Martin has a pencil case which contains 4 blue pens and 3 green pens. Martin picks a pen at random from the pencil case. He notes its colour, and then replaces it. He does this two more times. Work out the probability that when Martin takes three pens, exactly two are the same colour. (3 marks)

Answers

Answer 1

Answer: How do you not understand this?

I understand it perfectly.

Step-by-step explanation:

Answer 2

The  probability that when Martin takes three pens, exactly two are the same color is 26.53%.

Probability

Given:

Blue pens=4

Green pens=3

Hence:

Probability=4³+3³÷(4+3)³

Probability=64+27/343

Probability=91/343

Probability=0.2653×100

Probability=25.53%

Therefore the  probability that when Martin takes three pens, exactly two are the same color is 26.53%.

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Related Questions

Can someone explain how to simplify radicals? (Please leave an example) Im so confused!!

Answers

Answer:

Sure!

Step-by-step explanation:

So a radical(or a root) is the opposite of the exponent(for example square root is the opposite of the square of a number). Graphically it's not but it's more simple to think of it like that. Simplifying integer radicals is simple. For example, the square of 11 is 121, so sqr121 (√121) is equal to 11. Other radicals/powers are similar. cuberoot27= 3 because 3^3 is 27. If you add variables, the same thing happens. You can think of the √ as a funnel where only the numbers "big enough" can leave. If you have √xy^2z^3,

the x would have to stay because it's only to the first power, the √y^2 would be reduced to just y, and one pair of zs can come out resulting in z√z. The final answer to √xy^2z^3 would be yz√xz. Hope that helps :)

pleaseeee help me solve for X.

Answers

Answer:

x-17.5

Step-by-step explanation:

angles in a triangle add to 180

3x+8+(2x-3)+5x = 180

simplify(collect like terms):

10x + 5 = 180

solve:

10x = 175

x=17.5

5x+2x-3+3x+8=180
X=17.5

Please help with this question

Answers

Answer:

160°

Step-by-step explanation:

Minor Arc NR is equal to the measure of its central angle, S.

S and 20 are supplementary angles, so they add up to 180.

So, s +20 =180

S = 160, so NR = 160 as well

I’ll give you brainiest to who ever gets it right

Answers

Answer:

Line a is the best fit.

Step-by-step explanation:

The dots are more evenly spread across line a while with line b the dots at the bottom are far away from it.  Line a passes through the center of the spread of the dots

if the length of a square is decreased by 1 unit , the area will be 8 square units.Write an equation for the area of the square

Answers

Answer:

(x-1)²=8.

Step-by-step explanation:

1) if the length before decreasing is 'x', then after decreasing it is x-1;

2) then the area is (x-1)²=8.

PS. the length before decreasing is 1+2√2.

The area of this rectangle is 132 square units.
h = 11
What is the base of the re
angle?

Please help begging u ..

Answers

Answer=12

Step-by-step explanation:

The area of a rectangle is h×b.

h=11

11×b=132

b=132/11=12 units

Triangle ABC has side lengths AB=25 units, BC=24 units, and AC=7 units. Triangle ABC is mapped to triangle A′B′C′ by a reflection across a horizontal line and translated left 12 units. What is the length of segment B′C′?

Answers

Answer:

C

Step-by-step explanation:

because yes so the 25 unit down 12 units up

Please Help! If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?

Answers

Answer:

A'(2,5)

Step-by-step explanation:

The position of point A is at (-2,5), and when you reflect it over the y-axis, you just have to switch the signs of the x-coordinate value.

Answer:

A'(2, 5)

Step-by-step explanation:

If the triangle is reflected over y-axis, the y-axis will be a symmetry line then the distance between A and y will remain the same but opposite sign which is 2 units ( -2 become 2 )

Ms. fudge recently gave an algebra 1 test. the scores were normally distributed with a mean of 74 and a standard deviation of 8. find each of the following. write as a percent.

Answers

Using the Empirical Rule, it is found that there is a 68% probability that a student scored between 66 and 82.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of  the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, considering the mean of 74 and the standard deviation of 8, we have that:

74 - 8 = 66

74 + 8 = 82.

Hence, there is a 68% probability that a student scored between 66 and 82.

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Please Help! will give Brainlest!

Answers

Answer:

y = 0

Step-by-step explanation:

the midline is positioned midway between the maximum and minimum values of the function.

maximum = 0.5 and minimum = - 0.5 , then

y = [tex]\frac{0.5-0.5}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0

the equation of the midline is y = 0 ( that is the x- axis )

Answer:

y=0

Step-by-step explanation:

y = 0.5−0.52\(0.5-0.5)(2)

2

0.5−0.5

= -0.02/0

= 0

The midline is y=0

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Answers

Answer:  x = 54°

Step-by-step explanation:

The sum of these three inter angles is equal to 180°.

36° + 90° + x° = 180

         126 + x = 180

                   x = 54°

Step-by-step explanation:

36° +90°+ x = 180° ( sum of all angle of triangle is 180°)

126° + x = 180°

x = 180° - 126°

x = 54°

Juana invests $1,500 in an account accumulating 3% interest according to the equation v = 1500(1.03), where v
represents the value of the account after y years. Marquez and Calvin invest the same amount of money at the sam
rate. Marquez invests three years before Juana, and Calvin invests two years after Juana. By what factor would
Calvin's investment need to be increased to equal Marquez's investment at any time after Calvin's investment is
made?

A.86.3%
B. 97.1%
C. 115.0%
D. 115.9%

Answers

Answer:

d 115.9

Step-by-step explanation:

The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D)

How to determine the investment needed by Calvin to equal Marquez's investment at any time

In this question we must apply the concept of compound interest to derive the initial investment to be done by Calvin. According to the statement, Calvin invests money five years later than Marquez.

To determine the initial investment to be deposited by Calvin such that his investment equals Marquez's investment at any time we resort to the following expression:

[tex]1500\cdot (1+0.03)^{t+5} = C_{C}\cdot (1+0.03)^{t}[/tex]     (1)

Then, we simplify the required initial investment:

[tex]C_{C} = 1500\cdot (1+0.03)^{5}[/tex]

[tex]C_{C} = 1738.911[/tex]

And the increase factor is:

[tex]r_{C} = \frac{1738.911}{1500}\times 100\,\%[/tex]

[tex]r_{C} = 115.927\,\%[/tex]

The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D) [tex]\blacksquare[/tex]

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FOR THE INVERSE VARIATION P- , FIND V>
WHEN P= 1/2

Answers

V and g = 2y 5899 4556 5688

50 POINTS CORRECT ANSWER ONLY!!
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 2), (2, 4), (3, 8), (4, 16)

!! Use an explicit formula to find the time she will complete the 10th station. Show your work. !!

Answers

Answer:

Step-by-step explanation:

Part A

The data is modeling a geometric sequence because they have a common ratio of 2.

Part B:

= 48

Step by Step Answer

f(n)=f(n-1)*r

f(n)=f(5-1)*2

f(n)=f(4)*2

f(n)=(24)2

f(n)= 48

Part C:

= 384

Step by Step Answer

f(n)=f(1)*r^n-1

f(n)=3*2^8-1

f(n)=3*2^7

f(n)=3*128

f(n)=384

Aurora will complete the 10th station in 1024 minutes (or 17 hours and 4 minutes).

What is a geometric sequence?

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios.

aₙ=a₁(r)ⁿ⁻¹

The given data represents a geometric sequence, where the common ratio between any two consecutive terms is 2.

We can find the common ratio by dividing any term by its preceding term.

Common ratio = 4/2 = 8/4 = 16/8 = 2

Let T₁ be the time taken to complete the first station (x = 1). Then the explicit formula for the nth term of the geometric sequence is:

Tₙ = T₁ r⁽ⁿ⁻¹⁾

where r is the common ratio.

We are given the first four terms:

T₁ = 2

T₂ = 4

T₃ = 8

T₄ = 16

We can use the formula to find the time taken to complete the 10th station (x = 10):

T₁₀ = T₁ r⁽¹⁰⁻¹⁾

T₁₀ = 2(2)⁹

T₁₀ = 2 x 512

T₁₀ = 1024

Therefore, T₁₀ = 1024.

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Find the value of x. X=?
Volume = 1500 ​

Answers

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

Solve the following equation for x:

[tex]1500=1/3(15)^{2} x[/tex]

need help :((((((((((((((((((((((

Answers

the answer is k = 11
4k + 39 = 7k + 6
Group like terms
7k - 4k = 39-6
3k = 33
Divide through by 3
k =11

what is the x and y intercepts for 2y = 8 - 8x

Answers

(1,4) is the x and y coordinate

Kelly read 30 pages of her 300-page book in 6 hours. at this rate, how long will it take her to read the entire book?

60 hours

5 hours

6 hours

30 hours

i am in middle school.

Answers

Answer:

60 hours

Step-by-step explanation:

300 ÷ 30 = 10

10 x 6 = 60

Hope this helps :)

Answer: 60 hours

Step-by-step explanation:

30=300- times 10

6=_60_

When 3 + 3x − 5 − 8x is simplified, the result is:
-5x − 2.
-5x − 8.
-11x − 15.
6x − 13x.

Answers

Answer: -5x - 2

Step-by-step explanation:

Combine like terms: (3x - 8x) + (3 - 5) → -5x - 2 :)

Sonia earned $2,100 at her uncle's orchard. if she worked for 70 weeks and earned the same amount of money each week, how much did she earn per week?

Answers

Answer:

30 dollars a week

Step-by-step explanation:

2100/70 is 30

After door-to-door canvassing, census workers determine the number of unoccupied homes. The table shown to the
right lists the number of homes, in millions, that were unoccupied in four census years.
Answer questions a through c.

Answers

The exponential regression equation of the census predicts the number of unoccupied homes

The exponential regression equation is y = 5.247256 * 1.033157^x

How to determine the exponential regression equation?

The dataset is given as:

x      y

0     5.3

10    7.3

20   9.7

30   14.3

To determine the exponential regression equation, we make use of a graphing calculator.

The calculation summary from the graphing calculator are:

Regression Equation:  y = 5.247256 * 1.033157^xCorrelation: r = 0.998002R-squared: r^2 = 0.996008

Hence, the exponential regression equation is y = 5.247256 * 1.033157^x

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Can someone please help me with these questions

Answers

Answer:

easy

bro

Step-by-step explanation:

so you have to calculate the equation

express the product of 0.54 and 0.35 in standard form

Answers

Answer:

First answer, 0.54 is 54% and for the second one, 0.35 is 35%

Step-by-step explanation:

1. You first mulitply the numerator by the denominator by 100 which would be 0.54 x 100 = 54

2. Once you get the answer you just add a percentage to the end of 54 which would equal 54% and thats your answer for 0.54 and to find 0.35 it is the same thing to find the percentage.

If 6 books costs $48, then the cost of 8 books will be

Answers

Answer is $8:00 each 48 Divede by 6

Evelyn needs to order some new supplies for the restaurant where she works. the restaurant needs at least 309 forks. there are currently 226 forks. if each set on sale contains 10 forks, what is the minimum number of sets of forks evelyn should buy?

Answers

Answer:

She needs to buy at least 9 sets of forks to have enough

The number of sets of forks Evelyn should buy is 9 if Evelyn needs to order some new supplies for the restaurant where she works.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Evelyn needs to order some new supplies for the restaurant where she works. the restaurant needs at least 309 forks. there are currently 226 forks.

Let x be the minimum number of sets of forks Evelyn should buy.

The value of x can be found as follows:

x = (309 - 226)/10

x = 83/10

x = 8.3 = 9 (because the restaurant needs at least 309 forks)

Thus, the number of sets of forks Evelyn should buy is 9 if Evelyn needs to order some new supplies for the restaurant where she works.

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on every 6th day Angelique goes to the gym to exercise. every 7th day Bentley goes to the gym to exercise. what is the First day Angelique And Bentley will be at gym on the same day?

Answers

Answer:

The day that Angelique and Bentley will be at the gym on the same day is; the 42nd day.

Angelique's days:
6, 12, 18, 24, 30, 36, 42

Bentley's days:
7, 14, 21, 28, 35, 42

In conclusion, the earliest day that Angelique and Bentley will be at the gym on the same day will be, the 42nd day.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

What is the value of x? ​

Answers

Answer:

I would say 30

Reasoning:

Because that thing your looking at is 180% degree angle and the other side is 90%. x is small it seems to be acute and I think 2x is about 60%.

If im incorrect im terribly sorry but at least my answer wasnt bad like the 1st guys

My party started at 1:30 p.m.
It lasted 2 hours, 45 minutes.
What time did the party end?

Answers

Answer:

4:15

Step-by-step explanation:

add 2 hours that is 3:30

3:30 +30=4:00

and there oly 15 min left so

its 4:15

I am doing a coordinate plane activity and i need help my teacher said it was going to be easy but to me it isn’t.

Answers

The layout of each of the coordinates is (x,y) so for the first coordinate (7, 13) you start at zero and go right 7 then up 13. And draw a little cross there or something. If it’s a negative number like (-13, -9) go left 13 from 0 and then go down 9 and draw a little cross again. After you have completed each line you have to join them up (like dot to dot) in the order that you drew them.

stephen had 4 cupcakes. He ate 3/4 of one cupcake. How many does he have now?

Answers

Answer:

He has 3.25 ([tex]3\frac{1}{4}[/tex]) cupcakes left

Step-by-step explanation:

Stephen starts with 4 cupcakes

If he eats [tex]\frac{3}{4}[/tex] of 1 cupcake, he will have [tex]\frac{1}{4}[/tex] of said cupcake left

[tex]1-\frac{3}{4} =\frac{1}{4}[/tex]

Since he has 3 other cupcakes, we will add the remaining [tex]\frac{1}{4}[/tex] of the other cupcake to the total.

[tex]3+\frac{1}{4} =3\frac{1}{4}[/tex]

Hope this helped!

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