determine whether the following statements are true and give an explanation or counterexample. a. all polynomials are rational functions but not all rational functions are polynomials.

Answer:

7:8=14:16

Step-by-step explanation:

just did this problem in class

Answer:

Step-by-step explanation:

y - 6 ≥ -22

OR

y ≥ 16

Hope that helps!

Answer:

y = 63

Step-by-step explanation:

A straight line is equal to 180 degrees.

180 = 2y - 18 + y + 9

180 = 3y -9

189 = 3y

189/3

y = 63

Answer:

63

Step-by-step explanation:

2y-18+y+9=180 degrees

3y-9=180 degrees

3y=189 degrees

y=63 degrees

Answer:

I think it’s 61 degrees.

Step-by-step explanation:

Answer:

\(x=77\)

Step-by-step explanation:

103 -x + 2x = 180

Answer: -(1/4)

Step-by-step explanation:

2x-3/4=x-3/3

=>2x-x = -3/3 + 3/4

=> x =     (-12+9)  /12                   [Taking LCM and solving]

=> x= -3/12

=> x= -1/4                   [After simplifying]

Answer: x = -1/4

Step-by-step explanation:

2x− 4/3 =x− 3/3

​

Divide 3 by 3 to get 1.

2x− 3/4 =x−1

Subtract x from both sides.

2x− 3/4−x=−1

Combine 2x and −x to get x.

x− 3/4 =−1

Add 3/4 both sides.

x=−1+ 3/4

​

Convert −1 to fraction − 4/4

​

x=− 4/4 + 3/4

​

Since − 4/4 and  3/4

​

 have the same denominator, add them by adding their numerators.

x= -4 +3 /4

​

Add −4 and 3 to get −1.

x=− 1/4

​

We can evaluate this expression to get: P(18) ≈ 0.02906

What is probability?

Probability is a measure of the likelihood of an event occurring.

This problem can be solved using the binomial distribution, which describes the probability of getting a certain number of successes (in this case, correct answers) in a fixed number of independent trials (in this case, the 30 questions), where each trial has the same probability of success (in this case, 1/4 since there are 4 choices and only one is correct).

The probability of getting exactly k correct answers out of n questions is given by the binomial probability formula:

P(k) = (n choose k) * \(p^{k}\) * \((1-p)^{(n-k)}\)

where (n choose k) represents the number of ways to choose k items from a set of n items, and p is the probability of success on each trial.

In this case, n = 30, k = 18, and p = 1/4. Plugging these values into the formula, we get:

P(18) = (30 choose 18) * \((1/4)^{18}\) * \((3/4)^{12}\)

Using a calculator or statistical software, we can evaluate this expression to get:

P(18) ≈ 0.02906

Therefore, the answer is D) 0.02906.

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Answer:

y=-6

Step-by-step explanation:

this is because y equal to 7 is flat so for it to be parallel the other line also has to be flat so the line will be passing through the same y value for the entire time which is -6

Hopes this helps pleae mark brainliest

Number of students should be sampled to be within 0.5 drink of population mean with 95% probability is 617 students.

To determine the sample size required to estimate the population mean with a given level of precision, we can use the formula for the margin of error

Margin of error = Z × (standard deviation / sqrt(sample size))

where Z is the critical value of the standard normal distribution corresponding to the desired level of confidence. For a 95% confidence level, Z is 1.96.

We want the margin of error to be no more than 0.5 drinks, so we can set up the equation

0.5 = 1.96 × (6.3 / sqrt(sample size))

Solving for the sample size, we get

sqrt(sample size) = 1.96 × 6.3 / 0.5

sqrt(sample size) = 24.82

sample size = (24.82)^2

sample size = 617

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Answer:

The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are  obtuse, scalene, equilateral, isosceles etc.

An isosceles triangle is a triangle with two equal sides, the base angles of an isosceles triangle is equal.

Since ΔMNP is an isosceles triangle with MN = PN, then:

∠QMN = ∠QPN (base angles of an isosceles triangle are equal)

∠MNQ = ∠PNQ (NQ bisects ∠MNP producing two equal angles)

∠MQN = ∠PQN (right angles)

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The graph has a line with a slope of 1/2 beginning at the origin and extending as far as you like into the first quadrant.

