let $x$ be a real number selected uniformly at random between 100 and 200. if $\lfloor \sqrt{x} \rfloor

In part a, since the population mean  is small, selections are independent and can be assumed to be so. In part b, the population size is too large for selections to be independent, so independence can not be assumed.

a. If mathematics departments had only four recent graduates total, the chance that the sample will consist of two graduates who intend to teach high school is

0.5 * 0.5

= 0.25.

b. If mathematics departments had 10 million recent graduates, the chance that the sample will consist of two graduates who intend to teach high school is

0.5 * 0.5

= 0.25.

c. The selections are technically independent in part a, since the population size is small enough that the selection of one person will not affect the probability of selecting the other person. The selections are not technically independent in part b, since the population size is so large that selecting one person affects the probability of selecting the other person. In part a, you can assume independence since the population size is small enough that it is reasonable to assume that the selections are independent. In part b, you cannot assume independence since the population size is too large to make this assumption.

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Mean Absolute Deviation (MAD) is a measure of accuracy for a forecasting model.

It measures the average distance between the actual value and the predicted value, and can be calculated using the following formula: MAD = 1/n * Σ |Ai-F i |, where n is the number of data points, Ai is the actual value, and Fi is the forecasted value. MAD is often used to compare the accuracy of different forecasting models. A lower MAD value indicates that the model has a better accuracy in predicting future values. Additionally, MAD can also be used to measure the accuracy of a single forecasting model over time. If MAD increases, then the accuracy of the forecasting model is decreasing.

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The value of the expression 59 + (1/6)r at r = - 1/2 will be 707/12.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 59 + (1/6)r

The value of the expression at r = - 1/2 will be given as,

⇒ 59 + (1/6)(-1/2)

⇒ 59 - 1 / 12

⇒ (708 - 1) / 12

⇒ 707 / 12

The value of the expression 59 + (1/6)r at r = - 1/2 will be 707/12.

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The above equation's midpoint is represented by the expression Midpoint = (3.5,2,2) (1.5,-4.8). ( 2.5,-1.3 )

Midpoint =( 2.5,-1.3 )

The formula for determining the midpoint is

[tex]$\left(x_m, y_m\right)=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$[/tex]

[tex]$\left(x_m, y_m\right)=$[/tex]the midpoint's coordinates

[tex]$\left(x_1, y_1\right)=$[/tex] the first point's coordinates

[tex]$\left(x_2, y_2\right)=$[/tex] the second point's coordinates

Divide the distance between the two endpoints by 2, then multiply it by 3. The middle of that line is at these distances from each end. As an alternative, multiply the sum of the two endpoints' x coordinates by 2. For the y coordinates, repeat the process. the location on a line when the distances to both ends are equal. a period of time midway between the start and finish of an event.

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Answer:

B, C

Step-by-step explanation:

A) No, factors of 15 = 1, 3, 5, 15... so 45 is not a factor of 15

B) yes, 45 is the third multiple of 15 ( 15×3=45)

C) yes, factor of 45 is the number that divides 45 without leaving any remainders (45÷15=3), therefore 15 is a factor of 45

D) No, multiples must be bigger in value than the actual number because( a multiple of 45) means, the number we get when we multiply 45 by an integer... Here we can't multiply an integer by 45 and get the answer 3

When two or more variables vary jointly, their product is always constant. In this case, if 'a' varies jointly with 'b' and 'c' it means that their product is always constant, so abc = k, where k is a constant value.

When a variable 'a' varies inversely as the square of another variable 'd', it means that a*1/d^2 = k, where k is a constant value.

So, if 'b' is tripled, 'c' is doubled and 'd' is doubled, we can see the effect on 'a' by substituting the new values into the equations.

abc = k => a3b2c = k

a1/d^2 = k => a1/(2d)^2 = k

So the effect on 'a' if 'b' is tripled, 'c' is doubled, and 'd' is doubled is that it will be divided by 4.

a3b2c = a1/(2d)^2 => a = k / (3b2c*(2d)^2) = (k/(12bcd^2))

So a = k/(12bcd^2) = a/4.

Therefore, the value of 'a' is decreased by a factor of 4.

