According to a 2017 Wired magazine article, 40% of emails that are received are tracked using software that can tell the email sender when, where, and on what type of device the email was opened (Wired magazine website). Suppose we randomly select 50 received emails. what is the expected number of these emails that are tracked? what are the variance (to the nearest whole number) & standard deviation (to 3 decimals) for the number of these emails that are tracked?

All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.

1.1 Formulation:

The problem can be formulated as follows:

Minimize: 0 (since it is a feasibility problem)

Subject to:

α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1

α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2

α1, α2, α3, α4 are unrestricted

β is unrestricted

y_i ≥ 0 for all points in S1

z_i ≥ 0 for all points in S2

The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.

1.2 Finding a feasible solution:

To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.

Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.

For S1:

(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible

(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible

(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible

(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible

For S2:

(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible

(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible

(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible

(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible

Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

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Therefore,  the dimensions that minimize the cost to build the fence around the fencing are 20 m by 10 m.

To minimize the cost of fencing a rectangular field of 200 m2, we need to find the dimensions with the least total cost. Let's use the variables x and y for the length and width of the field, respectively. The area of the field is A = xy = 200 m2.
First, we'll find an equation relating x and y using the area: y = 200/x.
Next, we'll find the cost equation: Cost = 3x + 3x + 8y + 8y = 6x + 16y.
Now, substitute y in the cost equation: Cost = 6x + 16(200/x).
To minimize the cost, we'll find the derivative of the cost function with respect to x and set it equal to zero:
d(Cost)/dx = 6 - 3200/x^2 = 0.
Solving for x, we get x = 20 m. Then, using y = 200/x, we find y = 10 m.
Therefore,  the dimensions that minimize the cost to build the fence around the fencing are 20 m by 10 m.

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Answer:

10

Step-by-step explanation:

10% of 80000 is 8000

thus 5% is 4000

Step-by-step explanation:

hope it will help you

please reply is this helpful to you or not

The probability of a prison sentence greater than 18 years for a person convicted of second-degree murder is 0.1056 or about 10.56%.

We must normalize the variable using the following method in order to determine the likelihood that a person convicted of second-degree murder will serve a jail term longer than 18 years:

\(z = (x - μ) / σ\)

where: mean of the distribution (15 years), delta: standard deviation, and x: value of interest (18 years in this example) (2.4 years).

When we enter the values, we will get that:

z = (18 - 15) / 2.4 = 1.25

Then, we can use a calculator or table of the standard normal distribution to determine the probability associated with this z-score. The likelihood of a sentence longer than 18 years is represented by the region to the right of the value z = 1.25. We determine that the region to the right of 1.25 is roughly 0.1056 using a common normal distribution table.

Hence, the likelihood that a person convicted of second-degree murder will serve a sentence in jail longer than 18 years is 0.1056 or roughly 10.56%.

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Answer:

$50.40

Step-by-step explanation:

To find how much Lana will pay in total follow these steps.

First, multiply 40 by 1.05.

40×1.05=42.

This is how much she will pay for the food plus tax.

Now, multiply 42 by 1.2.

42×1.2=50.40

This is how much she will pay for the food, tax, and tip.

Lana will pay a total of $50.40.

Hope this helps!

Answer: -5x+6

Step-by-step explanation:

simplify by distributing the numbers on the outside, to the ones in the binomial

Answer:

-5x + 6

Step-by-step explanation:

First, rearrange the terms, you will have -2x-4(3x-10) Next, Distribute, you will have -2x-4-3x+10. Now, add the numbers without variables, you'll get -2x+6-3x. Finally, combing the like terms and you arrive with -5x+6.

So basically, there are 3 red, 5 blue, 4 green and 3 purple.

When you take out a blue, you have 4 blue left.

And so, by adding a red and purple, you have 4 of each color, which make it fair

Hope it helps you understand :D

The maximal amount of medically unsupervised weight loss that an adult should aim for in one week is generally 1-2 pounds (0.5-1 kg). This is because losing weight too quickly can be harmful to your health and lead to a number of negative side effects, such as muscle loss, fatigue, dehydration, and gallstones.

