∠A and ∠B are vertical angles. If angle A=(8x-23) and angle B=(6x-5) then find the measure of ∠A.

After solving the function S(t) = 12 + 2 sin [(2π)/(365)t], the amount of sunlight becomes 12 hours for the first time is obtained as option B: t = 365/2.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given function is -

S(t) = 12 + 2 sin [(2π)/(365)t]

Here, t is the number of days after 1st January.

S(t) is the number of hours of sunlight in a particular location.

In order to figure out when the amount of sunlight becomes 12 hours for the first time, substitute the value of S(t) = 12 and solve the function for t -

S(t) = 12 + 2 sin [(2π)/(365)t]

12 = 12 + 2 sin [(2π)/(365)t]

Simplifying the equation to get the result -

0 = 2 sin [(2π)/(365)t]

0 = sin [(2π)/(365)t]

π = (2π)/(365)t

Simplify the equation further -

365π = 2πt

t = 365π/2π

t = 365/2

Therefore, the value for t is obtained as t = 365/2.

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The number of hours of sunlight in a particular location S(t) can be modeled by the function S(t) = 12 + 2 sin [(2π)/(365)t], where t is the number of days after January 1st. (That is, t = 0 means January 1st.) After how many days will there be 12 hours of sunlight for the first time during the year?

365 over 4 days

365 over 2 days

1095 over 4 days

1095 over 2 days

The acute angles between two curves at their points of intersection are the angles between the tangent lines of the two curves at those points. The angles should be rounded to one decimal place and given in a comma-separated list.

The acute angles between two curves at their points of intersection can be found by calculating the angles between the tangent lines of the two curves at those points. To calculate this angle you will need to calculate the gradient of the tangent lines at each point of intersection. To do this, you need to take the derivative of each curve's equation at each point of intersection. Once you have the gradients, you can then use the equation for the angle between two lines to calculate the angle between the two tangent lines. Then, the angles should be rounded to one decimal place and given in a comma-separated list.

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The statement regarding the percentages of men and women admitted is true.

A percentage is obtained similarly to a proportion, with the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.

The number of applicants for each department is given as follows:

The percentages of admitted people for each department is 50% men and 50% women, meaning that the statement in this problem is true.

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Answer:

D

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

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To find the temperature in Reigate, which is halfway between St. Petersburg and Rome, we need to find the average of the two temperatures.

Average = (Temperature1 + Temperature2) / 2

Average = (-7 + 15) / 2 = 8 / 2 = 4

So, the temperature in Reigate was 4°C.

Answer:

4°C

Step-by-step explanation:

Try drawing it on a number line and counting 11 from -7° C and 11 from 15°C you'll end up with 4°C as the middle

Less than 2 units separate the median from the lower quartile for customers making purchases. The correct option is E.

Quartile deviation: The three values known as quartiles divide sorted data into four equal-sized portions, each with an equal number of observations. An example of a quantile is a quantile. First quartile: Also referred to as the lower quartile or Q-1. The median or second quartile is also referred to as Q-2. Third quartile: Also referred to as the higher quartile or Q-3.

Half of the difference between the upper and lower quartiles can be used to define the quartile deviation analytically. Here, the upper quartile (Q-3) and lower quartile (Q-1) can be used to depict quartile deviation as the letters Q-D. The term "quartile deviation" is sometimes used to refer to the semi-interquartile range.

The coefficient of quartile deviation serves as a gauge for a collection of data's variability or spread. It is determined by taking the square root of the difference between the upper and lower quartiles, squaring the result, and dividing it by two. Comparing data sets is simple because it is expressed as a percentage.

Therefore, the correct answer is option E.

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Answer: x=6

Step-by-step explanation: The absolute value | x | of a real number is a positive value of x even if the value of x had a sign(negative sign, etc.).

The correct answer choice is the last one, your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14).

What is marginal utility?

Marginal utility refers to the additional satisfaction or benefit that a consumer derives from consuming one more unit of a good or service. It is the change in total utility resulting from a change in the quantity consumed. It is a way to measure the additional benefit a consumer receives from consuming one more unit of a good or service.

your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14). The law of diminishing marginal utility states that as the consumption of a good or service increases, the additional satisfaction or utility from consuming one more unit of the good or service will decline. In this example, as you consume more slices of pizza, the marginal utility of each slice decreases (8 utils for the first slice, 3 utils for the third slice). This is consistent with the law of diminishing marginal utility. Therefore, choice A is incorrect.

Hence, The correct answer choice is the last one, your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14).

