a bag contains 10 playing cards . 7 of which are Black and 3 Red . Two cards are drawn one after the other from the bag without replacement. A. Find the probability that a Red and a Black cards were drawn.
Answers
Number of red balls =3
Number of black balls =7
Total number of balls =10
Let ,P(A)= Probability that first is red
P(B)= Probability that second is red
If second is red, there are 2 possible ways
Either first is red and second is red.
Or first is black and second is red.
So,
P(B)=
10
3
C
1
×
9
2
C
1
+
10
7
C
1
×
9
3
C
1
=
90
6
+
90
21
=
90
27
=
10
3
Probability that first is red, given second is red
P(A/B)=
P(B)
P(A∩B)
=
10
3
10
3
C
1
×
9
2
C
1
=
10
3
90
6
=
90
6
×
3
10
=
27
6
=
9
2
Related Questions
Land surveyors outlined a park as shown. What is the area of the park?
Answers
Answer:
70.875
Step-by-step explanation:
Area of park=Area of rectangle+Area of triangle
Area of park=13.5*4.8+(0.5)*(13.5)*0.9=70.875
What is the sum of the interior angles of a regular polygon with 13 sides?
giving 20 points!!
Answers
Answer:
1980
Step-by-step explanation:
13 sides
Number of sides n=13
The sum of interior angles of polygon =(2n−4)×90o
=(2×13−4)×90o
=(26−4)×90o
=22×90o
We get,
=1980
Consider the formula 4(h-3k)= h+7.
(a) Make k the subject of the above formula.
(b) If the value of h is decreased by 8, write down the change in the value of k.
guys I really need help
plzzzzzz
Answers
Answer:
=k=0.25h-7/12
Step-by-step explanation:
4(h-3k)=h+7
=4h-12k=h+7
collecting like terms and leaving characters with k on 1 side, we get;
12k=3h-7
=k=0.25h-7/12
A boat travels 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.
Answers
the speed of the boat is 5.418 km/h and the speed of the stream is 2.167 km/h
Let's define the variables:
B = speed of the boat in still water.
S = speed of the stream.
When the boat travels downstream, the total speed of the boat will be equal to the sum of the speed of the stream and the speed of the boat in still water:
speed = B + S
When the boat goes downstream, the speed will be:
speed = B - S
Now, also remember the relation:
speed*time = distance.
The given information is:
In 8 hours the boat can:
go 12 km upstream and 40km downstream.
We now need to define another variable, T, as the time that the boat travels upstream.
Then we can write this as:
12km = (B - S)*T
If the boat travels T hours upstream, and travels for a total of 8 hours, then the amount of time that travels downstream is 8h - T, then we can write:
40km = (S + B)*(8h - T)
Similarly, when we have:
"it can go 16 km upstream and 32 km downstream in the same time."
we can define a new variable T', and write:
16km = (B - S)*T'
32km = (S + B)*(8h - T')
Then we have a system of 4 equations:
16km = (B - S)*T'
32km = (S + B)*(8h - T')
40km = (S + B)*(8h - T)
12km = (B - S)*T
And we need to solve this for S and B.
To do it, we need to isolate one of the variables in one of the equations.
Let's isolate T in the last equation:
T = 12km/(B - S)
now we can replace that in the third equation to get:
40km = (S + B)*(8h - 12km/(B - S))
So now we have 3 equations:
16km = (B - S)*T'
32km = (S + B)*(8h - T')
40km = (S + B)*(8h - 12km/(S - B))
Now we need to do the same thing, this time let's isolate T' in the first equation and replace it in the second one:
T' = 16km/(B - S)
Replacing it in the second equation we get:
32km = (S + B)*(8h - T')
32km = (S + B)*(8h - 16km/(B - S))
So now we have two equations:
40km = (S + B)*(8h - 12km/(B - S))
32km = (S + B)*(8h - 16km/(B - S))
Let's simplify these:
40km = 8h*(S + B) - 12km*(S + B)/(B - S)
32km = 8h*(S + B) - 16km*(S+ B)/(B - S)
Now we can multiply both equations by (B - S) to get:
40km*(S - B) = 8h*(S + B)*(B - S) - 12km*(S + B)
32km*(S - B) = 8h*(S + B)*(B - S) - 16km*(S+ B)
Let's keep simplifying this:
40km*(B - S) + 12km*(S + B) = 8h*(S + B)*(B - S)
32km*(B - S) + 16km*(S+ B) = 8h*(S + B)*(B - S)
Now we get:
52km*B - 28km*S = 8h*(S^2 + B^2)
48km*B - 16km*S = 8h*(S^2 + B^2)
Notice that the right side of these equations is the same thing, then we can write:
52km*B - 28km*S = 48km*B - 16km*S
(52km - 48km)*B = (28km - 18km)*S
4km*B = 10km*S
B = (10/4)*S
B = (5/2)*S
Now we can replace this in one of our two equations, let's use the first one:
48km*B - 16km*S = 8h*(S^2 + B^2)
48km*(5/2)*S - 16km*S = 8h*( S^2 + ( (5/2)*S)^2)
Now we can solve this for S
104km*S = 8h*( S^2 + 25/4*S^2)
104km*S = 8h*(29/4*S^2) = 48h*S^2
104km*S = 48h*S^2
dividing at both sides by S we get:
104km = 48h*S
104km/48h = S = 2.167 km/h
And using B = (5/2)*S
We can find the speed of the boat:
B = (5/2)*2.167 km/h = 5.418 km/h
Then:
the speed of the boat is 5.418 km/h and the speed of the stream is 2.167 km/h
If you want to learn more about this topic, you can read:
https://brainly.com/question/17300107
What error did Leah make?
