Find the value(s) of k that makes the given function continuous. f(x) 5 -3x – 2 if x

The height of the rainwater on the roof is

H = V/A = 1539.8/5000 = 0.308 m

Step 1: Calculate the radius of the cylindrical tank by dividing its diameter by two.

Diameter = 14 m

Radius = 14/2 = 7 m

Step 2: Calculate the volume of the cylindrical tank by using the formula V = [tex]\pi[/tex][tex]r^2[/tex]h.

V = [tex]\pi[/tex] * [tex]7^2[/tex] * 10 = 1539.8 m^3

volume of the cylindrical tank is 1539.8 m^3

Step 3: Calculate the area of the roof by using the given value.

A = 5000 [tex]m^2[/tex]

Area of the roof  5000 [tex]m^2[/tex]

Step 4: Calculate the height of the rainwater on the roof by dividing the volume of the tank by the area of the roof.

H = V/A = 1539.8/5000 = 0.308 m

The height of the rainwater on the roof is 0.308 m

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The Answer is 2.557 when 17.9 is divided by 7

Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

Let X be a random variable representing the minimum value among 20 fair six-sided dice rolls. We are interested in finding P(X = 1).

The event {X = 1} occurs if and only if all 20 dice rolls result in a 1. The probability of a single dice rolling a 1 is 1/6, and the rolls are independent, so the probability of all 20 dice rolling a 1 is (1/6)^20. Hence,

P(X = 1) = (1/6)^20 = 1.275 * 10^-9.

Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.

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Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

Let X be a random variable representing the minimum value among 20 fair six-sided dice rolls. We are interested in finding P(X = 1).

The event {X = 1} occurs if and only if all 20 dice rolls result in a 1. The probability of a single dice rolling a 1 is 1/6, and the rolls are independent, so the probability of all 20 dice rolling a 1 is (1/6)^20. Hence,

P(X = 1) = (1/6)^20 = 1.275 * 10^-9.

Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.

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No, it does not follow that y is an interval or a ray in x. A convex subset of an ordered set is a set that contains all the points between any two points in the set.

This means that a convex subset of an ordered set could be a collection of points, it could be an interval, or it could be a ray. A proper subset of an ordered set is any subset except the entire set, so a proper subset of an ordered set could be any of these possibilities.

Therefore, while a proper subset of an ordered set that is convex in that set must be a collection of points, an interval, or a ray, it does not necessarily have to be one of those three options.

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Answer:

the cubic centimeters has the same value of millimeters so you just need to multiply by one

basically copy the same number

The volume of a cubic centimeter is equal to one milliliter (mL). Because of this, mL is preferable to centimeter cube.

Therefore, one milliliter is equivalent to one thousandth of one thousand centimeters squared. This means that one milliliter is equal to one cubic centimeter. One centimeter in length and height defines a cubic centimeter. The volume of a cubic centimeter is equal to one milliliter (mL). Because of this, mL is preferable to centimeter cube.

A milliliter and a cubic centimeter have identical volumes. One liter contains one thousand cubic centimeters. The metric units of volume are cubic centimeters (cm³) and liters (L). The U-100 indicates that one milliliter has 100 units. 0.3 milliliters of U-100 insulin equals 30 units.

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For, the function f(x) = 4x² - 40x + 97, a) f(4) = 1 b) f(-2) = 193 c) f(a) = 4a² - 40a + 97 d) For f(x) = 2 , x = 4, 6.  

Given a function f(x) = 4x² - 40x + 97

To evaluate the value of a function f(x) at a point x = a, we replace x with a in the expression for f(x) and simplify.

a) f(4) = 4(4)² - 40(4) + 97

     = 1

b) f(-2) =  4(-2)² - 40(-2) + 97

       = 193

c) f(a) = 4a² - 40a + 97

d) f(x) = 1

    4x² - 40x + 97 = 1

    4x² - 40x + 96 = 0

       x² - 10x + 24 = 0

 x² - 6x - 4x + 24 = 0

  x(x - 6) - 4(x - 6) = 0

         (x - 4)(x - 6) = 0

                          x = 4, 6

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For an nth root, there are n solutions of the equation z^n = ω.

To find these solutions, we use the polar form of z = r * e^(iθ). Substituting into the equation, we get:

r^n * e^(iθn) = s * e^iφ

Comparing the magnitude of both sides, we have:

r^n = s

Comparing the phase of both sides, we have:

nθ = φ + 2πk (where k is an integer)

So, we can set:

r = s^(1/n)

θ = (φ + 2πk) / n

Therefore, the n solutions are:

z = s^(1/n) * e^(i(φ + 2πk) / n)

for k = 0, 1, 2, ..., n-1.

