find the rules for the composite functions f ∘ g and g ∘ f.

The measure of angle BCA in the given circle O is 32°.

The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.

Given that, A, B, C and D lie on the circumference of the circle.

A and C lie on a straight line segment.

B and D lie on a straight line segment.

Here, ∠ADB=∠BCA=32° (Angles in same segment are equal)

Therefore, the measure of angle BCA in the given circle O is 32°.

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Euler's method is used to find the solution of the first-order derivative. The solution of Euler's method can calculate by using a calculator.

What is the first-order derivative?

The direction of the function—whether it is increasing or decreasing—is revealed by the first-order derivatives. One interpretation of the first derivative or first-order derivative is an instantaneous rate of change. It can also be predicted based on the tangent line's slope.

First-order methods, such as the Euler method, have local errors that are proportional to the square of the step size and global errors that are proportional to the step size.

Step 1: Go to Mode and select SEQ on the 5th line and then press enter.

Step 2: Input step value, and initial conditions

Step 3: Put the formula u(x) = u(x-1)+ h dy/dx.

Step 4: Press 2nd + table

Step 5: From the table, you can find the solution to the equation.

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Answer:

$19,987,500.00

Step-by-step explanation:

I= prt

I= 41,000 * 3.25 * 15

41,000 * 3.25 * 15

= 19,987,500

Answer:

1 + 1 = 2.

Step-by-step explanation:

Answer NOBODY KNOWS THAT

Step-by-step explanation: MATHMATIONS HAVE BEEN TRYING TO FIND THAT OUT FOR YEARS  AND YOU THINK YOU'LL FIND IT ON BRAINLY THE EQUATION IS FAR TO COMPLEX FOR HUMAN MINDS THE ONLY WAY YOU'LL GET THE ANSWER IS IF YOU ASKED GOD HIMSELF: but i think 1 + 1 = 2

C. The probability of getting a male and getting someone with blue eyes.

P(MIB) is the probability of getting both a male and someone with blue eyes. This means that it represents the combined probability of both events happening. P(BIM) is the probability of getting a male, given that someone with blue eyes has been selected. The two probabilities are not the same because they measure different events. P(MIB) is measuring the combined probability of two events happening at the same time, while P(BIM) is measuring the probability of one event given the other has already happened.

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The equation which represents total pay P and number of copies sold N is P =1800 + 70N and the total pay for 28 copies sells will be $3760.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

From the question, we were given the following parameters

P = total pay

N = copies sold

P = 1800 +70N

replace N with 28

P=1800 + 70(28)

P=1800 + 1960

P= 3760 is her total pay selling 28 copies

Hence The equation which represents total pay P and a number of copies sold N is P =1800 + 70N and the total pay for 28 copies sells will be $3760

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The number is 225. This number is an example of a number whose units digit is double the tens digit and triple the hundreds digits.

This number meets the criteria of having the units digit being double the tens digit and triple the hundreds digit. To get this number, we multiplied the hundreds digit by 3 and the tens digit by 2. The hundreds digit was 2, so 2 x 3 = 6. The tens digit was 5, so 5 x 2 = 10. Adding these together gives us 6 + 10 + 5 = 21. Lastly, we multiplied the sum of 21 by 10 to get the final result of 225. This number is an example of a number whose units digit is double the tens digit and triple the hundreds digit.

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160 ounces or 10 pounds of cheese is $ 15 and 84 cents.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Direct Variation

When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. For instance, a rise in the quantity of commodities will result in higher costs.

Indirect Variation

A change in one quantity will directly affect a change in another, known as a direct variation. A rise in the quantity of goods, for instance, will result in higher costs.

We can say 1 pound = 16 ounces

10 pounds = 10 * 16 = 160 ounces

10 ounces of cheese is 99 cents

1 ounce of chess is 99/10 cents

160 ounces of cheese is 99*160/10 = 1584 cents = $ 15 and 84 cents.

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The Ratio Test is inconclusive for the series sum_(n=2)^infinity 6/n^3.

What is ratio ?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

The Ratio Test is given by:

lim_(n->infinity) |a_n+1 / a_n| = L

If L < 1, then the series converges. If L > 1, then the series diverges. If the limit L does not exist or is equal to 1, then the test is inconclusive.

