Recall the following trigonometric identities. If the legs of the right triangle have lengths a and b, the hypotenuse has length c, and the side a is adjacent to an angle θ, then:

[tex]\begin{gathered} \sin \theta=\frac{b}{c} \\ \cos \theta=\frac{a}{c} \end{gathered}[/tex]Then, for the given right triangle:

[tex]\begin{gathered} \sin (30º)=\frac{x}{8} \\ \cos (30º)=\frac{y}{8} \end{gathered}[/tex]Then, x and y are given by the expressions:

[tex]\begin{gathered} x=8\cdot\sin (30º)=8\cdot\frac{1}{2}=4 \\ y=8\cdot\cos (30º)=8\cdot\frac{\sqrt[]{3}}{2}=4\cdot\sqrt[]{3} \end{gathered}[/tex]**Therefore, the answers are:**

A Christmas tree is supported by a wire that is 3 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 21 meters shorter than the height of the tree. What is the height of the tree?

The **height **of the Christmas **tree **is 12 meters

Represent the **height **of the **tree **with h

So, we have the following parameters

Tree height = hBaseline = h - 21Anchor = h + 3The figure that illustrates the above parameters is added as an attachment

From the figure, we have the following equation by **Pythagoras theorem**

(h + 3)² = h² + (h - 21)²

Expand the exponents

h² + 6h + 9 = h² + h² - 42h + 441

Evaluate the like terms

6h + 9 = h² - 42h + 441

So, we have

h² - 48h + 432 = 0

Expand

h² - 36h - 12h + 432 = 0

Factorize the equation

(h - 36)(h - 12) = 0

Solve for h

h = 36 and h = 12

When h = 36, the **baseline **will be negative

So, we make use of h = 12

Hence, the **tree **has a **height **of 12 meters

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In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to

a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?

The probability that a female will be born using this technique is approximately

(Type an integer or decimal rounded to three decimal places as needed.)

Does the technique appear effective in improving the likelihood of having a female baby?

O No

O Yes

The **probability** of having female baby is 0.95

**What is probability?**

**Probability** is a discipline of mathematics that deals with statistical models of how probable an event is to exist or how likely a statement is to be true. The **probability** of an occurrence is a value between 0 and 1 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the **probability** of "tails," and because no other outcomes are possible, the **probability** of either "heads" or "tails" is 1/2.

The **probability** of having female baby is = 284/(284 + 15) = 0.95

** **

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Solve the equation for all complex and real solutions. Use potential zeros and synthetic division[tex]5x^4+7x^3+119x^2+175x-150=0[/tex]

**Answer: the complex solutions are:**

**Step-by-step explanation: x = 5i , -5i , 3/5 ,-2**

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y > x + 2y > -2 x - 7I NEED THE CORDINATES

**Given:**

There are given that the set of inequality is:

[tex]\begin{gathered} y>x+2 \\ y>-2x-7 \end{gathered}[/tex]**Explanation:**

From the given system of inequality, we need to draw the graph and find the set of points, where both of the graphs will intersect.

Now,

The graph of the given system of inequality is shown below:

**Final answer:**

Hence, **the set of the point from the given system of inequality is shown below:**

Printer A prints 36 pages every 1.5 minutes. Printer B prints 114 pages every 3 minutes.

Printer C prints 115 pages every 5 minutes. Which printer prints the fastest?

Printer B= 114 pages per 3 minutes. **Printer B is the fastest printer.** I did scratchwork on paper but I still sent it to you. Sorry my handwriting is sloppy. ; ) I hope it helps.

A cylinder shaped jelly jar has a radius of 2 cm and a height of 6 cm. How much jelly can the jar hold?

**Question:** A cylinder-shaped jelly jar has a radius of 2 cm and a height of 6 cm. How much jelly can the jar hold?

**Explanation:**

The cylinder-shaped jelly has a volume of gelatin equal to its cylindrical volume. Therefore, we must find the volume of the given cylinder. The volume V of the cylinder with radius r and height h is given by the following formula:

[tex]V=h\pi r^2[/tex]Applying the data of the problem, we obtain:

[tex]V=h\pi r^2=6\text{ * }\pi\text{ * \lparen2}^\text{\rparen}^2\text{ = 24}\pi\text{ =75.398}[/tex]**Answer**: we can conclude that** the correct answer is:**