--The question is not readable, answering to the question below--

"With ω = se^iφ, where s ≥ 0 and φ ∈ r , solve the equation z^n = ω in C where n is a natural number. How many solutions are there?"

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1. f(-1) = 9

2. the domain of the function f(x) = (x+3)/(x-1) is: x ∈ R {1} or x ∈ R {- 1}

3. y = 3x + 2

4. y = 2/3x + 1

The formula for a straight line, written as y = mx + b, where m denotes the line's slope and b its y-intercept. When the slope of the line being studied is known, and the provided point is also the y-intercept, the slope-intercept formula, y = mx + b, is utilized (0, b). b  stands in for the y value of the y-intercept point in the formula.

1.

Given f(x) = 4x² - 3x + 2

f(-1) = 4(-1)² - 3(-1) + 2

f(-1) = 4 + 3 + 2

f(-1) = 9

2.

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

x - 1 ≠ 0

x ≠ 1

therefore, x ∈ R {1} or x ∈ R {- 1}

3.

Two points (1, 1) and (2, 4)

(x₁, y₁) = (1,1)

(x₂, y₂) = (2, 4)

Two points form an equation:

y - y₁ = {(y₂ - y₁) / (x₂ - x₁)} (x - x₁)

y - 1 = {(4 - 1) / (2 - 1)} (x - 1)

3x - y = 2

x/ (2/3) + y / (-2) = 1

intercept form: x/a + y/b = 1

y = 3x + 2

this is slope intercept form.

4.

given slope (m) = 2/3

y - intercept (c) = 1

y = mx + c

y = 2/3x + 1

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The histogram doesn't support Alfonso's claim and the correct option is 5: No, the distribution is skewed to the left with a mean age greater than 36.

What is a histogram?

A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. A series of rectangles with bases equal to the distances between class boundaries and areas proportional to frequencies in the associated classes make up the area diagram.

Consider the given histogram at the photo below. It is an left-skew histogram, since it has a long tail to the left side.

We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.

For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.

1. midpoint = 32, probability= 0.03

2. midpoint = 33, probability = 0.04

3. midpoint = 34, probability = 0.05

4. midpoint = 35, probability = 0.1

5. midpoint = 36, probability =0.11

6. midpoint = 37, probability = 0.13

7. midpoint = 38, probability = 0.2

8. midpoint = 39, probability = 0.09

So, it is obtained that -

μ = 0.03 · 32 + 0.04 · 33 + 0.05 · 34 + 0.10 · 35 + 0.11 · 36 + 0.13 · 37 + 0.25 · 38 + 0.20 · 39 + 0.09 · 40

μ = 37.15

Therefore, this histogram is left-skewed with mean greater than 36.

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The length of BD is approximately 8.62 cm and the length of CD is approximately 4.30 cm.

AB = 10 cm and BC = 18 cm and angle ADB = 56 degrees.

A: Length of BD:

Using the law of sines, BD can be calculated as:

BD = 10 * sin(56) = 8.62 cm (approx)

B: Length of CD:

Using the Pythagorean theorem, AD can be calculated as:

AD = sqrt(BD^2 + AB^2 - 2 * BD * AB * cos(56)) = 12.92 cm (approx)

And then, CD can be calculated as:

CD = AD - BD = 12.92 cm - 8.62 cm = 4.30 cm (approx)

So, the length of BD is approximately 8.62 cm and the length of CD is approximately 4.30 cm.

"

Complete question

ABCD is a trapezium AD and BC are parallel

where AB = 10cm and BC = 18cm and angle ADB = 56degree

Find

A: work out the length of BD

B:  work out the length of CD

"

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The equation that justifies why[tex]27^{(1/3)}[/tex] is equivalent to the cube root of 27 is:[tex]27^{(1/3)} = (27^{1)^{(1/3)}} = 27^{(1/3)}[/tex]

The cube root symbol is represented by the number "3". In the square root case, only the root symbol—also known as a radical—was employed. Therefore, the cube root of different numbers can be symbolically represented as follows: 5 divided by its cube = 3. 11 has a cube root of 311 and so on.

The cube root of three is the same as the number 1.442224957031. The cube root of three has the radical representations 33 and 31/3. " denotes the square root.

The cube root formula aids in computing the cube root of any given number that is represented by the symbol in radical form. It can be determined by first determining the number's prime factorization and then using the cube root formula. Assume that x is any number such that it equals y, y, and y.