Part A

4x10 – 64x2

= 4x2 * x8 – 4x2 * 16

= 4x2 * (x8 – 16) by distributive property

Part B

x8 is (x4)2 and 16 = 42 so a difference of squares is seen in the parentheses. The pattern a2 – b2 = (a + b)(a – b) can be used.

4x2 * (x8 – 16)

= 4x2 * (x4 + 4) * (x4 – 4)

x4 = (x2)2 and 4 = 22 so there is another difference of squares in the last factor. Use the pattern again.

= 4x2 * (x4 + 4) * (x2 + 2) * (x2 – 2)

Answer:

Below.

Step-by-step explanation:

The GCF = 4x^2

So its 4x^2(x^8 - 16)

This can be further factored

= 4x^2(x^4 - 4)(x^4 + 4)

= 4x^2(x^2 - 2)(x^2 + 2)(x^4 + 4)

Answer:

1 jacket  =  9 buttons

Step-by-step explanation:

45 ÷ 5 = 9

(-x - 8) - (-6x + 5)

open the parenthesis

-x - 8 + 6x - 5

Re-arrange

-x + 6x -8 -5

5x - 13

The activity ratio in the value stream measures the efficiency of the production process by evaluating the ratio of value-added activities to non-value-added activities.

The activity ratio is a performance metric used in value stream mapping, which is a lean management tool for analyzing and improving the flow of materials and information in a production process.

It focuses on distinguishing value-added activities, which directly contribute to meeting customer requirements, from non-value-added activities, which do not add value but consume resources and time.

By calculating the activity ratio, organizations can assess the proportion of time and resources spent on value-added activities versus non-value-added activities.

A higher activity ratio indicates that a greater portion of resources is dedicated to value-added activities, indicating improved efficiency and reduced waste.

Conversely, a lower activity ratio suggests a higher proportion of resources being utilized for non-value-added activities, indicating potential areas for improvement and waste reduction.

The activity ratio serves as a valuable diagnostic tool for organizations to identify process inefficiencies, bottlenecks, and areas for improvement. By analyzing the activity ratio, organizations can streamline their processes, eliminate waste, and optimize resource allocation to enhance overall productivity and customer value.

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There are an infinite number of planes that are orthogonal to a given plane in space, and this is due to the fact that a plane can be thought of as a flat surface that extends indefinitely in all directions.

Orthogonal Planes in Space: In three-dimensional space, a plane is said to be orthogonal to another plane if the two planes are perpendicular to each other, i.e., their normal vectors are perpendicular. Since the normal vectors of two orthogonal planes are perpendicular to each other, this means that the angle between them is equal to 90 degrees.

Given a plane in space, there are an infinite number of planes that are orthogonal to it. This is because a plane can be thought of as a flat surface that extends indefinitely in all directions.

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The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Step 1: Find the length of sequences A and B. If either of the sequences is less than 150, return "not possible" as it is too short to form a local alignment.

Step 2: Compute the Needleman-Wunsch (NW) score for the global alignment of sequences A and B.

Step 3: Compute the Smith-Waterman (SW) score for the local alignment of sequences A and B.

Step 4: Identify the optimal score from the SW score matrix. This score should be the maximum value in the matrix.

Step 5: Check if the optimal SW score is equal to the NW score. If they are equal, then the optimal global alignment is also an optimal local alignment. If they are not equal, then the optimal global alignment is not an optimal local alignment.

Return the appropriate result. A local alignment is optimal if its score is maximum among all possible local alignments of the sequences. A global alignment is optimal if its score is maximum among all possible global alignments of the sequences. Therefore, to check if an optimal global alignment is also an optimal local alignment, we need to compare their scores using the SW algorithm.