Here is the probability model for the blood type of a randomly chosen person in the United States:Blood Type O А B ABProbability 0.14 0.32 0.01 ?(a) This probability model isA. discrete.B. continuousC. equally likelyD. None of the above.(b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that arandomly chosen American can donate blood to Maria?A. 0.01B. 0.15C. 0.33D. None of the above.(c) What is the probability that a randomly chosen American does not have type O blood?A. 0.86B. 0.68C. 0.14D. None of the above

**a) **A probability distribution is called continuous if its distribution function is continuous.

• Answer a: B. continuous.,

**b)**

• Answer b: B. 0.15

**c)**

• Answer c: A. 0.86

3х-7-(-2х) +9 simplify

[tex]3x-7-(-2x)+9[/tex][tex]\begin{gathered} 3x-7+2x+9 \\ (3+2)x+(-7+9) \\ 5x+2 \end{gathered}[/tex]

Which graph correctly represents ? 1/5y - 1/2x > 2

A **graph** which represents the solution to this **inequality** is shown in the image attached below.

An **inequality** can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):

Next, we would evaluate and simplify the given **inequality** in order to determine the **graph** which represent its solution as follows:

1/5y - 1/2x > 2

Subtracting 2 both sides, we have:

1/5y - 1/2x - 2 > 2 - 2

1/5y - 1/2x - 2 > 0

(2y - 5x - 20)/10 > 0

2y - 5x - 20 > 0

2y > 5x + 20

Dividing both sides by 2, we have:

y > 5x/2 + 10

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Liam is setting up folding chairs for a meeting. If he arranges the chairs in 8 rows of the same length, he

has 3 chairs left over. If he arranges the chairs in 6 rows of that same length, he has 13 left over. How many

chairs does Liam have?

Liam has

chairs.

The most appropriate choice for **linear equation** will be given by-

Liam have 43 chairs

**What is linear equation?**

At first, we need to know the meaning of **algebraic expressions.**

**Algebraic expressions** consists of **numbers **and **variables** connected with **addition,subtraction, multiplication and division sign.**

**Equation** shows the **equality **between **two algebraic expressions** by connecting the two **algebraic expressions** with an **equal to sign**

A **one degree equation** is known as **linear equation.**

Let the number of chairs in one row be x

Number of chairs in 8 rows = 8x

3 chairs are left

Total number of chairs = 8x + 3

Number of chairs in 6 rows = 6x

13 chairs are left

Total number of chairs = 6x + 13

By the problem,

[tex]8x+3=6x+13\\8x-6x=13=3\\2x=10\\x=\frac{10}{2}\\x=5[/tex]

Number of chairs Liam has =

[tex]6\times 5 + 13\\30+13\\43[/tex]

Liam has 43 chairs

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You pick a card at random. Without putting the first card back, you pick a second card at random.4567What is the probability of picking an even number and then picking an even number?Simplify your answer and write it as a fraction or whole number.

Given:

**4 5 6 7**

Given that you picked a card at random, without replacement, you then pick a second card at random.

Let's find the probability of picking an even number and then picking an even number.

Number of possible events = 4

Number of even numbers = 4, 6, ==> 2 even numbers.

Hence, to find the probability, we have:

[tex]\begin{gathered} P=\frac{2}{4}*\frac{1}{3} \\ \\ P=\frac{2*1}{4*3} \\ \\ P=\frac{2}{12}=\frac{1}{6} \end{gathered}[/tex]**Therefore, the probability of picking an even number and then picking an even number is 1/6.**

**ANSWER:**

x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function?

The **vertex **is the **turning** **point **of a function while the **range **is the **interval **of the value of the **function** thus **vertex **of the given **function **is at (-4,0) while the **range **is [0,6].

A function's **range **is the set of all values that the function **accepts**, and its domain is the **set **of all **values** for which the **function **is defined.

The **domain** is for the independent variable while the **range **is for the dependent **variable**.

As per the given function,

x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6

The **graph** of this **function **has been **plotted **below,

The **vertex** is the point where the function is **changing **its **sign** of **slope **or turning point.

It is clear that at (-4,0) it is changing its **slope** of **sign **therefore (-4,0) will be the vertex.

The **range** is the interval where the **function exists **since the given function goes from y = 0 to y = 6 so [0,6] will be the **range **of the **function**.

Hence "The **vertex **is the **turning** **point **of a function while the **range **is the **interval **of the value of the **function** thus **vertex **of the given **function **is at (-4,0) while the **range **is [0,6]".

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if your 1952 what year will you be 26?

**Answer:**

16 January 1952, Wednesday, 70 Years, 8 Months, 26 Days or 848 months, or 3691 weeks, or 25837 days, or 37205280 minutes, or 2232316800 seconds.

**Step-by-step explanation:**

**Answer:**

**Step-by-step explanation:**

answer:1978

18. A student turned in the following incorrect work. - In what line was the mistake made? - What should the correct step be? - What is the correct final answer?

Be sure to describe your answer in 4-5 sentences.

**Answer:**

4y³/x³

**Step-by-step explanation:**

Line 1 is completely correct.

Line 2 has an error.

The 4/1 from line 1 should remain as 4/1 in Line 2, but the student wrote it as 1/4 on Line 2.

To fix it, rewrite Line 2, but change the first fraction, 1/4, to 4/1.

The correct final answer is 4y³/x³

3x+3=2(x+7)

What does x equal?

**Answer:** x = 11

**Step-by-step explanation:**

To solve we will **isolate **the **variable**, x.

**Given**:

3x+3=2(x+7)

**Distribute**:

3x+3=2x+14

**Subtract **3 and 2x from both sides of the **equation**:

x = 11

Choose two consecutive points on the graph and find the rate of change. Is the slope the same or different?

Choose two consecutive points on the graph and find the rate of change.

We will start with t = 1000 and t = 1500:

[tex]P(1000)=12.643(1.0027)^{1000}=187.4412[/tex][tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex]Remember that the rate of change is found by the difference in y over the difference in x.

[tex]RATEOFCHANGE=\frac{721.7263-187.4412}{1500-1000}[/tex][tex]RATEOFCHANGE=\frac{534.2851}{500}\approx1.0686[/tex]Let's do it now for t = 1500 and t = 2000.

[tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex][tex]P(2000)=12.643(1.0027)^{2000}=2778.9454[/tex]In this case the rate of change would be:

[tex]\text{rateofchange=}\frac{2778.9454-721.7263}{2000-1500}[/tex][tex]\text{rateofchange}=\frac{2057.2191}{500}\approx4.1144[/tex]The slopes are different and due to the type of function they will always increase when taking larger values.

What is the net price of merchandise listing for $5,900 less a trade discount rate of 45%?

A percentage is a number or ratio that represents a fraction of 100.

If there is a trade discount of 45% on the price of the merchandise of $5900, the **net** **price** of the **merchandise** is $3245.

A percentage is a number or ratio that represents a fraction of 100.

We have,

**Merchandise** price = $5,900

**Discount** rate = 45%

45% = 45/100 = 9/20

The **net** **price** of the **merchandise**:

= 5900 - (45% of 5900)

= 5900 - 9/20 x 5900

= 5900 - 9 x 295

= 5900 - 2655

= 3245

Thus,

If there is a trade discount of 45% on the price of the merchandise of $5900, the **net** **price** of the **merchandise** is $3245.

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pls help. this is so confusing on how to find the p=S(t)=r+i part of the word problem.

Using a **linear **function, it is found that:

**a)** Sales are **increasing **at a constant **rate **of 30 purchases/month.

**b)** The** linear function** is: p = S(t) = 30t + 3990.

**c) **The total **purchases **will be of 5130 in **June 2010**.

**d) **The **sales **will be of 5400 in **March of 2011.**

A linear function, in **slope-intercept **format, is modeled according to the following rule:

y = mx + b

In which:

The coefficientFor this problem, we have that:

The reference month is of April 2007, hence theThe slope of 30 is the **constant rate** of purchases per month, and the **linear function **is given by:

p = S(t) = 30t + 3990.

**June 2010 **is 3 x 12 + 2 = 38 months after April 2007, hence the **purchases **will be of:

S(38) = 30 x 38 + 3990 = 5130.

The sales will be of 5400 in t months after April 2007, for which:

S(t) = 5400

Hence:

30t + 3990 = 5400

t = (5400 - 3990)/30

t = 47 months.

