Mainline is choosing 3 of her 10 best flowers displays to be entered in a competition. How Many different selections are possible?

Using FOIL method for the multiplication, we have:

1: 3x (5x - 4) = 15x² - 12x

2: x²(5x² + 3y + 1) = 5x⁴ + 3x²y + x²

3: (4x + 3)(4x -5)  = 16x² - 8x - 15

4: (7x - 3)(4x - 5) = 28x² - 47x + 15

FOIL is an acronym that stands for "First, Outer, Inner, Last". It is a mnemonic device that is commonly used to remember the process of multiplying two binomials.

No. 1

3x (5x - 4) = 3x*5x + 3x*(-4)

                 = 15x² - 12x

No. 2

x²(5x² + 3y + 1) = x²*5x² + x²*3y + x²*1

                        = 5x⁴ + 3x²y + x²

No. 3

(4x + 3)(4x -5) = 4x(4x-5) + 3(4x-5)

                    = 4x*4x + 4x*(-5) + 3*4x + 3*(-5)

                    = 16x² - 20x + 12x - 15

                    = 16x² - 8x - 15

No. 4

(7x - 3)(4x - 5) = 7x(4x - 5) - 3(4x - 5)

                      = 7x*4x  + 7x*(-5) - 3*4x - 3*(-5)

                      = 28x² - 35x -12x + 15

                      = 28x² - 47x + 15

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If the objective function coefficient for variable 1 decreases by 20, the solution will shift in the direction of the decrease in the objective function coefficient. It means that the optimal solution that was obtained previously will no longer remain optimal, and the new optimal solution will be found with the new objective function coefficient.

In linear programming, the objective function determines the maximum or minimum value that can be attained in the solution, subject to the constraints. The constraints in the problem can be either equalities or inequalities, which limit the range of values that the decision variables can take on.

The change in the objective function coefficient will change the direction of the optimal solution, and it may affect the feasibility of the solution. It means that some constraints may no longer be satisfied, or some variables may become infeasible.

In such cases, it will be necessary to revise the constraints or the variables to ensure the feasibility of the solution.

The solution can also be affected if the constraints of the problem change. The new constraints may limit the range of values that the variables can take on, or they may add new variables to the problem. These changes can affect the feasibility of the solution, and it may require the problem to be solved again to obtain the new optimal solution.


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Applying the triangle proportionality theorem, the value of x is calculated as: D. 15.

The Triangle Proportionality Theorem (also known as the Side-Splitter Theorem) states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally

Based on the triangle proportionality theorem, we have:

x - 6 / 3 = x / 5

Cross multiply:

5(x - 6) = 3x

5x - 30 = 3x

Combine like terms to find the value of x:

5x - 3x = 30

2x = 30

x = 30/2

x = 15

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Hence, the value of  variable in the given expression x is 8

An angle is formed when two straight lines  meet at a common endpoint.

∠1 = 7x - 4

∠2 = 3x + 28

A secant line that crosses two parallel lines produces these angles. After that, these angles were congruent, which means that their measures are equal.

Then, equaling  both given expressions and solving for x,  we get:

Step1: subtract 3x both sides

7x - 4 = 3x + 28

Step2: add 4 both sides

7x - 3x - 4 = 28

Step2: simplify like terms

7x - 3x = 28 + 4  

Step3: divide by 4 both sides

4x = 32  

x = 32/4

x = 8

Hence, the value of x is 8.

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The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is  0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.

Given that mean μ = 4.2 , standard deviation σ = 1.3

1. P(X >= 5) = P((X - μ)/σ >

                    = (5 - 4.2) /1.3

                    = P(Z ≥ 0.6154)

                    = 1 - P(Z < 0.6154)

                    = 1 - 0.7324

                    = 0.2676

The required probability is 0.2676.

2.Given that n = 8 then  [tex]\bar x[/tex] = σ/[tex]\sqrt{(n)[/tex]  = 1.3/√(8) = 0.4596

P(x-bar ≥ 5) = P(([tex]\bar x[/tex] - μ)/σx-bar ≥ (5 - 4.2)/0.4596)

                        = P(Z ≥ 1.7406)

                        = 1 - P(Z < 1.7406)

                        = 1 - 0.9591

                        = 0.0409

The required probability is 0.0409.

