if decision variables for a problem have to be integers then rounding the linear programming optimal solution for that problem will group of answer choices always result in feasible but not optimal solution may result in either a feasible or infeasible solution always result in an optimal solution always result in a feasible and the optimal solution

Let assume the probability of the three events as P(A), P(B), and P(C), respectively. Then:

(a) The probability that at least one of the three events occurs is given by:

P (A or B or C) = 1 - P (not A and not B and not C) = 1 - P (not A) * P (not B) * P (not C)

where P (not A) is the complement of P (A), and similarly for P (not B) and P (not C).

(b) The probability that exactly one of the three events occurs can be calculated by adding the probabilities of each event occurring individually and then subtracting the probability that two events occur simultaneously.

P (exactly one) = P(A) + P(B) + P(C) - 2 * P (A and B) - 2 * P (A and C) - 2 * P(B and C) + 3 * P (A and B and C)

Note that the above formulas assume that the events are mutually exclusive and exhaustive, meaning that one and only one of the events must occur and the sum of the probabilities of the individual events is equal to 1.

If this is not the case, the probabilities need to be adjusted accordingly.

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Answer:

x=11/5, or x=2.2.

Step-by-step explanation:

9-3(x+4)=2(x-3)-8

9-3x-12=2x-6-8

9-12-3x=2x-14

-3-3x=2x-14

-3-3x-2x=-14

-3-5x=-14

5x=-3-(-14)

5x=-3+14

5x=11

x=11/5

x=2.2

Answer:

A.) Negative

Step-by-step explanation:

Any line that goes from top to bottom has a negative slope.

Answer:

when the coefficient of x^2 is negative

Step-by-step explanation:

2²ˣ ⁻ ⁵ = 128

Any equation with a variable in the exponent position is clearly an exponential equation.

The given solution for an exponential equation is x = 6.

For making this in expression form we need to add some values to it

hence multiply by 2 on both sides

2x = 12

subtract by -5 on both sides

2x- 5  =  7

multiply with ln 2 on both sides

2x - 5 ln2  =  7 ln 2

after taking antilog

2²ˣ ⁻ ⁵ = 128

Therefore, 2²ˣ ⁻ ⁵ = 128 is an exponential equation whose solution is x= 6.

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Answer:

2

Step-by-step explanation:

Slope is (y2-y1)/(x2-x1)

Answer:

2

Step-by-step explanation:

(y2)8- (y1)6= 2

(x2) 1- (x1) 0 = 1

2/1 =2

Final answer would be 222222

The group that would be the most stable based on size would be 10 people. So, the correct answer is c. 10 people.

A group is a set of people or objects that are deemed to be equivalent or share a common feature. Group members may collaborate and share knowledge to achieve a common goal. The group's performance is frequently greater than the sum of its members' individual efforts, and this is known as the group effect.

Group stability is defined as the ability of a group to remain together and keep working toward its objective over time. It is essential for a group to achieve its objectives and is typically linked to the group's size and objective. A stable group can withstand external pressures and is less susceptible to breaking up or being disbanded.

A group's size has a significant influence on its stability. Small groups are often more cohesive and productive than large groups. On the other hand, as a group's size grows, it becomes more challenging to sustain cohesion and productivity. A group of 10 people would be the most stable since it's not too large or too small. Thus, the correct option is c. 10 people.

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Answer:

Incomplete question

...

If the alternative hypothesis is that the proportion of items in population 1 is larger than the proportion of items in population 2, then the null hypothesis should be that there is no significant difference in the proportion of items between population 1 and population 2.

Based on the information provided, the null hypothesis should be:

The null hypothesis is that the proportion of items in population 1 is less than or equal to the proportion of items in population 2.

This is denoted as H₀: P₁ ≤ P₂. The alternative hypothesis, as you mentioned, is that the proportion of items in population 1 is larger than the proportion of items in population 2, which is represented as H₁: P₁ > P₂.

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Answer:

if f(x) = x^2 which equation represents function g?

Step-by-step explanation:

maby ( C) am not sure

The equation represents the function is g(x) = 3f(x).

A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

We have,

Function, f(x) = x²

The function g(x) is compressed horizontally by a factor of 3, to get the function g(x)

g(x) = kf(x)

Where k = 3.

So, we have:

g(x) = 3f(x)

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Answer:

180°

------------------------------------------------------------------------------------

Hope it helps, if you have any question comment, down below!

