What kind of angle is this

The  y(t) represents the amount of salt in the tank t minutes after the process started, and y(0) = 20 represents the initial amount. The y(t) is [tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex].  It will take approximately 6.875 minutes for the amount of salt in the tank to be reduced to 20% of the initial amount.

From the given data,

A super large tank was initially filled with brine solution of 20 liters.

At some point, fresh water starts to flow in at a rate of 8 liters per minute, and the well mixed solution flows out at half of the rate.

The initial value problem (IVP) to describe the above problem can be set up as follows:

⇒[tex]\frac{d}{dt} y(t)=\frac{1}{2} (8-y(t))[/tex]

⇒y(0)=20

Where y(t) represents the amount of salt in the tank t minutes after the process started, and y(0) = 20 represents the initial amount.

Part II:

To solve the IVP, we need to find y(t) for a given t. This can be done using numerical methods or analytical methods, such as separation of variables. Using separation of variables, we have:

⇒[tex]\frac{d}{dt} y(t)=\frac{1}{2} (8-y(t))[/tex]

⇒[tex]\frac{dy}{dt}=\frac{1}{2}(8-y)[/tex]

⇒2dy = (8 - y) dt

⇒2dy = (8 - y)dt

Integrating both sides with respect to t, we get:

⇒∫2dy = ∫(8 - y)dt

⇒2y = 8t - (1/2)y^2 + C

where C is a constant of integration. Using the initial condition y(0) = 20, we can find the value of C:

⇒[tex]2y=8t-\frac{1}{2}y^{2} +C[/tex]

⇒[tex]2y=8t-\frac{1}{2}y^{2} +20[/tex]

Solving for y, we get:

⇒[tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex]

Therefore, the y(t) is [tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex].

Part III:

To find the time it takes for the amount of salt in the tank to be reduced to 20% of the initial amount, we can solve for t when y(t) = 0.2 * y0:

⇒[tex]y(t) = 4 + 8t -\frac{1}{2}y^2 = 0.2 * y0[/tex]

⇒[tex]4 + 8t - \frac{1}{2} y^2 = 0.2 * 20[/tex]

Solving for t, we get:

⇒t =[tex]\frac{1}{8}[/tex](4 - 0.2 * 20) = approximately 6.875 minutes.

Hence, it will take approximately 6.875 minutes for the amount of salt in the tank to be reduced to 20% of the initial amount.

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The line of best fit is a mathematical representation of the general trend of the data points.

Number is a mathematical object used to count level and measure it is the fundamental concept in mathematics and is used in many different way number can be used to represent anything from quantities of object to ideas and concept additionally number are used to describe relationship between different object or concept. Numbers are also used to represent position in space as well as represent that time graph of table.

It gives an estimate of the expected quiz score when given a certain number of hours studied. In this case, the expected quiz score for someone who studied 6 hours would be around 85. However, it is important to note that this is only an estimate and the actual score could be higher or lower depending on the individual's knowledge and preparation for the quiz.

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If a family has 3 children of different ages and all combinations of boys and girls are considered equally likely:

a) the sample space and probability measure that describes the gender of the three children in their birth order is:  1/8.

b) Assuming we see the parents with two girls and there is no other information beyond that, the probability that the child we have not yet seen is a boy is: 1/4.

c). If we see the parents with two girls, and the parents tell us that these are the two youngest children, the probability that the oldest child we have not yet seen is a boy is: 1/8

a) The sample space for the genders of three children can be represented as a set of strings of length 3, each consisting of B (for boy) or G (for girl).

