Two events, X and Y, are independent of each other. P(Y)= and P(X and Y)=. What is P(X) written as a decimal? Round to the nearest tenth, if necessary. 0.2 0.3 0.4 0.5

Answer:

7/14, so 50%

Step-by-step explanation:

Mr. Merkel contributes $159.00 at the end of each six months, which means there are 40 contributions over the 20-year period. The interest rate is 3% per annum, compounded annually.

Using the formula for compound interest, the future value (FV) of the RRSP can be calculated as:

FV = P * (1 + r)^n

Where P is the contribution amount, r is the interest rate per period, and n is the number of periods.

Substituting the given values, we have P = $159.00, r = 3% = 0.03, and n = 40.

FV = $159.00 * (1 + 0.03)^40

Evaluating the expression, we find that Mr. Merkel will have approximately $10,850.58 in the RRSP after 20 years.

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Answer:

Lixin is the fastest typist

Step-by-step explanation:

Amirah = 45

Lixin = 46

Shirley = 42

We divide the words by minutes which is basically Unit rate

So we take each person and divide by their words and minutes

\(\frac{words}{minutes}\)

ALWAYS when ur finding unit rate divide the buggest number by the smallest!

Answer:

see below

Step-by-step explanation:

8- 2x - 5- 13x = 6

Combine like terms

-15x+3=6

Subtract 3 from each side

-15x+3-3=6-3

-15x = 3

Divide each side by -15

x = 3/-15

x = -1/5

Check

8 - 2(-1/5) -5 -13(-1/5) = 6

8 + 2/5 -5 +13/5 = 6

3 + 15/5 = 6

3+3=6

6=6

Answer:

ur answer should be C. But I'm not really sure..

The table in which y is a linear function of x is; Choice C

According to the question;

The slope of a linear function is always constant.

Hence, By observing the table in Choice C;

Slope = (8-6)/(0-(-1)) = (10-8)/(1-0) = 2.

Hence, since slope of the function is constant, the required table is: Choice C.

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The value of quadratic function is,

⇒ y = 9x² + 54x - 63

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ y = 9 (x - 1) (x + 7)

Now, We can find the quadratic equation as;

⇒ y = 9 (x - 1) (x + 7)

⇒ y = 9 (x² + 7x - x - 7)

⇒ y = 9 (x² + 6x - 7)

⇒ y = 9x² + 54x - 63

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The answer reporting to the correct number of significant numbers is 26.937. Then required correct answer for the given question is Option A.

In the event of adding numbers with significant figures, the answer shouldn't always have  more decimal places in comparison to the number with the fewest decimal places in the calculation.

Now, for the given case,

9.19 has two decimal places whereas 4.877 and 12.87 have three decimal places.

      12.87

        4.877

+       9.19

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

       26.937

Then, we have to round off the correct answer to two decimal places which gives us 26.937.

The answer reporting to the correct number of significant numbers is 26.937.

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Answer: It would be b B. For every 2.0 gram decrease in carbohydrates, the number of calories decreases by about 30.0.

Step-by-step explanation:

Answer: The domain of a function refers to the set of all possible input values for which the function is defined. In the case of the function y = 2x - 6, the domain is all real numbers since the function is defined for any value of x.

The range of a function, on the other hand, refers to the set of all possible output values that the function can produce. To find the range of the function y = 2x - 6, we need to determine the lowest and highest values that the function can produce.

Since the coefficient of x in the function is positive (i.e. 2), the function is increasing as x increases. This means that as x increases, the value of y also increases without bound. Similarly, as x decreases, the value of y also decreases without bound.

Therefore, the range of the function y = 2x - 6 is all real numbers.

Step-by-step explanation:

The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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This is the number 80 thousand

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

Explanation:

1/2, aka 2/4, of the original fund was given to his wife and 1/4 was given to his son. That totals 3/4 since 2/4+1/4 = (2+1)/4 = 3/4.

In short, 3/4 of the fund is distributed between the wife and son. That leaves 1/4 of the fund for the two brothers to share equally.

Imagine a cake cut into quarters. Then cut each slice in half to get eighths, i.e. there are 8 equal slices. This means each brother gets 1/8 of the fund.

Since each brother got Rs 10000, this must mean the original fund is worth 8*10000 = 80000

Taking 1/8 of Rs 80000 will get us Rs 10000 for each brother.

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

Checking the answer:

original fund amount = 80000

1/2 of 80000 = 40000 is the amount the wife gets

1/4 of 80000 = 20000 is the amount the son gets

That totals 40000+20000 = 60000 leaving 80000-60000 = 20000 leftover for the two brothers to share. Cut that 20 thousand figure in half to arrive at Rs 10000 for each brother. These steps help confirm the answer.

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

Another method using algebra:

x = original amount of the fund

W = x/2 = 2x/4 = half of the fund = amount wife gets

S = x/4 = quarter of the fund = amount the son gets

W+S = (2x/4) + (x/4) = (2x+x)/4 = 3x/4

W+S represents the sum of the wife's and son's amounts.

