Determine the exact value of (sin 45 °) (cos 45 ) + (sin 30°) (sin 60°)
(Don't leave radicals in the denominator)

338 students went on the field trip.

Given:

Four-ninth of the total participants rode a large bus, and the rest rode a smaller bus.

156 people rode the larger bus.

Let x be the total participants.

4/9 x = 156

multiply by 9 on both sides

4*9/9 x = 156*9

4x = 156*9

4x = 1404

divide by 4 on both sides

4x/4 = 1404/4

x = 1404/4

x = 351.

number of students = total participants - adult chaperones.

= 351 -13

= 338 students

Therefore 338 students went on the field trip.

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Answer: Inequality form: x is less then or equal to 6 or xis greater then or equal to 8

Interval Notation: (-infinity,6] u [8,infinity)

Answer:

x ≤ 6 ∨ x ≥ 8

Step-by-step explanation:

x-7 ≥ 0

when

x≥7

if x≥7

x-7≥ 1

x ≥ 7 + 1

x ≥ 8

if x < 7

-x + 7 ≥ 1

-x ≥ -7 + 1

-x ≥ -6

x ≤ 6

Final solution

x≤ 6 ∨ x ≥ 8

Solution:

As you can see in the diagram, there are two triangles. We will separate the two triangles into the smaller and the bigger one.

For the smaller triangle:

Now we will use the Pythagorean Theorem. The theorem states that the square of the longest side is equal to the sum of the squares of the two other sides.

To solve for the value of b, we will have:

For the bigger triangle:

We will also use the pythagorean theorem to find the value of c and by using the value of b we got from the smaller triangle.

ANSWER:

b = 4 cm

c = 7.2 cm

The difference between the two investments after 35yrs is $4700 and  Bank of America is offering higher interest than 5/3rd banks.

Most interest is compounded semiannually, quarterly, or monthly. Continuous compounding assumes that interest is compounded indefinitely and reentered on the balance sheet. The continuous compounding formula takes into account four variables.

For the given question,

5/3rd bank offers continuous interest:

For continuous interest, A = P[tex]e^{rt}[/tex]

where,

P = the initial amount

A = the final amount

r = the rate of interest

t = time

e is a mathematical constant where e ≈ 2.7183.

A = 10000 × [tex]2.71^{0.042*35}[/tex]

A =  10000 × 4.04

A = $40400 approximately

Interest = Amount - Principle

Interest = 40400 - 10,000

Interest = $30400

Bank of America offers compound interest:

For compound interest:

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

A = 10000 × 4.51

A = $45100

Interest = Amount - Principle

Interest = 45100 - 10,000

Interest = $35100

The above calculation explains Bank of America is offering higher interest than 5/3rd bank by $35100 - $30400 = $4700

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The slope-intercept form of the equation of a straight line is given to be:

where m is the slope and b is the intercept on the y-axis.

The slope is calculated using two points on the line by the formula:

Therefore, for this line, the slope will be:

Therefore, this value for the slope is substituted back into the equation for the line:

At the point (6, 0), we can calculate the value of b to be:

Therefore, the equation is:

The length of each piece of wire is 2.5 inches.

Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.

Let the number of pieces = x

The length of the wire = 5/8 inches

The length of one piece of wire = 1/4 inch

According to the question,

1/4 x = 5/8

So, x = 5/8 × 4

x = 20/ 8

x = 5/2

x = 2.5 inch

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the initial expression is:

so to rest them we want to have the same radical so we can rewrite the root of 20 so:

A line in slope-intercept form is represented by the following equation:

Parallel lines have the same slope, then if the line is parallel to the line y=-2x+5, the slope of the parallel line would be -2 too.

Now, by the given point (2,1) and knowing the slope of the line, we can use the slope-point form of the line equation to get the slope-intercept form:

Substituting:

Notice that the parallel line would be the same original line, y=-2x+5.

Given:

Surveyed Sample = 500 students

Number of students who listen to music = 300

The probability of students that listens to music is given by the formula:

In a sample of 1500 students, to find the probable number of students that will listen to music

we will multiply the probability we obtained initially by the sample space

=>

It is likely that 900 students will listen to music while studying

5 + 3 = 8

3 + 5 = 8

The represent the same expression

The formula for calculating the amount of money after compounding for a period of time is expressed as;

A = P(1+r/n)^nt

P is the principal (amount deposited)

r is the rate

t is the time

n is the time of compounding

Given

P = 200.00

r = 9% = 0.09

t = 2 years

n = 1 year

Substitute the given parameters into the formula

A = 200(1+0.09/1)^1(2)

A = 200(1.09)^2

A = 200(1.1881)

A = 237.62

Hence he will be able to spend 237.62 on the bike

To find the new coordinates, we just have to use the given rule

Let's apply it to each vertex

Remember that

The data set is a function if every element of the domain corresponds to exactly one element of the range

so

Verify each option

I ------> is a function (every element of the domain corresponds to exactly one element of the range)

II -----> is not a function (every element of the domain does not correspond to exactly one element of the range)

III ---> is a function (every element of the domain corresponds to exactly one element of the range)

IV ----> is not a function (every element of the domain does not correspond to exactly one element of the range)

therefore

The answer is

A Point-Slope equation of a straight line models this scenario: y -50,000 = -3,000(x -10).

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

We can recognize any points of the graph.

(0,80000) ; (10,50000)

Given that;

y -50,000 =______(x -10)

We need to find the slope.

Slope = Change in y / Change in x

Slope = 80,000 - 50,000 / 0 - 10 = 30,000 / -10

= -3,000

The slope is equal to -3000 that is Choice A; y -50,000 = -3,000(x -10)

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The complete question is;

The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x = 0 representing the year 2000, the graph below models this scenario.

