Two numbers are randomly selected from the following set without replacement.
{3, 16, 2, 11, 15, 6, 14, 7, 10, 1}
a. What is the probability that they are both even?
b. What is the probability that they are both prime? Note: 1 is not prime.
c. What is the probability of the sum of the two numbers being even?
d. What is the probability of the product of the two numbers being odd?
The last two problems are based on a single draw from the set.
e What is the probability that a prime number was drawn from the set, given that it
is an odd number.
f. What is the probabilityselected from the set. that a prime number was drawn from
the set, given that it is an even number.

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

Equation - [tex]10=2x[/tex]

Solve - divide both sides by 2 - [tex]5 = x[/tex]

Answer:

X is equal to 15

Step-by-step explanation:

Vertical angles are equal to each other so just make the two equal to each other and solve, If you need to find what each angle is just substitute x with 15

Answer:

18

Step-by-step explanation:

24*0.74 = 18

Answer: 1.

Yes , the data franchise owner is collecting, will be helpful in order to counter the criticism from the critic. As he has a record for every delivery they are making on daily basis.

2.

The scenario is that for every fifth customer , the owner cross the four lines he makes. Thus a pack of five and easy to remember. As the data on regular week days is less, As can do the same for the third customer. Crossing the 2 lines for 3rd customer.

3.

With this provision of crossing the third customer, the owner can have a better check on the late delivery. As it will bring in his notice earlier as compared to fifth crossing.

4.

With the data as provided in the table, we can come to the conclusion that on weekends , i.e. both on time delivery and late deliveries are high in numbers. It must be because of high demand on that days. So owner must make some provision like hiring some more delivery boys for weekend in order to reduce the late deliveries.

Step-by-step explanation:

Answer:

the radius is 10 since 10 plus ten is 20

The correct matching of the confidence level with the confidence interval for μ is as follows:

x ± 1.96 --> A. 95%

x ± 2.575 --> B. 99%

x ± 1.645 --> C. 90%

A confidence level of 95% corresponds to a critical value of 1.96. This means that if we construct a confidence interval by taking the sample mean (x) and adding or subtracting 1.96 times the standard error, we can be 95% confident that the true population mean (μ) falls within this interval.

A confidence level of 99% corresponds to a critical value of 2.575. Similarly, constructing a confidence interval using the sample mean and adding or subtracting 2.575 times the standard error will give us a wider interval within which we can be 99% confident that the true population mean falls.

A confidence level of 90% corresponds to a critical value of 1.645. Constructing a confidence interval using the sample mean and adding or subtracting 1.645 times the standard error will give us a narrower interval within which we can be 90% confident that the true population mean lies.

These critical values are based on the standard normal distribution and are chosen to achieve the desired level of confidence.

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Answer:

2√73 I believe

Step-by-step explanation:

Input x with 3

2(3) = 6

5(3) + 1 = 16

16 squared is 256

6 squared is 36

A square plus B squared is C squared

square root of 292

Answer:

M=13

Step-by-step explanation:

Take the average of the two numbers:

(0+26)/2=13

Answer:

cos 0° = 1, because the cosine and sine are complements

Step-by-step explanation:

Here is the formula: sin 0 = cos (90°- 0) or cos 0 = sin (90°- 0)

So it would be: cos 0° = sin (90° - 0°) = sin 90° = 1

Answer:

well if you where talking about the dice the awnser is 6 and if you are tlking about the shirts then you can do 3 times 3 i thik is the right awnser

Step-by-step explanation:

1. a dice is a cube a cube has 6 sides a single number dice is a dice that only has numbers that are by themselves so the awnser can only be on the dice 6 to 9 so now we know that it is 6 now 6 times 2 is 12 because it got rolled twice

2.

Answer:

x=4

Step-by-step explanation:

Consecutive sides in a trapezoid are supplementry, which means they add up to 180. So, your equation is 14x-15+139=180

14x+124=180 (first make the numbers as clean as you can on both sides)

14x=56 (move all of the numbers to one side, so subtract 124 from both sides)

x=4  (simplify to get your answer, so divide by 14)

(hope this helps :P)

After inspecting the expression and comparing it with the standard equation of the parabola, the location of the vertex is (x, y) = (- 2, 7). (Correct choice: D) #SPJ5

The vertex is the bound point that characterizes parabolas and which can be a maximum or a minimum but never both. As we know the standard equation of the parabola, we can determine the location of the vertex, whose coordinates are (x, y) = (h, k), by just interpretating the equation, whose form is:

y - k = a · (x - h)²     (1)

After inspecting the expression and comparing it with the standard equation of the parabola, the location of the vertex is (x, y) = (- 2, 7). (Correct choice: D) #SPJ5

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The standard equation of the sphere is (x + 6)² + y² + z² = 36. The sphere is tangent to the yz-plane, the radius is the distance from the center (-6, 0, 0) to the yz-plane, which is 6 units.

