Find the trigonometric ratio using the diagram. Write the fraction in itssimplest form.

Find out the difference

so

(4.65-2.83)=$1.82

therefore

The sampling distribution can be approximated to follow the normal distribution if the sample size is large, and the values of 'np' and 'n(1-p)' are much greater than 10.

Consider option A,

Consider option B,

Consider option C,

Consider option D,

It is observed that only the values in option D, give that 'np' and 'n(1-p)' are greater than 10. Therefore, option D will be the correct choice.

Solution

We have the original function defined as:

And we want to obtain the new red line so then we need to check how many units down and right the function moves:

And we have 3 units to the right and 2 units down then the answer is:

Then the final answer is:

h(x) = -sqrt(x-3) -2

Given:

The cube root of D = 4

so, we can write the following expression:

cube both sides to find d

So,

So, the answer will be D = 64

Given:

The number of girls =10 and the total number of students =30.

The percentage of the total amount of girls is

Hence the percentage of the total amount of girls is 33.33 %.

Answer:

The total volume of fluid ounces of water she have is;

Explanation:

Given that she has 4 containers that are 2 1/2 quarts each

Recall that to convert quarts to ounce;

Also, she has 3 containers that are 4.25 cups each;

To convert cups to ounces;

So;

The total volume of fluid ounces of water she have is;

substituting the values;

Therefore, the total volume of fluid ounces of water she have is;

For the conditions stated, y=1500+2250t and y=1200+1200t, respectively, will be necessary equations because both Rachel and Jeffery are opening savings accounts. Rachel places $1,500 in a savings account that accrues annual compound interest of 1.5%. Jeffery places $1,200 in a savings account that accrues continuously compounded interest of 1% per year.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

according to given condition,

y=1500+1500*1.5t

y=1500+2250t

y=1200+1200*1t

y=1200+1200t

So the required equation will be y=1500+2250t and y=1200+1200t for the conditions given as Rachel and Jeffery are both opening savings accounts. Rachel deposits $1,500 in a savings account that earns 1.5% interest, compounded annually. Jeffery deposits $1,200 in a savings account that earns 1% interest per year, compounded continuously.

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AC = 2.332

AB = 5.517

Explanation:

Given:

BC = 5.

Angle B = 25 degree.

Angle C = 90 degree.

The objective is to find AC and AB.

By the trigonometric functions, Consider AB as hypotenuse, AC as opposite and BC as adjacent.

Then, the relationship between opposite (AC) and adjacent (BC) cnbe calculated by trigonometric ratio of tan theta.

Now, the length AB can be calculated by Pythagorean theorem,

Let's check the value using trigonometric ratios.

For the relationship of opposite and hypotenuse use sin theta.

Thus both the answers are matched.

Hence, the length of the side AC = 2.332 and the length of the side AB = 5.517.

Explanation

Step 1

Domain:The domain of a function is the complete set of possible values of the independent variable, by the graph is it a continuous line, so the domain is

Step 2

Range:The range is the set of all second elements of ordered pairs (y-coordinates), by the graph is it a continuous line, so the range is

Step 3

x-intercept

it is when y= 0 , by the graph :

Step 4

y-intercept

it is when x= 0 m by the graph:

Step 5

rate of change

Let

P1(-2,0) P2(0,4)

rate of change:2

Given two sides of a triangle, x, and z, such that

then the third side y must satisfy the following condition

x =13, and z = 17

Then, the third side y

lies in

17-13 < x < 17 +13

4 < x < 30

Hence the largest possible whole number of the third side is 29

Explanation

We are required to determine the coterminal, quadrant and reference angle of 707°.

This can be achieved as:

Therefore, the reference angle can be gotten as:

Hence, the reference angle is 13°.

The angle lies in the fourth quadrant.

The cotermi

If a figure has a vertex, (x, y) and it is rotated 180 degrees counterclockwise, the corresponding vertex of the new image would have a coordinate of (- x, - y)

Looking at the given figure, we would compare the corresponding coordinates of a given vertex. Looking at vertex A,

For the original figure, the coordinate is (1, 3)

For the ratated figure, the coordinate of A' is (- 1, - 3)

This corresponds to what was we stated earlier

Thus, it was rotated 180 degrees in the counterclockwise direction

From the image given, the dinning room table is a rectangle.

Given:

Length in inches = 90 inches

Width in inches = 45 inches

The scale of the length is 3 centimeters.

Now, let's find the scale of the table:

This means that 30 inches represents 1 centimeter.

Also, let's find the width in centimeters:

Thus, we have:

Length of scale drawing = 3 cm

Width of scale = 1.5 cm

To find the Area of the scale drawing, use the area of a rectangle:

A = Length x Width

Therefore, the length of the scale drwing is = 4.5 cm²

ANSWER:

We can choose one reference book or one instructional manual from the bookshelf in 48 different ways.

Given,

Number of novels = 5

Number of reference books = 4

Number of magazines = 3

Number of instruction manuals = 2

Total number of books = 5 + 4 + 3 + 2 = 14 books

We have to find the number of ways of choosing one reference book or one instructional manual.

Number of ways = 4! x 2!

Number of ways = 24 x 2

Number of ways = 48

That is,

We can choose one reference book or one instructional manual from the bookshelf in 48 different ways.

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We have to graph this piecewise function.

It will be two horizontal lines that change when x = -1: to the left it will be y = 5, as x ≤ 1, and to the right, it will be y = -3.

We can see it graphed as:

b) The range is the set of values that f(x) takes for the domain for which it is defined.

We can see that f(x) only takes two values: y = -3 and y = 5, so the set {-3,5} is the range of f(x).

Answer:

a) Graph

b) Range = {-3, 5}

As per given by the question,

There are given that a graph.

Now,

1. The given graph is cosine graph.

2. The aplitute of the given graph is,

From the graph, it is lie between -2 to 2.

So,

The amplitude of the given graph is 2.

Now,

3. The equation of the midline is,

Now,

4.The period of the fumction is,

Now,

The equation of the function.

First the general form of cosine graph function is,

Then,

Now,

Where, D is vertical shift.

Hence, the equation of the function is,

The completion of the statements about the number of students in Mr. Baker's class is as follows:

A prime number is a number divisible by itself and 1 only.

When a prime number is divided by another number except by itself and 1, there is always a remainder in the quotient.

Some examples of the prime numbers in Mr. Baker's class include 19, 23, 29, 31, or 37 students.

Thus, these numbers of students cannot be divided by another number without a remainder because they are prime numbers.

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1. The number of students in his class must be a --- number.

2. The quotient from the division of the students into equal-sized groups is .... because there must be a .....

ANSWER

EXPLANATION

The graphical solution to the given equation is obtained at the points where the two graphs of the two functions intersect each other on the coordinate plane.

To graph f(x), we simply draw a straight horizontal line at the point y = -5.

To graph g(x), we have to find coordinate points by substituting values of x into the function and obtaining values for g(x).

Let us find the value of g(x) when x = -3, -1, 1:

Now, we have three points to plot the graph with: (-3, -5), (-1, -9), (1, -5)

Let us now plot the graphs of the functions:

Therefore, the solutions to the equation f(x) = g(x) are:

Answer:

Solving the expression gives;

Explanation:

Given the expression;

Applying the rule of BODMAS or PEMDAS;

multiplication comes first;

Then we can do the addition;

Therefore, solving the expression gives;

The height of the mountain is 2936.39 feet.

Given,

In the question:

The angle of elevation to the top of the mountain is 25°.

To find the height of the mountain, we can draw triangles as in the image attached.

Now, According to the question:

Let's call the height of the mountain 'h', and the distance from the first point (25degrees) to the mountain 'x'.

Then, we can use the tangent relation of the angles:

tan(29) = h/x

tan(25) = h/(x+1000)

tan(25) is equal to 0.4663, and tan(29) is equal to 0.5543, so:

h/x = 0.5543 -> x = h/0.5543

using this value of x in the second equation:

h/(x+1000) = 0.6009

h/(h/0.5543 + 1000) = 0.4663

h = 0.4663 * (h/0.5543 + 1000)

h = 0.8412h + 466.3

0.1588h = 466.3

h = 466.3 / 0.1588 = 2936.39 feet

Hence, the height of the mountain is 2936.39 feet.

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Let the number be x.

Twice the number means 2 * x = 2x

Twice the number decreased by 6 means

2x - 6

Given that the result is 8, we have

2x - 6 = 8

First we will calculate the vertical asymptote, is when the denominator of the function given is equal to zero

then we will calculate the horizontal asymptote because the degree of the numerator and the denominator is equal we can calculate the horizontal asymptote with the next operation

a= the coefficient of the leading term of the numerator

b=the coefficient of the leading term of the denomintor

in our case

a=4

b=2

As we can see the graph that shown the asymptotes of the function is the graph in the option C.

We are asked to find the area of the given circle.

Recall that the area of a circle is given by

Where π is a constant and r is the radius of the circle.

From the figure, we see that the diameter is 22 km

Recall that the radius is half of the diameter.

So, the radius of the circle is

So, the area of the circle is

Therefore, the area of the circle is 380.1 square km (rounded to the nearest tenth)

The general rule of P(A or B) is given by the formula

To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:

As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:

As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4

Our final answer will be x = -4

b)

Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph

As we can see it touches the graphic at y = 2, hence, f(0) = 2

To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:

As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:

As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4

Our final answer will be x = -4

b)

Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph

As we can see it touches the graphic at y = 2, hence, f(0) = 2

She landed on the number 25 on the hundred chart.

What is an 100 chart?

It consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows.

We are given that she was on 57th number

Then she moved down 3 rows

Each row contains 10 elements Hence we subtract 30 for 3 rows

57-30=27

Then also she took 2 steps back

Hence we again subtract 2 from 27

We get 27-2=25

Hence she is at 25th number

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Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. To get the decimal of the form a.bcd, we will count the digits that are there after the decimal point; then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.

Given that Jason's Work:

0.105

Jason provided the work when asked to convert 0.105 to its simplest fraction form which could be;

0.105 = 105/1000

= 21/200

Hence, Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200

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The number of minutes when they would both paint the same strip of wood is 8 minutes.

The linear equation that represents the total strip of wood that is painted by Henry is: amount of strips already painted + (strips painted per minute x minute)

14 + (3½x m)

14 + 3½m

The linear equation that represents the total strip of wood that is painted by Sandy is: amount of strips already painted + (strips painted per minute x minute)

10 + (4 x m)

10 + 4m

When both people paint the same strip of wood, the two above equations would be equal.

10 + 4m  = 14 + 14 +3½m

4m - 3½m = 14 - 10

0.5m = 4

m = 4 / 0,5 = 8

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To find the solution we need to graph both lines on the plane. To do this we need to find two points for each line.

First we graph the line y=x+2. To find a point we give x a value, whichever value we like, and then find y.

Let x=0, then:

Then we have the point (0,2).

Let x=1, then:

Then we have the point (1,3).

Then we plot this points in the plane and join them with a line:

Now let's plot eh second line, y=3x-4.

Let x=0, then:

So we have the points (0,-4).

Let x=1, then:

so we have the point (1,-1).

Now we plot this points and join them with a line:

Once we have both lines graph in the plane the solution is the intersection of the lines. Looking at the graph we conclude that the solution of the system is x=3 and y=5.