The total number of combinations of boys and girls is 2^3 = 8. Each combination has the same likelihood of occurring, so each combination can be assigned a probability of 1/8. So the sample space and probability measure can be described as:

Sample space: {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}

Probability measure: P(BBB) = P(BBG) = P(BGB) = P(BGG) = P(GBB) = P(GBG) = P(GGB) = P(GGG) = 1/8

b) Assuming we see the parents with two girls, the possible combinations for the genders of the three children are:

The probability of the third child being a boy is 1/2. So, given two girls, the probability that the child we have not yet seen is a boy is:

c) Assuming we see the parents with two girls and they tell us that these are the two youngest children, the possible combinations for the genders of the three children are:

The only possible combination is GBG, so the probability of the oldest child being a boy is 1. So, given two girls and that they are the youngest children, the probability that the oldest child we have not yet seen is a boy is:

Complete Question:

"Suppose a family has 3 children of different ages and all combinations of boys and girls are considered equally likely.

a) Precisely formulate the sample space and probability measure that describes the gender of the three children in their birth order.

b) Given that the parents have two girls and no other information is available, what is the probability that the remaining child is a boy?

c) If the parents have two girls and they inform us that they are the two youngest children, what is the probability that the oldest child is a boy?"

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The mean of the population is 14, which is the point estimate of the population mean that was determined from the simple random sample.

The mean of the population is a measure of the central tendency of the population. It is calculated by taking the sum of all the values in the population and dividing by the total number of values. In this case, the mean of the population would be calculated by adding the values of the sample (13, 15, 14, 16, 12) and dividing by the total number of values (5). The mean of the population is then 14 (13 + 15 + 14 + 16 + 12 / 5 = 14).

To calculate the mean of the population, we first need to calculate the sum of all the values in the population. This is done by adding the values of the sample together (13 + 15 + 14 + 16 + 12 = 70). We then divide the sum of the values by the total number of values in the population (70 / 5 = 14). This gives us the mean of the population, which is 14.

The mean of the population is a measure of the central tendency of the population, and it is calculated by taking the sum of all the values in the population and dividing by the total number of values. In this case, the mean of the population was 14, which is the point estimate of the population mean that was determined from the simple random sample.

The mean of the population is 14, which is the point estimate of the population mean that was determined from the simple random sample.

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There are 4840 yards in two and three-fourths miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know 1 mile is equal to 1760 yards.

Therefore, The number of yards in two and three-fourths miles can be obtained by multiplying the unit equivalent of one mile with two and three-fourths miles which is,

= 1760×[tex]2\frac{3}{4}[/tex] yards.

= 1760×(11/4) miles.

= 440×11 yards.

= 4840 yards.

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Answer: 4840

Step-by-step explanation:

The number of batches of muffins she can make will be 5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that at a berry farm, Clayton picks 1¹/₄ cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins.

The number of the batches of muffins can be calculated as:-

Number = ( 1¹/₄ + 2 x 1 ¹/₄ ) / ( 3 / 4 )

Number = [  ( 5 / 4 ) + ( 5 / 2 ) ] / ( 3 / 4 )

Number = [ ( 15 / 4 ) / ( 3 / 4 ) ]

Number = 5

Therefore, the number of batches of muffins will be 5.

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The ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1) is 8:1, and the coordinates of the point are 8/3 and -1/9

The given data is, the line 2x+3y-5= 0 and the points are (8, -9) and (2, 1)

Let us consider the ratio to be α: 1

To find the values of a and b we need to use the midpoint formula:

[tex]X=\frac{m_1x_1+m_2x_2}{m_1+m_2} ,\frac{m_1y_1+m_2y_2}{m_1+m_2}[/tex]

For Points (8,–9) and (2, 1) by applying the section formula we get,

[tex]X=\frac{2\alpha +8}{\alpha +1} ,y=\frac{\alpha -9}{\alpha -1}[/tex]

Given equation of line is 2x + 3y–5 = 0 substitute the values of x,y in the equation of line:

[tex]X=2(\frac{2\alpha +8}{\alpha +1} )+3(\frac{\alpha -9}{\alpha -1})-5=0[/tex]

4α+16+3α-27-5α-5

2α=16

α=8

Hence the ratio is 8:1.

