5.4 prove by induction on n that, for any real number x ≠ 1 and for integers n >0.
n
∑ x^I = 1 – x^(n+1) / 1 - x
i=0

Answer:

AB=14

Step-by-step explanation:

First you write the equation 2(2x-4)=28 because if b is the midpoint then AB is half of the line so you multiply that half by two the make it equal to the whole line.

Then you distribute the two and get 4x-8=28.

Then you add 8 to 28 and get 36.

Then you divide 36 by 4 because the 4 and x are being multiplied together so you have to divide to get them apart.

So then you get x=9 and you aren't done yet because you have to plug x into 2x-4.

So it is 2(9)-4 which is 18-4 which equals 14.

The statement ''If the order of the input numbers were altered or if we use a different algorithm, we will always end up with the same combination of numbers as answer.'' is false because the order of the input numbers and the choice of algorithm can indeed affect the resulting combination of numbers that maximizes the sum.

The maximum sum of a continuous subsequence within an array depends on the values and arrangement of the numbers.

Different orders of the input numbers can lead to different maximum sums and different combinations of numbers that achieve those sums.

Similarly, the choice of algorithm can also impact the result. Different algorithms may employ different strategies for finding the maximum sum subsequence, which can yield different combinations of numbers as the optimal solution.

Therefore, it is incorrect to claim that altering the order of input numbers or using a different algorithm will always result in the same combination of numbers as the answer.

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Answer:

24

Step-by-step explanation:

dont exaclty have an explanations - its just the calculations

The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

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Answer:

F

Step-by-step explanation:

H and J have slopes of 3, not -3, and G has an infinite slope, so it's F

Answer:

the answer to this question is 1/4

Answer:

jgcoyc9t9yf9ycrcuflc

Floridyne would use an equivalent unit labor of 166,340 unit to calculate the cost per equivalent unit for direct labor.

Under weighted average, we do not make distinction between started and finished and just finished. Thus we work with finished and ending WIP only:

Finished         162,000

Ending - WIP    6,200 ending at 70% complete

Equivalent units for labor = Finished + Percentage of completion ending units

= 162,000 + 6,200 x 70%

= 166,340

Therefore, he would use an equivalent unit labor of 166,340 unit to calculate the cost per equivalent unit for direct labor.

Missing word "Floridyne, Inc. manufactures mouthwash. They had no finished goods inventory at the beginning of 2019. They have only one processing department for this product. A review of the company’s inventory records shows the following: At the beginning of January 2019, Floridyne has 4,500 gallons of mouthwash in process. (costs $8,410 for materials, 1,663 for labor and 4,990 for overhead) During 2019, Floridyne finishes/transfers 162,000 gallons of mouthwash. On December 31, 2019, Floridyne has 6,200 gallons of mouthwash that is 70% complete. Direct materials are added half at the beginning of the process and half after the process is 60% complete. During 2019 $349,000 of direct materials and $92,500 of direct labor were added. Using the weighted average approach to process costing,"

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18x+48+32+12x

18x+80+12x

30x+80

that's 3 different expressions equivalent to the original

Answer:

You can first remove the parentheses to get 18x+48+32+12x

Then you can combine like terms to get 30x+48+32

Finally you can finish combining like terms to get 30x+80

You could also enter 10(3x+8) because of the distributive property.

Step-by-step explanation:

A different term for a quadratic function's zeros is "roots." The zeros or roots of a quadratic function are the points on the x-axis where the function meets or crosses it.

They stand in for the x values at which the quadratic function equals zero. Depending on the discriminant of the quadratic equation, the zeros or roots of a quadratic function can either be real or complex integers. The quadratic has two unique real roots if the discriminant is positive. The quadratic has a single real root, also referred to as a double root or repeating root, if the discriminant is zero. The quadratic has two complex roots that can be represented as a + bi if the discriminant is negative.

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Answer:

-2 6/7

Step-by-step explanation:

I hope that helps.

Answer:

Step-by-step explanation:

you cant divide fractions so you multiply the reciprocal so your answer would be

1 11/16

It took me 120 minutes to answer 25 questions. How long did each question take?

120/25 = 4.8 minutes per question

Answer:

Triangle Area = (1/2) * base * height

base = 2 * Area / height

base = (2 * 162) / 18

base = 324 / 18

base = 18 meters

Step-by-step explanation:

The answer that describes the polygon RSTU is as follows:

A quadrilateral is a polygon with 4 sides. Therefore, let's use the properties to find the name of the shape  RSTU as follows:

The polygon has 4 sides therefore, it is a quadrilateral.

The quadrilateral has opposite side parallel to each other. The opposite sides are RS and TU.

A trapezoid is a quadrilateral with only one pair of opposite side parallel to each other.

Therefore, the shapes that defines the polygon are as follows:

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Answer:

A) 3 times more apple juice is used than carrot juice aka 22 more millimeters

B) 66 millimeters

Step-by-step explanation :

3 : 1 : 2     aka     33 : 11 : 22

You have the ratio, so you just have to divide 33/3 and you know you have to multiply that awnser times the other ratios.

So...

33/3 = 11

3 x 11 = 33

1 x 11 = 11

2 x 11 = 22

So the ratio is 33 : 11 : 22

Then, A is asking you how much more apple juice than carrot juice, so subtract ( amount of apple juice - amount of carrot juice )

33 - 11 = 22 millimeters more apple juice than carrot juice

Then, B is asking you how much juice is there in total. So just add all the juices together....

33+22+11 = 66

So 66 milimeters of juice all together

(a) The apple juice is 22 ml more than the carrot juice.

(b) The total amount of the mixture is 66 ml.

Important information:

(a)

Let the quantity of Apple, carrot, and celery is 3x, x, 2x respectively.

\(3x=33\)

\(x=11\)

Difference between Apple and carrot juice is:

\(3x-x=2x\)

\(3x-x=2(11)\)

\(3x-x=22\)

Therefore, the apple juice is 22 ml more than the carrot juice.

(b)

The total amount of the mixture is:

\(3x+x+2x=6x\)

\(3x+x+2x=6(11)\)

\(3x+x+2x=66\)

Therefore, the total amount of the mixture is 66 ml.

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Answer:

728.307 is less than 729.07

Step-by-step explanation:

We can disregard the numbers after the decimal because 728 is less than 729.

Thus, the answer would be 728.307 is less than 729.07.

Hope this helps!!

Answer:

728.307 is less than 729.07

Step-by-step explanation:

might be wrong

Multiply each payout by the corresponding probability and take the total:

E[X] = 0×0.5 + 5×0.2 + 8×0.15 + 10×0.1 + 15×0.05 = 3.95

The expected value = 3.92

"It describes the average of a discrete set of variables based on their associated probabilities."

\(E(x)=\Sigma[ xP(x)]\)

Multiply each value of the random variable by its probability and add the products.

For given question,

We have been given a payout probability distribution.

We need to find the expected value of the winnings.

First we multiply each value of the random variable by its probability .

0 × 0.5 = 0

5 × 0.2 = 1

8 × 0.15 = 1.2

10 × 0.1 = 1

15 × 0.05 = 0.75

Now, we find the sum of above products.

0 + 1 + 1.2 + 1 + 0.75 = 3.95

By using the formula of expected value,

\(\Rightarrow E(x)=\Sigma[ xP(x)]\\\\\Rightarrow E(x)=3.92\)

Therefore, the expected value = 3.92

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y = 1/2x + 8



y = cx + 10

In the system of equations above, c is a constant. If

the system has no solution, what is the value of c?

so, y=y

this equation is indefinde when 1/2 - c= 0, there is not value for x that makes the equation true

so, the value of c =0.5

The PDA you provided has three transition rules.  The first rule says that if the current state is 0, the input symbol is 'a', and the top symbol on the stack is 'X', then push a new 'X' onto the stack and stay in state 0.

The second rule says that if the current state is 0, the input symbol is 'b', and the top symbol on the stack is 'X', then do nothing (i.e., don't push or pop any symbols), and transition to state 1.

The third rule says that if the current state is 1, the input symbol is 'b', and the top symbol on the stack is 'X', then pop the 'X' from the stack and stay in state 1.

Note that if the PDA reads any other input symbol than 'a' or 'b', it will get stuck in state 0 with 'X' on the top of the stack, since there are no rules for transitioning on any other input symbol.

In terms of the language recognized by this PDA, it appears that it can recognize strings of the form a^n b^n, where n is a non-negative integer.

To see why, suppose we have a string of the form a^n b^n. We can push n 'X' symbols onto the stack, and then for each 'a' we read, we push another 'X' onto the stack.

Once we have read all the 'a's, the stack will contain 2n 'X' symbols. Then, for each 'b' we read, we pop an 'X' from the stack.

If the input is indeed of the form a^n b^n, then we will end up with an empty stack at the end of the input, and we will be in state 1.

On the other hand, if the input is not of this form, then we will either get stuck in state 0, or we will end up in state 1 with some symbols left on the stack, indicating that the input is not in the language.

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Based on the given polygon, the true statement on the polygons is that Polygon A is similar to Polygon B because Polygon B is a rotation of Polygon A.

Polygon A is related to Polygon B because to create Polygon B, Polygon A was dilated.

When a polygon is dilated, it means that it is either made to be larger in size, or smaller in size. In this case, Polygon A was made to be larger in size to create polygon B.

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Answer:

2

Step-by-step explanation:

The area of the parallelogram in the diagram given is: 1,330 in.²

Area of a parallelogram = (base × height)

Given the following dimensions of the parallelogram:

Base = 38 in.

Height = 35 in.

Area of the parallelogram = 38 × 35

Area of the parallelogram = 1,330 in.²

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Answer:

90 gallons

Step-by-step explanation:

5 people at 9 minutes each = 45 minutes

2 gallons per minutes * 45 minutes

90 gallons

Answer:

90 Gallons

Step-by-step explanation:

So to start we know that

a. every 1 min = 2 gallons

b. 5 ppl shower for 9 minutes each (on average)

so we can solve we multiplying amt. of ppl showering and the mins. they shower which is 5 and 9 respectively => and we get 45 minutes taken.

We know that each minute equals 2 gallons so we simply multiply 45 and 2 = 90 => and thus, we have our answer of 90 gallons.

Hope this helps!

The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.

To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:

Given:

u = 4i - 6j

v = 5i + 4j

Step 1: Calculate the dot product of u and v.

The dot product of two vectors u and v is given by:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.

To calculate the dot product, we multiply the corresponding components of u and v and sum them:

u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4

Step 2: Calculate the magnitudes of vectors u and v.

The magnitude of a vector is given by:

|u| = √(u₁² + u₂²)

For vector u:

|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21

For vector v:

|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40

Step 3: Calculate the angle θ.

Using the dot product formula mentioned earlier, we have:

-4 = (7.21)(6.40)cosθ

Solving for cosθ:

cosθ = -4 / (7.21 * 6.40) ≈ -0.086

To find θ, we can take the inverse cosine (arccos) of cosθ:

θ ≈ arccos(-0.086) ≈ 1.66 radians

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The first three non-zero terms of the series for e^(2x) cos(3x) are 1 + 2x + 2\(x^{2}\)

To find the terms of the series, we can expand the exponential function and the cosine function separately using their respective power series representations.

The power series expansion of e^(2x) is given by the sum of (2x)^n/n!, where n ranges from 0 to infinity. The first three terms of this expansion are 1 + 2x + 2x^2.

The power series expansion of cos(3x) is given by the sum of (-1)^n(3x)^(2n)/(2n)!, where n ranges from 0 to infinity. However, since the cosine function is an even function, only even powers of x contribute non-zero terms. Therefore, the first non-zero term is 1, followed by -9x^2/2.

Multiplying the corresponding terms of the two expansions, we obtain the first three non-zero terms of the series for e^(2x) cos(3x) as 1 + 2x + 2x^2.

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Answer:

1/6 feet/second

Step-by-step explanation:

The total feet traveled would be 40 feet. The seconds would be 240 giving 40/240 feet/second. Simplify this by dividing 40 by 240 giving an answer of 1/6. This makes the average speed 1/6 feet/second. Alternatly it would be 10 feet/minute