities: C (n + r − 1, r)
Since he can choose any coin any number of time, repetition is there. Also, order in which coins are chosen is not important, thus it is a combination.
Therefore, the third option is correct. This is a combination with repetition problem.
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Find the missing length indicated
Answer:
x = 240
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of large triangle)² = ( part of hypotenuse below it) × (whole hypotenuse)
x² = 144 × 400 = 57600 ( take the square root of both sides )
x = [tex]\sqrt{57600}[/tex] = 240
x = 240
Using Pythagoras' theorem on the 3 triangles of sides (as shown in the graphic - the 2 smaller inner triangles and the large main triangle) it can be shown that the height is the square root of the product of both segments of the baseline.
let's call the 2 segments p and q.
p+q = 400
p = 144
q = 400 - 144 = 256
so, as said before, height = sqrt(p×q) = sqrt(144×256) = 192
now the main Pythagoras with the smallest triangle to get x
x² = 192² + 144² = 36864 + 20736 = 57600
x = 240
now, FYI, why is that formula true ?
as we said, we called the segments of the long baseline p and q.
then we can the sides of the main triangle x and y.
and the height is simply h.
so, then we have for the main rectangular triangle
(p+q)² = x² + y²
and for the 2 smaller triangles
x² = p² + h²
y² = q² + h²
=>
p² +2pq + q² = p² + h² + q² + h²
2pq = 2h²
h² = pq
h = sqrt(pq)
and there you have it. just as simple as that.
4[30-(10-2)x3] what is the answer?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{4[30-(10-2)\times3]}}[/tex]
[tex]\huge\boxed{\rightarrow\mathsf{4[30 - (\bold{8}}) \times3]}[/tex]
[tex]\huge\boxed{\rightarrow \mathsf{4[30 - \bf 24]}}[/tex]
[tex]\huge\boxed{\rightarrow \mathsf{4(30) + 4(-24)}}[/tex]
[tex]\huge\boxed{\rightarrow \mathsf{\bf 120 - 96}}}[/tex]
[tex]\huge\boxed{\rightarrow\mathsf{\bf 24}}[/tex]
[tex]\huge\boxed{\rm{Answer: \mathsf{24}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
24Step-by-step explanation:
4[30 - (10 - 2)*3] = 4[30 - 8*3] =4[30 - 24] = 4*6 = 24Help ! With step by step solution
Answer:
the correct answer is C
Step-by-step explanation:
first step you change the x and y powers to the square root(showing in the pic).
second the number outside of the parenthesis times the numbers inside the parenthesis and then you just figure it out how it works...
When x + y = 30 and x < 13, which of the following must be true?
y = 30
y > 17
y = 17
y < 17
y > 30
Answer:
y>17
Step-by-step explanation:
[tex]x + y = 30 \\ 13 + y = 30 \\ y = 17 \\ for \: x < 13 \\ y > 17[/tex]
Answer:
y>17
Step-by-step explanation:
x+y=30
x<13
What + 13 is 30?
17. So if x+y=30. Because x will be less than 13, y must make up the differnce by being greater than 17.
Ex: x=12
y+12=30
y=18
18 is greater than 17.
This is a great way to check because if your not sure, it elimates the other options!
Hope this helps!
Simplify the complex number √-16+8.
Answer:
[tex]\sqrt{-16} +8[/tex]
[tex]=4i+8[/tex]
OAmalOHopeO
using Euclids division algorithm, find the largest number that divides 475 and 871 leaving 7 as the remainder in each case
Answer:36
Step-by-step explanation:
gcd(475-7,871-7)=gcd(468,864)=36
[tex]\begin{array}{c|c|c|c|c|c}&0&1&1&5&2\\468&864&468&396&72&\boxed{36}\\468&396&72&36&0\\\end{array}[/tex]
brianna practices the panio 30 minutes each day write an expression for the number of hours she practises in d days
= X
20
100
60
Please help me
Answer:
x = 100
Step-by-step explanation:
(100-40)/2
= 60/2
= 30
So it's 100
Answered by GAUTHMATH
Hey guys ♡
hw r u all doin
pls solve this question for me ⤵️
(m-1)/2 - (m-2)/3 = ( m - 4 )/7
Answer:
m = - 31
Step-by-step explanation:
Given
[tex]\frac{m-1}{2}[/tex] - [tex]\frac{m-2}{3}[/tex] = [tex]\frac{m-4}{7}[/tex]
Multiply through by 42 , the LCM of 2, 3 and 7 , to clear the fractions
21(m - 1) - 14(m - 2) = 6(m - 4) ← distribute parenthesis
21m - 21 - 14m + 28 = 6m - 24
7m + 7 = 6m - 24 ( subtract 6m from both sides )
m + 7 = - 24 ( subtract 7 from both sides )
m = - 31
A phone company charges each customer a monthly fee of $11.25. In addition, it charges $0.03 per minute for in-state calls and $0.11 per minute for out-of-state calls. What is the total monthly charge for a customer who made 340 minutes of in-state calls and 84 minutes of out-of-state calls?
340 x 0.03 = 10.2 (in state)
84 x 0.11 = 9.24 (out of state)
10.2 + 9.24 + 11.25
= $30.69 monthly charge
hope it helps :)
The total monthly charge for a customer is given as $30.69.
What is simplification?Simplifying allows us to test each process and strategy to determine which is the most efficient and best suited for its specific goal.
here,
A phone provider costs each customer $11.25 per month. Furthermore, it charges $0.03 per minute for in-state calls and $0.11 for out-of-state calls.
Charge within the boundary of state for 340 minutes = 340 x 0.03 = 10.2
Charge beyond the boundary of state for 84 minutes = 84 x 0.11 = 9.24
Total monthly charge = 10.2 + 9.24 + 11.25
= $30.69 monthly charge
Thus, A customer's total monthly price is shown as $30.69.
Learn more about simplification here:
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I need help to find Y =
Answer:
3
Step-by-step explanation:
In the diagram, what is the measure of angle 1 to the nearest degree?
33 degrees
55 degrees
75 degrees
105 degrees
Answer:
75 degrees
Step-by-step explanation:
From the first part of the diagram,
vertically opposite angles are equal,
hence we have
125° + (4x-5)° + 125° + (4x-5)° = 360°
(Angles about a point equals 360°)
4x – 5 + 4x – 5 + 125 + 125 = 360
8x + 250 – 10 = 360
8x = 360–250 + 10
8x = 120
x = 15°
Now we have (5x)° in the second part.
5x = 5 × 15 = 75°
1 is vertically opposite to angle 75°
hence it is equal to 75 degrees.
Answer:75
Step-by-step explanation:
La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6, la probabilidad de que apruebe un estudiante B es 0.4 y la probabilidad de que ambos estudiantes aprueben es 0.3. ¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?
Answer:
0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.
Step-by-step explanation:
La probabilidad condicional :
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
En el cual:
P(B|A) es la probabilidad de que ocurra el evento B, dado que A sucedió.
[tex]P(A \cap B)[/tex] es la probabilidad de que ocurran tanto A como B.
P(A) es la probabilidad de que ocurra A.
En esta pregunta :
Evento A: Estudiante A aprueba.
Evento B: Estudiante B aprueba.
La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6
Entonces [tex]P(A) = 0.6[/tex]
La probabilidad de que ambos estudiantes aprueben es 0.3
Entonces [tex]P(A \cap B) = 0.3[/tex]
¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3}{0.6} = 0.5[/tex]
0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.
Let f(x)=1/2|x−2|. Write a function g whose graph is a translation 7 units to the left of the graph of f.
Answer:
g(x) = -2(x - 6) - 7
Step-by-step explanation:
Sorry if I'm wrong
Which linear inequality is represented by the graph?
Answer:
D
Step-by-step explanation:
The correct answer is D
Answer:
D
Step-by-step explanation:
y<2/3 x-1 is the answer
