Simplify the trigonometric expression. cos(theta+pi/2)

The most appropriate choice for annular region will be given by

This graph represents an annular region shown in the figure

What is annular region?

Annular region represents the space between two concentric circles of different radii.

Equation of annular region centered at (0, 0) is

[tex]a^2 \leq x^2+y^2\leq b^2[/tex]

Here,

[tex]x^2 + y^2\geq 16\\x^2 + y^2 \geq 4^2\\[/tex]

It denotes the outside of a circle of radius 4 centered at (0, 0)

[tex]x^2 + y^2\leq 25\\x^2 + y^2 \leq 5^2\\[/tex]

It denotes the inside of a circle of radius 5 centered at (0, 0)

So the complete graph is being attached here.

This region is known as annular region

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Answer:

x=6

Step-by-step explanation:

3 (x+1) -22 +13=12

3x+3 -22+13=12

3x+3-9=12

3x-6= 12

3x= 12+6

3x= 18

x= 18/3

x= 6

There are 20 numbers to choose from. Thus, the total sample space is 20.

If you choose one number, the probability of choosing that number is:

Now, if after choosing one number in the first round, you proceed to choose another number in the second round.

The probability of choosing a number for this second round will be:

Note that you are allowed to repeat numbers, so therefore, this is a probability problem with replacement.

For the third round, you choose another number from 1 to 20. The probability is the same as the previous two:

The probability that a person guesses these 3 numbers is the same as the probability of actually choosing the numbers randomly.

Thus the final answer:

Therefore, the final answer is:

Answer:

f(7) = -5

Step-by-step explanation:

To find f(7), we would need to first find on the graph 7 on the x-axis.

We would next need to see where 7 on the x-axis meets with the graph. In this case, we would go down.

Now that we see where 7 on the x-axis meets with the graph, we would now look at the number on the y- axis that spot on the graph matches with.

In this case, we would go left from the graph all the way to the y-axis, where the correspo ding number would be -5.

Answer:

40%

Step-by-step explanation:

to change a fraction to a percentage multiply by 100% , that is

[tex]\frac{20}{50}[/tex] × 100% = 0.4 × 100% = 40%

Answer:

40%

Step-by-step explanation:

The grouping (a · c) method is another method for factoring trinomials of the form ax² + bx + c.

The process of factoring a trinomial using the grouping method is,

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f(n+1) is

Therefore, substitutig, we get, option c.

Answer:

Step-by-step explanation:

0.95x*0.9=0.855

350/0.855=409.35

x=409.35

Given:

(3,2)

Reflection on x axis: (3,-2)

Reflection on y-axis: (-3,2)

Reflection of y=x : (2,3)

Reflection on y=-x : (-2,-3)

Relation 1 and Relation 3 are functions while Relation 2 and Relation 4 are not functions.

Function is a relation which maps a set to another set with some criteria.

It includes a property that one element of the domain set should only be related to exactly one element in the range set. That is, same element from the domain cannot be related to different elements in the range. Also all elements in the domain should have images in the range also.

Now we will check all the relations given one-by-one.

In relation 1, the relations are:

Chair ---------> 0

Pencil --------> 0

Paper ---------> 4

Star ------------> 1

Here All the domain elements are mapped only once to one element from the range. So it is a function.

In relation 2, the relations are:

4 ----------------> 5

4 ----------------> 9

0 ----------------> -9

1 -----------------> 4

8 -----------------> -4

Here 4 is mapped to both 5 and 9. So it does not satisfy the definition of a function and hence is not an function.

In relation 3, the relations are:

z -----------------> c

k -----------------> a

a -----------------> k

c ------------------> c

Here also all elements in the domain are mapped only once to an element from the range. So it is a function.

In relation 4, the relations are:

-4 -----------------> m

-4 -----------------> d

-4 -----------------> c

9 -----------------> s

Here, -4 is mapped to m, d and s. So it cannot be a function as it has more than one images.

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ANSWER :

A. (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.

B. Domain : (-∞, ∞)

C. Range : (-16, ∞)

D. Degree : 4

E. f(x) = (x + 3)(x + 1)(x - 1)(x - 3)

EXPLANATION :

From the problem, we have a graph in the illustration.

A. Roots are the points in which the graph intersects the x-axis.

Multiplicity means how many times the graph intersects at the specific point.

Roots :

The graph intersects at (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.

B. Domain and Range.

Domain is the set of x-values in the graph.

Range is the set of y-values in the graph.

From the graph,

Domain :

x values are all real numbers. (-∞, ∞)

Range :

y values are from y = -16 to the positive infinity. That will be (-16, ∞)

C. Degree : 4

D. The equation of a function with a degree of 4 is given by :

where a = coefficient

b, c, d and e are the roots of the function.