It's important to note that the amount of weight an individual can lose in a week can vary depending on factors such as their starting weight, body composition, and overall health. In some cases, a doctor or other medical professional may recommend a faster rate of weight loss under close supervision, but this is generally reserved for people who are severely overweight or have medical conditions that require rapid weight loss.

Ultimately, it's important to approach weight loss in a healthy and sustainable way, with a focus on making long-term lifestyle changes rather than relying on quick fixes or fad diets. A balanced diet, regular exercise, and a consistent sleep schedule are all important components of a healthy weight loss plan.

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Step-by-step explanation:

k(-5)= 6.(-5)+100

=30 + 100

=70

Answer:

70

Step-by-step explanation:

We can substitue -5 in for x:

k(-5) = 6(-5) + 100 = 70.

Answer:

20xy

Step-by-step explanation:

1. Multiply the numbers together

2. Add the variables next to it.

5 × 2 = 10

10 × 2 = 20

20 -> 20xy

(I'm new to this so I hope this helps )

The answer is b, my teacher explained it to me on a test. Don't know if he's right because he was a substitute.

Since McKenzie fills the 2-quart pitcher 2 times, there are a total of 4 quarts.

2 quarts × 2 times filled = 4 quarts

Recall that

1 quart = 4 cups

Since each quart is 4 cups, having 4 quarts is equivalent to

4 quarts × 4 = 16 cups

Therefore, there are a total of 16 cups of juice that was made.

Answer:

y=-3x-2

Step-by-step explanation:

y=mx+b

y=-3x+b

y=3x-2

m is the slope, b is the y intercept

Answer:

y = -3x - 2

Step-by-step explanation:

At first glance, it is clear the slope is negative as the y value decreases as the x value increases.

The rise/run looks to be -3/1, so the slope is -3

The y value at x = 0, or y-intercept, is -2

The correct equation would be y = -3x - 2

Answer:

-7

Step-by-step explanation:

To find f(-2), plug in -2 as x

F(-2)=2(-2)-3

-4-3

-7

Answer:  3∛3

Step-by-step explanation:

81^(1/3) = ∛(81) = ∛(27 × 3) = 3∛3

Thymus—Function 1; Pituitary—Function 2 is the correct to depict the function of the glands, thymus is associated with the immune system, hence option C is correct.

Thymus associated with the immune system, it reaches its peak size during adolescence.

The pituitary produces hormones needed for different bodily activities, including development.

The pituitary gland is known as the "master gland" because it uses hormones to monitor and control a variety of body functions. Growth and sexual development is the function of this gland.

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Answer:

355

Step-by-step explanation:

We have the sequence:

12, 19, 26, 33...

And we want to find the 50th term.

First, notice that this is an arithmetic sequence. This is because each subsequent term is 7 more than the previous term. So, this is increasing linearly.

Therefore, we can write an explicit formula for our sequence. The standard form for the explicit formula for an arithmetic sequence is:

\(x_n=a+d(n-1)\)

Where a is the initial term, d is the common difference, and n is the nth term.

We can see from our sequence that our initial term a is 12.

We also know that d is +7 because each term is 7 more than the previous term.

So, substitute 12 for a and 7 for d. This yields:

\(x_n=12+7(n-1)\)

To find the 50th term, let's substitute 50 for n:

\(x_{50}=12+7(50-1)\)

Evaluate. Subtract within the parentheses:

\(x_{50}=12+7(49)\)

Multiply:

\(x_{50}=12+343\)

Add:

\(x_{50}=355\)

So, the 50th term is 355.

And we're done!

Answer:

The pattern goes by adding 7 to the previous number to get the result.

