All perfect squares are divisible by 2.
A.) true
B.) False, counterexample of 16
C.) False, counterexample of 15
D.) False, counterexample of 25

The quadratic equation with the roots  3+i and 3-i is:

x^2 - 6x + 10 = 0

We know that a quadratic equation with the roots a and b is written as:

(x - a)*(x - b) = 0

Here the roots are 3 + i, and 3 - i.

Replacing that we get:

(x - 3 - i)*(x - 3 + i) = 0

Expanding the product on the left we get:

x^2 + x*(-3) + x*i + (-3)*x + (-3)*(-3) + (-3)*i + (-i)*x + (-i)*(-3) - i^2 = 0

Remember that i^2 = -1, then:

x^2 -3x + x*i - 3x + 9 - 3i - x*i + 3i + 1 =0

x^2 - 6x + 10 = 0

That is the equation for the given roots.

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A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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The approximate probability that a student chooses a computer elective and an art elective is 0.22727.

To calculate the probability, we need to find the ratio of favorable outcomes (students choosing a computer elective and an art elective) to the total number of possible outcomes.

The number of computer electives is 5, and the number of art electives is 3. Since each student can choose two electives, we can calculate the total number of possible outcomes by multiplying the number of computer electives by the number of art electives:

Total number of possible outcomes = 5 * 3 = 15

The number of favorable outcomes is the number of ways a student can choose one computer elective and one art elective, which is the product of the number of computer electives and the number of art electives:

Number of favorable outcomes = 5 * 3 = 15

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 15 / 15

Probability = 1

However, it's important to note that the given options for the probability (0.11364, 0.21212, 0.22727, 0.42424) are all rounded approximations. Among these options, the closest approximate probability to the actual probability of 1 is 0.22727.

Therefore, the approximate probability that a student chooses a computer elective and an art elective is approximately 0.22727.

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Answer:

A = 125º

Step-by-step explanation:

Missing angle is the supplement of 157.5

180 - 157.5 = 22.5

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

Sum of angles in triangle is 180

22.5 + (-10x) + (-x + 20) = 180

Combine like terms

-11x + 42.5 = 180

Subtract 42.5 from both sides

-11x = 137.5

Divide both sides by -11

x = -12.5

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

A = -10(-12.5)

A = 125º

A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

Total amount of book in library are 2500 ,

Out of that 40% are fiction so the number of the non fiction books are 60%

so 60% of 2500 will give us the value of non fiction books,

Number of non fiction = 2500 x 60%

= 2500 x 60/100

= 25 x 60

= 1500

Therefore,  Number of non fiction books are 1500.

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Answer:

The difference between the area of the original triangle and the area of the new triangle is \(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\).

Step-by-step explanation:

The equation for the area of a triangle (\(A_{\bigtriangleup}\)) is:

\(A_{\bigtriangleup} = \frac{1}{2}\cdot b \cdot h\)

Where:

\(b\) - Base, dimensionless.

\(h\) - Height, dimensionless.

The expression for each triangle are described below:

First Triangle (\(b = 3\cdot x + 7\), \(h = 5\cdot x - 1\))

\(A_{\bigtriangleup,1} = \frac{1}{2}\cdot (3\cdot x+7)\cdot (5\cdot x -1)\)

Second Triangle (\(b = 3\cdot (3\cdot x+7)\), \(h = 2\cdot (5\cdot x -1)\))

\(A_{\bigtriangleup,2} = 3\cdot (3\cdot x+7)\cdot (5\cdot x -1)\)

The difference between the area of the original triangle and the area of the new triangle is:

\(\Delta A_{\bigtriangleup} = A_{\bigtriangleup,2}-A_{\bigtriangleup,1}\)

\(\Delta A_{\bigtriangleup} = 3\cdot (3\cdot x+7)\cdot (5\cdot x-1)-\frac{1}{2} \cdot (3\cdot x+7)\cdot (5\cdot x-1)\)

\(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\)

The difference between the area of the original triangle and the area of the new triangle is \(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\).

given events a and b are conditional independent events given c, with p(a ∩ b|c)=0.08 and p(a|c) = 0.4, find p(b | c) = 0.2.

