evaluate f(−5), f(0), and f(3) for the piecewise defined function. f(x) = x^2 + 3 if x < 0 x if x ≥ 0 f(−5) = f(0) = f(3) =

Answer:

7

Step-by-step explanation:

it is a 16 digit credit card number. Therefore, start from the first digit and double alternating digits. Add them and the non doubled digits. should be divisible by 10. For double digits, they are added to make single digit.

9+3+8+3+9+4+7+5+6+1+5+3+4+3+3+x = 73+x

final number should be divisible by 10.

x=7

Answer: 25%

Step-by-step explanation:

Given

Total students on a field trip are 68

Out of 68, only brings the camera

The percentage of students that bring the camera is given by

\(\Rightarrow \dfrac{17}{68}\times 100\\\\\Rightarrow \dfrac{1}{4}\times 100=25\%\)

Thus, only 25% of students bring a camera.

The equations kx – 2y = 3 and 3x + y = 5 will have a unique solution for k ∈ R - {-6}

Here we have equations  kx – 2y = 3 and 3x + y = 5

Here we need to find a value for k such that the following equations have a unique solution.

a system of 2 linear equations

a₁x + a₂y + a₃ = 0

b₁x + b₂y + b₃ = 0

does not have a unique solution only when

a₁/b₁ ≠ a₂/b₂

Here

k = a₁,          -2 = a₂

3 = b₁            1 = b₂

Hence,

k/3 ≠ -2

or, k ≠ -6

Hence the equations will have a unique solution for k ∈ R - {-6}

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Complete Question

For what value of k do the equations kx – 2y = 3 and 3x + y = 5 represent two lines intersecting at a unique point?

Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

The value of fxy (-1,2)=-256 sin(5)+256 ln(cos 513), which is approximately equal to -121, and therefore, option (C) is the correct answer.

We are given the function f(x,y)=x^6(y^4+1)+x2+y4+1(x+1)2[sin(x+y^2)+x8ln(cos(x^8+y^9))] which we need to evaluate for fxy(-1, 2).

First, we differentiate the function partially with respect to y and then with respect to x. We then take the cross-derivative of f(x,y) and substitute the values for x and y as given.fxy=(-32)(4)(2)(sin((-1)+(2)^2)+(-1)^8ln(cos((-1)^8+(2)^9)))=-256 sin(5)+256 ln(cos 513)

Now, we substitute the value of fxy (-1,2)=-256 sin(5)+256 ln(cos 513).

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The value of y when x is 9 for the proportional relationship between is 31.5.

The constant of proportionality is used to show the proportional relationship between the numbers given.

In this case, when x is 2, y is 7. This will be illustrated thus:

y = kx

7 = 2k

Divide

k = 7/2

k = 3.5

Therefore, when x is 9, the value of y will be:

y = kx

y = 3.5 × 9

y = 31.5

Therefore, y is 31.5.

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a collection of 65 coins contains one with two heads. the remainder of the coins are fair. if a coin, selected randomly from the collection, turns up heads 6 times in 6 tosses, 1/65 is the probability it’s a two-headed coin

Definition of probability

(1) : the chance that a given event will occur. (2) : the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

We know that one coin in a collection of 65 has two heads. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row. We calculate the probability that it is the two-headed coin.

We calculate  the number of possible combinations:

C₁⁶⁵= 65!/1!(65-1)!

     = 65

Number of favorable combinations is 1.

Therefore, the probability is

P=1/65.

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Answer:

100cm

Step-by-step explanation:

The relationship between the ratio and the heights is 20. i.e 4 : 5 = 80 : 100

Hope this helps, please tag brainliest.

The height of the taller boy is 100cm.

Ratio, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

Let the height of the taller boy be x cm and smaller boy be y cm.

According to the given question.

The ratio of height of the two boys is 4:5.

Since, it is obvious that 4:5 is the ratio of the height of smaller boy to the taller boy. Because k will be the ratio of proportionality then 4k will given the smaller value and 5k will give the larger value therefore, 4:5 represents the ratio of height of smaller boy to the taller boy.

\(\implies \frac{y}{x} =\frac{4}{5}\)

Also, the height of the shorter boy is 80cm.

Therefore,

\(\frac{80}{x} = \frac{4}{5}\)

\(\implies 80\times 5 = 4\times x\)

\(\implies 400 = 4\times x\)

\(\implies x = \frac{400}{4}\)

\(\implies x = 100cm\)

Hence, the height of the taller boy is 100cm.

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The probability that x < y is 1/8 or 0.25 .