To find the standard equation of the sphere with the given characteristics, we can use the formula for the equation of a sphere:

(x - h)² + (y - k)² + (z - l)² = r²

where (h, k, l) represents the center of the sphere and r represents the radius.

In this case, the center of the sphere is (-6, 0, 0) and it is tangent to the yz-plane. Since the yz-plane is defined by x = 0, the x-coordinate of the center of the sphere matches the x-coordinate of any point on the yz-plane. Therefore, the distance between the center of the sphere and the yz-plane is the radius of the sphere.

Since the sphere is tangent to the yz-plane, the radius is the distance from the center (-6, 0, 0) to the yz-plane, which is 6 units.

Plugging these values into the equation of a sphere, we have:

(x - (-6))² + (y - 0)² + (z - 0)² = 6²

(x + 6)² + y² + z² = 36

Thus, the standard equation of the sphere is (x + 6)² + y² + z² = 36.

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Answer:

It would be 828 inches cubed

Step-by-step explanation:

Because the boxes on top and bottom are both 6x8x6 and the middle portion is 6x7x6

6x8x6=288

6x7x6=252

288+288+252=828

When two four-sided dice are rolled, it creates a total of 16 possible outcomes. Because there are four numbers on each die, there are four possible outcomes on each die.  

To make a tree diagram for this situation, we begin with the first die rolled and the second die rolled. In the next level of the tree diagram, we list all of the possible outcomes.

The tree diagram is as follows:2. Only the pairs of numbers that contain different numbers are listed below:{(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}.There are 12 pairs of numbers that include different numbers.

Users can visualize the probabilities and possible outcomes of a situation using a tree diagram. Tree diagrams, which are also known as decision trees, are particularly useful for plotting the outcomes of dependent events, in which a change in one component has a significant impact on the outcome as a whole.

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Answer:

A = -2.3

Step-by-step explanation:

Answer:

6 units

Step-by-step explanation:

Answer:

6 units (B)

Step-by-step explanation:

8 - 2 = 6

Answer:

the second, and fourth one's are triangles, and the 1st and 2nd are not

Step-by-step explanation:

We know that the angles in a triangle add up to 180 degrees. So we need to find which angles add up to 180 degrees. We have:

56+34+42=132

That means the first one can't be a measures of a triangle.

75+55+50=180

Second one is a triangle.

35+32+23=90

Third isn't a triangle

124+64+16=180

So all in all, the second, and fourth one's are triangles, and the 1st and 2nd are not

Let X be the duration of a particular type of criminal trial. We know that the mean of X is μ = 24 days and the standard deviation of X is σ = 8 days.

We are asked to find the 66th percentile of X, which is the value x such that P(X ≤ x) = 0.66. Using the standard normal distribution, we have Z = (X - μ) / σ ~ N(0, 1).Thus, we can write: P(X ≤ x) = P(Z ≤ (x - μ) / σ) = 0.66We need to find the value of x that satisfies this equation. Using a standard normal distribution table or calculator, we can find that the corresponding z-score is approximately 0.43.

Thus, we have:0.43 = (x - μ) / σ0.43 * 8 = x - 24x ≈ 27.44Therefore, the 66th percentile of the duration of a particular type of criminal trial is 27.44 days (rounded to two decimal places).Part (a): The 66% of all trials of this type are completed within 27.44 days (rounded to two decimal places).

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Answer:

the correct one would be quadrant 3

Step-by-step explanation:

Answer:

The two coordinates should be (6, 3) and (10, 4).

Step-by-step explanation:

rise / run

y-value of the 2nd coordinate = 3 + 1 = 4

x-value of the 2nd coordinate = 6 + 4 = 10

The two coordinates should be (6, 3) and (10, 4).

The given function is y = 1/x. We need to use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width).

Given Function: y = 1/x Number of Subintervals: 6Width of Subinterval: (b-a)/n = (5-1)/6 = 4/6 = 2/3For Lower Sum, we take the minimum value of each subinterval and sum them up.

