Mahidol University Wisdom of the Land Exercise If X, and X, are independent random variables with = 4,₂= 2, 0₁-3, O₂ = 5, and Y = 4X₁-2X₂, determine the following. ▪ E(Y) ▪ V(Y) ▪ E(2Y) ▪ V(2Y) 53

The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Sequence of transformations carries ABCD onto HGFE are translation and reflection.

In mathematics, reflection refers to a transformation of a geometric figure in which the figure is flipped across a line or a plane. The line or plane across which the figure is flipped is called the line or plane of reflection, and it acts as the mirror for the reflection.

ABCD is a rectangle in 4th quadrant

Step1: Translate it by2 units in vertical direction

rectangle will shift to 1st quadrant with new coordinates.

Step2: Reflect the rectangle w.r.t y axis

The final rectangle will be in 3rd quadrant

Hence,   sequence of transformations carries ABCD onto HGFE are translation and reflection.

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The tangent of an obtuse angle with a sine of 0.53 is approximately 0.5592.

To find the tangent of an angle, we can use the relationship between the sine and tangent functions. The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle. Since we are given the sine of the obtuse angle as 0.53, we need to find the cosine of the angle.

However, the sine alone does not provide enough information to determine the cosine and thus the angle itself. Therefore, it is not possible to calculate the exact value of the tangent based solely on the given information. However, if additional information or a specific angle measure is provided, we could determine the tangent using the trigonometric functions.

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Answer:

Value of each circle = 34

Value of each triangle = 33

Step-by-step explanation:

3 circles = 102

1 circle and 2 triangles = 100

Let x represent a circle and y represent a triangle.

3x = 102

x + 2y = 100

Now, we turn the two equations into a system of equations.

Isolate x in the first equation by dividing both sides by three:

x = 34

Plug 32 in for the second equation and solve for y:

34 + 2y = 100

34 + 2y - 34 = 100 - 34

2y = 66

2y / 2 = 66 / 2

y = 33

So...

The value of each circle is 34

The value of each triangle is 33

Answer:

C: 75%

Step-by-step explanation:

27 out of 36 are red.  You find the percentage by diving 27 by 36 and then moving the decimal place over to the right 2 spaces.  27 / 36 = .75

Division of a given length of an item into required length, would result to a length lesser than the initial length of the fabric. This ensures that the required length of each piece is \(\frac{1}{12}\).

The given fabric has been divided into equal proportion. The length of the small pieces of the given fabric can be determined by dividing the total length of fabric by the number of pieces.

Let the length of each piece required be represented by x.

So that;

given that the total length of the fabric is 2 yards, then;

24x = 2

divide both sides by 24 to have;

x = \(\frac{2}{24}\)

  = \(\frac{1}{12}\)

x = \(\frac{1}{12}\) yards.

Thus, each piece of the 24 pieces of fabric has a length of \(\frac{1}{12}\) yards.

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Answer:

3 Inches

Step-by-step explanation:

1/12 Yards = 2.99988

2.99988 Rounds Up To 3

Answer:

Option B is correct

Answer:

B there is enough raspberries to make 4 pie they can 6 pies if they 2 more of raspberries

The statements that are true about the pyramid are

From the question, we are to determine the statements that are true about the pyramid

The diagram shows a square pyramid,

The length of a side of its base is 756 ft

and

The height / altitude of a triangular face is 612 ft

Since the pyramid is a square pyramid,

Then, the base must be a square with each side measuring 756 feet

∴ The first statement is true

Since the height of a triangular face is 612 ft,

Then,

∴ The slant height of the pyramid is 612 feet

NOTE: Slant height of a pyramid is the altitude of the triangle comprising a lateral face

Thus, the second statement is true

Since the triangular faces each have a base of 756ft and a height of 612 ft,

Then,

All four triangular faces are congruent

∴ The fourth statement is true

NOTE: Lateral sides of a solid are the faces on the sides of the shape

The pyramid has four lateral faces which are each a triangle

∴ The last statement is true

Hence, the statements that are true about the pyramid are

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The critical region is determined based on the alpha level, which is the probability of making a Type I error (rejecting the null hypothesis when it is true). An alpha level of .01 means that there is a 1% chance of making a Type I error.

If Chastity ran a hypothesis test with an alpha level of .01 and her test statistic fell outside of the critical region, it means that the test statistic does not provide enough evidence to reject the null hypothesis.

In this case, Chastity should fail to reject the null hypothesis and accept it as the plausible explanation. This implies that there is not enough evidence to support the alternative hypothesis.

When a test statistic falls outside of the critical region, it indicates that the observed data is not extreme enough to reject the null hypothesis. The critical region is determined based on the alpha level, which is the probability of making a Type I error (rejecting the null hypothesis when it is true). An alpha level of .01 means that there is a 1% chance of making a Type I error.