Consider the series sum_(n=2)^infinity 6/n^3. We have:

|a_n+1 / a_n| = |6 / (n + 1)^3 / (6 / n^3)| = |n^3 / (n + 1)^3| = n^3 / (n + 1)^3

As n approaches infinity, n^3 / (n + 1)^3 approaches 1, so the limit of |a_n+1 / a_n| does not exist or is equal to,

Hence, The Ratio Test is inconclusive for the series sum_(n=2)^infinity 6/n^3.

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Answer:

x = 48

Step-by-step explanation:

x/12 = 4

Multiply both sides by 12:

[x = 48]

The coordinates of the vertices of the given isosceles trapezoid centered in the origin, with base 2a and OR=c are,

S(-a, 0) , Z(a, 0) , T(-b, c) and W(b, c)

Completed question :

Which could the coordinates of the vertices of the following isosceles trapezoid centered in the origin, with base 2a and OR=c?

Given data :

Given an isosceles trapezoid centered in the origin, with base 2a and OR = c.

We have to find the coordinates of vertices of the given isosceles trapezoid.

Since  O is at center then , coordinates of O (0,0).

And base SZ given to be 2a .

So SO = OZ

SO + OZ = SZ ⇒ 2 (SO) = 2a ⇒SO = a

Since point S lies in second quadrant and x coordinates in second quadrant are negative, thus Coordinate of S is (-a, 0)

and Z lies in first quadrant , both x and y are positive,

So, coordinate of Z is (a, 0)

given OR = c so R lies on y axis , so R has coordinate (0,c)

Since point T lies in second quadrant and x coordinates in second quadrant are negative, thus Coordinate of T is of the form (-x, c)

also, W lies in first quadrant , both x and y are positive. Thus, coordinate of W is of the form  (x,c)

When we compare from the given options, we get possible value of x is b,

Thus, the coordinates of the vertices of the given isosceles trapezoid centered in the origin, with base 2a and OR=c are,

S(-a, 0) , Z(a, 0) , T(-b, c) and W(b, c)

Option (3) is correct.

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Rounding to the nearest tenth of an ounce, the estimated weight of a bluegill with a length of 9.5 inches is 11.8 ounces.

The goal of linear regression is to find the line of best fit, which is a straight line that minimizes the sum of the squared differences between the observed and predicted values. This line can be used to make predictions about the dependent variable based on the independent variable(s). The line is represented by an equation, called the regression equation, in which the dependent variable is a linear combination of the independent variable(s) and a constant term. In simple linear regression, there is only one independent variable, whereas in multiple linear regression, there can be two or more independent variables.

The weight of a bluegill can be estimated using a linear regression model based on the given length and weight data. To do this, we need to first find the equation of the line of best fit for the data.

The equation for a line in the form y = mx + b, where m is the slope and b is the y-intercept, can be found using the method of least squares. The slope can be calculated using the formula:

m = Σ(x - x')(y - y') / Σ(x - x')²

where x' and y' are the sample means of the length and weight data, respectively. The y-intercept can be found using the formula:

b = y' - mx'

Once we have the equation of the line of best fit, we can plug in the length of 9.5 inches to estimate the weight of a bluegill with that length.

Using the data in the table, the estimated weight of a bluegill with a length of 9.5 inches can be calculated as follows:

m = (41)(0.8) / (24) = 0.895833

b = 10.5 - (0.895833)(10) = 3.04167

y = (0.895833)(9.5) + 3.04167 = 11.80208 ounces

Rounding to the nearest tenth of an ounce, the estimated weight of a bluegill with a length of 9.5 inches is 11.8 ounces.

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De Morgan's laws state: (A∪B)^c = A^c∩B^c and (A∩B)^c = A^c∪B^c.

What is Venn diagram ?

A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory.

The first law states that the complement of the union of two sets is equal to the intersection of their complements:

(A ∪ B)’ = A’ ∩ B’

This law can be illustrated with a Venn diagram, where the complement of a set is represented by shading the region outside the set. In this diagram, the shaded region outside the union of A and B is equal to the overlap of the shaded regions outside of A and B individually.

