let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 4, h'(1) = 4, g'(2) = 4, and "f '(4) = 7". find r'(1). r'(1)

The value of g in the following equation is 6.25. The solution has been obtained using trigonometry formula.

What is trigonometry?

The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. Therefore, applying the trigonometric formulas, functions, or trigonometric identities aids in locating the unknown or missing angles or sides of a right triangle. In trigonometry, angles can be stated in either degrees or radians. For calculations, the most common trigonometric angles are 0, 30, 45, 60, and 90 degrees.

We are given g sin 34° =3.5

⇒ g = 3.5/sin34°     (Dividing both sides by sin34°)

Now, value of sin34° = sin(30+4)° = 0.5592

So, we get

⇒ g = 3.5/0.5592

⇒ g = 6.25

Hence, the value of g in the following equation is 6.25.

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In the equation below, g has a value of 6.25. The trigonometric formula has been used to arrive at the solution.

The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry." In order to find the unknown or missing angles or sides of a right triangle, one can apply the trigonometric formulae, functions, or identities. Angles can be expressed in radians or degrees in trigonometry. The most frequent trigonometric angles used in computations are 0, 30, 45, 60, and 90 degrees.

Given is g sin 34° = 3.5.

g = 3.5/sin34° (both sides divided by sin34°)

The cost of sin today

34° = sin(30+4)° = 0.5592

So, we obtain

⇒ g = 3.5/0.5592

⇒ g = 6.26

Thus, the importance of g in the following equation is 6.26.

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Answer:

5

Step-by-step explanation:

diameter = 4 so radius =2

open up the cylinder so its top & bottom circle's circumference = 2πr =4π

top & bottom circle's area = πr² = 4π each, 8π for both

total surface = 28π

so lateral surface = 28π - 8π = 20π

so 20π = 4π* height

so height is 5

The cheaper plan is given as follows:

Shop ZYX.

The cost of a single plum at Shop ZYX is given as follows:

$2.4.

To obtain the cheaper plan, we must obtain the cost of a single plum for each shop.

The cost of a single plum for each shop is obtained using a proportion, with the division of the total cost by the number of plums.

Hence the cost per plum in each shop is given as follows:

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There are a total of 6 vacant positions to be filled at a company, with 3 of those positions being given to men, 2 to women and 1 being either gender.

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The quotient is n^2+5n-5 and the remainder is 9. The solution has been obtained by using the synthetic division.

What is synthetic division?

Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1."

We are given the expression as (n^3+3n^2-15n+19)

The expression is to be divided by (n-2)

So, by using the synthetic division, we get

2 |  1     3     -15      19    

     -     2      10     -10        

     1     5      -5       9    

Quotient =  n^2+5n-5

Remainder = 9

Hence, the quotient is n^2+5n-5 and the remainder is 9.

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1. The amounts of flour, considering 4 cups of sugar for each recipe, are given as follows:

2. The constant for each recipe is given as follows:

A proportional relationship is modeled as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

From the table, the constant is given as follows:

k = (3/4)/(1/2)

k = 3/2.

Meaning that for each cup of sugar, 3/2 cups of flour are needed.

Hence the relation is:

y = 3x/2.

The amounts of flour, considering 4 cups of sugar for each recipe, are obtained as follows:

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Answer:

Step-by-step explanation:

- Hope this helps!

If the value be 5/6 then the equation be [tex]$x \times \frac{2}{3}=\frac{5}{9}$$[/tex].

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

A fraction is a piece of a whole number and a means to divide a number into pieces that are each equal. The numerator, also known as the number of equal parts being counted, is expressed as being greater than the denominator, also known as the number of parts in the entire.

Let the value be 5/6 then

simplifying the equation as

[tex]$x \times \frac{2}{3}=\frac{5}{9}$$[/tex]

Multiply both sides by 3

[tex]$3 x \frac{2}{3}=\frac{5 \cdot 3}{9}$$[/tex]

Simplifying the above equation, we get

2x = 5/3

Divide both sides by 2, we get

[tex]$\frac{2 x}{2}=\frac{\frac{5}{3}}{2}$$[/tex]

x = 5/6

Therefore, the correct answer is option a.