Lower Sum: ∑ i=1^n f(x_i*)Δx=∑ i=1^n f(a+iΔx)ΔxNow,

we calculate the Lower Sum: ∑ i=1^6 f(x_i*)Δx=∑ i=1^6 f(1+i(2/3))2/3=∑ i=1^6 2/(3(i+1))=0.903

For Upper Sum, we take the maximum value of each subinterval and sum them up.

Upper Sum: ∑ i=1^n f(x_i**)Δx=∑ i=1^n f(a+(i-1)Δx)ΔxNow,

we calculate the Upper Sum: ∑ i=1^6 f(x_i**)Δx=∑ i=1^6 f(1+i(2/3))2/3=∑ i=1^6 2/(3i)=1.361

Hence, the Lower Sum of the given function is 0.903 and the Upper Sum is 1.361.

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Answer:

No.

Step-by-step explanation:

Here i put it in a graph for you to see.

Answer:

20

Step-by-step explanation:

-10-5x(-6)

-10+30

20

We have proved the first assertion that "If x is even and y is odd, then x + 2y is even" using direct proof. However, the second assertion "If x and y are odd, then (x + 3) + y is odd" is not true.

A.

The truth value of statement a) VX EN, x + 4 < 2 is false because there is no natural number x in the set N = {1, 2, 3, 4, 5} that satisfies the inequality x + 4 < 2.

The truth value of statement b) 3x EN, x + 2 > 5 is true because for all natural numbers x in the set N = {1, 2, 3, 4, 5}, the inequality 3x + 2 > 5 holds.

The negations of the given statements are:

Negation of a): ~ (VX EN, x + 4 < 2) which is EX EN, ~(x + 4 < 2), i.e., there exists an x in N such that x + 4 is not less than 2.

Negation of b): ~ (3x EN, x + 2 > 5) which is EX EN, ~(x + 2 > 5), i.e., there exists an x in N such that x + 2 is not greater than 5.

B.

To prove the assertion "If x is even and y is odd, then x + 2y is even" using direct proof, we assume that x is even and y is odd. We can express x as 2a (where a is an integer) and y as 2b + 1 (where b is an integer). Substituting these values into x + 2y, we get 2a + 2(2b + 1) = 2(a + 2b + 1), which is clearly an even number. Hence, x + 2y is even.

To prove the assertion "If x and y are odd, then (x + 3) + y is odd" using direct proof, we assume that x and y are odd. We can express x as 2a + 1 and y as 2b + 1. Substituting these values into (x + 3) + y, we get (2a + 1 + 3) + (2b + 1) = 2(a + b + 2), which is clearly an even number. This contradicts the assertion, and therefore, it is not true.

In summary, we have proved the first assertion that "If x is even and y is odd, then x + 2y is even" using direct proof. However, the second assertion "If x and y are odd, then (x + 3) + y is odd" is not true.

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Step-by-step explanation:

400 in. is the correct answer

For a pyramid, volume= (1/3) x b x h where

B= base area, and

h= height .

So, volume= (1/3) x (200in^2) x (6in) = 400in^3.

- Chilio

Answer:

135

Step-by-step explanation:

the answer is 60 :) good luckStep-by-step explanation:

Answer:

If 31 is a option I would pick it.

Step-by-step explanation:

The problem we are solving is:

15% of ____ is 4.65.

This means that 0.15 x ? = 4.65

So ? = 4.65 / 0.15

Therefore ? = 31.

So the original number is 31.

Answer:

4. H

5. A

6. H

Step-by-step explanation:

For 4

Supplementary angles have a sum of 180

so 3x + 96 = 180

now we just use basic algebra to solve for x

step 1 subtract 96 from each side

180 - 96 = 84

now we have 84=3x

step 2 divide each side by 3

3x/3=x

84/3=28

we're left with x = 28

so the answer to #4 is H

For 5

Remember the sum of the angles in a triangle is 180

So we can calculate the missing angle by subtract the given angles (90 and 66 in this case) from 180 NOTE: ( the 90 came from the little square at the bottom right of the triangle. This square indicates that the angle is a right angle and a right angle has a measure of 90 degrees)

so x = 180 - 90 - 66

180 - 90 = 90

90 - 66 = 24

so we can conclude that x = 24 and the answer is A

For 6

Angle 2 and angle 4 are vertical angles

If you didn't know vertical angles are congruent

SO if one angle equal 120 degrees the other angle also equal 120 degree therefore the answer to number 6 is H