Mathematics College

## Answers

**Answer 1**

A lookout tower above a canyon is 4 meters above ground level. The depth of the canyon is 16 meters below ground level. If 0 represents ground level, which number sentence correctly compares their distances above and below ground level?

level ground

we need to take a level as a reference , our reference level will be the ground,

up will be positive and down will be negative, as the y-axis

so, check every level

the lookout tower is 4 meters above the ground level , it is

[tex]th\text{e lookout tower: +4}[/tex]

The depth of the canyon is 16 meters below ground level, it is

[tex]he\text{ depth of the canyon :-16}[/tex]

## Related Questions

A pile of sand is in the form of a right circular cone of altitude 4m and slant height 7m. What is the weight of the sand, if the sand weighs 50kg/m^3?

### Answers

h = 4m

slant height = 7m

volume of the cone:

[tex]V\text{ = }\frac{1}{3}\pi r^2h\text{ }[/tex]

But first we need to find the radius, as follows:

now the volume of the cone is:

[tex]V\text{ = }\frac{1}{3}\pi(5.74)^2(4)=138.23m^3[/tex]

if the sand weighs 50kg per m³, then

50 x 138.23 = **6911.5 kg** is the weight of the sand

Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.2лम2л五COS(15) w() - Sin(ਤੋਂ ) sin()-(COS

### Answers

The sum identity for Cosine is given as:

[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]

This is the same for the given equation in the equation, assuming:

[tex]\begin{gathered} A=\frac{2\pi}{5} \\ B=\frac{\pi}{12} \end{gathered}[/tex]

**Hence, the correct answer is:**

[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]

find the number of possible outcomes in the sample space. then list the possible outcomes

### Answers

Solution

Step 1:

Possible Outcomes – a list of all the resulting possibilities from an event.

Step 2

Possible outcome = (A, B , C, D, E, F , 1 , 2, 3)

Number of possible outcomes = 9

PLEASE HELP :Order the following numbers below in ascending order(smallest to largest) -10/2 , 2 1/2 , -0.52, 51.5%

### Answers

Arranging in ascending order we have,

[tex]\frac{-10}{2},\text{ -0.52, 51.5\%, 2}\frac{1}{2}[/tex]

Pure sounds produce single sine waves on an oscilloscope. Find the amplitude and period of the sine wave graph. On the vertical scale, each square represents 0.5; on the horizontal scale, each square represents 30° or pi/6.

### Answers

To solve the question, we will need to understand some definition

PERIOD: The period is the time it takes for one complete cycle of a harmonic oscillation

AMPLITUDE: The amplitude is the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.

To find the amplitude, we will have to count how many boxes there are from the equilibrium or mean position on the vertical axis and then multiply by 0.5.

The number of boxes is 8

Therefore, the amplitude will be

[tex]\begin{gathered} 0.5\times8=4 \\ =4 \end{gathered}[/tex]

**Amplitude = 4 units**

For the period, we will have to count the number of boxes within one period

There are four boxes within one period. Since we know that each box on the horizontal axis is 30 degrees

or pi/6

The period will be

[tex]\begin{gathered} 30^0\times4=120^0 \\ or \\ \frac{\pi}{6}\times4=\frac{2}{3}\pi \end{gathered}[/tex]

20% of 55 is what number

### Answers

The percentage equation can be written as,

[tex]\begin{gathered} \text{Percent}=\frac{Number}{Total}\times100 \\ \text{Number}=\frac{Percent\text{ }}{100}\times Total \end{gathered}[/tex]

We have to find 20% of 55. So, percent=20% and total=55.

Now, putting the values in equation, we get

[tex]\text{Number}=\frac{20}{100}\times55=11[/tex]

Therefore, the number is **11**.

What is the reason for each step in the solution of the inequality?4(x+6)>−5(x+5)−14Select the reason for each step from the drop-down menus. 4(x+6)>−5(x+5)−14 Given 4x+24>−5x−25−14Choose... 4x+24>−5x−39Choose... 4x+63>−5xAddition Property of Order63>−9xSubtraction Property of Order −7

### Answers

In the second step, they used the** Distributive Property of Multiplication over a sum**:

**a(b + c) = ab + ac**

**4(x + 6) = 4x + 4*6 = 4x + 24**

and

**5(x + 5) = 5x + 5*5 = 5x + 25**

In the third step, they **added **the numbers **-25** and** -14**, which resulted in** -39**.