The result of the convolution integral is the same as the solution obtained in part (a).

a. Solving the ODE with y(0) = 0 using integrating factors,

multiplying both sides of the equation by e^4t, we get

e^4t y' + 4e^4t y = 4e^-te^4t

Integrating both sides,

∫ (e^4t y' + 4e^4t y) dt = ∫ 4e^-te^4t dt

Therefore,

e^4t y = ∫ 4e^-te^4t dt + C

Since y(0) = 0, C = 0,

y = 1/4 ∫ 4e^-te^4t dt

Using integration by parts,

y = 1/4 [te^-t + 4/3 e^-t]

Therefore,

y(t) = 1/4 [te^-t + 4/3 e^-t]

b. The transfer function of the system is given by

H(s) = Y(s)/F(s) = 1/4s/(s+4)

c. The impulse response of the system is given by

h(t) = L^-1[H(s)] = 1/4e^-t

d. The convolution integral (h*f)(t) can be evaluated as follows,

(h*f)(t) = ∫ h(t-w)f(w)dw

= ∫ 1/4e^-(t-w) 4e^-w dw

= 1/4 ∫ 4e^-(t+w) dw

= 1/4 [te^-t + 4/3 e^-t]

The result of the convolution integral is the same as the solution obtained in part (a).

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Answer: 34.3527303398

Step-by-step explanation: hope it is right

The value of the conditional Probability is P(A|B) is 1/3.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The main distinction between a probability and a conditional probability is that a probability is the likelihood of an event, such as A, occurring, whereas a conditional probability assumes that another event, such as B, has already happened in order to define the probability of an event, such as in the conditional probability of A given B.

Conditional probability is the likelihood that any event A will occur in the presence of another event B that is related to A. P(A|B) illustrates it.

By, Conditional Probability :

P (A∩B) =P (A∩B') - P(B)= 4/9 - 1/3 = 1/9

P(A|B) = P (A∩B)/ P(B)

           = (1/9)/(1/3) =  1/3

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It will take approximately 270.28 minutes, or 4 hours and 30.28 minutes, to fill the reservoir at a rate of 250 gallons per minute.

we can use the formula:

time = volume ÷ flow rate

where volume is the capacity of the reservoir in cubic feet and flow rate is the rate at which the reservoir is filled in cubic feet per minute.

Since the capacity of the reservoir is given in cubic feet and the flow rate is given in gallons per minute, we need to convert the flow rate to cubic feet per minute. One gallon is equal to 0.133681 cubic feet, so:

250 gallons/minute x 0.133681 cubic feet/gallon = 33.342 cubic feet/minute

So the flow rate in cubic feet per minute is 33.342. Now we can calculate the time it takes to fill the reservoir:

time = 9000 cubic feet ÷ 33.342 cubic feet/minute = 270.28 minutes

So it will take approximately 270.28 minutes, or 4 hours and 30.28 minutes, to fill the reservoir at a rate of 250 gallons per minute.

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The image of the function after the translation is g(x) = log(x + 1) + 4

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

f(x)=logx

How to determine the equation of g(x)?

From the graph, the given parameters are:

f(x) = log(x)

From the graph, we can see that:

The graph of f(x) is translated left by 1 unit

The graph of f(x) is translated up by 4 units

This transformation is given as

g(x) = f(x + 1) + 4

Mathematically, this transformation can be represented as

(x, y) = (x + 1, y + 4)

When represented as a function, we have

g(x) = f(x + 1) + 4

Substitute the equation f(x) = log(x)

f(x + 1) = log(x + 1) + 4

So, we have the following equation

g(x) = log(x + 1) + 4

Hence, the equation of g(x) is g(x) = log(x + 1) + 4

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The area of the region inside the circle (x−1)^2+y^2=1 and outside the circle x^2+y^2=1  is 4.

The area of the region inside the circle (x−1)^2+y^2=1 and outside the circle x^2+y^2=1 can be calculated using polar coordinates.

The equation of the inner circle in polar coordinates is r_1^2=1+2cosθ and the equation of the outer circle in polar coordinates is r_2^2=1.

The intersection points of the two circles can be found at θ=±π/3.

The area of the region can be calculated using the integral:

Area=∫_π/3^-π/3 (1+2cosθ)dθ=(2+4sinθ)|_π/3^-π/3=(2+4sin(-π/3))-(2+4sin(π/3))=4.

