From the sample space S=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) a single number is to be selected at random. Given event A, that the selected number is even, and event B, that the selected number is a multiple of 4, find P(AIB)
Answer:
[tex]P(A|B) = 1[/tex]
Step-by-step explanation:
Given
[tex]S = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}[/tex]
[tex]A = \{2,4,6,8,10,12,14\}[/tex]
[tex]P(A) = 7/15[/tex]
[tex]B = \{4,8,12\}[/tex]
[tex]P(B) = 3/15[/tex]
Required
[tex]P(A|B)[/tex]
This is calculated as:
[tex]P(A|B) = \frac{P(A\ n\ B)}{P(B)}[/tex]
Where
[tex]A\ n\ B = \{4,8,12\}[/tex]
[tex]P(A\ n\ B) = 3/15[/tex]
So, we have:
[tex]P(A|B) = \frac{P(A\ n\ B)}{P(B)}[/tex]
[tex]P(A|B) = \frac{3/15}{3/15}[/tex]
[tex]P(A|B) = 1[/tex]
pls help for both 12 and 13!!
Answer:
The answer to 12 is 40 cubic units
Step-by-step explanation:
Which of these fractions are equivalent to -3/2
Study the given values of the data and then choose the best suitable answers for all the questions.
10,10, 18, 24,28
Answer:
Mean = 18 and Mode = 10
Step-by-step explanation:
The given data is :
10,10, 18, 24,28
We can find the mean of the data,
[tex]Mean=\dfrac{\text{sum of observations}}{\text{total no of observations}}[/tex]
[tex]M=\dfrac{10+10+18+24+28}{5}\\\\=18[/tex]
Mode is the repetition of data.
Here, 10 repeats 2 times.
So, the mode is 10.
Write an inequality representing the following phrase:
Three more than five times a number t is less than thirty.
Answer:
5t + 3 < 30
Step-by-step explanation:
Five times a number t is 5t.
Three more just means add 3 more to your first term (in this case it's 5t).
Less than thirty means not less than or equal to 30 but just less then 30.
A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 8 ft.
(a) Find the force exerted by the milk on one end of the tank when the tank is full. (Round your answer to the nearest integer.) lb
(b) What if the tank is half full?
Answer:
a) 12989 Ib
b) 2756.3 Ib
Step-by-step explanation:
Density of milk = 64.6 Ib/ft^3
Diameter of tank = 8 ft
radius = 4 ft
a) Calculate force exerted by milk on one end of tank when Tank is full
pressure on strip ≈ 64.6 ( 4 - yi ) i.e. surface of milk = 4
Total force = 129.2 * [tex]\int\limits^4_4 {4-y} \sqrt{16-y^2} \, dx[/tex]
∴Force exerted = 129.2 * Area of semicircle( radius =4 ) * radius
= 129.2* 8π * 4 ≈ 12989 Ib
b) Force exerted when Tank is half full
pressure on strip ≈ 64.6 ( 0 - yi ) i.e. surface of milk = 0
Total force = 129.2 * [tex]\int\limits^0_4 {0-y} \sqrt{16-y^2} \, dx[/tex]
∴ Force exerted ≈ 2756.3 Ib
Given the circle, find the arc measure.
Please help I’ll mark brainliest
Answer:
arc KLJ = 205°
Step-by-step explanation:
Recall: measure of arc equals measure of central angle
Therefore:
measure of arc LJ = 56°
measure of arc KL = 149°
arc LJ + arc KL = arc KLJ
Substitute
56° + 149° = arc KLJ
205 = arc KLJ
arc KLJ = 205°
fill in a base 6 multiplication table. and use the table and the standard algorithm to solve.
Answer:
See in bold
1 x 1 = 1
1 x 2 = 2
1 x 3 = 2
1 x 4 = 4
1 x 5 = 5
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
2 x 4 = 8
2 x 5 = 10
3 x 1 = 3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12 Total 70
3 x 5 = 15
4 x 1 = 4
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16 total 125
4 x 5 = 20
5 x 1 = 5
5 x 2 = 10
5 x 3 = 15 total 175
5 x 4 = 20
5 x 5 = 25 total 220
Total = 220
Algorithm Finding 142 = 220 - 78 = 142
-78 = 6 x 13 therefore 142six = 13
Algarithm Finding X 230six = X diagonal
X diagonal list on table shows;
1 x 1 = 1
2 x2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
Total = 91
230/91 = 2.52747253 if diagonal algorithm
or 230 taken from the last 5 x 5 algorithm total = 220
1 x 6 = 6 220 + 6 = 226 x = 4+ then 1 x 6
2 x 6 = 12 = 18 220 + 18 = 38 x = 8 - then 2 x 6
as X230 = 8- 230 = 2 x 6
or X230 = 4+ 230 = 1 x 6
How do you solve for A in the following question?
Answer:
4x + 17 + x + 23 = 180 ( being straight line )
5x + 40 = 180
5x = 180 - 40
5x = 140
X = 140 / 5
X = 28 (answer)
Which graph shows the point (-4, 0)?
