Please write your own linear equation of any form.

A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately.

Because the equation is not in the form of y = a x . So, it does not represent direct variation.

Hence, a sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately.

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Answer:

Our problem is \(x^2-2x+6=0\), but as we can see, we are unable to factor. We have to use the quadratic equation to solve.

\(x^2-2x+6=0\)

\(\frac{-b+-\sqrt{b^2-4ac}}{2a}\)

Positive Quadratic Formula:

\(\frac{-(-2)+\sqrt{(-2)^2-4(1)(6)}}{2(1)}\)

\(=\frac{2+\sqrt{4-24}}{2}\\=1+\frac{\sqrt{-20}}{2}\)

Negative Quadratic Formula:

\(\frac{-(-2)-\sqrt{(-2)^2-4(1)(6)}}{2(1)}\)

\(=\frac{2-\sqrt{4-24}}{2}\\=1-\frac{\sqrt{-20}}{2}\)

Since both of our answers are the square root of a negative number, we know that the quadratic equation has no real solution.

*We could have also used the Discriminant Test to determine whether the quadratic equation has real roots or not. However, for our means, the quadratic equation seems enough.

Answer:

D. No real Solution

Step-by-step explanation:

Hello!

Let's use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

In our equation:

This comes from the standard form of a quadratic: \(ax^2 + bx + c\)

Now, solve:

Since the radicand (-5) is negative, there are no real solutions. The correct answer is Option D.

Answer:

The type of number that represents -4/2 is:

Choice B) Integer

Choice C) Rational

Step-by-step explanation:

The number -4/2 is an integer because it represents a whole number (-2) and it is also a rational number because it can be expressed as a fraction of two integers.

-4/2 is an :

Solution:

Before we make any decisions about the type of number -4/2 is, let's simplify it first.

It's the same as -2. Now, let's familiarize ourselves with the sets of numbers out there. Where does -2 fit in?

______________

This set incorporates only positive numbers and zero. So -2 doesn't belong here.

This set incorporates whole numbers and negative numbers. So -2 belongs here.

This set has integers, fractions, and decimals. So -2 does belong here too.

This is a set for numbers that cannot be written in fraction form (a/b, where b ≠ 0). So -2 doesn't belong here.

-4/2 belongs in the integer and rationals set.

Answer:

It is 5mmxb3m

Step-by-step explanation:

It is what it is

An equation to model the price based on the size of the pack. Let t be the number of tomatoes. Let p be the price per pack is p=0.25*t.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units. What can units and values be?

Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value. While solving a problem using the unitary method, it is important to recognize the units and values.

Cherry tomatoes are old at the store. A 12-pack cost $3, a 16-pack cost $4, and a 24-pack cost $6.

let

Where t represents the number of tomatoes, and p represents the price per pack. The terms in the equation represent the cost per tomato for each pack size.

we know that.

pack 12 costs ⇒ $3

1 pack ⇒ x

x=\(\frac{3}{12}\)

x=$0.25 (cost of one tomatoes)

An equation for the function

p=0.25*t

Therefore, the answer is p=0.25*t.

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Answer:

Top one is A, then false, then C

Step-by-step explanation:

Ez

Answer:

26.411

Step-by-step explanation:

In 3a+bc-c you have to substitute

a=8.6, b=2.3, c=0.47

3*8.6 + 2.3*0.47 - 0.47 first do the multiplication then addition and subtraction

25.8 + 1.081 - 0.47=

26.411

Answer:

54π

Step-by-step explanation:

To find the volume of the cylinder, you will be using V=π(r^2)h

r = radius = 3

h = height = 6

V = π(3^2)(6) = 54π

The bracket means to multiply.

Answer:

54

Step-by-step explanation:

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Answer:

7. Dr. Agoncillo completed a total of 14 years of post-secondary education. (4 years undergrad + 4 years medical school + 5 years residency + 1 year fellowship = 14 years)

8. Dan consumed a total of 124 fluid ounces. (2 x 20 + 3 x 16 + 1 x 32 = 40 + 48 + 32 = 120 fluid ounces)

9. There are 175 ACE wraps in stock at this physical therapy clinic. (27 x 2 + 43 x 1 + 93 x 1 + 12 x 1 = 54 + 43 + 93 + 12 = 175 ACE wraps)

10. Karen consumed a total of 67 grams of sugar, 19 grams of fat, and 5 grams of protein in this snack. (Snickers: 20g sugar + 11g fat + 3g protein = 34g total; Doritos: 1g sugar + 8g fat + 2g protein = 11g total; Mt. Dew: 46g sugar + 0g fat + 0g protein = 46g total; 34g + 11g + 46g = 91g total sugar; 11g + 0g + 0g = 11g total fat; 3g + 2g + 0g = 5g total protein)

Step-by-step explanation:

Mark Brainliest!!

Answer:

C, the third choice

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

B...............................

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The statement about rectangles and rhombuses that is always true is that both figures are quadrilaterals.

A quadrilateral is a closed, two-dimensional shape which has four straight sides.

In other word, a quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

Quadrilateral has four sides.

Rhombuses and rectangles have four sides. Therefore, they are both quadrilaterals.

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The statement follows by induction, and T(n) = n log n when n = 2k for some positive integer k.

To prove that T(n) = n log n using induction, we will follow these steps:

Base case: Show that the statement holds true for the smallest possible value of n (n = 2).
Inductive hypothesis: Assume the statement is true for some arbitrary positive integer k (n = 2k).
Inductive step: Prove that the statement is true for n = 2(k+1) using the inductive hypothesis.

Base case
Given that T(n) = 2 when n = 2, we can verify that T(2) = 2 log 2:

T(2) = 2
2 = 2 * log_2(2)
2 = 2 * 1
2 = 2

Thus, the base case holds true.

Inductive hypothesis
Assume T(n) = n log n for n = 2k, where k is a positive integer.

Now, we will prove that T(2(k+1)) = 2(k+1) log(2(k+1)).

Using the given equation T(n) = 2T(n/2) + n, we have:

T(2(k+1)) = 2T((2(k+1))/2) + 2(k+1)

T(2(k+1)) = 2T(k+1) + 2k + 2

Now, we apply the inductive hypothesis to T(k+1), so T(k+1) = (k+1) log(k+1):

T(2(k+1)) = 2((k+1) log(k+1)) + 2k + 2

T(2(k+1)) = 2(k+1) log(k+1) + 2k + 2

Now, we need to show that this expression is equal to 2(k+1) log(2(k+1)):

2(k+1) log(2(k+1)) = 2(k+1) log(2) + 2(k+1) log(k+1)

Since log(2) = 1:

2(k+1) log(2(k+1)) = 2(k+1) + 2(k+1) log(k+1)

Comparing this expression to our previous result:

T(2(k+1)) = 2(k+1) log(k+1) + 2k + 2

We can see that both expressions are equal. Therefore, the statement follows by induction, and T(n) = n log n when n = 2k for some positive integer k.

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By the principle of mathematical induction, the statement T(n) = n log n is true for all positive integers n = 2, 4, 6, ..., 2k, 2k+1, ....

To prove T(n) = n log n using induction, we need to show that the statement is true for the base case (n = 2) and that if it is true for n = 2k, then it is also true for n = 2k+1.

Base case: n = 2

T(2) = 2

2 log 2 = 2

The statement is true for n = 2.

Inductive step: Assume that the statement is true for n = 2k. That is, T(2k) = 2k log 2k.

We need to show that the statement is also true for n = 2k+1. That is, T(2k+1) = (2k+1) log (2k+1).

T(2k+1) = 2T((2k+1)/2) + (2k+1)

= 2T(k+1/2) + (2k+1)

= 2((k+1/2) log (k+1/2)) + (2k+1)

= (k+1) log (k+1) + (2k+1)

= k log (2k) + log (k+1) + 2k + 1

= (k+1) log (2k+2)

= (2k+1) log (2k+1)

Therefore, the statement is true for n = 2k+1.

By the principle of mathematical induction, the statement T(n) = n log n is true for all positive integers n = 2, 4, 6, ..., 2k, 2k+1, ....

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False. A probability distribution for a discrete variable is not exclusive, collectively exhaustive list of numerical outcomes for that variable and the probability of occurrence associated with each outcome.

A probability distribution for a discrete variable is a list of all possible values that the variable can take on, along with the probability of each value occurring. The values must be collectively exhaustive (meaning they include all possible outcomes) and mutually exclusive (meaning that each outcome cannot occur at the same time as any other outcome). However, the numerical outcomes do not have to be exclusive, as they can have the same probability of occurring. For example, a coin toss has two possible outcomes (heads and tails) with equal probability, and a dice roll has six possible outcomes with equal probability. These probabilities can be represented using a probability distribution.

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The fourth quadrant, often known as Quadrant IV, is the bottom right quadrant. The x-axis in this quadrant is positive, whereas the y-axis is negative.

Two-dimensional Cartesian axes separate the plane into four infinite areas known as quadrants, each of which is bordered by two half-axes. These are frequently numbered 1 through 4.

90° arc; one-fourth of a circle. the region enclosed by such an arc and two sketched radii, one at each extreme. a component of a machine that has a quarter-circle form.

The x- and y-coordinates are both positive in quadrant I.

The x-coordinate is negative and the y-coordinate is positive in quadrant II.

The x- and y-coordinates are positive in quadrant III.

Quadrant IV: The x-coordinate is positive and the y-coordinate is negative.

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There is no solution in this case. Finally, we write the solution set as:1 < x < 6

Given quadratic inequality is x² - 7x + 6 ≤ 0To find: solution set for this inequality.

The quadratic expression can be factorized as follows:x² - 7x + 6 = (x - 1)(x - 6)Now, the quadratic inequality can be written as:

(x - 1)(x - 6) ≤ 0

The product of two factors is less than or equal to zero only when one factor is positive and the other factor is negative.  

So, we consider two cases:

Case 1: (x - 1) > 0 and (x - 6) < 0

In this case, x > 1 and x < 6. But the inequality (x - 1) > 0 is redundant because it is already implied in (x - 6) < 0.

So, the solution is 1 < x < 6.Case 2: (x - 1) < 0 and (x - 6) > 0In this case, x < 1 and x > 6. But the inequality (x - 6) > 0 is redundant because it is already implied in (x - 1) < 0.

Therefore, there is no solution in this case. Finally, we write the solution set as:1 < x < 6

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Answer:

6037.2 pounds of bamboo shoots does the female panda eat.

Step-by-step explanation:

Total pandas = 3

Total bamboo shoots eaten = 18112 pounds

Let baby panda eats bamboo = x

Male panda eats bamboo= 3x

Female panda eats bamboo = 2x

So, the equation will become

\(x+3x+2x=18112\)

Now solving the equation to find value of x

\(x+3x+2x=18112\\6x=18112\\x=\frac{18112}{6}\\x=3018.6\)

The value of x we get : x=3018.6

So, baby panda eats bamboo shoots = 3018.6 pounds

Male panda eats bamboo shoots = 3x = 3(3018.6) = 9055.8 pounds

Female panda eats bamboo shoots = 2x = 2(3018.6)= 6037.2 pounds

So, 6037.2 pounds of bamboo shoots does the female panda eat.

The standard deviation and proportion value is obtained as 0.02 and 0.05 respectively.

What is standard deviation?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

To find the standard deviation of the sample proportion, we can use the formula -

σp = √(p(1-p)/n)

where p is the population proportion (0.045) and n is the sample size (400).

σp = √(0.045(1-0.045)/400) ≈ 0.0208

To find the value of p that corresponds to a 40% chance of the sample proportion being no greater than that value, we can use the z-score formula -

z = (\(\hat{\rho}\) - p) / σp

where \(\hat{\rho}\) is the sample proportion and p is the population proportion.

For a 40% chance, the corresponding z-score is 0.25 (since 0.40 is halfway between 0.25 and 0.50 on the standard normal distribution).

So we have -

0.25 = (\(\hat{\rho}\) - 0.045) / 0.0208

\(\hat{\rho}\) - 0.045 = 0.0208 × 0.25

\(\hat{\rho}\) ≈ 0.0517

Therefore, the value of p is 0.05, and the value of σp is 0.02.

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Answer:

The slope of line m can be found using the slope formula:

m = (y2 - y1)/(x2 - x1)

m = (1 - 3)/(5 - (-2))

m = (-2)/(7)

m = -0.286

To find the slope of a line perpendicular to line m, we need to take the negative reciprocal of m:

slope = -1/m

slope = -1/(-0.286)

slope = 3.496

Therefore, the slope of a line perpendicular to line m is 3.496.

Answer:

Step-by-step explanation:

Marsha's family traveled 3/10 of the distance to her aunt's house on Saturday.

Remaining distance is:

They traveled 3/7 of the remaining distance on Sunday, which is:

Answer:

  53.52°

Step-by-step explanation:

The cosine function relates the angle to the sides shown:

  Cos = Adjacent/Hypotenuse

  cos(x°) = (22 ft)/(37 ft) = 22/37

The inverse cosine function is used to find the corresponding angle.

  x° = arccos(22/37) ≈ 53.52°

Answer:

471

Step-by-step explanation:

741-270=471

In simplest form, 0.25 hour is equivalent to 15 minutes. So, the answer is 15 minutes. The correct answer is not provided in the options given.

To find out how long the students had to work on homework, we need to subtract the time Mr. K spent working problems on the board from the total length of the math class.

Mr. K's math class is 1 hour long. After spending 45 minutes on working problems on the board, he gave the rest of the class period to the students for homework.

To calculate the time the students had to work on homework, we can subtract the time Mr. K spent on the board from the total class period:

1 hour - 45 minutes

To subtract these times, we need to convert 45 minutes to hours. Since 1 hour is equal to 60 minutes, we can divide 45 minutes by 60 to get the fraction of an hour:

45 minutes / 60 minutes = 0.75 hour

Now we can subtract 0.75 hour from 1 hour to find the time the students had to work on homework:

1 hour - 0.75 hour = 0.25 hour

Therefore, the students had 0.25 hour to work on homework.

In simplest form, 0.25 hour is equivalent to 15 minutes. So, the answer is 15 minutes.

The correct answer is not provided in the options given.

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A study is designed to examine effect of exercise on knee pain, with measurements taken at 1, 3 and 6 weeks. The appropriate design would be C. two-way analysis of variance with one repeated measure.

A two-way mixed-design ANOVA with one repeated measure would be the best choice. This is so because exercise and time are the two variables being investigated. Exercise becomes a between-subjects factor when individuals are randomly assigned to circumstances that involve exercise or no exercise. The repetitive measure is due to the fact that each participant's measurements are collected after 1, 3, and 6 weeks, respectively.

The two-way ANOVA examines the primary impacts of time and exercise as well as their interactions. When there are both within-subjects and between-subjects variables, the mixed-design ANOVA is used. Because it combines autonomous and repetitive measures, it is known as a "mixed" measure. In this situation, leisure is the within-subjects component and exercise is the between-subjects factor.

Complete Question:

A study is designed to examine the effect of exercise (against no exercise) on knee pain, with measurements taken at 1 week, 3 weeks, and 6 weeks. Participants are randomly assigned to one of the exercise conditions. The appropriate design would be?

A. one-way repeated measures analysis of variance.

B. two-way analysis of variance.

C. two-way analysis of variance with one repeated measure.

D. one-way analysis of variance.

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Standard deviation - The value of x is 1.96.

What is standard normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

As given, for a standard normal distribution, 95% of the data points are contained in the interval [ -x , x ].

The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1. By transforming its values into z-scores, any normal distribution can be standardised. Z-scores indicate how far away from the mean each number is from.

Hence, from the standard normal table, the value of x = 1.96 for 95% confidence level.

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Answer:

c

Step-by-step explanaticcon: