Evaluate the piecewise defined function at the indicated values.
{x² + 4x if x <equal/greater to -1
f(x) = { x if - 1<x< equal/greater to 1
{-1 x > 1
f(-2)=
f(-3/2)=
f(-1) =
f(0) = 0
f(25) =​

Answer:

4π/7 radians is 102.86°

Step-by-step explanation:

changing radian to degrees: 1 radian → \(\frac{180}{\pi }\)

changing radians to degrees:

\(\dfrac{4\pi }{7} *\frac{180}{\pi }\)

\(\dfrac{4*180}{7}\)

\(\dboxed{102.86}\)

\(\\ \rm\longmapsto \dfrac{4\pi}{7}\times \dfrac{180)(\pi}\)

\(\\ \rm\longmapsto \dfrac{180(4)}{7}\)

\(\\ \rm\longmapsto 720/7\)

\(\\ \rm\longmapsto 102.8°\)

Given sin(x) = 0.5 and cos(x) = 0.866, we can use the sum identity for cosine to find cos(x+45). The sum identity for cosine states that cos(a + b) = cos(a)cos(b) - sin(a)sin(b).

Let's find cos(x + 45) using the given values of sin(x) and cos(x):

cos(x + 45) = cos(x)cos(45) - sin(x)sin(45)

We know that cos(45) = √2/2 and sin(45) = √2/2.

Substituting these values, we have:

cos(x + 45) = (0.866)(√2/2) - (0.5)(√2/2)

Simplifying further:

cos(x + 45) = 0.866√2/2 - 0.5√2/2

cos(x + 45) = (√2/2)(0.866 - 0.5)

cos(x + 45) = (√2/2)(0.366)

To calculate the final value, we simplify:

cos(x + 45) ≈ 0.256

Therefore, using the sum identity for cosine, the value of cos(x + 45) is approximately 0.256.

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Answer:

-8

Step-by-step explanation:

-2*(x+5)=6

Divide both sides by -2

x+5=-3

x=-3-5

x=-8

The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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Answer:

b

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The numerator for the given rational expression is 3 + 5k.

In the given rational expression, (3 + 5k) represents the numerator. The numerator is the part of the fraction that is located above the division line or the horizontal bar.

In this case, the expression 3 + 5k is the numerator because it is the sum of 3 and 5k. The term 3 is a constant, and 5k represents the product of 5 and k, which is a variable.

The numerator consists of the terms 3 and 5k, which are combined using addition (+). Therefore, the numerator can be written as 3 + 5k.

To clarify, the numerator is the value that contributes to the overall value of the fraction. In this case, it is the sum of 3 and 5k.

Hence, the correct answer for the numerator of the given rational expression (3 + 5k) / (74/k^2) is 3 + 5k.

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The next logical number in the sequence is 6, 14, 30, ....   is 62.

In the given sequence, each number is obtained by adding the next odd integer and doubling the result. Let's analyze the pattern step by step:

Starting with 2:

Add the next odd integer, which is 3: 2 + 3 = 5

Double the result: 5 * 2 = 10

Starting with 5:

Add the next odd integer, which is 5: 5 + 5 = 10

Double the result: 10 * 2 = 20

Starting with 10:

Add the next odd integer, which is 7: 10 + 7 = 17

Double the result: 17 * 2 = 34

Starting with 17:

Add the next odd integer, which is 9: 17 + 9 = 26

Double the result: 26 * 2 = 52

Starting with 26:

Add the next odd integer, which is 11: 26 + 11 = 37

Double the result: 37 * 2 = 74

Starting with 37:

Add the next odd integer, which is 13: 37 + 13 = 50

Double the result: 50 * 2 = 100

Starting with 50:

Add the next odd integer, which is 15: 50 + 15 = 65

Double the result: 65 * 2 = 130

Therefore, the next number in the sequence is 62.

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The set of numbers whose decimal representations are neither repeating nor terminating is known as the set of irrational numbers.

Irrational numbers are numbers that cannot be expressed as fractions and have non-repeating and non-terminating decimal representations. Examples of irrational numbers include √2, π (pi), and e (Euler's number). These numbers are infinite and non-repeating, meaning their decimal representation goes on forever without following a specific pattern. The proof that √2 is irrational was first demonstrated by the ancient Greeks, and the irrationality of π and e was proven much later in history. Irrational numbers play a significant role in mathematics and are essential for understanding concepts like limits, calculus, and geometry.

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What is the mathematical term for the set of numbers whose decimal representations are neither terminating (finite decimal) nor repeating (infinite periodic decimal)?