In the last step, they found an equivalent inequality by **dividing both sides** by the same factor (**-9**):

**63/(-9) = -63/9 = -7**

**-9/(-9) = 9/9 = 1**

Notice that the symbol **<** eas changed to **>**. This happens when we **multiply **an **inequality **by a **negative number**.

Fix the marbleslide homework.Find the function that crosses in the stars.

### Answers

**Answer**

[tex]y=5\sin(\frac{1}{2}(x-\pi))[/tex]

**Explanation**

• Original function

[tex]y=2\sin(\frac{1}{2}(x-\pi)[/tex]

To get to the other pair of stars we have "shrink" in the function, which means that we have to multiply the function times a whole number. For example:

[tex]y=5\sin(\frac{1}{2}(x-\pi))[/tex]

To get a more precise function we would have to know the exact coordinates.

in a museum, a ratio of adults to Children is 12 to 9. If there are 252 people in the museum how many children are there?

### Answers

Ratio of ADULT : CHILDREN =12:9

Total number of people = 252

Number of children:

[tex]\begin{gathered} \frac{9}{21}\times252 \\ \frac{2268}{21}\text{ = 108 children} \end{gathered}[/tex]

write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define the variables that you used to write the system.

### Answers

Step 1: Problem

write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define the variables that you used to write the system.

Step 2: Concept

Form a system of linear equations

Step 3: Method

Let m = number of bracelet

Let n = number of necklace

6 grams of gold in each bracelet and 16 grams of gold in each necklace.

Total weight of gold = 178 grams

6m + 16n = 178 .................................. 1

There are 7 necklaces more than the bracelet

n - m = 7 ..................................... 2

Step 4: Final answer

**Let m = number of bracelet**

**Let n = number of necklace**

**System of equations**

**6m + 16n = 178**

**n - m = 7**

find the mean graphically 4,4,1,7what is the sum of the numbers

### Answers

Given data:

The given data are 4, 4, 1, 7.

The mean of data is,

[tex]\begin{gathered} x=\frac{4+4+1+7}{4} \\ =\frac{16}{4} \\ =4 \end{gathered}[/tex]

The sum of the numbers is,

[tex]\begin{gathered} a=4+4+1+7 \\ =16 \end{gathered}[/tex]

use the unit circle and special right triangle to find the exact value. No decimalssin(pi)

### Answers

Use the unit circle and the special right triangle

According to the image, sin (pi) is 0

graph they system of linear inequalities. Give two orders pairs that are solutions and two that are not solutions.question 9

### Answers

Given the inequality system:

[tex]\begin{cases}y\ge3x+3 \\ y<-2\end{cases}[/tex]

To draw the inequalities, first, you have to determine the line that represents the known endpoint of the inequality.

For the first inequality:

[tex]y\ge3x+3[/tex]

To draw this line, you have to determine two points of it, plot them and then plot the line. Choose two values of x, replace them in the inequality and calculate the corresponding value of y:

I will use x=1 and x=-1

For x=1

[tex]\begin{gathered} y\ge3x+3 \\ y\ge3\cdot1+3 \\ y\ge3+3 \\ y\ge6 \end{gathered}[/tex]

The first ordered pair is (1,6)

For x=-1

[tex]\begin{gathered} y\ge3x+3 \\ y\ge3\cdot(-1)+3 \\ y\ge-3+3 \\ y\ge0 \end{gathered}[/tex]

The second ordered pair is (-1,0)

The inequality has the symbol "≥" which indicates that the points on the line are included in the definition of the inequality, when you draw it you have to use a solid line. This symbol also indicates that the inequality includes all values greater than or equal to the given expression, so you have to shade the area above the line.

For the second inequality:

[tex]y<-2[/tex]

The inequality indicates all values less than -2, to draw this inequality you have to draw a horizontal line at y=-2, the symbol "<" indicates that -2 is not included in the definition of the inequality, so the line must be a dotted line and you have to shade the area below the line.

As you can see, there is a part where both shaded areas overlap, any point within this area will be a solution for the system.

For example:

**2 solutions**

**(-6,-4)**

**(-5,-3)**

Any point outside the area where both shades overlap will not be a solution of the system:

**2 non-solutions**

**(4,2)**

**(-4,3)**

Mr. Shift bought TNT stock at $30 per share and sold it at $45per share. What was his percent profit?

