1. Jessica finishes her book in 2 1/3

hours. Eric takes 1 1/2

times longer than
Jessica to finish his book.
This model represents the amount of time Jessica takes to finish her
book. It has a width of 1 and a length of 2 1/3

. The model is 2 1/3 out of 3

We can replace trigonometric terms in formulas with trigonometric terms of smaller powers using the trigonometric power reduction identities. This is significant for using calculus to integrate the powers of trigonometric expressions, among other applications.

2cos2 will be equal to 1 plus cos 2. We arrive at an equation for cos2 by dividing by 2. Because they enable us to reduce the power on one of the trig functions when the power is an even integer, these are commonly referred to as "power reduction formulae."

An integral problem can be solved using a reduction formula by first breaking it down into simpler integral problems, which can then be broken down into simpler problems, and so on.

P = E/t is the equation, where P stands for power, E for energy, and t for time in seconds. According to this equation, power is defined as the amount of energy consumed per unit of time.

The Equivalent expression for Cos 4x= 8cos4(x) - 8 cos2(x) + 1.

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Given the following trinomial:

To factor the trinomial, we need two numbers the product of them = 42

And the sum of them = -13

Two of the numbers of factors of 42 = -6, and -7

So, the factor of the trinomial will be as follows:

So, the answer will be option B. x - 7

This is a problem of binomial probability. We have two possible outcomes:

• the article selected is an editorial,

• the article selected is not an editorial.

The probability of success (select an article that is an editorial) is:

Because we have 12 total articles submitted, and 5 of them were editorials.

To calculate the probability that selecting 5 random articles, getting as a result that exactly 3 of the chosen articles are editorials, we use the binomial probability formula:

Where:

• n = the number of trials = the number of articles selected randomly = 5,

• x = the number of success = the number of editorials that we expect = 3,

• p = the probability of getting an editorial = 5/12,

• C(n,x) = n! / (x! (n-x)!).

Replacing the data in the formula above, we get:

Answer

Rounded to four decimal places, the probability that exactly 3 of the chosen articles are editorials is 0.2462.

The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (-5.3, 1). The finishing point will be at(1, -5.3). Quadranto Quadrant P Quadrant Quadrants Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points) Part B: A checkpoint will be at (5.3, 1). In at least two sentences, describe the difference between the coordinates of the starting point and the checkpoint, and explain how the points are d. (4 points)​

Part A

we have

starting point of the race is (-5.3, 1)

the x-coordinate is negative and the y coordinate is ;positive

that means-------> is located on quadrant Q

finishing point is (5,3, 1)

x-coordinate is postive and y coordinate is positive

that means -----> is located on Quadrant P

Answer:

Step-by-step explanation:

part A

A'(1,1)

B' (6,5)

C' (6,1)

Explanation

Step 1

Let

A(1,-1)

B(5,-6)

C(1,-6)

Step 2

find the image (A'B'C')

When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

Hence

so, the coordinates of the image are

A'(1,1)

B' (6,5)

C' (6,1)

I hope this helps you

Length of the dimensions of the finished stock shown are as follow:

A = 13/4 inches , B = 3/4 inches , C =5/2 inches , D = 3/16 inches.

As given in the question,

Mechanist must follow part drawing with scale 1 to 16.

Dimensions of the finished stock shown in the figure

A represents the length .

B represents the height

C represents the length

D represents the height

Length of A is

= 3 1/4 inches

= 13 /4 inches

Height of B is

=3/4 inches

Length of C is

= 2 1/2 inches

= 5/2 inches

Height of D is

= 3/16 inches

Therefore, length of the dimensions of the finished stock shown are as follow: A = 13/4 inches ,B = 3/4 inches ,C =5/2 inches , D = 3/16 inches.

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Based on Cassie's financial goal to eliminate her credit card debt, the graph that would best model her situation in terms of scale and label is B. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)

When modeling a graph, the time period is often the independent variable. This means that the time period which are in months (months that Cassie makes monthly payments) need to be on the x-axis and will be labelled from 0 to 12 months for the months of the year.

The amount of credit card debt would then be on the y-axis. It is best to have a scale that is larger than the maximum debt Cassie has to that the data can be included properly. So a limit of 0 - 8,000 is best and would properly incorporate the $5,000 she already owes.

