Which of the following statements is TRUE? O a. If f(a) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) attains its global maximum at x = d, then the function f(x) · g(x) attains its global maximum on [a, b] at x = cºd. O b. All of the statements are false. a O c. Every local maximum is a global maximum d. The global maximum value of a differentiable function f(x) on a closed interval (a, b) must occur at a critical value or an endpoint e. The critical points of f'(2) are same as the critical points of f(x)

Answer:

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

Let the side of the square is x and side of the octagon is y.

Set equation for sides:

The perimeter of square is same as the perimeter of the octagon:

Simplify and then substitute:

Find x:

If Joe deposits $264,954.31 today then he will reach his goal

Define Present Value

Finding the appropriate quantity of money to deposit today in order to ensure a specific amount of future payments is one objective of financial analysis. The target payment amount, the quantity and frequency of payments, and the interest rate all influence the present value, which is the value in today's dollars.

Given,

Joe want to receive each month = $22,000

Interest rate = 6%

number of payment = 22 years

We know, the formula of present value is

Present value = pmt * (1 - (1/ (1+r)ⁿ) ) / r

pmt = $22,000

r = 0.06

n = 22 years

Now, plug in the values

Present value = $22,000( 1 - (1/(1+0.06)²² ) / 0.06

                       =$22,000( 1 - (1/(1+0.06)²² ) / 0.06

                       ≈ $264,954.311

Hence, If Joe deposits $264,954.31 today then he will reach his goal.

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For any confidence level C, the value of the sample proportion will always be considered a plausible value for p is a true statement.

For any given confidence level, the sample proportion of a given sample will always be within the range of values that are considered plausible for the population proportion. This range is determined by the confidence interval, which is calculated based on the confidence level C. Thus, the sample proportion will always be considered a plausible value for p.

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Missing part of the equation is 6.0 × [tex]10^{-8}[/tex] [tex]m^{3}[/tex].

It is given that students sets up the equation (0.060 [tex]cm^{3}[/tex])(_) = (_) [tex]m^{3}[/tex].

i.e. we have units of [tex]cm^{3}[/tex] and wants units of [tex]m^{3}[/tex] .

We know that 100 cm = 1 meter

i.e. 100cm/1 meter

⇒  [tex](100cm/1 meter)^{3}[/tex] = 1 × [tex]10^{6} cm^{3}/m^{3}[/tex]

⇒1/(1 × [tex]10^{6} cm^{3}/ m^{3}[/tex]) = (1 × [tex]10^{-6} m^{3}/cm^{3}[/tex])

We can use this new conversation factor to convert volume from [tex]cm^{3}[/tex] to [tex]m^{3}[/tex].

(0.060 [tex]cm^{3}[/tex])(1 × [tex]10^{-6} m^{3}/cm^{3}[/tex]) = (_) [tex]m^{3}[/tex]

(0.060 [tex]cm^{3}[/tex])(1 × [tex]10^{6} cm^{3}/m^{3}[/tex]) = 6.0 × [tex]10^{-8} m^{3}[/tex].

This is the required equation.

If we want to convert measurement,

to convert a smaller unit to a larger init, divide it by the number of smaller units which are needed to make larger unit. To convert from a larger unit to a smaller one, multiply. To convert from a smaller unit to a larger one, divide.

A conversation factor is a number used to change one set of units to another, by multiplying or dividing.

Given question is incomplete.

a student sets up the following equation to convert a measurement. (the stands for a number the student is going to calculate.) fill in the missing part of this equation  (0.060 [tex]cm^{3}[/tex])(_) = (_) [tex]m^{3}[/tex].

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The given equation is solved to obtain Q = -1/21.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given equation is as below,

12/7Q - 1/21Q = Q - 2/3

It can be simplified as follows,

12/7Q - 1/21Q = Q - 2/3

=> 12/7Q - 1/21Q - Q = -2/3

=> (36 - 1 - 21)Q = -2/3

=> 14Q = -2/3

=> Q = -1/21

Hence, the solution of the given equation is -1/21.

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The greatest common factor of the given term is 26.

What is the greatest common factor?

The greatest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.

The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization. You can obtain the necessary reduced form by determining the GCF of the denominator and numerator of a fraction or ratio.

Given, [tex]\frac{52}{78} = \frac{26*2}{26*3}[/tex]

So, the simplest form is [tex]\frac{2}{3}[/tex].

Hence, the greatest common factor is 26.

