if
h²+k²-m²-n² = 15
and
(h²+k²)²+(m²+n²)² = 240.5
what is
h²+k²+m²+n²

9514 1404 393

Answer:

  -12

Step-by-step explanation:

The number halfway between the middle two is the average of the four numbers: -54/4 = -13.5. Then the middle two numbers are -14 and -13. The greatest of the four consecutive integers is -12.

__

Those integers are -15, -14, -13, -12.

The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

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Answer:

D

Step-by-step explanation:

Given the expression:

The expression shows the distribution property of addition

So, 6 ( 3 +4 ) = 6 * 7 = 42

Which will give the same result if we distribute 6 over 3 and 4

So, 6 (3) + 6(4) = 18 + 24 =42

Show the following diagram:

As shown, the rectangle on the left side has 3 rows + 4 rows

Which will give us 7 rows when divided to 6 column will give 42 squares

While the rectangles on the right side. we have divided it to 3 rows and 4 rows, each one of them is divided to 6 column which will give us 18 squares and 24 squares the sum of them will give us 42 squares

So, 6 ( 3 + 4 ) = 6(3) + 6 (4)

Answer:

(100 ft^2) / (75 people) is a ratio:  1.3333... ft^2/person

Step-by-step explanation:

There are 75 people in a 100 square foot area.  The amount of space (floor space) is (100 ft^2) / (75 people) = 1 1/3 square feet.

(100 ft^2) / (75 people) is a ratio:  1.3333... ft^2/person

Answer:

x = 3

y = -7

Step-by-step explanation:

y = -4x + 5

y = 3x - 16

Substitute y in the first equation with 3x - 16

3x - 16 = -4x + 5

+4x         +4x

7x - 16 = 5

+16         +16

7x = 21

÷7    ÷7

x = 3

Then, put x = 3 in y = -4x + 5

y = -4(3) + 5

y = -12 + 5

y = -7

Answer:

x = 3; y = -7

Step-by-step explanation:

Both equations are solved for y.

Let's substitute what y is equal to in the first equation, -4x + 5, for y in the second equation.

The original second equation is:

y = 3x - 16

Now we plug in -4x + 5 for y in the second equation.

-4x + 5 = 3x - 16

Subtract 3x from both sides.

-7x + 5 = -16

Subtract 5 from both sides.

-7x = -21

Divide both sides by -7.

-7x/-7 = -21/-7

x = 3

Now that we know the value of x, we use substitution again.

Take the first original equation, y = -4x + 5, and substitute 3 for x. Then solve for y.

Here is the first original equation:

y = -4x + 5

Substitute 3 for x:

y = -4(3) + 5

y = -12 + 5

y = -7

The solution is: x = 3; y = -7

We can check the solution to make sure it is correct.

Take each original equation and plug in the values we found for x and y. Simplify both sides and see if they are equal. If the two sides are equal, the solution is correct.

Check first equation:

y = -4x + 5

-7 = -4(3) + 5

-7 = -12 + 5

-7 = -7

The solution works on the first equation.

Check second equation:

y = 3x - 16

-7 = 3(3) - 16

-7 = 9 - 16

-7 = -7

The solution works in the second equation.

This shows that our solution is correct.

Answer: x = 3; y = -7

Your answer is correct, the function is not a quadratic function.

A quadratic is a polynomial function such that the degree of the polynomial (this is the maximum exponent of the polynomial) is 2.

In the given one we have:

f(x) = 4x³ - 5x + 2

You can see that the maximum exponent is 3, so this is not a quadratic function,. so your answer is correct.

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The experimental probability that the next client to get a haircut at Cameron's salon will have blond hair is 4/18, or 22.2%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.

This means that there is a 22.2% chance that the next client at Cameron's salon will have blond hair. This probability is calculated by taking the number of clients with blond hair (4) and dividing it by the total number of clients (18).

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Well, does she earn this interest per month?? or is it per year.

4% of $1000 is $40 dollars

so it would take her 2 years (If this 4% is due every year. if not just change the "year" to months) to reach 80 dollars. She just needs 20 dollars which is half of the 40 she earns per year. half of a year is 6 months so the answer would be

Sonja would need to keep her 1000 dollars in the savings account for 2 and a half years to earn 100 dollars exact.