The second law states that the complement of the intersection of two sets is equal to the union of their complements:

(A ∩ B)’ = A’ ∪ B’

De Morgan's laws state: (A∪B)^c = A^c∩B^c and (A∩B)^c = A^c∪B^c.

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formula for the tangent line is y=x-1 and differentiation of ln(x) is 1/x

A straight line without crossing the curve , it touches the curve at one single point is called tangent . Finding the derivative of a function or a variable in mathematics is called differentiation.

The ratio of the vertical to the horizontal distance between any two points on it  is called slope of ray or line or line segment in analytical geometry.

y-y1 = m(x-x1)

If the function passes through (1,0)  and the slope equals to 1 is:

y-0 = 1(x-1)

y=x-1

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Tangents are straight lines that only touch curves at a single spot rather than crossing them. Differentiation in mathematics refers to the process of determining a function's or variable's derivative.

The slope of a ray, line, or line segment in analytical geometry is the ratio of the vertical to the horizontal distance between any two locations on it.

y-y1 = m(x-x1) (x-x1)

If a function goes through the point (1, 0) and its slope is 1, then:

y-0 = 1(x-1) (x-1)

y=x-1

The coordinates of point P along the directed line segment AB is (10, 13).

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

The line AB.

P is the point between the line AB.

Now,

A = (4, 10) = (a, b) and B = (14, 15) = (c, d)

m : n = 3 : 2

So,

P = (x, y)

The coordinates is given by:

x = (mc + na) / (m + n)

y = (md + nb) / (m + n)

So,

x = (42 + 8) / 5

x = 10

y = (45 + 20) / 5

y = 13

Now,

P = (10, 13)

Thus,

The coordinates of point P is (10, 13).

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The roots of a polynomial are values that make the polynomial equal zero.

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The first three terms of the sequence are -4 , -1, 4. The 10th term of the sequence is given as 95

The general form of the nth term of a sequence can be represented as an expression involving n, such as n^2 - 5.

The first three terms of the sequence are:

n = 1, term = 1^2 - 5 = -4

n = 2, term = 2^2 - 5 = -1

n = 3, term = 3^2 - 5 = 4

The tenth term of the sequence is:

n = 10, term = 10^2 - 5 = 95

So, the first three terms are -4, -1, 4, and the tenth term is 95.

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The complete two way relative frequency table shown below:

A statistical table called a two-way or contingency table displays the observed quantity or frequency for two variables, with the rows denoting one category and the columns denoting the other. In this case, the gender (male or female) row category. They can opt to have a yes or no column category.

Given:

Color     Car      Truck      Total

Blue       25          16            41

Red        21           13            34

Total       46         29            75

Now, the two way relative frequency table

Blue Car:   25 /75 x 100 = 33.33%

Blue Truck: 16/75 x 100 = 21.33%

Blue total = 41 /75 x 100 = 54.66%

Red car: 21/75 x 100 = 28%

Red Truck: 13/75 x 100 = 17.33%

Red total: 34/75 x 100 = 45.33%

Total car: 46/75 x 100 = 61.33%

Total truck: 29/75 x 100 = 38.66%

Total to total = 75/75 x 100 = 100%

so, the table is

Color     Car               Truck            Total

Blue       33.33%        21.33%       54.66%

Red        28%             17.33%        45.33%

Total       61.33%        38.66%          100%

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The proof should be written in paragraph format as follows;

Since AOB forms a line segment, ∠XOB and ∠AOX are supplementary by the linear pair theorem. Using the definition of supplementary angles, m∠XOB + m∠AOX = 180°. Since it is given that ∠XOB ≅ ∠AOX, then m ∠XOB = m ∠AOX. Applying the substitution property of equality, then 2m ∠XOB = 180°. After dividing, m∠XOB = 90°.

In Mathematics, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.

According to the linear pair theorem, ∠XOB and ∠AOX are supplementary because AOB forms a line segment. Therefore, we have:

m∠XOB = m∠AOX

m∠XOB + m∠AOX = 90° + 90° = 180°

By applying the substitution property of equality, we have:

2(m∠XOB) = 2(90°) = 180°.

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Answer:

I just got it right on the test

Step-by-step explanation:

The value of a from the equation  5y = x + 47 with slope 1/5 is 11.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

The slope of the line = 1/5

The line passes through (8,a) and (3,10)

The equation of the line is

y = mx + c

where m is slope and c is y-intercept

or , y = x/5 + c

putting (3,10) in the line

10 = 3/5 + c

⇒ c = 47/5

The equation of the line is y = x/5 + 47/5

or, 5y = x + 47

putting (8,a) in the line

5a = 8 + 47

⇒ a = 55/5 = 11

The value of a from the equation  5y = x + 47 with slope 1/5 is 11.

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If the medium drink cost $1. 50, the inequality that represents the cost of a popcorn is x ≤ 3.5. Hence, the most he can pay for each popcorn is $3.5.

To translate a word problem into an inequality:

In this problem, let:

x = the cost of 1 popcorn

Three popcorns means = 3x

The cost of a medium drink = 1.5

The amount he need to pay for a medium drink and 3 popcorn:

amount = 1.5 + 3x

However, he only has 12 dollars. Hence,

1.5 + 3x ≤ 12

Subtract both sides by 1.5

3x ≤ 12 - 1.5

3x ≤ 10.5

Divide both sides by 3

x  ≤ 10.5/3

x ≤ 3.5

Hence, the maximum price of a popcorn is $3.5

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Answer:

12

Beth has read 12 books.

Step-by-step explanation:

2/3 of 18 is

2/3 × 18

= 2/3 × 18/1

= 36/3

= 12

or "cancel" the 3 and 18 so the work looks more like:

2/3 × 18

= 2/1 × 6

= 12

Or skip the fraction math and logic it out. 18 in three parts is 6books, 6books and 6books.

Beth has read 2 parts:

6books and 6books

She read 12 books.

The image coordinates for A, B, C are:

A' = (1, -7)

B' = (-7, 5)

C' = (-11, -4)

A translation refers to a transformation in which an object is moved a certain distance in a certain direction without changing its size or orientation. The effect of a translation is to shift the position of the object, while leaving its shape unchanged.

Since the translation rule is (x, y) => (x-1, y-3). This means you will subtract 1 from x and subtract 3 from y to get the image coordinates for A, B, C. That is:

A = (2, -4) => A' =  (2-1, -4-3) = (1, -7)

B = (-6, 8) => B' =  (-6-1, 8-3) = (-7, 5)

C = (-10, -1) => C' =  (-10-1, -1-3) = (-11, -4)

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{(-5)}}} \implies \cfrac{-12}{5 +5} \implies \cfrac{ -12 }{ 10 } \implies - \cfrac{ 6 }{ 5 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{ 6 }{ 5 }}(x-\stackrel{x_1}{(-5)}) \implies y -4 = - \cfrac{ 6 }{ 5 } ( x +5) \\\\\\ y-4=- \cfrac{ 6 }{ 5 }x-6\implies {\Large \begin{array}{llll} y=- \cfrac{ 6 }{ 5 }x-2 \end{array}}[/tex]

Among all the given equations, the one that  shows the best estimate for 4,310 ÷ 72 using compatible numbers is 4,200 ÷ 70 = 60. Hence, Option B is correct.

What are compatible numbers?

Numbers that are simple to mentally add, subtract, multiply, or divide are known as compatible numbers in mathematics. Compatible numbers are close in value to the real numbers, which facilitates estimation of the solution and simplifies problem-solving.

Compatible numbers are pairwise comparisons of numbers that are simple to mentally add, subtract, multiply, or divide. Replace real values with equivalent ones when using estimation to approximate a calculation.

When the given equation that is  4,310 ÷ 72 will solved, the derived value will be 59.86 and the selected equation will resulted in 60.

Therefore, Option B is correct.