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Answer:

The shape of each cut surface is a rectangle. The dimensions of the first cut surface are 8 inches by 10 inches, and the dimensions of the second cut surface are 10 inches by 20 inches.

The area of the first cut surface is 8 inches x 10 inches = 80 square inches. The area of the second cut surface is 10 inches x 20 inches = 200 square inches.

To find the total area Jenny needs to paint, we need to add the area of the first cut surface to the area of the second cut surface.

Total area = Area of first cut surface + Area of second cut surface

Total area = 80 square inches + 200 square inches

Total area = 280 square inches

Therefore, Jenny needs to paint a total area of 280 square inches.

Answer:

1/2

Step-by-step explanation:

options in a 6 sided die= 1,2,3,4,5,6

greater than 3 = 4,5,6

so three  sides  out of a 6 sided die is greater than three

P(not greater than 3) = [tex]\frac{6-3}{6} = \frac{1}{2}[/tex]

Answer:

1/2 or 0.5

Step-by-step explanation:

The probability of rolling a number greater than 3 on a six-sided die is 3/6 or 1/2, since there are three numbers (4, 5, 6) out of six that are greater than 3.

To find the probability of not rolling a number greater than 3, we can subtract the probability of rolling a number greater than 3 from 1:

P(not greater than 3) = 1 - P(greater than 3)

P(not greater than 3) = 1 - 1/2

P(not greater than 3) = 1/2

Therefore, the probability of not rolling a number greater than 3 is 1/2 or 0.5.

Answer:

Of the given options, "an engine" is the most reasonable abstraction for a car.

An engine is a fundamental component of a car that powers its movement, and it is present in almost all cars. The number of miles driven and the driving car color are characteristics of a specific car rather than abstractions of a car itself. For example, a car can still be considered a car even if it has not been driven any miles yet or if it has no color at all.

Therefore, an engine is a more reasonable abstraction for a car as it captures an essential feature of a car that is present in all cars.

The solution is, D. Driving, a reasonable abstraction for a car includes. Driving is an action or behavior associated with a car, as it involves operating or using the car to travel from one place to another. It is an essential aspect of the car's purpose and function.

Here, we have,

we know that,

An engine is a machine designed to convert fuel into mechanical energy that can be used to power other machines or devices. In the context of automobiles, an engine is the primary source of power that drives the vehicle. It typically operates by burning fuel in a combustion chamber to generate high-pressure gases that drive a piston, which in turn rotates a crankshaft that ultimately powers the car's wheels.

Car color and number of miles driven are characteristics or properties of a car, while an engine is a component that helps to power the car. Driving, on the other hand, is an action or behavior associated with a car, as it refers to the act of operating or using the car to travel from one place to another.

Therefore, driving is a reasonable abstraction for a car, as it captures an essential aspect of the car's purpose and function.

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The linear measure of arc KML on OO is approximately 3.33 units, rounded to two decimal places.

Since KM is a diameter, angle KOM is a right angle. Therefore, angle KOL is a straight angle, which means that angle MOL is 180 - 145 = 35 degrees.

Now, we can use the fact that the measure of an arc is proportional to the measure of the angle it subtends. In particular, if the measure of an angle in degrees is θ and the radius of the circle is r, then the length of the arc it subtends is given by:

length of arc = (θ/360) * 2πr

In this case, the radius of the circle is half of the diameter KM, which is 36/2 = 18. So we have:

length of arc KML = (35/360) * 2 * 3.14 * 18

≈ 3.33

Therefore, the linear measure of arc KML on OO is approximately 3.33 units, rounded to two decimal places.

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The sum of the matrices A and C from the list of options is the matrix B

Given the following matrices

Matrix A

| 0  6  2 |

| 1  5  -2 |

Matrix C

| -2  5  3 |

| -1  -7  3|

To find the sum of matrices A and C, we add the corresponding elements in each matrix:

So, we have: A + C

| 0 - 2  6 + 5  2 + 3 |

| 1 - 1    5 - 7  -2 + 3|

Evaluate the sum

| -2  11  5 |

| 0   -2  1 |

This represents option B

Therefore, the sum of matrices A and C is (B)

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Complete question

What is the sum of A+C?