Also, the coordinates are

[tex]X=\frac{2\alpha +8}{\alpha +1}=\frac{2(8) +8}{8+1}=\frac{24}{9}=\frac{8}{3} \\\\ y=\frac{\alpha -9}{\alpha -1}=\frac{8-9}{8-1}=\frac{-1}{9}[/tex]

∴ The coordinates are (x,y) = (8/3,-1/9).

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The angle x in the heptagon is 98 degrees.

The polygon above has 7 sides. Therefore, the name of the polygon is heptagon. Therefore, the sum of interior angles of a polygon can be represented as follows:

sum of interior angles of a polygon = 180(n - 2)

where

Therefore,

sum of interior angles of the heptagon =  180(7- 2)

sum of interior angles of the heptagon = 180(5)

sum of interior angles of the heptagon = 900 degrees

Hence, let's find x as follows:

122 + 146 + 142 + 140 + 110 + 142 + x = 900

x = 900 - 802

x = 98 degrees

Hence,

x = 98 degrees

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Length of LY = 20 inches.

Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical.

Given triangles,

ΔHKS and ΔDLY

and ΔHKS ≅ ΔDLY

If two triangles are said to be congruent, all three corresponding sides are equal.

So, LY = SK (corresponding side)

LY = 20 inches

Hence, 20 inches is length of LY.

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Note: By the figure DL = 24 inches, it should be 15 inches if triangles are congruent.

The missing length is 6.

8

4

2

10

From the numbers shown above, it is found that the difference from one length to the other is  2.

Therefore, the missing length is 6.

Length is described as a measure of distance.

In the International System of Quantities, length is also a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.

In conclusion, the base unit for length is the meter in the International System of Units system the base unit for length is the meter.

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The intersection point is the solution of inequalities is (15, 7.5).

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given system of inequalities are 13x+37y≤481 -----(i) and 27x+21y≤567 -----(ii)

Here, x≥4 and y≥2

From the graph we can see that, inequalities are intersecting at (15, 7.5)

Therefore, the intersection point is the solution of inequalities is (15, 7.5).

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y=3x-9 is the  equation of the line with the given slip and y-intercept slope is 3 y intercept is -9

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the equation of the line with the given slip and y-intercept slope is 3 y intercept is -9

m=3 and y intercept is -9

y=3x-9

Hence, y=3x-9 is the  equation of the line with the given slip and y-intercept slope is 3 y intercept is -9

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The total change in size of the tumor in the first 3 months is 13.5 cubic millimeters. The average rate of change of the tumor in the first 3 months is 4.5 cubic millimeters per month.

The total change in size of the tumor in the first 3 months can be calculated by subtracting the size at the beginning (4.5 cubic millimeters) from the size at the end of the 3-month period (S(3) = 4.5 * 3 = 13.5 cubic millimeters). Therefore, the total change in size of the tumor in the first 3 months is 13.5 cubic millimeters.

To calculate the average rate of change in the size of the tumor in the first 3 months, we need to divide the total change in size (13.5 cubic millimeters) by the time (3 months).

Therefore, the average rate of change of the tumor in the first 3 months is 4.5 cubic millimeters per month.

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There are a total of 13 different ornaments to choose from, with 3 types of ornaments.

Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.

When Cherry chooses at least 1 of each type, she will have to select a total of 5 ornaments. This means that Cherry can make a total of 13C5 (13 choose 5) different selections. This is equal to 715 different selections.

This can also be calculated by first selecting 1 ornament from each of the 3 types, which gives 3 different selections. Then, for the 2 remaining ornaments, Cherry can select any of the 13 ornaments, giving a total of 3 x 13 = 39 different selections. In total, this gives 3 + 39 = 42 different selections.

To conclude, Cherry can make a total of 715 different selections when she chooses at least 1 of each type of ornament.

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The correct graph is "Option 3". The solution  is −11 < x < − 4  or x > 2.

Let's work through your inequality piece by piece.

[tex]\frac{x^2+9x-22}{x+4} > 0[/tex]

Let's locate the inequality's crucial points.

[tex]\frac{x^2+9x-22}{x+4} = 0[/tex]

[tex]x^2+9x-22=0[/tex]

(Add x+4 to both sides)

(x−2)(x+11)=0

(Left side of the equation factor)

x−2=0 or x+11=0

(Set all variables to 0)

x=2 or x=−11

Verify any potential weak points.

x=2(Works in original equation) (Works in original equation)

x=−11(Works in original equation) (Works in original equation)

Important points:

x=2 or x=−11

(Equalizes both sides)

x=−4

(Sets the left denominator to 0)

Check the gaps between important points. Test the interval values to see if they are effective.

(Works incorrectly in the original inequality) [tex]x < -11[/tex]

(Works in original inequality)[tex]-11 < x < -4[/tex]

(Not applicable to the original inequality) x > 2 (Works in original inequality)

The answer is [tex]-11 < x < -4 $ or $ x > 2~[/tex]

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The values of x are 13 and -1. Option A

Algebraic expressions are defined as  expressions that have terms, variables, coefficients, constants and factors.

They are made up of arithmetic operations.

Given that;

(x - 7)²= 36

expand the bracket

x² - 7x - 7x + 49 = 36

collect like terns

x² - 14x + 49 = 36

x² - 14x + 13

Factorize the expression

(x² - 13x) + (x - 13)

Factor the common terms

x(x - 13) + 1(x - 13)

x = 13. x = -1

Hence, the values are 13 and -1

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The value of a is 3√2 when the two geometric sequences of positive real numbers of 6, a,b and 1/b, a,54.

A sequence of the numbers in which all the numbers are arranged in such a manner so that the ratio of two successive numbers is always constant,

The geometric progression and the constant ratio are known as the common ratio (r).

A general G.P. can be represented as:

a,ar,ar²,ar³,...............,arⁿ⁻¹,........

Where a=First term, r is the Common ratio and the n=Number of terms.

The nth term of a G.P.:

an=arⁿ⁻¹

Some of the infinite terms of a G.P.:

S∞=a/1−r

Here  r<1

Let:

[tex]a_n=a_1q^n^-^1\\a_n_-_1=a_1q^n^-^2\\a_n_+_1=a_1q^n[/tex]

Now multiply the last two equations:

[tex]a_n_-_1 a_n_+_1=a_1q^n^-^2a_1q^n\\\\a_n_-_1 a_n_+_1=a_1^2+q^n^-^2q^n\\\\a_n_-_1 a_n_+_1=a_1^2+q^n^+^n^-^2\\\\a_n_-_1 a_n_+_1=a_1^2+q^2^n^-^2\\\\a_n_-_1 a_n_+_1=a_1^2+q^2^(^n^-^1^)\\\\a_n_-_1 a_n_+_1=a_1^2+q^(^n^-^1^)^2\\\\\sqrt{a_n_-_1 a_n_+_1} =a_1^2+q^(^n^-^1^)\\\\\sqrt{a_n_-_1 a_n_+_1}=a_n[/tex]

Formula:

[tex]a_n=\sqrt{a_n_-_1a_n_+_1}[/tex]

a=√6b-----(1)

a=√1/b*54----(2)

By Equalating both equations:

6b=√1/b*54

b²=54/6

b²=9

b=3

substitute the b value in equation(1)

a=√6b

a=√6*3

a=√18

a=3√2

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6 is the intersection point mean in the given situation.

Two or more expressions with an Equal sign is called as Equation.

Given that Andre started with $15 and deposits $5 per week.

Noah started with $2.50 and deposits $7.50 per week.

Noah's Savings is given and his equation is y = 7.5x + 2.5, where x represents the number of weeks and y represents his savings.

The equations for Andre's savings is y = 5x + 15

The intersection point of the two equations is the point at which both Andre and Noah have the same amount in their savings.

5x+15=7.5x + 2.5

Subtract 7.5x on both sides

-2.5x + 15 = 2.5

Add 2.5x to both sides

Divide both sides by 2.5

x = 6

Hence, 6 is the  intersection point mean in this situation.