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Answer: The PMT function in Sheets is used to calculate the monthly payment for a loan. The syntax of the function is PMT(rate, nper, pv, [fv], [type]).

Rate: the interest rate per period

Nper: the total number of payments

Pv: the present value (the total amount of the loan)

Fv: the future value of the loan (optional)

Type: the number 0 or 1 indicating when payments are due (0 = end of period, 1 = beginning of period)

Given the information in the problem, Ben's mortgage is for 10 years, so the total number of payments is 10*12 = 120. The present value of the loan is $196000 and the down payment is 25% of the home's cost so 25%*196000 = $49000. Therefore, the present value of the loan is $196000 - $49000 = $147000

Based on this information, the following commands would be used to determine the monthly payment:

PMT(0.076/12,120,-$147000)

PMT(0.076/12,120,-196000+$49000)

The first command uses the annual interest rate divided by 12 to convert it to a monthly rate, and the total number of payments is 120 (10 years * 12 months/year). The second command also uses the same monthly rate and total payments and the present value which is $147000

The other commands

Step-by-step explanation:

Step-by-step explanation:

To have an equal number of buns and sausages, Arthur needs to find the least common multiple (LCM) of 6 and 10.

The LCM of 6 and 10 is 30.

Therefore, he should buy at least 30 packs of buns and 30 packs of sausages to get an equal number of buns and sausages.

That way, he would have 30/6 = 5 packs of buns and 30/10 = 3 packs of sausages.

The probability that at least one of 10 randomly chosen Americans has O-negative blood is 0.722.

The probability that at least one of 10 randomly chosen Americans has O-negative blood can be calculated by first determining the probability that none of them have O-negative type blood. Since 7.2% of the population has O-negative blood, the probability that one of 10 randomly chosen Americans has O-negative blood is (1 - 0.072)^10. To determine the probability that at least one of 10 randomly chosen Americans has O-negative blood, we subtract this value from 1. Therefore, the probability that at least one of 10 randomly chosen Americans has O-negative blood is 1 - (1 - 0.072)^10, which is equal to 0.722.

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The scale factor is equivalent to {k} = 4/3.

        {K} = L{final}/L{initial}

Given is that figure 2 is a scale image of figure 1.

We can write the scale factor as -

K = {y}/{x} = 8/6 = 4/3

Therefore, the scale factor that is applied to figure {1} to get figure {2} is equivalent to {k} = 4/3.

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The area of the given image design is; 15 in²

The formula to find the area of a triangle is;

Area = ¹/₂(base * height)

Let us divide the image into two triangles and as such;

Area of biggest triangle = ¹/₂(14 * 15)

= 85 in²

We will now deduct the rectangle that was removed by finding its' area to get;

Area of rectangle = length * width

= 10 * 7 = 70 in²

Thus;

Area of image = 85 - 70

Area of image = 15 in²

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The quadratic equation 4 · x² - 7 · x = 3 · x + 24 has the following roots: x₁ = 19 / 4 and x₂ = - 9 / 4.

In this question we find the case of a quadratic equation, whose form is defined below:

y = a · x² + b · x + c

Where:

The procedure find the solutions to the quadratic equations:

Now we proceed to determine the solutions to the quadratic equation:

4 · x² - 7 · x = 3 · x + 24

4 · x² - 10 · x - 24 = 0

4 · [x² - (5 / 2) · x - 6] = 0

4 · [x² - (5 / 2) · x + 25 / 4] = 4 · 6 + 4 · (25 / 4)

4 · (x - 5 / 4)² = 49

(x - 5 / 4)² = 49 / 4

x - 5 / 4 = ± 7 / 2

x = 5 / 4 ± 7 / 2

The solutions to the quadratic equation 4 · x² - 7 · x = 3 · x + 24 are x₁ = 19 / 4 and x₂ = - 9 / 4.

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So, the last three digits of m*n is 001.

Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.

Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:

p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2

Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.