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Answer:

C is the answer

Step-by-step explanation:

The measure of the angle at the library is 90 degrees.

Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.

In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:

180 degrees / 2 = 90 degrees

So, the measure of the angle at the library is 90 degrees.

An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.

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The measure of the angle at the library is 90 degrees.

Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.

In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:

180 degrees / 2 = 90 degrees

So, the measure of the angle at the library is 90 degrees.

An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.

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The original length of the string is 6/10 m or 0.6 m

Now the string is divided into three parts:

So, the total length of string = 1/10 + 2/10 + 3/10 = 6/10 m = 0.6 m

Let the original length of string be=x

Length cut by Meera=x/10

Length cut by Lilian=2x/10

Length of remaining string=3/10

According to the question:-

Original length of string=Length cut by Meera +Length cut by Lilian+ Remaining part of string

=>x=x/10+2x/10+3/10

=>x=3x+3/10

=>10x=3x+3

=>10x-3x=3

=>7x=3

=>x=3/7m

Ans. Hence, original length of string is 3/7m

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The actual time it took Tory to travel 30 km is 0 hours.

As per the data given in the question,

Speed of the boat of both the person Tory and Emillio are same.

Let's call the time it took Tory to travel 30 km as "t" (in hours).

Emilio travelled for t + 3 hours, and during that time, he covered a total distance of 100 km.

So, we can write the equation:

30 + (t + 3) * 30 = 100

Solving for t:

30 + 30t + 90 = 100

30t = -60

t = -2

Since time cannot be negative, the actual time it took Tory to travel 30 km is 0 hours.

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(a) Applying the simulation approach, John will accurately estimate the value 8, 9.6% of the time.

(b) John will underestimate the value 8, 28.1% of the time.

(c) John will overestimate the value 8, 62.3% of the time.

(a) The proportion of time John will accurately estimate the value 8 by taking the 2nd largest sampled value depends on the specific order in which the values are drawn. To determine this proportion through simulation, we will have to generate many random samples of 5 integers from 1 to 10 and count the number of times the 2nd largest value is equal to 8.

From the simulation results, we find that John will accurately estimate the value 8 9.6% of the time.

(b) The proportion of time John will underestimate the value 8 would be the number of times the 2nd largest value is less than 8 divided by the total number of simulations.

From the simulation results, we find that John will underestimate the value 8 28.1% of the time.

(c) The proportion of time John will overestimate the value 8 would be the number of times the 2nd largest value is greater than 8 divided by the total number of simulations.

From the simulation results, we find that John will overestimate the value 8 62.3% of the time.

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The length of segment GF in the triangle is 8 inches

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

The triangle

On the triangle, we have the following ratio

3 : 6 = 4 : GF

So, we have

GF = 6/3 * 4

Evaluate

GF = 8 inches

Hence, the length is 8 inches

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The probability of selecting a chocolate chip cookie from the batch is unlikely.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies.

If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.

Then the probability of selecting a chocolate chip cookie from the batch is unlikely.

Unlikely means there's a small chance that an event will happen.

Hence, the probability of selecting a chocolate chip cookie from the batch is unlikely.

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The value of segment RN is:

Rn = 1.8

Now, According to the question:

An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that make it unique and help us differentiate it from the other quadrilaterals.

The figure shows:

MQ is parallel to NP

MN ≅ QP

So MNPQ is an isosceles trapezoid. That means that the two diagonals, MP and QN, are congruent and therefore are equal in length;

MP = QN

By the Segment Addition Postulate, QN = QR + RN and QR = 4.1:

MP = QN

5.9 = 4.1 + RN

RN = 5.9 - 4.1

RN = 1.8

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The given question is incomplete, complete question is:

Quadrilateral MNPQ is shown.

If MP = 5.9, what is RN? Round your answer to the nearest tenth.

[tex]\huge\begin{array}{ccc}f(-3)=-33\to\boxed{A.}\end{array}[/tex]

We have the function:

[tex]f(x)=2x-3x^2[/tex]

We need

[tex]f(-3)=?[/tex]

Substitute [tex]x=-3[/tex] to [tex]f(x)[/tex]:

[tex]f(-3)=2\cdot(-3)-3\cdot(-3)^2=-6-3\cdot9=-6-27=-33\to\boxed{A.}[/tex]

Answer:

The equation 81a^2 + 5b^2 cannot be factored further as a polynomial expression because it is in the standard form of a sum of squares, and the coefficients are not perfect squares. Factoring a sum of squares means writing it as the product of two binomials, each of which is the square root of one of the terms. Since 81 and 5 are not perfect squares, the equation 81a^2 + 5b^2 cannot be written as the product of two binomials.

The equation  [tex]81a^2 + 5b^2[/tex]  cannot be written as the product of two binomials.

An equation is defined as an expression that shows the relationship between two or more numbers and variables.

Given equation as  [tex]81a^2 + 5b^2[/tex]  

Since we know that Factoring a sum of squares means writing it as the product of two binomials, each of that is the square root of one of the terms.

Hence, 81 and 5 are not perfect squares.

The given equation [tex]81a^2 + 5b^2[/tex] cannot be factored further as a polynomial expression because it is in the standard form of a sum of squares, and the coefficients are not perfect squares.

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Answer: She can buy 2 sweatshirts and 3 T-Shirts or 1 sweatshirt and 4 T-Shirts

Step-by-step explanation:

Marcus's father would require 189 if he wanted to completely redo the tent's cover, including the bottom.

He needs 55 to completely cover the tent's one rectangular side with the rip. 55

Marcus's father would require 189 if he wanted to completely redo the tent's cover, including the bottom.

3 rectangular sides = 165

2 triangular sides = 24

165 + 24 = 189

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The pressure gradient is a function of the pressure itself, the local acceleration due to gravity, and the density of the fluid.

The sum-of-forces equation is 0=∑ify,i=pa−(p dp)a−ρagdy. Rearranging the equation to isolate dp yields the following expression:

dp = (pa - ρagdy) / p

Differentiating both sides with respect to y yields the differential equation for pressure:

dp/dy = (a(pa - ρagdy) - (dp)(pa)) / p

This equation can be further simplified using the product rule to yield:

dp/dy = pa2/p2 - ρag/p.

This differential equation shows that the pressure gradient is a function of the pressure itself, the local acceleration due to gravity, and the density of the fluid.

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Los números racionales son números que se pueden expresar en la forma a/b donde a y b son números enteros y b ≠ 0.

Los números racionales también se conocen como números fraccionarios. En los números racionales de la forma a/b, el número a representa el cuantificador y b es el denominador del número racional.

Qué pasa si el valor de b = 0?

Si un número fraccionario o racional tiene un denominador de 0, como 1/0; 2/0; 10/0; y otros, entonces el número fraccionario o racional no está definido.

Los números racionales también se pueden reclasificar en números enteros, números enteros, números naturales y otros grupos de números que forman parte de los números racionales.

Algunos ejemplos de números racionales como 1/2, 2/3, 5/7, 12/7 y otros.

En los números racionales también hay varias operaciones simples como la suma, la resta, la multiplicación, la división y otras operaciones numéricas.

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Step-by-step explanation:

Expanding and simplifying 2(x + 7) + 3(x + 1):

2(x + 7) = 2x + 14

3(x + 1) = 3x + 3

Adding the two expressions:

2x + 14 + 3x + 3 = 5x + 17

So 2(x + 7) + 3(x + 1) = 5x + 17.

[tex] \sf2(x + 7) + 3(x + 1) \\ \sf2x + 14 + 3x + 3 \\ \sf5x + 17[/tex]

The average rate of change and the instantaneous rate of change are same for ƒ(x) = 2x + 5. The solution has been obtained by using the concept of rate of change.

What is rate of change?

The pace at which one quantity changes in relation to another is described by the rate of change function. Simply expressed, the amount of change in one item is divided by the same amount of change in another to determine the rate of change. The relationship between how one quantity changes in relation to a change in another quantity is provided by the rate of change formula.

The average rate of change is:

[tex]r_{avg} =\frac{f(b)-f(a)}{b-a}[/tex], on interval [a,b]

Here, we are given  ƒ(x) = 2x + 5

So,

[tex]r_{avg} =\frac{(2b+5)-(2a+5)}{b-a}[/tex]

[tex]r_{avg} =\frac{2b-2a}{b-a}[/tex]

[tex]r_{avg} =2[/tex]

The slope of f assessed at a single point, such as f′(c), where c is a predetermined point, is the definition of the instantaneous rate of change.

So, for ƒ(x) = 2x + 5,

f′(c) = 2

Therefore, instantaneous rate of change is 2.

Hence, the average rate of change and the instantaneous rate of change are same for ƒ(x) = 2x + 5.

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20 feet per minute is equal to 400 yards/hour

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

For 1 minute 20 feet

For 60 minutes , 60*20=1200 feet

1 hour = 60 minutes

Thus, we have 1200 feet per hour

3 feet = 1 yard

So, 1200 feet = 1200/3 yrads = 400 yards

Thus, 20 feet per minute is equal to 400 yards/hour

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