Answer:
5x = 25|:5
x = 5
Two cards are drawn without replacement from an ordinary deck, find the probability that the second is not a black card, given that the first is a black card. What is the conditional probability?
(a) [tex]\frac{26}{51}[/tex]
(b) [tex]\frac{26}{51}[/tex]
Step-by-step explanation:(i) Probability is the likelihood of whether or not an event will occur. It is given by the ratio of the number of favourable outcomes to the number of expected outcomes. i.e
P = number of favourable outcomes / total number of possible outcomes
For drawing a first card which is black,
number of favourable outcomes = 26 (since there are a total of 26 black cards in a deck of card)
total number of possible outcomes = 52 (since the total number of cards in a deck of card is 52)
∴ Probability of drawing the first black card = 26 / 52 = 1 / 13
Since the second card is not a black card, it is a red card.
number of favourable outcomes = 26 (since there are a total of 26 red cards in a deck of card)
total number of possible outcomes = 51 (since a black card has been previously picked from the deck)
∴ Probability of drawing a second black card = 26 / 51
The probability that the second is not a black card is 26 / 51
(ii) The conditional probability of a given event B is the probability that the event will occur knowing that a previous event A has already occurred,
It is given by;
P(B|A) = P(A and B) ÷ P(A)
In this case;
event B is drawing a second card which is not black
event A is drawing a first card which is black
This implies that;
P(A and B) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex]
P(A) = [tex]\frac{1}{13}[/tex]
Substitute these values in the equation for conditional probability as follows;
P(B|A) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex] ÷ [tex]\frac{1}{13}[/tex]
P(B|A) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex] x [tex]\frac{13}{1}[/tex]
P(B|A) = [tex]\frac{26}{51}[/tex]
Therefore the conditional probability is [tex]\frac{26}{51}[/tex]
please help me asap! i’ll give brainliest!
Answer:
1/9
Step-by-step explanation:
First find the area of each circle with the formula a= Pi(r^2)
Area of circle with a radius of 4
a= Pi(4^2)
a= 16pi
Area of circle with radius of 12
a= Pi(12^2)
a= 144pi
Now use these values to represent the areas of the circles as a ratio
16pi/ 144pi
The pi's cancel out in this ratio
So we are left with
16/144
We can then go ahead and simplify these numbers as well to get the ratio in the simplest form
1/9
CAN SOMEONE HELP ME PLS
A because they are preserving? I guess that's the best way for me
The half life of a drug in the bloodstream is 18 hours. What fraction of the original drug dose remains in 36 hours? in 72 hours?
Answer:
1/4 in 36 hours
1/8 in 72 hours
To determine the fraction of the original drug dose remaining after a certain time, we can use the concept of half-life. The half-life is the time it takes for half of the drug to decay or be eliminated from the bloodstream.
Given that the half-life of the drug is 18 hours, we can calculate the fraction of the original drug dose remaining after a certain number of hours.
After 18 hours (one half-life), half of the drug remains, which is equal to 1/2 or 0.5 of the original dose.
To find the fraction remaining after 36 hours (two half-lives), we can halve the remaining amount from the previous step:
(1/2) * (1/2) = 1/4 or 0.25
Therefore, after 36 hours, 1/4 or 0.25 of the original drug dose remains.
To find the fraction remaining after 72 hours (four half-lives), we can continue halving the remaining amount:
(1/2) * (1/2) * (1/2) * (1/2) = 1/16 or 0.0625
Therefore, after 72 hours, 1/16 or 0.0625 of the original drug dose remains.
In summary:
After 36 hours, 1/4 or 0.25 of the original drug dose remains.
After 72 hours, 1/16 or 0.0625 of the original drug dose remains.
To know more about fraction here
https://brainly.com/question/30154928
#SPJ2
What value is closest to the area of the damaged section?
