Lonnie’s employer will match up to 5% of his salary in contributions to his 401(k). His starting salary with the company is $2,500 a month, and the company allows him to contribute up to 12% of his salary to his 401(k). What is the minimum amount of his salary that Lonnie should contribute each month to maximize his employer’s matching contribution?

b =(17,6x 8,9):19,7=7,95

The number of possible king-queen pairs can be determined by multiplying the number of candidates for king by the number of candidates for queen.

To calculate the number of king-queen pairs, we multiply the number of candidates for king by the number of candidates for queen. In this case, there are four candidates for homecoming queen and three candidates for king. Therefore, the total number of king-queen pairs would be 4 multiplied by 3, which equals 12.

Each candidate for king can be paired with each candidate for queen, resulting in multiple possible combinations. By multiplying the number of candidates for each position, we account for all possible pairings. In this scenario, there are three potential kings and four potential queens. For each king, there are four possible queens he can be paired with. Since there are three kings, we multiply 3 by 4 to get the total number of 12 king-queen pairs.

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Putting it all together, we have:

P[Y1 ≤ 3/4 | Y2 > 1/3] = (1/4) (7/12) / (5/6) = 7/20

To find E[Y1 + Y2], we can use the fact that the expected value of a sum is the sum of the expected values:

E[Y1 + Y2] = E[Y1] + E[Y2]

To find E[Y1], we need to integrate Y1 times the joint PDF over the region where Y1 and Y2 are both positive and Y1 ≤ Y2:

E[Y1] = ∫∫ y1 f(y1, y2) dy1 dy2

= ∫[0,1] ∫[y1,1] y1 f(y1, y2) dy2 dy1

= ∫[0,1] ∫[y1,1] 2y1 dy2 dy1

= ∫[0,1] [2y1(1 - y1)] dy1

= 1/3

Similarly, we can find E[Y2]:

E[Y2] = ∫∫ y2 f(y1, y2) dy1 dy2

= ∫[0,1] ∫[0,y2] y2 f(y1, y2) dy1 dy2

= ∫[0,1] ∫[0,y2] 2y2 dy1 dy2

= ∫[0,1] [y2^2] dy2

= 1/3

Therefore, we have:

E[Y1 + Y2] = E[Y1] + E[Y2] = 2/3

To find P[Y1 ≤ 3/4 | Y2 > 1/3], we can use Bayes' theorem:

P[Y1 ≤ 3/4 | Y2 > 1/3] = P[Y2 > 1/3 | Y1 ≤ 3/4] P[Y1 ≤ 3/4] / P[Y2 > 1/3]

We can find the numerator and denominator separately. First, we find P[Y2 > 1/3 | Y1 ≤ 3/4]:

P[Y2 > 1/3 | Y1 ≤ 3/4] = ∫[1/3,1] ∫[0,y2] 2 dy1 dy2 / ∫[0,1] ∫[0,1] 2 dy1 dy2

= 1/4

Next, we find P[Y2 > 1/3]:

P[Y2 > 1/3] = ∫[1/3,1] ∫[0,y2] 2 dy1 dy2 / ∫[0,1] ∫[0,1] 2 dy1 dy2

= 5/6

Finally, we find P[Y1 ≤ 3/4]:

P[Y1 ≤ 3/4] = ∫[0,3/4] ∫[y1,1] 2 dy2 dy1 / ∫[0,1] ∫[0,1] 2 dy1 dy2

= 7/12

Putting it all together, we have:

P[Y1 ≤ 3/4 | Y2 > 1/3] = (1/4) (7/12) / (5/6) = 7/20

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The equation sin^2(x) = 1/2 - 1/2cos(2x) is an identity that holds true for all values of x. It can be used to simplify expressions involving sine and cosine functions.

The equation sin^2(x) = 1/2 - 1/2cos(2x) is a trigonometric identity, which means it holds true for all values of x. To understand why this identity is true, we can use the double angle formula for cosine, which states that cos(2x) = cos^2(x) - sin^2(x). Rearranging this formula gives sin^2(x) = cos^2(x) - cos(2x).

Now, we can substitute the identity cos^2(x) + sin^2(x) = 1 into the above equation, which gives sin^2(x) = 1 - cos^2(x) - cos(2x). Rearranging further gives sin^2(x) = 1/2 - 1/2cos(2x), which is the desired identity.

This identity can be useful in simplifying expressions involving sine and cosine functions. For example, if we have an expression with both sin(x) and cos(x), we can use this identity to express everything in terms of sin(x) or cos(x) only.

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Answer: Third Option: The car was at -60 feet at one second after it passed the camera. When was the car 5 feet to the west of the camera?

Step-by-step explanation:

The negatives in the equation most match the the numbers in the third option and it also the one that makes the most sense.

Hope this helps!! :)

In summary, it takes approximately 4.92 hours for 2 milligrams to be left in the body and the half-life of the drug is approximately 2.29 hours.

To determine when 2 milligrams is left in the body, we can substitute A = 2 into the equation given: 2 = 10(0.8)^t. Then, we can solve for t by dividing both sides by 10 and taking the natural logarithm of both sides to isolate t: t = ln(2/10) / ln(0.8). Using a calculator, we find that t is approximately 4.92 hours.