We'll subtract this from the original amount x to find out what's left

x - (W+S) = x - (3x/4) = (4x/4) - (3x/4) = (4x-3x)/4 = x/4

This shows that 1/4 of the fund is left over after distributing to the wife and son.

The amount x/4 is then cut in half to get x/8 to represent the amount each brother gets. We're told that amount is Rs 10000

So,

x/8 = 10000

x = 8*10000

x = 80000

The original fund is worth Rs 80000

The null hypothesis refers to the population, whereas the research hypothesis refers to the sample.

We have,

In statistics, the null hypothesis is a statement that assumes there is no significant difference between two groups or variables being compared.

It represents the default position that there is no relationship or effect between the variables of interest.

The null hypothesis is typically formulated as a statement about the population parameter.

On the other hand, the research hypothesis (also known as the alternative hypothesis) is a statement that proposes a significant difference or relationship between the variables being studied.

The research hypothesis is typically formulated as a statement about the sample, which is a subset of the population.

Thus,

The null hypothesis refers to the population, whereas the research hypothesis refers to the sample.

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Answer:

$256.25

Step-by-step explanation:

The amount Trent pays back is the principal ($250) plus the interest after one year (\($250\times 0.025 = 6.25\)). We add the total to obtain $256.25.

Bob lifts a 15N rock through a distance of 1.7m, 25.5 J work does Bob do

An item should be converted to energy before being moved. The use of force is one way to transfer energy. The amount of energy used by a force to move an item is referred to as the work done.

The amount of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Pushing a block with force "F" causes the body to move more quickly, meaning that work has been completed.

Work done (W) = F × s

Where, F = force

s = displacement

Now putting the values, we get-

or, W = 15 N × 1.7 m

or, W = 25.5 N-m or Joule

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Fraction of students taking mandarin: 3/40

Hope it helps.

Answer:

So that it is safe from insects. insects cant open large boxes bottles or a steel can.

Why manufacturers frequently package their products in tall boxes, bottles, or cans is: To protect the product.

Food packaging is important as it help to protect a product and to as well prevent the product from damaging when been shipped from the seller to buyer.

Manufacturer or producer tend to package their product  so as to keep the product safe and to as improve the product Shelf Life etc.

Therefore why manufacturers frequently package their products in tall boxes, bottles, or cans is: To protect the product.

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Answer:

d) {(-2,0), (-1,0), (1,0), (2,0)}

Step-by-step explanation:

We know that,

→ A set function has different x values.

Then the set function will be,

a) {(1,0), (1,1), (2,2), (2,2)}

→ The x values underlined are repeated.

Hence, it is not a set function.

b) {(0,0), (1,1), (1,1), (3,3)}

→ The x values underlined are repeated.

Hence, it is not a set function.

c) {(0,-2), (0,-1), (0,1), (0,2)}

→ The x values underlined are repeated.

Hence, it is not a set function.

d) {(-2,0), (-1,0), (1,0), (2,0)}

→ There are no repeated values for x.

Hence, it is a set function.

A second linearly independent solution of y₂ is \(-\frac{1}{6x^3}\)

The general Equation is y" + P(x)y' + q(x)y = 0 ...............(i)

where P(x), Q(x) are continues in the internal I ≤ R.

If y₁(x) is a solution of equation 1 in I then y₁(x) ≠ 0.

Then y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\) is another solution.

The differential equation is x²y" + xy' – 9y = 0 where x > 0.

As y₁(x) = x³ is one solution of differential equation.

Divide throughout by (x²) to given differential equation.

1/x² (x²y" + xy' – 9y = 0)

y" + (y'/x) – (9/x²)y = 0 ................(ii)

By comparing equation (i) & (ii) we get:

p(x)=1/x , q(x)= –are continuous for x>0

So, another solution,

y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\)

Now putting the values of P(x) And Q(x)

y₂(x) = \(x^3\int\limits {\frac{e^{\int(1/x)dx} }{(x^3)^2}} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{\frac{1}{x} }{x^6} }} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{1}{x^7} }} \, dx\)

y₂(x) = \(x^3\int\limits {x^-7} } \, dx\)

y₂(x) = \(x^3\left[\frac{x^{-7+1}}{-7+1}\right]\)

y₂(x) = \(-\frac{1}{6}(x^3\times x^{-6})\)

y₂(x) = \(-\frac{1}{6x^3}\)

So, the answer of this question is \(-\frac{1}{6x^3}\).

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Answer:

She does not arrive at London before 10:00am

Step-by-step explanation:

Given

\(Distance = 156\ miles\)

\(Departure =07:30am\)

\(Speed = 60mph\)

Required

Determine if she arrives at London before 10:00 am

Using:

\(Speed = Distance/Time\)

We calculate the time spent on the journey.

So, we have:

\(60 = \frac{156}{Time}\)

Make Time the subject

\(Time = \frac{156}{60}\)

\(Time = 2.6\)

This means that, she travels for 2.6hour from Rotterdam to London.

Her Arrival Time is:

\(Arrival=Departure + 2.6hours\)

\(Arrival=7:30am+ 2.6hours\)

\(Arrival=10:10am\)

This implies that she does not arrive at London before 10:00am

Answer:

156/60= 2.6 hours.  