In summary, when Chastity's test statistic falls outside of the critical region, she should fail to reject the null hypothesis and accept it as the plausible explanation. This means that there is not enough evidence to support the alternative hypothesis at the given alpha level of .01.

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Answer:

AB = 5/2 A'B'

Step-by-step explanation:

the other answers:

2)    (−1, 3/2)

3)    8 inches

4)    The scale factor is between 0 and 1

5)     (8, −4) and (−4, −12)

I just took the quick check, these are the answers. I know you already took it so this isn't helpful but if anyone else needs it^^

Answer:

option 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here are the conditions.

The car must go at least 55 mph. That means that 55 is included. Use ≥

The car's speed must be greater than 55. That means s>55 Notice the open end of the arrow is towards the s. The point is towards 55. The large end must be towards the largest entity (s in this case).

The answer uses ≥

The answer is s ≥  55

Using the Central Limit Theorem, it is found that the correct option is:

(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.

By the Central Limit Theorem, for a distribution with mean \(\mu\) and standard deviation \(\sigma\), considering the sampling distribution of sample means of size n, the measure of variability is the standard error, which is given by:

\(s = \frac{\sigma}{\sqrt{n}}\)

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Solution:

Given:

The radius and tangent to a circle at the point of intersection are perpendicular to each other.

Hence, considering the right triangle;

Hence, the length of the missing side can be gotten using the Pythagorean theorem.

Therefore, to the nearest tenth, the length of the missing side is 6.3

Answer:

17

Step-by-step explanation:

Since there is no variables in the equation they are all like terms. So just do addition or subtraction. But if it wants you to separate addition and subtraction the answer would be 31-12.

If this is for Imagine Math:

Question:

Simplify the expression by combining like terms.

15+12−5+4−7

Answer:

7x +4y + 8

You must select 1,096 teenagers to ensure that 4 of them were born on the exact same date.

To ensure that 4 teenagers were born on the exact same date (mm/dd/yyyy), you must consider the total possible birthdates in a non-leap year, which is 365 days.

By using the Pigeonhole Principle, you would need to select 3+1=4 teenagers for each day, plus 1 additional teenager to guarantee that at least one group of 4 shares the same birthdate.

Therefore, you must select 3×365 + 1 = 1,096 teenagers to ensure that 4 of them were born on the exact same date.

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Answer:

john has 9 baseball cards left

Step-by-step explanation:

30 - 14 - 7 = 9

Answer:

John has 9 baseball cards left.

Step-by-step explanation:

First, you have to find how many baseball cards John has in the begining before he starts giving them away. In the problem, it states that John had 30 baseball cards.

Next, you have to find how how many he gave away. In the problem, it states that he gave 14 to Mike and 7 to Jeff. Instead of subtracting the numbers one by one, we'll make it easier. Add 14 to 7 and you'll get 21.

Then, you subtract 21 from 30, and you'll get 9.

John has 9 basball cards left.

P.S. If you want the equation, the equation is 30-(14+7)=x or 30-21=x

Answer:

A

Step-by-step explanation:

Hope this helps

can you go to my profile and help me with my recent one. plzssss

Answer: A

Step-by-step explanation:

Answer:

3. 2(MB) = AB

Step-by-step explanation:

1. This is not true because CM is less than CD.

2. This is not true because 2(AB) is greater than AM.

3. This is true because AB = 2(MB) or 2(AM).

4. This is not true because 1/2(AM) is less than AB.

Let's put some values on number 3 to check if it's, indeed, true.

Let's say AB's distance is 50 meters, then AM and MB should be half of it; that is: AM/MB = 25 meters. Let's check:

2(MB) = AB

2(25) = 50

50 = 50

Answer:

Dear Johnson,

Answer to your query is provided below

The expression 3.14 x 10^3 is scientific notation for 3,140.

Step-by-step explanation:

The purpose of scientific notation is to write very large, or very small, numbers with ease.

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

a x 10^b

Follow the steps below to see how 3,140 is written in scientific notation.

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 3,140

New Number: 3.140

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 3 . 1 4 0

Decimal Count: 1 2 3

There are 3 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10^b

a = 3.14 (Please notice any zeroes on the end have been removed)

b = 3

Now the whole thing:

3.14 x 10^3

Step 4

Check your work:

10^3 = 1,000 x 3.14 = 3,140

Rosa bought 8 cans of juice for herself and her friends.

To calculate how many cans of juice Rosa bought, we first need to calculate the total amount of money she gave the cashier:

2/3 of 15 quarters = (2/3) x 15 = 10 quarters (since each quarter is worth 25 cents,

10 quarters are worth 10 x 25 = 250 cents)

3/5 of 10 nickels = (3/5) x 10 = 6 nickels (since each nickel is worth 5 cents, 6 nickels are worth 6 x 5 = 30 cents)

Therefore, Rosa gave the cashier 250 + 30 = 280 cents.

Now, we need to find out how many cans of juice Rosa can buy with 280 cents:

1 can of juice costs 35 cents, so 280 cents can buy 280/35 = 8 cans of juice.

Therefore, Rosa bought 8 cans of juice for herself and her friends.

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The smallest sample size n that provides the desired accuracy is 10.

To find the smallest sample size n that provides the desired accuracy, we can use the formula:

n = (Z-value * standard deviation / margin of error)²

Where:
Z-value = the critical value for the desired confidence level (in this case, 1.96 for 95% confidence)
Standard deviation = the preliminary sample standard deviation (1.5 in this case)
Margin of error = the desired accuracy (0.3 units in this case)

Substituting the values, we get:

n = (1.96 * 1.5 / 0.3)²
n = 9.8

Since we cannot have a fractional sample size, we round up to the nearest whole number, giving us:

n = 10

Therefore, the smallest sample size n that provides the desired accuracy is 10.

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Answers:

(a)  9 cm

(b)  2 cm

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

Work shown for part (a)

A = s^2

s = sqrt(A)

s = sqrt(81)

s = 9

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

Work shown for part (b)

P = 4s

s = P/4

s = 8/4

s = 2

The side length of the square with area of 81 cm² is :

The side of the square with the perimeter of 8 m is :

Solution:

We're given the area of a square : 81 cm².

To find one of its sides, we need to take the square root of that.

So we have:

\(\sf{Side\:length{\square}=\sqrt{81}} \\ \\ \sf{Side\:length\square=9}\)

We know that if we take the square root of 81, we will get two solutions: 9 and -9; however we cannot use -9, because having a negative side length is impossible.

__________________________

To find the side length when given the perimeter, we divide it by 4, because the formula for a square's perimeter is P = 4a.

So if we rearrange that for a, we will get : a = P/4.

where a = side length

Solving,

Answer:

Step-by-step explanation:

Use Pythagorean theorem to calculate:

Same method for FA, the diagonal of rectangle ABFE

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The test is one of the form  Hₐ <  ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀

According to problem ststement : We need to solve  an Hypotesis test proportion so:

H₀    P₀ = 0,4              and    Hₐ  < 0,4   ( Alternative hipotesis)

From a random sample of 700 employes 305 are determined to earn more than $ 50000

Proportion                    pₐ = 305/700 = 0,4357     pₐ  = 0,4357

proportions are p = 0.4  and q = 0,6

We will asume a confidence level of 95 % hence α=  1-0,95     α = 0,05

so from z table we find z(c) = 1,64

Therefore we must calculate our z(p) = ( pₐ-p₀) ÷√(p*q)/n

Calculating   z(p)  =  0,0357 /0,01851   ⇒  z(p) 1.9286

Our test is one of the form  Hₐ <  ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀

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The partially ordered set (poset) (In, <=) is isomorphic to (2^n, ) where 2^n is the power set of [n]. Isomorphism is defined as the function mapping items of In to subsets of [n]. M(S, T) is (-1)^(|T\S|) if S is a subset of T and 0 otherwise.

To establish the isomorphism between (In, <=) and (2^n, ⊆), we can define a function f: In → 2^n as follows: For an element (e1, e2, ..., en) in In, f((e1, e2, ..., en)) = {i | ei = 1}, i.e., the set of indices for which ei is equal to 1. This function maps elements of In to corresponding subsets of [n]. It is easy to verify that this function is a bijection and preserves the order relation, meaning that if (e1, e2, ..., en) <= (f1, f2, ..., fn) in In, then f((e1, e2, ..., en)) ⊆ f((f1, f2, ..., fn)) in 2^n, and vice versa. Hence, the posets (In, <=) and (2^n, ⊆) are isomorphic.

For part (b), the function M(S, T) is defined to evaluate to (-1) raised to the power of the cardinality of the set T\S, i.e., the number of elements in T that are not in S. If S is a subset of T, then T\S is an empty set, and the cardinality is 0. In this case, M(S, T) = (-1)^0 = 1. On the other hand, if S is not a subset of T, then T\S has at least one element, and its cardinality is a positive number. In this case, M(S, T) = (-1)^(positive number) = -1. Therefore, M(S, T) evaluates to 1 if S is a subset of T, and 0 otherwise.

In summary, the poset (In, <=) is isomorphic to (2^n, ⊆), and the function M(S, T) is defined as (-1)^(|T\S|) if S is a subset of T, and 0 otherwise.

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Answer:

A. 0.0000009 m

B. 6,130,000,000 people

C. 100,000 light years

D. 0.00001 mm

E. 0.0000001 kg