What is probability of an event?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

Given, the vertices of the rectangle are (0, 0), (4, 0), (4, 1), (0, 1).
On carefully analyzing and plotting the vertices roughly, we get that the given rectangle has a width of 4 units and a height of 1 unit.
Therefore, the area of the given rectangle = Width*Height = 4*1 = 4 units²
Also, it can be assessed that the line x = y passes through the points of the rectangle at (0, 0) and (1, 1).
Thus, the area for which x < y will be an isosceles triangle with side length of 1 units and co-ordinates of vertices as (0, 0), (0, 1) and (1, 1).
The area of the isosceles triangle thus assumed = 0.5 × 1² = 0.5 units²
Probability that x < y is P(E): 0.5/4 = 1/8 = 0.25
Therefore, the probability that x < y is 1/8 or 0.25 .

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For the playpen area to be 1000 square feet and perimeter to be 150 feet, the length of the playpen should be at least 17.35 feet and at most 57.66 feet .

In the question ,

it is given that ,

the shape of the playpen = rectangle .

the perimeter of the playpen = 150 feet

let the length of the playpen = x feet

let the width of the playpen = y feet

So , 2(x + y) = 150

an , the area of the playpen = 1000

x*y = 1000

So , y = 1000/x

Substituting y = 1000/x  in the perimeter ,

we get ,

2(x + 1000/x ) = 150

x² + 1000 = 75x

x² - 75x + 1000 = 0

Applying Quadratic Formula , we get

x = [ -(-75) ± √(-75)² - 4*1*1,000]/2*1

on simplifying further ,

we get ,

x = 57.66 or 17.35

Therefore , For the playpen area to be 1000 square feet and perimeter to be 150 feet, the length of the playpen should be at least 17.35 feet and at most 57.66 feet .

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Answer:

no solutions

Step-by-step explanation:

6n - 6n - 12 = 14 - 2 = 12 ( add 12 to both sides )

0 = 24 ← not possible

this indicates the equation has no solution

Step-by-step explanation:

\(3w - 4z = 8 \\ 2w + 3z = - 6 \\ 3w = 8 + 4z \\ w = \frac{8}{3} + \frac{4z}{3} \\ 2( \frac{8}{3} + \frac{4z}{3} ) + 3z = - 6 \\ 5.33 + 2.67z + 3z = - 6 \\ 5.67z = - 11.33 \\ \)

\(z = - 1.99 = - 2 \\ w = \frac{8}{3} - \frac{8}{3} = 0\)

The probability that a randomly chosen sophomore is taking Algebra 2, given that they do not take Chemistry, is 19/36.

To find the probability that a randomly chosen sophomore is taking Algebra 2, given that they are not taking Chemistry, we need to consider the number of students taking Algebra 2 who are not taking Chemistry.

Given that there are 318 sophomores in total, and 102 are taking Chemistry, it means that 318 - 102 = 216 sophomores are not taking Chemistry.

Out of the 140 sophomores taking Algebra 2, 26 are also taking Chemistry. Therefore, the number of sophomores taking Algebra 2 but not taking Chemistry is 140 - 26 = 114.

Since we are considering only the students who are not taking Chemistry, the total number of students in this group is 216.

The probability of a randomly chosen sophomore being in this group (taking Algebra 2 but not taking Chemistry) is given by:

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 114 / 216

Simplifying the fraction, we get:

Probability = 19 / 36

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Answer:

D is the answer

-(3x + 2)

d) -3x-2

Answer:

d

Step-by-step explanation:

Given

- (3x + 2) which is equivalent to

- 1 (3x + 2) ← multiply each term in the parenthesis by - 1

= - 3x - 2 → d

Answer:

  none

Step-by-step explanation:

You want the number of solutions to the equation ...

  6z + 1 = 2(3z - 1)

  6z +1 = 6z -2

  3 = 0 . . . . . . . . . . add 2 -6z to both sides

There are no values of z that will make this false statement true.

There are no solutions to the equation.

<95141404393>

Yes - if it were linear it would have be a straight line.

Answer:

B (yes, bc it does not have a constant rate of change)

Step-by-step explanation:

Answer: 9,28

4,22

Step-by-step explanation:

i just did it

The first occurrence of the highest temperature and lowest temperature in the cycle are days with temperatures of 28°C and 22°C, respectively

The function is given as:

\(f\left(x\right)=3\cos\left(\frac{\pi}{5}x\ +\ \frac{\pi}{5}\right)\ +\ 25\)

As a general rule, we have:

\(\cos(\theta) = -1\) --- minimum

\(\cos(\theta) = 1\) --- maximum

This means that the highest value and the lowest value of \(\cos\left(\frac{\pi}{5}x\ +\ \frac{\pi}{5}\right)\) are 1 and -1, respectively.

So, we have:

Highest temperature

\(f\left(x\right)=3\cos\left(\frac{\pi}{5}x\ +\ \frac{\pi}{5}\right)\ +\ 25\)

\(f\left(x\right)=3 * 1\ +\ 25\)

\(f\left(x\right)=28\)

Lowest temperature

\(f\left(x\right)=3\cos\left(\frac{\pi}{5}x\ +\ \frac{\pi}{5}\right)\ +\ 25\)

\(f\left(x\right)=3 * -1\ +\ 25\)

\(f\left(x\right)=22\)

Hence, the first occurrence of the highest temperature and lowest temperature in the cycle are days with temperatures of 28°C and 22°C, respectively

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Answer:

5 foot

Step-by-step explanation:

The fundamental difference between t-test and z-score is: t-test is used to determine the difference in data sets, the standard deviation and the z-score is used to to draw data from a given population with different means and standard deviation. A) The t statistic uses the sample mean in place of the population mean

T-test is a statistic model which is used to find how averages of different data sets differ in case the standard deviation and Z-scores statistic helps to draw data from populations with different means and standard deviations and also place them on a common scale.

The z-core formula is:

Z₁=\(\frac{x-m}{s}\)

Therefore the fundamental difference is that the t-test uses the variance in place of the population variance.

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Complete question:

Which of the following is a fundamental difference between the t statistic and a z-score?

A) The t statistic uses the sample mean in place of the population mean

B) All of the choices are differences between t and z.

C) The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n.

D) The t statistic uses the sample variance in place of the population variance.

Answer:

Graphing the equation we have;

Explanation:

Given the equation;

the slope of the line can be derived by expressing the equation in slope-intercept form;

So, the slope and y-intercept are;

to graph the equation, let us find the x-intercept;

Graphing the equation we have;

Other points on the graph includes;

The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.  

To find actual dimensions multiply the given measurement with the measurement given in scale.

In the given problem, given that 1 in = 10 feet which is the scale given, we need to multiply the given measurements that are in the plan with the scale measurement 10 feet.

Here we have

A floor plan is given for the first floor of a new house.

One inch represents 10 feet.

The walk-in closet is 2/5 in. × 2/3 in. on the floor plan  

As we know 1 inch  = 10 feet

=> 2/5 in = (2/5) × 10 feet = 4 feet

=> 2/3 in = (2/3) × 10 feet = 6.67 feet

Therefore,

The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.  

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The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is

||A - A1||₂=0 where A is 2×2 matrix.

We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]

note here that C₂= 3C₁

where Cᵢ --> iᵗʰ column

v = [ 5 ; 6 ; -1 ; -4 ; 2]

||v||² = 82 => ||v|| = √82

and A At v = 820 v

and A At = [ 82 246 ; 246 738]

AAt [1;3] = 820[1;3]

=> v1 = 1/√10(1,3)^t

Then the best rank of 1 approx

= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]

= A

Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0

Hence, the minimal Approx. ||A - A1||2 = 0 .

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Complete question:

Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?

Answer:

$28.92

Step-by-step explanation:

Find the discount

28.99 × 0.05 = 1.4495

28.99-1.4495 = 27.5405

Calculate the tax of the discounted item

27.5405 x 0.05 = 1.377

27.5405 + 1.377 = 28.9175

Answer:

Step-by-step explanation:

Given the dimension

Length of the rectangle = 8cm

Width = 5cm

Note that when the scale was 1:7, syla multiplied the width by a factor of 7 i.e 5*7 = 35m

If syla changes the the scale to 1 cm : 10 m for the rectangle, then the width of the shorter side will be multiplied by a factor of 10 due to the change in scale i.e;

5 * 10 = 50m

Hence the width of the new stage will be 50 m

Answer:

50m

Step-by-step explanation:

took the quiz on edg

The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

from the question, we have the following parameters that can be used in our computation:

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

Using the above as a guide, we have the following:

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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The equation representing the cost of the canoe rental company is given by y = 30x + 20 .

Let the total cost for renting a canoe be y.

Let the canoe is being rent for x hours.

now the cost for renting the canoe at 30 dollars per hour = 30x

Total cost of renting the canoe = 30x + 20

But the total cost is y.

Hence the equation to represent this situation is given by

y = 30x + 20 which is a straight line of the form y = mx +c, where the slope is 30 and the y-intercept is 20.

Now we will plot the graph for this equation.

At x = 0 , y = 20

At x = 1 , y = 50

At x= -3 , y = -70

Hence the graph of the line passes through these points on the cartesian plane.

The graph of the line is attached below.

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As per Big M method for the given linear programming the minimum value of z is -3, and values of x₁ and x₂ are 2 and 0 respectively.

To solve the given linear programming problem (LP) using the Big M method, introduce slack variables, create the initial tableau,

and iteratively perform the simplex method until an optimal solution is reached.

