A square rug has an inner square in the center. The side length of the inner square is x inches, and the width of the outer region is 3 in. What is the area of the outer part of the​ rug?

The number of three-digit numbers less than $500 that cab be formed is 90.

The formation of the numbers involves the permutation of the first three even digits. Also, permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear.

The sequence include the following:  $1$, $2$, $3$, $4$, $5$,

The number must be less than $500$.

In order to find the number of even digits numbers to be fixed, we select the even numbers.

So, the number of possible arrangements = [tex]6_{P_{2} }[/tex]

[tex]\frac{6!}{(6-2)!}[/tex]

=[tex]\frac{6*5*4*3*2*1}{4*3*2*1}[/tex]

6*5

=30

Similarly, fixing the units digit as 4

The number pf possible arrangements =    [tex]6_{P_{2} }[/tex]

=6*5=30

Fixing the unit digit as 6

The number of arrangements possible is [tex]6_{P_{2} }[/tex]

5*6 = 30

Therefore three-digit even numbers  that can be formed is:

30+30+30=90

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If new data will be collected (i.e., primary data collection), the researcher can easily recruit an adequate number of participants is false.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given,

We need to check whether if new data will be collected (i.e., primary data collection), the researcher can easily recruit an adequate number of participants is true or false.

The given statement is false because Primary data collection is a process of collecting original data, directly from the source.

Hence, if new data will be collected (i.e., primary data collection), the researcher can easily recruit an adequate number of participants is false.

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Answer:

Line A

Step-by-step explanation:

The slope of 2x is a positive slope so it can't be line d(which is negative) or line c(which is horizontal).

That leaves us with lines a and b. 2x is a steep slope and line a has a steep slope while line b has a shallow slope so it is line a.

As movie ticket prices rise, demand decreases or declines. When the cost of the neighborhood Internet service provider rises, demand likewise decreases. Demand decreases as cappuccino prices rise.

Demand is the quantity of things that consumers are willing and able to purchase at various prices within a specific time frame. The term "demand curve" refers to the relationship between price and quantity demanded. Demand is just a consumer's desire to buy products and services immediately and to pay the price associated with them. Demand can be defined as the quantity of things that consumers are prepared and willing to purchase at various prices within a specific time frame.

Given,

As movie ticket prices rise, demand decreases or declines.

When the cost of the neighborhood Internet service provider rises, demand likewise decreases.

Demand decreases as cappuccino prices rise.

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A complex number is represented as a + bi, where a denotes the real part and bi denotes the imaginary part, to represent it in standard form.

How to find the value of i ?

Its value is fixed which is  √-1

A complex number is, for instance, 5 + 2 i. The same is true for 3+4i.

Consequently, a complex number is a straightforward illustration of the addition of two integers, namely a real number and an imaginary number. There are two distinct halves to it: one is entirely real, and the other is fantastical.

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The value of r is found as 3/2 such that line that passes through the pair of points.

The slope is given bye the equation;

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

For the given question, the points are given as;

(x1, y1) = (r, -5),

(x2, y2) = (3, 13)

m = 8

8 = (13 + 5)/(3 - r)

8(3 - r) = 18

8r = 6

r = 3/2

Thus, the value of r is found as 3/2 such that line that passes through the pair of points.

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The correct question is-

Find the value of r so the line that passes through each pair of points has the given slope. (r, -5), (3, 13), m = 8

Answer: The zero of a function is the value of y when x equals zero.

Step-by-step explanation:

The zero of a function is the value of y when x equals zero. It is also known as an x-intercept. In this case, the zero lies at (0,3) where x is zero and y is positive 3.

The probability that a college student will get to work in 30 mins or less is 0.4 or 40%.

What does uniformly distributed probability mean?

Uniform distribution refers to a type of probability distribution in which all outcomes are equally likely to occur.

According to the given question:

Since the time is uniformly distributed, every possible travel time has the same likelihood of occurring.