Answer:
Graph C is the correct answer
Step-by-step explanation:
Hope this helps and,
let me know if it was correct.
Please help me with this problem
Question: 5d - 6 + 8 -3d = 12
5d - 6 + 8 - 3d = 12
Combine like terms:
2d + 2 = 12
Subtract 2 from both sides
2d = 10
Divide both sides by 2
D = 5
Answer:
d = 5
Step-by-step explanation:
5d - 6 + 8 -3d = 12
Regroup
5d - 3d - 6 + 8 = 12
Combine like terms
2d + 2= 12
Subtract 2 from both sides
2d = 10
Divide both sides by 2
d = 5
A gardener has 840 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a
river and so it does not need any fencing.
river
garden
What dimensions would guarantee that the garden has the greatest possible area?
shorter side:
ft (feet)
longer side:
ft (feet)
ft2 (square feet)
greatest possible area:
Question Help: Message instructor
Submit Question
Answer:
Shorter side: 210
Longer side: 420
area: 88200
Step-by-step explanation:
work below
If you haven't learned derivatives yet just use the vertex formula
don't mind the yt but how/?
r = 44
12 = r -(34-2)
12 = r -(32)
12 = r-32
r = 32+12
r = 44
A spinner has three unequal sections: red, yellow, and blue. The table shows the results of Nolan's spins.
Find the experimental probability of landing on each color. Enter your answers as simplified fractions.
Color
Red 11
Yellow18
Blue4
Frequency
The probability of landing on red is
The probability of landing on yellow is
The probability of landing on blue is
Answer:
Yellow will have the best chance because it’s more red will have the second best chance because it is the second biggest and blue you probably will never get it
Step-by-step explanation:
Can someone’s please help
Answer:
4.87 ft
Step-by-step explanation:
The height of the skylight =
The height of the blue △ - the height of the red △
Let b ft be the height of the blue △.
sin 60° = [tex]\frac{b}{25} [/tex]
b = 25 sin 60°
Let r ft be the height of the red △.
tan 40° = [tex] \frac{r}{20} [/tex]
r = 20 tan 40°
The height of the skylight
= 25 sin 60° - 20 tan 40°
= 4.87 ft (rounded to the nearest hundredth)
If anyone can please help
Answer:
Pretty sure it's H
Step-by-step explanation:
The two parabolas intersect at (-1,0) and (0,-1)
Pythagorean theorem.
I hope this is help full to you
Answer:
3
Step-by-step explanation:
because this is the formula of Pythagorean theorem a^2 + b^2 = c^2 so all I did was 5^2 = 25 - 4^2 = 25-16 = 9 and square root of 9 = 3 i hope this helps. :D please give brainliest
Two photographers offer different pricing plans for their services. The graph below models the prices Photographer A charges. The table below shows the prices Photographer B charges. Each photographer charges a one-time equipment fee and an hourly rate. a. Which photographer charges the greater hourly rate? By how much? b. Which photographer charges the greater one-time fee? By how much?
Answer:
a. Photographer A by $10
b. Photographer B by $25
Suppose that S and T are points on the number line.
If ST = 18 and S lies at -3, where could T be located?
If there are several locations, separate them with commas.
The volume of a particular die is 12100 mm3. Use the fact that 10 mm equals 1 cm to convert this volume to cm3.
Instructions: Find the value of x
Please help I’ll mark brainilest.
all the lenses inside the circle ar equal and the two chords are also equal distance from the center point so arc x would equal arc CD
X = 50 degrees
You make a scale drawing of a banner for a school dance. You use a scale of 1 inch =3 feet. What is the actual width of the banner?
the width was 6 inches
What is the solution to
3x*2-2x+4=0
Answer:
Step-by-step explanation:
[tex]3x^2 - 2x + 4 = 0[/tex]
a = 3, b = -2, c = 4
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\\\x = \frac{2 \pm \sqrt{2^2 - (4 \times3 \times 4} )}{2 \times 3}\\\\x = \frac{2 \pm \sqrt{4 - 48} }{6}\\\\x = \frac{2 \pm \sqrt{-44} }{6}\\\\x =\frac{2 \pm 2i \sqrt{11} }{6}\\\\x =\frac{1 + i \sqrt{11} }{3}\ , x =\frac{1 - i \sqrt{11} }{3}\\\\\\\\[/tex]
What are the coordinates for b?
Answer:
Step-by-step explanation:
(0,-3.5)
Answer:
(0, -3.5)
Step-by-step explanation:
The x coordinate is first
We stay on the y axis so the x coordinate is 0
The y coordinate is second
We go down 3 1/2 units so the y coordinate is -3 1/2
(0, -3.5)
13) The graph
represents the
function g(x).
a) Based on the graph
what is g(0)?
-4
-3
b) What is the
domain and range
of the function?
Hi there! g(0) means the value of g(x) at x = 0. Look at x = 0 and see which y-point makes x = 0.
See that y = 4 makes x = 0 for the graph. Thus, g(0) = 4.
Next is to find the domain and range. Domain is the set of all x-values while Range is the set of all y-values.
For domain, look at the horizontal x-axis plane and the graph. Notice how the graph infinitely goes up for both negative and positive. Since the graph is in negative and positive as well. That means the domain is all real numbers
For range, look at the vertical y-axis and the graph. Notice how when y < -2, there are no points that are part of the graph. The graph goes infinitely for range as well but there're no y-values less than -2 for the graph.
Therefore, range is y >= -2.
Answer
g(0) = 4domain is set of all real numbers.range is y >= -2A rectangular metal tank with an open top is to hold cubic feet of liquid. What are the dimensions of the tank that require the least material to%E2%80%8B build?
Answer:
[tex]h = 3.5[/tex]
[tex]w = 7[/tex]
[tex]l = 7[/tex]
Step-by-step explanation:
Given
[tex]Volume = 171.5ft^3[/tex]
Required
The dimension that requires least material
The volume is:
[tex]Volume = lwh[/tex]
Where:
[tex]l \to length[/tex]
[tex]w \to width[/tex]
[tex]h \to height[/tex]
So, we have:
[tex]171.5 = lwh[/tex]
Make l the subject
[tex]l = \frac{171.5}{wh}[/tex]
The surface area (A) of an open-top rectangular tank is:
[tex]A = lw + 2lh + 2wh[/tex]
Substitute: [tex]l = \frac{171.5}{wh}[/tex]
[tex]A = \frac{171.5}{wh} * w + 2*\frac{171.5}{wh}*h + 2wh[/tex]
[tex]A = \frac{171.5}{h} + 2*\frac{171.5}{w} + 2wh[/tex]
[tex]A = \frac{171.5}{h} + \frac{343}{w} + 2wh[/tex]
Rewrite as:
[tex]A = 171.5h^{-1} + 343w^{-1} + 2wh[/tex]
Differentiate with respect to h and w
[tex]A_h = -171.5h^{-2} +2w[/tex]
[tex]A_w = -343w^{-2} +2h[/tex]
Equate both to 0
[tex]-171.5h^{-2} +2w=0[/tex]
Make w the subject
[tex]2w = 171.5h^{-2}[/tex]
Divide by 2
[tex]w = 85.75h^{-2}[/tex]
[tex]-343w^{-2} +2h = 0[/tex]
Make h the subject
[tex]2h = 343w^{-2}[/tex]
Divide by 2
[tex]h = 171.5w^{-2}[/tex]
[tex]h = \frac{171.5}{w^2}[/tex]
Substitute [tex]w = 85.75h^{-2}[/tex] in [tex]h = \frac{171.5}{w^2}[/tex]
[tex]h = \frac{171.5}{(85.75h^{-2})^2}[/tex]
[tex]h = \frac{171.5}{85.75^2*h^{-4}}[/tex]
[tex]h = \frac{2}{85.75*h^{-4}}[/tex]
Multiply both sides by [tex]h^{-4}[/tex]
[tex]h^{-4} * h = \frac{1}{85.75*h^{-4}} * h^{-4}[/tex]
[tex]h^{-3} = \frac{2}{85.75}[/tex]
Rewrite as:
[tex]\frac{1}{h^3} = \frac{2}{85.75}[/tex]
Inverse both sides
[tex]h^3 = 85.75/2[/tex]
[tex]h^3 = 42.875[/tex]
Take cube roots
[tex]h = 3.5[/tex] ---- height
Recall that: [tex]w = 85.75h^{-2}[/tex]
[tex]w = 85.75 * 3.5^{-2}[/tex]
[tex]w = 7[/tex] --- width
Recall that: [tex]l = \frac{171.5}{wh}[/tex]
[tex]l = \frac{171.5}{3.5 * 7}[/tex]
[tex]l = 7[/tex] --- length
Bilal's fishing line was on a spool with a radius of 4 cm. Suddenly, a fish pulled on the line, and the spool spun
16 times before Bilal began to reel in the fish.
What is the distance the fish pulled the fishing line?
Round your answer to the nearest cm.
Answer:
402 cm
Step-by-step explanation:
Given :
Radius = 4 cm
The Circumference of a circle :
C = 2πr
C = 2 * π * 4 = 8π
Spool is spun 16 times :
Circumference * 16
8π * 16
8 * 3.14 * 16
= 401.92
= 402 cm
Answer:
402 cm
Step-by-step explanation:
please help (math) brainliest
Answer:
the answer is the first one
Create an example of a situation where there is a negative cash flow.?
Which expressions are equivalent to p+p+p+p+p+p+p? Choose ALL that apply.
7р
6p+2p
4p + 3p
Sp
3p + 5p
5p + 2p
Answer:
It would be 7p, 4p + 3p, and 5p + 2p
Step-by-step explanation:
Overall there is 7 p's
4 + 3 = 7 and 5 + 2 = 7
Unless there is more information, those are the answers.