Determine which set of side measurements could be used to form a right triangle. 17, 6, 20 10, 15, 13 5, 12, 13 9, 3, 11

The probability that they finish within 10 minutes of each other here their times are independent

i.e P( -10 < X₂ - X₁ < 10) where X₂ - X₁ = D Normally distributed, is 0.78 ..

Let X₁ be a random variable as taylor cleans the exterior of each car.

mean , μ₁ = 20 ,

standard deviations, σ₁ = 4.8

let X₂ be a random variable as sam cleans the interior of each car.

mean, μ₂ = 18

standard deviations, σ₂ = 6.4

If the two random variables are normal, then their difference , X₂ - X₁ also be normal.

As two normal variables here are normally distributed, therefore the distribution of the difference between the two variables here is given as: X₂ - X₁ = X

with mean, μ = μ₂ - μ₁ = 2

standard deviations, σ = σ₁² + σ₂²

= 6.4² + 4.8² = 64

To any bivariate Normal distribution of (X₁,X₂) Thus the variable

Z = (X−μ)/σ = (X₂−X₁ −(μ₂ - μ₁))/(√σ₁² + σ₂²)

= X - 2 /√64 = (X - 2 )/8

The probability here is computed as:

P( -10 < X₂ - X₁ < 10) = approx P(∣D∣<10)

where D is difference between their finishing times. Converting it to a standard normal variable, we have here:

= P( (-10 - 2) / 8 < Z < (10 - 2) / 8)

= P( -1.5 < Z < 1)

= P(Z < 1 ) - P(Z < -1.5)

Getting it from standard normal tables,

= 0.8431 - 0.0668

= 0.7763

Therefore 0.7763 is the required probability here.

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Complete question:

Sam and Taylor own and operate a car wash service. Sam cleans the interior of each car and Taylor cleans the exterior. The time it takes Sam to finish the interior has a mean of 20 minutes with a standard deviation of 6.4 minutes. The time it takes Taylor to finish the exterior has a mean of 18 minutes with a standard deviation of 4.8 minutes. Both of their finishing times are approximately normally distributed.

Suppose we select a car at random, and define the random variable D as the difference between their finishing times. We can assume that their times are independent.

Find the probability that they finish within 10minutes of each other.

You may round your answer to two decimal places.

P\left(|D|<10\right)\approxP(∣D∣<10)≈P

Answer:

Based on the given polynomial, g(x) = 5x + 17x5, it is a polynomial of the sixth degree because it contains six terms (one constant term, one linear term, and one quintic term). Thus, another name for this polynomial is a sixth-degree polynomial.

Step-by-step explanation:

Because it permits one to assume that the sampling distribution of the mean would typically be normally distributed, the central limit theorem is helpful when examining big data sets. This makes statistical analysis and inference simpler.

Hypothesis :

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

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The slope of all lines parallel to the line 3x + 7y = -7 is 3/7.

To find the slope of the line 3x + 7y = -7, we can use the slope-intercept formula y = mx + b, where m is the slope.

We can rearrange the equation 3x + 7y = -7 to the slope-intercept form 7y = -3x -7.

We can then divide both sides of the equation by 7 to get the slope, m = -3/7.

Therefore, the slope of all lines parallel to the line 3x + 7y = -7 is 3/7.

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118,813,760 different combination license plates can the country produce

Permutations and combinations:

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor. By considering the ratio of the number of desired subsets to the number of all possible subsets for many games of chance in the 17th century, the French mathematicians Blaise Pascal and Pierre de Fermat gave impetus to the development of combinatorics and probability theory.

Given that

In a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the roman alphabet

X = 10 × 26 × 26 × 26 × 26 × 26

  = 10 × 11881376

  = 118,813,760

118,813,760 different combinations license plates can the country produce

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The mean square for error in the ANOVA provides an estimate of the variance of an individual treatment average.

What is a variance?

Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance serves as a proxy for dispersion, or the degree to which a set of numbers deviates from their mean.

Here, We have

The mean square for error in the ANOVA provides an estimate

ANOVA = Analysis of VarianceThe correct answer is (B)

The mean square for error (MSE) in the analysis of variance (ANOVA) provides an estimate of the variance of an individual treatment average.

Unlike option C which refers to an individual observation,

option B refers to a group of observations that are classified into a single treatment sample.

The MSE measures (gives an estimate of) the variation within this treatment sample. In this case, the variation is in the average or the mean. This could be average texture, average strength, average penetration, etc.

Hence, the mean square for error in the ANOVA provides an estimate of the variance of an individual treatment average.

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Yes, the sum of 2 whole numbers is always a whole number.

Any number that ranges from 0 to infinity with 1 as the denominator in its smallest form is called a whole number.

For example- 0, 3, 78, 9363, etc.