To find the half-life of the drug, we need to determine the time it takes for half of the initial dose (10 milligrams) to be eliminated from the body. This occurs when A = 5 milligrams. We can use the same equation and substitute A = 5: 5 = 10(0.8)^t. Then, we can solve for t using the same method as before: t = ln(0.5) / ln(0.8). Using a calculator, we find that t is approximately 2.29 hours.

In summary, it takes approximately 4.92 hours for 2 milligrams to be left in the body and the half-life of the drug is approximately 2.29 hours.

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In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.

The correct answer is Option D.

The key concept here is that a plane is defined by having at least three non-collinear points.

When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.

Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.

Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.

The correct answer is Option D.

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Answer:

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

Step-by-step explanation:

I hope that helped a bit ;)

Answer: $88.90

Step-by-step explanation:

$39.95 x 2 + 0.06 x 150

The probability density function of y = e^x when x is normally distributed.

If x is normally distributed with mean μ and variance σ^2, then y = e^x is a log-normal distribution with the following probability density function:

f(y) = (1 / (y * σ * sqrt(2π))) * e^(-((ln y - μ)^2 / (2σ^2)))

where ln y is the natural logarithm of y.

To see why this is the case, we can use the change of variables formula for probability density functions. Let g(x) = e^x, so that y = g(x). Then, the inverse function is x = ln y, and we can compute the derivative of the inverse function as dx/dy = 1/y.

Using the change of variables formula, we have:

f(y) = f(g^(-1)(y)) * |(dg^(-1)/dy)(y)|

where f(g^(-1)(y)) is the probability density function of x, and |(dg^(-1)/dy)(y)| is the absolute value of the derivative of the inverse function evaluated at y.

Plugging in the normal distribution density function for f(x) and the derivative dx/dy = 1/y, we get:

f(y) = (1 / (y * σ * sqrt(2π))) * e^(-((ln y - μ)^2 / (2σ^2)))

This is the probability density function of y = e^x when x is normally distributed.

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These are the specified parameters:

The water rate is $1.33 per 751 gallons.

a. Determine the water bill

The water bill = 40,000 gallons × \(\displaystyle \frac{\$1.33}{751\ gallons}\)

                       = \(\displaystyle\frac{\$53,200}{751}\)

                       = $70,84

b. Determine many gallons of water can a customer use

Many gallons = $130 : \(\displaystyle \frac{\$1.33}{751\ gallons}\)

                       = $130 × \(\displaystyle \frac{751\ gallons}{\$1.33}\)

                       = \(\displaystyle \frac{97,630}{1.33}\) gallons

                       = 73,406 gallons

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Answer:

10

High Hopes

                        Barry-

Answer:

10

Step-by-step explanation:

I believe the answer is ten! I hope this helps you!

Answer:

2 < x < 3

Step-by-step explanation:

4x - 4 < 8    AND    9x + 5 > 23

4x < 12  AND   9x > 18

x < 3 AND x > 2 so the answer is 2 < x < 3.

  Solve  :    9x-28 = 0

Add  28  to both sides of the equation :

                     9x = 28

Divide both sides of the equation by 9:

                    x = 28/9 = 3.111

Answer:

Step-by-step explanation:

john lennon

Independent variable = w ( number of weeks )

It does not depend of another variable.

Dependent variable = p ( price ) it depends of the number of weeks

Variable amount = 0.3 ( depends of the number of weeks)

Fixed amount = 2.399

Answer:

Step-by-step explanation:

There are 10 common trig identities which I am aware of.

Some are in the image attached

The first image is known as b

Basic Identities

The second are known as Trigonometric / Pythagorean Identities .

The third : Co-function identities

and many more.

I'm only allowed to post five images so that's all I have.

Answer:

5.73

Step-by-step explanation:

The difference is 5.73.

Answer:

should be option one:)

Step-by-step explanation:

Answer:

Pls mark me brainliest!

Step-by-step explanation:

It is option 2!

The statement "there exists a function f such that f(x) < 0, f'(x) > 0, and f''(x) < 0 for all x" is True.

1. f(x) < 0: This means the function is always negative.
2. f'(x) > 0: This means the function is always increasing.
3. f''(x) < 0: This means the function is always concave down.

A function that satisfies all these conditions is f(x) = -e^x.

1. For all x, f(x) = -e^x is always negative because e^x is always positive and the negative sign in front makes it negative.
2. The first derivative of f(x) is f'(x) = -e^x, which is always positive because e^x is always positive and the negative sign cancels out.
3. The second derivative of f(x) is f''(x) = e^x, which is always negative because e^x is always positive.

Therefore, the statement is true.

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Answer:

V = 14130 inches cubed

Step-by-step explanation:

the volume formula for a sphere is  \(V=\frac{4}{3} \pi r^{3}\). To solve plug in the values for each part of the equation. Pi will equal 3.14, and r will equal 15.

Algebraically, find the roots of x² - 4x - 5 = 0

x² - 4x - 5 = 0 (Given equation)

Here a = 1, b = -4 and c = -5

\( \therefore \) b² - 4ac = (-4)² - (-4) × 1 × -5 = 16 - 20 = -4 < 0

Answer:

504 ways fr

Step-by-step explanation: