What is the range of the function y = |x+2 | −2 if the domain is a x € R?

The probability of rolling a number greater than 4 on a number cube is 1/3 or 0.33.

A number cube is a cube-shaped object with six sides, numbered from 1 to 6. When rolling the number cube, there are six possible outcomes, each with an equal chance of occurring. Since we are interested in finding the probability of rolling a number greater than 4, we need to determine how many of the six possible outcomes meet this condition.

There are two possible outcomes that satisfy the condition: rolling a 5 or rolling a 6.

So, as there are two outcomes = 2/6

= 1/3

Therefore, the probability of rolling a number greater than 4 is 1/3.

This can also be simplified to 0.33 or 33.3% as a decimal or percentage, respectively.

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Answer:

180 sq. in.

Step-by-step explanation:

The formula for the volume of a circular cone is V = (πr^2h)/3

So, 900 = (15πr^2)/3

2700 = 15πr^2

180 = πr^2 = area of the circular base

Answer:

3x^2 + 6x

Step-by-step explanation:

Just distribute

3x(x + 2)

3x(x) = 3x^2

3x(2) = 6x

3x^2 + 6x

The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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The solution of the inverse Laplace transforms is mathematically given as

1)

Generally, the equation for the function is  mathematically given as

\($F_{1}(s)=\frac{6 s^{2}+8 s+3}{s\left(s^{2}+2 s+5\right)}$\)

By Applying the Partial fractions method

\(\frac{6 s^{2}+8 s+3}{s\left(s^{2}+2 s+5\right)}=\frac{A}{s}+\frac{B s+C}{s^{2}+2 s+5}\)

\($6 s^{2}+8 s+3=A\left(s^{2}+2 s+5\right)+(B s+C) s$\)

\(\begin{aligned}&3=5 A \\&A=\frac{3}{5}\end{aligned}\)

Considers s^2 coefficient

\(\begin{aligned}&6=A+B \\&B=6 \cdot A \\&B=\frac{27}{5}\end{aligned}\)

Consider s coeffici ent

\(\begin{aligned}&8=2 A+C \\&C=8-2 A \\&C=\frac{34}{5}\end{aligned}\)

Putting these values into the previous equation

\(&F_{1}(s)=\frac{3}{5 s}+\frac{27 s+34}{5\left(s^{2}+2 s+5\right)} \\\\&F_{1}(s)=\frac{3}{5 s}+\frac{27(s+1)}{5\left((s+1)^{2}+4\right)}+\frac{7 \times 2}{10\left((s+1)^{2}+4\right)}\)

By taking Inverse Laplace Transforms

\(f_{1}(t)=\frac{3}{5}+\frac{27}{5} e^{-t} \cos (2t) + \frac{7}{10}\\\\\)

\(f_{1}(t)=e^{-t}\sin (2 t)\)

For B

\($F_{2}(s)=\frac{s^{2}+5 s+6}{(s+4)(s+1)^{2}}$\)

By Applying Partial fractions method

\(\begin{aligned}&\frac{s^{2}+5 s+6}{(s+4)(s+1)^{2}}=\frac{A}{s+1}+\frac{B}{(s+1)^{2}}+\frac{C}{s+4} \\\\&s^{2}+5 s+6=A(s+1)(s+4)+B(s+4)+C(s+1)^{2}\end{aligned}\)

at s=-1

\(1-5+6=3 B \\\\B=\frac{2}{3}\)

at s=-4

\(&16-20+6=9 C \\\\&9 C=2 \\\\&C=\frac{2}{9}\)

at s^2 coefficient

1=A+C

A=1-C

A=7/9

inputting Variables into the Previous Equation

\(\begin{aligned}&F_{2}(s)=\frac{A}{s+1}+\frac{B}{(s+1)^{2}}+\frac{C}{s+4} \\&F_{2}(s)=\frac{7}{9(s+1)}+\frac{2}{3(s+1)^{2}}+\frac{2}{9(s+4)}\end{aligned}\)

By taking Inverse Laplace Transforms

\(f_{2}(t)=\frac{7}{9} e^{-t}+\frac{2}{3} e^{-t}+\frac{2}{9} e^{-4 t}\)

For C

\($F_{3}(s)=\frac{10}{(s+1)\left(s^{2}+4 s+8\right)}$\)

Using the strategy of Partial Fractions

\(\frac{10}{(s+1)\left(s^{2}+4 s+8\right)}=\frac{A}{s+1}+\frac{B s+C}{s^{2}+4 s+8}\)

\(10=A\left(s^{2}+4 s+8\right)+(B s+C)(s+1)\)

S=-1

10=(1-4+8) A

A=10/5

A=2

Consider constants

10=8 A+C

C=10-8 A

C=10-16

C=-6

Considers s^2 coefficient

0=A+B

B=-A

B=-2

inputting Variables into the Previous Equation

\(&F_{3}(s)=\frac{2}{s+1}+\frac{-2 s-6}{\left((s+2)^{2}+4\right)} \\\\&F_{3}(s)=\frac{2}{s+1}-\frac{2(s+2)}{\left((s+2)^{2}+4\right)}-\frac{2}{\left((s+2)^{2}+4\right)}\)

Inverse Laplace Transforms

\(f_{3}(t)=2 e^{-t}-2 e^{-2 t} \cos (2 t)-e^{-2 t} \sin (2 t)\)

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The reason for packaging wieners in groups of 8 would depend on the specific manufacturer and the market they are serving.