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The value of 1st number is 4 + 4/√3 and value of 2nd number is 4 - 4/√3

let the 2 number be a,b

given a+b=8 -- (i)

let the difference of the number is x

so let a-b =x

a-b = x ---(ii)

adding equation (i) and equation (ii) we get

2a = 8 +x

=> a = (8+x)/2

so a = 4+x/2

subtract (ii) from (i) we get:

2b = 8-x

=> b = (8-x)/2

so b = 4-x/2

now the product of both number and their difference is given as a*b*x

=> (4+x/2)*(4-x/2) *x

=> (16 - x²/4)*x

=> 16x - x³/4

let the above value be A

so A = 16x - x³/4

in order to find maximum value of A we have to made dA/dx = 0

=> d(16x - x³/4)dx

=>  16 - 3x²/4

so 16 -  3x²/4 =0

=> 3x²/4 = 16

=> 3x² = 64

=> x² = 64/3

so x = 8/√3

now we got value of x

so a = 4+ x/2

=> 4 + 8/2√3

=> 4 + 4/√3

so value of a =  4 + 4/√3

value of b = 4 - 4/√3

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a) The sheep will not be able to eat grass from the neighbor's field. The leash is 20 meters long and is tied to a pole at the point (40, 20) in the field. The farthest point the sheep can reach is a point on the circle with radius 20 centered at (40,20), which is completely contained within the rectangular field.

b) The sheep will be able to eat grass from the neighbor's field. The leash is 20 meters long and is tied to a pole at the point (180,160) in the field. The farthest point the sheep can reach is a point on the circle with radius 20 centered at (180,160), which extends beyond the east and north boundaries of the rectangular field. Specifically, the sheep can reach the area on the northeast corner of the field.

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Yes. An equilateral triangle has rotational symmetry of 120 and 180 degrees about the origin.

A triangle is a three-sided polygon, with three angles and three sides. It is one of the most basic and fundamental shapes in geometry, and is used in many different areas of math and science. Triangles are also often used in architecture, art, and other areas of design. Triangles come in many different forms, such as equilateral, isosceles, and scalene, and can be classified by their angles, sides, or both.

This means that the triangle can be rotated by 120 degrees or 180 degrees around the origin and still maintain its shape.


Yes,  rotational symmetry of 120 about the origin applies to the equilateral triangle. This means that the triangle can be rotated by 120 degrees about the origin and the resulting shape will be exactly the same as the original triangle.

No, rotational symmetry of 180 about the origin does not apply to the equilateral triangle. This is because an equilateral triangle has rotational symmetry of 60 degrees about the origin, not 180 degrees.

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Answer:

76ft^3

Step-by-step explanation:

Volume of a cube is Length x Width x Height, basically: 4 x 4 x 4 which is 64 ft^3. Add that to the small box gives you 64 + 12 or just 76 ft^3

Similarly, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy. Award winning best actors are 71 years old or younger.

The percentile of a number is the percentage of numbers that are equal to or less than that number. In this case, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy Award winning best actors are 71 years old or younger.

The percentile of a number is the percentage of numbers that are equal to or less than that number. For example, among the 32 Academy Award winning best actors, 37 is the 14th smallest number, so the percentile of 37 is 14/32, which is equal to 43.75%. This means that 43.75% of the Academy Award winning best actors are 37 years old or younger. Similarly, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy Award winning best actors are 71 years old or younger.

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b = (2,-1,6) is a linear combination of a1 = (1,-2,0), a2 = (0,1,2) and a3 = (5,-6,8) with weights (1,3,1) respectively.

To determine if b is a linear combination of a1, a2, and a3, we can set up a system of equations using the coefficients of the linear combination and the variables a1, a2, and a3. The equation for a linear combination of the form b = k1a1 + k2a2 + k3a3, where k1, k2 and k3 are the coefficients, can be written as:

b = k1 × (1,-2,0) + k2 × (0,1,2) + k3 × (5,-6,8)

So,

x = k1 + 5k3

y = -2k1 + k2 - 6k3

z = 2k2 + 8k3

We know the values of x,y,z from b = (2,-1,6)

So, we can set up the following system of equations:

x = k1 + 5k3 = 2

y = -2k1 + k2 - 6k3 = -1

z = 2k2 + 8k3 = 6

We can solve the system of equations using methods such as substitution or elimination to find the values of k1, k2, and k3.

k1 = 1, k2 = 3, k3 = 1

Therefore, we can express b as a linear combination of a1, a2, and a3 with the weights k1, k2, and k3 which are (1, 3, 1) respectively.

b = 1a1 + 3a2 + 1 × a3

This means that b is a linear combination of a1, a2, and a3 with weights (1, 3, 1) respectively.

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The question is -

Determine if b is a linear combination of a1, a2, and a3.

a1=(1,-2,0)

a2=(0,1,2)

a3=(5,-6,8)

b=(2,-1,6)

Using the substitution method the equation 4x - y = 3 and 6y = 4 + 2x is solved to be

In this method, the equation 4x - y = 3 will first be written in terms of y

4x - y = 3

y = 4x - 3

substituting y = 4x - 3 into 6y = 4 + 2x

6y = 4 + 2x

6(4x - 3) = 4 + 2x

24x - 18 = 4 + 2x

collecting like terms

24x - 2x = 18 + 4

22x = 22

x = 1

substituting x = 1 into y = 4x - 3

y = 4x - 3

y = 4(1) - 3

y = 4 - 3

y = 1

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The evaluation of the values of the derivative of the function f, using Lagrange's theorem indicates that the true statements is the following option;

Lagrange Theorem states that there is a point, c between points a and b of an arc such the slope at c is the same as the average slope of the arc between points a and b.

The evaluation of the statements in the question are as follows;

I. If f'(x) exists and is nonzero for all x, then f(1) is not equal to f(0)

If f'(x) exists and the value is non zero, then the slope is not infinite, and the sign of the slope of the function f(x) never changes, such that the as the input (x) value increases the output value decreases, when the slope is negative, or increases when the slope of f(x) is positive, therefore;

The value of f(1) is either larger than or lesser than the value of f(0), which proves that f(1) is not equal to f(0).

II. If f is differentiable for all x and f(-1) = f(1), then there is a number c, such that |c| < 1 and f'(c) = 0

The condition if f is differentiable for all x, then according to Lagrange's, mean value theorem, we get;

When f(|c| < 1) < f(1)

f'(c) < (f(1) - f(-1))/(1 - (-1)) = (f(1) - f(-1))/(2)

f'(c) < (f(1) - f(-1))/(1 - (-1)) = (f(1) - f(-1))/(2) = 0

f'(c) < 0

Similarly, when  f(|c| < 1) > f(1), then, f'(c) < 0

Therefore, f'(c) ≠ 0

III. If f'(c) = 0, then f has a local maximum or minimum at x = c.

The slope of the function f at point x = c is f'(c)

A local maximum or minimum is a point after which the slope of the graph changes sign, and the point at which the slope is zero as the change in the output variable is zero

Therefore, if f'(c) = 0, the graph has a local maximum or minimum at the point f = c

The true statements from the specified options, and based on the possible options in the question, obtained from a similar question posted online are;

The possible question options are;

I and II only

I and III only

I only

II only

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The domain of the given set of functions is (Alex, Alesia, Bob,  Yolanda, Maria , Elvis)

The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A-> B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The domain of the given set of functions is (Alex, Alesia, Bob,  Yolanda, Maria , Elvis)

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Answer:

A tangible asset is an asset that has physical substance. Examples include inventory, a building, rolling stock, manufacturing equipment or machinery, and office furniture. There are two types of tangible assets: inventory and fixed assets.

Step-by-step explanation:

Answer:

“Song of myself ” is written by Walt Whitman in 1855

Answer:

The Song of Myself is written by Walt Whitman in 1855

Step-by-step explanation:

A cluster sample is a type of sampling technique wherein clusters of subjects that are similar in certain characteristics are selected for the study. In this case, the sample includes 3 owners, 6 players, and 20 fans, all of whom have something in common - an interest in basketball. Therefore, the sample described is a cluster sample.

A cluster sample is a type of sampling technique wherein clusters of subjects that are similar in certain characteristics are selected for the study. In this case, the sample includes 3 owners, 6 players, and 20 fans, all of whom have something in common - an interest in basketball. Therefore, the sample described is a cluster sample. This type of sample is helpful when the researcher is interested in specifically examining a certain group of people and their opinions. A cluster sample is relatively easy to implement and can be used to quickly obtain a large amount of data in a short period of time. It also eliminates the need to identify and select individuals from a population. By using a cluster sample, the sports columnist was able to quickly get feedback from a variety of individuals who may have different opinions on the potential basketball lockout.

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The matrix expression for this model is given by

T=

[ 1-a, a, 0; 0, 1-B, B; 0, 0, 1]

When a = 0.10 and B = 0.05, the matrix expression becomes:

T=

[ 0.90, 0.10, 0; 0, 0.95, 0.05; 0, 0, 1]

This matrix expression describes the transition probabilities of the virus over time. Specifically, it describes the probability of a person who has never been infected (S) becoming infected (I) in the next day (a = 0.10), the probability of a person who is infected (I) in the current day  in the next day (B = 0.05), and the probability of a person who has recovered (R) staying recovered in the next day (1). Thus, this matrix expression models the progression of a contagious virus through a population over time.

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Answer:

0.5

Step-by-step explanation:

If you flip a coin, the probability of getting a head is 0.5 or 0.5 on the probability scale.

It is worth noting that when a coin is fair, the probability of getting a head or a tail is always 0.5 or 50%.

So in the probability scale you should place a cross on the point 0.5 which indicates the probability of getting a head.

(a) Average velocity over [1,5] is -21. (b) Average velocity over [1,4] is -14. (c) Average velocity over [1,3] is -7. (d) Average velocity over [1, 1+h] is -7t + 70 where h is any real number.

Calculating average velocity requires the calculation of the change in position divided by the change in time.

For a: The change in position is -70 and the change in time is 4. So, the average velocity is -70/4 = -17.5.

For b: The change in position is -56 and the change in time is 3. So, the average velocity is -56/3 = -18.67.

For c: The change in position is -35 and the change in time is 2. So, the average velocity is -35/2 = -17.5.

For d: The change in position is -7t and the change in time is h. So, the average velocity is -7t/h = -7t + 70.

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A complete question: The position of an object moving along a line is given by the function s(t) = -7t^2 +70t. Find the average velocity of the object over the following intervals.

(a)​ [1,5]

​(b) ​[1,4​]

​(c)​ [1,3​]

​(d) ​[1, 1​+h] where h > 0 is any real number

Answer: 5 11/12 not sure

The solution of the system of equation in ordered pair is,

⇒ (- 0.84, 4.88)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 3x + 4y = 17  .. (i)

⇒ 4x - 3y = - 18 ... (ii)

Now, We can solve the equations as;

Multiply by 4 in equation (i) and subtract from (ii) × 3, we get;

⇒ 12x + 16y - 12x + 9y = 68 - (- 54)

⇒ 25y = 68 + 54

⇒ 25y = 122

⇒ y = 4.88

And, From (i);

⇒ 3x + 4y = 17

⇒ 3x + 4×4.88 = 17

⇒ 3x + 19.52 = 17

⇒ 3x = 17 - 19.52

⇒ 3x = - 2.52

⇒ x = - 0.84

Thus, The solution is,

⇒ (- 0.84, 4.88)

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The product of the binomial factors is x² - 10x + 25.

Binomials are kind of polynomials which consist of only two terms.

The given binomial factor is x - 5

We have to find the product of this binomial with itself, (x - 5)².

We have to use the special product of square of a binomial difference, which is defined as,

(a - b)² = a² - 2ab + b²

The given product of the binomial factors is (x - 5)².

(x - 5)² = x² - (2 × x × 5) + 5²

           = x² - 10x + 25

Hence the product of the binomial factors is x² - 10x + 25.

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Each interval (a, a), [a, a), and (a, a] represents the empty set, whereas [a, a] denotes the singleton set {a}

What do you meant by interval?

a )  [0, 2]

The empty set is represented by the intervals (a, a), [a, a), and (a, a, while the singleton set an is denoted by [a, a].

b ) iv

If a function f(x) is continuous on a closed interval [ a, b], then f(x) has both a maximum and minimum value on [ a, b].

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Answer:

[tex]2 \frac{6}{11}\; \rm days\;[/tex]

2 days 13 hours 5 minutes 27 seconds

Step-by-step explanation:

First hose:

Second hose:

When both hoses are being used to fill the pool, their rates are additive:

[tex]\implies \dfrac{1}{7}+\dfrac{1}{4}=\dfrac{4}{28}+\dfrac{7}{28}=\dfrac{11}{28}[/tex]

Therefore, both hoses can fill 11/28 of the pool in 1 day.

To calculate how long it will take to fill the pool, divide 1 day by the combined rate:

[tex]\implies 1 \div \dfrac{11}{28}=1 \times \dfrac{28}{11}= \dfrac{28}{11}=2 \frac{6}{11}\; \rm days\;[/tex]

Therefore it takes 2 ⁶/₁₁ days to fill the pool if both hoses are used.

To find the time it takes in days, hours, minutes and seconds:

Therefore, it takes:

The value of the equation is A = 11,025

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 105²

On simplifying the equation , we get

A = ( 100 + 5 )²

The equation is of the form ( a + b )² = a² + 2ab + b²

On further simplification , we get

A = ( 100 )² + 2 ( 100 ) ( 5 ) + ( 5 )²

A = 10000 + 1000 + 25

A = 11,025

Hence , the equation is A = ( 100 + 5 )² = 11,025

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