An experiment consists of tossing a coin and rolling a six-sided die simultaneously. Step 1 of 2 : What is the probability of getting a head on the coin and the number 2 on the die

Answers

Answer 1

Answer:

[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Independent events:

If two events, A and B are independent, the probability of both events happening is the multiplication of the probabilities of each event happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Probability of getting a head on the coin:

Head or tails, fair coin, so:

[tex]P(A) = \frac{1}{2}[/tex]

Probability of getting the number 2 on the die:

6 numbers, one of which is 2, so:

[tex]P(B) = \frac{1}{6}[/tex]

What is the probability of getting a head on the coin and the number 2 on the die?

[tex]P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]

[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die


Related Questions


A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40°W and reaches point Finally, it turns S 40°E and returns to point A
The total distance covered by the boat is______miles

A. 14.95
B. 18.44
C. 20.04
D. 25.88

Answers

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

[tex]\angle A+40+100=180[/tex]

[tex]\angle A+140=180[/tex]

[tex]\angle A=180-140[/tex]

[tex]\angle A=40[/tex] degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

[tex]\implies BC=AC [/tex]

Now, Sine law

[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]

Using the sine law

[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]

[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]

[tex]BC=\frac{8\times sin40}{sin 100}[/tex]

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save money at the monthly rate to buy the item for its cash price.
A bunk bed with a cash price of $1,998, at $143 per month for 15 months

Answers

Answer:

$2,145 ; $147 ; 14 months

Step-by-step explanation:

Given that :

The cash price, that is, the amount that would be paid if customer is to pay the entire amount item is worth at once = $1998

Monthly payment = $143

Period = 15 months

The total installment price ; total amount paid on a monthly pay for 15 months :

(monthly payment * period)

($143 * 15)

= $2,145

The carrying charge :

Installment pay - Cash amount

$(2,145 - 1,998)

= $147

The number of month needed to save at Monthly rate to buy item at it's cash price :

Cash price / monthly payment

$1998 / $143

= 13.97

= 14 months

Part 1: Joe and Hope were both asked to factor the following polynomial completely. Is one of them correct? Both of them? Neither of them? Explain what each of them did was correct and/or incorrect.

Part 2:

Find all the values of k so the the quadratic expression factors into two binomials. Explain the process used to find the values.

3x^2 + kx - 8​

Answers

Part 1

If we simplify, both Joe and Hope factored the polynomial correctly but Joe didn't complete it fully.

The first binomial can be further factored:

8x + 12 = 4(2x + 3)Part 2

The quadratic expression needs to have two roots in order to be factored as two binomials.

The discriminant must be positive or zero:

D = b² - 4ac ≥ 0

We have a = 3, b = k, c = -8

So we get following inequality:

k² - 4*3*(-8) ≥ 0k² + 96 ≥ 0

Since k² is positive for any value of k, the solution is any value of k:

k ∈ R

Hope this attachment helps you.

Please HELP!

How many pairs (A, B) are there where A and B are subsets of {1, 2, 3, 4, 5, 6, 7, 8} and A ∩ B has exactly two elements?

Answers

Answer:

There are 256 pairs in all.

12x + 1 - 2(y + 2) = 12x - ______ - 2y

Answers

Answer:

-3

Step-by-step explanation:

12x + 1 - 2(y + 2)

=> 12x + 1 - 2y - 4

=> 12x - 3 - 2y

Answer:

-3

Step-by-step explanation:

12x+1-2y-4

12x+1-2y-4

12x-2y-3

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with A random sample of 12 sample specimens has a mean compressive strength of psi. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete. Enter your answer; 95% confidence interval, lower bound Enter your answer; 95% confidence interval, upper bound (b) Calculate the 99% two-sided confidence interval on the true mean compressive strength of concrete.

Answers

Answer:

95%: (3278.354 ; 3270.083)

99% : (3221.646 ; 3278.354)

Step-by-step explanation:

Given :

Sample size, n = 12

Mean, xbar = 3250

Sample standard deviation = √1000

The 95% confidence interval :

Mean ± Margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 0.05, df=12-1 = 11 ;

Tcritical at 95% = 2.20

Hence,

Margin of Error = (2.20 * √1000/√12) = 20.083

Confidence interval : 3250 ± 20.083

Lower boundary = 3250 - 20.083 = 3229.917

Upper boundary = 3250 + 20.083 = 3270.083

2.)

The 99% confidence interval :

Mean ± Margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 0.01, df=12-1 = 11 ;

Tcritical at 99% = 3.106

Hence,

Margin of Error = (3.106 * √1000/√12) = 28.354

Confidence interval : 3250 ± 28.354

Lower boundary = 3250 - 28.354 = 3221.646

Upper boundary = 3250 + 28.354 = 3278.354

Round 100.9052 to the nearest hundredths

Answers

To round 100.952 to the nearest tenth consider the hundredths’ value of 100.952, which is 5 and equal or more than 5. Therefore, the tenths value of 100.952 increases by 1 to 0.

100.952 rounded to the nearest tenth = 101.0

The lifespan, in years, of a certain computer is exponentially distributed. The probability that its lifespan exceeds four years is 0.30. Let f(x) represent the density function of the computer's lifespan, in years, for x>0. Determine an expression for f(x).

Answers

Answer:

The correct answer is "[tex]0.300993e^{-0.300993x}[/tex]".

Step-by-step explanation:

According to the question,

⇒ [tex]P(x>4)=0.3[/tex]

We know that,

⇒ [tex]P(X > x) = e^{(-\lambda\times x)}[/tex]

⇒     [tex]e^{(-\lambda\times 4)} = 0.3[/tex]

∵ [tex]\lambda = 0.300993[/tex]

Now,

⇒ [tex]f(x) = \lambda e^{-\lambda x}[/tex]

By putting the value, we get

           [tex]=0.300993e^{-0.300993x}[/tex]


Which law would you use to simplify the expression
(P/q)^3?

power of a power
power of a quotient
quotient of powers
power of a product

Answers

Answer: Power of a quotient

Step-by-step explanation:

The power of quotient basically is:

[tex](\frac{P}{q})^{3} =\frac{P^3}{q^3}[/tex]

Can someone help me with this question an also the rest of my school work?

Answers

Answer:

I think this one is B

Step-by-step explanation:

Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.)
f(x) = 7/(1+x), a = 2
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]
f(x) = e−5x
f(x)=
[infinity]
n = 0
=
Find the associated radius of convergence R.
R =

Answers

Answer:

A) [ 7/3,  (-7/9)(x/2),  7/27(x-2)^2,  (-7/81)(x-2)^3 ]

B) attached below

Step-by-step explanation:

A)  Using the definition of a Taylor series

The first four nonzero terms of the series for f(x) = 7/ (1 +x), a = 2

= [ 7/3,  (-7/9)(x/2),  7/27(x-2)^2,  (-7/81)(x-2)^3 ]

attached below is the detailed solution

B) Finding Maclaurin series for f(x)

f(x) = e^-5x

attached below

Associated radius of convergence = ∞  ( infinity )

On Friday Evelyn sold 9 dresses and 20 pairs of pants. On Saturday she sold twice as many dresses and 10 more pants than Friday. How many dresses did Evelyn sell on Friday and Saturday?

Answers

Answer: 27 Dresses and 50 Pants

Step-by-step explanation:

If she sold 9 pairs of pants and

9 x 2 = 18

18 + 9 = 27

20 + 10 = 30

30 + 20 = 50

Evelyn sold 9 dresses and 20 pairs of pants on Friday, and on Saturday, she sold 18 dresses and 30 pairs of pants.

Evelyn's sales of dresses and pants over two days, Friday and Saturday. We'll use some mathematical expressions and reasoning to find out how many dresses Evelyn sold on each day.

Let's start by assigning some variables to represent the number of dresses and pants Evelyn sold on Friday and Saturday. We'll use "F" for Friday and "S" for Saturday. So, let [tex]D_F[/tex] be the number of dresses sold on Friday, [tex]D_S[/tex] be the number of dresses sold on Saturday, [tex]P_F[/tex] be the number of pants sold on Friday, and [tex]P_S[/tex] be the number of pants sold on Saturday.

According to the problem, on Friday, Evelyn sold 9 dresses, which can be expressed as:

[tex]D_F[/tex] = 9

She also sold 20 pairs of pants on Friday:

[tex]P_F[/tex] = 20

Now, let's move on to Saturday's sales. It says she sold twice as many dresses as Friday, which means the number of dresses on Saturday is double that of Friday's sales:

[tex]D_S = 2 * D_F[/tex]

Additionally, she sold 10 more pairs of pants on Saturday compared to Friday:

[tex]P_S = P_F + 10[/tex]

We already know that [tex]D_F = 9[/tex], so we can find the number of dresses sold on Saturday by substituting this value into the equation for [tex]D_S[/tex]:

[tex]D_S = 2 * 9 = 18[/tex]

Next, we'll calculate the number of pants sold on Saturday using the given information. Since [tex]P_F = 20[/tex], we can find [tex]P_S[/tex]:

[tex]P_S = 20 + 10 = 30[/tex]

So, to summarize, Evelyn sold 9 dresses and 20 pairs of pants on Friday, and on Saturday, she sold 18 dresses and 30 pairs of pants.

To know more about Equation here

https://brainly.com/question/15977368

#SPJ2

I NEED HELP ILL MARK!!!

Answers

Answer:

c) tan

Step-by-step explanation:

For the 63-deg angle, YZ is the opposite leg. The unknown side, AY, is the adjacent leg. The trigonometric ratio that relates the opposite and adjacent legs is the tangent.

Answer: c) tan

Please help solve and explain this thank you

Answers

Answer:

hi

Step-by-step explanation:

Find the measure of of RA.

Answers

Answer:

RA = 24

Step-by-step explanation:

Since the triangle is isosceles ( 2 equal sides ) , then LU is a perpendicular bisector , so

AU = RU , that is

4r = 18 - 2r ( add 2r to both sides )

6r = 18 ( divide both sides by 6 )

r = 3

Then

RA = 18 - 2r + 4r = 18 + 2r = 18 + 2(3) = 18 + 6 = 24

What value of x will make the equation true?

Answers

Answer:

5

Step-by-step explanation:

When a square root of an expression is multiplied by itself, the result is that expression

5=x

Find the area of the surface generated when the given curve is revolved about the y-axis. The part of the curve y=4x-1 between the points (1, 3) and (4, 15)

Answers

Answer:

Step-by-step explanation:

Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.

Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1

4x = y + 1

[tex]x = \dfrac{y+1}{4}[/tex]

[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

By integration, the required surface area in the revolve is:

[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]

where;

g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]

[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]

[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]

[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]

Expand (2x - 4)2 using the square of a binomial formula.
(x)2 + 2(x)(4) + 42
O (2x)2 + 2(2x)(4) - 42
O(x2 - 2(x)(4) - 42
(2x)2 - 2(2x)(4) + 42

Answers

Step-by-step explanation:

We have to expand,

[tex]\longrightarrow [/tex] (2x 4)²

(a ― b)² = a² + b² ― 2ab

[tex]\longrightarrow [/tex] (2x)² + (4)² ― 2(2x × 4)

[tex]\longrightarrow [/tex] 4x² + 16 ― 2(8x)

[tex]\longrightarrow [/tex] 4x² + 16 ― 16x

[tex]\longrightarrow [/tex] 4x² ― 16x + 16

Hence, solved!

Answer:

D is the correct answer (2x)2 – 2(2x)(4) + 42

Step-by-step explanation:

PLEASE HELPPPP WILL GIVE BRAINLIESTTTT

Factor the following expressions completely. Show and check all work on your own paper.
9x2-18x+9

Answers

Hi there!

[tex]\large\boxed{9(x - 1)^{2}}[/tex]

9x² - 18x + 9

We can begin by factoring out a 9 from each term:

9(x² - 2x + 1)

Now, find two terms that add up to -2 and equal 1 when multiplied. We get:

9(x - 1)(x - 1)

Or:

9(x - 1)²

-3xy^2+5xy^2
Operations with polynomials

Answers

9514 1404 393

Answer:

  2xy^2

Step-by-step explanation:

The terms are "like" so can be combined. It might be helpful to think of this as an application of the distributive property.

  -3xy^2 +5xy^2 = (-3 +5)xy^2 = 2xy^2

HELP HELP QUICK QUICK

Answers

Answer:

multiplication by -1 will reflect over the x-axis

multiplication by a positive number will "scale" or "stretch" the function

Step-by-step explanation:

what is the answer to 10% of 900​

Answers

Answer:

90 cause 90 times 10 is 900 and 10% times 10 is 100%

Step-by-step explanation:

Answer: 90

Step-by-step explanation: 900 × .10 = 90

A movie theater has a seating capacity of 283. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2060 on a sold out night, how many children, students, and adults attended

Answers

Answer: adults = 79

children = 158

student = 46

Step-by-step explanation:

Let a = adults

Let c = children

Let s = student

From the information given,

a + c + s = 283 ....... i

c/a = 2, c = 2a ....... ii

5c + 7s + 12a = 2060 ...... iii

Put the value of c = 2a into equation i

a + c + s = 283

a + 2a + s = 283

3a + s = 283

s = 283 - 3a

Note that c = 2a

From equation iii

5c + 7s + 12a = 2060

5(2a) + 7(283 - 3a) + 12a = 2060

10a + 1981 - 21a + 12a = 2060

10a + 12a - 21a = 2060 - 1981

a = 79

Note c = 2a

c = 2 × 79 = 158

Since a + c + s = 283

79 + 158 + s = 283

s = 283 - 237

s = 46

adults = 79

children = 158

student = 46

-3/8 divided by -1/4

Answers

Flip the -1/4, cross deduct and should get 3/2

Answer:

It might be 3/2 or 1 and 1/2.

posters n tees sold 486 items yesterday; one-third of these were t-shirts.how many t-shirts sold? how many posters?

Answers

Answer:

162 t-shirts, 324 posters

Step-by-step explanation:

Assuming they only sold t-shirts and posters, you can find the amount of t-shirts sold by dividing 486 by 3, or multiplying it by 1/3. This equals 162. This is because one third were t-shirts. To find the rest you just subtract 162 from the total of 486, or multiply 162 by 2. (since you already know the amount of 1/3, 2/3 is double that.)

486/3 = 162; 486 - 162 = 324

therefore there were 162 t-shirts and 324 posters

Simplify -|-5 + 2|
someone help quick

Answers

Answer:

-3

Step-by-step explanation:

Pls answer
Subtract -37 from -53

Answers

Answer:

-37 subtract -53

-53 subtract -37 = -16

Step-by-step explanation:

Answer:

The answer is 16

Step-by-step explanation:

-37-(-53) = -37 + 53

You can flip it to 53 - 37 which equals 16.

Hope this helps! :)

*Heads up you can also search this up* ^^

HELP ME WITH THIS TO EARN BRAINLIEST!!!!!!

Answers

Answer:

Step-by-step explanation:

answer C looks good  

Answer:

option c is answer

Step-by-step explanation:

as we can see r^2 =(d/2)^2

r^2=(6/2)^2

r^2=36/4=9

A=πr^2

A=9π

If [infinity]∑n=0cn9n is convergent, does it follow that the following series are convergent? (a) [infinity]∑n=0cn(−3)n

Answers

Given: The series ∑cₙ[tex]9^n[/tex] is convergent

To find: The series ∑cₙ[tex](-3)^n[/tex] is convergent or not.

Solution: If the radius of convergence R the we can conclude that R≥4

So, the series will converge as -3<9.

Use Cramer's Rule to solve (if possible) the system of linear equations.

x1 + 2x2 =8
- x1 + x2 = 1

Required:
Find the coefficient matrix.

Answers

Answer:

x1 = 2

x2 = 3

Step-by-step explanation:

[tex]x_1=\frac{D_{x1}}{D}\\\\x_2=\frac{D_{x2}}{D}[/tex]

Here D is the coefficient matrix.

Hence

[tex]x_1=\frac{6}{3}\\x_1=2[/tex]

&

[tex]x_2=\frac{9}{3}\\x_2=3[/tex]

Other Questions
11111 Power 2 sovle Why must beta particles be used to detect leaks in a pipe?Why must beta particles be used to detect leaks in a pipe?A. Beta particles will not be absorbed by the soil like gamma radiation, but won't pass through the pipe before reaching the leak like alpha radiation would.B. Beta particles will not cause an electrical discharge like alpha particles when they interact with the metal pipe, or contaminate the water like gamma radiation.C. Beta particles are not used, only alpha particles are used because they are not harmful to humans.D. Beta particles will not be absorbed by the soil like alpha particles, but won't pass through the pipe before reaching the leak like gamma radiation would. PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree. The sum of two numbers is is 49 and the difference between these two numbers is 9 what are these two numbers please show the workout which propaganda technique is a statement that creates a strong emotional response in the audience, which may prevent them from examining the author's logic? Patrick's family finally convinces him to see a mental health specialist, and he has subsequently been diagnosed with a personality disorder. If Patrick is diagnosed with an odd or eccentric personality disorder, which is most likely his specific diagnosis 1.where does short stories originated from? 2 when was this first used and developed? I forgot everything I learned He drove the car carefully. (Underline the adverb in the sentence) The perimeter of a rectangle is 40 inches. If the width is 9 inches, what is the area of the rectangle? Contrast the Brazilian post colonial experience with that of Spanish AmericaHelp please an electron is moving at 3.6 x 10^3 m/s. a photon with what wavelength would have the same momentum???? Is the Use of energy to move particles against the concentration gradient The area of an isosceles triangle is 52 square inches. The height is 8 in. What is the length of the base? The question is in the picture O is the center if the regular polygon beloe. Find its perimeter. Round to the nearest tenth if necessary HURRY what do you mean by scattering of light In which tab will the user find the Cell Styles gallery? I wanted to know what the answer for the picture that I sent would be What is object? How is Od different from Oi? Example.