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The probability that the second is a club, given that the first is not a club is  0.1911

According to the question,

We have a ordinary deck

An ordinary deck contain 52 cards

Number of club an ordinary have = 13

Let the first event of not getting a club at first draw be "A"

and "B" for getting a club at second draw

P( not getting a club) = P(A) = 1 - P(getting a club)

=> 1 - 13/52

=> 39/52

Now , We are drawing card without replacement

Number of cards we have after first draw = 51

P(getting a club) = P(B) = 13 / 51

The probability that the second is a club, given that the first is not a club

P(A).P(A)=> 39/52 . 13/51

=> 507/2652

=> 0.1911

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On solving the provided question, based on the information, we can say that there are 35 X 6 = 210 ways

Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.

[tex]^nC_{r} = \frac{n!}{r!(n - r)!}[/tex]

ways can this company buy them are - 35 X 6 = 210 ways

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The smoothing constant is the correct option.

What is exponential smoothing?

The exponential window function is a general method for smoothing time series data known as exponential smoothing. Exponential functions are used to assign weights that decrease exponentially over time, as opposed to the simple moving average, which weights previous observations equally.

Forecasts using exponential smoothing are precise.

This method generates reliable and accurate forecasts that anticipate the following period.

Demand projections and actual demand are shown in the forecast. This makes it possible to effectively plan for demand, which leads to accurate inventory levels.

In exponential smoothing,  the higher the smoothing constant, the greater is the weight assigned to the values from the most recent  period.

Hence, the smoothing constant is the correct option.

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Answer:

[tex]\frac{4(8-1)}{6}[/tex]

6

Step-by-step explanation:

[tex]\frac{4(8 + 1) }{6}[/tex]

[tex]\frac{4(9)}{6}[/tex]

[tex]\frac{36}{6}[/tex]

6

Answer:

The expression is:

4(8+1)/6

Simplify:

= 6

Step-by-step explanation:

The expression is:

4(8+1)/6

Simplify:

= 4(9) / 6

= 36/6

= 6

The test statistic value for the given sample data with population mean difference is equal to optic C. 3.156.

As given in the question,

Given population mean difference μd = 0

sample size 'n' = 9

Sample data is:

x                y                [tex]d_{i}[/tex] ( x - y)                   [tex]( d_{i} - \bar{d} )^{2}[/tex]

168           162             6                                15.21

180           178              2                                62.41

157            145             12                               4.41

132            125             7                                  8.41

202           171              31                               445.21

124            126              -2                              141.61

190            180              10                              0.01

210            195              15                               26.01

171              163             8                                3.61

                                    ∑[tex]d_{i}[/tex] = 89                 ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] = 706.89

[tex]\bar{d}[/tex] = ( 1/ n ) ∑[tex]d_{i}[/tex]

  = (1/9) (89)

  = 9.889

  = 9.9

Standard deviation of the mean difference '[tex]S_{d}[/tex]'

= √[1 / (n - 1)]( ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] )

= √706.89/ 8

=√88.361

= 9.4

test statistic

t = ( [tex]\bar{d}[/tex] - μd)/ ( [tex]s_{d} /\sqrt{n}[/tex] )

 = ( 9.9 - 0) / ( 9.4 / √9)

 = 9.9/ 3.133

 = 3.156

Therefore, the test statistic value for the given sample data is equal to option C. 3.156

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According to the figure, the side congruent to line GK is line HL

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by Angle - Side - Angle = ASA to ensure that the the triangles are congruent

The Angle and sides used for the proof include

< F = < J

FL = JK

<  L = < K

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Answer:

  A.  HL

Step-by-step explanation:

You want to identify the side corresponding to GK in the figure showing congruent triangles.

The larger triangles on the left and right each have an angle marked with one arc, an angle marked with two arcs, and the segment between those angles marked with one hash mark. This identical marking of two angles and the side between them means you can declare the triangles congruent by the ASA (angle-side-angle) congruence postulate.

When we name the triangles in order of the number of marks on the angles (0–2 arcs), we find the congruence statement to be ...

  ∆HLF ≅ ∆GKJ

The segment of interest is GK, which is identified by the first two letters of its triangle designator in the congruence statement. The corresponding side is identified by the first two letters in the other triangle designator: HL.

  ∆HLF ≅ ∆GKJ

Side HL is congruent to GK.

__

Additional comment

Like a lot of math, this requires you to match patterns.

To multiply fractions with multiple denominators, you have to change the fraction to get the same denominator.

For example, if you have 1/3 * 1/2, you will have to find the least common multiple of 3 and 2, which is 6. Then, multiply the numerator by the same number that you multiplied the denominator to get 6.