Answer:
6.0 square feet
Step-by-step explanation:
6 ÷ 2 = 3(radius)
are of the damaged section = x
77/360 = x/3²π
=> x = 77 × 9π ÷ 360 = 6.0445 <= 6.0 square feet is the closest to this number
What is the median of this set of data?
32,36,38,39,42
Answer:
38
Step-by-step explanation:
To find the median, make sure the number are in increasing order (they are), then start crossing out the outside numbers until you meet in the middle:
32 36 38 39 42
/ 36 38 39 /
/ / 38 / /
The only number left is 38, so the median is 38.
If there were two numbers remaining, you would take the average of the two.
(Add both numbers and divide by 2)
A rope is 50 meters long. It is cut into two pieces and one piece is 8 meters longer than the other. What are the two lengths?
Show work please
Answer:
21 meters and 29 meters
Step-by-step explanation:
x + (x + 8) = 50
2x + 8 = 50
2xc = 42
x = 21
x + 8 = 29
If g(x)= x+1/x-2 and h(x)= 4-x, what is the value of (g•h)(-3)?
Answer:
8/5
Step-by-step explanation:
First find h(-3)
h(-3)= 4-(-3) = 4+3 = 7
Then take this result and find g(h(-3)) = g(7)
g(7) = (7+1)/( 7-2) = 8/5
Can anyone help me find the function for this trig graph ? i need a specific answer for the function , not just telling me how to find it . 80 pts
Answer:
y = 5 sin (2x) + 4
Step-by-step explanation:
this is sines function,
the amplitude is [9 - (-1)]/2 = 10/2 = 5
the period is 2πx/π = 2x
the x-axis of actual function is at y = 4
so, the function is :
y = 5 sin (2x) + 4
In 2015, there were approximately 3,774,000 births in a country. Find the birth rate in births per minute.
Answer:
7.18 / minute.
Step-by-step explanation:
The number of minutes in 2015 = 365 * 24 * 60 = 525,600.
So birth rate = 3,774,000 / 525,600
= 7.18
please help will mark brainliest for right answer! No links...
Let f(x)=2x^3−x . What is the average rate of change of f(x) from 2 to 8 ?
Answer:
[tex]f(x) = {2x}^{3} - x \\ \delta \: f(x) = \frac{f(8) - f(2)}{2} \\ = \frac{(2 {(8)}^{3} - 8) - (2 {(2)}^{2} - 2)}{2} \\ = \frac{(1016 - 6)}{2} \\ = \frac{1010}{2} \\ = 505[/tex]
The cost to fill a car’s tank with gas and get a car wash is a linear function of the capacity of the tank. The costs of a fill-up and a car wash for three different customers are shown in the table. Write an equation for the function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with a truck whose tank size is 26 gallons.
Tank size (gal)(x)
Total cost ($)f(x)
11
24.15
12
26.05
17
35.55
Answer:
Step-by-step explanation:
If this is linear, then the difference between each x/y coordinate is constant, representing the slope of a straight line. We can find the slope of that line by using the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For use we will use the coordinates (11, 24.15) and (12, 26.05) from the data as our x and y values respectively. Filling in the formula:
[tex]m=\frac{26.05-24.15}{12-11}[/tex] which gives us the cost per gallon of gas as
m = 1.90
Now that we know the cost per gallon of gas (which is also the slope of the line we are looking for), we will use that slope value, m, and write the equation in point-slope form and then solve it for y. Point-slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex] where y1 and x 1 are the coordinates from a given data point. We can use either one; regradless of the point we choose as x and y, we'll get the same exact answer every time. Let's use the coordinate (12, 26.05) and fill in the point-slope form of the line:
y - 26.05 = 1.90(x - 12) and then we will distribute and solve for y:
y - 26.05 = 1.90x - 22.80 and
y = 1.90x + 3.25
That's the equation we need to solve for what the second part of the question is asking us to, which is to find the cost, y, of filling a tank that is 26 gallons, x. Fill in 26 for x and solve for y:
y = 1.90(26) + 3.25 and
y = 49.40 + 3.25 so
y = $52.65
Plz help 10 pts
X=
4
6
12
Answer:
x = 12
Step-by-step explanation:
The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.