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Answer:

It's been a hot minute since I have done these, but if I'm correct the answer is 13%

Step-by-step explanation:

6/7 is .86 or an 86% chance. Followed by 1/6 which is .16 or a 16% chance. .86 multiplied by .16 is .13 giving the sequence a 13% chance.

Kylie has to try at most 3,024 different combinations in order to call Katerina if she does not dial repetitive phone numbers.

Kylie only recalls the first six numbers of Katerina's phone number, so she must guess the last four. Because she cannot repeat any of the numbers she has already successfully predicted, the first remaining digit has just nine viable alternatives (all digits from 0 to 9 except the one she already knows). Similarly, the second remaining digit has just eight options, the third has seven, and the fourth has six.

Therefore, the total number of possible combinations is:

9 x 8 x 7 x 6 = 3,024

This implies Kylie will have to try at most 3,024 different combinations to reach Katerina, provided she gets it right on the last try.

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Therefore , the solution of the given problem of graph comes out to be option A f(n) = 7 - 2(n-1)

Theoretical physicists use graphs to analytically chart or visually represent claims rather than values. A graph point typically depicts the relationship between any number of things. A specific type of non-linear train assembly made up of clusters and lines is known as a graph. Glue should be used to connect the networks, also referred as the boundaries. In this network, the nodes had the numbers 1, 2, 3, and 5, whilst edges had the numbers 1, 2, 3, and 4, as well as the numbers (2.5), (3.5), (4.5), and yet also (4.5). (4.5).

Here,

We can use the following method to determine the general term of an arithmetic series:

=> f(n) = a + (n-1)d

where the usual difference is "d" and "a" is the first term.

Since the series begins at 7, "a" is 7, as shown by the graph. Additionally, since each term reduces by 2, we can see that the common difference is 2.

Consequently, the following is the arithmetic sequence's stated rule:

A) f(n) = 7 - 2(n-1)

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For both tree A and tree B calculated slope is less than 0.06. Then it does not satisfy the slope constraint.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

To use the treehouse as the start of the zip line, the cable needs to be attached to the starting tree at a height of 18 feet above the ground.

To meet the slope constraint, Esteban wants to change the height to 7 feet and end the zip line at a height of 11 feet above the ground.

He claims this vertical change meets the slope constraint.

The slope for tree A will be

\(\rm Slope \ A = \dfrac{7}{120}\\\\Slope \ A = 0.0583\)

The slope for tree B will be

\(\rm Slope \ B = \dfrac{7}{160}\\\\Slope \ B = 0.043\)

For both tree A and tree B calculated slope is less than 0.06. Then it does not satisfy the slope constraint.

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To find the inverse function of F(x) = 2x - 3, we replace F(x) with y, swap the positions of x and y, and solve for y. The inverse function is f⁻¹(x) = (x+3)/2.

To find the inverse function of F(x) = 2x - 3, follow these steps

Replace F(x) with y. The equation now becomes y = 2x - 3.

Switch the positions of x and y, so the equation becomes x = 2y - 3.

Solve for y in terms of x. Add 3 to both sides: x + 3 = 2y.

Divide both sides by 2 (x + 3)/2 = y.

Replace y with the notation for the inverse function, f⁻¹(x): f⁻¹(x) = (x + 3)/2.

So, the inverse function of F(x) = 2x - 3 is f⁻¹(x) = (x + 3)/2.

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--The given question is incomplete, the complete question is given

" How do I find the inverse function of F(x) = 2x - 3"--

The best estimate for the total amount of time Tim would spend answering e-mails over the course of 100 days is 100 hours with a standard deviation of 0.53 hours.

To find the total amount of time Tim would spend answering emails over the course of 100 days, we need to use the concept of the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approaches a normal distribution regardless of the underlying distribution.

To calculate the standard deviation of the total amount of time Tim spends answering emails over 100 days, we can use the formula:

standard deviation = square root of (n * variance)

where n is the number of days and variance is the variance of the amount of time Tim spends in a day answering emails.

Substituting the values, we get:

standard deviation = square root of (100 * 0.0028) = 0.53 hours

Therefore, Tim would spend an average of 100 hours over the span of 100 days responding to emails, with a standard deviation of 0.53 hours, according to the best estimate.

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The magnitude of the average velocity vector is approximately 3.651 m/s.

To find the magnitude of the average velocity vector, we need to calculate the displacement and divide it by the time taken.

Representation:

Initial position: D1 = (50 m North, 10 m East)

Final position: D2 = (5 m North, 35 m East)

Time taken: t = 15 seconds

Equations:

Displacement vector (ΔD) = D2 - D1

Average velocity vector (\(V_{avg}\)) = ΔD / t

Algebra work:

ΔD = D2 - D1

   = (5 m North, 35 m East) - (50 m North, 10 m East)

   = (-45 m North, 25 m East)

|ΔD| = √((-45)^2 + 25^2)  [Magnitude of the displacement vector]

\(V_{avg}\) = ΔD / t

       = (-45 m North, 25 m East) / 15 s

       = (-3 m/s North, 5/3 m/s East)

|\(V_{avg}\)| = √((-3)^2 + (5/3)^2)  [Magnitude of the average velocity vector]

Symbolic answer:

The magnitude of the average velocity vector is approximately 3.651 m/s.

Units check:

The units for displacement are in meters (m) and time in seconds (s). The average velocity is therefore in meters per second (m/s), which confirms the units are consistent with the calculation.

Therefore, the magnitude of the average velocity vector is approximately 3.651 m/s.

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The most commonly used explicit of an arithmetic sequence is given as,

an = a + (n - 1) d

Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,

2nd row seat = 12+ 1x2

3rd row seat = 12 + 2 x2

nth seat = 12 + (n-1) x 2

16th row seat = 12 + (16–1) x2 = 42

Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows,

Average number of seats per row = (12 +42)/2= 27.

So total seats = average per row x number of rows.

= 27 x 16 = 432.

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A flat circular plate of 1.25m diameter is immersed in water,

1. The force exerted on one face by the water pressure is 10819N

2. The position of the center of pressure is 0.6493m

1. Diameter of the circular plate = 1.25 m, Greatest depth = 1.5 m, Least depth = 0.6 m

We can use the following formula to calculate the force exerted on one face by the water pressure:

F = ρgΔhA

where ρ = density of water = 1000 kg/m³,

g = acceleration due to gravity = 9.8 m/s²,

Δh = difference in depth = (1.5 - 0.6) m = 0.9 m

A = area of the circular plate = πr² where r = radius of the circular plate = diameter/2 = 1.25/2 = 0.625 m

So, A = π(0.625)²= 1.2266 m²

Substituting the values in the formula, we get, F = 1000 × 9.8 × 0.9 × 1.2266 ≈ 10818.612 N ≈ 10819N

Therefore, the force exerted on one face by the water pressure is approximately 10819 N.

2. To determine the position of the center of pressure, we can use the following formula:

Xp = Xcg + Ix / (A × d)

where Xp = position of the center of pressure,

Xcg = position of the center of gravity,

Ix = moment of inertia about the axis of symmetry

A = area of the plate = πr² = 1.2266 m²

d = distance between the centroid and the center of pressure can be calculated as d = 2/3 × (r × π/2) = 2/3 × (0.625 × π/2)≈ 0.654 m

So, A × d = 1.2266 × 0.654 ≈ 0.8022 m³

Now, let's calculate the position of the center of gravity.

Since the plate is flat and circular, its center of gravity will lie at its geometrical center.

Therefore, Xcg = 0.5 m

Now, let's calculate the moment of inertia about the axis of symmetry.

For a circular plate, it can be given as Ix = πr⁴/4

Ix = π(0.625)⁴/4= 0.1198 m⁴

Substituting the values in the formula, we get: Xp = 0.5 + 0.1198 / (1.2266 × 0.654)≈ 0.6493 m

Therefore, the position of the center of pressure is approximately 0.6493 m.

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Answer: x = -4 or 8

Step-by-step explanation:

    To solve, we will isolate the x-variable. Since this is a parabola (as shown by the square) we will either have 1 or 2 answers.

    Given:

6(x - 2)² + 7 = 223

    Subtract 7 from both sides of the equation:

6(x - 2)² = 216

    Divide both sides of the equation by 6:

(x - 2)² = 36

    Square root both sides of the equation:

* Since we square rooted, we will have the positive and negative result

x - 2 = 6           x - 2 = -6

    Add 2 to both sides of the equation, for both equations:

x = 8           x = -4

          x = -4 or 8

The total charges of both companies is the same at 24 months.