1/3 * 1/2

LCM = 6

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

Then, multiply across the numerator

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

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Answer:  The top right table

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Given: [tex]\textsf{y = 30 - 3x}[/tex]

Find:  [tex]\textsf{Match the table of values with the equation}[/tex]

Solution: First we must understand what form our equation is in and what each of the numbers represent.  This form is known as the slope intercept form which is formatted as y = mx + b.  Our equation is slightly re-ordered but we can change that by converting it to y = -3x + 30 where m is equal to -3 and b is equal to 30.  Let us know talk about what m and b are.  M is the slope of the equation or also known as the rise/run or the change in y over the change in x.  B is the y-intercept which is basically the value of y when x is equal to 0.  In this case, our b is equal to 30.

Looking at the tables we can see what the value of y when x is equal to 0 for each table.  The only table that matches up stating that y is equal to 30 when x is 0 is the top right table.

You do not have to go any further but if you want to confirm that the slope is as expected we can do the following:  [tex]\frac{y_2\ -\ y_1}{x_2\ -\ x_1}[/tex].

Plug in the values and simplify

Therefore, we can confirm that the slope matches up with the given equation as well.  So, the final answer would be that the top right table would correspond to the equation y = 30 - 3x.

The volume of cylinder is denoted as πr²h

The density of a cylinder is determined by its volume, which indicates how much material it can hold or how much can be submerged inside it. The volume of a cylinder can be calculated using the formula r2h, where r denotes the radius of the circular base and h denotes the height of the cylinder. Any substance that can be evenly put into the cylinder, including liquid, may be used as the material. Shape volumes can be seen here.

This article contains a basic explanation of cylinder volume as well as examples with solutions for your convenience. The study of shapes and their characteristics is a key component of geometry in mathematics. Any three-dimensional shape must have both volume and surface area.

Hence, the volume of cylinder is denoted as πr²h

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Since the graph has a line from 0 comma 0 and going through 25 comma 8, C. Yes, it is proportional because it is a line that goes through (0, 0).

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it starts from the origin (0, 0) and as such, it is proportional.

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Answer:

Jordan worked 18 hours lifeguarding and 15 hours walking dogs.

Step-by-step explanation:

To solve this problem, we can set up a system of two equations to represent the given information. Let "L" represent the number of hours Jordan worked lifeguarding and "W" represent the number of hours he worked walking dogs.

The first equation will represent the total amount of money Jordan earned:

13L + 10W = 177

The second equation will represent the difference in hours between the two jobs:

L - W = 3

We can solve this system of equations using either substitution or elimination.

Using substitution, we can solve for one variable in terms of the other and substitute that expression into the other equation to solve for the other variable.

Solving the second equation for L, we get:

L = W + 3

Substituting this expression for L into the first equation, we get:

(W + 3) + 10W = 177

Combining like terms, we get:

11W + 3 = 177

Subtracting 3 from both sides, we get:

11W = 174

Dividing both sides by 11, we get:

W = 15.818181818181818

Since the number of hours worked must be a whole number, we can round down to 15 hours. Substituting this value back into the equation L = W + 3, we get:

L = 15 + 3 = 18

Therefore, Jordan worked 18 hours lifeguarding and 15 hours walking dogs.

[tex]1 + cot^{2}2t = csc^{2}2t[/tex]  can be manipulated from  [tex]sin^{2}2t +cos^{2}2t =1[/tex]

What is Pythagorean Identity?

An identity, in mathematics, is an equation that is true for all possible values.(It is always true regardless of the values that are substituted into the equation.)

A trigonometric identity is an equation that involves trigonometric functions and is true for every single value substituted for the variable (assuming both sides are "defined" for that value) You will find that trigonometric identities are especially useful for simplifying trigonometric expressions.

The most common trigonometric identities are those involving the Pythagorean Theorem.

When studying the unit circle (radius of 1), it was observed that a point on the unit circle (a vertex of the right triangle) can be represented by the coordinates (cos 2t, sin 2t ).

Since the legs of the right triangle in the unit circle have the values of sin 2t and cos 2t, the Pythagorean Theorem can be used to obtain [tex]sin^{2}2t +cos^{2}2t =1[/tex]

Given Equation :   [tex]sin^{2}2t +cos^{2}2t =1[/tex]

To proof :  [tex]1 + cot^{2}2t = csc^{2}2t[/tex]

[tex]1 + cot^{2} \alpha = csc^{2} \alpha [let \alpha =2t] \\\\1 + cot^{2} \alpha = 1 + \frac{cos^{2}\alpha }{sin^{2} \alpha } \\\\1 + cot^{2} \alpha = \frac{sin^{2}\alpha }{sin^{2} \alpha } + \frac{cos^{2}\alpha }{sin^{2} \alpha }\\\\1 + cot^{2} \alpha = \frac{sin^{2}\alpha + cos^{2} \alpha }{sin^{2} \alpha }\\ \\1 + cot^{2} \alpha = \frac{1 }{sin^{2} \alpha } [ since ,sin^{2}\alpha + cos^{2}\alpha = 1]\\\\1 + cot^{2}\alpha = sec^{2} \alpha\\\\or\\1 + cot^{2}2t = sec^{2} 2t[/tex]

