Let f and g be the functions in the table below. x f(x) g(x) f '(x) g'(x)
1 3 2 4 6
2 1 3 5 7
3 2 1 7 9 (a) If F(x) = f(f(x)), find F '(1).
F '(1) = ___________________.
(b) If G(x) = g(g(x)), find G'(2).
G'(2) = ___________________.

This formula is used to get the values of the sine and cosine products for angle A and to solve different trigonometry issues.

SinA cosA = sin2A / 2 is the formula for sinA and cosA. This formula is used to get the values of the sine and cosine products for angle A and to solve different trigonometry issues.

Let LHS =

[tex]\frac{tan A}{1+ tan^{2} A} + \frac{cot A}{1+ cot^{2} A}[/tex]

= [tex]\frac{tan A}{(sec^{2}A) ^{2} } +\frac{cot A}{(cosec^{2}A) ^{2} }[/tex]

= [tex]\frac{\frac{sin A}{cos A} }{\frac{1}{cos^{4}A } } + \frac{\frac{cos A}{sin A} }{\frac{1}{sin^{4}A } }[/tex]

= [tex]sin A cos^{3} A + cos A sin^{3}A[/tex]

= [tex]sin A cos A (sin^{2}A + cos^{2}A)[/tex]

= [tex]sin A cos A[/tex] = R.H.S

Hence proved  as L.H.S= R.H.S

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The complete question is:

Prove that (tan A)/((1 + tan2 A) 2) + (cot A)/((1 + cot2 A) 2) for cotA  = sinA cosA.

Answer:
4 1/2 divided by 2/5 equals to 45/4
Simplified : 45/4 = 11 1/4

With a 96% confidence level, we can be sure that the true population mean of SAR levels for cell phones falls between 0.918 and 1.130.where the critical value falls between 2.492.

We require the sample mean, population standard deviation, and sample size to determine the 96% confidence range for the population mean SAR level of cell phones. The standard error may be determined using a sample mean of 1.024, a population standard deviation of 0.337, and a sample size of 20.

After that, the confidence interval is determined as 1.024 (2.492) × (0.095) = (0.918, 1.130). This suggests that the genuine population mean of SAR values for cell phones falls between 0.918 and 1.130 with a 96% confidence level.

The formula for the 96% confidence interval for the population mean is given by:
Sample mean ± (Critical value) × (Standard error)

Where the critical value is 2.492 for a 96% confidence level and n = 20 degrees of freedom (sample size - 1). The standard error can be calculated as:

Standard error = Standard deviation / √n
Plugging in the given values:
Standard error = 0.337 / √20 = 0.095

The confidence interval is then:
1.024 ± (2.492) * (0.095) = (0.918, 1.130)

So, with a 96% confidence level, we can be sure that the true population mean of SAR levels for cell phones falls between 0.918 and 1.130.

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The highest score with an "F" grade is the 10th percentile score. To find the 10th percentile score, count 10% of the total number of scores, which is 100. So, the 10th percentile score is the 10th score from the bottom, which is 43.

A percentile score is a value on a scale that indicates the percentage of a set of observations that are below it. For example, a score of 80% on a test means that 80% of the test-takers scored below that score and 20% scored above it. In other words, the score separates the bottom 80% from the top 20%.

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The complete question is as follows:

Answer: 44

Step-by-step explanation:

The interior and exterior in these type of problems equal 180. 180 – 136 = 44

The midline of function be 5 , an amplitude of 4 and a period of 3/2 then the sine function be y = 4 sin (4π/3 x) + 5.

The ratio of the opposing side's length to the hypotenuse of a right-angled triangle is known as the sine function in trigonometry. A right triangle's unknown sides or angle can be determined using the sine function.

The ratio of the lengths of the opposing side and the hypotenuse of a right-angled triangle is known as the sine function in trigonometry. Use the sine function to calculate the unknown side or angles of a right triangle.

The sine of the angle is the ratio of the hypotenuse to the perpendicular of a right-angled triangle. The formula for sin is sin = Perpendicular / Hypotenuse.

General sine function a sin b (x - c) + d

amplitude = absolute value of a

b = 2π / period

c = phase shift (horizontal shift)

d = vertical shift (midline is y = d)

Here a = 4, d = 5, and b = 2π / (3/2) = 4π/3, c = 0

Therefore, the sine function be y = 4 sin (4π/3 x) + 5,

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The customer must pay a sum of $1,090 for the two x-rays. He will pay the $100 deposit as well as 40% of the x-ray costs ($700 x 0.4 = $280 + $930 x 0.4 = $372). $100 + $280 + $372 = $1,090.

Insurance is a contractual arrangement between two parties - the insurer and the policyholder. It is often referred to as insurance coverage or insurance policy. The insurer primarily offers coverage for the insured's damages that may occur under specified conditions.

Step 1: Determine the deductible amount: $100

Step 2: Determine the coverage amount: 60% of the x-rays' total cost

Step 3: Determine the value of the first x-ray: $700 x 0.6 = $420

Step 4: Determine the cost of the second x-ray: $930 x 0.6 = $558

Step 5: Total the deductible and coverage portions: $100 + $420 + $558 = $1,090

As a result, the user must pay a total of $1,090 for the two x-rays.