Therefore, the last three digits of m*n is 001.

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Answer: To find the numbers that Deshaun could choose, we need to find the least common multiple (LCM) of 4, 7, and 14. The LCM is the smallest number that is a multiple of all the given numbers.

We can find the LCM using the prime factorization method:

4 = 2^2

7 = 7

14 = 2 * 7

The least common multiple of 4, 7, and 14 is 2^2 * 7 = 28

So, the numbers Deshaun could choose are multiples of 28, which means they must be in the form of 28n, where n is a positive integer.

The numbers between 49 and 95 that are multiples of 28 are: 56, 84

So the numbers that Deshaun could choose are 56, 84.

Step-by-step explanation:

The probability of getting blue and an odd number will be 1/10.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The probability of getting blue is 2/10 and the probability of getting odd number is 5/10.

Therefore, the probability of getting blue and an odd number will be:

= 2/10 × 5/10

= 1/10.

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Answer:

1. b1=-2, b2=2
2. x1= -3/2, x2=7

3. x1=-4, x2= 23/5

Follow formula

b = -b [+][-] sq| b^2-4ac/ 2a

The shift of the function y = log(x+4) -3 is 4 units left and 3 units down

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

y = log(x + 4)

The above equation is a logarithmic equation

So, the parent function is

y = log(x)

When the parent function is compared to the given function, we have

3 units down and 4 units left

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Answer: 1400

Step-by-step explanation: If it is saving 40% of the original price than it is 60% of the original price.  840=60/100*x, and so we divide both sides by 60/100. 840*100/60=1400. Therefore, 1400 is the original price.

The largest possible value for the probability of A4 is 0.3.

If events A1, A2, A3, and A4 are pairwise mutually exclusive with the exception that A1 and A2 occur simultaneously, then the probability of A1 and A2 occurring together is 0.1. This means that the probability of A1 occurring separately is 0.3 - 0.1 = 0.2, and the same is true for A2.

Since A1, A2, A3, and A4 are pairwise mutually exclusive, the probability that they all occur together is 0. Therefore, the sum of their individual probabilities is also 0. Therefore, the probability of A4 is the remaining probability after accounting for the probability of A1, A2, and A3. The largest possible value for the probability of A4 is the total probability minus the probability of A1, A2, and A3.

So, the largest possible value for the probability of A4 would be:

1 - (0.2 + 0.2 + 0.3) = 1 - 0.7 = 0.3

Therefore, the largest possible value for the probability of A4 is 0.3.

The difference between the lightest bag of grapes that has been recorded by Colton will be 3/2 or 1 - 1/2.

[tex]2 - \frac{1}{2} [/tex]

[tex] = \frac{4}{2} - \frac{1}{2} [/tex]

[tex] = \frac{3}{2} or \: 1 - \frac{1}{2} [/tex]

Data gathering, analysis, interpretation, presentation, and organization are all topics covered in the study of statistics. In other words, gathering and summarizing data is a mathematical discipline. Additionally, statistics can be considered a subfield of applied mathematics.

Uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can be used to determine the uncertainty and variation in various fields. Probability, which has a significant impact on statistics, essentially determines these uncertainties.

Note that the graph for the following question is: (check the attached image).

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Step-by-step explanation:

this distance YZ is the height of the triangle WXY.

it splits the main triangle into 2 right-angled triangles WYZ and XYZ.

we can use Pythagoras

c² = a² + b²

with any of the 2 smaller right-angled triangles to get YZ.

remember, "c" is the Hypotenuse (the side opposite to the 90° angle). a and b are the legs.

so, when picking the larger one :

26² = 24² + YZ²

676 = 576 + YZ²

100 = YZ²

YZ = sqrt(100) = 10 = distance of Y to WX.

Answer: To find the percent of the decrease in the number of laps jogged from Saturday to Sunday, we can use the following formula:

percent decrease = (change in value / original value) x 100

In this case, the original value is the number of laps jogged on Saturday, which is 21 laps. The change in value is the difference in the number of laps jogged from Saturday to Sunday, which is 21 - 16.5 = 4.5 laps.

So, substituting these values into the formula:

percent decrease = (4.5 / 21) x 100

percent decrease = 0.214 x 100

percent decrease = 21.4%

Rounded to the nearest tenth, the percent of decrease in the number of laps jogged from Saturday to Sunday is 21.4%.

Step-by-step explanation:

If the vertices of the triangle BCD with vertices B(-8,3), C(-4, 6), and D(2, 0) , and if they are reflected across x axis and dilated by a scale factor of 0.5 then the coordinates of B"C"D" are B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0)    .

If the point (x,y) is reflected across the x axis , then the reflected points are (x,-y) .

the vertices of the triangle BCD are : B(-8,3), C(-4, 6), and D(2, 0) ;

So , the reflected vertices are : B'(-8,-3) , C'(-4,-6) and D'(2,0) ;

if the point (x,y) is dilated by a scale factor of "k" , then the dilated vertices are written as : (kx , ky) .

the dilation factors is = 0.5 ;

So , the vertices B'(-8,-3) , C'(-4,-6) and D'(2,0) after dilation will be written as :

⇒ B''(-8×0.5 , -3×0.5) , C"(-4×0.5 , 6×0.5) and D"(2×0.5 , 0) ;

After simplifying further ,

we have ;

⇒ B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) ;

Therefore , the coordinates of the triangle B"C"D" are B''(-4,-1.5) , C"(-2,3) and D"(1,0)  .

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Each ml of the vial contains 10 mg of Vitamin K. So to obtain 15 mg of Vitamin K, we needs a volume  1.5 ml of the solution.

We can calculate the required amount in two ways. We can use either proportions, or we can use the unit value determination.

In 1 ml we have 10mg , to get 15 mg we can use x ml

 [tex]\frac{1}{10} = \frac{x}{15}[/tex]

[tex]x = \frac{15* 1}{10}[/tex]

 x = 1.5

So, to get 15 mg of Vitamin K, we need 1.5 ml of solution.

Volume required to get 10 mg of vitamin K = 1 ml

Volume required to get 1 mg of vitamin K = [tex]\frac{1}{10}[/tex] ml = 0.1 ml

Volume required to get 15 mg of Vitamin K = 15 × 0.1 = 1.5 ml

So volume required to get 15mg = 1.5 ml

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Applying the sum of angles on a straight line, we have:

Equation = x + 70 + 60 = 180

Measure of x = 50°.

In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.

A straight line angle equals 180 degrees.

Therefore, the sum of all the angles on a straight line = 180 degrees.

Thus, the equation to solve for x would be:

x + 70 + 60 = 180

Solving for x

x + 130 = 180

x = 180 - 130

x = 50°

Hence, 50° is the measure of angle x.

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Answer:

Step-by-step explanation:

in every there w234e

If the trend continued, the number of CDs that were sold in 2019 is approximately equal to: D. 2,000​.

In order to write a linear function that models the data point contained in the table and determine the slope, we would have to use the point-slope form to determine the line of best fit based on the data points provided on the scatter plot (see attachment).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

y - 800 = (700 - 800)/(2005 - 2002)(x - 2002)

y = 33.33(x - 2002) + 800

y = 33.33x - 65,266

When x = 2019, the number of CDs sold is given by:

y = 33.33(2019) - 65,266

y = 2,027 ≈ 2,000 million CDs.

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Complete Question:

The scatter plot shows a number of CD's (in millions) that were sold from 1999 to 2005. If the trend continued, about how many CDs were sold in 2019?

A. 3000

B. 8500

C.3500

D. 2,000​

The correct option regarding the number of kettles that can be filled with the potion is given as follows:

C. Between 2 and 3.

The number of kettles is obtained applying the proportions in this problem, dividing the total number of litters by the number of liters of each kettle.

The parameters for this problem are given as follows:

Hence the number of kettles is obtained as follows:

11/4 = 2.75.

Meaning that the correct option is given by option C.

A kettle holds 4 liters of magic potion. There are 11 liters of potion.

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