the attention span of a two-year-old is exponentially distributed with a mean of about 8 minutes. suppose we randomly survey 60 two-year-olds.

The main activity that is performed by accountant include the safe keeping of financial records and preparation of financial statements that are helpful in order to represent the current financial positions of a company.

An accountant is a qualified personnel who is the responsibility of maintenance of accounting records and safe keeping of the books of accounts of a firm. apart from maintenance of the accounting records and accountant also has to ensure that the financial statements are true and fair.

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The volume of the composite figure is A) 69[tex]\pi ft^3[/tex].

What is volume?

 The area occupied within an object's three-dimensional bounds is referred to as its volume. Another name for it is an object's capacity. The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Volumes vary depending on the shape.

Here the given figure contains cone and cylinder.

In cone height = 5f , radius r = 3 ft.

Then Volume of the cone is ,

=> V = 1/3 ([tex]\pi r^2[/tex]h) cubic unit

=> V = 1/3 (3.14*9*5)

=> V = 15[tex]\pi ft^3[/tex]

Now In cylinder Height = 6ft and radius = 3ft.

Then Volume of cylinder is ,

=> V=[tex]\pi r^2h[/tex] cubic unit.

=> V= [tex]\pi[/tex]*9*6

=> V=54 [tex]\pi[/tex][tex]ft^3[/tex]

Then Total volume of the figure is ,

=> Volume of cone+ volume of cylinder

=> 15[tex]\pi[/tex]+54[tex]\pi[/tex]

=> 69[tex]\pi ft^3[/tex].

Therefore the volume of the composite figure is  69[tex]\pi ft^3[/tex].

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Answer:

[tex]\frac{(x-3)^2}{(3-x)(3+x)}[/tex]

Step-by-step explanation:

1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]\frac{(x-3)^2}{(3-x)(3+x)}[/tex]

Thanks.

Given the function h(x) = x² - 7x - 8. The extremum of the function is the minimum one and its value is h(x) = -32.5

The relation between symmetry of the graph and the extremum point is:

Suppose x = p is the line equation of the graph's symmetry, then f(p) is the extremum value.

The given function is:

h(x) = x² - 7x - 8

Find the x-intercepts:

h(x) = 0

x² - 7x - 8 = 0

(x + 1) (x - 8) = 0

x = -1 or x = 8

The symmetry lies in the middle of x-intercepts. Hence, the symmetry occurs at:

x = (-1 + 8) / 2

x = 3.5

The extremum point is:

h(3.5) = 3.5² - 7 x 3.5 - 8 = -32.5

Since the quadratic term x²  has a positive coefficient, the graph is open downward, hence the extremum point is the minimum one.

Complete question:

Find the extremum of each function using the symmetry of its graph. classify the extremum of the function as a maximum or a minimum and state the value of x at which it occurs. h(x) = x² - 7x - 8

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The linear functions of the tables are y = 6x - 2 and y = 2.5x - 1

Table 1

From the table, we have the following points that can be used in our computation:

(x, y) = (1, 4)  and (2, 10)

The equation of the line is then calculated using the following equation

y = m(x - x₁) + y₁

Where

m = slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

So, we have

m = (10 - 4)/(2 - 1)

Evaluate

m = 6

Recall that

y = m(x - x₁) + y₁

So, we have

y = 6(x - 1) + 4

So, we have

y = 6x - 6 + 4

Evaluate

y = 6x - 2

Table 2

From the table, we have the following points that can be used in our computation:

(x, y) = (1, 1.5)  and (2, 4)

The equation of the line is then calculated using the following equation

y = m(x - x₁) + y₁

Where

m = slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

So, we have

m = (4 - 1.5)/(2 - 1)

Evaluate

m = 2.5

Recall that

y = m(x - x₁) + y₁

So, we have

y = 2.5(x - 1) + 1.5

So, we have

y = 2.5x - 2.5+ 1.5

Evaluate

y = 2.5x - 1

Hence, the linear function is y = 2.5x - 1

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For the given relation for (x , y) ∈R if x ≥ y defined on the set of positive integers only transitive relation holds true.

