assume that the height of college males is normally distributed with mean=71 inches and standard deviation=2 inches. The probability that the randomly selected college male is at most 75 inches.

Answer:

-12C

Step-by-step explanation:

Simply take 22 and subtract it by 34.

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer: <less than >greater than ≥ greater than or equal to ≤ less than or equal to

Step-by-step explanation:

If each video uses 0.87 gigabytes, then the number of videos that Elliot can stream is 5 videos.

To determine how many 30 minute videos Elliot can stream with 4.35 gigabytes of data, we divide the total data by the data consumed per video,

⇒ Number of videos = (Total data)/(Data per video);

We know that each video uses 0.87 gigabytes of data,

Substituting the values,

We get,

⇒ Number of videos = 4.35/0.87,

⇒ Number of videos = 5

Therefore, Elliot can stream 5, "30 minute" videos with his 4.35 gigabytes of data.

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The correct options are A)  X-1 <1 and D) X+4 < 6.

Given, we need to find all the inequalities for which the solution set is x < 2. We know that if x < a then the solution set will lie on the left side of a in the number line. Therefore, for x < 2 the solution set will be on the left side of 2 on the number line. So, let's check each option:

A. X-1 <1 - Adding 1 to both sides of the inequality we get: X < 2

Here, the solution set is x < 2. So, option A is correct.

B. X2 <0 - There is no real value of x for which x² < 0. So, the solution set is null. Therefore, option B is incorrect.

C. X 3 < 1 - Subtracting 3 from both sides we get: X < -2. The solution set is x < -2. So, option C is incorrect.

D. X+4 < 6 - Subtracting 4 from both sides we get: X < 2. Here, the solution set is x < 2. So, option D is correct.

Therefore, the correct options are A and D.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

5 groups ===> 1

1 group ====> 5

Step 02:

We must apply the algebraic rules to find the solution.

5 groups * 1 = 1 group * 5

5 * 1 = 1 * 5

5 = 5

The answer is:

Brent is correct

8/19 or 42.1%

add all values up to a total, then find the percentage from that total.

8 + 2 + 1 + 3 + 5 = 19 balls total

8 tennis valls to 19 total.

8/19 or 42.1%

Answer:

(-2, -4)

Step-by-step explanation:

Given the coordinate (x, y), if rotated 90degrees, counterclockwise, the resulting coordinate will be (-y, x)

For the coordinate (-4, 2)

When rotated 0 degrees  counterclockwise, the resulting coordinate will be at (-2, -4)

Note that the coordinates were switched and the x negated

If a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The mean of the normal distribution = 4

Standard deviation of the normal distribution = 1.5

The value of x = 5.5

The z-score of the normal distribution = The mean of the normal distribution / Standard deviation of the normal distribution

Substitute the values in the equation

The z-score of the normal distribution  = (5.5 - 4) / 1.5

Substract the terms

= 1.5 / 1.5

= 1

Hence, if a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The complete question is:

suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x = 5.5

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Answer:

x=19

Step-by-step explanation:

y=7 - 2=(y) 5 then x=21 - 2=(x)19

The coordinate of the centre of the circle inscribed in a triangle whose vertices are (−36,7), (20,7) and (0,−8) is (-1,0).

The formula for calculating the coordinate of the centre of the circle inscribed in a triangle whose vertices are \((x1,y1), (x2,y2), (x3,y3)\):

(x,y) = \((\frac{ax1+bx2+cx3}{a+b+c} , \frac{ay1+by2+cy3}{a+b+c})\)

where,

a is the side of triangle opposite vertex (x1, y1)

b is the side of triangle opposite vertex (x2, y2)

c is the side of triangle opposite vertex (x3, y3)

Given vertices of triangle as (−36,7), (20,7) and (0,−8),

By distance formula,

a = \(\sqrt{(20-0)^2+(7+8)^2}\) = 25

b= \(\sqrt{(-36-0)^2+(7+8)^2}\) = 39

c = \(\sqrt{(20+36)^2+(7-7)^2}\) = 56

The coordinates of triangle become:

x = \(\frac{25*-36 + 39*20 +0*56}{25+39+56}\) = -1

y = \(\frac{7*25+39*7-8*56}{25+39+56}\) = 0

(x,y) = (-1,0)

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The complete question is given below:

Find the coordinates of the centre of the circle inscribed in a triangle whose vertices are (−36,7), (20,7) and (0,−8) ?