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Answer:

the 3 answer is the right one

The slope-intercept equation of a linear function f whose graph satisfies the given condition is y = 5.

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

y - y₁ = m(x - x₁)

Where:

Since the line is perpendicular to x = 6, which is a vertical line, the other line must be horizontal with a slope of zero (0). Therefore, the required equation is given by:

y - y₁ = m(x - x₁)

y - 5 = 0(x - (-5))

y - 5 = 0(x + 5)

y - 5 = 0

y = 5.

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Answer:

Step-by-step explanation:

D

The right expression will be -3x + 3 = 3( 1 - x ) for the given expressions.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that there are different expressions the correct expression choice is calculated s below:-

-3x + 3 = 3( 1 - x )

-3x + 3 = 3 - 3x

-3x + 3 = -3x + 3

Hence, the correct ex[ression would be -3x + 3 = 3( 1 - x ).

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The solution to the two functions is the ordered pair (x, y) = (1, 3).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given that,

f(x) = 3ˣ and g(x) = -x + 4

The solution to the both functions is the intersection of both graphs.

That is, f(x) = g(x)

3ˣ = -x + 4

When x = 1, then the value of both the functions is 3.

So the solution is (1, 3).

This indicates that number of visitors at temperature 1 is 3, which is equal to the number of people who leave the park at temperature 1.

Hence the solution to the functions f(x)  and g(x) is the intersection of both the functions at the point (1, 3).

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The correct option: C. Graphs should have a lot of adornments is the statement which is least accurate.

Data that are gathered and/or generated through statistics during the course of statistical observations through statistical data processing are known as statistical data.

The guidelines below apply to vertical bar charts. Change "vertical" to "horizontal" and "horizontal" to "vertical" in these rules for horizontal bar charts.

Thus, the statement which is least accurate is "Graphs should have a lot of adornments"

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If a and b are integers that divide c and are relatively prime, then ab divides c. If a and b are not relatively prime, then ab need not divide c.

If a and b are integers that divide c, this means that c is divisible by both a and b. Additionally, if a and b are relatively prime, this means that they have no common factors besides 1. In this case, since a and b both divide c, then it follows that their product, ab, also divides c.

However, if a and b are not relatively prime, this means that they have common factors besides 1. In this case, the common factors of a and b may not divide c, so it is not necessarily true that ab divides c.

For example, if a = 6, b = 8, and c = 24, then 6 and 8 both divide 24, but 6 and 8 are not relatively prime (they have a common factor of 2). In this case, 6 * 8 = 48 does not divide 24.

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a. Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b.   the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

To estimate the probability that a randomly selected house  has a value less than $500,000:

P( x < 500,000)=P(x=0)+P(x=500)

=0.34+0.37+

=0.71

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume a normal distribution.

-The probability can therefore be calculated as:

P(x')=P( z < (x' -u)/σ.sqrt(n)))

P(z< (500-403)/(578sqrt(40)))

=P(z<2.2068)

=0.986336

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

The complete question is -

a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.

(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.

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The vertex of the hyperbolic mirror is (17, 8.5). To find the vertex of a hyperbolic mirror, you need to find the midpoint between its two foci.

In this case, the focus has coordinates (17, 0) and the mount at the top edge of the mirror has coordinates (17, 17). To find the midpoint, you average the x-coordinates and the y-coordinates.

The x-coordinate of the midpoint is: (17 + 17) / 2 = 17.

The y-coordinate of the midpoint is: (0 + 17) / 2 = 8.5

Therefore, the vertex of the hyperbolic mirror is (17, 8.5).

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Answer:

Given f(x) = 3x - 3 and g(x) = -x, to find g(f(x)), we first need to substitute f(x) into g(x).

So, g(f(x)) = g(3x - 3) = -(3x - 3) = -3x + 3.

Step-by-step explanation:

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

4x and 6x are like terms so we add them together

x2 +10x +24