Answers
Answer:
the lines arent parallel, so you cant use corresponding angles theorem
The error is corresponding property does not apply.
What are parallel lines?Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions. For example, the opposite sides of a rectangle represent parallel lines.
We know that when two lines are parallel they the following property:
Alternate interior angleCorresponding angleco- interior angles.As, there is no parallel lines line.
So, the measurement if <1 = 88 can't be true because corresponding doesn't apply.
Learn ore about parallel lines here:
https://brainly.com/question/12860077
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Find AC (Round to the nearest tenth) PLS HURRY
Answers
Answer:
Does the answer help you?
Does anyone know how to do these. Its due in the morning. Pls help
Answers
Answer:
15)Given equation:
y = 2/5x - 3To plot the line first find two points:
1. x = 0 ⇒ y = -32. x = 5 ⇒ y = -1Plot (0, -3) and (5, -1) and connect the points with a line. This will be the required line.
16)Use Pythagorean to find the missing leg:
[tex]x = \sqrt{13^2 - 5^2} = \sqrt{144} = 12[/tex] unitsate
at?
20) A triangular garden has sides that
1
5
6- 7
feet.
6
What is the perimeter of the garden?
Answers
Answer:
Since all the three sides of the triangle are of equal length, we can find the perimeter by multiplying the length of each side by 3. 20 + 20 + 20 = 3 × 20 = 60 cm.
In circle O, the length of OB is 6 inches, and the measure of ∠AOB is 120°. What is the length of arc AB, in inches (show your answer in terms of π)? *
Answers
Answer:
4π inches
Step-by-step explanation:
Formula for finding length of arc AB = θ/360*2πr
Where,
Central angle (θ) = 120°
Radius (r) = 6 inches
Length of arc AB = 120/360*2*π*6
Length for arc AB = ⅓*12π
= 4π inches
I need help finding y
Answers
to solve for y, we must multiply by t on both side to get ride of the t in the denominator. By doing this, we will get:
[tex] {t}^{3} [/tex]
on the right side.
Subtracting 3, and we have successfully isolated y.
It would be impossible to get a quantitative value for y if we don't know the value of t.
respuesta listsdafddfssdffd
the volume of a cube that is 6 units on an edge in exponential form
Answers
Answer:
[tex] {6}^{3} = 216[/tex]
Correct answer gets brainliest and 5 stars
Answers
Answer:
A is false
Step-by-step explanation:
notice how in both diagrams, there are 4 triangles with lengths a, b, c, but in each diagram the triangles are just rotated and positioned differently. if there are the same amount of triangles in both diagrams, and the have equal lengths then the area of the remaining figure, should both match up.
basically the area of the big square in Step 2, is equal to both of the shaded squares, combined area, in Step 1.
A circle has a radius of \sqrt{45} 45 square root of, 45, end square root units and is centered at (-2.4,-4.8)(−2.4,−4.8)left parenthesis, minus, 2, point, 4, comma, minus, 4, point, 8, right parenthesis.
What is the equation of this circle?
Answers
Answer:
(x + 2.4)² + (y + 4.8)² = 45Step-by-step explanation:
Circle equation:
(x - h)² + (y - k)² = r², where (h, k) is the center, r - radiusSubstitute the values to get the equation:
(x - (- 2.4))² + (y - (-4.8))² = (√45)²(x + 2.4)² + (y + 4.8)² = 45Answer:
(x+2.4)^2 + (y+4.8)^2 =45
Step-by-step explanation:
Which of the following is equivalent to the expression below?