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Answer:

Step-by-step explanation:

The formula for momentum is:

p = m * v

m_arrow * v_arrow = (m_arrow + m_apple) * v_final

m_arrow * v_arrow = (0.05 kg + 1.2 kg) * 3.6 m/s

m_arrow * v_arrow = 1.25 kg * 3.6 m/s

v_arrow = p_final / m_arrow

v_arrow = (1.25 kg * 3.6 m/s) / 0.05 kg

v_arrow = 90 m/s

So the initial velocity of the arrow was 90 m/s.

The answer to this question requires the use of the Poisson distribution and the cumulative distribution function.

(a) We are asked to find the probability that the fourth person weighed is the first person to be overweight. Since 63% of Americans are overweight, this means that the probability of a randomly selected American being overweight is 0.63. The probability of the first overweight person being the fourth person weighed is given by P(X=3) where X is the number of overweight people in the first 4 people weighed. Using the binomial distribution formula, we have:

[tex]P(X=3) = (4 choose 3) * (0.63)^3 * (0.37)^1\\\\ = 4 * (0.63)^3 * (0.37)[/tex]

(b) We are asked to find the probability that it takes more than 4 people to observe the first overweight person. This is equivalent to finding the probability that none of the first 4 people weighed are overweight. Using the complement rule, we have:

[tex]P(X=0) = 1 - P(X > 0)\\\\ = 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4)]\\\\ = 1 - [ (4 choose 1) * (0.63)^1 * (0.37)^3 + (4 choose 2) * (0.63)^2 * (0.37)^2 + P(X=3) ][/tex]

(c)  The expected value (mean) of a binomial distribution is given by μ = np, where n is the number of trials and p is the probability of success in each trial. In this case, n=4 and p=0.63. Thus, the mean number of overweight people in 4 trials is 4 * 0.63 = 2.52. The variance of a binomial distribution is given by σ^2 = np(1-p), so in this case the variance is 4 * 0.63 * 0.37 = 1.41. The standard deviation is the square root of the variance, so the standard deviation is approximately [tex]\sqrt{(1.41) } = 1.19[/tex]. This means that the number of overweight people in 4 trials is expected to be around 2.52, with a standard deviation of 1.19.

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The names for the radius of the circle with center F are FA, FC, EF, BF, DF

The radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary.

Given that, circle with center at point F. Points A, B, C, D and E are on the circle. Line segments FA, FC, AFC, EF, BF, EFB, DF and AB are drawn.

Since, the radius is the distance from center to a point on the circumference,

Therefore, FA, FC, EF, BF, DF are showing the distance from center to a point on the circumference,

Hence, the names for the radius of the circle with center F are FA, FC, EF, BF, DF

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a) k/6 = 1 → k=6 is the distribution of the median of Y1,Y2,··· ,Yn when n is an odd integer

b) P(Y1 ≤ 3/4, Y2 ≥ 1/2) =  9/16

a) if distribution

f (y1, y2) = k(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1,  0, elsewhere

for f to be a probability density function , has to comply with the requirement that the sum of the probability of all the posible states is 1 , then

P(all possible values) = ∫∫f (y1, y2) dy1*dy2 = 1

then integrated between

y1 ≤ y2 ≤ 1 and 0 ≤ y1 ≤ 1

∫∫f (y1, y2) dy1*dy2 =  ∫∫k(1 − y2) dy1*dy2 = k  ∫ [(1-1²/2)- (y1-y1²/2)] dy1 = k  ∫ (1/2-y1+y1²/2) dy1) = k[ (1/2* 1 - 1²/2 +1/2*1³/3)-  (1/2* 0 - 0²/2 +1/2*0³/3)] = k*(1/6)

then

k/6 = 1 → k=6

b)

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = P (0 ≤Y1 ≤ 3/4, 1/2 ≤Y2 ≤ 1) = p

then

p = ∫∫f (y1, y2) dy1*dy2 = 6*∫∫(1 − y2) dy1*dy2 = 6*∫(1 − y2) *dy2 ∫dy1 =

6*[(1-1²/2)-((1/2) - (1/2)²/2)]*[3/4-0] = 6*(1/8)*(3/4)=  9/16

therefore

P(Y1 ≤ 3/4, Y2 ≥ 1/2) =  9/16

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Answer:

Step-by-step explanation:

I hope this helps you