Answer:

X-intercept: -15

Y-intercept: 6

Step-by-step explanation:

The x-intercept of a graph is the x-coordinate of the graph when it crosses the x-axis, that is, when y=0. So to find the x-intercept given the equation for a graph, we find x when y=0:

-2x+5y=30

-2x+5(0)=30

-2x=30

x=-15

Similarly, the y-intercept of a graph is the y-coordinate of the graph when it crosses the y-axis, that is, when x=0. So to find the y-intercept given the equation for a graph, we find y when x=0:

-2x+5y=30

-2(0)+5y=30

5y=30

y=6

Answer:

95

Step-by-step explanation:

15 * 5 = 75

5 * 4 = 20

20 + 75 = 95

Answer:

x = 7

Step-by-step explanation:

To solve:

Distribute 5 among everything inside the first parentheses. You'll get 5x - 15.

Next distribute -2 among everything in the second parentheses. You'll get

-2x - 2.

All together: 5x - 15 -2x - 2 = 4

Now combine like terms:

5x - 2x = 3x and -15 - 2 = - 17

All together: 3x - 17 = 4

Add 17 on both sides to get 21, and then divide both sides by 3. Answer is x = 7.

________________________________

Last, don't forget to check your work.

You can plug in 7 for x to get:

5(7 - 3) = 20

5 × 7 = 35

5 × -3 = -15

35 - 15 = 20

-2(7 + 1) = -16

-2 × 7 = -14

-2 × 1 = - 2

-14 -2 = -16

20 - 16 = 4

⬆⬆⬆Therefore this is correct.

Sorry this is a bit lengthy, but hope this helps :)

Answer:

5 < 10x - 3

Step-by-step explanation:

5 - 2x < 8x - 3

Add '2x' to both the sides

5 - 2x + 2x < 8x + 2x - 3

5 < 10x - 3

The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.

The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.

z + 3x4 = 15 + 3x4

= 15 + 12

= 27

Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).

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____The given question is incomplete , the complete question is given below:

Evaluate the expression, where z = 15

z + 3x4

A. 27

B. 32

C. 56

D. 1,304

Answer:

Below in bold.

Step-by-step explanation:

i) Amount = 15000(1 + 0.10)^2 = 18,150.

Interest = 3,150.

ii) Amount = 15620(1 + 0.08/2)^(3/2*2)

= 15620(1 + 0.04)^3

= 17,570.38.

Interest =1,950.38.

iii) Amount = 100000(1 + 0.04/4)^(3)

= 100000(1 + 0.01)^3

= 103,030.1

Interest = 3030.1.

Answer:

1450 residents

Step-by-step explanation:

Number of residents who live in Harris

= 5800 pounds ÷ 4 pounds

= 1450 residents

Answer:

Concave Up: x<-1 and x>1

Concave Down: -1<x<1

Step-by-step explanation:

To determine the intervals of concavity for a continuous function f, we must determine the second derivative and figure out at what points its sign changes (aka. our inflection points):

\(f(x)=e^{-\frac{1}{2}x^2}\\\\f'(x)=\frac{d}{dx}(-\frac{1}{2}x^2)*e^{-\frac{1}{2}x^2}\\\\f'(x)=-xe^{-\frac{1}{2}x^2}\\\\f''(x)=[\frac{d}{dx}(-x)](e^{-\frac{1}{2}x^2})+(-x)(\frac{d}{dx}e^{-\frac{1}{2}x^2})\\ \\f''(x)=-e^{-\frac{1}{2}x^2}+x^2e^{-\frac{1}{2}x^2}\\\\f''(x)=e^{-\frac{1}{2}x^2}(x^2-1)\)

Next, we determine where \(f''(x)=0\) to find our inflection points:

\(0=-e^{-\frac{1}{2}x^2}(x^2-1)\\\\x=-1,x=1\)

Our intervals of concavity can be determined by testing points around our inflection points. I will use the points \(x=-2\) and \(x=2\):

\(f''(-2)=e^{-\frac{1}{2}(-2)^2}((-2)^2-1)=e^{-2}(4-1)=\frac{3}{e^2}>0\\ \\\\f''(2)=e^{-\frac{1}{2}(2)^2}(2^2-1)=e^{-2}(4-1)=\frac{3}{e^2}>0\)

Since the factor \(x^2-1\) is a second-order polynomial with a leading positive coefficient, we know that the sign is negative in the interval between the roots, and positive outside. Therefore:

Concave Downward: \((-\infty,-1) \cup(1,\infty)\)

Concave Upward: \((-1,1)\)

This means that the 4th option is correct. Refer to the graph for a visual.