Answers
Answer:
4
Step-by-step explanation:
ln(e)=1 since ln= log_e
log(x^y)=y*log(x) so ln(e^4)=4*ln(4)=4*1=4
Answer:
D
Step-by-step explanation:
ln(e^4)
The 4 comes down in front of the natural log (ln). You get 4 ln(e)
The natural log of e (ln e ) is 1.
So the answer is 4 * 1 = 4
That may not be clear to you. We could try it another way.
e = 2.718281828
ln (2.718281828) = 1
ln(2.718281828)^4 = 4. The calculator gags until you get it right. You need the y^x key (or the x^y key of ^) It does come back with 4.
You have to monkey around with the calculator to get this to happen.
Will Mark Brainlest helppp plss
Answers
Answer:
you can ask from it will be easy for you actually I don't know answern
Find the median, first quartile, third quartile, interquartile range, and any outliers for each set of data. 111, 68, 93, 88, 74, 152, 119, 87, 88, 105, 84, 102, 151, 115, 112 A. Median: 102, Q1: 87, Q3: 113, IR: 28, outliers: none B. Median: 102, Q1: 87, Q3: 115, IR: 28, outliers: 68 C. Median: 102, Q1: 87, Q2: 115, IR: 28, outliers: none D. Median: 102, Q1: 87, Q3: 115, IR: 27, outliers: none
Answers
Answer:
Q1 = 87 ;
Q2 = 102 ;
Q3 = 115 ;
IQR = 28
OUTLIER = None
Step-by-step explanation:
Given the data:
111, 68, 93, 88, 74, 152, 119, 87, 88, 105, 84, 102, 151, 115, 112
Ordered data : 68, 74, 84, 87, 88, 88, 93, 102, 105, 111, 112, 115, 119, 151, 152
Sample size, n = 15
The first quartile, Q1 = 1/4(n+1)th term
Q1 = 1/4(15+1)th term
Q1 = 1/4(16) = 4th term
Q1 = 87
The Median , Q2 = 1/2(n+1)th term
Q2 = 1/2(15+1)th term
Q2 = 1/2(16) = 8th term
Q2 = 102
The third quartile, Q3 = 3/4(n+1)th term
Q3 = 1/4(15+1)th term
Q3 = 3/4(16) = 12th term
Q3 = 115
The interquartile range, IQR = Q3 - Q1
IQR = (115 - 87) = 28
Q1 = 87 ;
Q2 = 102 ;
Q3 = 115 ;
IQR = 28
OUTLIER = None
I NEEEDDDD HELPPPP ITS URGENTTTTT!!!!!! I’ll mark you brainliest
Answers
Answer:
(x+2)^2 + (y-15)^-1 = 64
Step-by-step explanation:
plz mark brainlist
if it’s urgent, trust me on this. desmos doesn’t lie ;))
Look at this rectangular prism:
If the height is quadrupled, then which of the following statements about its volume will be true?
Answers
Answer:
the new volume Will be 4 times the old volume
Step-by-step explanation:
I have put the photo 3
Easton is going to invest $340 and leave it in an account for 8 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for Easton to end up with $420?
Answers
Answer:
100.7%
Step-by-step explanation:
Since the interest is compounded quarterly, and there are 4 quarters per year, that would leave us with 32 quarters total where interest is acquired. Now, we need to find the interest rate, that would be required in order to end up with 420 dollars after 32 quarters.
We can setup a formula using our period of time and the money he invested into the bank:
[tex]340(x)^{32}=420[/tex]
We can divide 340 from both sides, and simplify the right side to 21 divided by 17:
[tex]x^{32}=\frac{21}{17}[/tex]
Taking the 32th root of 21/17 is equal to 1.00662, which is equal to 100.0662%. To the nearest tenth of a percent, this is equal to 100.7%.
what is the length of the third side triangle?
Answers
Answer:
x = 8cm
Step-by-step explanation:
17² = 15² + x²
289 = 225 + x²
- x² = 225 - 289
x² = 64
x = √64
x = 8
Good Luck! :)[tex]{ \boxed{ \sf \color{blue}{answer}}}[/tex]
x = 8 cm
Step-by-step explanation:
17² = 15² + x²
289 = 225 + x²
x² = 225 - 289
x² = 64
x = √64
x = 8
___________________Teorema pythagoras
what is the simplification of 9^8 / 9^7?