2.6 hours is 156 minutes (2 hours, 36 minutes).

9:36 is when Kim won't reach London, so no

2.6 hours which is greater than 2.5 hours.

Step-by-step explanation:

The true statement about the function is that (c) the domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.

The complete question is added at the end of this solution

From the complete question, we have the following equation

f(x) = g(x)/h(x)

The above equation means that

The function f(x) is the quotient of the functions g(x) and h(x)

For the function f(x) to have real values, the function h(x) must not equal 0

i.e. h(x) ≠ 0

This is so because

A number or an expression divided by 0 is not a real number

Hence, the true statement is that the domain of f(x) consists of all values of x where h(x) does not equal 0.

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Complete question

which of the following statements is true about a rational function of the form where g and h are polynomial functions?

A. If the rational function has a removable discontinuity, then it cannot have a vertical asymptote. g(x)

B. The rational function f(x) h(x) will have a removable discontinuity at x = a if g(a) = 0. g(x)

C. The domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.

D. If the rational function has a removable discontinuity, then it cannot have a horizontal asymptote.

Approximately 204.11 years ago, your great, great, great, great grandmother left you $2 in a bank account that has grown to $150,000 today.

To calculate the number of years, we can use the compound interest formula:

\(A = P(1 + r/n)^ {nt}\)

where A is the final amount, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal amount is $2, the final amount is $150,000, the annual interest rate is 5.5% (0.055 as a decimal), and the interest is compounded weekly (n = 52), we can solve for t:

\(50,000 = 2(1 + 0.055/52)^{52t}\)

Dividing both sides by $2 and isolating the exponent, we get:

\(75,000 = (1.0010576923076923)^{52t}\)

Taking the logarithm of both sides, we have:

\(log(75,000) = log(1.0010576923076923)^{52t}\)

Using logarithm properties, we can rewrite the equation as:

log(75,000) = 52t * log(1.0010576923076923)

Solving for t by dividing both sides by 52 * log(1.0010576923076923), we find:

t ≈ 204.11 years

Therefore, approximately 204.11 years ago, your great, great, great, great grandmother left you $2 in the bank account.

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Answer:

a = 3

Step-by-step explanation:

2 + \(\frac{2a}{3}\) = 4

\(\frac{2a}{3}\)  = 4 - 2

\(\frac{2a}{3}\)  = 2

2a = 2 x 3

2a = 6

a = 3

Therefore , the solution of the given problem of angle comes out to be the angle at point B is therefore a right angle.

An angle is a shape in Euclidean geometry composed of two rays, referred to as the sides of circle, that diverge at the angle's tip and the peak, which is situated in the middle. Within the plane they are located in, two rays can join to form an angle. Angle is another outcome of two objects interacting. They are known as dihedral angles. Two line beams with ends can be arranged in a variety of ways to create an angle in 2 dimensions.

Here,

We can determine whether this triangle is a right triangle by using the Pythagoras theorem:

=> AC² = AB² + BC²

=> 13² = 5² + 12²

=> 169 = 25 + 144

=> 169 = 169

It is a right triangle because the Pythagorean formula holds true for this triangle. The angle at point B is therefore a right angle.

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Answer:

Step-by-step explanation:

Step 1: Use point-slope form and substitute in the x and y values

y-y1=m(x-x1)

y-(1)=2(x-(-3))

Step 2: Simplify the expression

y-1 = 2(x+3)

Add one to the other side

y= 2(x+3)+1

Multiple 2 by (x+3)

y=2x+6+1

Add common terms

y=2x + 7

The most effective chunking of the digit sequence 14929111776 would depend on the purpose of chunking.

However, a possible effective chunking could be 14-92-91-11-77-6, which groups the digits into pairs or triplets based on their similarity or pattern. Another possible chunking could be 1492-911-1776, which separates the digits based on significant historical events. Ultimately, the effectiveness of chunking would depend on the context and intended use of the sequence. The most effective chunking of the digit sequence 14929111776 would be to group the numbers into smaller, manageable chunks. One possible way to chunk the sequence is: 149-29-11-17-76. This breaks the sequence into five groups, making it easier to remember and process.

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There are 66,960 number of ways to set up a batting order of 9 players from among the 12 players on the baseball team.

To determine the number of ways to set up a batting order of 9 players from among the 12 players on a baseball team, we can use the concept of permutations.

Since the order matters in a batting order, we can use the formula for permutations.

The number of permutations of selecting 9 players from a pool of 12 players is given by:

P(12, 9) = 12! / (12 - 9)!

Calculating this, we have:

P(12, 9) = 12! / 3!

= (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4) / (3 * 2 * 1)

= 12 * 11 * 10 * 3 * 7 * 2

= 66,960

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Answer:

8

Step-by-step explanation:

For the smallest possible length, this has to be one of the shorter sides. Let the length of this side be x.

So, by the triangle inequality theorem, 1+x>8, which means x>7.

So, the smallest possible whole number length is 8.