Therefore, the area of the region is 4.

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At 95% confidence level, the proportion will be between .0.19912815 and 0.200086, when you have a mean of 0.2 and a standard error of 0.00053.

How do you calculate population proportion?

P′ is equal to x / n, where x is the total number of successes and n is the sample size. As a point estimate for the genuine population proportion, the variable p′ represents the sample proportion.

FPC = (N-n)/(N-1), where Z/2 is the critical value of the Normal distribution at /2, p is the sample proportion, n is the sample size, and N is the size of the population (for example, at a confidence level of 95%, is 0.05 and the critical value is 1.96).

A portion of a population that possesses a certain characteristic, given as a percentage, fraction, or decimal of the entire population. The population percentage for a finite population is equal to the population's size divided by the proportion of its members who possess a given attribute.

Given data :

p = 60 / 300 = 0.2

q = 1 - p = 0.8

mean proportion = p = .2

standard error = sqrt(p * (1-p / 300) = sqrt(0.2 * 0.8/ 300) =0.00053333333

critical z-score at 95% confidence level is plus or minus 1.645.

use the z-score formula to find the critical raw score.

for the low side, z = (x - m) / s becomes:

-1.645 = (x - 0.2) / 0.00053

solve for x to get:

x = -1.645 * 0.00053 + 0.2 = 0.19912815

for the high side, z = (x - m) / s becomes:

1.645 = (x - 0.2) / 0.00053

solve for x to get:

x = 1.645 * 0.00053 + 0.2 = 0.200086125

At 95% confidence level, your proportion will be between .0.19912815 and 0.200086, when you have a mean of 0.2 and a standard error of 0.00053.

Here's what it looks like on a z-score normal distribution calculator output.

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Based on this information, the conclusion about weight and calories burned per minute that is true is: D. For each additional pound of weight, calories burned per minute increases by 0.05 calories.

In Mathematics, the slope-intercept form of a line can be represented or modeled by using this linear equation:

y = mx + c

Where:

Based on the information provided about the data for weight (in pounds) and calories burned per minute, a regression equation that models the situation is given by:

ŷ = 2.2 + 0.05x

Where:

In conclusion, we can logically deduce that the amount of calories burned per minute increases by 0.05 calories for each additional pounds of weight.

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Complete Question:

a.) For each additional pounds of weight, calories burned per minute increases by 2.2 calories.

b.) For each additional pounds of weight, calories burned per minute stays relatively the same.

c.) For each additional pounds of weight, calories burned per minute decreases by 0.05 calories.

d.) For each additional pounds of weight, calories burned per minute  increases by 0.05 calories.

The solution for the given equation; 7x+5(x-1)=-5+12x as required to be determined is; Infinitely many solutions.

It follows from the task content that the solution for the given equation; 7x+5(x-1)=-5+12x is to be determined.

Since the given equation is; 7x + 5 (x-1) = -5 + 12x

Hence, by the distributive property; we have that;

7x + 5x - 5 = -5 + 12x

12x - 5 = 12x - 5

On this note, since both sides of the equation are same, it follows that the equation has infinitely many solutions.

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Answer:

The rectangle (option 2)

Step-by-step explanation:

A quadrilateral is any enclosed polygon with four sides. Only the rectangle (option 2) is a quadrilateral.

The other options are not quadrilaterals because they don't have four sides (options 1 and 3) or are not enclosed (option 4). Hope this helps!

For the first graph, the function is increasing when the graph is sloping upwards, which is the case between the points (-1,1) and (1,3). For the second graph, the function is increasing when the graph is sloping upwards, which is the case between the points (0,2) and (2,4).

For the first graph, the function is increasing from interval (-1,1) and decreasing from interval (1,3).

For the second graph, the function is increasing from interval (0,2) and decreasing from interval (2,4).

For the first graph, the function is increasing when the graph is sloping upwards, which is the case between the points (-1,1) and (1,3). This indicates that the function is increasing on the interval (-1,1). Similarly, the function is decreasing when the graph is sloping downwards, which is the case between the points (1,3) and (3,1). This indicates that the function is decreasing on the interval (1,3).