By definition of conditional probability, we have:

p(a ∩ b | c) = p(a | c) * p(b | c)

Substituting the values given in the problem, we get:

0.08 = 0.4 * p(b | c)

Solving for p(b | c), we get:

p(b | c) = 0.08 / 0.4 = 0.2

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Answer:

sqrt(x)=x^1/2

Step-by-step explanation:

The root of a number is the same as writing that number to 1 over the root. In a square root, it is what number multiplied by itself (x*x), as you can see there are two, so it is that number to the 1/2 power. another example is something to the seventh power. that is calculating what number multiplied by itself 7 times would equal the nmber you are taking the root of. (x*x*x*x*x*x*x) so this would be a number to the 1/7 power.

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:

the curse of dimensionality

Step-by-step explanation:

the cause of dimensionality has to do with the different phenomena that comes up whenever data is to be analyzed or organized in high dimensional spaces which do not happen in low dimensional spaces. This curse can be explained simply as having error increase just as there are increases in the number of features. when the features we have is more than the observations, it could cause the model to be overfitted.

Answer:

That's not full question

Answer:

2 x ^2 − 2 x + 4 = 0

x ^2 − 2 x + 4 = 0

2 x ^2 − x = 0

Step-by-step explanation:

\(w(f(m(2))) = 593\)

We can write how \(w(f(m(x)))\) will be defined but that's too much work and it's only useful when we are evaluating \(w(f(m(x)))\) with many inputs.

First let's solve for \(m(2)\) first. As you read through this answer, you'll get the idea of what I'm doing.

Given:

\(m(x) = -4x +1\)

Solving for \(m(2)\):

\(m(2) = -4(2) +1 \\ m(2) = -8 +1 \\ m(2) = -7\)

Now we can solve for \(f(m(2))\), since \(m(2) = -7\), \(f(m(2)) = f(-7)\).

Given:

\(f(x)=3x-1\)

Solving for \(f(-7)\):

\(f(-7)=3(-7)-1 \\ f(-7) = -21 -1 \\ f(-7) = -22\)

Now we are can solve for \(w(-22)\). By now you should get the idea why \(w(f(m(2))) = w(-22)\).

Given:

\(w(x) = x^2 -5x -1\)

Solving for \(w(-22)\):

\(w(-22) = (-22)^2 -5(-22) -1 \\ w(-22) = 484 -5(-22) -1 \\ w(-22) = 484 +110 -1 \\ w(-22) = 593\)

The number of cups of bananas is represented by x

The number of cups of strawberries is represented by y

Note that:

27/5 cups of strawberry is used for 27/25 cups of banana

1 cup of strawberry is used for x cups of banana

x = 27/25 ÷ 27/5

x = 27/25 x 5/27

x = 1/5

1/5 cups of banana is used for 1 cup of strawberry

Comparing the values of x with values of y in the table and writing the relationship in the form y = kx:

y = 5x

where k = 5

The constant of proportionality = 5

Answer:

In the problem, the sum of the two functions is 2x + 2

Step-by-step explanation:

For this problem, we have to add together f(x) and g(x).

f(x) = 9 - 3x

g(x) = 5x - 7

(f + g)(x) = (9 - 3x) + (5x - 7)

Combine like terms.

(f + g)(x) = 2x + 2

So, when you combine the two functions together, you will get 2x + 2.

The value of f(x)+g(x) according to the question given is; 2x + 2.

To evaluate the sum of functions f(x) and g(x); we have;

Therefore;

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The correct option regarding the scale factor and the statement in this problem is given as follows:

D. The statement is false. Because there are 3 feet in one​ yard, there are 9 square feet in one square yard.

The scale factor between the length dimensions of the yard are given as follows:

3 feet = 1 yard.

(as these length dimensions are given in yards).

Then for the square units, the correct scale factor is found applying the proportion as follows:

(3 feet)² = (1 yard)².

9 feet squared = 1 square yard.

Hence the statement given in this problem, that because there are 3 feet in one​ yard, there are also 3 square feet in one square yard, is false, and the correct option is given by option D.

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Answer:

x = 8, y = 13

Step-by-step explanation:

Me disculpo de antemano por cualquier error de idioma, ya que estoy usando un traductor.

Como ya tenemos "y" en la primera ecuación, simplemente necesitamos usarlo como sustituto en la segunda ecuación.

x + ( x + 5 ) = 21

2x + 5 (-5) = 21 (-5)

2x = 16

x = 8

Entonces podemos usar el valor de "x" en la primera ecuación para encontrar "y".

y = (8) + 5

y = 13

The lower cost will occur at the extreme point, that is if the number of videos rented daily is 8 pieces and the cost will be $550.