Answer:

21 to the tenth power or 21^10

Step-by-step explanation:

when multiplying exponents with the same base, you would add the exponents together

The expression represents the height of a tree that begins at 6.7 feet and increases by 2.6 feet per year will be h=6.7+2.7t.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given that, the expression that represents the height of a tree begins at 6.7 feet and increases by 2.6 feet per year.  

Expression is the combination of constants and variables with mathematical operators.

Suppose t represents the number of years and h represents the height of a tree,

The obtained expression for the given condition,

h=6.7+2.7t

Thus, the expression represents the height of a tree that begins at 6.7 feet and increases by 2.6 feet per year will be h=6.7+2.7t.

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The measure of angle b is 112° and the measure of angle c is 68°

From the question, we are to determine the measures of the missing angles

From the diagram,

b = 112° (Vertically opposite angles)

∴ b = 112°

Also,

112° + c = 180° (Sum of angles on a straight line)

c = 180°- 122°

∴ c = 68°

Hence, the measure of angle b is 112° and the measure of angle c is 68°

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Rounding to the nearest thousandth, the margin of error for this survey, expressed as a proportion, is approximately 0.020.

To calculate the margin of error for a survey, we can use the formula:

Margin of Error = Z × √((p × (1-p)) / n)

Where:

Z represents the z-score corresponding to the desired confidence level,

p represents the proportion of respondents who preferred candidate A,

n represents the sample size.

The sample size (n) is 1900, and the proportion of respondents who preferred candidate A is 1520/1900.

p = 1520/1900

≈ 0.8

We need to find the z-score corresponding to a 95% confidence level. For a 95% confidence level, the z-score is approximately 1.96.

Substituting the values into the formula:

Margin of Error = 1.96 × √((0.8 × (1-0.8)) / 1900)

Calculating the expression inside the square root:

(0.8 × (1-0.8)) ≈ 0.16

Margin of Error = 1.96 × √(0.16 / 1900)

Calculating the square root:

√(0.16 / 1900) ≈ 0.01016

Margin of Error = 1.96 × 0.01016

≈ 0.0199

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Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Answer:

15% increase

Step-by-step explanation:

Subtract 407100 minus 354000

Divide that amount by the absolute value of the starting value

Multiply by 100 to get a percent increase

The midpoints of the first and last parts are 4/5m units apart

The length of the line segment is given as

Length = m units

From the question, the number of partitions is given as

Partition = 5

So, the length of each partition is

Each partition = Length/Partition

This gives

Each partition = m/5

The midpoint of a partition is

Partition midpoint = m/5 x 1/2

Evaluate

Partition midpoint = m/10

The distance between the midpoints of the first and last segments is then calculated as

Distance = Length - 2 x Partition midpoint

So, we have

Distance = m - 2 x m/10

Evaluate

Distance = m - m/5

This gives

Distance = 4/5m

Hence, the distance is 4/5m units

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Answer:

It should be 16

Answer:

18.78

Step-by-step explanation:

\(a^{2} + b^{2} = c^{2} \\8^{2} + 17^2 = c^2\\64 + 289 = 353\\\sqrt{353} = 18.78\)

Height of the ladder is 13 m.

How to differentiate the function with two or more variables?

The partial derivatives of a function z=f(x,y) are dz/dx and dz/dy. These derivatives provide the instantaneous rates of change for each of the independent variables

Let us assume that the ground is horizontal and the ladder has a constant length.

Let, the heigth of the ladder on the wall = y

distance between the bottom of the wall and the bottom of the ladder = x

length of the ladder = h

As the ladder is sliding down the wall, so y is decreasing at the rate of 0.375 m/s

\(\frac{dy}{dt}\) = -0.375  m/s

The bottom of the ladder is sliding away from the wall, so x is increasing at the rate of  0.9  m/s when x = 5 m

\(\frac{dx}{dt}\) = 0.9 m/s when x = 5 m

By using pythagoras theorem,

\(x^{2} +y^{2} =h^{2}\)

On differentiating both sides,

\(2x\) \(\frac{dx}{dt}+2y\frac{dy}{dt} =0\)

2(5)(0.9) + 2y(-0.375) = 0

9 - 0.75y = 0

9 = 0.75y

y = 9/0.75 = 12

When x = 3 , we have y = 12

Also, \(x^{2} +y^{2} =h^{2}\)

\(5^{2}+12^{2} =h^{2}\)

25 + 144 = \(h^{2}\)

169 = \(h^{2}\)

\(13^{2}=h^{2}\)

h = 13

Therefore, height of the ladder is 13 m.

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Answer:

Step-by-step explanation:

4x2−y2−24x+4y+28=0⇒(4x2−24x)−(y2−4y)+28=0

The maximum possible face area of a parallelogram with a fixed positive perimeter P is 0.25 times the square of the perimeter.