For the second graph, the function is increasing when the graph is sloping upwards, which is the case between the points (0,2) and (2,4). This indicates that the function is increasing on the interval (0,2). Similarly, the function is decreasing when the graph is sloping downwards, which is the case between the points (2,4) and (4,2). This indicates that the function is decreasing on the interval (2,4).

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Answer:The t-intercept of a function is the point at which the function crosses the t-axis. To find the t-intercept of the function A(t) = 14,820 - 247t, we need to find the value of t when A(t) = 0. Setting A(t) = 0 and solving for t, we get:

14,820 - 247t = 0

t = (14820/247)

The t-intercept of the function is 60 months, which means that after 60 months (or 5 years) the amount owed on the car will be $0.

The y-interval of a function is the point at which the function crosses the y-axis. To find the y-intercept of the function A(t) = 14,820 - 247t, we need to find the value of A(t) when t = 0.

At t = 0, A(t) = 14,820 - 247(0) = 14,820.

The y-intercept of the function is $14,820 which means that before making the first payment, the cost of the car including tax and interest is $14,820.

Step-by-step explanation:

A line segment is a piece of a line that can connect two places. Hence  ar (ABC) = ar (ABD)

Given

[tex]$\triangle \mathrm{ABC}$[/tex] and [tex]$\triangle \mathrm{ABD}$[/tex] are two triangles on the same base [tex]$\mathrm{AB}$[/tex].

To show :

ar(ABC)=ar(ABD)

Proof :

Since the line segment [tex]$\mathrm{CD}$[/tex] is bisected by [tex]$\mathrm{AB}$[/tex] at [tex]$\mathrm{O}[/tex] . [tex]\mathrm{OC}=\mathrm{OD}$[/tex].

In [tex]$\triangle \mathrm{ACD}$[/tex], We have [tex]$\mathrm{OC}=\mathrm{OD}$[/tex].

So, [tex]$\mathrm{AO}$[/tex] is the median of[tex]$\triangle \mathrm{ACD}$[/tex]

Also we know that median divides a triangle into two triangles of equal areas.

∴ar(ΔAOC)=ar(ΔAOD) _______ (1)

Similarly , In[tex]$\triangle \mathrm{BCD}$[/tex],

[tex]$\mathrm{BO}$[/tex]is the median. ([tex]$\mathrm{CD}$[/tex] bisected by [tex]$\mathrm{AB}$[/tex] at [tex]$\mathrm{O}$[/tex])

∴ar(ΔBOC)=ar(ΔBOD) _______ (2)

On adding equation (1) and (2) we get,

ar(ΔAOC)+ar(ΔBOC)=ar(ΔAOD)+ar(ΔBOD)

∴ar(ΔABC)=ar(ΔABD)

The complete question is,

In figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar (ABC) = ar (ABD).

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The solution for h according to the given equation a = bh as required is; h = a / b.

It follows from the task content that the solution for the given equation for variable, h be determined.

On this note, since the given equation is;

a = bh

To solve for variable, h; divide both sides of the equation by b so that we have;

h = a / b.

Ultimately, the required solution for variable, h is; h = a / b.

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The number of square centimeters of the cylinder that Mariah painted is given as follows:

36π cm².

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

Mariah made a cylinder out of clay that had a radius of 6 cm and a volume of 72π cm^3, hence the height of the cylinder is obtained as follows:

36πh = 72π

h = 2.

The surface area of a cylinder is obtained as follows:

S = 2π r h + 2π r

Hence it's value is of:

S = 2π x (2 x 6 + 6)

S = 36π cm².

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Numbers written from 30 to 65 including 30 and 65 = 36 numbers

A number is a basic component of mathematics. Numbers are used for counting, measuring, keeping things in order, indexing, etc. We have different types of numbers based on their properties such as natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc.

Given,

Numbers 30 to 65

30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65

Total count of numbers 30 to 65 = 36

Hence, 36 numbers are written from 30 to 65 including 30 and 65.

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Answer:

the distance between (4,-2) and (0,4) is √(52) or approximately 7.2 units.