Lower boundary (L) = 20 minutes

Upper boundary (U) = 45 minutes

The probability that a student finishes her trip in 30 minutes or less is:

P (t ≤ 30) = (30 - L)/(U - L)

              = (30 - 20)/(45 - 20)

              = 10/25

              = 0.4 or 40%

The probability that she will get to work in 30 mins or less is 0.4 or 40%

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A formula for the nth term of the sequence is [tex]a_n[/tex] = 2n+1.

Given:

A sequence follows a plus 2 pattern: 3, 5, 7, 9, ...

here

first term a = 3

common difference d = 5-3

= 2

here common difference is same throughout the sequence so given sequence are in Arithmetic progression.

so nth term:

[tex]a_n = a+(n-1)d[/tex]

= 3 + (n-1)2

= 3+2n-2

= 2n+1

Therefore  A formula for the nth term of the sequence is [tex]a_n[/tex] = 2n+1.

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Answer:

4.2

Step-by-step explanation:

you look at where x=-1.5 and it’s about 4.2 where it is

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The width of the rectangular walkway is 3 feet around.

The walkway has a uniform width around the rectangle.

Let the width of walkway be x

The total length of the garden and walkway will be (12+2x) feet

The total width of the walkway and garden would be (8+2x) feet

Area of the garden and the walkway together are 252 square

Let’s express this mathematically:

(8+2x)(12+2x) = 252

Let’s open the brackets;

96+ 16x+ 24x + 4x^2 = 252

4x^2 + 40x + 96 = 252

4x^2 + 40x + 96-252 = 0

4x^2 + 40x - 156 = 0

Let’s divide all through by 10. We have;

x^2 + 10x -39 = 0

X^2 +13x-3x-39 = 0

x(x + 13) -3(x+ 13) = 0

(x-3)(x + 13) = 0

x -3 = 0 or x + 13 = 0

x = 3 or -13

We ignore x = -13 since width cannot be negative in size

Therefore, the width of the rectangular walkway is 3 feet around.

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The required relative frequency based on the frequency distribution of the students is 8.33%

The relative frequency is the frequency fraction of the number of observations the events occur to the total number of observations. The relative frequency provides a clear understanding of the distribution. This also helped to make a histogram and chart.

The number of times a value appears in a dataset is its frequency. The pattern of frequencies for a variable is known as a frequency distribution. The frequency with which each potential value of a variable appears in a dataset.

The frequency distribution is given.

Total number of student=36

The relative frequency for the class with lower-class limit 31 is calculated as;

R.F=No. of students in class interval/Total no.of students

=3/36

=0.0833

=8.33%

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The average rate of change is 37.5.

Define Rate of change

Given function is,

f(x) = 5(2) ^ x

where, x = 1 to x = 5

We know, the formula of rate of change is

Rate of change = ( f(b) - f(a) ) / (b - a)

for x = 5, for that put value of x in given function

f(x) = 5(2) ^ x

f(5) = 5(2) ^ 5

f(5) = 160

for x = 1, for that put value of x in given function

f(x) = 5(2) ^ x

f(1) = 5(2) ^ 1

f(1) = 10

Now, plug in the values in rate of change formula

Rate of change = ( f(5) - f(1) ) / (5 - 1)

                         = ( 160 - 10) / 4

                         = 150 / 4

                         = 37.5

Hence, the average rate of change is 37.5

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The expression that shows how many hot dog buns were ordered is 8p.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Given that the school cook ordered p packages of hot dog buns for the year-end picnic and each package contains 8 buns.

The expression will be the multiplication of the variables. This will be:

= 8 × p

= 8p

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The equation 4x + 2(x -5) = 3(2x - 4) does not have any solutions.

From the given equation:

We have 4x + 2(x -5) = 3(2x - 4)

By opening the brackets, we have:

2x+ 4x + - 10 = 6x - 12

6x - 10 = 6x - 12

By collecting the like terms, we have:

6x - 6x = -12 + 10

0 = -2

Thus, since there is no constant to a variable, then there is absolutely no solution at all.