3*x = 6^2
3x = 36
Divide each side by 3
3x/3 = 36/3
x = 12
Find the surface area l=12 w=4 h=2
Answer:
SA=160
Step-by-step explanation:
surface area of cuboid=2lw+2wh+2hl
=2(12)(4)+2(4)(2)+2(2)(12)
=96+16+48
=160
MARK ME BRAINLIEST THANKS MY ANSWER PLEASE
Maria has $5.00 more than José. Together they have. $37.50.
Which of these equations would you use to find the amount of money José has?
Answer:
B
Step-by-step explanation:
Maria has $5.00 more than José
Maria, M
Jose, j
M = j + $5
j + M = $37.50
j + j + $5 = $37.50
The amount of money José has is $16.25.
What is the equation?An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
Maria has $5.00 more than José.
Together they have. $37.50.
Let, the amount of money José has be x.
Based on the given conditions, formulate:
[tex]\rm 5+2\times x=37.50\\\\5+2x=37.50\\\\2x=37.50-5\\\\2x=32.50\\\\x=\dfrac{32.50}{2}\\\\x= 16.25[/tex]
Hence, the amount of money José has is $16.25.
Learn more about equation here;
brainly.com/question/21511618
#SPJ2
I need an answer ASAP
The proportion of iphone users over other smart phones is said to be 42%. We believe the propotion may be greater. Determine the sample size needed to test this claim using alpha = 0.05, beta = 0.05, and the maximum error we will allow is 0.10.
A.
322
B.
379
C.
504
D.
269
Ik its another one of these
Find the measure of angle x in the figure below:
Which function represents the total cost for Lorenzo to rent x number of tables and the chairs he needs to go with them? 12x 12x2 + 40 12x + 40 8x + 40
Complete question is;
Lorenzo wants to know how much it will cost to rent tables and chairs for an event. He investigates renting tables and chairs and decides to use two different companies. Company A $4 per table (seats 4) and a $25 one-time delivery and pickup fee Company B $2 per chair and a $15 one-time delivery and pickup fee Each table seats 4 people, so Lorenzo needs to rent 4 chairs for every table. x = number of tables Cost to rent tables from Company A: f(x) = 4x + 25 Cost to rent chairs from Company B: g(x) = 2(4x) + 15 Which function represents the total cost for Lorenzo to rent x number of tables and the chairs he needs to go with them?
A) 12x
B) 12x² + 40
C) 12x + 40
D) 8x + 40
Answer:
C: 12x + 40
Step-by-step explanation:
We are told that the Cost to rent tables from Company A is;
f(x) = 4x + 25
Also, we are told that the Cost to rent tables from Company B is;
g(x) = 2(4x) + 15
Thus, total cost for Lorenzo to rent x number of tables and the chairs he needs is;
Total = f(x) + g(x)
Total = 4x + 25 + 2(4x) + 15
Total = 4x + 25 + 8x + 15
Total = 12x + 40
A basket contains 20 red apples. The rest of the apples are green. The
number of red apples is 80% of the total number of apples. How many
total apples are in the basket?
Answer: 25 total apples
Step-by-step explanation:
so you would set up an equation where 20 = 0.80x
20 is 80 percent of the total (x)
so then solve for x, which would be 20 divided by 0.8
That's 25
20
What is the perimeter of the quadrilateral below? If necessary, round to the nearest tenth.
Answer:
Perimeter = 33.4 units.
Step-by-step explanation:
The 2 horizontal lines are 10 and 3 units long.
The vertical line is 9 units long.
By Pythagoras the length of the sloping line
= sqrt(9^2 + 7^2)
= sqrt(130)
= 11.4017.
Perimeter = 10 + 3 + 9 + 11.4
= 33.4 units.
The General Social Survey reported a sample where about 61% of US residents thought marijuana should be made legal. If we wanted to limit the margin of error of a 95% con dence interval to 2%, about how many Americans would we need to survey?
Answer: we need to survey 2285 Americans.
Step-by-step explanation:
When population proportion (p) is known, then the formula to evaluate the sample size( minimum) is given by :-
[tex]n=p(1-p)(\frac{z^*}{E})^2[/tex], where E = margin of error , z* = critical z-value.
Given: p= 0.61, E=0.02, Critical z value for 95% = 1.96
Required sample size: [tex]n=(\frac{1.96}{0.02})^2(0.61)(1-0.61)[/tex]
[tex]=(98)^2(0.61)(0.39)\\\\=9604(0.61)(0.39)\\\\\approx$$2285[/tex]
Hence, we need to survey 2285 Americans.
Who has larger pieces of pizza? Joey has a slice of pizza cut from pizza with a radius of 8 in and cut into 6 slices. Susie has a slice of pizza cut from a pizza with a radius of 9 in and cut into 8 slices
Which one of these is written in the slope-intercept form? A. x = mb + y B. x + y = 1/3m C. y = mx + b B. y + b = m+ x
Answer:
C
Step-by-step explanation:
y = mx + b is the standard form of a Slope-Intercept
I need the surface area for this prism. If you could provide a formula too, that would be great!
Answer:
136 [tex]m^{2}[/tex]
Step-by-step explanation:
Back of the shape area/ front of the shape area
A = [tex]\frac{1}{2}[/tex] [tex](bh)[/tex]
A = [tex]\frac{1}{2}[/tex] (6 × 4)
A = [tex]\frac{1}{2}[/tex] (24) Divide 24 ÷ 2
A = 12
Bottom of the shape area
A = l · w
A = 7 · 6
A = 42
Left side of the shape area/right side of the shape area
A = l · w
A = 7 · 5
A = 35
---------------------------------------------------------------------------------
35 + 35 + 42 + 12 + 12 = 136 [tex]m^{2}[/tex]
SA = 136 [tex]m^{2}[/tex] Surface Area = 136 [tex]m^{2}[/tex]
Help besties please flip the picture to see better
Answer:
E. C= 80+ 12n
Step-by-step explanation:
____________
A runner runs a distance of 450 metres in a time of 50 seconds. What is his average speed?
Answer:
0.279 miles / 0.449 km
Step-by-step explanation:
convert the meters into miles/kilometers to get your answer
The average speed of the runner is 9 meters per second.
What is the difference between average and instantaneous speed?The average speed is calculated for a period of time while instantaneous speed is calculated at certain instant of time.
For instantaneous speed and average speed are equal for an object moving with constant speed.
The distance travelled and time are given as 450 meters and 50 seconds respectively.
The average speed is given as,
Total distance travelled ÷ Total time taken
= 450 ÷ 50
= 9
Hence, the runner has the average speed of 9 m/s.
To know more about speed click on,
https://brainly.com/question/28224010
#SPJ2
Estimate the given product 61 x 47 =
The hypotenuse of a right triangle is 10cm long. One of the triangle’s legs is three times the length of the other leg. Find the lengths of the three sides of the triangle. In case of non-integer answer(s), round your answer(s) to the nearest hundredth.
Answer:
side_1 = 10
side_2 = 3.16
side_3 = 9.49
Step-by-step explanation:
pitagora's theorem
[tex]x^2+(3x)^2=10^2\\x^2+9x^2=10^2\\10x^2=10^2\\x^2=10\\x=\sqrt{10}[/tex]
What is the value of m in the equation 4m + 2(m + 1) = 9m + 5?
1. −1
2. 1
3. 7
4. 17
Answer:
hhhhhhhhhhooooooooooooooooooooo
Step-by-step explanation: