the table above represents the relationship between the independent variable x and the dependant variable y. identify the domain and the range based on the table.

Answer:

1.10

Step-by-step explanation:

Given the probability distribution :

x : ___ 0 ___ 1 ___ 2

p(x)__0.15 _0.60 __0.25

The expected value is obtained by:

Σ(X * p(x))

(0 * 0.15) + (1 * 0.60) + (2 * 0.25)

0 + 0.60 + 0.50

= 1.10

Answer:

400+100c<550+70c

Step-by-step explanation:

Second salesperson makes more money weekly

The number of cars will be 5.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

One car salesperson makes a weekly salary of $400, plus $100 commission for each car sold.

And, The other car salesperson makes a weekly salary of $550, plus $70 commission for each car sold.

Now,

Let the number of cars = c

So, We can formulate;

⇒ 400 + 100c = 550 + 70c

Solve for c as;

⇒ 100c - 70c = 550 - 400

⇒ 30c = 150

⇒ c = 5

Thus, The number of cars will be 5.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

The maximum area of the surfboard correct to 2 places is 0.67 m².

Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.

Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = \(4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r\) -----(1)

Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)

We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)

Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.

To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),

we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.

Area of surfboard =

\(l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3\)

\(-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\\)

for such more questions on quadratic equations

https://brainly.com/question/30164833

#SPJ11

10 hours 55 minutes pm

Step-by-step explanation:

(10:55 pm)

Answer:

A

Step-by-step explanation:

   It would be A, because the two bisector lines that cut through this trapezoid  are the same length, so 5.9-4.1=1.8. So the length of RN would be 1.8. Hope this helps!

Answer:

1.8

Step-by-step explanation:

To determine the speed of the car at the bottom of the hill, we can use the principle of conservation of energy. As the car rolls down the hill, it will convert its potential energy at the top into kinetic energy at the bottom, neglecting any energy losses due to friction or air resistance.

The potential energy of the car at the top of the hill is given by the formula:

Potential Energy = mass × gravity × height

Since the mass of the car is not provided, we can assume it to be a constant value for the purpose of this calculation. Gravity is approximately 9.8 m/s².

The kinetic energy of the car at the bottom of the hill is given by the formula:

Kinetic Energy = (1/2) × mass × velocity²

Since the potential energy at the top is equal to the kinetic energy at the bottom, we can equate the two equations and solve for velocity.

mass × gravity × height = (1/2) × mass × velocity²

Simplifying the equation, we find:

velocity² = 2 × gravity × height

Taking the square root of both sides, we get:

velocity = √(2 × gravity × height)

Substituting the given values, with gravity as 9.8 m/s² and height as 50 m, we can calculate the velocity. Plugging the values into the equation, we find: velocity = √(2 × 9.8 m/s² × 50 m) ≈ 31.3 m/s

Therefore, the car will be going at approximately 31.3 meters per second (m/s) at the bottom of the hill.

Learn more about kinetic energy  here:

https://brainly.com/question/999862

#SPJ11

(a) The sequence of numbers in array A after calling Build-Max-Heap is ⟨8, 6, 3, 2, 4, 1, 5, 9, 7⟩.

(b) The sequence of numbers in array A after the first partition (Partition(A, 1, 9)) is ⟨4, 1, 2, 5, 6, 8, 9, 10, 7⟩.

(a) To build a max heap from the given array A: ⟨3, 2, 1, 6, 4, 8, 5, 9, 7⟩, we can follow the steps of the Build-Max-Heap algorithm:

1. Start with the given array A.

  Tree:                       3

                            / \

                           2   1

                          / \ / \

                         6  4 8  5

                        / \

                       9   7

2. Starting from the last non-leaf node (index n/2 - 1) and going up to the root (index 0), perform Max-Heapify operation for each node.

  Max-Heapify ensures that the maximum element is at the root of the subtree rooted at the current node.

  Max-Heapify(A, 2):

  Tree:                       3

                            / \

                           2   8

                          / \ / \

                         6  4 1  5

                        / \

                       9   7

  Max-Heapify(A, 1):

  Tree:                       3

                            / \

                           6   8

                          / \ / \

                         2  4 1  5

                        / \

                       9   7

  Max-Heapify(A, 0):

  Tree:                       8

                            / \

                           6   3

                          / \ / \

                         2  4 1  5

                        / \

                       9   7

3. After performing Max-Heapify for all nodes, the resulting array will be:

  A: ⟨8, 6, 3, 2, 4, 1, 5, 9, 7⟩

(b) To perform the first partition on the array A: ⟨7, 6, 4, 10, 1, 8, 9, 2, 5⟩ using Partition(A, 1, 9), we can use the Lomuto partition scheme. The first partition is performed as follows:

1. Select the pivot element. In this case, we choose the element at index 1 (6) as the pivot.

2. Reorder the elements in A such that all elements less than or equal to the pivot are on the left side, and all elements greater than the pivot are on the right side.

  After the partition:

  A: ⟨4, 1, 2, 5, 6, 8, 9, 10, 7⟩

The sequence of numbers in array A after the first partition is: ⟨4, 1, 2, 5, 6, 8, 9, 10, 7⟩.

To know more about Build-Max-Heap, refer to the link below:

https://brainly.com/question/32388238#

#SPJ11

Complete Question:

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

To know more about function visit:

brainly.com/question/30721594

#SPJ11

Answer:

y = - \(\frac{1}{2}\)

Step-by-step explanation:

Given

\(\frac{3}{4y+2}\)

The denominator of the expression cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that y cannot be, that is

4y + 2 = 0 ( subtract 2 from both sides )

4y = - 2 ( divide both sides by 4 )

y = \(\frac{-2}{4}\) = - \(\frac{1}{2}\) ← excluded value

The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.

To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.

Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.

With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.

To calculate the required percentage reduction in overtime hours, we can set up the following equation:

(1.05R) * (1 - x) * H = 1.03B

where x represents the required percentage reduction in overtime hours.

Simplifying the equation, we have:

(1 - x) * H = (1.03B) / (1.05R)

Now, let's solve for x:

1 - x = (1.03B) / (1.05R * H)

x = 1 - [(1.03B) / (1.05R * H)]

Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.

It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.

By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.

Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.

Learn more about budget here

https://brainly.com/question/29154668

#SPJ11

Answer:

14.6mm

Step-by-step explanation:

The formula for finding the circumference of a circle is 2πr.

The circumference is 91.688 millimeters inorder to find the radius we have to do the opposite or inverse of multiplication which is division.

So we divide the circumference by 2 and pi which is 3.14 which will give us the radius

r = radius = 91.668 ÷ 3.14 ÷ 2 = 14.6

Answer: its c

Step-by-step explanation:

The kinetic energy of the Mars Climate Orbiter spacecraft is approx    3.31 x 10^7 joules.

To determine the kinetic energy of the Mars Climate Orbiter spacecraft, we can use the formula:

Kinetic energy = (1/2) * mass * velocity^2

Given:

Mass of the spacecraft (m) = 629 kg

Velocity of the spacecraft (v) = 1.20 x 10^4 km/h

First, we need to convert the velocity from km/h to m/s:

1 km = 1000 m

1 h = 3600 s

Velocity in m/s = (1.20 x 10^4 km/h) * (1000 m/km) / (3600 s/h) ≈ 333.33 m/s

Now, we can calculate the kinetic energy:

Kinetic energy = (1/2) * (629 kg) * (333.33 m/s)^2

Kinetic energy ≈ 3.31 x 10^7 joules

Therefore, the kinetic energy of the Mars Climate Orbiter spacecraft is approximately 3.31 x 10^7 joules.

To know more about kinetic energy refer here:

https://brainly.com/question/999862?#

#SPJ11

The probability that the average weight of a random sample of 10 cars will be 70.7 tons or more is approximately 0.977, or 97.7%.

To calculate the probability that the average weight of a random sample of 10 cars will be 70.7 tons or more, we need to make some assumptions about the population of cars and the sampling process.

Assuming that the weights of cars follow a normal distribution, we can use the central limit theorem to approximate the distribution of sample means. This states that as the sample size increases, the distribution of sample means becomes approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Without knowing the population means and standard deviation, we can use the sample mean and standard deviation as estimates. Let's say we have a sample of 10 cars and their weights have a sample mean of 72 tons and a sample standard deviation of 2 tons. We can calculate the standard error of the mean by dividing the sample standard deviation by the square root of the sample size, which gives us 0.63 tons.