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Answer:

4658

Step-by-step explanation:

Answer:

h + 4

Step-by-step explanation:

given

f(x) = x² - 2x + 1

then

f(3 + h)

= (3 + h)² - 2(3 + h) + 1 ← expand (3 + h)² using FOIL

= 9 + 6h + h² - 6 - 2h + 1 ← collect like terms

= h² + 4h + 4

and

f(3) = 3² - 2(3) + 1 = 9 - 6 + 1 = 4

then difference quotient

[tex]\frac{f(3+h)-f(3)}{h}[/tex]

= [tex]\frac{h^2+4h+4-4}{h}[/tex]

= [tex]\frac{h^2+4h}{h}[/tex] ← factor out h from each term on the numerator

= [tex]\frac{h(h+4)}{h}[/tex] ← cancel h on numerator/ denominator

= h + 4

Answer:

The first answer

Step-by-step explanation:

Area of a rectangle

a = l x w

Area of a circle

a = [tex]\pi r^{2}[/tex]

Set them each to each other and substitute 8 for w and for r

l x 8 = [tex]\pi 8^{2}[/tex]  We can divide both sides by 8

l = [tex]\pi[/tex]8

Answer:

A. x = 3

Step-by-step explanation:

See picture

The ordered pair that describes the location of R′′ is (-4,-2)

Explanation:

When a point is reflected over the x-axis, the x-coordinate remains the same and the y-coordinate changes sign. So, the point R' will be (4,-2)

When a point is reflected over the y-axis, the x-coordinate changes sign and the y-coordinate remains the same. So, the point R′′ will be (-4,-2)

A' ∩ B ∩ C is region VI where B ∩ C but A is not included.

A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.

Given:

The region I represent A.

and, The region III represent B

and, The region VII represent C.

and, the region show A∩B.

and, the region IV shows A ∩ C

and, the region VI shows B ∩ C

and, the region V shows A ∩ B ∩ C.

Now, we want a region where B and C should be intersected but not include region A (A').

So, the regions shows A' ∩ B ∩ C is region VI where B ∩ C but A is not included.

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the height of fall of the bungee jumper is 9216 feet.

What is Distance?

a velocity is a unit of measurement for the Distance an object travels in a predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by dividing the total Distance traveled by the journey time.

Diane and Douglas both drive at an average rate of 50 miles per hour. So if they travel for the same time they will end up covering the same Distance as well.

As we know velocity = rate of change of displacement

The distance the bungee jumper falls is estimated as follows when the time of motion is 6 seconds;

6 = [tex]\frac{\sqrt{d} }{16}[/tex]

√d = 16*6

√d = 96

d = 9216

Hence the height of fall of the bungee jumper is 9216feet.

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(a) The probability that at least 29% of the sample are from poverty level households is 0.0466.

(b) Based on the answer to part (a), there is not enough evidence to suggest that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.

The probability of finding at least 29% of the sample from poverty level households is low, indicating that the difference between the observed percentage and the national value is not statistically significant.

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Answer:

16 % points

Step-by-step explanation:

From the table   1963-1972   is 58 %

                          2003 - 2013 is 42%

58 - 42 =  16 percentage points

The correct answer is B. While the measures of variation can be found they do not make sense because the data are nominal, they don't measure or count anything.

Any difference between the individuals in a species or between groups of organisms from any species is referred to as variation. Genetic variety is mostly caused through mutation, although other processes like sexual reproduction and gene flow also play a role.

Environmental variation refers to environmental elements that can contribute to variances. Inherited variation refers to the variance that is genetically transmitted during reproduction from parents to children.

The variable of interest is a nominal variable, which means it merely belongs to categories and doesn't actually have any "numerical" values. Only the categories' names—1, 2, 3, and 4—have been utilized.

Only "sample proportions" can be determined for nominal variables, and the variance between sample proportions of various samples may be calculated and compared, but measurements of variation within a single sample (as is the case here) are useless for nominal variables.

Therefore, Option B is the correct answer.

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Dummy variables:

Ice Clean Flavor, Gender, Shoe Color, Number on an Athlete's Jersey, Ice Cream Flavor

Quantitative Variables:

Time to run a marathon, Flat-Screen TV, Height, Hours Spent Researching Core, Calories in Desserts

A dummy variable, often known as an indicator variable or simply a dummy, is a variable in regression analysis that accepts the values 0 or 1 to signify the lack or presence of a category effect that would be anticipated to change the outcome. 

Any variable where the data indicate amounts is referred to be a quantitative variable (e.g. height, weight, or age). Any variable where the data represent groupings is referred to as a categorical variable. This comprises categories (like where people placed in a race), rankings (like cereal brands), and binary results (e.g. coin flips).

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The complete question is:

For use in a linear regression model, categorize which of the following variables should be represented as dummy variables and which can be represented as quantitative variables.

ITEMS

CATEGORY

The volume of the given triangular prism is 384 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the area of the base is

Area of a rectangle = 1/2 ×Base×Height

= 1/2 ×12×4

= 24 cm²

Now the volume is 24×16

= 384 cm³

Therefore, the volume of the given triangular prism is 384 cm³.

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The arc of length on the unit circle corresponds to the point (√3, 1) on the unit circle because the unit circle is a circle with a radius of 1, centered at the origin (0, 0).

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The number of the outcomes at two of the coins will turn up as head is 11

In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.

To solve this problem the formula and the combination procedure we must use is:

C(n/r) = n! / [(n-r)! *r!]

Where:

Information about the problem:

Applying the combination formula we have:

C(n/r) = n! / [(n-r)! *r!]

C(4/2) = 4! / [(4-2)! *2!]

C(4/2) = 4! / [(2)! *2!]

C(4/2) = 4*3*2! / [(2)! *2!]

C(4/2) = 4*3/2!

C(4/2) = 6

C(4/1) = 4! / [(4-1)! *1!]

C(4/1) = 4! / [(3)! *1!]

C(4/1) = 4*3! / [(3)! *1!]

C(4/1) = 4 / [1!]

C(4/1) = 4

C(4/0) = 4! / [(4-0)! *0!]

C(4/0) = 4! / [(4)! * 0!]

C(4/0) = 1

Total number of outcomes = 4C0 + 4C1 + 4C2

Total number of outcomes = 1 + 4 + 6

Total number of outcomes = 11

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The student is -3.75 ft below sea level, and the absolute value is 3.75 ft.

The vertical number line starts at negative 5.5 and the tick marks are every one half unit up to positive 1.5. The value negative 3.75 is labeled. Therefore, the student is -3.75 ft below sea level.

The absolute value represents the distance between the plotted value and zero (sea level) without considering the direction (above or below). In this case, the absolute value is 3.75 ft.

It takes 27min Joseph to run from mile marker 1 to mile marker 4 and the Joseph's average speed as [tex]& \frac{3}{27} \text { miles/min }[/tex], Joseph's average speed be as he travels from mile marker 9 to the finish line is 0.1078.9 miles/min.

(a) - Time taken by Trevor to ran from mile maker 1 to mile makers

      time taken by Trevor to ran from mile maker 1 to 2-mile maker.

     ran from mile maker 2 to 4.

[tex]$$\begin{aligned}& \text {= } \quad 8+19 \\& =\quad 27 \text { min }\end{aligned}$$[/tex]

(b) Average speed as he ran from mile maker 1 to mile maker 4.

speed = [tex]\frac{\text { distance }}{\text { time }} \\[/tex]

[tex]& =\frac{3 \text { miles }}{27 \text { min }} \\[/tex]

[tex]& =\frac{3}{27} \text { miles/min }[/tex]

(c).

Average speed Trevor to finish race in 113 min.

After 75 min. he passed 9 miles. Still, he have to ran 4.1 mile. [tex]$\left(\begin{array}{c}\text { Total - } 9 \text { miles } \\ 13.1-9 \text { miles }\end{array}\right)$[/tex]

remaining time = 113-75

                         = 38 min

avg. speed =[tex]\frac{\text { remaining distance }}{\text { remaining time }} \\[/tex]

[tex]& =\frac{4.1}{38}[/tex] miles/min

[tex]& =\frac{41}{380}[/tex] miles/min

=0.1078 .9 miles/min

Therefore, it takes 27min Joseph to run from mile marker 1 to mile marker 4 and the Joseph's average speed as [tex]& \frac{3}{27} \text { miles/min }[/tex], Joseph's average speed be as he travels from mile marker 9 to the finish line is 0.1078.9 miles/min.

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Answer:

x = 5

Step-by-step explanation:

5(2x-11) = -5

5(2x-11) = -510x - 55 = -5

5(2x-11) = -510x - 55 = -510x - 55 + 55 = -5 + 55

5(2x-11) = -510x - 55 = -510x - 55 + 55 = -5 + 5510x = 50

5(2x-11) = -510x - 55 = -510x - 55 + 55 = -5 + 5510x = 5010x / 10 = 50 / 10

x = 5

A addition to a large number line is indeed a diagram of a graduated single direction used to represent real numbers in introductory mathematics.

2 November 2020 A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number just on line could be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when a point.graphing

The midpoint is indeed the "average" of a two numbers, so for the first: (4 + (-6))/2 = -2/2 = -1 for such second,

you are provided the "average," so choose one of the ends as x, multiplying by 2 to get 2+x = -8 and x = -10.

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If an object is moving in a uniform circular motion, its period is given by the time interval for the object to make one revolution.

The movement of a body follows in a circular path is called a circular motion. The motion of a body moving with a constant speed along a circular path is called Uniform Circular Motion.

In the case of uniform circular motion, the acceleration is:

ar=v2/r=ω2r

If the mass of the particle is m, we can say from the second law of motion that:

F=ma

mv2/r= mω2r

With the number of revolutions displacements from the initial point to the final point also changes. As both these factors change velocity also changes. But in that uniform circular motion what remains constant is speed.

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Answer:

If a certain company has 900 employees and two out of every five employees have worked for the company for 10 years or more, then that company would have 360 employees who have worked for the company for 10 years or more.