Step-by-step explanation:

hope you can understand

The coordinate -2, 4 implies -2 is the value on the x or horizontal axis and 4 is the value on the y or vertical axis.

This a plane used for graphs or points that is based on a vertical axis (y) and a horizontal axis (x).

The first number, -2 indicates the value in x or the horizontal axis, while the second number 4 indicates the position on y or the vertical axis. You can see this in the imaged attached (red dot).

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The coordinate -2, 4 implies -2 is the value on the x or horizontal axis and 4 is the value on the y or vertical axis.

What is a coordinate plane?

This a plane used for graphs or points that is based on a vertical axis (y) and a horizontal axis (x).

How does -2,4 look on a coordinate plate?

The first number, -2 indicates the value in x or the horizontal axis, while the second number 4 indicates the position on y or the vertical axis. You can see this in the imaged attached (red dot).

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78 inches is equivalent to 6 feet and 6 inches in human height. Human height is typically measured in feet and inches, with one foot equaling 12 inches.

In this case, 78 divided by 12 equals 6 with a remainder of 6, meaning that 78 inches is equivalent to 6 feet and 6 inches. This is a relatively tall height, as it is above the average height for both men and women in many countries. Understanding height measurements can be important for various reasons, including clothing and furniture sizing, sports performance, and medical evaluations. Therefore, if a person's height is 78 inches, we can convert it into feet and inches by dividing the total number of inches by 12.

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The average price in 1992 and 2013 was given. It is required to find the percentage increase in the average price over these years.

Recall that the formula for Percentage Increase is:

Substitute initial price=12500 and final price= 22000 into the formula:

Hence, the percent increase in the average price is 76%.

Answer:

depends on whether or not the dealerships are scammers

Step-by-step explanation:

Step-by-step explanation:

raise 1³ and 4³:

1×1×1 = 1 and 4×4×4 = 64

so the result is 1/64

As per the concept of probability, the number of parts should they order under their regular shipment for the next six months is approximately 18.

In this scenario, the demand rate is given as a Poisson distribution with a mean of 6.5. The holding cost is $5 per part, and the unit cost under regular, semiannual shipment is $32 per part, while the cost of an emergency shipment is $50 per part.

Since we know that orders are placed semiannually, we need to find the order quantity that will last for six months. To do this, we can divide the total annual demand by 2. Therefore, the annual demand for part 1aa-66 is 6.5 x 2 = 13.

Now, we can use the EOQ formula to find the optimal order quantity:

EOQ = √(2DS/H)

Where D is the demand rate, S is the ordering cost, and H is the holding cost.

Plugging in the values, we get:

EOQ = √(2 x 13 x $32 / $5) = √332.8 ≈ 18.23

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Answer:

3 2 − 6 − 1

   2

− 3

Step-by-step explanation:

Answer: -13

Step-by-step explanation:

\(\frac{M(3)+M(2)}{2} =\frac{[-2(3)^{2}] +[-2(2)^{2}]}{2}=\frac{(-2)(9)+(-2)(4)}{2}=\frac{-18-8}{2}=\frac{-26}{2}=-13\)

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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In this representation, the numbers are placed from left to right in order of most pounds eaten to fewest pounds eaten.

To plot the number of pounds eaten each week on a number line and order them from most pounds eaten to fewest pounds eaten, we'll consider the negative rational numbers representing the weight in pounds of doggie treats eaten by Darius. Here's an example ordering:

1. -3.5
2. -2.7
3. -2.5
4. -1.8
5. -1.2
6. -0.9
7. -0.5
8. -0.2

To visualize this on a number line, let's place these numbers accordingly:

```
-3.5                    -2.7        -2.5
    |---------------------|-----------|
-1.8       -1.2         -0.9         -0.5   -0.2
 |-----------|-----------|-----------|
```

In this representation, the numbers are placed from left to right in order of most pounds eaten to fewest pounds eaten. Each number is marked with a vertical line segment, and the length of the line segment corresponds to the magnitude of the number. The numbers are positioned such that they are evenly spaced along the number line.

Please note that this is just one possible ordering and arrangement of the numbers on the number line. The exact values and spacing may vary based on the actual data.

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