45°

Diagrams attached for better understanding

Answer:

Approximately 0.11 acres can be planted with one pound of seed

Step-by-step explanation:

You use the rule of 3

66 pounds / 7 acres = ? pounds / 1 acre

? = 66 x 1 ÷ 7

? = 66 ÷ 7

? ≈ 9.23 pounds / acre

Now you know how many pounds you have for 1 acre. You reuse the formula from before

9.23 pounds / 1 acre = 1 pound/ ? acres

? = 1x1 ÷ 9.23

? = 1 ÷ 9.23

? = 0.11 acres/pound

Verify the answer:

0.11 x 9.23 ≈ 9.33, which is approximately 1 pound

Answer:

90 pounds per acre

Step-by-step explanation:

Im right

The maximum and minimum measurements are 5 and -3 respectively.

f ( x ) = -x^3 +3x^2+ 45 x + 10

f' l x ) = 0

0 = - 3x^2 +6x +45

x = 5,- 3.

f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174

f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58

f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1

+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185

Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}

                        = 185 at x=5

Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}

                      = - 71 at x= -3

In light of this, the maximum and minimum values are 5 and -3, respectively.

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Answer:

Caitlin had bought 6 CD's for herself.

Step-by-step explanation:

We know that:

Since she had $10 gift certificate and used it in the $7 bargain bin, we know that 32 + 10 must've been her real cost without crediting the gift card. When we divide the real cost by 7, we get the number of CD's bought by Caitlin.

Work:

This means that the real cost was $42.

Hence, Caitlin had bought 6 CD's for herself.

Hoped this helped.

\(BrainiacUser1357\)

Answer: 31.5

Step-by-step explanation:  
6*4=24 (Shaded Rectangle)

3*5=15  15/2=7.5 (Shaded Triangle)
7.5 + 24 = 31.5

The answer is: a. Yes, the forecast fails the bias test.

To determine whether the forecast fails the bias test, we need to compare the Average Error (AE) with zero.

If the AE is significantly different from zero, it indicates the presence of bias in the forecast. If the AE is close to zero, it suggests that the forecast is unbiased.

In this case, the Average Error (AE) is -2.0, which means that, on average, the forecast is 2.0 units lower than the actual values. Since the AE is not zero, we can conclude that there is a bias in the forecast.

Therefore, the answer is:

a. Yes, the forecast fails the bias test.

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Answer:

11.74

Step-by-step explanation:

I hope this helps you

Answer:

$9.99

Step-by-step explanation:

The goal is to get d all by itself. To do that first subtract 5.22 on both sides. Then you have 3d=29.97. Then you need to get rid of the 3. Divide the 3 on both sides to get d=9.99. D represent a dozen, so one dozen bagels equals $9.99.

Answer:

Mr. Marcum bought 5 child tickets and 2 adult tickets.

Step-by-step explanation:

First, assume that Mr. Marcum bought either 7 tickets of child tickets or 7 tickets of adult tickets. I'm using 7 child tickets for this working.

If Mr. Marcum bought 7 child tickets,

total money spent = $4 * 7 = $28

This is not equal to $40 and there has to be more money spent.

We should also calculate the price difference between the adult ticket and the child ticket.

Price difference per ticket = $10 - $4 = $6

This means that if Mr. Marcum bought an adult instead of a child ticket, he would spend $6 more.

In this case, Mr. Marcum has to spend $40- $28 = $12 more.

Hence, the number of adult tickets replacing the child tickets is $12/$6 = 2.

The number of child tickets = 7 - 2 = 5

Answer: C slope= 1/2 y-intercept =2

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

7x(92+7) = 693

(7x92) = 644

(7x92) +

(7x7) = 49

644 + 49 = 693

Decomposition is used to perform ANOVA and test the significance of the independent variable and its interaction effect on the dependent variable.

The expression SS stands for "sum of squares", which is a statistical concept used in analysis of variance (ANOVA) to quantify the variation in a dataset. The components of this expression, a, b, c, and d, represent different sources of variation in the dataset, and their meanings are as follows:

a. (df)(s^2): This component represents the sum of squares due to the effect of the independent variable, also known as the factor or treatment. It is calculated by multiplying the degrees of freedom (df), which is the number of levels of the factor minus one, by the variance of the data within each level (s^2). This component quantifies the amount of variation in the dependent variable that can be explained by the independent variable.

b. (df)(s): This component represents the sum of squares due to the interaction between the independent variable and other factors, also known as the interaction effect. It is calculated by multiplying the degrees of freedom (df) by the standard deviation (s) of the data. This component quantifies the amount of variation in the dependent variable that is due to the joint effect of the independent variable and other factors.

c. (n)(s^2): This component represents the sum of squares due to the variation within groups, also known as the error or residual sum of squares. It is calculated by multiplying the sample size (n) by the variance of the data within each group (s^2). This component quantifies the amount of variation in the dependent variable that is not explained by the independent variable or other factors.

d. (n)(s): This component represents the sum of squares due to the variation between the sample mean and the overall mean, also known as the total sum of squares. It is calculated by multiplying the sample size (n) by the standard deviation (s) of the data. This component quantifies the total amount of variation in the dependent variable.

