Let X be a random variable representing the number of rolls of a fair die until we see the first 6. Next, choose with replacement a sample of size X from an urn with 5 red and 4 green balls. Let Y be the number of green balls in the sample. Find Var(Y).

Answer:

One.

Step-by-step explanation:

Every possible plane section of a sphere will produce a circle.

Answer:

55000×100/90

61,111.111

Answer:

I think it's either A or E sorry if I'm wrong

Using Central Limit Theorem, it is found that the option which best describes the sampling distribution of p, the sample proportion of people who voted in the 2014 elections is:

The Central Limit Theorem states that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

In this problem:

Hence, the mean and standard error are given by:

\(\mu = p = 0.38\)

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.38(0.62)}{40}} = 0.076\)

Also approximately normal, hence, option A is correct.

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Combining like terms yields 7x⁵ - x³ - x² + 4x.

The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)

Divide both sides by 433.4:

\(e^{(0.032t)} = 1.836\)

Take the natural logarithm of both sides:

\(ln(e^{(0.032t)}) = ln(1.836)\)

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

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The function that expresses the area of the 160 square feet carpet remaining after t minute is; A(t) = 160 - 9·t

A function is a rule that maps the elements of a set known as the input of the function, to the elements of another set, known as the output of the function, such that each element of the input is mapped to exactly one element of the output set.

The area Julian's carpet covers = 160 square feet

The area the Carpet Pro cleaning service is able to clean every minute = 9 square feet.

A table of values showing the area of the carpet remaining after each minute of cleaning by Carpet Pro, can be presented as follows;

Time, t (minute)    \({}\)    Area remaining to be cleaned (square feet), A(t)

0          \({}\)                              160

1          \({}\)                               151

2          \({}\)                              142

3          \({}\)                              133

4          \({}\)                              124

5          \({}\)                              115

The change in the area of the carpet remaining is a constant and therefore, the first difference of the values in the above table is a constant which indicates that the relationship is a linear relationship, with an equation of the form y = m·x + c

Where;

m = The slope = (151 - 160)/(1 - 0) = -9

c = The y-intercept  The value of the function when the input (time) is zero, which is 160

c = 160

x = The number of minutes that elapse, t

y = The number of square feet remaining after t minutes, A(t)

Plugging in the above value, we get;

A(t) = -9·yt + 160

The function that expresses the number of square feet remaining A(t) after t minutes from the time the carpet cleaner began cleaning the carpet is; A(t) = 160 - 9·t

The possible options based on a similar question posted online and the 160 square feet area of the carpet specified in the question are;

A(t) = 160 - 9·t

A(t) = 160 - 0.1^t

A(t) = 160·(0.1)^t

A(t) = 160·(0.9·t)

A(t) = 160 - 0.9·t

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i. The second angle that will make the 2 angles complementary is 33^o.

ii. The second angle that will make the 2 angles supplementary is 123^o.

Complementary angles are measure of given angles whose addition gives a right angle i.e 90^o. While two or more angles are supplementary when their addition produces 180^o.

a. To find the second angle that will make the 2 angles complementary, we have;

let the second angle be represented by x, then;

x + 57 = 90

x = 90 - 57

  = 33

x = 33^o

b. To find the second angle that will make the 2 angles supplementary, we have;

let the second angle  be represented by y; so that;

y + 57 = 180

y = 180 - 57

  = 123

y = 123^o

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Total number of postage stamp having total mass 1 kg = 50000 stamps

Unitary Method: What is it?

The unitary method involves first establishing the value of a single unit, followed by the value of the required number of units. What can be numbers and units?

Let's say you go to the store to purchase six apples. You are told by the shopkeeper that he is selling 10 apples for Rs 100. In this example, the value and the units are the cost of the apples. Understanding the units and values is crucial when using the unitary technique to a problem.

Always write the things that need to be estimated on the right side and the variables that are known on the left side to simplify the task. In the important in the current, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are addressed using the concepts of ratio and proportion.

Given That :

1 postage stamp is = 1 cg

now we will convert cg into g

1 cg = 0.01g

1 postage stamp is = 0.02g

now we will convert g into kg

1 g = 0.001 kg

0.01g = 0.00001kg

1 postage stamp is = 0.00002kg

so now

total number of stamp in 1 kg = 1/0.00002 = 50000

Hence the ans is 50000 stamps

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Hello!

∠AED and ∠BEC are opposite angles

so ∠AED = ∠BEC = 36°.

The appropriate domain for this situation is t ≥ 0.

This is because the height of the rocket is a quadratic equation, which can only be positive. Thus, the time after launch must be greater than or equal to 0.

The domain can be calculated by solving the quadratic equation for t. To do this, the equation must be rearranged to the form \(ax^2 + bx + c = 0\). After rearranging, the equation is \(16t^2 - 112t - 60 = 0\). Using the quadratic formula, the two solutions for t are t = 3.75 and t = -4.25. Since the time after launch must be a positive value, the only valid solution is t = 3.75. Therefore, the domain of this equation is t ≥ 3.75. However, since this is a toy rocket, it is reasonable to assume that the launch time was 0, which would make the domain t ≥ 0.

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Answer: D. -5

Step-by-step explanation:

Imagine you are $17 in debt.

You earn $12.

Now you are only $5 in debt.

Answer:

 \(\frac{16r^3}{3} \)

Step-by-step explanation:

In this cross sections problem, we can integrate from -r to +r (so that the integral covers the entire base of the solid).

\(\int\limits^r_a {2(x^2+r^2 )} \, dx \)

The formatting for the integral did not let me put -r on the lower bound, so i replaced it with a, just know that a represents -r here.

Evaluating the integral gives use that it is equal to;

\(\frac{16r^3}{3} \)

Caution: this answer may not meet your needs, but this is the answer I have come up with with the given information.

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Answer:

8 m is the answer.

Step-by-step explanation:

a = ?

b (Brennan and Hannah) = 6 m

c (Jayce and Hannah) = 10 m

According to the Pythagoras theorem,

a² + b² = c²

a² + 6² = 10²

a² + 36 = 100

a² = 100 - 36

a² = 64

a = 8 m

∴ Jayce and Brennan are 8 m apart.

The solution is erroneous. Now, let us determine the error and find the correct solution via two distinctive approaches.

Error: Randy wrongly divided the figures.

Student #1 (Hannah):

Problem: 23.5 ÷ 11.2

Hannah's Solution: 2632.0

The result is incorrect. Let us now find the cause of the issue and its accurate solution utilizing two distinct strategies.

Error: It seems Hannah multiplied the numbers rather than dividing them.

Correct Solution (Strategy 1): Direct Division  

23.5 ÷ 11.2 ≈ 2.098

Correct Solution (Strategy 2): Long Division  

23.5 ÷ 11.2 ≈ 2.098

Note to Hannah:

Dear Hannah,

It appears that you inadvertently multiplied the figures instead of dividing them. When dividing 23.5 by 11.2, the accurate solution is nearly 2.098. You can utilize either direct division or long division to achieve this answer. Don't forget to pay attention to the operation needed for solving the problem. Keep practicing, and you will get better!

Best regards,

Your Tutor

Student #2 (Randy):

Problem: 14.68 ÷ 1.02

Randy's Solution: 7.34

The solution is erroneous. Now, let us determine the error and find the correct solution via two distinctive approaches.

Error: Randy wrongly divided the figures.

Correct Solution (Strategy 1): Direct Division  

14.68 ÷ 1.02 ≈ 14.392

Correct Solution (Strategy 2): Long Division  

14.68 ÷ 1.02 ≈ 14.392

Note to Randy:  

Dear Randy,

It appears you made a slight mistake in your division. The exact solution for the equation 14.68 ÷ 1.02 is roughly 14.392. You can use either direct division or long division to obtain the accurate solution. Continue practicing and verifying your calculations; this will help you to get better!

Best regards,

Your tutor

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Problem 1

-------------

Explanation:

The tickmarks tell us which segment pieces are equal to one another. For instance, CD = DE because of the triple tickmarks. This in turn means point D is the midpoint of segment CE. Points F and D are midpoints, which connect forming midsegment FD.

Midsegment FD is parallel to the segments AB, BC, and AC. Use similar logic for the other midsegments.

=================================================

Problem 3

-------------

Explanation:

The midsegments are half as long compared to the side they are parallel to. Example: FH is half as long as KL.

Since KL = 48, half of this is FH = KL/2 = 48/2 = 24

We use this idea in reverse to go from a known midsegment length to an unknown parallel side. FG = 37 doubles to JL = 74 as one example of what I mean. As another example, GH = 30 doubles to KJ = 60.

Once we know KJ = 60, split that in half to get FJ = 30. This is because point F is the midpoint of segment KJ.

The measure of FH = 24,  JL = 74, KJ = 60, and FJ = 30 and the parallel line segment will be  YZ || RT, RS || XZ, and XY || TS.

What is coordinate geometry?

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

1)

The equal lines can be characterized as two lines in the very plane that are at equivalent separation from one another and never meet.

The line segment YZ is parallel to RT.

The line segment RS is parallel to XZ.

The line segment XY is parallel to TS.

The parallel line segment will be  YZ || RT, RS || XZ, and XY || TS.

2)

As given in the question,

F, G, and H are the midpoints of the sides of ΔJKL.

F is the midpoint of KJ, G is the midpoint of KL, H is the midpoint of JL

Measure of the required sides are as follows:

FH = (KL / 2)                        

   = (48/2)

   = 24

JL = 2 x FG

 = 2 x 37

 = 74  

KJ = 2 x GH            

  = 2 x 30

  = 60

FJ = GH = 30      

Therefore, the measure of FH = 24,  JL = 74, KJ = 60, and FJ = 30 and the parallel line segment will be  YZ || RT, RS || XZ, and XY || TS.

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Answer:

6 inches is 152.39999999999998 millimeters

Step-by-step explanation:

Answer:

x²+x-1=0

3x²-12x-9=0

Undefined

Answer: Green is 25%  Blue is 0.5% Red is 0.5%  Yellow is 50%.

Step-by-step explanation:

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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The translation form of each shape is given as follows:

a) X to Z: (x, y) -> (x + 5, y + 2).

b) Z to X: (x, y) -> (x - 5, y - 2).

The four translation rules are defined as follows:

For the composition of translations, we add the coordinates, hence:

Hence the rule from X to Z is given as follows:

(x, y) -> (x + 5, y + 2).

From Z to X, we have the inverse rule, hence:

(x, y) -> (x - 5, y - 2).

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False. While large neural networks (NNs) can often outperform traditional learning algorithms in certain tasks, this is not always the case.

The performance of a large NN depends on the size of its training dataset, the type of problem it is being used to solve, the amount of data preprocessing and feature engineering that has been done, the size of the network, the type of optimisation algorithm being used, and the quality of the hyperparameters used. There is no single formula or calculation that can be used to determine which type of algorithm will be better than another.

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Answer:

x=4

Step-by-step explanation:

3/4(x+8)=9

simplify

3/4x+6=9

-6 -6

3/4x=3

multiply 4

3x=12

divide 3

x=4

Answer:

The cost of the bottle of drink is P4.85. The refund for an empty bottle is 25 thebe.

To express the refund as a percentage of the cost of the drink, we need to convert the refund to the same unit as the cost of the drink.

1 thebe = 0.038 Philippine pesos (as of June 2023)

25 thebe = 0.95 Philippine pesos

Therefore, the refund for an empty bottle is 0.95/4.85 x 100% = 19.59%

So the refund for an empty bottle is 19.59% of the cost of the bottle of drink.

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Answer:

Step-by-step explanation:

Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

The range of the function is {1,-1,10} for function f(x)=2x³−3x .

A relation is a function if it has only One y-value for each x-value.

In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.

The given function is f(x)=2x³−3x

The domain is {-1,1,2}

Now f(-1)=2(-1)³-3(-1)

=-2+3=1

f(1)=2(1)³-3(1)=2-3=-1

f(2)=2(2)³-3(2)=16-6=10

Hence, the range of the function is {1,-1,10} for  f(x)=2x³−3x .

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