As given in the question,

Given (x , y) ∈R

To check whether relation reflexive, symmetric, antisymmetric, transitive, and/or a partial order is true or not:

a. Reflexive : If (x, x)∈R for all x ∈R

x ≥ x for all x ∈ R which is not true.

b. Symmetric : If 'x' is related to 'y' then 'y' is also related to 'x' for all      (x, y) ∈R.

Here, x ≥ y ⇒ y ≥ x for all (x, y) ∈R , which is not true.

c. Antisymmetric : If 'x' is related to 'y' and 'y' is related to 'x' then x = y for all (x , y)∈ R.

Here, x ≥ y and y ≥ x ⇒ x = y is not true.

Not antisymmetric.

d. Transitive: If 'x' is related to 'y' and 'y' is related to 'z' then 'x' is related to 'z' for all x, y, z ∈R.

Here,  x ≥ y , y ≥ z ⇒ x ≥ z for all x, y, z ∈R.

True.

Therefore, for the given relation for (x , y) ∈R if x ≥ y defined on the set of positive integers only transitive relation holds true.

The complete question is:

Determine whether the relation is reflexive, symmetric, antisymmetric, transitive, and/or a partial order.

(x, y)∈R if x ≥ y when defined on the set of positive integers.

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The potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

What is function?

In arithmetic, a perform from a collection X to a collection Y assigns to every part of X specifically one part of Y.

Main body:

p(x) = x⁴+ 22x² - 16x - 12

From the rational root theorem,

All the possible roots of the function are in the form of a rational number.

x =  ± p/q

x = ± (Factors of the constant term)/ (Factors of leading coefficient)

In the given polynomial,

The constant term is - 12

The leading coefficient is 1

The factors of - 12 are ±1, ±2, ±3, ±4, ±6, ±12

Factors of 1 are ±1.

From the rational root theorem, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

Therefore, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

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The example of the experimenter-expectancy effect is option (b)  The experimenter "expects" females to experience more difficulty on a math task so the experimenter unintentionally behaves in ways that undermine the performance of females on the math task

The experiment-expectancy is defined as the unintended effect of the hypotheses that is obtained from the the result of the research participant.

It is also defined as how the perceived expectations of an observer can influence.

Hence, the example of the experimenter-expectancy effect is option (b)  The experimenter "expects" females to experience more difficulty on a math task so the experimenter unintentionally behaves in ways that undermine the performance of females on the math task

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After plotting all the three points, we get the parabolic equation in the form is 2(x - 1)²-34.

Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line.

General equation of the quadratic equation,

Y = ax² + bx +c

Given points,

(-2, 0),

(-1, -10),

(4, 0).

Putting the points in the general equation,

Putting (-2, 0), we get

0 = 4a - 2b + c

Putting (-1, -10), we get

-10 = a - b +c

Putting (4, 0), we get

0 = 16a + 4b +c

Solving all equations we get,

a = 2 , b = -4 , c = -16

After putting the values,

Y = 2x²- 4x- 16

2(x² - 2x - 8)

2(x²- 2x + 1 - 1 - 16)

=2(x - 1)²-34

Hence we get the required equation in the parabolic form.

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To find the length, width, and height of a rectangular prism with the volume, you need to know the formula for volume of a rectangular prism. The formula is V=lwh, where l is the length, w is the width, and h is the height.

A rectangular prism is a three-dimensional figure with six faces that are all rectangles. The length, width, and height of a rectangular prism can be found using the formula V=lwh, where V is the volume, l is the length, w is the width, and h is the height. To solve for one of the variables, you need to rearrange the equation. For example, to solve for h, you would rearrange the equation to h=V/lw. This would give you the height in terms of the other two variables.

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The dimensions of a norman window of maximum area if the total perimeter is 14 feet are 2 ft and 4 ft respectively.

Given:

a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window

we are asked to  find the dimensions of a norman window of maximum area if the total perimeter is 14 feet.

the area of the semicircle is given by:

A = πr²/2

The area of the rectangle is just the product of its length and width.

Letting A be the area of the window and adding the two ares, we have:

A = xy + π(y/2)²/2

= xy + π(y²/4)/2

= xy+πy²/8

we know the circumference = πd

the circumference of a semicircle is half of that. The perimeter of a rectangle is the sum of twice the length and twice the width. However, one of the sides is replaced by the semicircle, so we remove it from the equation.

Hence, we have the following equation for the perimeter.

14 = 2x+y+πy/2

let us isolate x from this equation

14 = 2x+y+πy/2

14-y-π/2 = 2x

x = 7-y/2-πy/4

substituting x to the equation for the area, w have:

A = xy + πy²/8

= (7 - y/2 - πy/4)y + πy²/8

= 7y - y²/2 - πy²/4 + πy²/8

= 7y - y²/2 - 2πy²/8 + πy²/8

= 7y - y²/2 - πy²/8

differentiating A with respect to x.

A = 7y - y²/2 - πy²/8

A' = 7 - y - πy/4

⇒ 7 - y - πy/4 = 0

⇒ 28 - 4y - πy=0

⇒ 28 = 4y+πy

⇒ 28=(4+π)y

⇒ y = 28/4+π ≈ 4 ft

perimeter:

14 = 2x+y+πy/2

14 = 2x + 28/4+π + π(28/4+π)/2

14(8+2π)=2x(8+2π)+28(2)+28π

112+28π = 16x+4πx+56+28π

112-56=16x+4πx

56=(16+4π)x

x=56/16+4π

= 14/4+π

x=14/4+π≈ 2 ft.

Hence the dimension are 2 ft and 4 ft.

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The ratio of even cards to odd cards that Jordan has is 2:5 or 2/3.

Given:

Jordan has some number cards that each have a whole number on them.

If he chooses a card at random, the probability that the number on it is even is 2/7.

Let x and y be the even and odd cards.

x / x+y  = 2/7

cross multiplication

7*x = 2(x+y)

7x = 2x + 2y

7x - 2x = 2y

5x = 2y

divide by 5 on both sides

5x/5 = 2y/5

x = 2/5 y

x/y = 2/5

x:y = 2:5.

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Answer:

10

Step-by-step explanation:

20% of 50 ads

=20/100*50 ads

=10 ads

Answer:

original price was $8

Step-by-step explanation:

Ashley buy a hamster wheel during the sale (25% off). If Ashley pay $6, what was the original price?

$6 = 75% of price

75% = 0.75

6 = 0.75x

divide both sides by 0.75:

6/0.75 = 0.75x/0.75

x = 8

original price was $8

Factoring the expression [tex]x^{6} - y^{6}[/tex] is[tex](x^{3} +y^{3})(x^{3}-y^{3})(x^{2}+y^{2}+xy)(x^{2}+y^{2}-xy)[/tex]

Given expression = [tex]x^{6}-y^{6}[/tex]

= [tex](x^{3})^{2} - (y^{3})^{2}[/tex]

Now, using the formula [tex]a^{2}-b^{2} = (a+b) (a-b)[/tex]

= [tex](x^{3}-y^{3})(x^{3}+y^{3})[/tex]

Here, using the formulas

[tex]x^{3}-b^{3} = (a-b)(a^{2}+b^{2}+ab)[/tex] and [tex]a^{3} + b^{3} = (a+b)(a^{2}+b^{2} -ab)[/tex]

Therefore, [tex](x^{3} +y^{3})(x^{3}-y^{3})(x^{2}+y^{2}+xy)(x^{2}+y^{2}-xy)[/tex]

When a number or other mathematical object is expressed as the sum of several factors, usually smaller or easier versions of the same kind, this is referred to as factorization. When an expression has been fully factorized, it must be enclosed in brackets by removing the factors with the highest common denominator. The simplest method of factorization is to find the phrase's highest common factor among all of its terms. The highest common factor (HCF) should be placed in front of any brackets.