Answers
Answer:
9
Step-by-step explanation:
We know that a^b / a^c = a^(b-c)
9^8 / 9^7
9^(8-7)
9^1
9
What are the solutions to the quadratic equation (5y + 6)2 = 24?
y = StartFraction negative 6 + 2 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction negative 6 minus 2 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction negative 6 + 2 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction 6 minus 2 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction negative 4 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction negative 8 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction 4 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction 8 StartRoot 6 EndRoot Over 5 EndFraction
Answers
there are two solutions:
a) y = [tex]\frac{-6+2\sqrt{6} }{5}[/tex]
b) [tex]y = \frac{-6-2\sqrt{6} }{5}[/tex]
Answer:
it's A
Step-by-step explanation:
Trust me I got the question right on the quiz
Please hurry I will mark you brainliest
Answers
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
A charity is holding a benefit at an Italian restaurant. The owner of the restaurant offers to donate $200 in addition to $4 for each person that attends. Write an equation where d is the total donation and p in the number of people that attend.
A. d=4p+200
B. d=4+200p
C. p=4+200d
D. p=4d+200
Answers
Answer:
A. d=4p+200
Step-by-step explanation:
The reason why this is, is because d is the total amount, equaling to 4 times p due to the fact that it is $4 for each person that attends.
4. What is the domain?
Answers
Find x (Round to the nearest tenth). PLS HURRY
Answers
Answer:
x = 28.4°
Step-by-step explanation:
The cos(x) = 15/17 ≈ 0.88
The acos(0.88) = 28.4°
Which of the following is a monomial?
Answers
9/x and 20x⁹ are the monomials.
The correct option A and D.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
A monomial is a polynomial with just one term.
From the given choices:
9/x and 20x⁹ are the monomials.
11x - 9 and 20x⁹ -7x are the binomial.
Therefore, A and D are the monomials.
To learn more about the Polynomials;
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5. Simplify: 2/5 +3/7+(-6/5)+ (-13/7)
Answers
Answer: -78 / 35
Step-by-step explanation:
Given
2/5 + 3/7 + (-6/5) + (-13/7)
Combine terms that have the same denominator
= 2/5 + (-6/5) + 3/7 + (-13/7)
= -4/5 - 10/7
Convert denominator by Least Common Multiple (LCM)
= (-4 × 7) / (5 × 7) - (10 × 5) / (7 × 5)
= -28/35 - 50/35
= -78 / 35
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex] \frac{2}{5} + \frac{3}{7} + ( - \frac{6}{5} ) + ( - \frac{13}{7} ) \\ \frac{2}{5} + \frac{3}{7} - \frac{6}{5} - \frac{13}{7} \\ ( \frac{2}{5} - \frac{6}{5} ) + ( \frac{3}{7} - \frac{13}{7} ) \\ \frac{2 - 6}{5} + \frac{3 - 13}{7} \\ \frac{ - 4}{5} + \frac{ - 10}{7} \\ \frac{ - 4}{5} - \frac{10}{7} \\ \frac{ - 28 - 50}{35} \\ \frac{ - 78}{35} \\ - \frac{78}{35} [/tex]
Given the function f(x) = -2c+cx-x^2, and f^-1(5) = -1, find c
Answers
Answer:
[tex]c=-2[/tex]
Step-by-step explanation:
We are given the function:
[tex]f(x) = -2c + cx - x^2[/tex]
And that:
[tex]\displaystyle f^{-1} (5) = -1[/tex]
And we want to determine the value of c.
Recall that by definition of inverse functions:
[tex]\displaystyle \text{If } f(a) = b, \text{ then } f^{-1}(b) = a[/tex]
So, since f⁻¹(5) = -1, then f(-1) = 5.
Substitute:
[tex]f(-1) = 5 = -2c + c(-1) - (-1)^2[/tex]
Simplify:
[tex]5 = -2c - c - (1)[/tex]
Combine like terms:
[tex]6 = -3c[/tex]
And divide. Hence:
[tex]c = -2[/tex]
In conclusion, the value of c is -2.
Can someone please answer B (PICTURE)
Answers
Answer:
The question is asking for the perimeter. There are three ways to answer this depending on the assumptions though so I'll let you choose.
Assumptions are basically the different scenarios
1st scenario being the trim covers the carpet and the tile, they'd need 48m of trim (12+12+4+8+8+4)
2nd scenario in which the trim covers the carpet but not the tiled area, they'd need 44m of trim (12+12+4+8)
3rd scenario where the trim only covers the the tiled area, 4m of trim
(just 4 since the tile only touches 4m of the wall)
Hope this helps!
Step-by-step explanation:
trim is just the perimeter since it covers the base of the wall