One month shy of four year, hence in **March of 2011.**

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Round 0.4275 to the nearest thousand

we have

0.4275

if we round to the nearest thousand, we look at the third digit of our number

0.42**75**

**do you know the answer now?**

**0.42 is not correct**

** and only 2 decimals will be rounded to the nearest hundreth**

**becuase we have a 5 after 7, the number will be rounded up**

**0.428**

**this is the answer**

if we would have for example

0.3521

the rounded to the nearest thousand would be 0.352

Select the correct inequality and graph for the statement. Samuel gets 25 or more for mowing the lawn. PLSSS HELP!!

The statement "Samuel will get **25 **or** more** for mowing the lawn" can be represented using the** inequality → x ≥ 25** and the** graph number [2]** represents the correct graph.

In mathematics, an inequality is a relation which makes a **non-equal comparison **between two numbers or other **mathematical expressions. **There are two types of inequalities namely **strict** and **slack inequalities.**

Given is the following statement - "Samuel will get **25** or** more** for mowing the lawn".

The given statement is -

Samuel will get **$25** or more for mowing the lawn.

Assume that Samuel gets **$x** for mowing the lawn.

Then according to the question, we can write the** inequality** as -

**x ≥ 25**

" ≥ " sign to represent either 25 or more.

So, the inequality can be written as** x ≥ 25** and the **graph number [2] **represents the **correct graph.**

Therefore, the statement "Samuel will get **25 **or** more** for mowing the lawn" can be represented using the** inequality → x ≥ 25** and the** graph number [2]** represents the correct graph.

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[Refer to image attached for complete question]

use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph (without drawing the graph) a graph with 4 vertices, each of 2 degree 2

[tex]\begin{gathered} \text{Handshaking theorem} \\ Sum\text{ of degre}e\text{ of all the vertices=2}\times Number\text{ of vertices} \\ So,\text{ } \\ n\times2=2\times4 \\ n=4(nu\text{mber of edge)} \end{gathered}[/tex]

identify the set of numbers that best describes each situation explain your choice. 9. the amount of money in a bank account

The sets of the real numbers are

Whole numbers

Integers

Rational numbers

Irrational numbers

The whole numbers mean positive integers with zero

The integers mean positive , negative whole numbers, and zero

Rational numbers mean

Bruno's hourly salary is $8.75. Last week he worked only 18 hours. How much did he earn

It’ll be 157.5 because 8.75 x 18 = 157.5 ^_^

Find the four terms of the arithmetic sequence given the 13th term (a_{13}=-60) and the thirty third term (a_{33}=-160).Given terms: a_{13}=-60 and a_{33}= -160Find these terms:a_{14}= Answera_{15}= Answera_{16}= Answera_{17}= Answer

**Given:**

13th term = -60

33rd term = -160

**Find:**

14th, 15th, 16th, and 17th term

**Solution:**

For us to determine the 14 - 17th term, we need to identify the common difference in this arithmetic sequence. The formula is:

[tex]\frac{a_{33}-a_{13}}{33-13}[/tex]Let's plug in the values of a₃₃ and a₁₃ in the formula above.

[tex]\frac{-160-(-60)}{33-13}[/tex]Then, solve.

[tex]\frac{-100}{20}=-5[/tex]*Hence, the common difference between the terms is -5.*

**So, the next 4 terms after a₁₃ are shown below:**

Larry and his brother wanted to put new carpet down in threerooms in his house. The three rooms measured 10' x 12, 13' x 15,and 12' x 12'. If the carpet Larry wants to use is $25.56 a sq. yd.and the roll of padding is $99 for a 30 sq.yd. roll, answer thefollowing questions. Remember that 1 square yard = 9 square feet.1. Total square footage to be covered with carpeting would besquare feet.2. How many square yards would that be?sq.yd.3. Based on the price of $25.56 a sq.yd., what would the total costbe for the carpeting? $4. To make sure Larry has enough padding, how many rolls wouldhe have to buy?What would that cost? $5. What would the total cost of the carpeting job be includingcarpet and padding? $

Part 1)**Part 3)****Part 4)**

Find the area of each room and then add the three areas.

[tex]\begin{gathered} 10\times12=120 \\ 13\times15=195 \\ 12\times12=144 \\ \\ 120+195+144=459 \end{gathered}[/tex]The total square footage to be covered is **459**.

Since each square yard has 9 square feet, divide the square footage by 9 to find how many yards is that equal to:

[tex]\frac{459}{9}=51[/tex]Then, the area is equal to **51 square yards**.