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The slope of the line y = - 4x + 10 is -4.

The slope of any line can be calculated using any two distinct points lying on the line. It is defined as the change in y coordinate with respect to the change in x coordinate of that line.

The net change in y coordinate is Δy, while the net change in the x coordinate is Δx, then the slope

                    m = Δy/Δx = dy/dx.

Here, we are given the line y = - 4x + 10

Differentiating the equation of line with respect to x, we get

                  dy/dx = - 4

⇒ slope m = dy/dx = -4.

Therefore, the slope of the line was found to be -4.

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NOTE : The question given here is not complete. The complete question is given below.

Question: What is the slope of y = - 4x + 10?.

Answer:

15/22

Step-by-step explanation:

15 red, 15 blue, 15 yellow

You draw a marble of any color.

Now the marbles left in the bag are 14 of the same color, and a total of 30 of different colors for a total of 44 marbles.

Your desired outcome is a marble of a different color.

There are 30 desired outcomes.

The total number of possible outcomes is all the marbles left in the bag: 44.

p(2 marbles of different colors) = 30/44 = 15/22

Answer:

Below

Step-by-step explanation:

angle 1 + 120 = straight line = 180    so angle 1 = 60°

angles 1  3  4  7   are all equal

angle 2 = 120° = angles 5 and 6

When we multiply two decimal numbers less than 1 then their product will be less than 1.

What do you mean by fraction?

A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. It is known as an improper fraction if the numerator is bigger and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder. By dividing the numerator by the denominator, any fraction can be expressed in decimal form. One or more digits may repeat indefinitely or the result may come to an end at some point.

If we multiply two decimal numbers less than 1 then their product will also be less than 1. Because we are determining a fractional portion of a quantity, this is the case.

Decimals are frequently multiplied by treating them as whole numbers before placing the decimal point in the result. Where the decimal point is placed in the solution depends on how many digits are present in the factors following the decimal points.

Therefore, when we multiply two decimal numbers less than 1 then their product will be less than 1.

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To translate triangle A to B, left 3, down 2 and to translate triangle B to A, up 2, right 3

There are two triangles in the graph

Consider the triangle on top as triangle A and the triangle on bottom as triangle B

The translation is the process of the changing the coordinates of the given shapes in the graph. The shape and size will be same only the coordinates will vary

Consider the triangle A

If we want triangle A to translate to triangle B

First translate 3 units to left and translate 2 units down

Now consider the triangle B

If we want to translate triangle B to triangle B

First translate 2 units up and translate 3 units right

Hence, to translate triangle A to B, left 3, down 2 and to translate triangle B to A, up 2, right 3

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13.5 Hrs long a player would have to practice batting to have 27 hits.

Given:

TIME (Hrs) 1  5  9  13  17

HITS         2 11 18 25 34

To have 27 hits :

= 13 + 1 + 17 + 5 - 9 / 2

= 14 + 22 - 9 / 2

= 36  - 9 / 2

= 27 / 2

= 13.5 hours

Therefore 13.5 Hrs long a player would have to practice batting to have 27 hits.

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The required work done in lifting the laptop to a height of 2 feet will be 263.79 foot-poundal.

Total weight of the laptop is 4.1 pounds

Acceleration due to gravity = 32.17 ft/[tex]s^{2}[/tex]

Now the height to which the laptop has been lifted = 2 feet

Since, there is no mentioned velocity of the laptop, therefore the kinetic energy will be zero

Therefore, the total work in lifting the laptop will be equal to the change in potential energy.

Potential energy is the energy that comes by virtue of its position with reference to other

Therefore, potential energy = mgh

Where, m = mass of the laptop = 4.1 pounds

g = acceleration due to gravity = 32.17 ft/[tex]s^{2}[/tex]

h = height to which the laptop is lifted =  2 feet

Therefore potential energy = (4.1)(32.17)(2) = 263.79 foot-poundal

263.79 foot-poundal is the required work done.