Consumer packaged goods (CPG) is defined as the items utilized day-to-day by average consumers that need routine substitute or replenishment.

Wieners might be packaged in groups of 8 for several reasons, including,

Convenience for the consumer: Packaging wieners in groups of 8 may make it easier for consumers to purchase the right amount for their needs, without having to buy a whole package or waste any leftovers.

Cost savings: Packaging wieners in larger quantities may help reduce the packaging and production costs, making it more cost-effective for the manufacturer.

Standardization: Packaging wieners in groups of 8 could be a standardization that has been established in the industry, making it easier for consumers to recognize the brand and compare it to other brands.

Portion control: Packaging wieners in groups of 8 may help people keep track of the number of wieners they have consumed, helping with portion control.

So, the reason for packaging wieners in groups of 8 would depend on the specific manufacturer and the market they are serving.

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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It is claimed that the sample of participants is generalizable since it reflects the characteristics of the population.

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According to Dr. Aguilera's findings, excessive levels of anxiety are associated with poor academic performance. Sleep duration, on the other hand, is unrelated to excellent or poor academic performance.

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Answer:48.125

Step-by-step explanation:

Step-by-step explanation:

i had made it in a pic see it

The distance between the bird and its prey is 19 feet. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry."

We are given that the angle on f depression between a bird and its prey is 70%.

This means that Theta = 70°

Also, the height of the bird from the ground is 18 feet.

Using trigonometry, we get

⇒sin theta = perpendicular side/hypotenuse

⇒sin 70 = 18/hypotenuse

⇒Hypotenuse = 18/sin 70

⇒Hypotenuse = 19.1 ≈ 19 feet

Hence, the distance between the bird and its prey is 19 feet.

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Answer:

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. polynomials with real coefficients are included in this since every real number is a complex number with its imaginary part equal to zero.

Can I please get brainliest?

Answer:

It is non-constant variable polynomial with in depth coefficients and an in depth root.

Step-by-step explanation:

Answer:

x = 5/2

Step-by-step explanation:

hope this helps!!!

Answer:

x = 5/2

Step-by-step explanation:

2x = 5

⇒ x = 5/2

Answer:

\(f(2x) = 8x^{2} +3\)

Step-by-step explanation:

f (x) = 2x²+3

f(2x) = \(2(2x)^{2}\) + 3

f(2x) = \(2(4x^{2} )\) + 3

f(2x) = \(8x^{2}\) + 3

Answer:

a = 12

Step-by-step explanation:

Part A:

a + a + a + a = 84

= a × 4 = 84

∴4a = 84 (Multiplication operation is applied here)

Part B:

4a = 84

a has to be isolated and made the subject of the formula:

\(4a = 84\)

\(a = \frac{84}{4}\)

∴ a = 12

Answer:

48

Step-by-step explanation:

72/6 =12

12(4)=48

The value of integer k is -5.

Polynomial equations formed with variables, exponents and coefficients .

Since the polynomial has three integer roots, we can express it as:

(x - r1)(x - r2)(x - r3) = 0

where r1, r2, and r3 are the three integer roots.

Expanding the left-hand side, we get:

x^3 - (r1 + r2 + r3)x^2 + (r1r2 + r1r3 + r2r3)x - r1r2r3 = 0

Comparing this with the given polynomial, we see that:

r1 + r2 + r3 = 1

r1r2 + r1r3 + r2r3 = k

r1r2r3 = 3

First we need to find the value of k. From the first equation, we see that one of the roots must be 1, since the sum of three integers that are not 1 cannot be 1. Without loss of generality, assume that r1 = 1. Then we have:

r2 + r3 = 0

r2r3 = 3

Since the roots are integers, the only possibility is r2 = -3 and r3 = 1.

Therefore, we have:

k = r1r2 + r1r3 + r2r3 = 1(-3) + 1(1) + (-3)(1) = -5

Therefore, the value of integer k is -5.

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The required value of te angle ∠3 = 100 degree.

A circle is a shape that is made up of all of the points in a plane that are at a certain distance from the center. Alternatively, it is the plane-moving curve traced by a point at a constant distance from a given point.

From the figure of the circle, we can identify that AD and CD are two diameter of the circle.

and ∠COA = ∠3 is inscribed angle made by up by 2 radian of the circle

So, arcCA = ∠3 = 100 degree

Thus, required value of te angle ∠3 = 100 degree.

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Answer:

-65

-61

20ab - 3bc - 3ac

Step-by-step explanation:

1.) Find the sum of 72−104+5and -32+ 4-10.

72 - 104 + 5 = - 27

- 32 + 4 - 10 = - 38

Sum of (-27 and - 38) = - 27 + (-38) = - 65

2.) What should be added to 32+32+3 to get 3+3

32 + 32 + 3 = 67

3 + 3 = 6

67 + x = 6

x = 6 - 67

x = - 61

3.) Subtract the sum of 12ab –10bc –18ac and 9ab +12bc + 14ac from the sum of ab + 2bc and 3bc –ac

(12ab –10bc –18ac) + (9ab +12bc + 14ac)

12ab + 9ab - 10bc + 12bc - 18ac + 14ac

= 21ab + 2bc - 4ac

(ab + 2bc) + (3bc - ac)

ab + 2bc + 3bc - ac

ab + 5bc - ac

(21ab + 2bc - 4ac) - (ab + 5bc - ac)

21ab + 2bc - 4ac - ab - 5bc + ac

21ab - ab + 2bc - 5bc - 4ac + ac

20ab - 3bc - 3ac

From the given graph, the numeric values of the expressions are given as follows:

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

On the graph of the function, the equivalent to this is that we have to find where the x-axis has the value, and find the value of y for which the function passes through the y-axis.

From the graph, when x = -1, f(x) passes the point at y = 12, hence f(-1) = 12.

For the second item, applying the same logic, we have that:

Hence:

f(1) - g(1) = 10 - 2 = 8.

For the third item, we have to look at the graph of g(x), and find the value of x when y = 4, hence g(x) = 4 when x = 2.

For the fourth item, the functions intersect at point (3,8), hence f(x) = g(x) when x = 3.

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The quadratic equation that has (3·x + β) ans (3·x + a) as the roots can be presented as follows;

9·x² - 7.5·x - 3 = 0

A quadratic equation is an equation that can be expressed in the form; y = a·x² + b·x + c, where, a ≠ 0, and a, b, and c are numbers.

The quadratic equation -2·x² - 5·x + 6 = 0, divided by a factor of -1 indicates that we get;

2·x² + 5·x - 6 = 0

The quadratic formula indicates that we get;

x = (-5 ± √(5² - 4 × 2 × (-6))/(2 × 2) = (-5 ± √(73))/4

Let a = (-5 + √(73))/4 and let β =  (-5 - √(73))/4)

(3·x + ((-5 + √(73))/4)) × (3·x + (-5 - √(73))/4) = 9·x² + 3·x·(-5 - √(73))/4) + 3·x·(-5 + √(73))/4) + ((-5 + √(73))/4)) × (-5 - √(73))/4)

9·x² + 3·x·(-5 - √(73))/4) + 3·x·(-5 + √(73))/4) + ((-5 + √(73))/4)) × (-5 - √(73))/4) = 9·x² - 15·x/2 - 3 = 0

Therefore, the equation that has (3·x + β) ans (3·x + a) as roots is the equation

9·x² - 15·x/2 - 3 = 9·x² - 7.5·x - 3 = 0

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The margin of error if we want a 90% confidence interval for the true population mean age is calculated to be 1.62 years, therefore option (a) is correct.

We can use the formula for the margin of error:

Margin of error = z × (σ / √(n))

where z is the z-score for the desired level of confidence, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the z-score is 1.645. Substituting the given values, we get:

Margin of error = 1.645 × (9.84 / √(100)) = 1.62

Therefore, the margin of error is 1.62 years, which is option (a).

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Answer:

The independent variable is the bill, and the dependent variable is the tip.

Step-by-step explanation:

The independent variable means it can stand alone on it's own.  The bill will always be $20 because that's how much the food costs.  The tip will be different depending on how much the bill is.

Answer:

since second company salary, $93,600, is more than first company yearly salary of $65000

Second company pays more

Step-by-step explanation:

To check what job pays more we have to compare yearly salary of both the company offer.

_________________________________________________

Yearly salary from one company = 65k = 65000

Weekly salary from another company = $1800

there are 52 weeks in a year

to get yearly salary , we need to multiply weekly salary with 52.

Yearly salary from another company = Weekly salary*no of wees in a year

Yearly salary from another company = 52*$1800 = $93,600

since second company salary, $93,600, is more than first company yearly salary of $65000

Second company pays more

Answer:

Step-by-step explanation:

y= 1x-1

Slope= 1

Y intercept= -1

Answer:

Step-by-step explanation:

Slope m = (5 - 1) / (6 - 2) = 1

y - 1 = 1(x - 2)

y = x - 1 Slope intercept form of linear equation

y-intercept is ( - 1)

x - y = 1 Standard form of linear equation

1 1/2 = 1 5/10

2/5 = 4/10

1 5/10 - 4/10 = 1 1/10

1 1/10 + 2 = 3 1/10

3 1/10 gallons of paint left

Answer: 31/10 gallons of paint.

Step-by-step explanation:

Find common denominators.

3/2 = 15/10

2/5 = 4/10

15/10 - 4/10 = 11/10

2 + 11/10 = 31/10