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)

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 :)

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

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

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

Answer: -5x - 2

Step-by-step explanation:

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

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_

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

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.

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).

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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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 )

Answer:

C

Step-by-step explanation:

because yes so the 25 unit down 12 units up

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

Solve the following equation for x:

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

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°

Answer:

easy

bro

Step-by-step explanation:

so you have to calculate the equation

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!

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

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.

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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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)

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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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.

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

It states that, for a normally distributed random variable:

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.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

Answer:

30 dollars a week

Step-by-step explanation:

2100/70 is 30

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

Answer=12

Step-by-step explanation:

The area of a rectangle is h×b.

h=11

11×b=132

b=132/11=12 units

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

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

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:

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

Read more about regression equations at:

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