The rise time of a reactor is measured in minutes (and fractions of minutes). Let the sample space be positive, real numbers. Define the events A and B as follows: A = { x | x < 72.5] and B = { x | x > 52.5]. Describe each of the following events: a. A' b. B' c. A ∩ B d. A ∪ B

Answer:

1a) 75

1b) 135

2a) 60

Step-by-step explanation:

Let's do the first 3 so you can see the pattern I use.

1a.) 150% of 50

First step I do is take the 150 and put a dot at the end.

150.

Next, I move that dot to the left two times, making it...

1.50

Now I take that and multiply by the number it's asking, which is 50

[tex]1.50 \times 50 = 75[/tex]

1b.) 150% of 90

150.

1.50

[tex]1.50 \times 90 = 135[/tex]

2a.) 100% of 60

100.

1.00

[tex]1.00 \times 60 = 60[/tex]

The rule of functions to solve for C(N(h)) is composition of functions. The cost when h = 8 hours is $3680.

To solve C(N(h)), the rule used is composition of functions, where the output of one function N(h) is used as the input to another function C(x).

First, evaluate C(x) to get its output and then plug that output into N(h) to get the final output.

Given the two functions, the cost in dollars to produce x shovels, C(x) = 12x + 450, and the number of shovels that can be produced in h hours, N(h) = 40h, we can find the cost when h hours of production time is used by finding C(N(h)).

To find C(N(h)), we first find N(h) to get the number of shovels produced in h hours and then plug that into C(x) to find the cost:

C(N(h)) = C(40h) = 12(40h) + 450 = 480h + 450

So, the rule for C(N(h)) is C(N(h)) = 480h + 450.

When h = 8 hours, the cost to produce shovels is given by C(N(8)) = 480(8) + 450 = 3680 dollars.

Therefore, it will cost $3680 to produce shovels in 8 hours.

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Calculating parking ratios involves dividing a building's entire rentable square footage by its overall parking spaces. This offers the square footage available for rent per parking space, which is commonly stated as 1 parking space. 200 SF

The dimensions of a typical perpendicular parking place are nine feet (9') wide by eighteen feet (18') long.

To start, multiply 8 by 24 to determine how far apart each parking space is from the others (in other words the width of the parking lot).

8×24= 192 feet

Given that the question asks for an answer in yards, you know that 1 foot equals 1/3 of a yard and that 192 feet equals 64 yards.

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All values of x that satisfy |x|<1/2, |cos x-(1-x^2/2)| is less than or equal to 1/4.

The Taylor series for the cosine function is given by:

cos x = 1 − x2/2! + x4/4! − x6/6! + x8/8! − x10/10! + . . .

For|x| < 1/2, we can ignore the higher order terms, and thus the series reduces to:

cos x = 1 − x2/2

Therefore,[tex]|cos x − (1 − x2/2)| = |x2/2| = |x|2/2[/tex]. Since |x| < 1/2, we have |x|2/2 < 1/4. Hence,

[tex]|cos x − (1 − x2/2)| < 1/4.[/tex]

Therefore, for all values of x that satisfy [tex]|x| < 1/2, |cos x-(1-x^2/2)|[/tex] is less than or equal to 1/4.

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Based on the information in the graphs, it can be inferred that the correct conclusion is Fewer shops sell sandwiches for under $10 near City College than near Main Line University.

To identify the correct conclusion we must read each of the options and compare with the graphics to verify the veracity of each of the statements. In accordance with the above, we can discard the first three statements and select the last option as the correct one because it is the one that matches the information in the graph.

In this case the percentage of stores that sell large sandwiches in City College is less than Main Line University.

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The function notation for A would be A(x) = y

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

This means that

The function can be expressed as

y = A(x)

This implies that:

The function A relates x and y

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Complete question

A is a relationship between two variables x and y such that every input x produce exact one output y​. What is the function notation of A

Answer:

The value 0.031 represents the interest rat, which means the annual compounded interest rate is 3.1%

First option

Step-by-step explanation:

The general equation for amount accrued A with a principal P at an annual compound interest rate of i%(r/100 in decimal) compounded n times a year for t years is given by

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]

Here r = i/100 which is a decimal

Looking at the specific equation
[tex]A = 2400\left(1 + \dfrac{0.031}{4}\right)^{4t}[/tex]

we can see that P = 2440, the initial investment

0.031 is the annual interest rate in decimal

Expressed as percentage that would be 0.031 x 100 = 3.1% per year

So the correct answer is the first option which states
The value 0.031 represents the interest rat, which means the annual compounded interest rate is 3.1%

The gross elasticity of demand for car polish with respect to the price of a car wash is 3.