### Answers

We have to use the formula for percent profit with the values given. Doing so, we have:

[tex]\begin{gathered} \text{ \% profit}=\frac{\text{ Selling price - Cost price}}{\text{ Cost price}}\times100=\frac{45-30}{30}\times100\text{ (Replacing the value)} \\ \frac{45-30}{30}\times100=\frac{15}{30}\times100\text{ (Subtracting)} \\ \frac{15}{30}\times100=50\text{ \%} \end{gathered}[/tex]

**The percent profit is 50%.**

The mapping diagram shows a function R(x).910111289Which mapping diagram shows the inverse of R(x)?O A.DOO VO6789INB.9101112AAA89c!1211→10989O D.9101112→ 8→ 7

### Answers

Since we want to find the values of the inverse function, we have to change the values of x for y values.

x r(x)

6 9

7 10

8 11

9 12

Changing x for y we have.

r'(x) x

6 9

7 10

8 11

9 12

1. Scott's monthly salary is $2,296. How much is withheld from Scott's payeach month for social security tax? Use a social security tax rate of7.65%a $164.25b. $175.64c. $158.20

### Answers

You have the following information:

**- Scott's montly salary is $2,296**

**- Social security tax rate is of 7.65%**

In order to calculate how much is withheld from Scott's pay each month, you have to calculate the 7.65% of the Scott's salary. You proceed as follow:

**(7.65/100)(2,296) = (0.0765)(2,296) = 175.64**

that is, the percentage is divided by 100. Next, the previous result is multiplied by the salary. In this way you can calculate the amount of money which corresponds to a 7.65%

**Hence, $175.64 are withhold from the Scott's salary**

The exponential models describe the population of the indicated country, A, in millions, t years after 2006. By what percentage is the population of that country increasing each year? A. Country 4. A= 25.8e^0.021t has the greatest growth. B. The population of that country is increasing by __% each year. (Round to the nearest tenth as needed)

### Answers

** Answer:**

**The population of that country is increasing by 2.1% each year.**

**Step-by-step explanation:**

The exponential model of the population on the greatest growth:

[tex]A=25.8e^{0.021t}[/tex]

To determine at what percentage is the population increasing each year, we can use the following ratio:

[tex]\frac{A(t+1)}{A(t)}[/tex]

Therefore,

[tex]\frac{A(t+1)}{A(t)}=\frac{25.8e^{0.021(t+1)}}{25.8e^{0.021t}}=e^{0.021}=1.021\text{ }[/tex]

**The population of that country is increasing by 2.1% each year.**

The pair of equations 3x + y + 4 = 0 and -3x - 6y + 1 = have * A unique solution*exactly two solutions*infinitely many solutions*no solutions

### Answers

**Given:**

3x + y + 4 = 0

-3x - 6y + 1 = 0

**Required:**

To calculate which option is correct

**Explanation:**

The given equations are

3x + y + 4 = 0

3x - 6y + 1 = 0

a1=3; b1=1 ; c1=4

a2=-3;b2=-6 ; c2=1

[tex]\frac{a1}{a2}=\frac{3}{-3}=-1[/tex][tex]\frac{b1}{b2}=\frac{1}{-6}=-\frac{1}{6}[/tex][tex]\frac{c1}{c2}=\frac{4}{1}=4[/tex][tex]\frac{a1}{a2}\ne\frac{b1}{b2}\ne\frac{c1}{c2}[/tex]

which means it is A unique solution

**Required answer:**

Option A

Kiana wants to have an average of at least 90 on her quizzes. If she took three quizzes and earned an 84, 90 and 97. write out the inequality that would help Kiana find the grade that she needs to make on her 4th quiz.PLESE HELP

### Answers

Her grades in the first three quizzes are 84, 90, and 97.

We will call the grade of the 4th quiz "x".

To find the average of the four quizzes, we need to add all of the scores and divide them by the number of quizzes. In this case, we need to add 84, 90, 97, and x, and divide by 4:

[tex]\frac{84+90+97+x}{4}[/tex]

And since she wants to have an average of at least 90, the last expression has to be greater or equal to 90, we express this with the symbol ≥.

The inequality that can help her find the grade that she needs is:

[tex]\frac{84+90+97+x}{4}\ge90[/tex]

From there, she can find the value "x" that she needs for the fourth quiz.

Answer:

[tex]\frac{84+90+97+x}{4}\ge90[/tex]

Determine whether the following statement is true or false. If false, explain why.A polynomial function having degree 20 and only real coefficients may have no real zeros.