An equation is deemed to be linear if the greatest power of the variable is consistently 1. It is also referred to as the one-degree equation. A linear equation with one variable typically has the form Ax + B = 0.

In this case, the variables x and A are the variables while only the variable B is a constant. A linear equation with two variables often has the form

Ax + By = C. The variables x and y, the coefficients A and B, and the constant C are present in this scenario.

Disclaimer : the complete question is :

How many solutions does the equation 4x + 2(x -5) = 3(2x - 4) have?.

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The empirical rule states that, for data having a bell-shaped distribution, the portion of data values being within one standard deviation of the mean is 68%

A bell curve is the informal name of a graph that depicts a normal probability distribution. The term obtained its name due to the bell-shaped curve of the normal probability distribution graph.

The bell curve is perfectly symmetrical. It is concentrated around the peak and decreases on either side.

The dispersion of the data on the bell curve is measured by the standard deviation.

According to the question,

The empirical rule states that, for data having a bell-shaped distribution, the portion of data values being within one standard deviation of the mean is 68%

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The mean absolute deviation (MAD), a measure of variability, illustrates the typical distance between an observation's mean and its variation. MAD uses the data's original units to facilitate interpretation.

Greater values indicate a wider range of data points than the average. The term "variability" refers to how much a data collection varies from one constituent to another. Variability measures reflect the level and magnitude of change within the data collection.

The interquartile range and the mean average deviation are the two methods for calculating variability that are required by the requirements for sixth-grade pupils.

The majority of the data values are fairly near to the mean, as shown by a tiny mean absolute deviation. We can infer from a large mean absolute deviation that numerous data values are dispersed widely from the mean.

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The required  local maximum and minimum values of f using both the First and Second Derivative Tests.

The local maxima is a point inside a stretch at which the capability has a most extreme worth. The outright maxima is likewise called the worldwide maxima and is the point across the whole area of the given capability, which gives the most extreme worth of the capability.

The local minima is the info an incentive for which the capability gives the base result values. The capability condition or the diagram of the capability isn't once in a while adequate to see as the nearby least. The subordinate of the capability is exceptionally useful in tracking down the nearby least of the capability.

f(x)=x/x^2+9

differentiate with respect to x

df(x)/dx = d(x/x^2+9)/dx = -2/x^2+2x^2/9

second derivative = 3/x^3+2x^3/3

Put this derivative equal to zero, then we will put given points, if it becomes negative then the point is on maxima, if it is positive then is on minima.

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The total cost of the ticket is AED 160.

What is the ticket price?

The term "ticket price" refers to the whole cost of a ticket, which includes the airfare as well as all applicable taxes, fees, surcharges, and charges for all optional and required services.

Given,  6 adults pay AED 20 each

And, 4 children pay AED 10 each

So, total cost of the ticket = 6*20 + 4*10 = 120 + 40 = 160

Hence, the total cost of the tickets is AED 160.

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Here is the answer

1. Landing in a shaded portion and landing on 3

2. landing on a unshaded portion and landing on a  number less than 2

Events that do not occur simultaneously are said to be mutually exclusive. When a coin is tossed, for instance, the outcome will either be head or tail, but we cannot get both outcomes.

Events with no intersection are called mutually exclusive event.

What is being asked of us now.

Landing on a shaded portion means landing on either 1 or 4, as landing on 3 is impossible and will only result in landing on 3. So, there is no overlap between these occurrences.

Landing on an unshaded portion means landing on either 2 or 3.  And landing on a number less than 2 means landing on 1.

There is no intersection.

So these events are mutually exclusive.

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By using the concept of Testing of Hypothesis, it can be concluded that

There has been no significant decrease in mean time per mile

What is Testing of Hypothesis?

Testing of Hypothesis is a method of inferencing which is used to decide whether a particular hypothesis can be supported with the help of the data at hand.