We have:

Company one:

This means that:

y = 20 + 25x + 40x

y = 20 + 65x

Company two:

This means that:

y = 30 + 700 + 35x

y =  730 + 35x

See attachment

On the attached graph, the point of intersection is at

(x, y) = (24, 1558)

This means that the total charges of both companies is the same at 24 months.

On the long run, phone company two has a better deal.

On the short run, phone company one has a better deal.

Because the function have lesser values after the point of intersection.

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Answer:

\(y = \frac{1}{5} x + 1\)

Step-by-step explanation:

the general equation of a line is y=mx+c

because the slop is 1/5, the equation of this line would be

\(y = \frac{1}{5} x + c\)

with the coordinates (20,5) , take 20=x and 5=y

and substitute these values into the equation above.

you should get:

5= 4 + c

so c = 1

therefore, the equation of the line is:

\(y = \frac{1}{5} x + 1\)

Answer:

Given

Step-by-step explanation:

Given the monthly salary of project managers modeled by the function

f(x)= x^4 -10x^2+10,000

To know the number of years that a project manager be eligible for a $20,000 monthly salary, we will substitute f(x) = 20,000 and solve for x as shown:

20,000 = x^4 -10x^2+10,000

x^4 -10x^2 = 20000-10000

x^4 -10x^2 = 10,000

x^4 -10x^2 - 10,000 = 0

(x^2)^2-10x^2 - 10000 = 0

let P = x^2

P^2 - 10P -10000 = 0

P = 10±√10²-4(-10000)/2

P = 10 ±√100+(40000)/2

P = 10 ±√40100/2

P = 10 ±200.2/2

P = 210.2/2

P = 105.1

Since P = x^2

105.1 = x^2

x = √105.1

x = 10.25

Hence it will take like after 10 years for the manager to earn a $20,000 monthly salary

Answer:

10 1/4

Step-by-step explanation:

Answer

Answer: 9+a^2 if d=10 OR 99 if d does not equal 10

Answer:

1,400

Step-by-step explanation:

300x5=1,500 and 1,500-100=1,400

To find the means, variances, covariance, and correlation coefficient of random variables X and Y with a joint PMF:

- Calculate the means: E[X] and E[Y].

- Compute the variances: Var(X) and Var(Y).

- Find the covariance: Cov(X, Y).

- Determine the correlation coefficient: ρ(X, Y).

Based on the covariance, we can determine if X and Y are independent or dependent.

Let the random variables X and Y have a joint probability mass function (PMF). We need to find the means (expected values), variances, covariance, and correlation coefficient of X and Y, and determine whether they are independent or dependent.

The mean of a random variable X is denoted by E[X] or μX, and it is calculated as the sum of all possible values of X weighted by their respective probabilities. Similarly, the variance of X, denoted by Var(X) or σ²X, measures the spread or dispersion of the values of X around its mean.

The covariance between two random variables X and Y, denoted by Cov(X, Y), measures the degree to which they vary together. It is calculated as the sum of the products of the differences of the values of X and its mean, and the differences of the values of Y and its mean, weighted by their joint probabilities.

The correlation coefficient between X and Y, denoted by ρ(X, Y), quantifies the strength and direction of the linear relationship between them. It is calculated by dividing the covariance of X and Y by the product of their standard deviations.

To determine the means and variances, we can use the following formulas:

E[X] = ∑x∑y x * P(X = x, Y = y)

E[Y] = ∑x∑y y * P(X = x, Y = y)

Var(X) = E[X²] - (E[X])²

Var(Y) = E[Y²] - (E[Y])²

To calculate the covariance, we use the formula:

Cov(X, Y) = E[XY] - E[X]E[Y]

Once we have the means and variances, we can calculate the correlation coefficient using the formula:

ρ(X, Y) = Cov(X, Y) / (√Var(X) * √Var(Y))

Based on the calculations of means, variances, covariance, and correlation coefficient, we can determine whether X and Y are independent or dependent. If the covariance is zero (Cov(X, Y) = 0), then X and Y are independent. Otherwise, they are dependent.

In summary, to find the means, variances, covariance, and correlation coefficient of X and Y, we use the formulas mentioned above. Based on the calculated values, we can determine whether X and Y are independent or dependent.

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

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Answer:

25

Step-by-step explanation:

A=1/2×b×h

A=1/2×5cm×10cm

A=25cm