Determine the following probabilities. Enter your final answers as reduced fractions. Two coins are flipped. Find the probability that the first coin land on heads and the second coin lands on heads. Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is black and the second card is a 8. A single digit between 0 and 9 is randomly chosen, and a single letter from A to Z is randomly chosen. Find the probability that the number is 4 and the letter is a consonant. Two dice are rolled. Find the probability that first die lands on an even number and the second die is less than 2.

Answers

Answer 1

The probability of an event occurring is given by the ratio of the number of

possible outcome to the number of required outcome.

First question: The probability that the first coin lands on heads and the second coin lands on tails is 0.25.Second question: The probability of drawing a black card and then a 8 is [tex]\underline{\dfrac{1}{13}}[/tex].

Third question: The probability that the number chosen is 4 and the letter chosen is a consonant, is [tex]\underline{\dfrac{21}{234}}[/tex].

Fourth question: The probability that the first die lands on an even number and the second die is less than 2, is [tex]\underline{\dfrac{1}{12}}[/tex].

Reasons:

First question:

The number of faces in a coin = 2; A head or a tail

The probability that the first coin lands on heads, P(H) = [tex]\dfrac{1}{2}[/tex]

The probability that the second coin lands on tails, P(T) = [tex]\dfrac{1}{2}[/tex]

The probability that the first coin lands on heads and the second coin lands

on tails = P(H ∩ T)

Which gives;

[tex]P(H \cap T) = \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}[/tex]

The probability that the first coin lands on heads and the second coin lands on tails = [tex]\dfrac{1}{4}[/tex] = 0.25

Second question:

The number of black cards in a pack of 52 = 26 cards

The number of cards that are a 8 in a pack of 52 cards = 8 cards

[tex]\mathrm{The \ probability \ of \ drawing \ a \ black \ card}, \ P(B) = \dfrac{26}{52} = \dfrac{1}{2}[/tex]

[tex]\mathrm{The \ probability \ of \ drawing \ a \ 8,} \ P(8) = \dfrac{8}{52} = \dfrac{2}{13}[/tex]

The probability of drawing a black card and then an 8, P(B∩8), is given as follows;

[tex]P(B \cap 8) = \dfrac{1}{2} \times \dfrac{2}{13} = \dfrac{1}{13}[/tex]

The probability of drawing a black card and then a 8 is P(B∩8) = [tex]\underline{\dfrac{1}{13}}[/tex]

Third question:

The probability that a number chosen between 0 and 9 is 4, P(4) = [tex]\dfrac{1}{9}[/tex]

The number of consonant in the alphabet = 21

The probability that a letter chosen from A to Z is a consonant, P(C) = [tex]\dfrac{21}{26}[/tex]

The probability that the number chosen is 4 and the letter chosen is a consonant, P(4 ∩ C)  = [tex]\dfrac{1}{9} \times \dfrac{21}{26} = \underline{ \dfrac{21}{234}}[/tex]

Fourth question:

The number of even numbers on a die = 3; (2, 4, 6)

The number of numbers less than 2 on a die = 1

The probability that the first die lands on an even number, P(E) = [tex]\dfrac{3}{6}[/tex]

The probability that the second die is less than 2. P(<2) = [tex]\dfrac{1}{6}[/tex]

Therefore;

The probability that the first die lands on an even number and the second die is less than 2, P(E ∩ <2) = [tex]\dfrac{3}{6} \times \dfrac{1}{6} = \dfrac{3}{36} = \underline{\dfrac{1}{12}}[/tex]

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Related Questions

Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )

Answers

Answer:

8p -12

Step-by-step explanation:

Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )

4(p + 3) +4(p - 6) =

4p + 12 + 4p - 24 =

8p -12

no need to explain just tell the answer

Answers

Answer: z = 18

Step-by-step explanation:

180 = 90 + (3z+4) + (2z-4)

z = 18

what is 4xy - 5y² - 3x² from 5x + 3y² - xy ? ​

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The equivalent expression is ~

[tex] \boxed{ \sf8 {y}^{2} + 3 {x}^{2} + 5x - 5xy}[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve ~

[tex]5x² + 3 {y}^{2} - xy - (4xy - 5y {}^{2} - 3 {x}^{2} )[/tex]

[tex]5x² + 3 {y}^{2} - xy - 4xy +5 {y}^{2} + 3 {x}^{2} [/tex]

[tex]3 {y}^{2} + 5 {y}^{2} + 3 {x}^{2} + 5x² - xy - 4xy[/tex]

[tex]8 {y}^{2} + 8 {x}^{2} - 5xy[/tex]

Which division problem is modeled

Answers

Answer:

The first one

Step-by-step explanation:

if you count, there are five full rows, and two extra, so 52/100. then you count the sections that the colored area is: 4. then count how many squares are in each colored section: 13.

Find the slope of the line given the following points on the line:

(-6, 4) and 2, 7)

Answers

Answer:

3/8

Step-by-step explanation:

Answer:

[tex]\boxed{\sf Slope:3/8}[/tex]

Step-by-step explanation:

To determine the slope of a line given the coordinates of two points on the line, use the slope formula.

[tex]\boxed{\sf \sf{Slope\;(m)}=\frac{y_2-y_1}{x_2-x_1}}[/tex]

x1 and y1 are the coordinates of the first point. The second point's coordinates are x2, y2.

Points: [tex]\sf (-6, 4) \:and \:(2, 7)[/tex]

[tex]\longmapsto\sf \left(x_1,\:y_1\right):\left(-6,\:4\right)[/tex]

[tex]\longmapsto\sf \left(x_2,\:y_2\right)=\left(2,\:7\right)[/tex]

_______________

[tex]\leadsto\sf m=\cfrac{7-4}{2-\left(-6\right)}[/tex]

[tex]\leadsto\sf m=\cfrac{3}{8}[/tex]

_________________________________________

What is the value of this expression when c = 3 and d = 7? 15+c2⋅d−c3

Answers

Answer:

The value of this expression is 48

Step-by-step explanation:

15 + c2 * d - c3

c = 3

d = 7

Substitute the values of c and d

15 + (3)2 * 7 - (3)3

Multiply the parenthesis first

15 + 6 * 7 - 9

Now multiply 6 and 7

15 + 42 - 9

Now add 15 and 42

57 - 9

Now subtract

= 48

Answer:

48

Step-by-step explanation:

When you write out the problem it should look like this

15+c⋅2⋅d-c⋅3

or in other form

15+3⋅2⋅7-3⋅3

You can solve using PEMDAS

Paratheses

Exponents

Multiplication

Division

Addition

Subtraction

Just use those in order and you should find to answer.

-Rocketgamer360

solve |8y+4|=2|y-1|
please show the work!

Answers

8y+4 = 2(y-1)
8y+4 = 2y-2
8y-2y+4 = -2
6y+4 = -2
6y = -2-4
6y = -6
y = -1

g
Pat a
mber
4. In a hockey league, 87 players play on seven
different teams. Each team has at least 12
players. What is the maximum number of players
on any one team?

Answers

Answer:

15

Step-by-step explanation:

since there is 7 teams and 12 can be the minimum we can do 7 x 12=84

this means that 3 people could possibly be on one single team.

the maximum number is 12+3=15

Complete the missing factors

6a^2 + 11b - 35b^2 = ( 3a _______)(2a______)

please help me, thank you.​

Answers

(3a-5b)•(2a+7b)
That’s the answer

Find the lowest common multiple (LCM) of 18 and 21.

Answers

LMC (18,21) = 126

ok done. Thank to me :>

HELLO PLEASE GIVE ME THE RIGHT ANSWER ASAP THANK YOU !

Answers

[tex]\large\underline{\sf{Solution-}}[/tex]

[tex]\textsf{Given expression;}\\[/tex]

[tex] \rm{23 = \frac{7}{9}(6x - 36) + 9 } \\ [/tex]

[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 256)}{9} + 9 \\ [/tex]

[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 256 + 81)}{9} \\ [/tex]

[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 175)}{9} \\ [/tex]

[tex] \rm{\longmapsto} \: \frac{23}{1} = \frac{(42x - 175)}{9} \\ [/tex]

[tex]\textsf{By doing cross multiplication, we get}\\[/tex]

[tex] \rm{\longmapsto}23(9) = 1(42x - 175) \\ [/tex]

[tex] \rm{\longmapsto}207 =42x - 175\\ [/tex]

[tex]\rm{\longmapsto} \: 42x = - 175 - 207 \\ [/tex]

[tex]\rm{\longmapsto} \: 42x = - 379 \\ [/tex]

[tex]\rm \therefore \: x = - \frac{375}{42} \\ [/tex]

[tex]\textsf{Hence, the value of x will be -375/42 respectively.}\\[/tex]

[tex]\textbf{Read more:}[/tex]

[tex]\textsf{Similar Questions}[/tex]

Solve the expression and find the value of x. [tex] \frac{x⁠…

https://brainly.com/question/25420312

The FM radio station KAMB broadcast from an antennae atop a 150 meter tall radio tower at a frequency of 90 MHz with a total radiated power of 40 kilowatts. Neighbors have complained about problems they attribute to excessive radiation from the tower, but the city engineer who measured the radiation level near the base of the tower found it to be well below the accepted standard. You have been hired by the HOA to assess the engineer's report. You know a few things about electromagnetic radiation and therefore conclude that we must find the optimum place on the ground to measure the maximum radiation emitted from the antennae. From your extensive knowledge in physics, you know that the intensity of radiation, I, is given by the formula:
I=12/32π*Psin2(θ)/r^2
where P is the power output, r is the distance from the top of the tower to the point on the ground, and θ is the angle measured from the tower to r.

Find the distance R from the base of the tower to the optimum location for taking the radiation reading. (m)
What is the maximum radiation reading from the ground in kw/m^2
If the city code requires that electromagnetic radiation be under 200 microwatts per square meter, is this antenna operating within city code? Yes or No

Answers

Answer: 150 m, 5.305*10^-5 kW/m^2, No

Step-by-step explanation:

See attachment, hope this helps

Using the radiation intensity formula we will have to:

a) [tex]150 m[/tex]

b) [tex]5.305*10^{-5} kW/m^2[/tex]

c)No

From the data informed, we have:

[tex]h=150m\\P=40KW[/tex]

Using the given formula and performing some mathematical operations:

[tex]I=\frac{12Psin^2(\theta)}{32(\pi)r^2} \\I= \frac{12(40)(R/r)^2}{32(\pi)r^2} \\= \frac{15R^2}{r^2\pi } \\= \frac{15R^2}{(R^2+150^2)^2\pi} \\[/tex]

deriving the given equation, we will have:

[tex]=\frac{(R^2+150^2)^22R-R^2(2(R^2+150^2))2R}{(R^2+150^2)^2}[/tex]

So from this equation we have that the answer of the letter A corresponds:

[tex]R=150[/tex]

For letter B we will have to develop this equation:

[tex]I= 5.30X10^{-5}[/tex]

As for the letter C, when converting the value found, it should give 200 microwatts, which is false.

Learn more: brainly.com/question/10148635

find the missing triangle measurements. I WILL GIVE BRAINLIEST! PLEASE

Answers

Answer:

ABC= 60

DCE= 65

DEF= 105

Step-by-step explanation:

Answer:

60°; 65°; 115°

Step-by-step explanation:

ΔABC is equilateral since all sides marked as congruent. Therefore:

m∠ABC = 60°

ΔCDE is isosceles since two sides marked as congruent:

m∠DCE = m∠DEC = 1/2(180° - 50°) = 1/2(130°) = 65°

∠DEF forms a linear pair with ∠DEC, so they sum to 180°:

m∠DEF = 180° - 65° = 115°

Please HELP!!!!PLSLSLSLSS​

Answers

Answer: where is the question??

what do you need help with?

. A triangle has an angle that measures 85°. The other two angles are in a ratio of 6:13. What are the measures of those two angles?


AND EXPLAIN THE STEPS

Answers

Answer:

Smaller angle : 30 degrees

Bigger Angle : 65 degrees

Step-by-step explanation:

85+6x+13x=180, 85+19x=180,19x=95,x=5

Smaller angle : 30

Bigger Angle : 65

Which circle has a radius that measures 10 units?
10
D
20
F
10
OG
20

Answers

Circle F 20
Hope this helps :))

Option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

What is Circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

The distance across a circle through the centre is called the diameter.

Diameter = 2 × radius

In the given figures, option B has a diameter of 20

so radius = diameter /2

=20/2

=10 units

Hence, option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ5

14. At a local fruit stand, Luisa spends $5.25 for 2 pounds of strawberries. At this rate, how much can she expect to pay for 3.5 pounds of strawberries? (round to the nearest hundredt
h) Proportion Answer

Answers

$6.25 jdhdhdhdhdhdbrr

What are the solutions of y=x^2+5x-7

Answers

Answer:

You have two variables, and only one condition. It means you have infinite solutions of the form [tex](t; t^2+5t-7)[/tex]. Technically correct, probably not what you want to know.

If you wanted to know if and where the RHS crosses the x axis, the points are the solution to

[tex]x^2+5x-7= 0 \rightarrow x=\frac12(-5\pm\sqrt{25+28})\\x_1= \frac12(\sqrt{53}-5); x_2=-\frac12(\sqrt{53}+5)[/tex]

If you wanted the graph it's a parabola passing through the two points we just found, (0;-7), and with an axis of equation [tex]x=-\frac52[/tex].

Find the slope for the table.

Answers

Answer:

2

Step-by-step explanation:

as x increases by 2, y increases by 4, slope= rise/run, so the slope= 4/2=2

please helpppppppppoppo

Answers

Step-by-step explanation:

360_90_110=1602a+3a=160a=32°

how many solutions does  3x+9=25x+14 have?

Answers

Answer:

one solution

Step-by-step explanation:

3x + 9 = 25x + 14

-3x         -3x

9 = 22x + 14

-14         - 14

-5 = 22x

Craig wants to create a right triangle with side lengths 4 centimeters, 6 centimeters, and 8 centimeters. Is this possible? Why or why not?

Answers

Answer:

It's not possible

Step-by-step explanation:

In right triangle hipotenuse must be the longest side so it'll be 8 and legs will be 4 and 6.

So

[tex]4 {}^{2} + 6 {}^{2} [/tex]

Doesn't equal to

[tex]8 {}^{2} [/tex]

16+36=52 not 64

Will mark brainiest if right Is this function linear or nonlinear?

y=3x−5

Answers

Answer: This function is linear because it forms a straight line when graphed.

Would appreciate brainly <3

write down three integers below 25 with the range of 10 and the mean of 13

Answers

Answer:

8, 13, 18

Step-by-step explanation:

Middle number is 13, there are only 3

Max is 10/2 more so 18

Min is 18-10

15 metres at a speed of 20 cm/s (answer in seconds) a ​

Answers

Here's the perfect answer.

PLEASE MARK ME BRAINLIEST

Which graph is right?

Answers

Answer:The first option is correct

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

3rd option because m is bigger than or equal -2 which means that it is going to be from [-2,infinity[

The hypotenuse of a right triangle measures 19 cm and one of its legs measures 4 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answers

Answer:

18.9

Step-by-step explanation:

Julissa is printing out copies for a work training. It takes 4 minutes to print a color copy, and it takes 2 minutes to print a grayscale copy. She needs to print no fewer than 8 copies within 25 minutes.

Which system of inequalities represents the number of color copies, x, and grayscale copies, y, that Julissa can print to meet her goal?

Answers

Answer:

4x  + 2y  ≤  25   ,      x + y ≥  8     is the required system of inequalities to represent the given situation.

Step-by-step explanation:

Here, let  the number of color copies =  x

Now, the time taken to print each color copy = 4 minutes

⇒Time taken to print x color copies = x times ( Time taken by each copy)

= 4 (x)   = 4x

and let  the number gray scale copies =  y

The time taken to print each gray scale copy = 2 minutes

⇒Time taken to print y gray scale copy = y times (Time taken by each copy)

= 2 (y)   = 2y

Total copies printed = x + y

Maximum time taken to print x  color copies and y grayscale copies

= 4x  + 2y

So, according to the question:

4x  + 2y  ≤  25 ( as maximum allotted time is 25 minutes)

and x + y ≥  8      (as minimum number of copies is 8)

hence, the above system is the required system of inequalities to represent the given situation.

I hope this helps.

please help
y∝1/√x If y=5
when x=36 find,
x when y=3

Answers

Answer:

x = 100.

Step-by-step explanation:

y ∝ 1/√x

y = k /√x    where k is a constant.

When x = 36 y = 5 so we have:

5 = k / √36

5 = k / 6

k = 30

So we have the relation:

y = 30 /√x

When y = 3

3 = 30/ √x

√x = 30/3 = 10

x= 100.

100 POINTS Suppose ܶTU is on a coordinate plane located at T(-6,-2) and U(2,-6) Under a dilation of scale factor 1/4, TU becomes T'U' with coordinates T'(-3/2,-1/2) and U'(1/2,-3/2) Where is the center of the dilation located ?

A(0,0)

B(2,2)

C(4,0)

D(4,4)

Answers

c because the center of dilation is the multiplicatory value of the original point

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