12+7 = 19

19+7 = 26

26+7 = 33

The  

Use the formula  \(a_{n} = a_{1}+d(n-1)\)

The sequence = 7n-2

Therefore the 50th term

= 7(50)-2

= 350-2

= 348

Answer:

The key chain's are 0.75 each

Step-by-step explanation:

THE CONTENTS OF THIS ANSWER CANNOT BE DISPLAYED ON YOUR DEVICE

Answer:

Below

Step-by-step explanation:

● (p+q) ×2 -(5-5)

● 2(p+q) - 0

● 2(p+q)

Replace p and q with 1

● 2 (1+1)

● 2 × 2

● 4

Answer:

it's blurry

Step-by-step explanation:

Answer:

105.3

Step-by-step explanation:

deltamath

Answer:

6.5

Step-by-step explanation:

side a measures 6

side b measuring 2.5

we are trying to find side c

fill the values into the equation

a^2+b^2= c^2

6^2 +2.5^2= c^2

36 +6.25= c^2

42.25= c^2

square root of 42.25 is 6.5, so c=6.5

The condition for an unhealthy temperature x as an inequality involving an absolute value is equals to the => x ≥ 96.2 degree F - 2.3 degree F and value of x is 93.9 degree F.

Inequlity is a relation which creates a non-equal comparison between two numbers or other mathematical expressions. It is mostly used to compare two numbers on the number line by their size. The symbols used to represents it are ≤, < , ≥, >. We have the normal temperature for a certain animal = 96.2 degree F. Let x degree F be required temperature. We have to determine the inequlity involving an absolute value, and solve for x. Now, from the statement, the inequality for condition an unhealthy temperature is written by x degree F

≥ normal temperature - 2.3 degree F

=> x ≥ 96.2 - 2.3

solve the above inequality,

=> x = 93.9 degree F

Hence, required value is 93.9° F.

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Answer:

The first one (circle split into 4), 5th one (rectangle split into 10), and last one (right triangle split into 2)

Step-by-step explanation:

You can do this by counting the amount of sections each shape is split into,  then seeing if the amount of shaded in parts is equal to the empty parts. If so, then half is shaded. There are exceptions, though, like the 4th image of a triangle. The top section is smaller and thinner than the bottom, making it not exactly 1/2. However the last triangle is 1/2 because both sections are equal.

Hope this helps!

#10.

If the two triangles are similar, then their sides are proportional.

EC we know immediately. If the whole side BC = 12 = BE + EC, and BE is 4, then EC = 8.

Therefore, I can say that BD / (BD + DA) = BE / (BE + EC). To solve the problem for side DA, x will be used in place of DA.

8 / (8 + x) = 4 / (4 + 8)

8 / (8 + x) = 4 / 12 || Cross-multiply

4(8 + x) = 12 * 8

32 + 4x = 96

4x = 64

x = 16

AD = 16

Then, if we know AD, we can easily find AB. AB = AD + DB. AB = 24.

Lastly, we need to find AC. All of the other lengths on the big triangle have been double that of the smaller triangle, so 6 x 2 = 12. AC = 12.

#11.

BC will be parallel to DE if the proportions are equal.

AE / AB = AD / AC

1 / 5 = 2 / 11

These fractions are not equivalent, therefore BC and DE are not parallel.

Hope this helps!! :)

The area of the teacher workroom is 64 feet squared

Answer:

0.00054

Step-by-step explanation:

Gold ball: we have one chance of choosing the correct ball from 1 to 48, so the probability is 1/48

White balls: we will pick 4 numbers from 1 to 51, so the total possibilities of groups of numbers we can choose is a combination of 51 choose 4:

C(51, 4) = 51! / (4! * 47!) = 51*50*49*48/(4*3*2)

If we want to correctly guess two numbers, we have groups of 2 winning numbers in the 4 numbers we guess, so a combination of 4 choose 2, and we also have to incorrectly guess the other 2 winning numbers in the 47 remaining numbers we didn't choose, so a combination of 47 choose 2:

C(4, 2) = 4! / (2! * 2!) = 4*3/2 = 6

C(47, 2) = 47! / (2! * 45!) = 47*46/2

The probability of the white balls case is the two combinations above over the total number of cases (the first combination we calculated):

P = C(4, 2) * C(47, 2) / C(51, 4)

P = (6 * 47 * 46/2) / (51 * 50 * 49 * 48/(4*3*2))

P = (3 * 47 * 46 * 4 * 3 * 2) / (51 * 50 * 49 * 48) = 0.026

Then the final probability is the probability in the gold ball case times the probability in the white balls case:

P = (1/48) * (3 * 47 * 46 * 4 * 3 * 2) / (51 * 50 * 49 * 48) = 0.00054