The cost for each square yard is $25.56. Multiply that amount by 51 to find the total cost:

[tex]25.56\times51=1303.56[/tex]The total cost for the carpeting is **$1303.56**.

Each roll of padding has 30 square yards. Since 51 yards must be covered, and two rolls would yield 60 square yards, then, the minimum amount of rolls needed is **2**.

The cost for **2** rolls would be 2*$99 = **$198.**

Add the cost of the two rolls of padding and the carpeting job to find the total cost:

[tex]\text{ \$}198+\text{ \$}1303.56=\text{ \$}1501.56[/tex]Then, the total cost of the carpeting job including the carpet and padding would be **$1501.56**.

**Therefore, the answers are:**

**Part 1) 459 square feet.**

**Part 2) 51 square yards.**

**Part 3) $1303.56**

**Part 4) 2 rolls for $198**

**Part 5) $1501.56**

Write three equations whose graphs are the same line as the equation x - 9y = 3/4

**y= 1/9x **

**y= 1/9x +2/24 **

**y = 1/9x + 3/36**

**1**) To be on the same line, they must share the slope and their points

Let's rewrite that into the standard form

x -9y =3/4

-9y = 3/4 -x

9y = 3/4 +x *Divide both sides by 9*

y = 1/12 + x/9

y= x/9 + 1/12

**2**) Since we have the slope 1/9, then we can write the first equation as

y= 1/9x *On the same line*

y= 1/9x +2/24 *2/24 is a multiple of 1/12, therefore on the same line*

y = 1/9x + 3/36 3/36 is a *multiple of 1/12, therefore on the same line*

The length of a rectangular room is 12 feet more than 3 times the height of the room. The floor of the room has an area that is represented by the function below, where h is the height of the room in feet. A(R) 9h2 + 45h + 36 Which statement best describes the width of the room? A. The width is 3 feet shorter than the length. B. The width is 9 feet shorter than the length. C. The width is 9 feet longer than the height. D The width is 3 feet longer than the height.ill send a picture of the question

Okay, here we have this:

Considering the provided information, and that the area of a rectangle is the product of its length and width, we obtain the following:

[tex]\begin{gathered} Width=\frac{Area}{Length} \\ Width=\frac{9h^2+45h+36}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3\left(h+4\right)} \\ =3\mleft(h+1\mright) \\ =3h+3 \end{gathered}[/tex]Now, to know if the width is greater or less than the length, we will subtract it, then we have:

[tex]\begin{gathered} (3h+12)-(3h+3) \\ =3h+12-3h-3 \\ =12-3 \\ =9 \end{gathered}[/tex]**Finally we obtain that the width is feet 9 shorter than the length, so the correct answer is the option B**

Solve using substitution. y=103x + 4y = 19

We want to find the solutions for the following system

[tex]\begin{cases}y=10 \\ 3x+4y=19\end{cases}[/tex]We already know the value for the **y** variable, if we substitute this value on the second equation it is possible to find the **x **value.

And those are the results for our system

[tex]\begin{cases}x=-7 \\ y=10\end{cases}[/tex]I will show you the pic

The general form of a linear equation is given by:

**y = kx**

where k is a constant.

From the given options you can notice that the only equation similar to the previous one is:

**y = 1/6 x**

**Then, the previous equation is the linear equation.**

- Lana had a fixed budget for a party. She spent one third of the

budget on decorations. Of the money that remained, she spent

on refreshments and the rest on door prizes for the guests.

If she spent $60 on door prizes, what was her budget?

Lana's fixed budget for a party is $**180.**

Let x be Lana's fixed budget for a party.

Lana spent one-third of the budget on decorations.

**x - 1/3x = 2x/3**

Remaining money,

**2x/3 -x + (2x/3-x)-x =0**

Since she spent $60 on door prizes

-x/3 + 60 = 0

-x/3 = -60

** x = 180**

Lana's fixed budget for a party is $**180.**

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Hay, Bee and Cee are partnership sharing profits in the ratio of 5:3:2.Before Bee's salary of $17,000, the firm's profit is $97,000. How much intotal will Bee receive from the firm as his share of profit?
A piece of aluminium foil is 8.01^-5cm thick . what is its thickness in micrometers?
write the following in the form a+bi (2+5) - (-6 +bi)
1) Apples cost $16 for an 8 pound bag at the local priceclub, but the club has a membership fee of $50.Write and solve an equation to determine how manypounds (p) of apples you can buy for $58.