The cost function is given by:

C(x) = 2x² - 32x + 678

The lowest cost happens at the extreme point. In this point the derivative of C(x) is equal to zero.

Take the derivative:

C'(x) = 4x - 32 = 0

4x = 32

x = 32/4 = 8

Hence, the lowest cost will occur if the number of video rented daily is 8 pcs.

Substitute x = 8 into the cost function:

C(8) = 2(8)² - 32.(8) + 678 =  550

Complete question:

The owner of a video store has determined that the cost c, C(x) = 2x² - 32x + 678 in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar

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Answer:

Less than symbol (<)

Step-by-step explanation:

For example:

A set of numbers that are in ascending order

1<2<3<4<5<6<7<8<9<10

The less than symbol is used to denote the increasing order.

Hope this helps

Answer:

\(x = 2~\text{and} ~x = -3\)

Step-by-step explanation:

\(~~~~~~f(x) = g(x)\\\\\implies -x +4 =x^2 -2\\\\\implies x^2 -2+x -4=0\\\\\implies x^2 +x -6 = 0\\\\\implies x^2 +3x -2x -6 =0\\\\\implies x(x+3) - 2(x+3) = 0\\\\\implies (x-2)(x+3) = 0\\\\\implies x = 2,~ x = -3\)

Answer:

x = -3 and x = 2

Step-by-step explanation:

Plotting the graphs :

f(x)

⇒ Find two points (preferably the x and y intercepts)

⇒ 0 = -x + 4

⇒ x = 4

⇒ Point 1 : (4, 0)

⇒ f(x) = 0 + 4

⇒ f(x) = 4

⇒ Point 2 : (0, 4)

g(x)

⇒ g(x) = 0 - 2

⇒ g(x) = -2

⇒ Point 1 : (0, -2)

⇒ g(x) = 2² - 2

⇒ g(x) = 2

⇒ Point 2 : (2, 2)

* Graph with both functions is attached below *

=============================================================

Finding the solutions :

⇒ Equate f(x) and g(x)

⇒ -x + 4 = x² - 2

⇒ x² + x - 6 = 0

⇒ x² + 3x - 2x - 6 = 0

⇒ (x + 3)(x - 2) = 0

⇒ x = -3 and x = 2

Answer:

2 to the third power is 8 and 1 to the third power is 1 answer=1/8

Step-by-step explanation:

The value of the angle A from the calculation is 27 degrees.

The solving of a triangle refers to the process of finding the unknown sides, angles, or other measurements of a triangle based on the given information. The given information can include known side lengths, angle measures, or a combination of both.

The process of solving a triangle typically involves using various geometric properties, trigonometric functions, and triangle-solving techniques such as the Law of Sines, Law of Cosines, and the Pythagorean theorem.

Using the cosine rule;

\(a^2 = b^2 + c^2 - 2bcCos A\\7^2 = 12^2 + 15^2 - (2 * 12 * 15)Cos A\)

49 = 144 + 225 - 360CosA

49 - (144 + 225) = - 360 CosA

A = Cos-1[49 - (144 + 225) /-360]

A = 27 degrees

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Answer:

a = 3
h = 1
k = 5

Step-by-step explanation:

Based on the information provided, we have two given values for x: 14 and 15. The range of values for x can be expressed as [14, 15].

However, you also mentioned the value "1620". If this is intended to be part of the range for x, please provide additional clarification or context.

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The correct answer is: 4.75; a puppy who is just born is predicted to weigh 4.75 ounces.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The equation of the line of fit is w = 4.75 + 0.5d, where w is the weight of the puppy in ounces and d is the age of the puppy in days.

The w-intercept of the line of fit is the value of w when d = 0, that is, the predicted weight of a puppy when it is just born.

From the equation, we see that when d = 0, we have:

w = 4.75 + 0.5(0) = 4.75

Therefore, the w-intercept of the line of fit is 4.75 ounces, and its meaning in terms of the scenario is that a puppy who is just born is predicted to weigh 4.75 ounces.

So, the correct answer is: 4.75; a puppy who is just born is predicted to weigh 4.75 ounces.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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The coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

The given parameters are

Number of pen = 2

Unit price = $2

This means that the total amount spent is

Total amount = Number of pen * Unit price

Evaluate the product

Total amount = 2 * 2

Evaluate the product

Total amount = 4

So, the coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

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