Matrix A

| 0  6  2 |

| 1  5  -2 |

Matrix C

| -2  5  3 |

| -1  -7  3|

The two composite figures cover the same area, A = 4+2+2+1= 9 units²

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

we know that

The area for both composite figures is equal to the area of a square plus the area of two isosceles right triangles plus the area of a smaller isosceles triangle

So

Area of the square

A = 2² = 4 units²

Area of the isosceles right triangle

A = (1/2) (2) (2) = 2 units²

Area of the smaller isosceles triangle

A = (1/2)(2)(1) = 1 units²

The area of the composite figure is

A =  4+2+2+1= 9 units²

Hence, the two composite figures cover the same area, A = 4+2+2+1= 9 units²

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fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1 , ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05 are the required functional estimations of a given representations.

However, we can estimate the partial derivatives with respect to x (fv) and y (ft) at the point (40,20) using the definition of partial derivatives:

fv = ∂f/∂x ≈ (f(40+h,20) - f(40,20))/h

where h is a small increment in the x direction. Similarly,

ft = ∂f/∂y ≈ (f(40,20+k) - f(40,20))/k

where k is a small increment in the y direction.

To estimate fv(40,20) and ft(40,20), we need to choose small values of h and k and evaluate the function at the corresponding points. Let's say h = 0.1 and k = 0.05:

fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1

ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05

We can then use these estimates to approximate the value of f(40.1,20.05) using the first-order Taylor approximation:

f(40.1,20.05) ≈ f(40,20) + fv(40,20)0.1 + ft(40,20)0.05

Note that this is an approximation and may not be very accurate if the function is highly nonlinear or has discontinuities. However, it can give us a rough idea of the value of f(40,20) and how it changes with small variations in x and y.

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He needs an additional $0.23 to buy the football with the coupon after the discount coupon.

A discount is a reduction in the price of a product or service. It is often used as a marketing tool to attract customers and increase sales. Discounts can be expressed as a percentage or a dollar amount.

The discounted price is the price of a product or service after a discount has been applied. The discount is usually expressed as a percentage or a dollar amount and is subtracted from the original price.

In the given question,

The discount Justin can get is 12% of the original price, which is:

0.12 x 22.99 = 2.76

So the discounted price of the football is:

22.99 - 2.76 = 20.23

Since Justin has exactly $20, he doesn't have enough money to buy the football with the coupon. He needs:

20.23 - 20 = 0.23

So he needs an additional $0.23 to buy the football with the coupon.

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Men will have completed oil changes in hours Therefore, Will and Gabriel will each have done 12 oil changes after 4 hours.

Hours is a unit of time measurement. It is used to measure a specific amount of time and is usually denoted by the symbol “h”. There are 24 hours in a day, 60 minutes in an hour and 60 seconds in a minute. Hours are used to measure both short and long periods of time. Commonly, hours are used to measure the length of a workday, the length of a school day, or the length of a movie. Hours are also used to measure how long a person has been alive, how long an event has been going on, or how long an item has been in use.

Let W be the total number of oil changes Will has completed, and G be the total number of oil changes Gabriel has completed.

System of equations:

W = 8 + 2t

G = 3t

Since they will be tied at some point during the day, W = G.

Substituting W into G's equation:

8 + 2t = 3t

Solving for t:

2t = 8

t = 4

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The best interpretation of the interval is: We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Option D is correct

A confidence interval is a measure of how accurately an estimate (such as the sample average) corresponds to the actual population parameter. It is a range of values that the researcher believes is very likely to include the actual value of the population parameter.

Here, a 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Thus, we can say that we are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Therefore, option D is correct.

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Answer: mean-16.75

population size- 4

Step-by-step explanation:

To calculate the monthly periodic interest rate from an annual percentage rate (APR), we need to divide the APR by 12 (the number of months in a year). We can use the following formula:

Monthly periodic interest rate = APR / 12

In this case, the APR is 16.75%, so we can plug it into the formula and simplify:

Monthly periodic interest rate = 16.75% / 12

Monthly periodic interest rate = 1.395833...%

Rounding to the nearest hundredth of a percent, we get:

Monthly periodic interest rate = 1.40%

Therefore, the monthly periodic interest rate for the primary credit card holder is 1.40%.

The linear function rule to model the cost y for any number of samples x is (y = x + 2.25) and this can be determined by forming the linear equation.

An international food festival charges for admission and for each sample of food.

Admission and 6 samples cost $8.25.

Admission and 8 samples cost $10.25.

The following steps can be used in order to determine the linear function rule to model the cost y for any number of samples x:

Step 1 - The linear equation is formed in order to determine the linear function.