In summary, the expression SS = a. (df)(s^2) + b. (df)(s) + c. (n)(s^2) + d. (n)(s) represents the decomposition of the total sum of squares into its components due to the independent variable, interaction effect, error, and total variation. This decomposition is used to perform ANOVA and test the significance of the independent variable and its interaction effect on the dependent variable.

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The monthly cost for 66 minutes of calls will be $15.84.

Monthly cost is the payment or the bill amount that needs to be paid at the end of the month.

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes)

The monthly cost for 45 minutes of calls = $14.40

The monthly cost for 102 minutes = $19.53

The above values can be paired in groups so as to satisfies the coordinates of a linear function

(45,14.40)  and (102,19.53)

Finding the slope of the graph using these points

slope, m=Δy/Δx

m=Δy=19.53 - 14.40 = 5.13

Δx=102 - 45 = 57

m = 5.13/57 =0.09

Finding the equation of the linear function using m = 0.09, and point (45,14.40)

m=Δy/Δx

0.09=y-14.40/x-45

0.09(x-45)=y-14.40

0.09x-4.05=y-14.40

0.09x-4.5+14.40=y

y=0.09x + 9.9

So for 66 minutes, the cost will be;

x = 66, y = ?

y=0.09*66 + 9.9

y=5.94+9.9 = $15.84

The monthly cost for 66 minutes of calls is $15.84.

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cot(θ) = -3/4: The cotangent of angle θ, when the terminal side passes through the point (-3, -4), is -3/4. .

Given that the terminal side of an angle θ passes through the point (-3, -4), we can determine the value of cot(θ), which is the ratio of the adjacent side to the opposite side in a right triangle. To find cot(θ), we need to identify the adjacent and opposite sides of the triangle formed by the point (-3, -4) on the terminal side of angle θ.

The adjacent side is represented by the x-coordinate of the point, which is -3. The opposite side is represented by the y-coordinate, which is -4. Using the definition of cotangent, cot(θ) = adjacent/opposite, we substitute the values:

cot(θ) = -3/-4

Simplifying the fraction gives us:

cot(θ) = 3/4 . Therefore, the exact value of cot(θ) when the terminal side of angle θ passes through the point (-3, -4) is 3/4.

In geometric terms, cotangent is a trigonometric function that represents the ratio of the adjacent side to the opposite side of a right triangle. By identifying the appropriate sides using the given point, we can evaluate the cotangent of the angle accurately.

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Answer:

C.

Step-by-step explanation:

Slope = m = (y2 - y1)/(x2 - x1) = (5-(-1))/(4 - 2) = 6/2 = 3

Slope - point form:

y - y1 = m(x -x1)

y - 5 = 3(x - 4)

y - 5 = 3x - 12

- 3x + y = - 12 + 5

- 3x + y = - 7

Answer:

Option C is the correct option.

Step-by-step explanation:

A line passes through ( 2 , -1 ) and ( 4 , 5 )

The equation of line:

\( \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1} \)

Plug the values

\( \frac{ y - ( - 1)}{x - 2} = \frac{5 - ( - 1)}{4 - 2} \)

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

\( \frac{y + 1}{x - 2} = \frac{5 + 1}{4 - 2} \)

Add the numbers

\( \frac{y + 1}{x - 2} = \frac{6}{4 - 2} \)

Subtract the numbers

\( \frac{y + 1}{x - 2} = \frac{6}{2} \)

Reduce the numbers with 2

\( \frac{y + 1}{x - 2} = 3\)

Apply cross product property

\(3x - 6 = y + 1\)

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

\(3x - y = 1 + 6\)

Add the numbers

\(3x - y = 7\)

\( - 3x + y = - 7\)

Hope this helps...

Best regards!

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

-15/22

Step-by-step explanation:

22t-26=-16-25

22t-26=-41

22t=-41+26

22t=-15

t=-15/22

Answer:

(-1,-2)

Step-by-step explanation:

The given coordinates are ,

Midpoint can be calculated by finding the mean of x coordinates and y coordinates . As ,

→ Midpoint = ( 4-2/2 , 10-6/2)

→ Midpoint = ( -2/2 , -4/2 )

→ Midpoint = ( - 1 , -2)

Answer:

2: 49500  3: 657024  4: 4200  5: 194880

Step-by-step explanation:

Answer:

Step-by-step explanation:

2. 275 minutes for every day of 180 days. So:

275 × 180 =

22000 +

27500 =

49500

3. 354 × 1856 =

+2124

+17700

+283200

+354000      

= 657024

4. 175 × 24=

+700

+3500

=4200

5. 4640 × 42 =

+9280

+185600

=194880