### Answers

**Simplify**: true /false

**Explanation: **if the polynomial has some non-real coefficients, there there may be no real zero.

hence the given statement is false.

a game spinner, circle O, is divided into 3 regions as shown. Line RP is a diameter. What's the area of the shaded sector ROS if RP = 8 in and angle POS = 45 degrees

### Answers

The rule of the area of the sector is

[tex]A=\frac{x}{360}\times\pi\text{ }\times r^2[/tex]

Where x is the central angle of the sector

r is the radius of the circle

Since the central angle of the sector is < ROS

Since < POS = 45 degrees

Since < ROS and < POS are linear angles, then

< ROS + 45 = 180

Subtract 45 from both sides

Since PR is the diameter of the circle O

Since PR = 8

Since the radius is half the diameter

The radius is 8/2 = 4

The value of x is 135 and the value of r is 4

Substitute them in the rule above

[tex]A=\frac{135}{360}\times\pi\text{ }\times(4)^2[/tex]

Use pi = 3.14

[tex]\begin{gathered} A=\frac{3}{8}\times3.14\times16 \\ A=18.84 \end{gathered}[/tex]

Round it to the nearest tenth

A = 18.8 square inches

The answer is H

Suppose that you draw 2 cards without replacement from a standard 52-cards deck. What is theprobability that all cards are aces? It is unusual probability. Write your answer with three decimal places

### Answers

**Answer:**

1/221 or 0.005

**Explanation: **

• The number of aces in a standard 52-cards deck = 4

,

• The total number of cards = 52

The probability of drawing two cards (Aces) without replacement is given below:

[tex]\begin{gathered} P(1st\text{ Ace)}=\frac{4}{52} \\ P(2nd\; \text{Ace)}=\frac{3}{51} \end{gathered}[/tex]

Therefore, the probability that all cards are aces is:

[tex]\begin{gathered} P(\text{all aces)}=\frac{4}{52}\times\frac{3}{51}=\frac{1}{221} \\ \approx0.005 \end{gathered}[/tex]

**The probability is 1/221 (as a fraction) and 0.005 (as a decimal correct to 3 decimal places).**

pat's pizza shack offers customers the choices of crust, sauce, and toppings shown below. if a 1-topping pizza is selected at random, what is the probability that it will be deep dish crust, with traditional sauce and green peppers?

### Answers

**Solution**

For this case we can find the number of total combinations like this:

2* 3* 4= 24

Since we have two options for Crust , 3 for Sauce and 4 for Toppings

Then the probability would be given by:

**1/24**

What is two plus two ?

### Answers

[tex]2+2=4[/tex]

The answer is four.

Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and one.

### Answers

**Given: ** x represent the number. A number decreased by the sum of the number and one.

**Required: **The algebraic expression for the english phrase and its simplification.

**Explanation: **

Given that x is the number.

Sum of the number and one = (x + 1)

Now, the number is decreased by the sum of the number and one.

So, the algebraic expression is

[tex]x-(x+1)[/tex]

Simplifyung further,

[tex]x-x-1=-1[/tex]

**Final Answer: The algebraic expression is x-(x+1) and after simplification, it is -1.**

A circle is centered at (2, 1) and contains the point (3,-2). Give the equation of the circleWord Bank+3 -2 -1 -1 3.16 10 -2 20 -3 6.32 -1 + 2Blank 1:Blank 2Blank 3.

### Answers

EXPLANATION

We already know that the equation of the circle centered at (h,k) and that contains the point (x,y) is as follows:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where h=2 and y=1.

Replacing terms:

[tex](x-2)^2+(y-1)^2=r^2[/tex]

Since (3,-2) is on the graph, we have:

[tex](3-2)^2+(1-1)^2=r^2[/tex]

Subtracting numbers:

[tex]1^2+0=r^2\text{ }\longrightarrow\text{ 1=r\textasciicircum{}2}\longrightarrow1=r\text{ }[/tex]

As r=1 our equation is as follows:

[tex](x-2)^2+(y-1)^2=1[/tex]

Put the pizzas in order by the area of a slice from smallest area to largest area

### Answers

**ANSWER**

Pizza 1, Pizza 2, Pizza 3

**EXPLANATION**

We want to put the pizzas in order by the area of a slice from smallest area to largest area.