Completion time                  Completion time                     Difference

before training                     after training                                            

  5.9                                            5.4                                            0.5

  7.5                                            7.1                                             0.4                  

  6.1                                            6.2                                           -0.1

  6.8                                           6.5                                             0.3

   8.1                                            7.8                                            0.3

Mean for the completion before training = [tex]\frac{5.9 + 7.5 + 6.1 + 6.8 + 8.1}{5} = 6.88\\[/tex]

Mean for the completion after training = [tex]\frac{5.4 + 7.1 + 6.2 + 6.5 + 7.8}{5} = 6.6\\[/tex]

Mean for the difference = [tex]\frac{0.5 + 0.4 -0.1 + 0.3 + 0.3}{5} = 0.28\\[/tex]

Standard deviation for the completion before training = [tex]\sqrt{\frac{(5.9-6.88)^2 + (7.5-6.88)^2 + (6.1-6.88)^2 + (6.8-6.88)^2 + (8.1-6.88)^2}{5} }= 0.928\\[/tex]

Standard deviation for the completion after training = [tex]\sqrt{\frac{(5.4-6.6)^2 + (7.1-6.6)^2 + (6.2-6.6)^2 + (6.5-6.6)^2 + (7.8-6.6)^2}{5} }= 0.908\\[/tex]

Standard deviation for the completion after training = [tex]\sqrt{\frac{(0.5-0.28)^2 + (0.4-0.28)^2 + (-0.1-0.28)^2 + (0.3-0.28)^2 + (0.3 - 0.28)^2}{5} }= 0.228\\[/tex]

The null hypothesis [tex]H_0 : \mu_d = 0[/tex]

The alternate hypothesis [tex]H_a = \mu_d < 0[/tex]

Here left tail test is used

Critical value of t at [tex]\alpha = 0.05[/tex] and Degree of Freedom = 5 - 1 = 4

is [tex]t_c[/tex] = -2.132

t = [tex]\frac{0.28}{\frac{0.228}{\sqrt{5}}} = 2.746[/tex]

Since 2.746 > -2.132, the null hypothesis is accepted

So there has been no significant decrease in mean time per mile

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The number of inflection points can a quadratic polynomial and a cubic polynomial have is zero and one respectively.

For the points of inflection,

We know that the roots of second derivatives give the inflection points of a function,

For inflection point , f(x)'' = 0

(a) For quadratic, there will be f(x)'' independent of x, So, there will be no point of inflection.

(b) For cubic, there is a second derivative have a linear function, So, only one point of inflection.

Any degree polynomial, it has (n-2) points of inflection, where n is the degree of the polynomial.

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Volume(V) of a sphere = 4πr^3

Charge within a small volume 'dV' is given by:

dq = ρ(r)dV

ρ(r) = C/r^2

Volume(V) of a sphere = 4/3(πr^3)

dV/dr = (4/3)×3πr^2

dV = 4πr^2dr

Therefore,

dq = ρ(r)dV ; dq =ρ(r)4πr^2dr

dq = C/r^2[4πr^2dr]

dq = 4Cπdr

FOR TOTAL ENERGY CHANGE 'Q', we integrate dq

∫dq = ∫4Cπdr at r = R and r = 0

∫4Cπdr = 4Cπr

Q = 4Cπ(R - 0)

Q = 4CπR - 0

Q = 4CπR

C = Q/4πR

Therefore, in the total energy change with all the terms given, the value of constant C in terms of Q, π and R is [Q/4πR].

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In this problem, 0.22 is a parameter.

Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ.

The range of possible values for a variable is known as a parameter. A parametric equation is an equation expressed in terms of parameters. In the equation y = 2x + 1, x is called the parameter. In statistics, a function variable whose variable is sought by means of evidence from the samples is called a parameter.

As per the given question,

⇒ 0.22 is the standard deviation of the random sample which is a measurement. Measurements of populations can be called parameters.

Therefore, the 0.22 value in the problem is called a parameter.

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The complete question is

A random sample of 121 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. In this problem, the value 0.22 is

A. a parameter

B. a statistic

C. the margin of error for a confidence interval

D. the average content of colognes in the long run

E. none of the above

Based on the Number of students who use mobile in a traditional class,

The joint relative frequency of students who use mobile in traditional classes is 62.162%

What is Joint Relative Frequency?

Joint relative frequency is defined as the ratio of the frequency that is not in total rows or the total columns to the frequency of total rows or columns.

According to the given information:

Courses/devices  Traditional class  Online class  Total rows

Computer                        28                      62                  90

Mobile device                 46                      64                  110  

Total Columns                74                      126                 200

Total Number of students who opted for traditional classes = 74 Number of students who use a mobile phone in traditional class = 46

Joint relative frequency of students who use mobile in a traditional class

                 = Number of students who use mobile in traditional class/Total

                    students who opted for traditional classes

                 = 46/74

Percentage of Joint relative frequency = 46/74 ×100      

                                                                   = 62.162%

Based on the Number of students who use mobile in a traditional class,

The joint relative frequency of students who use mobile in traditional classes is 62.162%

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Calculating the obtuse angle or value of a triangle.

Finding obtuse angle value:

steps:

1)  Square the length of both sides of the triangle that intersect to create the obtuse angle, and add the squares together.

For example, if the lengths of the sides measure 4 and 2, then squaring them would result in 16 and 4. Adding the squares together results in 20.

2)  Square the length of the side opposite the obtuse angle. For the example, if the length is 5, then squaring it results in 25.

3) Subtract the combined squares of the adjacent sides by the square of the side opposite the obtuse angle. For the example, 25 subtracted from 20 equals -5.

4)  Multiply the lengths of the adjacent sides together, and then multiply that product by 2. For the example, 4 multiplied by 2 equals 8, and 8 multiplied by 2 equals 16.

5) Divide the difference of the sides squared by the product of the adjacent sides multiplied together then doubled. For the example, divide -5 by 16, which results in -0.3125.

The obtuse angle value is obtained by inverse of cos:

cos^-1(-0.3125)

= 108.209 degrees.

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The use exponential regression to model C as an exponential function t is C=29.490×1.076t.

Given that,

In the picture we can see the full question.

That is

The table shows the estimated value C, in dollars, of an 1877 Indian Head Cent in very fine condition t years of 1950.

The table has 2 columns

t=time in years                      C= value

since 1950                           in dollars

       0                                          25

      30                                        400

      45                                        625

      54                                        1750

      60                                       2000

We have to find the use exponential regression to model C as an exponential function t.

We know that,

The base reciprocal's multiplication factor is indicated by a negative exponent. For instance, it can be expanded as 1/aⁿ if aⁿ is given. It implies that we must multiply a's inverse, or 1/a, by n. When writing fractions with exponents, negative exponents are employed.

Therefore, The use exponential regression to model C as an exponential function t is C=29.490×1.076t.

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He has enough memory space to download a song that will use 0.12 gigabytes of memory

The memory capacity of new cell phone = 1.5 gigabytes

The memory capacity that already used = 1.35 gigabytes

The remaining space = The memory capacity of new cell phone  - The memory capacity that already used

Substitute the values in the equation

Here we have to use the subtraction

The remaining space = 1.5 - 1.35

Subtract the terms

= 0.15 gigabytes

The size of the song = 0.12 gigabytes

We know 0.15 > 0.12

Hence, he has enough memory space to download a song that will use 0.12 gigabytes  of memory

The complete question is

Devin has a new cell phone that holds 1.5 gigabytes if memory for music. He has already used 1.35 gigabytes of the memory. Will he have enough space to download a song that will use 0.12 gigabyte of memory? Explain.

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Answer:  4 pencil

Step-by-step explanation: