We have a parallelogram and we have to find the length of side RQ.

Opposite sides of a parallelogram besides being parallel, they also have the same length.

Then, we can write:

[tex]PS=QR[/tex]We can use that to find the value of x as:

[tex]\begin{gathered} PS=QR \\ -1+4x=3x+3 \\ 4x-3x=3+1 \\ x=4 \end{gathered}[/tex]Knowing x = 4, we can find RQ as:

[tex]QR=3x+3=3(4)+3=12+3=15[/tex]**Answer: QR = 15**

Find the exact value of the indicated trigonometric function of θ.

cos θ = (2/5), tan θ < 0 Find sin θ.

The exact value of indicated **trigonometric function**, sin θ is -0.92

The **sine relation** is the ratio of the height to the hypotenuse. Meanwhile, the **cosine relation **is the ratio of the base to the hypotenuse.

The **relation of sine and cosine** is given as follows:

[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}[/tex]

It is given that cos θ = (2/5)

So, the **sine value** can be obtained from the given value.

[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}\\=\pm\sqrt{1-(2/5)^2}\\=\pm\sqrt{21}/5\\ =-0.92[/tex]

So, the **sine value** for the given **cosine value** is - [tex]\sqrt{21}/5[/tex] or -0.92.

Note that we omitted the positive value because it is given that **the tangent value** is negative, so the angle lies in the fourth quadrant, where **the sine value** is also negative.

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HELP ASAP 100 POINTS!!!!!!!!!

The points (6,2) and (10,4) fall on a particular line. What is its equation in point-slope form?

Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

**Answer:**

[tex]y-2=\dfrac{1}{2}(x-6)[/tex]

**Step-by-step explanation:**

To find the **equation **of a** line** that passes through two given **points**, first find its **slope **by substituting the given points into the **slope formula**.

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Define the points:

(x₁, y₁) = (6, 2)(x₂, y₂) = (10, 4)**Substitute** the points into the **slope formula**:

[tex]\implies m=\dfrac{4-2}{10-6}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Therefore, the **slope **of the line is ¹/₂.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

To find the **equation **in **point-slope form**, substitute the found **slope **and one of the given **points **into the **point-slope formula**:

[tex]\implies y-2=\dfrac{1}{2}(x-6)[/tex]

HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS

**Answer:**

**Step-by-step explanation:**

h = number of hours

s = number of shirts made

28h+2s=144

4h=s

h=4, s=16

(Didn't I already answer this? i think i might have.. lol)

For each relation, decide whether or not it is a function.

Relation 1: No, the inputs of desk and leaf each correspond to two different outputs.

Relation 2: No, the input of 7 corresponds to three different outputs.

Relation 3: Yes, each input corresponds to only one output.

Relation 4: No, the input of -7 corresponds to two different outputs: a and h.

Helppppp please !!!

Both sides of the coordinate plane are both clearly different from each other.

The left side of the coordinate plane has the coordinates, -3:3, -4:1, -2:-1, and -2:2.

To be more specific, the coordinates above are in order ABCD.

The right side is also in order of ABCD. 3:2,0:4, 2:-2, and 2:1. Both sides are both very different from each other, in other words, the right side is lower then the left. :)

Hope this helps!

The left side of the coordinate plane has the coordinates, -3:3, -4:1, -2:-1, and -2:2.

To be more specific, the coordinates above are in order ABCD.

The right side is also in order of ABCD. 3:2,0:4, 2:-2, and 2:1. Both sides are both very different from each other, in other words, the right side is lower then the left. :)

Hope this helps!

1) Movie Checkout for the week Days 2 3 4 A. 10 How many movies were checked out on Day 1? Number of Movies 30 45 60 C. 20 B. 15 D. 25

B. 15 because this is a ratio box

15 movies.

Subtract day 4 from day 3 and you get 15

Subtract day 3 from day 2 and you get 15

Every day fifteen more movies are sold that the last, so to find the first you would need to subtract day 2 by 15

30 - 15 = 15

This would only work if the graph is proportional, meaning the increase or decrease is the same for every day.

Subtract day 4 from day 3 and you get 15

Subtract day 3 from day 2 and you get 15

Every day fifteen more movies are sold that the last, so to find the first you would need to subtract day 2 by 15

30 - 15 = 15

This would only work if the graph is proportional, meaning the increase or decrease is the same for every day.

what number is not part of the solution set for the inequality below?3x-18> 1210, 11, 15,8 _

First, let's solve for x in the inequality to find an interval, the options that are not included in the interval are not part of the solution set, we can do it by following these steps:

1. 3x-18> 12 , add 18 on both sides:

3x - 18 + 18 > 12 + 18

3x > 30

2. Divide both sides by 3:

3x/3 > 30/3

x > 10

So, to be a part of the solution, x must be greater than 10, then the interval that represents the solution is (10, ∞). From the given options, the only one that is not included in this interval is 8, because it is less than 10, then **the answer is 8.**

In the figure above, if k II I, what is the value of y?

B. 45

C. 50

A. 40

D. 60

The values of measure of** angle y** is found as **65 degrees**.

For the given question;

Line k || Line l

(x + 5) + (3x + 15) = 180 (linear pair)

Solving;

4x + 20 = 180

4x = 160

x = 40

Put the value of x in angles (2x + 30)

2x + 30 = 2×40 + 30 = 110

Now,

2x + 30 = y + (x + 5) (**alternate interior** **angles**)

Solving;

110 = y + 40 + 5

y = 110 - 45

y = 65 degrees.

Thus, the values of measure of** angle y** is found as 65 degrees.

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What is a rule for the nth term of Geometric sequence -3,-6,-12,-24,-48

The sequence is given as,

[tex]-3,\text{ -6, -12, -24, -48.......}[/tex]For the given sequence,

[tex]\begin{gathered} First\text{ term\lparen a\rparen = -3} \\ Common\text{ ratio\lparen r\rparen = }\frac{-6}{-3}=\text{ 2} \end{gathered}[/tex]nth term of a geometric progression is given as,

[tex]a_n\text{ = ar}^{n-1}[/tex]Where,

a = First term

r = common ratio

Therefore the nth term is calculated as,

[tex]a_n=\text{ -3\lparen2\rparen}^{n-1}[/tex]Thus the required answer is,

[tex]a_n=\text{ -3\lparen2\rparen}^{n-1}[/tex]1 5/6+1 3/6 pls help

**Answer:**

10/3

**Step-by-step explanation:**

[tex]1\frac{5}{6} = \frac{11}{6}\\ \\\ 1\frac{3}{6} = \frac{9}{6}[/tex]

11/6 + 9/6 = 10/3 =3.333333333

Write the exponential function y - 45(1.085)^t in the form y = ae^kt(a) Once you have rewritten the tormula, give & accurate to at least four decimal places.K=If T is measured in years, indicate whether the exponential function is growing or decaying and find he annual and continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing decay the negative rate is implied).(b) The annual (growth/decay) rate is ___ % per yearC) The continuous (growth/decay) rate is ___ % per year

**EXPLANATION**

Given the exponential function:

45(1.085)^t

We have that 45=a is the initial value and 1.085 is the growth rate,

1.085 - 1 = 0.085* 100 = 8.5 % (This is the growth rate)

Let's compute the function with two values of t, as for instance, t=0 and t=1:

[tex]f(0)=45(1.085)^0=45\cdot1=45\longrightarrow\text{ (0,45)}[/tex][tex]f(1)=45\cdot(1.085)^1=48.825\text{ }\longrightarrow\text{(1,48.825)}[/tex]Now, the function in the form y = ae^kt will be as follows:

[tex]y=45\cdot e^{kt}[/tex]Substituting t by 1:

[tex]y(1)=45\cdot e^k=48.825[/tex]Dividing both sides by 45:

[tex]e^k=\frac{48.825}{45}=1.085[/tex]Applying ln to both sides:

[tex]k=\ln 1.085[/tex]Computing the argument:

[tex]k=0.0816[/tex]The expression will be as follows:

[tex](a)---\longrightarrow y=45e^{0.0816t}[/tex]As this is a **growing function**, the **rates are positive**.

The annual growth rate is **8.5%** and It's was calculated above.

Now, we need to compute the continuous rate because It's given by the value of k:

k = 0.0816 --> Multiplying by 100 --> 0.0816 * 100 = 8.16%

The continuous growth rate is **8.16%**

Express 55 miles per hour in kilometers per hour.km/hr(Round to the nearest whole number as needed.)

Okay, here we have this:

Considering the provided amount in miles per hour, we are going to convert it to kilometers per hour, so we obtain the following:

[tex]\begin{gathered} \frac{55mi}{h}\cdot\frac{1.6km}{1mi} \\ =\frac{55\cdot1.6km}{h} \\ =88\frac{\text{ mi}}{h} \end{gathered}[/tex]**Finally we obtain that 55 miles per hour are equivalent to 88 kilometers per hour.**

Which situation yields data with variability?The distance covered by different vehicles traveling at a constant rate of 60 mph for 45 minutes The length of different professional American football fieldsThe weight of 6th grade studentsThe moon cycle duration in a year

**Answer:**

**The weight of 6th-grade students**

**Explanation:**

We have variability if each value in the data is different.

When a vehicle travels at a constant rate for the same amount of time, the distance covered will be always the same. So, this situation doesn't yield data with variability.

In the same way, the length of a professional American football field and the moon cycle duration in a year are standard, they always have the same value so these situations don't yield data with variability.

Finally, each student of 6th grade has a different weight, so this is the situation that yields data with variability.

Therefore, the answer is:

The weight of 6th-grade students

The variable cost for a product is $1.00 and the total fixed costs are $88,000. The company sells the products for $3.00 each. How many products will the company have to sell to break even?

The breakevenpoint is the point at which costs and sales are equal to each other and therefore, the profit is zero.

The breakeven point in terms of number of units sold can be determined as follows;

[tex]\begin{gathered} Breakeven\text{ units=}\frac{Fixed\text{ costs}}{\text{ Selling price per unit-}Variable\text{ cost per unit}} \\ \text{Breakeven units=}\frac{88000}{3-1} \\ \text{Breakeven units=}\frac{88000}{2} \\ \text{Breakeven units=44000} \end{gathered}[/tex]In order to breakeven, the company will have to sell 44,000 units

A manufacturing machine has a 4% defect rate.

If 9 items are chosen at random, what is the probability that at least one will have a defect?

The **probability **that at least one will have a defect is** 19%.**

What is probability?

Simply put, **probability **is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. **Statistics **is the study of events that follow a **probability distribution**.

By simply dividing the favorable number of **possibilities **by the entire number of possible outcomes, the **probability **of an occurrence can be determined using the **probability formula**.

**p = 4% = 0.04**

q = Prob of a defective product is 0.03; hence, **Prob(non-defective)** = 1 - 0.04 = 0.96.

**Prob**(at least one flaw) is now equal to 1 - Prob (0 defects)

= 1 - 9C0 x 0.04^0 x 0.96^9

= 1 - 1 x 1 x 0.815

**= 0.19 or 19%**

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Which term describes the slope of the line below?

•

A. Undefined

B. Zero

• C. Positive

D. Negative

**Answer: **

**D. Negative**

**Step-by-step explanation:**

The slope is negative because the line goes down from left to right. In other words, as x increases, y decreases.

A slope would be positive when the line goes up from left to right. In other words, as x increases, y increases.

A slope would be zero if the line is horizontal, so as x increases, y remains constant.

A slope would be undefined if the line is vertical. It is undefined because x remains constant while y changes. Lines are functions, which mean for every input there is exactly 1 output. If there are multiple y values for 1 x value, then this is not a function and therefore has an undefined slope.

(a) Give a secant line.(b) Give a chord.(c) Give a tangent line.

Solution

Secant is a line that touches a circle at two distinct points

See figure below

Chord is a straight line that touches two points on the the circumference of the circle

A

Find the intercepts (if an answer does not exist enter DNE) be sure to graph the line as well

**Question:**

**Solution:**

**x-intercept:**

the x-intercept is when y= 0. Thus replacing this value into the given equation we get:

[tex]15x+10(0)\text{ = 30}[/tex]this is equivalent to:

[tex]15x+0\text{= 30}[/tex]this is equivalent to:

[tex]15x\text{ = 30}[/tex]solving for x, we get:

[tex]x\text{ = }\frac{30}{15}\text{ = 2}[/tex]so the point of **x-interception is :**

**y-intercept:**

the y-intercept is when x= 0. Thus replacing this value into the given equation we get:

[tex]15(0)+10y=30[/tex]this is equivalent to:

[tex]0\text{ + 10y = 30}[/tex]this is equivalent to:

[tex]10y\text{ = 30}[/tex]solving for y, we get:

[tex]y\text{ = }\frac{30}{10}=\text{ 3}[/tex]so the point of **y-interception is :**

We can conclude that **the correct answer is:**

**x-intercept :**

**y-intercept is :**

(d) Find the domain of function R. Choose the correct domain below.

**Answer:**

d

**Step-by-step explanation:**

Since the number of years must be non-negative, we can eliminate all the options except for d.

help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

**Answer:**

55.17

**Step-by-step explanation:**

[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]

(d) Find the domain of function R. Choose the correct domain below.

Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

Are the following ratios equivalent?5cookies:9 glasses of milk and 3 cookies :12 glasses of milk

**Answer:**

No

**Step-by-step explanation:**

5:9 and 3:12 do not divide with the same number

For example:

3:6 and 9:18 would be equivalent as dividing 9:18 by 3 would give 3:6

What is the rate of return when 12 shares of Stock

A, purchased for $22/share, are sold for $465? The

commission on the sale is $9.

Rate of Return = profit or loss

total cost

First, calculate the total cost.

Hint: 12 shares were purchased for $22

each. So first, we'll multiply 12 - 22.

12- $22= $[?]

The** rate of return** of the 12 shares purchased by A is 72.72%.

Here, we are given that A purchases 12 shares at $22 per share.

So the cost price of 12 shares will be = 12 × 22

= 264

A sold these shares at $465.

The commission on sale = $9.

Thus, the** total cost** of the shares will be = 264 + 9

= $273

Hence, the **total profit** of A will be-

465 - 273

= 192

The rate of return is calculated as-

Rate of return = profit/cost price × 100

Thus, here-

Rate of return = 192/264 × 100

= 0.7272 × 100

= 72.72%

Thus, the** rate of return** on these 12 shares purchased by A is 72.72%.

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3. How many tens are there between 9,312 and 9,522? Explain your thinking

The number of **tens **between the given **numbers** are 1883.

The **number** of tens between two numbers can be calculated by the concept of **proportions**. A proportion is a **fraction** of a total amount, and the measures are related using a rule of three. Due to this, relations between **variables**, either direct or **inverse** proportional, can be built to find the desired measures in the problem. Now, to find the number of tens we **divide** the number by 10. So, the number of tens in the given numbers are

9312/10 = 931 (approximately)

9522/10 = 952 (approximately).

Now, the numbers of** tens **between the two given numbers can be calculated by adding the number of tens in them that is,

952 + 931 = 1883 tens between the two **numbers**.

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Please Answer the following 2 questions asked in the image provided, Asap.

1 Fristly you do M1=M2 as it is parallel

You get M2 then use it to find equation

note that y= -1.5

2 for second question you find coefficient of X and y you get M1 then find equation of given line easily.

#note equaction of straight line passing through two points is y-y1=m(x-x1)

Write in terms of the cofunction of a complementary angle.

given the expression

[tex]sin(\frac{\pi}{15})[/tex]since

[tex]sin(\theta)=\frac{1}{csc(\theta)}=cos(\frac{\pi}{2}-\theta)[/tex]then

[tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{\pi}{2}-\frac{\pi}{15})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{(15-2\pi)}{30})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=cos(\frac{13\pi}{30})[/tex]ten the correct answer is

**Option C**

Your grandmother was in the hospital and was put on a liquid diet. After examining her chart, a mistake was found stating that her weight was 500 kg. The dietician decided my grandma weighed too much and put her on a liquid diet. How much did they believe that she weighed in pounds? (Show all work using dimension analysis, round to nearest whole pound)

Your grandmother was in the hospital and was put on a liquid diet. The approximate **weight **of grama in pounds is 1100 **pounds**

This is further explained below.

What is the conversion?Generally, Simply rephrasing the query as "what is the **equivalent **of 500 kg in **Pounds**" will accomplish the same thing.

In order to do this, we need to know how many **kilograms **are in one pound: It weighs something about 2.2 pounds.

Therefore, one hundred and ten kilograms is equal to five hundred and two point two **pounds **(and a little more since one kg is a little more than 2.2 **pounds**).

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i only need help with 12 & 13 only and show work please. note the picture is sideways

**Answer:**

12. 65:6 = 65/6 = 65 to 6

13: 21:4 = 21/4 = 21 to 4

**Step-by-step explanation:**

You want the numerical values of the given **ratios of blood donors** **written three ways**.

In each case, replace the blood type with the corresponding number of donors. Ratios can be written using a colon, a division bar, or the word "to".

12. A+ and B+ to AB+Using the numbers, this is ...

(45 +20) : 6 = **65 : 6 = 65/6 = 65 to 6**

Using the numbers, this is ...

(21 +0) : 4 = **21 : 4 = 21/4 = 21 to 4**

I have a question for quantitative reasoning. Alcohol use by high school seniors in a certain state decreased from 50.3% in 2000 to 32.7% in 2015. Describe this change as an absolute change in terms of percentage points and as a relative change in terms of a percentage.

**The **of **senior high school** students who reported consuming alcohol is mathematically given as

33.99% o**f**

This is further explained below.

WhatAbsolute change is the straightforward **difference **between the indicator's two time periods.

Absolute change = final value - initial value

Absolute change =(33 *1-50.3)% points

=-17.2% points

Decrease absolute change $=17.2% point

- ve hours decreased

+ve shows increased

The percentage of high school seniors using **alcohol **decreased by 17.2%. point

Relative change expresses absolute change as the ax of the value in the initial period

[tex]$=\frac{\text { absolute change }}{\text { intial value }} \times 100$$=\frac{33.1-50.3}{50.3} \times 100$[/tex]

=-33.99 %

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A pole that is 3.1 m tall casts a shadow that is 1.46 m long. At the same time, a nearby tower casts a shadow that is 38.5your answer to the nearest meter.long. How tall is the tower RoundIM

**82 meters**

**Explanation**

**Step 1**

Draw:

as the angle of the sun´s ligth is the same for both, we have two congruent trianges, then we can make a proportion

[tex]\text{ratio}=\frac{heigth}{\text{shadow}}[/tex]so

[tex]\begin{gathered} \text{ratio}_1=ratio2 \\ \text{replacing} \\ \frac{3.1}{1.46}=\frac{x}{38.5} \\ to\text{ solve, multiply both sides by 38.5} \\ \frac{3.1}{1.46}\cdot38.5=\frac{x}{38.5}\cdot38.5 \\ 81.74\text{ m=x} \\ \text{rounded} \\ x=82 \end{gathered}[/tex]therefore, the heigth of the tower is

**82 meters**

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