The linear equations of the graph are y = 2/3x + 1. Option D.

Solution:

Let's find the slope of the graph using the coordinates (0, 1) (-3, -1)

m = y₂ - y₁ / x₂ - x₁

m = -1 - 1  / -3 - 0

m = -2/-3

m = 2/3

Using the slope-intercept form,

y = MX + c

where

m =  slope

c = y-intercept(This is when x = 0)

Therefore,

c = 1

Finally, the equation will be y = 2/3 x + 1.

An equation is a mathematical statement consisting of two expressions joined by an equal sign. The ID applies to all values ​​of the variable. Constraint expressions apply only to specific values ​​of variables. A mathematical expression that expresses the relationship between two terms on either side of a letter.

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When we reflect a point over y = x, the x and y coordinates become swapped and switch places, that is why (x,y) results to (y,x).

Therefore, the answer is true.

The equation is given as

The value of x is 3/16.

The slope of the given line is [tex]-\frac{3}{5}[/tex]

What is slope of a line?

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

m = [tex]tan\theta[/tex]

If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

slope = [tex]\frac{y_2-y_1}{x_2 - x_1}[/tex]

The given line passes through ( -1, -5) and  (4, -8)

Slope of the line  =

                               [tex]\frac{-8-(-5)}{4-(-1)}\\-\frac{3}{5}\\\\[/tex]

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The diameter of the Sun that she needs to draw, considering the scale, is of:

2.15 m.

The meaning of the scale of a drawing is how much each unit in the drawing represents in actual distance.

In this problem, the actual diameters are given as follows:

The drawn diameters are given as follows:

From the scale of the earth, the number of km represented with each cm is given as follows:

13000/2 = 6500 km represented by each cm.

(division of the actual distance by the scale).

Hence the number of cm that is needed to represent 1,400,000 km is of:

1400000/6500 = 215 cm.

(division of the total distance by the scale).

Each cm is composed by 100, the diameter of the Sun in meters is of:

215/100 = 2.15 m.

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Answer:

B (2, 3)

The two lines intersect near that point.

The values of c and d that would make that the given expression represent a real number are c = –3, d = –2.

For the given question;

The expression is given as;

= i(2 + 3i)(c + di)

Simplify the expression;

= i(2c + 2di + 3ci + 3di²)

= 2ci + 2di² + 2ci² + 3di³

= (2c - 3d)i - 2d - 3c

In order is for expression to yield a real number, the coefficient of must now be zero.

Check the values from option;

2c - 3d = 2 x 2 - 3x 3 = -5

2c - 3d = 2 x -2 - 3 x -3 = -13

2c - 3d = 2 x 3 + 3 x -2 = -1

2c - 3d = 2 x -3 -3 x - 2 = 0

Thus, the correct values for the expression to becomes real number is

c = –3, d = –2.

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Answer:

= 4.875 × 105

(scientific notation)

= 4.875e5

(scientific e notation)

= 487.5 × 103

(engineering notation)

(thousand; prefix kilo- (k))

SOLUTION:

Step 1:

we are to find the measure of minor arc cut off by one of the diagonals;

The sum of interior angles in a pentagon is:

Each interior angle of a regular pentagon is

So the size of the major arc can be gotten by the circle theorem; the angle at the centre is twice the angle at the circumference.

Then recall,

Step 2:

We are to find the length of the same minor arc in problem;

Where our angle (titan) is 144 and radius is 10

So the length of the minor arc, given that the radius is 10 cm is 8 pi

Answer:

Step-by-step explanation:

This is a sketch graph of y= sin x° for 0 ≤ x ≤360.

It is called as Sine curve. A mathematical curve described in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

1/3(x+18)= 7

x = ?

Step 02:

We must apply the algebraic rules to find the solution.

The answer is:

x = 3

What percent of 120 is 180

we know that

120 represent the 100%

so

Applying proportion

100/120=x/180

solve for x

x=(100/120)*180

x=150%

Answer:

x = 1.5°

Step-by-step explanation:

8 days = 12°

1 day = x

cross-multiply

8x = 12

Divide both sides by the coefficient of x, which is 8

8x/8 = 12/8

x = 1.5°

Hence, 1 day = 1.5°

we have the system

3x +y = -3

3x +y = 3

In this problem we have two different parallel lines

Remember that the solution of the system is the intersection point both lines

In this problem the lines don't intersect (are parallel)

therefore

the system has no solution NS

isolate the variable y in the first equation

y=-3x-3 -----> equation 1

isolate the variable y in the second equation

y=-3x+3 -----> equation 2

Solve the system of equations

equate equation 1 and equation 2

-3x-3=-3x+3

solve for x

-3x+3x=3+3

0=6 ------> is not true

that means

the system has no solution (NS)

As we Know that, ΔTUV[tex]\sim[/tex] ΔXWV

So, for the given proportion TV(y) = 21.

What is Proportion?

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

What is Ratio?

The link between two or more things in terms of quantity, amount, or size.

Given that,

ΔTUV[tex]\sim[/tex] ΔXWV

∠T = ∠X

∠U = ∠W

∠TUV = ∠XWV

So, TU/WX = TV/WV

10/10 = TV/21

1 = TV/21

TV = 21

So, for the given proportion the value for the side TV(y) = 21

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Answer:

-6x - 39

Step-by-step explanation:

-3(x + 7) -3x -18  Fist distribute the -3

-3(x) + -3(7) -3x -18  Simplify  (a negative times a positive is a negative)

-3x -21 -3x -18  Now combine like terms

-6x -39