Step 2 - The linear equation that represents the situation "admission and 6 samples cost $8.25" is:

8.25 - 6c = d   --- (1)

Step 3 - The linear equation that represents the situation "admission and 8 samples cost $10.25" is:

10.25 = 8c + d    --- (2)

Step 4 - Substitute the value of 'd' in equation (2).

10.25 = 8c + 8.25 - 6c

2 = 2c

c = 1

Step 5 - Substitute the value of 'c' in the equation (1).

d = 8.25 - 6

d = 2.25

Step 6 - So, the linear function rule to model the cost y for any number of samples x is:

y = x + 2.25.

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Answer:

f(x) = (x + 5)² + 3

Step-by-step explanation:

f(x) = x² + 10x + 28

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 10x

f(x) = x² + 2(5)x + 25 - 25 + 28

     = (x + 5)² + 3 ← in vertex form

In the question given, The inequality will be h₂< h₁<h₃. Thus, Daniel is tallest.

In Mathematics, Inequality defines the relationship between two values that are not equal. When two values are not equal, we use “not equal sign (≠)”. But if there is a comparison between two values, whether it is less than or greater than, different inequalities are used. For example 5<7 , 8>4.

The following problem is to model an inequality situation.

Given that ,

Najid is taller than Emily and shorter than Daniel.

 Let, height of Najid is h₁

         height of Emily is h₂

  and height of Daniel is h₃

By the condition h₁>h₂ and h₁< h₃

Combining both the statement we have the inequality

              h₂< h₁<h₃

From this inequality we have the person having h₃ height is tallest.

Hence, Daniel is tallest.

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In the given triangle, the value of x = 5.

What is a triangle's definition?

A triangle is a geometrical shape that is defined as a polygon with three sides and three angles. It is a closed figure with three line segments as its sides, and these sides intersect at three points, which are called vertices. When we add all the angles of a triangle then the result will always be 180°.

Now,

As we know the property of a triangle that

sum of all angles of triangle=180°

given angles are (9x-1)°, 74° and 62°

then,

        9x-1+74+62=180°

9x+135=180

9x=45

x=5

Hence,

           the value of x is 5.

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Answer:  ^4√11^5 = 11^(5/4)

Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.

So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:

^4√11^5 = (11^5)^(1/4) = 11^(5/4)

Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.

Hope this helps, and have a great day!

Answer:

4m^2+15-5m

Step-by-step explanation:

Remove parentheses.

4m^2-5-5m+20

Collect like terms.

4m^2+(-5+20)-5m

Simplify

4m^2+15-5m

Answer:

Area: 81*pi

Circumference: 18*pi

Step-by-step explanation:

Area: 9^2= 81

So it would be 81*pi

Circumference: 9*2= 18

So it would be 18*pi

If you want the full area then it's 81*pi= 254.34

If you want the full circumference it's 18*pi= 56.55

Answer: 4y - (2/3)x + 20

Step-by-step explanation:

Write out problem: 4(y+5) - (2/3)x

Expand: 4y + 20 - (2/3)x

Reorder: 4y - (2/3)x + 20

The company's total income, expenditure and profit is given respectively as follows:

a.) £180

b.) £146

C.) £34

To calculate the profit of the company the formula such as given below is used.

Profit = total income - total expenditure

The total income = 25+20+35+100 = £180

The total expenditure = 110+20+6+10 = £146

Profit = 180-146 = £34

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The modular inverse of 11, modulo 1000 is 901. Expressing the answer in integer form.

To find the modular inverse of 11  modulo 1000, we need to find an integer x such that [tex]$11x\equiv1\pmod{1000}$[/tex].

One way to find the modular inverse is to use the extended Euclidean algorithm. Using this algorithm, we can find the greatest common divisor of 11 and 1000 and express it as a linear combination of 11 and 1000.

We can then use the coefficients of this linear combination to express 1 as a linear combination of 11 and 1000.

Applying the extended Euclidean algorithm, we have:

1000= 11 *90 + 10

11 = 10 *1 + 1

Working backward, we can express 1 as a linear combination of 11 and 1000:

1 =11 - 10* 1

= 11 - (1000 - 11*90)

= 901 * 11 - 1 *1000

Therefore, the modular inverse of 11 modulo 1000 is 901, since

11*901=1 mod{1000}.

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