Full question is:

Cassie's latest financial goal is to eliminate her credit card debt. She has about $5,000 in credit card debt. She determines that she can afford to make

monthly payments of about $500. To track her progress, she plans to create a graph to model her situation. How should Cassie label and scale her

graph?

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Answer:

y = 2x + 3

Step-by-step explanation:

You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.

Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.



The slope is 2. Fill in 2 in place of m in

y = mx + b

y = 2x + b

Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.

y = 2x + 3

ANSWER:

24.63%

STEP-BY-STEP EXPLANATION:

The first thing is to mention that it is a profit because it was bought at a lower amount than it was sold, therefore

We take 100% as the lowest value, and thus we calculate the profit percentage

Then the difference between both percentages is the profit percentage

To find the number of page she read per minute

First let's chenge the 8 hours to minute

8 hours = 8 x 60 = 480 min

Since she read 600 pages

Number of pages read per min = 600/ 480

=1.25 pages

We are given the following inequalities:

First, we will solve for inequality 1. To do that we will add 5 to both sides:

Solving the operations:

Now we divide both sides by 3:

Solving the operations:

Now we solve for "x" in inequality (2). To do this we will add 1 to both sides:

Solving the operations:

Now we divide both sides by 2:

Solving the operations:

Therefore, the solution to the system is:

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

Step 01:

Data:

sampling error and non-sampling error

Step 02:

statistics:

Sampling error:

It is the error that arises in a data collection process as a result of taking a sample from a population rather than using the whole population.

Non-sampling error:

It is the error that arises in a data collection process as a result of factors other than taking a sample.

non-response errors, coverage errors, interview errors, and processing errors

As given by the question

There are given that the side length is (2x+3) and perimeter is 60 cm.

Now,

From the formula of perimeter:

So,

Then,

Put the value of x into the given side length (2x+3)

So,

Hence, the one side of length is 15 cm.

The surface area of a pyramid is given as:

where p is the perimeter of the base, l is the slant height and B is the area of the base.

In this case the slant height is 4 in.

Now, since the base is a square which sides that has length 5 in. then the perimeter is:

The area of the base is the length of the side squared, then we have:

Once we know the values we plug them in the formula, then we have:

Therefore the surface area is 65 squared inches.

Let's draw a right triangle to guide us:

Every right triangle will have one hypotenuse side and two leg sides. The hypotenuse is always the bigger one and it is always opposite to the right angle, so in this triangle the hypotenuse is a (the letter can change from exercise to exercise, but it is always the opposite to the rignt angle).

The legs can be classified as adjancent or opposite legs, but this is with respect to the angle we are using.

So, if we are using angle C, the opposite leg is the leg that is opposite to angle C, that is, c.

Thus, the adjancent leg is the leg that is touching the angle C, that is, b.

So, with respect to angle C, we have:

Hypotenuse - a

Opposite leg - c

Adjacent leg - b

The sine is the ratio between the opposite leg and the hypotenuse, always.

The cosine is the ratio between the adjacent leg and the hypotenuse, always.

The tangent is the ratio between the opposite leg and the adjacent leg, always.

For, for angle C, we have:

For angle B, we do the same, however now, the legs are switched, because the leg that is opposite to angle B is b and the leg that is adjance to angle B is c, so, for angle B:

Hypotenuse - a

Opposite leg - b

Adjacent leg - c

And we follow the same for sine, cosine and tangent but now for angle B and with the legs switched:

Questions regaring these ratios normally will present 2 values and ask for a third value. One of the values will be an angle, the other will be side (usually). So, we need to identify which angle are we working with and which sides are the hypotenuse, the opposite leg and adjancent leg with respect to the angle we will work with. Then we identify which of the side we will use and pick the ratio thet relates the sides we will use.

To get an unitless ratio, both of our quantities have to be in the same units. Let's convert that hour into minutes:

Thereby, our ratio would be:

Let's check the ratios:

First one is already reduced. Let's reduce the 2nd fraction by dividing top and bottom by 3, so

So, they are equal.

Next ratio:

Let's divide both top and bottom by 2 (1st fraction) and top and bottom by (3) in 2nd fraction:

They aren't equal. So, we have already found our answer.

OB. 2:14 and 3:42 --- is our answer.

We will have that the set of rational roots for the expression will be:

[Option C].

it's letter A. Between 13 and 14 meters

Because one side measure 14, and the height (depth) could not be

higher than 14 meters .

The length of the pond can be calculated using the Pythagorean theorem

length^2 = 36^2 + 14^2

length^2 = 1296 + 196

length^2 = 1492

length = 38.6 m

to write the expression as a product between two factors you must identify the common factor between all the terms in tis case the common factow will be 2

From the table, the root of the function is a point where y = 0.

Therefore,

The root of the function are ( 4, 0 ) and ( -3, 0 )

Final answer

I and III only Option B

The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.

The function is given to be:

where A and k are positive constants.

We can find the derivative of the function as follows:

Step 1: Pull out the constant factor

Step 2: Apply the product rule

Let

Therefore, we have:

Step 3: Simplify

QUESTION A

At t = 0, the instantaneous rate of change is calculated to be:

The rate of change is:

QUESTION B

At t = 30, the instantaneous rate of change is calculated to be:

The rate of change is:

QUESTION C

When the rate of change is equal to 0, we have:

We can make t the subject of the formula using the following steps:

Step 1: Apply the Zero Factor principle

Step 2: Collect common terms

Step 3: Apply the Zero Factor Principle:

or

The time will be:

Given the scale reading:

Each weight weighs 0.2 kilograms

If the class put 16 weights on the scale

Then the scale reading will be

Hence the scale reading will be 3.2kg

ANSWER

$12.75

EXPLANATION

The store is selling the perfumes at 15% off the original price, so if a bottle of perfume costs $30, then they are selling it at,

But you also have a coupon for 50% off, so you get to buy the perfume at half that price,

Hence, the final price of the perfume is $12.75.

Answer:

y = 2x + 6

Step-by-step explanation:

Parallel lines have the same slope, so the slope is 2.

y = mx + b  

When need the slope which is given to be 2

We will use the point given (-6,-6) for an x and y on the line

m= 2

x -= -6

y = -6

y=mx+ b

-6 = 2(-6) + b  Sole for b

-6 = -12 + b  Add 12 to both sides

6 = b

y = 2x + 6

Answer:

100 ounces of 12% solution and 60 ounces of the 20% solution.

Step-by-step explanation:

Let x ounces be the amount of 12% solution, then there will be 160-x ounces of the 20% solution.

So, we have the equation:

0.12x + 0.20(160 - x) = 0.15* 160

0.12x - 0.20x + 32 = 24

-0.08x = -8

x = 100.

So, it is 100 ounces of 12% solution and 60 ounces of the 20% solution.

The  increase in area of the circle  when the radius is increased by 2 is 13.8 in.

Area of a circle  can be described as the region that is been taken by the circle.

The area of the circle can be expressed as A=πr^2

We were told that the radius of the circle is been given as 0.10 in.

Then we can calculate the are of the circle by input the given radius into the formula above as:

A=πr^2

r= radius of the circle

A= area of the circle

A=3.14 (0.10)^2 =0.0314 in.

Then we were told that the radius is increased by 2 in.

Then the area of the circle will now be A=3.14* (2.10)^2 =13.85 in.

Then the the increase in area can be calculated as : (13.85 in. - 0.0314 in.) = 13.8 in.

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The median is the value of the data set that separates the sample in halves.

To determine the median of a determined data set, you have to calculate its position.

The given sample has n=7 elements, to determine the position of the median given that the data set is odd, you have to use the following formula:

Replace it with n=7

This result indicates that the media is the fourth observation of the data set.

Next, you have to order the data set from least to greatest:

Original data set: 4, 7, 9, 10, 5, 12, 6​

Ordered from least to greatest: 4, 5, 6, 7, 9, 10, 12

Once the data set is ordered, you have to count starting from the left until you reach the fourth observation:

O4, 5, 6, 7, 9, 10, 1

The fourth value of the data set is 7, which means that the median of the data set is 7.

Median=7

2

Parallel lines are lines that have the same direction and there is always the same distance between them

Skew lines are lines that are not on the same plane (they are not coplanar) and also they do not intersect.

Intersecting lines are lines that cross at a point, they can be on the same plane or on different planes.

Let's analyze the parts of this problem.

DE and AB.

These two lines are shown in red and blue in the following diagram:

These are not parallel lines because one line is vertical and the other line is horizontal. They are also not intersecting lines because they do not cross at any point. Lines DE and AB are skew lines because they do not intersect and they are on different planes.

--> DE and AB --> skew

CB and

Solve: