The scale for Karima's drawing is 2 cm to 5 m. Explain what this means in your own words.

So the change of rate of x is -1/3 .

The Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given that object is decreasing at constant rate of 2 units per second so we have \(y = 2x^2 + 1\)

\(\frac{dy}{dt} = 4x \frac{dx}{dt}\)

given dy/dt = -2

when x = 3/2

-2 = 4(3/2) dx/dt

-2 = 6 dx/dt

dx/dt = -2/6

         = -1/3

Hence the change of rate of x is -1/3 .

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If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.

Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.

Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.

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Answer:x1=-2,x2=2

Step-by-step explanation:

Answer:

2.25

Step-by-step explanation:

(3^2•5^0/4)

9x1/4

9/4

2.25

find the area the get the premiraterStep-by-step explanation:add

Answer:

a) 1/8

b) 8

Step-by-step explanation:

a) 1/2 x 1/2 x 1/2 = 1/8

b) since the exponent is negative it becomes positive when placed in the denominator

so 1/2 ^-1 is equal to 1/1 ÷ 1/2 which is equal to 2

therefore, (1/2)^-3 is equal to 2 x 2 x 2 or 8

Answer:

60

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

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Answer: 4 side faces and one base faces I believe im sorry times a 100 if its wrong

Step-by-step explanation:

Answer:

Final amount = $5357.52

Step-by-step explanation:

Formula to be used,

Final amount = \(\text{Initial amount}\times (1+\frac{r}{n})^{nt}\)

Here, n = number of compounding in a year

t = Duration of investment

Now we substitute the given values in the question.

Final amount = \(1210(1+\frac{0.115}{12})^{12\times 13}\)

                      = \(1210(1.009583)^{156}\)

                      = 1210(4.4277)

                      = $5357.52

The equation that represent the average price of a house as a function of the year can be presented as follows;

The average of a value, such as the average price of a houses is the ratio between the sum of the prices of the houses to the number of houses.

The average cost of a family house in 1997 = $156,100

The average cost of the family house in 2010 = $254,400

The equation for the price (p) of a house as a function of the year, t where t = 0 corresponds to 1997, can be found as follows;

The slope of the equation is; (254,400 - 156,100)/(2010 - 1997) = 98300/13

98300/13 = 7561 7/13

The linear equation is therefore;
p - 156100 = (98300/13) × (t - 0)

p = (98300/13) × t + 156100

p = (7561 7/13) × t + 156100

The average price of a house today, 2023 can be found by plugging in the value, t = 2023 - 1997 = 26 in the above equation as follows;

p = (98300/13) × 26 + 156100 = 352,700

The price of a house today is $352,700

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If 74 amplifiers are sampled, the probability that the mean of the sample would differ from the population mean by less than 2.8 watts is approximately 0.

The question is asking for the probability that the mean of the sample would differ from the population mean by less than 2.8 watts. We are given that the mean output of the amplifier population is 321 watts with a variance of 144, and that 74 amplifiers are sampled.

To find the probability, we can use the standard deviation, which is the square root of the variance. Therefore, the standard deviation is √144 = 12 watts.

Since we are dealing with a sample mean, we can use the formula for the standard error of the mean, which is the standard deviation divided by the square root of the sample size. In this case, the sample size is 74.

The standard error of the mean is 12 / √74 ≈ 1.3922 watts.

To find the probability that the mean of the sample would differ from the population mean by less than 2.8 watts, we can use the standard normal distribution. We can calculate the z-score using the formula: (x - μ) / σ, where x is the difference in means (2.8 watts), μ is the population mean (321 watts), and σ is the standard error of the mean (1.3922 watts).

The z-score is (2.8 - 321) / 1.3922 ≈ -231.0971.

To find the probability, we need to find the area under the standard normal curve to the left of the z-score. Using a standard normal table or a calculator, the probability is essentially 0 (rounded to four decimal places).

Therefore, the probability that the mean of the sample would differ from the population mean by less than 2.8 watts is approximately 0.

Complete Question: The mean output of a certain type of amplifier is 321 watts with a variance of 144. If 74 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 2.8 watts? Round your answer to four decimal places.

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The answer is d. +0.5. A correlation coefficient of +0.5 provides the greatest risk reduction.

A correlation coefficient of +0.5 indicates a moderate positive correlation between two variables, meaning they are somewhat related. When two variables are moderately correlated, the risk reduction is greater than when they are not correlated at all (correlation coefficient of 0) or perfectly correlated (correlation coefficient of 1 or -1).

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Answer:

First three would all be correct

Step-by-step explanation:

mutually exclusive refers to two things that can occur but only result in one thing

(Think tossing a coin: can be heads or tails but it cannot be both)

In 609638400 ways eight men and five women can stand in a line so that no two women stand next to each other.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. There is no alternative way to organize the components of set A, as you can see.

In contrast to combination, where the order of the parts is irrelevant, permutation calls for a specific arrangement of the elements in many ways.

We genuinely wonder how the timetables of trains, buses, and airlines are set up in accordance with the convenience of the general population. Of course, the permutation is quite useful in planning the departure and arrival timetables for these.

How to solve?

For 8 men in a line: 8! = 40320  

In order to separate 2 women, we have to choose 5 out of 9

C(9,5) = 9! / 5!4! = 126

Random place 5 women in the 5 chosen places: 5! = 120

Total ways= 40320 * 126 * 120 = 609638400

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5400

4500 multiplied by 1.2

Answer:

The original price would be $5,625

Step-by-step explanation:

The formula to finding out the original price is -

OP = SP/1 - P

- OP = Original Price

- SP = Sale Price

- P = Percent Discount

Now just put in the respected values and you'll get -

OP = 4500/1 - 0.20

Now solve :D

OP = 4500/1 - 0.20

= 4500/0.8

= 5625

So the original price is $5,625

Hope this helped! :D

Answer:

Considering the sign behavior of each function and the angle and its multiples.

Step-by-step explanation:

1) Firstly, look at the Unit Circle below. In the Unit Circle we can with the aid of symmetry, find angles with the same height, and also the same angle value.

2) We need to remember or get to know the behavior of the trigonometric functions, in order to know whether it is positive or negative. Let's work with the tree basic ones: sine, cosine and tangent.

3) Let's take the 60º angle, to exemplify.

Symmetric angles have the same height proportional values for their angles.

Notice that the angle of 60º ∈ Quadrant II, and 120º ∈ Quadrant II and 240º for Quadrant III and 300º for Quadrant IV as well.

We can calculate their values, considering their sign behavior each quadrant for cosine function.

Similarly, for the sine function, don't forget to consider sign behavior for each quadrant

\(cos60^{\circ}=\frac{1}{2}\\cos 120^{\circ}= -cos60^{\circ}=-\frac{1}{2}\\cos 240 ^{\circ}=-cos60^{\circ}=-\frac{1}{2}\\cos 300^{\circ}= cos60^{\circ}=\frac{1}{2}\)

Similarly, for sine function, don't forget to considering sign behavior for each quadrant

\(sin 60^{\circ}=\frac{\sqrt{3}}{2} \\sin 120^{\circ}=sin 60^{\circ}=\frac{\sqrt{3}}{2} \\\\sin 240^{\circ} =-sin 60^{\circ}=\frac{-\sqrt{3}}{2} \\\\sin 300^{\circ} =-sin 60^{\circ}=\frac{-\sqrt{3}}{2}\)

And finally, for the tangent function

\(tan 60^{\circ}=\sqrt{3} \\tan 120^{\circ}=-tan 60^{\circ}=-\sqrt{3}\\tan 240^{\circ}=tan 60^{\circ}=\sqrt{3}\\tan 300^{\circ}=-tan 60^{\circ}=-\sqrt{3}\)

We can take advantage of symmetry in the determination of coordinates of points by using two orthogonal axes of symmetry and by establishing a consistent notation to identify each quadrant.

In somewhat intuitive words, a circle is a figure which have infinite axes of symmetry passing on its surface and though its center. Hence, the four quadrants are formed by two orthogonal axes of symmetry.

Now we must establish a notation to distinguish one quadrant from another. In this case we decided to use the well-known right-hand notation, in which each of the four quadrants is labeled counterclockwise.

This system allows to create a guide to determine where the point is:

In a nutshell, we can take advantage of symmetry in the determination of coordinates of points by using two orthogonal axes of symmetry and by establishing a consistent notation to identify each quadrant. \(\blacksquare\)

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Answer:

10

Step-by-step explanation:

yup that's all have sorry

since the population standard deviations (σ1 and σ2) are not provided, we cannot calculate the exact test statistic Z.

To test the null hypothesis H0: (μ1 - μ2) = 0 versus the alternative hypothesis Ha: (μ1 - μ2) ≠ 0, we can use a two-sample z-test. The test statistic is calculated as:

Z = (x bar1 - x bar2) / sqrt((σ1^2 / n1) + (σ2^2 / n2))

Where:
X bar1 and x bar2 are the sample means of the two groups,
σ1 and σ2 are the population standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.

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Answer:

y = 12 + 2x

Step-by-step explanation:

Given that :

Let number of butterflies = y

Number of moths = x

y = 12 more than twice the number of moths

y = 12 + 2x

Hence, the expression which relates the number of butterflies he has is :

y = 12 + 2x

Answer:

Alicia is 18

Step-by-step explanation:

14 + 16 + 18 = 48

Answer: 18

Step-by-step explanation:

Answer:

number of glasses he bought = 60

Step-by-step explanation:

Let the variable x represent the number of glasses he bought

Total cost of x glasses at Rs. 12 each = 12x

5 glasses broke so remaining number of glasses = x- 5

He sold this quantity of glasses for Rs. 16 each

Total sale price of (x - 5) glasses = 16(x - 5)

Total profit = Total sales - Total cost = 160

=> 16(x - 5) - 12x = 16

Expand brackets for 16(x - 5): 16x - 16 x 5 = 16x - 80

Therefore we get

16x - 80- 12x = 160

4x - 80 = 160

Add 80 on both sides:

4x -80 + 80  = 160 + 80

4x = 240

x = 240/4 = 60

There are 45 different ways in which two of them can be selected as the best students in the class.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations).

A k-combination of a set S is officially defined as a subset of S's k unique elements.

Total number of students = 10

Number of students to be selected = 2

No. of ways = 10C2

                   = (10*9)/2

                   = 5*9

                   = 45

Hence, there are 45 different ways in which two of them can be selected as the best students in the class.

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The smallest number a such that A + BB is regular for all B > a can be determined by finding the eigenvalues of the matrix A. The value of a will be greater than or equal to the largest eigenvalue of A.

A matrix A is regular if it is non-singular, meaning it has a non-zero determinant. We can consider the expression A + BB as a sum of two matrices. To ensure A + BB is regular for all B > a, we need to find the smallest value of a such that A + BB remains non-singular. One way to check for singularity is by examining the eigenvalues of the matrix A. If the eigenvalues of A are all positive, it means that A is positive definite and A + BB will remain non-singular for all B. In this case, the smallest number a can be taken as zero. However, if A has negative eigenvalues, we need to choose a value of a greater than or equal to the absolute value of the largest eigenvalue of A. This ensures that A + BB remains non-singular for all B > a.

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Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

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

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

Answer:

456748

Step-by-step explanation:

you 463uy2iuswhk then 13456

Answer:

1.)

Area = 144

Perimeter = 16

2.)

Area = 225

Perimeter = 16

3.)

Area = 2025

Perimeter = 28

4.)

Area = 576

Perimeter = 22

Step-by-step explanation:

Formula:

Area = w • w • l • l

Perimeter = w + w + l + l

1.) Area = 144; Perimeter = 16

w = 2

l = 6

Area = 2 • 2 • 6 • 6 = 144

Perimeter = 2 + 2 + 6 + 6 = 16

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

2.) Area = 225; Perimeter = 16

w = 3

l = 5

Area = 3 • 3 • 5 • 5 = 144

Perimeter = 3 + 3 + 5 + 5 = 16

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

3.) Area = 2025; Perimeter = 28

w = 9

l = 5

Area = 9 • 9 • 5 • 5 = 2025

Perimeter = 9 + 9 + 5 + 5 = 28

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

4.) Area = 576; Perimeter = 22

w = 3

l = 8

Area = 3 • 3 • 8 • 8 = 576

Perimeter = 3 + 3 + 8 + 8 = 22

Answer:

F

Step-by-step explanation:

the box plot is divided into quarters, the line on the end to 20 being 1/4th, the start of the box to the line in the box being another 1/4th, the middle line to the end of the box is another 1/4th, and the last line is the last 1/4th

 The puppy will weigh 61.9 pound at the end of four weeks as puppy gained 2.10 pond each week.

It is the degree of the pressure of gravity appearing on a body. The system for weight is given by: w = mg. As weight is a pressure its SI unit is likewise similar to that of pressure, SI unit of weight is Newton (N).

According to the question, puppy weighed 53.5 pound when alexi got it. Puppy gained 2.10 pound each week for four weeks.

So the weight puppy gained in four weeks can be calculated as :

2.10 *4 = 8.4

The puppy gained 8.40 pounds in 4 weeks and now the total weight of puupy after four weeks is 53.5 + 8.4 =61.9 pounds.

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