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Answer:the answer is 8070

Step-by-step explanation:

because it is

The solution of the inequality will be;

⇒ 5.5 ≤ x

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 10 ≤ 2x - 1

Now,

Since, The inequality is,

⇒ 10 ≤ 2x - 1

Hence, Solve the inequality as;

⇒ 10 + 1 ≤ 2x - 1 + 1

⇒ 11 ≤ 2x

⇒ 5.5 ≤ x

Thus, The solution of the inequality will be;

⇒ 5.5 ≤ x

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The sample required to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence is 158.

Given:

You wish to conduct your own study to estimate the miles per gallon on a 2007 Ford Taurus.

How large a sample would you need to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence  = ?

if you read in a previous study that the standard deviation of miles per gallon for a 2007 Taurus is 3.21.

we know that :

z value of 95% is 1.96

Margin of error = E = z × sd/√n

we have:

n = (z×sd/E)²

= 158.33

= 158

Hence we get the sample as 158

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If many random samples of size 30 are selected from the population of all customers, approximately 90% of the constructed intervals would capture the true mean time it takes for her employees to mow a lawn.

Thus, option (D) is correct.

A confidence interval represents a range of values that is likely to contain the true population parameter with a certain level of confidence.

The 90% confidence interval (40 to 55 minutes) suggests that if repeatedly take random samples of size 30 from the population and construct confidence intervals, about 90% of those intervals would contain the true mean time.

The confidence level gives us a measure of how confident we are in the estimate, indicating that in the long run, approximately 90% of the constructed intervals would capture the true mean time it takes for her employees to mow a lawn.

Thus, option (D) is correct.

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Answer:

daymn

it's gonna be okay

Answer: Part A 20.8 divided Part B 2 places to the left Part C 0.208

Step-by-step explanation:

Part A the question ask each time and when it ask each time it means dividing Part B when dividing you move to the left and their are two 0s and moving the decimal two places to the left would get you 0.208 so, therefor the answer is 0.208

Answer:

Step-by-step explanation:

you have to use the vertex

The correct location of the point is (d) between Quadrant II and Quadrant III.

We must choose the response that accurately describes the position of the point whose coordinates have a negative abscissa and a zero ordinate.

Any point with a negative abscissa and a zero ordinate on the XY plane in two dimensions can be represented as

Where a > 0, (x, y) = (-a, 0).

Let's plot (-1, 0), (-2, 0), (-3, 0), etc. on the coordinate plane as an example. The corresponding figure illustrates this.

The figure shows that every point of the type (-a, 0) is located on the X-axis' negative side.

The location of the negative X-axis between Quadrants II and III is known. As a result, the supplied point is situated between Quadrants II and III.

the appropriate answer is (d).

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Answer:

$16.67

Step-by-step explanation:

$19.38*14%=$2.71

$19.38-2.71=$16.67

The point slope form of the slope of escalator and distance is y-24 = 3/4(x-32).

The general point slope form is given by the equation -

y - y1 = m (x - x1)

Now we are given the slope as 3/4. So, keeping the values of y1 and x1 in the equation. Let us assume the points as (32, 24). As per the points, 32 is x1 and 24 is y1.

y - 24 = 3/4(x - 32)

y - 24 = 3x/4 - 3/4×32

Performing division on Right Hand Side of the equation

y - 24 = 3x/4 - 3×8

y - 24 = 3x/4 - 24

Rewriting the equation

y - 3x/4 = - 24 + 24

Solving the equation on Right Hand Side of the equation

y - 3x/4 = 0

y = 3x/4

Thus, the equation is y - 24 = 3/4(x - 32).

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Answer:

1027

Step-by-step explanation:

By combining the methods of row reduction and cofactor expansion the determinant of the given matrix is 1 .

In the question ,

it is given that ,

the matrix is   [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex]

we need to compute the determinant using the row reduction that means  using the row values [0 4 1 ] to find the determinant .

using the row [0 4 1]  , the signs on the values on the first row will be  +0, -4 and +1

the by applying the cofactor expansion , determinant will be equal to

= 0 -4[5×1 - 0] + 1[5×3 + 3×2]

= -4(5) + (15 + 6)

= -20 + 21

= 1

Therefore , the determinant is 1 .

The given question is incomplete , the complete question is

Combine the methods of row reduction and cofactor expansion to compute the determinant of the matrix [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex]  .

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