Now if we take up two numbers say 34 and 78.

34 + 78

= 112

According to the definition of the whole number, we can say that this is a whole number.

Another example can be 0 + 237

The sum is 237

which again is a whole number.

The last example can be 2365 + 930

= 3295

This too is a whole number.

Hence the sum of two whole numbers will always be a whole number.

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Answer: 7

Step-by-step explanation:

If a graph have 12 vertices and 3 connected components, then  the largest number of edges it might have is 45.

What is vertex?

One of the items joined together in a graph is referred to as a vertex (or node). Edges or links are the connections between the vertices in any graph.

As given in the question,

The vertices (n) = 12,

Connected components (k) = 3

let m be the number of edges it the graph might have,

The number of edges in the graph can be calculated by the following formula:

[tex]m \le \frac{(n-k+1) \times (n-k)}{2}[/tex]

putting the values from the question,

[tex]m \le \frac{(12-3+1) \times (12-3)}{2}[/tex]

[tex]m \le \frac{(10) \times (9)}{2}[/tex]

[tex]m \le 45[/tex]

By the above equation, we can say that maximum number edges of is 45.

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In terms of relative growth rate Exponential growth is characterized by a constant relative growth rate.

Exponential growth is the process of increasing quantity over time. Occurs when the instantaneous rate of change of a quantity over time is proportional to the quantity itself. The exponential growth model has the form

y (t) = C eᵏᵗ, where k is the rate constant.

Relative Growth Rate:Relative growth rate (RGR) is the rate of growth relative to size. That is, the rate of growth per unit time relative to the size at that point in time and y'(t)/y(t) is the relative growth rate of a function y at time t.

1/y dy/dt = 1/y d(C eᵏᵗ)/dt

= 1/y(kC eᵏᵗ)

= 1/y ( ky) ( since, y (t) = C eᵏᵗ)

= k

Therefore a constant relative growth rate.

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Complete question:

In terms of relative growth rate, what is the defining property of exponential growth? Choose the correct answer below.

A. The relative growth rate at time t is the slope of the exponential function at time t.

B. dy dt If y represents a population, then the relative growth rate can be represented by dy/dt

C. The relative growth rate is proportional to the size of the population

D. The relative growth rate is constant.

6% slope means on a run of 100 units, there is just a 6-unit rise. The basic definition of slope is the gradient or incline of the terrain.

A steep slope is an abrupt incline, and a gentle slope is a gradual incline. The river's route flows between the steep, forested hills and their softer counterparts.

This is accomplished by comparing the vertical and horizontal changes, which are frequently stated as rise/run.

Since "percent" or "%" denotes "out of 100" or "per 100," x% can be expressed as

For instance

You can come across a road sign that says "6% Grade" or "Steep Grade" while driving down a highway. The road's grade is essentially its slope, multiplied by 100.

6% thus equals 6/100.

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Step-by-step explanation:

"to solve for h" just means to transform the equation, so that instead of V we get h alone on one side of the equation.

V = pi×r²×h

h = V / (pi×r²)

that's it.

for the slope question :

the slope is the factor of x (2/3 and 3/2) and indicates how steep the line is. and it is expressed as y/x ratio defining how many units y changes, when x changes a certain amount of units.

the bigger the number, the steeper the line.

so, the 4th answer option is correct. g(x) is steeper than f(x).

the lines are not parallel, because they do not have the same slope.

they are not perpendicular, because perpendicular slopes turn the y/x ratio upside down AND flip the sign.

e.g. the perpendicular slope of 2/3 would be -3/2.

Answer:

both cost the same price of 6 dollars for each

Step-by-step explanation:

we can make a system of equation

d- daylilies

o- ornamental glass

5d+5o=60

8d+5o=78

-8d.      -8d

5o=78-8d

5d+78-8d=60

-3d+78=60

     -78. -78

-3d= -18

/-3.   /-3

d=6

5(6)+5o=60

30+5o=60

-30.      -30

5o=30

/5.  /5

o=6

they both are 6 dollars each

hopes this helps

To graph a rational function on a graphing calculator, enter the equation into the Y= editor, then press the graph button. The calculator will display the graph of the rational function.

1. Enter the equation for the rational function into the Y= editor of your graphing calculator. Be sure to include all terms, coefficients, and operators.

2. Press the graph button. This will tell the calculator to generate the graph of the equation.

3. The calculator will display the graph of the rational function, including any asymptotes, zeroes, and intercepts.

4. Adjust the window settings as desired to get a better view of the graph. This can be done by pressing the WINDOW button, then setting the appropriate Xmin, Xmax, Ymin, and Ymax values.

5. Press the GRAPH button again to view the adjusted graph.

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Answer:

Available credit = $2,416.42

Step-by-step explanation:

$1,374.90

$266.21

39.46

$903.01

Sum = $2,583.58

$2,583.58 was spent. Subtract this from $5,000 to find Marianne's available credit.

$5,000

- $2,583.58

Available credit = $2,416.42

Answer:

4.82803

Step-by-step explanation:

3 x 1.6

The solutions for the given equation are [tex]2+\sqrt{31}[/tex] and [tex]2-\sqrt{31}[/tex]. These are calculated by applying the quadratic formula since the given equation is a quadratic equation.

The quadratic formula is used for finding the roots of a quadratic equation in the form of ax² + bx + c = 0.

The formula is,

x  = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

The given equation is

x² - 27 = 4x

On rewriting the equation, we get

x² - 4x - 27 = 0

thus, it is in the form of ax² + bx + c = 0. So, this is a quadratic equation.

Then, applying the quadratic formula for finding roots is nothing but its solutions.

Where a = 1; b = -4; c = -27

⇒ x = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

      = [tex]\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-27)} }{2(1)}[/tex]

      = (4 ± [tex]\sqrt{16+108}[/tex])/2

      = (4 ± [tex]\sqrt{124}[/tex])/2

      = (4 ± 2[tex]\sqrt{31}[/tex])/2

      = 2 ± [tex]\sqrt{31}[/tex]

So, the roots of the given equation are 2 + [tex]\sqrt{31}[/tex] and 2 - [tex]\sqrt{31}[/tex].

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The slope of the line passing through the two points [tex](-1,3)[/tex] and [tex](4,7)[/tex] is [tex]\frac{4}{5}[/tex]

The formula for finding the slope when two points are given

[tex]y=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\y=\frac{7-3}{4-(-1)} \\y=\frac{4}{4+1} \\y=\frac{4}{5}[/tex]

The slope of the line is [tex]\frac{4}{5}[/tex]

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Answer:

.33m+65=C

Step-by-step explanation:

to solve the equation you will need to multipy .33 x the amount of miles drove after you get the answer for that you will need to add 65 then thats your final answer

The surface area of that part of the plane 10x+7y+z=4 inside the elliptic cylinder x^2/25+y^2/9=1 is equal to πab, where a=5 and b=3. Therefore, the surface area is equal to 45π.

Total area on a three-dimensional shape's surface is known as surface area. The surface area of a cuboid with six rectangular faces can be calculated by adding the areas of each face. Alternatively, you can write down the cuboid's length, width, and height and use the formula surface area (SA)=2lw+2lh+2hw.

The general formula for a cube's surface area is as follows: The area of the base plus the area of the cube's vertical surfaces will add up to the cube's total surface area. The cube's total surface area is calculated using the formula 6a2, where an is the side length.

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Tomika and Mark claim a medical deduction in the amount of $1,839.8.

To determine how much Tomika and Mark can claim as a medical deduction, you first need to calculate the number of medical expenses that are covered by their insurance.

The first step is to calculate medical insurance :

Medical insurance = 7.5 % of $101,598

Medical insurance = 7.5% x $101,598

Medical insurance =  $7,619.88.

Medical deduction claim = $7,619.88 - (100% - 60%)x $3,800

Medical deduction claim = $7,619.88 - 40% x $3,800

Medical deduction claim = $7,619.88 - $1,520

Medical deduction claim = $6,099.88

Therefore, they can claim a medical deduction in the amount of $1,839.8.

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The algebraic expression for the given statement total number of hours present in y hours and 45 minutes is equal to ( y + 0.75 ) hours.

As given in the question,

Given statement is equal to :

The total number of hours present in y hours and 45 minutes .

Here we have to convert whole equation into hours we have :

1 hour = 60 minutes

⇒ 1 minute = ( 1 / 60 ) hours

⇒ 45 minutes = ( 45 / 60 ) hours

⇒ 45 minutes = 0.75 hours

Algebraic expression for the given statement in hours  is given by :

y hours and 45 minutes

= y hours + 45 minutes

= y hours + 0.75 hours

= ( y + 0.75 ) hours

Therefore, the algebraic expression for the given statement is given by

( y + 0.75 ) hours.

The complete question is:

Write an algebraic expression for the total number of hours in y hours and 45 minutes.

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The best prediction of the population in the year 2015 will be 4150

rate of decrease involves The rate of reduction expressing a decrease as a percentage of the initial value.To compute a percentage drop, first determine the difference (decrease) between the two values being compared. Then, divide the reduction by the original number and multiply the result by 100.

Given that an island's peasant population is falling at a rate of 1.7% per year,

A 1.7% decrease means that 98.3% will remain.

as a result, decrease = 0.983/year

A(t) = A(original) multiplied by (0.983)^t

As a result, after 6 years, A(6) = 4600 x (0.983)6 = 4150

As a result, the population in 2009 will be 4150.