Now, let's call the length of the parallelogram l and the height h.

The perimeter P is the sum of the lengths of all four sides, which are equal in a parallelogram. So we can write:

P = 2l + 2h

Simplifying this equation, we get:

l = (P - 2h) / 2

Now, let's look at the formula for the area of a parallelogram:

A = l * h

Substituting the value we found for l, we get:

A = [(P - 2h) / 2] h

Expanding and simplifying, we get:

A = 0.5 P h - h²

Now, to find the maximum possible area, we need to find the value of h that maximizes this equation.

We can do this by finding the derivative of A with respect to h and setting it to zero:

dA/dh = 0.5 × P - 2h = 0

Solving for h, we get:

h = 0.25P

Substituting this value back into the equation for A, we get:

A = 0.25 × P²

Therefore, the maximum possible face area of a parallelogram with a fixed positive perimeter P is 0.25 times the square of the perimeter.

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Answer:

The y-intercept is -6.

Step-by-step explanation:

Answer:

Assuming she has to do all of that before she leaves she needs to start at 4:40pm

Step-by-step explanation:

All of the things needed to do before she leaves equals 80 min and that is 1 hour and 20 min. Subtract that from 6:00pm and you get 4:40pm.

(Ps there is no number line)

There is only a 5% chance that the observed results occurred randomly, providing greater confidence in the validity of their findings.

Statistical significance is important because it allows psychologists to draw conclusions about the relationship between variables and make generalizations about a population based on the sample they studied.

In order to be 95% certain that psychologists' results didn't occur by chance, they need to achieve a statistical significance level of 0.05.

To be 95% certain that their results didn't occur by chance, psychologists need to achieve a statistical significance level of 0.05.

This means that there is only a 5% chance that the observed results occurred randomly, providing greater confidence in the validity of their findings.

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Answer:

Step-by-step explanation:

The following parts can be solved by the concept of Sets.

(a) KnF is definitely compact and closed.

(b) Fc U Kc is definitely closed, but not necessarily compact.

(c) K\F is definitely closed, but not necessarily compact.

(d) KnFc is definitely neither compact nor closed.

(a) KnF:

Since K is compact and F is closed, their intersection KnF is also closed, as the intersection of any finite number of closed sets is closed. Moreover, since K is compact, every open cover of K has a finite subcover, and thus, KnF is compact by the finite intersection property.

(b) Fc U Kc:

Fc is closed since the complement of a closed set is open, and Kc is closed since K is compact (and thus, closed) and the complement of a closed set is open. The union of two closed sets is also closed, so Fc U Kc is closed. However, Kc may not be compact, so Fc U Kc is not necessarily compact.

(c) K\F:

K\F is closed because it is the complement of the open set F. However, K\F may not be compact, as K itself may not be compact. For example, if K is the real line and F is the open interval (0,1), then K\F is not compact.

(d) KnFc:

KnFc is neither compact nor closed. To see that it is not compact, consider the sequence {x_n} in K given by x_n = (1 + 1/n, 0). This sequence converges to the point (1, 0), which is outside of K, but every term of the sequence is in K. Thus, K is not closed. On the other hand, since F is closed, Fc is open and contains K, so KnFc is not closed either.

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Answer:

Each friend is running a half mile.

They are running 1/2 mile.

The operations of addition, subtraction, multiplication, division, exponentiation, and modulus are carried out by the arithmetic operators.

They cover the study of numbers, including the order of operations, which are useful in algebra, data handling, and geometry, among other areas of mathematics.

Given Hotah and his 3 friends are each running 1/4 of a 2-mile relay race

total distance covered by them out of 2 miles is

2 x 1/4 = 1/2 miles

Therefore each person runs at 1/2 a mile.

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Answer:

The 12 ounce cup

Step-by-step explanation:

Just divide the cup size with its price and the lowest number is the best deal

Answer:

The equation x²+12x+43=0 is a quadratic equation that can be solved by factoring or using the quadratic formula.

Factoring the equation:

x²+12x+43=(x+7)(x+6)=0

x+7=0 or x+6=0

x=-7 and x=-6

Therefore, the solutions for the equation are x=-7 and x=-6.

Alternatively, you can use the quadratic formula:

x = (-b± √(b²-4ac))/2a

Where a=1, b=12, c=43

x = (-12± √(12²-4143))/2*1

x = (-12± √(144-172))/2

x = (-12± √(-28))/2

x = (-12± i*√28)/2

x = (-12+ i2√7)/2 or x = (-12- i2√7)/2

These solutions are complex numbers, x = (-6+2i√7) or x = (-6-2i√7)

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15