The elasticity of demand refers to the change in demand when there is a change in another economic factor, such as price or income.

Given that, Sparkle clean car decreased the price of a car wash from $12 to $9 and noticed that the weekly quantity demanded for car polish increased from 200 to 350.

We are asked to find elasticity of demand,

First, we will find the increase in the customers:

Customer increasing = 350 - 200 / 200 × 100

= 75

Now, the fluctuation in the price =

Price fluctuation = 12 - 9 / 12 × 100

= 25

Elasticity = increased rate / fluctuated price

= 75 / 25

= 3

The elasticity of demand is 3 which is greater than 1, so, that mean, the demand is elastic.

Hence, the gross elasticity of demand for car polish with respect to the price of a car wash is 3.

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The total cost of the taxi ride is given by the equation A = $ 19.25

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 total cost of taxi ride be represented as A

Now , the equation will be

The initial cost for the pickup = $ 3.50

The cost of the ride per mile = $ 1.75

The cost for riding 9 miles = 9 x cost of the ride per mile

Substituting the values in the equation , we get

The cost for riding 9 miles = 9 x 1.75 = $ 15.75

So , the total cost of taxi ride A = initial cost for the pickup + cost for riding 9 miles

The total cost of taxi ride A = 3.50 + 15.75

The total cost of taxi ride A = $ 19.25

So , if the ride is m miles long , the cost is A = 3.50 + ( 1.75 )m

Hence , the equation is A = $ 19.25

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The correct statement is: She should calculate the ratio between the number of calories she burned versus the number of miles she ran.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here: The table containing data calories vs miles run.

You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are all the same, the table shows a proportional relationship.

Thus calculating the ratio for each pair of entries we get

1) ratio=118/1.2

      =295:3a  or unit rate 98.33 calories per mile

2) 190/2= 95:1 or unit rate 95 calories per mile

3) 226/2.4=565:6 or unit rate94.1

clea,rly the ratios are different.

Hence, The table containing the data doesn't form a proportional relationship.

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Here's a sample code in Python that uses the scikit-learn library to perform linear regression on the given data:

import numpy as np

from sklearn.linear_model import LinearRegression

# Angle data

angle = np.array([0, 30, 45, 60, 90]).reshape(-1, 1)

# Modeling the relationship using Linear Regression

reg = LinearRegression().fit(angle, angle)

# Predicting the values

angle_pred = reg.predict(angle)

print("Predicted values: ", angle_pred)

The task is to develop a Python program that uses a linear regression model to predict the relationship between a dependent variable (angle) and an independent variable (in this case, the angle itself).

The code above models a trivial relationship between the angle and itself. This is just a simple example to show how linear regression can be performed in Python. Please make sure to use appropriate data and fit the model based on the problem statement.

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To calculate the number of gallons of gasoline required, you need to know the energy consumption of the car in MJ and the distance of the trip.

The first step is to determine the energy consumption of the car in MJ per unit distance (e.g. per mile or per kilometer). This information can be obtained from the car's fuel consumption specifications or from real-world tests.

Once the energy consumption is known, the number of gallons of gasoline required for a given trip can be calculated by dividing the total energy consumption of the trip by the energy content of a gallon of gasoline (120 MJ). This will give you the number of gallons of gasoline required to make the trip.

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Answer:

-3/5

Step-by-step explanation:

I attached a photo so you can see my work

First, we can simplify the left side of the equation:

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

Now, we can substitute this expression into the equation:

-3x - 6 = 5y

Next, we can isolate the y variable on one side of the equation by dividing both sides by 5:

-3x/5 - 6/5 = y

Finally, to find the value of y when x = -1, we substitute -1 for x in the expression:

-3(-1)/5 - 6/5 = y

-3/5 - 6/5 = y

-9/5 = y

So, when x = -1, y = -9/5.

The circumference of the circle is 6.28 .

Circle is a closed figure or curve that we get by drawing a line which passes through the points which are at an equal distance from a common point.

Perimeter of a closed figure is the total length of the line used for making that closed figure.

For example if we have three sticks of Length 2 cm, 3 cm, 5 cm. We make a triangle using the above sticks so the perimeter of the triangle will be

       = 2+3+5= 10 cm

This indicates that total length of stick used to form the triangle is 10 cm.

For a circular figure its perimeter is known as circumference.

Now for the given question:

Diameter of the circle ( D ) = 2 yards.

π= 3.14         ( given in question)

Circumference of a circle = π×D

                                          = 3.14×2

                                          = 6.28

Hence circumference of the circle is 6.28 yards.

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The value of H is 20 in the proportion 4 over H equals 5 over 25.

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

4 over H equals 5 over 25

4/H=5/25

Apply cross multiplication

4×25=5H

100=5H

Divide both sides by 5

20=H

Hence, the value of H is 20 in the proportion 4 over H equals 5 over 25.

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the branch of statistics for the scenario given regarding 10,000 Students is Descriptive Statistics.

In a study, descriptive statistics are used to describe the fundamental characteristics of the data. They provide brief summaries regarding the measures and samples. They serve as the foundation for virtually every quantitative data analysis, along with straightforward graphics analysis.

In most cases, descriptive statistics are different from inferential statistics. When you use descriptive statistics, you simply describe what the data show or are. With inferential statistics, you are attempting to draw inferences from data that go beyond the immediate facts. For instance, we attempt to infer what the general population might think from the sample data using inferential statistics.

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Both of the solutions differ in their constant integration.

A. ∫6x³(x⁴+1)dx

if we apply the distributive property:

∫6x³(x⁴+1)dx = ∫(6x⁷+ 6x³)dx = (6/8)x⁸ + (6/4)x⁴ + C = (3/4)x⁸ + (3/2)x⁴ + C

A. ∫6x³(x⁴+1)dx

If we use the substitution

w = x⁴+1

⇒ dw = 4x³dx  ⇒  x³dx = (1/4)dw

we have

∫6x³(x⁴+1)dx = 6∫w*(1/4)dw = (6/4)∫w dw = (3/2) (w²/2) + C = (3/4)w² + C

returning the change we get

∫6x³(x⁴+1)dx = (3/4)(x⁴+1)² + C

For these answers, we can apply Notable Identities as follows

(x⁴+1)² = (x⁴)² + 2*x⁴*(1) + (1)² = x⁸ + 2x⁴ + 1

then

(3/4)(x⁴+1)² + C₂ = (3/4)(x⁸ + 2x⁴ + 1) + C = (3/4)*x⁸ + (3/2)*x⁴ + (3/4) + C

We can assume (3/4) + C as a constant, then

∫6x³(x⁴+1)dx = (3/4)*x⁸ + (3/2)*x⁴ + C

Both of the solutions differ in their constant integration.

Both solutions are primitive of the same function, which must only fulfill a condition that is to differentiate into a constant, and in this case, they fulfill it.

It is not usual that using different methods of integration obtain different primitives, but it is not uncommon, there are quite a few known cases in which this happens and absolutely nothing happens.

It is normal. Two functions that differ in a constant have the same derivative and therefore, both functions are primitive of that same derivative.

C is often forgotten as a result.

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The number of 20-sided die in 80 is 33

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

The table of values

On the table, we have

20-sided = 5

Total = 12

So, we have

P(20-sided) = 5/12

For 80 dice, we have

Expected value = 5/12 * 80

Expected value = 33

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El grafico de la ecuación cuadratica se puede ver en la imagen del final.

Digamos por ejemplo que queremos completar la tabla de abajo:

x: -1, 0, 1, 2

y:

Para ello, debemos evaluar la ecuación cuadratica que nos dieron en esos valores de x.

si x= -1

y = 2*(-1)²+3 = 5

si x = 0

y = 2*(0)²+3 = 3

si x = 1

y = 2*(1)²+3 = 5

si x = 2

y = 2*(2)²+3 = 11

Entonces the table is:

x: -1, 0, 1, 2

y:  5, 3, 5, 11

Para graficar esto, simplemente grafica todos los puntos que conocemos y debemos conectarlos con una curva, el grafico está abajo.

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Option C is correct, the graph shows a dashed line, which passes through a point negative 2 comma 0 and a point 0 comma negative 2, with shading above the line.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is −3x − 3y < 6

Minus three times  of x minus three times of y less than six.

Now let us solve for y

-3y<6+3x

Divide both sides by 3

-y<2+x

y>-x-2

The graph of the inequality is given in the attachment.

When we observe the graph the line is dashed line, which passes through a point negative 2 comma 0 and a point 0 comma negative 2, with shading above the line.

Hence, Option C is correct, the graph shows a dashed line, which passes through a point negative 2 comma 0 and a point 0 comma negative 2, with shading above the line.

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9) The two column proof below has been used to prove that EG bisects HF.

10) The two column proof below has been used to prove that EG ≅ HF

11) The two column proof below has been used to prove that EI ⊥ KT

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

9) We want to prove that EG bisects HF.

In a rectangle opposite sides are equal and parallel.

In ΔMHE and ΔMFG, ∠MEH = ∠MGF

[Alternate interior angles; HE ∥ GF and EG as transversal]

HE = GF [Opposite sides of a rectangle are equal]

∠MHE = ∠MFG

[Alternate interior angles; HE ∥ GF and HF as transversal]

Thus;

ΔMHE ≅ ΔMFG

[By ASA congruence rule]

Equating the corresponding parts of congruent triangles, we get:

HM = FM

GM = EM

Diagonals of a rectangle bisect each other.

10) The proof that EG ≅ HF is as shown above in the previous proof.

11)  TIKE is a Kite //Given

(2) KI = KE                     //(1) definition of a kite

(3) KP = KP                    //Common side, reflexive property of equality

(4) ∠IKT ≅ ∠EKT // (1), in a kite the axis of symmetry bisects the angles at those corners

(5) △KPI ≅ △KPE      //Side-Angle-Side postulate.

(6) ∠KPI ≅ ∠KPE   //Corresponding angles in congruent triangles (CPCTC)

(7) EI ⊥ KT     //Linear Pair Perpendicular Theorem

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The total number of points scored is given by the equation A = 23 points

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 total points scored be represented as A

Now , the equation will be

Substituting the values in the equation , we get

A = 3x + 2y + z   be equation (1)

where x = red team = 3 points

y = yellow team = 5 points

z = blue team = 2 points

So , A = 3 ( 3 ) + 2 ( 5 ) + 2

A = 9 + 10 + 2

A = 21 points

Hence , the equation is A = 21 points

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Answer:

[tex]3 \frac{3}{4} [/tex]

Answer:

3.75 or 15/4

Step-by-step explanation:

3⋅5 = 15

8 divided by 2 = 4

15/4

Answer:

$137.80

Step-by-step explanation:

We can solve for [tex]\frac{1}{3}[/tex] of Luis's money using this equation:

Subtracting that from the total cost:

275.59 is the leftover cost of the new gaming console that the siblings have to evenly split. To find out how much the sibling have to pay each, you can use this equation:

Therefore, to pay for the new gaming console, Benjamin and Audrey will need to each contribute $137.80 to evenly pay for the remaining cost.

The area of the composite figure is equal to 71.07 in² square yards.

The composite figure is made up of a trapezium and a quarter of a circle, so we shall calculate for the areas of the two figures and then add the result to get the total area of the composite figure as follows:

area of the trapezium = [(6 + 10)/2] yd × 8 yd

area of the trapezium = (16/2) yd × 8 yd

area of the trapezium = 8 yd × 8 yd

area of the trapezium = 64 yd²

area of circle = πr²

area of circle = 22/7 × 3 × 3

area of circle = 198/7

a quarter area of the circle = 198/7 ÷ 4

a quarter area of the circle = 7.07 square yard

total area of the composite figure = 64 yd² + 7.07 yd²

total area of the composite figure = 71.07 yd²

Therefore, the area of the composite figure is equal to 71.07 yd² square yard.

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You and three friends buy a pizza with 8 slices to share. Each friend gets 2 slices each because 1 divided by 1/4 is 25% and 25% of that pizza is 2 slices