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The range of function f(x) = sin(x) is the set of all real numbers lying between [-1, 1].

Although they can sometimes be written as functions, the sine, cosine, and tangent of such an angle really are defined on the basis of trigonometry.

Thus, range of function f(x) = sin(x) is the set of all real numbers lying between [-1, 1].

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Answer:

See below

Step-by-step explanation:

= {(1, 3), (2, 5), (3, 7), (4, 9), (5, 9)}

Domain:

All the x-values of the relation are domain.

So,

Range:

All the y-values of the relation are range.

So,

[tex]\rule[225]{225}{2}[/tex]

The Confidence Interval for the hypothesis test at the 5% level to determine if 68% represents California is 0.65, 0.90.

First, we need to find H₀ and Hₐ. In this case, we want to check whether California community colleges take 68% of the online classes thought by full-time faculties, or not.

H₀ : p = 0.68; Hₐ : p ≠ 0.68

Second, we need to determine the distribution needed. State what our random variable P’ represents.

Normal: N

Test Statistic : z = 0.1873

Third, we have to calculate he p-value using the normal distribution for proportions.

p-value = 0.1873

If the null hypothesis is true (the proportion is 0.68), thus there is a 0.1873 probability which the estimated proportion is 0.773 or more.

Fourth, we need to compare [tex]\alpha[/tex] and the p-value, then indicate the correct decision (reject or do not reject the null hypothesis).

[tex]\alpha[/tex] = 0.05

Decision : Do not reject the null hypothesis

Reason for decision : p-value > 0.05

At the 5% level, the data do not provide statistically significant evidence that the true proportion of online courses taught by full-time faculty is not 68%.

Last, define the confidence interval. The confidence interval is (0.6275, 0.8725) = (0.65, 0.90).

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Answer:

Step-by-step explanation:

First get the slope of the line. This is (7-3)/(-3-3)=4/-6=-4/6=-2/3

Using slope intercept form, we get the equation

(-2/3)x+5=y

Scaffold instruction mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.

What is scaffold instruction?

Hence, Scaffold instruction mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.

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The proportionate reduction in error for knowing the value of the independent variable is 0.54.

The variable which does not depend on any variable and hence independent are known as independent variable.

Given that,

sum of squares for a regression equation was 153.7 = SST

error sum of squares was 82.6 = SSE

SS (reg) = SST - SSE

                153.7 - 82.6

                 SS(reg) = 71.1

The proportionate reduction in error for knowing the value of the independent.

             = 1 - [tex]\frac{(SS)reg}{SST}[/tex]

             = 1 - [tex]\frac{71.1}{153.7}[/tex]

             = 1 - 0.46

             = 0.54

The proportionate reduction in error for knowing the value of the independent variable is 0.54.

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The equation for the direct variation will be 5y-3x=0.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, For the data in the table, does y vary directly with x

X: 5, 8, 9

Y: 3, 5, 7

y ∝ x

y=kx

3=k5

k=3/5

For x as 5 and y as 3, the obtained equation is,

y=kx

y=3/5x

5y=3x

5y-3x=0

Thus, the equation for the direct variation will be 5y-3x=0.

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Measurements taken in a different frame of reference reveal a decrease in their dimensions—the only component that is parallel to the motion—and a delay in time—commonly referred to as "Length Contraction" and "Time Dilation"

when the objects are moving at a speed that is comparable to the speed of light and is in the order of C. The following is a discussion of the given relativistic issue.

The length AC is the only length that observers using the platform frame of reference would perceive as being shorter (the length).

What is change in measurement?

Estimation of progress alludes to the evaluation of fluctuation from one viewpoint, and to the appraisal of progress in a smaller sense then again. Short-term and reversible fluctuations (such as mood state variability) are characteristics of variability.

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