To find the probability that the sample mean is 70.7 tons or more, we need to standardize the distribution of sample means using the z-score formula:

z = (sample mean - population mean) / standard error of the mean

In this case, the population mean is unknown, so we can use the sample mean as an estimate. Plugging in the values, we get:

z = (70.7 - 72) / 0.63 = -2

Using a standard normal distribution table, we can find the probability that a z-score is less than -2, which is approximately 0.023.

To learn more about probability

https://brainly.com/question/30034780

#SPJ4

Complete question:

What is the probability that the average weight of a random sample of 10 cars will be 70.7 tons or more if the filling equipment is working properly?

Answer:

-19.

Step-by-step explanation:

4 + 7 + 9 + 5 - 44

Doing the adds first;

= 25 - 44

= -19.

Answer:

1 -66

2. 162

3.11/-2

4. 8/-11

5.12/0

6. 0

7. 15/14

8. 2/-5

Step-by-step explanation:

Answer: The price has gone up .07.

Step-by-step explanation:

07/2.80   x 100 = 2.5% increase

Answer:

V ≈ 1847.26

Step-by-step explanation:

Circular Cone Formulas in terms of radius r and height h:

The volume of a cone:

V = (1/3)πr2h

Slant height of a cone:

s = √(r2 + h2)

Lateral surface area of a cone:

L = πrs = πr√(r2 + h2)

The base surface area of a cone (a circle):

B = πr2

The total surface area of a cone:

A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

Therefore, the solution V = πr 2h / 3 = π·142·9/  3 ≈ 1847.25648

a) The time it takes for the ball to hit the ground is given as follows: 2.5 seconds.

b) The time it takes for the maximum height is of: 1 second.

c) The maximum height is of: 36 feet.

d) The equation would be of: h(t) = 30 + 32t - 16t².

The quadratic function for the ball's height is given as follows:

h(t) = 20 + 32t - 16t².

In which:

The coefficients are given as follows:

a = -16, b = 32, c = 20.

Then the discriminant is of:

D = b² - 4ac

D = 32² - 4 x (-16) x 20

D = 2304.

The positive root gives the time it takes for the ball to hit the ground, as follows:

t = (32 + sqrt(2304))/32

t = 2.5 seconds.

The time to reach the maximum height is the t-coordinate of the vertex, hence:

t = -b/2a

t = -32/-32

t = 1 second.

The maximum height is of:

h(1) = 20 + 32 - 16

h(1) = 36 feet.

More can be learned about quadratic functions at https://brainly.com/question/1214333

#SPJ1

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

Learn more about parallelogram at: https://brainly.com/question/10744696

#SPJ1

The median of the data set would be affected as the median points per game decreases. That is option C.

The median of a data set is defined as the value of a data set the is found in the middle of a data after it has been arranged in an ascending order.

The first number line plots points per game;

= 16, 17 ,18 ,19 ,20 ,21 = 18+19 = 37/2 = 18.5

The second number line plots points per game;

= 21, 22, 23, 24 = 22 + 23 = 45/2 = 22.5

The third number line plots points per game:

= 9 points through 35 points

= 22 as the median.

Therefore, the scores of the next two games led to a decrease in the median determined per game point.

Learn more about median here:

https://brainly.com/question/26177250

#SPJ1

Answer:

Queen Messy here!

0.451

moving the decimals to the left when dividing (:

Step-by-step explanation:

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

Learn more about Normal distribution:

https://brainly.com/question/1846009

#SPJ11

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

To know more about "standard normal distribution" refer here:

https://brainly.com/question/29509087#

#SPJ11

The Solution.

The given number is

By fractional index law of indices, we have

This implies that:

Hence, the correct answer is: a = 3, b = 6, and c = 5.

Answer:

933.3333333

Step-by-step explanation:

Answer:

10,000

Step-by-step explanation:

1 dekagram = 1000 centigrams

10 dekagrams = 10 x 1000 = 10,000 centigrams

So, the answer is 10,000

Answer:

has a slope of 5/2 and passes through the point (0,-2)

Step-by-step explanation:

I took the quiz and got it correct

Answer:

200 students vote in the election

Step-by-step explanation:

We know

120 votes = 60%

1% = 2 votes

To find how many students vote in the election, we take

2 x 100 = 200 votes

So, 200 students vote in the election