Find the solution of the inequality 5 > r – 3.

The difference between the circumference of the circle and the perimeter of the triangle is 28.2 units. (Option B)

To find the length of each side of triangle, the distance is calculated between the vertices using the formula:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Hence,

AB =√((-4 – 0)^2 + (9 – 0)^2) = 9.85 units

AC = √((9 – 0)^2 + (4 – 0)^2) = 9.85 units

BC = √((9 – (-4))^2 + (4 –9)^2) = 13.93 units

Hence, the perimeter of the triangle = 9.85 + 9.85 + 13.93 = 33.6 units

As AB and AC is the radius of the circle, the circumference of the circle is:

C = 2πr = 2π(9.85) = 61.8 units.

Hence, the difference between the circumference of the circle and the perimeter of the triangle = 61.8 – 33.6 = 28.2 units.

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Answer:

A) [tex]g(x) = (x - 2 )^{2}[/tex]

Explanation:

Since the equation g(x) is similar to f(x), but translated horizontally, then we can conclude that there is a change in the x value.

Since, the equation g(x) is slide to the right by 2 factor, then there will be a change in x value by -2 factor.

For equation B, the graph will move to the left of f(x) by two factor.

For equation C, the graph will move up of f(x) by two factor.

For equation D, the graph will move down of f(x) by two factor.

The meaning of the y-coordinate of the graph when x = 15 is given as follows:

B. Erin has completed 25% of her exercise program.

The graph is a relation that represents a function between two variables.

The variables for this problem are given as follows:

One ordered pair for the graph in this problem is given as follows:

(15, 25).

This means that when Erin spends 15 minutes exercising, she has completed a percentage of 25% of her exercise program, and thus option B is correct.

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Comparison analysis is defined as describing the data in the sample with the use of percentages or averages. Hence, option A is the most suitable answer to this question.

Comparative analysis talks about the comparison of two or more data sets, or other objects. Comparing data becomes very easy when the data is consolidated with the help of average or mean, percentages, and rounding up of the decimals.

Comparison is a very important method to check the difference in the parameters of the two data sets. Not just comparing, summarization of this data is vital for understanding what that data actually means. Hence, we can say that comparison analysis is defined as describing the data in the sample with the use of percentages or averages.

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The complete question is -

Fill in the blanks -

________ analysis is defined as describing the data in the sample with the use of percentages or averages.

A) Comparison

B) Generalization

C) Relationship

D) Summarization

E) Confidence

Answer:

hey

4y = 2x – 8

Step-by-step explanation:

2x – 4y = 8

–4y = –2x + 8

multiply both sides by (–)

–(–4y) = –(–2x + 8)

4y = 2x – 8

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The appropriate distribution to use is t distribution with df = 80.

Variance

Distribution

Given that:

n1 = 37

n2 = 45

The variances of the populations are not know so we can use t distribution

Degree of freedom = n1 + n2 - 2

                                = 37 + 45 - 2

                                = 80

Therefore, t distribution with df = 80

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Answer:

1

Step-by-step explanation:

subtract the two numbers

Answer: 19

Step-by-step explanation: Imagine a number line -9 is on the left side and 10 is on the other. Now you have to clculate how many jumps or spaces it takes to reach 10. Which is 19, or 9 + 10.

I hope this helps.

The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft

According to the question,

A norman window has the shape of a rectangle surmounted by a semicircle.

Let The width of rectangle be x and height be y

It is given that  the diameter of the semicircle is equal to the width of the rectangle

Therefore , Diameter of circle = x

Radius = x/2

Perimeter of window  = 32 = Perimeter of rectangle + Perimeter of semi-circle

=> 32 = Width + 2height + πr

=> x + 2y + πx/2 = 32

=> 2x + 4y +  πx = 64

Solving for y,

=> 4y = 64 - 2x - πx

=> y = 64  - 2x - πx/ 4 ----------(1)

Area of the window = Area of rectangle + area of semi-circle

=> A = Width × hiegth +  πx²/8

=> A = xy + πx²/8

Substituting the value of y from equation (1)

=> A =  x (  64  - 2x - πx/ 4  ) + πx²/8

[tex]A = x ( \frac{64 - 2x -\pi x}{ 4} ) + \frac{\pi x^2}{8}\\A = ( \frac{ 64x - x^2 ( 2 + \pi)}{4 } ) + \frac{\pi x^2}{8}[/tex]

Differentiating A w.r.t x

=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4}[/tex]

Now , To find a maximum area

dA/dx = 0

=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4} = 0[/tex]

Solving for x ,

64 - 4x - 2π + πx = 0

=> x = 64 / 4 + π ------(2)

Differentiating A again w.r.t x

=> d²A / dx² = -2(2 + π)/4 + π/4

=> -π+4 / 4 which is less than zero

Therefore,

Area is maximum when x = 64 / 4 + π

The exact value of x (in ft) so that the greatest possible amount of light is admitted is  8.96 ft

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Answer:

$14000

Step-by-step explanation:

= (3500 x 0.8 x 5) / 100

= $14000

I hope my answer helps you.