Step-by-step explanation:

To find the distance between two points in a Cartesian coordinate plane, we can use the distance formula:

distance = √((x2-x1)² + (y2-y1)²)

In this case, the two points are (4,-2) and (0,4). So,

x1 = 4, y1 = -2 and x2 = 0, y2 = 4

By substituting these values in the distance formula, we get:

distance = √((0-4)² + (4-(-2))²)

distance = √((-4)² + 6²)

distance = √(16 + 36)

distance = √(52)

So the distance between (4,-2) and (0,4) is √(52) or approximately 7.2 units.

The decimal representation of 1/70000000 is 0.0000000142857142857....

In math, what is a fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To find the digit that occurs in the 2023rd place after the decimal point, we can use long division to divide 1 by 70000000 and track the remainders.

Since the decimal representation of 1/70000000 is repeating every 6 digits, we can find the digit at the 2023rd place by taking the remainder when 2023 is divided by 6.

2023 % 6 = 1

So the digit in the 2023 place is the first digit after the repeating decimal, which is 4.

Therefore the digit in the 2023rd place after the decimal point is 4.

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Taking w as the unknown number, the equation for the given statement is 2(w-8) = 5.

To solve this problem, we need to convert the given statement in mathematical form.

We assume that "w" is the unknown number in the equation.

First, we have to take a closer look at the given statement. It was stated that "twice the different of...  is equal to 5".  It shows that the result of equation 5 is the double value of another equation. We assume the unknown equation as y. Then:

2y = 5

Next, the rest of the statement stated that "a number and 8". From this part of statement, we know that the unknown equation "y" we assume above should be replace with "w-8". Hence:

2(w - 8) = 5

If we want to solve this question, we can solve it by dividing both sides with 2:

2(w - 8) = 5

------------------- : 2

w - 8 = 5/2

w = 5/2+ 8

w = 10.5

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The inequality equation which represents Ten less than twice a number is equal to at least 52 is 10 - 2x ≥ 52 and x ≤ -21

Let

The unknown number = x

Ten less than twice a number is equal to at least 52;

10 - 2x ≥ 52

Subtract 10 from both sides

- 2x ≥ 52 - 10

- 2x ≥ 42

divide both sides by - 2

x ≤ 42/-2

x ≤ -21

Hence, x ≤ -21 is the solution to the inequality 10 - 2x ≥ 52 if x comes first.

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Answer: D. 0.70

Step-by-step explanation:

42/60= 0.7

The total distance ran by the wide receiver is given as follows:

195.6 yd.

Suppose that we have two points with coordinates given as follows:

[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

Then the formula for the distance between these two points is given as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For the out route, the distance is given as follows:

[tex]D = \sqrt{(60 - 30)^2+(50 - 20)^2} = 42.43[/tex]

To the end zone, the distance is given as follows:

[tex]D = \sqrt{(60 - 80)^2+(50 + 30)^2} = 82.46[/tex]

From the end zone back to the huddle, the distance is given as follows:

[tex]D = \sqrt{(80 - 30)^2+(-30 - 20)^2} = 70.71[/tex]

Hence the total distance is of:

42.43 + 82.46 + 70.71 = 195.6 yd.

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Scalar quantities of these do not include direction distance, Force, Acceleration, or Velocity.

scalar, a physical quantity whose sole description is its magnitude. Scalars include, but are not limited to, time, energy, mass, volume, density, and speed.

A scalar quantity is one that doesn't depend on movement in any direction. Vector quantities can have a magnitude and a direction. Scalar quantities have just a magnitude.

All of the option values are scalar, with the exception of impulse. A force can be an impulse. Similar to force, it has both magnitude and direction.

Additional examples of scalar quantities are mass, velocity, distance traveled, time passed, energy, density, volume, temperature, work, etc.

Since speed has a simple magnitude and no discernible direction, it is a scalar number.

A scalar quantity is something like distance. Any quantity that has both a direction and a magnitude is a vector.

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The bookstore has 30 copies of books left after they sold (4/7)th today.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A bookstore had 84 copies of a magazine.

Yesterday it sold 1/6 of them which is, (84 - (1/6)×84).

= 84 - 14 books remaining.

= 70 books remaining.

Today it sold 4/7 of what remaining which is,

= (70 - (4/7)×70).

= 70 - 40.

= 30 books.

So, Now the bookstore has 30 books left.

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