Let's introduce slack variables s₁ and s₂ to convert the inequality constraints into equations,

2x₁ + x₂ + s₁ = 4 (constraint 1)

x₁- x₂ + s₂= -1 (constraint 2)

Rewrite the objective function in terms of the decision variables and slack variables,

z = 2x₁ + 3x₂ + 0s₁+ 0s₂

Now, create the initial tableau,

Basic Variables x₁ x₂ s₁ s₂ Solution

                     z -2 -3 0 0 0

    constraint 1 2 1 1 0 4

   constraint 2 1 -1 0 1 -1

To apply the Big M method, we introduce artificial variables a₁ and a₂ for each constraint,

z = 2x₁ + 3x₂ + 0s₁ + 0s₂ - Ma₁ - Ma₂

Modify the tableau accordingly

Basic Variables x₁ x₂ s₁ s₂ a₁ a₂ Solution

                      z -2 -3 0 0 -M -M 0

    constraint 1 2 1 1 0 0 0 4

   constraint 2 1 -1 0 1 0 0 -1

Now, perform the simplex method to find the optimal solution.

The most negative value in the "z" row is -M, indicating the entering variable.

Select the entering variable as x₁ because it has the most negative coefficient in the objective function.

To determine the leaving variable,

find the minimum non-negative ratio of the constants in the solution column to the corresponding coefficient of the entering variable.

Here, the minimum ratio occurs for constraint 2, indicating that x₁ should leave the basis.

Dividing the solution column by the coefficient of x₁ in constraint 2, we get:

Basic Variables x₁ x₂ s₁ s₂ a₁ a₂ Solution

                     z 0 -1 0 3 2 -2 -2

    constraint 1 0 2 1 -1 -1 1 6

   constraint 2 1 -1 0 1 0 0 -1

Next,  perform row operations to make the entering variable's coefficient in the objective function row equal to 1

and the rest of the coefficients zero.

Subtract the corresponding row multiplied by its coefficient from each row,

Basic Variables x₁ x₂ s₁ s₂ a₁ a₂ Solution

                     z 0 -1/2 0 7/2 2 -2 -1

      constraint 1 0 3/2 1 -3/2 -1 1 5

      constraint 2 1 -1 0 1 0 0 -1

Repeat the process until there are no negative values in the "z" row.

Now, the tableau represents the optimal solution,

Basic Variables x₁ x₂ s₁ s₂ a₁ a₂ Solution

                     z 0 0 3 6 4 -2 -3

    constraint 1 0 0 1 -1 1 1 4

   constraint 2 1 0 1 2 -2 0 2

From the final table, determine the optimal solution,

x₁ = 2

x₂ = 0

z = -3

Therefore, using Big M method the minimum value of z is -3, and the corresponding values of x₁ and x₂  are 2 and 0, respectively.

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From the attached image, I have drawn the required elevations of the prism with given cross section.

In a building of a 3 dimensional figure, we can say that;

- The front elevation is the 2dimensional view that you see when you look at the figure from the front.

- The plan of the figure is defined as the view that you see when you look at it from above.

- The side elevation is defined as the view that you see when you look at the object from the side.

- The rear elevation is defined as the view you see when you look at the object from the back.

On the centimeter grid in the second attached file , I have drawn the front elevation and the side elevation of the prism ​Using a scale of 2 cm to 1 m.

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Therefore, the ground state (n = 1) comes closest to satisfying the uncertainty principle, as it achieves the smallest possible values for Ox and Op in the infinite square well.

To calculate the values and check the uncertainty principle for the nth stationary state of the infinite square well, we need to consider the following:

(x): The position of the particle in the nth stationary state is given by the equation x = (n * L) / 2, where L is the length of the well.

(x^2): The expectation value of x squared, (x^2), can be calculated by taking the average of x^2 over the probability density function for the nth stationary state. In the infinite square well, (x^2) for the nth state is given by ((n^2 * L^2) / 12).

(p): The momentum of the particle in the nth stationary state is given by the equation p = (n * h) / (2 * L), where h is the Planck's constant.

(p^2): The expectation value of p squared, (p^2), can be calculated by taking the average of p^2 over the probability density function for the nth stationary state. In the infinite square well, (p^2) for the nth state is given by ((n^2 * h^2) / (4 * L^2)).

Ox: The uncertainty in position, Ox, can be calculated as the square root of ((x^2) - (x)^2) for the nth state.

Op: The uncertainty in momentum, Op, can be calculated as the square root of ((p^2) - (p)^2) for the nth state.

Now, let's analyze the uncertainty principle by comparing Ox and Op for different values of n. As n increases, the uncertainty in position (Ox) decreases, while the uncertainty in momentum (Op) increases. This means that the more precisely we know the position of the particle, the less precisely we can know its momentum, and vice versa.

The state that comes closest to the uncertainty limit is the ground state (n = 1). In this state, Ox and Op are minimized, reaching their minimum values. As we move to higher energy states (n > 1), the uncertainties in position and momentum increase, violating the uncertainty principle to a greater extent.

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