High off the ground the top of the ramp’s incline is 108.19 inch

Trigonometric ratios are what?

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

Given that :

hypotenuse = 153 inch

and angle is pi/4

Let h be the height

so sin pi/4 = h/153

h = 153 . sqrt 2/2

h = 108.19

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The true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable is 0 < F(x) < 1. and F(x) = 1 for at least one value of x,  F(x) = 1 for all values of x > a, where a is a constant.

What is meant by probability density function?

In math, probability density function refers most commonly associated with absolutely continuous univariate distributions.

Here we need to find the true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable.

In order to find the correct statement, we must know the definition of the cumulative density function also.

The cumulative density function means the probability function that X will take a value less than or equal to x.

Based on the both definition option (A), (B) and (C) are true.

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The circumference of this circle is 2π

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

The arc is the circumference.

C = 2πr

C = 2x πx 6

C = 12π

A circle is 360 degrees.  The  arc is covering 60 degrees

60/360 = 1/6

The arc is 1/6 of the circle, so it will be 1/6 of the circumference

1/6 C = 1/6 (12π)

arc = 2π

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The set of all  T's fixed points is {(x,0): x € R} of the linear transformation of vector(v).

linear transformation:

It is a function from one vector space to another that respects the structure of each vector space, which is also known as a linear operator or map

Two important examples of linear transformations are zero and identity transformation. The zero transformation defined by T(→x)=→(0) for all →x is an example of a linear transformation.

Similarly, the identity transformation defined by T(→x)=→(x) is also linear.

Note that the representation matrix for the reflection in the y-axis:

                              [tex]\left[\begin{array}{ccc}1&0\\0&-1\\\end{array}\right][/tex]

Here the condition

T(x,y)=

         [tex]\left[\begin{array}{ccc}1&0\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}x\\-y\\\end{array}\right] =\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]

can only happen when y=0 and x is arbitrary.

Thus the fixed points for all T are points with y=0 or all points on the x-axis

Thus, The set of all T's fixed points is {(x,0): x€R}

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The solution to the system of equations is x = 3 and y = -7. The correct option is C. (3, -7).

The system of equations is given as follows:

2x + 3y = −15  ....(1)

3x + y = 2       ....(2)

Multiply Equation 2 by 3:

9x + 3y = 6      ....(3)

Now, we can subtract Equation 1 from Equation 3 to eliminate y:

(9x + 3y) - (2x + 3y) = 6 - (-15)

9x + 3y - 2x - 3y = 6 + 15

7x = 21

x = 21/7

x = 3

Substituting the value of x into Equation 2 to solve for y:

3(3) + y = 2

9 + y = 2

y = 2 - 9

y = -7

Therefore, the solution to the system of equations is x = 3 and y = -7.

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Complete question:

Solve the system of equations using elimination.

2x + 3y = −15

3x + y = 2

A. (0, 5)

B. (1, −1)

C. (3, −7)

D. (4, −10)

Answer:

  a. $461.67

  b. $12771.73

Step-by-step explanation:

You want to know the monthly payment and total amount paid for a car that costs $12500 when $4000 is the down payment and the interest is 3.8% for 19 months.

The formula for the monthly payment is ...

  A = P(r/12)/(1 -(1 +r/12)^-n)

where P is the amount borrowed at interest rate r compounded monthly for n months.

Here, the down payment of $4000 reduces the loan amount to ...

  $12500 -4000 = 8500

So, the monthly payment is ...

  A = 8500(0.038/12)/(1 -(1 +0.038/12)^-19) ≈ 461.67

Matteo needs to pay $461.67 each month.

The total Matteo pays for the car will be the sum of the down payment and the 19 monthly payments:

  total = $4000 +19×461.67 = $12771.73

Matteo will end up paying $12771.73 for his car.

Hypotheses: H0: μ1 = μ2 and H1: μ1 ≠ μ2.This hypothesis test is a two-tailed test.

Calculate the pooled standard deviation of the two samples.

Let x1 and x2 be the sample means of the National League and American League, respectively. Let s1 and s2 be the sample standard deviations of the National League and American League, respectively. Let n1 and n2 be the sample sizes of the National League and American League, respectively.

Pooled standard deviation = √[( (n1 - 1)s1^2 + (n2 - 1)s2^2 ) / (n1 + n2 - 2)]

s1 = 6.9282

s2 = 6.3246

n1 = 2

n2 = 2

Pooled standard deviation = √[( (2 - 1)6.9282^2 + (2 - 1)6.3246^2 ) / (2 + 2 - 2)]

Pooled standard deviation = 6.6759

Calculate the degrees of freedom (df).

Degrees of freedom (df) = n1 + n2 - 2

df = 2 + 2 - 2

df = 2

Calculate the t-statistic.

Let μ1 and μ2 be the population means of the National League and American League, respectively.

t-statistic = (x1 - x2 - (μ1 - μ2)) / √(s^2 / n1 + s^2 / n2)

x1 = 18

x2 = 19

μ1 = μ2

s2 = 6.6759

n1 = 2

n2 = 2

t-statistic = (18 - 19 - (μ1 - μ2)) / √(6.6759^2 / 2 + 6.6759^2 / 2)

t-statistic = (-1) / (4.4518)

t-statistic = -0.2244

At a significance level of 0.10,

The critical value for a two.

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The Venn Diagram is shown at the end of the answer.

From the diagram, the percentages are given as follows:

The Venn Diagram is filled starting at the intervals involving most variables, that is, the intersections.

2% of people answered all three, hence space V on the diagram has a value of 2%, which is the intersection of the three sets.

3% of people answered light rail and bus, hence space IV has a value of 1%, as light rail and bus also involve light rail, bus and carpool.

6% of people answered light rail and carpool, hence space II has a percentage of 4%, following the same logic above.

2% of people answered carpool and bus, hence space V has a percentage of 0%.

11% of people answered carpool, hence space III has a percentage of 5%, as this percentage is a combination of:

From the total bus and light rail percentages, the percentages are given as follows:

The percentage of people that use at least one of these mediums is given as follows:

9 + 7 + 5 + 1 + 2 + 4 = 28%.

The percentage of people who use none of these mediums is given as follows:

100 - 28 = 72%.

Then the missing percentages at the end of the problem, along with their spaces, are given as follows:

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When the data set is extremely small, the algorithm might fail to detect the inherent clusters in the data set. When the data set has a high degree of overlap between clusters, the algorithm might generate too many clusters and fail to capture the underlying structure of the data.

Partitional clustering algorithms can automatically determine the number of clusters, which is often perceived as an advantage. However, this is not always the case. For example, when the data set is small the algorithm might be unable to detect the true clusters in the data set. Additionally, when the data set has high levels of overlap between clusters, the algorithm might generate too many clusters and fail to recognize the underlying structure of the data. In these cases, the automatic determination of the number of clusters can be disadvantageous as it fails to capture the true structure of the data.

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The polynomial f(x) of degree 3 is

f(x) = x³ + x² - 20x

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The zeroes of the polynomial are 0, -5, and 4.

This can be written as,

x = 0, x

x = -5, (x + 5)

x = 4, (x - 4)

x(x + 5)(x - 4)

(x² + 5x)(x - 4)

x³ - 4x² + 5x² - 20x

x³ + x² - 20x

Thus,

The polynomial is f(x) = x³ + x² - 20x

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The conclusion is that there is insufficient proof that the new training method increases training time at the 0.02 level of significance.

Hypothesis test: Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H₀

The average amount of time required to obtain an advanced driving license using conventional techniques is μ=90 hours.

According to the researcher, the new method can result in a longer training period.

A researcher tests the hypothesis with 190 pupils.

At the significance threshold of α=0.02, the researcher fails to reject the null hypothesis.

To put to the test

H₀:The average amount of time required for the new method to obtain an advanced driving license is 90 hours, or μ=90

Hₐ: The new method often requires more than 90 hours, or μ>90, to obtain an advanced driving license.

Failure to reject the null hypothesis indicates that there was insufficient data in our sample to draw a conclusion on the existence of the effect. The absence of data, however, does not demonstrate that the effect is unreal.

The new method takes fewer than 90 hours on average to get an advanced driving license as a result.

Therefore, the researcher's assumption that the new method would increase training time was unfounded.

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The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20

Logical or deductive reasoning involves using a given set of facts or data to deduce other facts by reasoning logically. It involves drawing specific conclusions based on premises.

Figuring out the triangle first is easiest because since 3 triangles make 30, then each triangle must be 10.

Now, we have our second equation become 10 + C + C = 20, and we get C=5 after solving for the value of the circle.

Our third equation will be 5 + S + S = 13, which becomes 5+2S=13, 2S=8, and then S=4, so the value of a square is 4

Our fourth equation will be 10 + 5*(1/2)(4) = ?, and we see that half of 4 is 2, so we have 10 + 5(2) = 10 + 10 = 20 as our answer.

Hence, The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20

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Answer: R(7, 9), S(6, 7), T(2, 3), U(8, 5), V(5, 5)

Answer:

1. 50 x 2 = 100

2. 60 x 3 = 180

3. 75 x 8 + 3 = 603

603 + 180 + 100 = 883

Step-by-step explanation:

Just multiply and add.

The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .

Given :

The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine .

From the table:

Take any two points ( 0 , 380 ) and ( 15 , 545 )

slope m = 545 - 380 / 15 - 0

= 165 / 15

= 33 / 3

= 11 / 1

= 11 feet

Hence the slope m is 11 feet .

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[tex]-4-4[/tex]

[tex]-4+(-4)[/tex]

[tex]=\fbox{-8}[/tex]

[tex]-4+(-4)[/tex] on a number line:

1)The regression equation is Age--26.7+809 LN [(1+(R/1))/(1-(R/L))]. Hence, the value of the regression coefficients by is-26.7 and by is 809

2)The forecasted value for 0.0901 LN [(1+(RL)) (1- (RL))) is 46.103.

3)The 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor is 41.013,51.193.

4)Yes, a man in Sherlock Holmes's neighborhood thought that the body because; the man's age comes under the age in years that is, the smaller age is 14 and the larger age is 69. Thus, this is the body of that man.

Exponential law=The first law states that to multiply two exponential functions with the same base, we simply add the exponents. The second law states that to divide two exponential functions with the same base, we subtract the exponents.

MINITAB procedure:

Choose Stat > Regression Regression

Step 2: In Responses, enter the column of Age (yrs)

Step 3: In Predictors, enter the column of LN [(1+(R/L))/ (1-(R/1))] Step 4: In Options, enter the value of Prediction interval for new observation as 0.0901

The regression equation  Age (year 26,7 809 28(13+1/233/4-1-26.7252.025 -13.20 0.00025.61 31.37 0.000)

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The expression that is equivalent to 6⁻¹⁰/(6⁴)(6⁰) is (d) 1/6¹⁴

From the question, we have the following parameters that can be used in our computation:

6⁻¹⁰/(6⁴)(6⁰)

Express 6⁰ as 1

So, we have the following representation

6⁻¹⁰/(6⁴)(6⁰) = 6⁻¹⁰/(6⁴) * 1

Evaluate the products

6⁻¹⁰/(6⁴)(6⁰) = 6⁻¹⁰/(6⁴)

Apply the law of indices

So, we have

6⁻¹⁰/(6⁴)(6⁰) = 1/6¹⁰⁺⁴

Evaluate the differences

6⁻¹⁰/(6⁴)(6⁰) = 1/6¹⁴

Hence, the expression is (d) 1/6¹⁴

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The estimated regression equation for these data is Ŷ = 23.194 + 0.318x for every i=1,...,6.

What is meant by regression equation?

In math, the linear regression analysis output delivers some important information, which helps the researcher to predict the estimation, accuracy, and efficiency of the model.

Here we have the data on price and the overall score for stereo headphones that were tested by consumer reports were as follows.

And we need to find the estimated regression equation for these data.

Here let us consider x be the price in dollars of the stereo headphones of brand ii (the independent variable). and let y be the overall score of the stereo headphones of brand ii (the dependent variable).

Here first, we will compute the value of SSE.

The formula is given by

= > SSE = 1∑n​ (yi ​− y​)²

Therefore, we will show the table of values of xi​, Ŷ​, Ŷ​​, (yi​−Ŷ​​) and (yi​−Ŷ​)².

Now, we have to calculate the value of yi​^​, plug in the value of xi​ in the equation 

=> Ŷ = 23.194 + 0.318x for every i=1,...,6.

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