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The required exponent form is obtained as 2 x 2 x 2 x 2 = 2⁴.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given expression is 2 x 2 x 2 x 2.

It can be written in exponent form as,

2 x 2 x 2 x 2

The number 2 is multiplied to itself by four times,.

Thus, the exponent form is given as 2⁴.

Hence, the exponent form of the given expression is 2⁴.

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Answer:

The diagram shows a line of reflection, labeled as "line r," and a point B on one side of the line. The image of point B, labeled as B', is shown on the other side of the line.

If point A is on line r, then the image of A would be A itself because a reflection in line r means that all points on the line remain unchanged.

If point B is not on line r, then line r would be the perpendicular bisector of line segment BB'. This means that line r would pass through the midpoint of line segment BB' and be perpendicular to it. The image of point B would be on the opposite side of line r from the original point B, but the distance between B and B' would remain the same.

a. The diagram that represents this situation is given by the image shown at the end of the answer.

b. The height of the building is of: 33.4 feet.

The three trigonometric ratios are defined as follows:

As shown by the diagram given at the end of the answer, this situation is represented by a right triangle in which:

Then the height of the building is calculated as follows:

tan(24º) = x/75

x = 75 x tangent of 24 degrees

x = 33.4 feet. -> height of the building.

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On your entire strategy at the expiration of the contract if the stock price at that time is $81.50 then the profit is $2189.

A portfolio is a collection of financial investments like stocks, bonds, commodities, cash and cash equivalents, including closed-end funds and exchange traded funds.

A stock is a security that represents the ownership of a fraction of the issuing corporation. Units of stock are called "shares" which entitles the owner to a proportion of the corporation's assets the owner equal to how much stock they own.

We know that,

Profit on the strategy

        = Profit on the shares + Profit from long calls + Profit from short puts

        = 200(81.50 - 70) + 200(Max(81.50-72,0)-5.75) + 300(-Max(68 - 81.50,0)+2.87)

        = 2300 + 750 - 861

        = 2189

Therefore profit on strategy is $2189.

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The linear function decreases when x is between –6 and 0.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+2. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=5 and b=2.

A function can be classified as:

From the graph is possible to see that the function decreases when x is between –6 and 0 because the values of y decrease with the increasing of x-values.

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The sample size be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence is 4148 , the correct option is (b)    .

In the question ,

it is given that ,

the confidence interval is 99% .

let us consider ,

A sociologist wishes to estimate the percent of the U.S. population living in poverty .

Here , preliminary estimate of population has been ,

p = q = 0.50 .

for given , 99% confidence interval z = 2.756 .

the error percent is 2% , the means E = 0.02  .

So , the required sample size (n) can be calculated using the formula ,

n = (0.50)(0.50)(2.576/0.02)²

n = 0.25 * 16589.44

n = 4147.36

n ≈ 4148 .

Therefore , the sample size is 4148 .

The given question is incomplete the complete question is

A sociologist wishes to estimate the percentage of the U.S. population living in poverty. What size sample should be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence ?

(a) 2401

(b) 4148

(c) 1692

(d) 2.575

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Answer:So looking at this question, we have two variables (1 - a glass of milk; 2 - a snack bar) and two equations to use to solve for the two variables. Remember that for any number of variables, you need that same number or more equations to solve for the variables.Let's say that a glass of milk is represented by g and a snack bar is represented by s.So we essentially have two equations here:4 glasses of milk + 3 snack bars = 88 carbs, or:4g + 3s = 882 glasses of milk + 4 snack bars = 74 carbs, or:2g + 4s = 74Now that we have this, we can solve for our equations. There are two ways to do this:SUBSTITUTION - solve for one variable, then substitute it inLet's solve for g using the second equation. First, we'll isolate g by subtracting 4s from both sides.2g = 74 - 4sNext, we can divide the whole equation by 2 to solve for g.g = 37 - 2sNow, we can substitute this into the first equation for g and solve for s.4g + 3s = 884(37 - 2s) + 3s = 88148 - 8s + 3s = 88148 - 5s = 88 (now subtract 88 from both sides and add 5s to both sides)60 = 5ss = 12Now we can use this to solve for g in the original equationg = 37 - 2sg = 37 - 2(12) = 37 - 24 = 13ELIMINATION - eliminate one variable to solve for the other, then use that to solve for the firstLet's look at our two equations4g + 3s = 882g + 4s = 74Let's eliminate the variable g first by multiplying the second question by -2.4g + 3s = 88-4g - 8s = -148If we add these two equations together, we get-5s = -60Divide both sides by -5 and we gets = 12Now, we can plug s into either equation to solve for g as we did above.