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Answer:

She plans to deposit money at a steady rate of $27.24 per week. We want to know how much money she'll have after 7 weeks. (27.24 x 7) - 23.34 = 167.34

Step-by-step explanation:

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

y >  6x -100  

Step-by-step explanation:

the slope intercept equation of the line is

y=mx+b

m is the slope = (y2-y1) / (x2-x1) so between the y-intercept (0,-100) and the given point (25, 50) we have m= -100-50/0-25 = -150/-25 = 6

y= 6x -100

now we have to figure the inequqlity part so take point (0, 0) that belongs to the solution and substitute in the equation

0 = 6*0 -100

0 = -100  for the equation to be true we have to make it 0 > -100, we also need to make it NOT greater or equal then because the line is doted not solid  so the inequality is

y >  6x -100  

Answer:

107126

Step-by-step explanation:

This is all direct proportions 133,922/23.09=5800

5800x18.47=107126

The $25,000 per month that Courtney's company is spending is its burn rate. Which is Option C) burn.

A burn rate is a metric that determines how quickly a startup or a new company spends its cash reserves until it reaches profitability, or the rate at which a business expends its venture capital to finance overhead prior to achieving profitability. The burn rate is determined by the difference between income and outflows.

Burn rate refers to the rate at which a company is spending its available capital or cash reserves before generating any revenue or reaching profitability. It is an important metric for startups and early-stage companies to track as it can indicate how long the company can continue to operate before it runs out of funds.

The following formula is used to calculate a company's burn rate:

Burn rate = Total expenditure / Time.

Hence, the answer is Option C) burn.

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The position function of a projectile fired vertically upward with a velocity of 96 ft/s can be represented by s(t) = -16t² + 96t, where s(t) is the height of the projectile at time t.

The position function s(t) = -16t² + 96t is derived from the kinematic equation for vertical motion, considering the initial velocity and the acceleration due to gravity.

The term -16t² represents the effect of gravity pulling the projectile downward, and the term 96t represents the initial upward velocity. By plugging in different values of t into the position function, we can calculate the height of the projectile at different time intervals during its flight.

The graph of the function s(t) represents the trajectory of the projectile.

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In both cases, the events are not mutually exclusive because they can both occur together.

1. For mutually exclusive events A and B, the Venn diagram would show that the sets A and B have no overlap. In this case, the probability of both A and B occurring at the same time is zero. Therefore, the probability of A or B occurring is simply the sum of their individual probabilities. Let's consider an example where A represents flipping a coin and getting heads, and B represents rolling a die and getting a 6. The probability of flipping heads is 1/2, and the probability of rolling a 6 is 1/6. Since the events are mutually exclusive, the probability of A or B is P(A) + P(B) = 1/2 + 1/6 = 4/6 = 2/3.

2. For non-mutually exclusive events A and B, the Venn diagram would show that there is an overlap between the sets A and B, indicating that they can occur together. In this case, the probability of A or B occurring would be the sum of their individual probabilities minus the probability of both A and B occurring. Let's consider an example where A represents drawing a red card from a deck of cards, and B represents drawing a heart. The probability of drawing a red card is 26/52 = 1/2, and the probability of drawing a heart is 13/52 = 1/4. Since there are 26 red cards and 13 hearts in a deck of 52 cards, the probability of both A and B occurring (drawing a red heart) is 13/52 = 1/4. Therefore, the probability of A or B is P(A) + P(B) - P(A and B) = 1/2 + 1/4 - 1/4 = 3/4.

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Answer:

A

Step-by-step explanation:

Edge

The probability of randomly selecting the chair and the ranking member is 1/105 or approximately 0.0095.

There are 15 members of the Senate Committee on Homeland Security and Governmental Affairs, two of whom are selected to serve as the committee chair and ranking member. Each member is equally likely to be chosen for either of these positions.

To begin, we must first determine the total number of ways two members can be selected from a committee of 15. This is calculated using the combination formula:

nCr = (n!)/((r!)(n-r)!)where n = 15 and r = 2.

Thus,

nC2 = (15!)/((2!)(15-2)!)

nC2 = (15x14)/(2x1)nC2

= 105

Now we must determine the probability of selecting one member to be the committee chair and the other to be the ranking member.

This is calculated as follows: P = 1/105 or approximately 0.0095. Hence, the probability of randomly selecting the chair and ranking member is 1/105 or approximately 0.0095.

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Answer:

The answer is 2.5 hours. That's how long it would take the train to travel 270 kilometers.

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The missing information for the SAS congruence theorem is given as follows:

B. SU = JL.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The congruent angles for this problem are given as follows:

<S and <J.

Hence the proportional side lengths are given as follows:

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