Since we already solved for the roots, that will be :

b = -3, c = -1, d = 1 and e = 3

The equation will be :

Plug in the given point (0, 9) then solve for the value of "a"

The equation will be :

If we have a function [Equation] it would look something like this:

3x+y=4

In order to solve for both values and graph it [If that's what you are trying to do], you solve for y and then replace values [Of your own choosing, or they are given to be studyed] in x, after we replace the values in x, we are going to have the respective value of y.

From our previous example, it would be:

y = -3x+4

So, when we start replacing the values of X, we will get the respective values for Y, let's try doing it from -3 to 3.

x = -3 => y = -3(-3)+4 => y = 13

x = -2 => y = -3(-2)+4 => y = 10

x = -1 => y = -3(-1)+4 ) => y = 7

x = 0 => y = -3(0)+4 => y = 4

x = 1 => y = -3(1)+4 => y = 1

x = 2 => y = -3(2)+4 => y = -2

x = 2 => y = -3(3)+4 => y = -5

From this, we would end up with the following points:

(-3, 13)

(-2, 10)

(-1, 7)

(0, 4)

(1, 1)

(2,

The mathematical statement is as follows:

(a) B ⊄ A

(b) C ⊂ A

(c) B ⊄ C

(d) ∅ ⊂ B

(e) C ⊂ C

(f) C ⊂ B

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.

The way that sets are represented by a person is always the same: as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.

Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) and C = {2, 4}.

The mathematical statement is as follows:

(a) B ⊄ A

(b) C ⊂ A

(c) B ⊄ C

(d) ∅ ⊂ B

(e) C ⊂ C

(f) C ⊂ B

belongs to ⊂ sign is used if an element belongs to the given set and vice versa.

The complete question is:

Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the resulting statements true.

(a) B __ A

(b) C __ A

(c) B __ C

(d) ∅ __ B

(e) C __ C

(f) C __ B

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ANSWER :

The answer is A. 2π

EXPLANATION :

Period can be determine by getting the measurement of one complete cycle.

From the graph.

One complete cycle is the blue mark.

Therefore, the period is 2π

Answer:

√30/4

I Hope that This Helped!

Percent change of 88%

1) Consider 50 as equivalent to 100% as well as 94 to x.

50 ----------- 100%

94 ------------ x

2) Now we can set the ratios and cross multiply then:

So 94 corresponds to 188%. Then we can see that there was an increase. Since 94 >50.

But we need to subtract from 100% to find out the percent change from 50 to 94.

188%-100%= 88%

3) Hence, the answer is an increase of 88%

An observation is considered an outlier if it is below -16.75

An observation is considered an outlier if it is above 33.25

Extremely low or high values in a data set are considered outliers. Outliers are a product of statistical observational errors and variability. They frequently produce significant statistical issues, hence they are frequently left out of the study.

We must think about if it meets the following criteria in order to identify an outlier:

Q₁ - 1.5 (IQQ) ⇒ for lower value

Q₃ + 1.5 (IQR) ⇒ for higher value

Q₁ stands for the lower quantile, Q₃ for the higher quantile, and IQR for the inter-quantile range. Using the previous data,

Q₁ and Q₃ come from:

Q₁ = (0 + 4) / 2 = 4 / 2 = 2

Q₃ = (12 + 17) / 2 = 29 / 2 = 14.5

IQR = Q₃ - Q₁ = 14.5 - 2 = 12.5

(a)  An observation is considered an outlier if it is below:

Q₁ - 1.5 (IQR) = 2 - 1.5 (12.5) = 2 -  18.75 = -16.75

An outlier is a number that is less than -16.75

(b) An observation is considered an outlier if it is above:

Q₃ + 1.5 (IQR) = 14.5 + 1.5 (12.5) = 14.5 + 18.75 = 33.25

An outlier is a number that is greater than 33.25

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SOLUTION

Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.

The problem can be modeled using the figure below

Notice that the triangle formed is a right triangle:

Therefore using Pythagorean theorem it follows:

Solve for x

Therefore the other leg no miss

Answer:

Choice C
==> Bank A

Step-by-step explanation:

Principal P = $2000

Bank A calculation

Simple Interest at 5% for 4 years  = Prt = 2000 x 5/100 x 4 = $400

Bank B Calculation

At 4% interest compounded quarterly, the accrued value(Principal + Interest) is given by the formula:

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

where

P = principal

r = annual interest rate as percentage

n = number of compounding per year

t = number of years

We have r = 4/ 100 = 0.04

n = 4 since interest is computed quarterly or 4 times a year

t = 4 years

[tex]A = 2000 ( 1 + 0.04/4)^{(4) \cdot (4)}\\\\A = 2000 (1.01)^{16} = \$2,345.16\\\\\text{Interest } = 2345.16 - 2000 = $345.16[/tex]

Since interest earned at bank A (400) > interest earned at bank B(345.16), the answer would be C.   ==> Bank A

Answer:

(9 x 27) x 5

Step-by-step explanation:

First we have to figure out the powers. 3 To the power of 2 is 9 and 3 to the power of 3 is 27 so we first multiply that and later multiply 5

Answer:

1 ÷ [tex]\sqrt{n\\}[/tex] = x

Step-by-step explanation:

For the given, "the quotient of 1 and the square of a number", the expression is 1+√n

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, Mathematicians have the ability to multiply, divide, add, and subtract. A mathematical operator, a number or variable, and an expression make up an expression.

The phrase "The quotient of 1 and the square of an integer" is presented.

The dividend and the amount being divided by the divisor are, respectively, referred to as the dividend and the amount being divided by it. The quotient is created by dividing the result.

If n is the number the expression can be written as,

=1+√n

Thus, for the given expression the expression is 1+√n.

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Answer:

[tex]\textsf{Let $\boxed{x}=\boxed{\textsf{The total dollar amount of all phone sales}}$}\:.[/tex]

[tex]\textsf{Let $\boxed{y}=\boxed{\textsf{The total dollar amount of all computer sales}}$}\:.[/tex]

System of Equations

[tex]\boxed{x + y = 3600}[/tex]

[tex]\boxed{0.04x + 0.06y = 178}[/tex]

Step-by-step explanation:

Given information:

Define the variables:

Convert the percentages into decimal form:

[tex]\implies \sf 4\%=\dfrac{4}{100}=0.04[/tex]

[tex]\implies \sf 6\%=\dfrac{6}{100}=0.06[/tex]

Therefore, the system of equations that could be used to determine the dollar amount of phone sales and computer sales is:

[tex]\begin{cases}x + y = 3600\\0.04x + 0.06y = 178\end{cases}[/tex]

Solving the system of equations

Rewrite the first equation to isolate y:

[tex]\implies x=3600-y[/tex]

Substitute the expression for x into the second equation and solve for y:

[tex]\implies 0.04(3600-y)+0.06y=178[/tex]

[tex]\implies 144-0.04y+0.06y=178[/tex]

[tex]\implies 144+0.02y=178[/tex]

[tex]\implies 0.02y=34[/tex]

[tex]\implies y=1700[/tex]

Therefore, Cameron made $1,700 of computer sales.

Substitute the found value of y into the first equation and solve for x:

[tex]\implies x+1700=3600[/tex]

[tex]\implies x=1900[/tex]

Therefore, Cameron made $1,900 of phone sales.

The sum of angles of a triangle is equal to 180 degree.

Determine the value of x, by using angle sum for the triangle.

The value of x is 24

The crate's density in pounds per cubic foot = 137.28 lb/ft³

Density is defined as the quantity that shows the relationship between the mass and volume of an object which is measured in kilograms per cubic meter or in pounds per cubic foot.

The density of the given crate of medicine = 2,200 kg / m³

To convert to pounds per cubic foot;

1 kg/m³ = 0.0624 lb/ft³

2,200 kg/m³ = X

Make X the subject of formula;

X = 2,200 × 0.0624/1

X = 137.28 lb/ft³

Therefore, when converter to pounds per cubic foot the density of the crate of the medicine= 137.28 lb/ft³.

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The value of x for the given similar triangle will be 5 units.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.

From the similarity concept, the value of x will be calculated as:-

( 10 / x ) =  ( 6 / 3 )

10 = 2x

x = 10 / 2

x = 5

Therefore, the value of x for the given similar triangle will be 5 units.

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We have two functions for the sales of popcorn:

being B(w) the number of buttered popcorn sold over "w" weeks and C(w) the number of caramel popcorn sold over "w" weeks.

We now have to calculate how much more he would have made after 12 weeks in sales of buttered popcorn than the sales of caramel popcorn.

We can calculate this as the difference of sales of buttered popcorn and the sales of caramel popcorn for w = 12.

Each sale will be the product of the cost per unit (in this case, is $11 for both types) and the number of units sold (B(w) or C(w), depending on the ytpe of popcorn).

Then, we can calculate the difference in sales as:

Answer: he would have made $374 more in sales from buttered popcorn than from caramel popcorn.

Step-by-step explanation:

:)))))))))))))))))))))

Since a right triangle is formed, the radius of the cross-section is the missing side of the triangle.

Apply the Pythagorean theorem:

C^2 = a^2 + b^2

Where:

c = hypotenuse = 5

a & b = the other 2 legs of the triangle = 4 and x

Replacing:

5^2 = 4^2 + x^2

solve for x ( radius of the cross-section)

25 = 16 + x^2

25-16 = x^2

9 = x^2

√9 = x

x = 3 cm