To do this, first, we have to first the area of each slice for each pizza. This is found by finding the area of each pizza and dividing it by the number of slices in the pizza.

Pizzas are shaped as circles, hence, the area of a pizza is:

[tex]A=\pi r^2[/tex]

where r = radius of the pizza

For pizza 1, its area is:

[tex]\begin{gathered} A_1=\pi *16^2 \\ \\ A_1=804.25\text{ }in^2 \end{gathered}[/tex]

And the area of each slice is:

[tex]\begin{gathered} \frac{804.25}{8} \\ \\ 100.53\text{ }in^2 \end{gathered}[/tex]

For pizza 2, its area is:

[tex]\begin{gathered} A_2=\pi *14^2 \\ \\ A_2=615.75\text{ }in^2 \end{gathered}[/tex]

And the area of each slice is:

[tex]\begin{gathered} \frac{615.75}{6} \\ \\ 102.63\text{ }in^2 \end{gathered}[/tex]

For pizza 3, its area is:

[tex]\begin{gathered} A=\pi *12^2 \\ \\ A=452.39\text{ }in^2 \end{gathered}[/tex]

And the area of each slice is:

[tex]\begin{gathered} \frac{452.39}{4} \\ \\ 113.10\text{ }in^2 \end{gathered}[/tex]

Therefore, in order of smallest slice area to largest slice area, the answer is:

**Pizza 1, Pizza 2, Pizza 3**

Add 3/7 plus 2/3 equals 23/21How to get denominator

### Answers

So, adding up:

[tex]\frac{3}{7}+\frac{2}{3}=\frac{23}{21}[/tex]

To get "21" in the denominator, what we do is to multiply both denominators of the fractions that are being added up.

find the values of the variables x , y and z in the parallelogram

### Answers

**Answer**:

The image below will be used to explain the question

From the image above,

We will have the following relationships

[tex]\begin{gathered} \angle\text{BCD}=\angle CDF(alternate\text{ angles ar equal)} \\ \angle\text{BCD}=35^0 \\ \angle CDF=x \end{gathered}[/tex]

With the relation above, we can conclude that

[tex]x=33^0[/tex]

**Hence,**

**The value of x = 33°**

**Step 2:**

**The following relation below will be used to calculate the value of y**

[tex]\begin{gathered} \angle CBD=\angle BDE(alternate\text{ angles are equal)} \\ \angle CBD=109^0 \\ \end{gathered}[/tex]

By applying this, we will conclude that

[tex]\angle BDE=109^0[/tex]

The relation below will be helpful to get the exact value of y

[tex]\begin{gathered} \angle BDE+\angle CDF+\angle CDB=180^0(SUM\text{ OF ANGLES ON A STRAIGHT LINE)} \\ \angle BDE=109^0 \\ \angle CDF=x=33^0 \\ \angle CDB=y \end{gathered}[/tex]

By substituting the values, we will have

[tex]\begin{gathered} \angle BDE+\angle CDF+\angle CDB=180^0 \\ 109^0+33+y=1180^0 \\ 142^2+y=180^0 \\ y=180-142 \\ y=38^0 \end{gathered}[/tex]

**Hence,**

**The value of y= 38°**

**The relation below will be used to figure out the value of z**

[tex]\begin{gathered} \angle BDE=\angle CFD(correspond\in g\text{ angles are equal)} \\ \angle BDE=109^0 \\ \angle CFD=z \\ z=109^0 \end{gathered}[/tex]

**Hence,**

**the value of z= 109°**

Use three. 144 pi or the pie button and round to the nearest hundredth volume of cone? ￼

### Answers

**Given:**

radius = r = 4.5 cm

height = 9 cm

**Required:**

The volume of the cone

**Explanation:**

The formula for volume of cone is given by

[tex]volume\text{ }of\text{ }cone=\frac{\pi r^2h}{3}[/tex]

Substituting the given values in the formula we get

[tex]\begin{gathered} volume\text{ }of\text{ }cone=\frac{\pi\times4.5^2\times9}{3}=\pi\times20.25\times3 \\ volume\text{ }of\text{ }cone=60.75\pi\text{ }cm^3 \\ \\ volume\text{ }of\text{ }cone=60.75\pi=60.75\times3.14 \\ volume\text{ }of\text{ }cone=190.755\text{ }cm^3 \end{gathered}[/tex]

**Final answer:**

The volume of cone is 190.75 cubic cm