What is the domain and the range for this graph

\(\angle PYZ=116^{\circ}\) (angles on a line add to 180 degrees)

\(\angle ZYQ=58^{\circ}\) (angle bisector)

\(\angle XYQ=122^{\circ}\) (angle addition postulate)

\(\angle QYP=58^{\circ}\) (angle bisector)

Reflex \(\angle QYP=302^{\circ}\) (an angle and its reflex angle add to 360 degrees)

Answer:

x = 3

y = 1/2

Step-by-step explanation:

\( {9}^{2y} \times {2}^{x} = 72 \\ \\ {9}^{2y} \times {2}^{x} = 9 \times 8 \\ \\ {9}^{2y} \times {2}^{x} = {9}^{1} \times {2}^{3} \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ {2}^{x} = {2}^{3} \\ \red { \bold{\implies x = 3}} \\ \\ {9}^{2y} = {9}^{1} \\ \implies \: 2y = 1 \\ \purple{ \bold{\implies \: y = \frac{1}{2} }}\)

Step-by-step explanation:

good..............................

Answer:

Yes

Step-by-step explanation:

So quadratic formulas help

The length of the hypotenuse is approximately 30.8 units.

The angle at vertex X is approximately 36.9 degrees.

The angle at vertex Y is approximately 35.2 degrees.

In your problem, we have a right triangle XYZ, where the angle at vertex Y is the right angle. The length of leg YZ is given as 18 units, and the length of leg XZ is given as 25 units.

In this particular problem, we can use the sine ratio to solve for the length of leg XY. Specifically, we have:

sin(XYZ) = XY / XZ

Since we know that XYZ is a right angle (i.e., 90 degrees), we can substitute in the appropriate values to get:

sin(90) = XY / 25

Since the sine of 90 degrees is 1, we can simplify this to:

1 = XY / 25

Multiplying both sides by 25 gives us:

XY = 25

So the length of leg XY is 25 units.

To find the other angles in the triangle, we can use the inverse trigonometric functions (such as arcsine or arccosine). For example, we can use the cosine ratio to solve for the angle at vertex X:

cos(XYZ) = XZ / hypotenuse

cos(90) = 25 / hypotenuse

0 = 25 / hypotenuse

Since the cosine of 90 degrees is 0, we know that hypotenuse = 25 / 0 is undefined. However, we can use the Pythagorean theorem to find the length of the hypotenuse:

hypotenuse² = XY² + XZ²

hypotenuse² = 25² + 18²

hypotenuse² = 625 + 324

hypotenuse² = 949

Taking the square root of both sides gives us:

hypotenuse = √(949) ≈ 30.8

Now that we know the lengths of all three sides of the triangle, we can use the sine and cosine ratios to solve for the other angles. For example, to find the angle at vertex X, we can use the cosine ratio:

cos(X) = XZ / hypotenuse

cos(X) = 25 / 30.8

cos(X) ≈ 0.811

Taking the inverse cosine (or arccosine) of both sides gives us:

X ≈ 36.9 degrees

Similarly, we can use the sine ratio to find the angle at vertex Y:

sin(Y) = YZ / hypotenuse

sin(Y) = 18 / 30.8

sin(Y) ≈ 0.584

Taking the inverse sine (or arcsine) of both sides gives us:

Y ≈ 35.2 degrees

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It will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute

Assuming that the filling rate of the hose is constant, we can use the formula:

time = volume / rate

where time is the time taken to fill the hot tub, volume is the volume of the hot tub (440 gallons), and rate is the filling rate of the hose (4.6 gallons per minute).

Substituting the values, we get:

time = 440 / 4.6

which simplifies to:

time = 95.65 minutes

To convert minutes to hours, we divide by 60 (since there are 60 minutes in an hour):

time = 95.65 / 60

which simplifies to:

time = 1.59 hours

Therefore, it will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute.

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It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.

To determine how many hours follow these steps:

First, we need to find out how many minutes it takes to fill the hot tub.

Divide the total volume of the hot tub (440 gallons) by the rate at which the hose fills (4.6 gallons per minute):

440 gallons ÷ 4.6 gallons/minute = 95.65 minutes

Now, we need to convert the minutes into hours.

Since there are 60 minutes in an hour, divide the minutes by 60:

95.65 minutes ÷ 60 minutes/hour = 1.594 hours

It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.

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The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Solve for x.

3 < -5x + 2x

3 < -3x

Divide both sides by 3.

1 < -x

Change sign.

x < -1

18 ≥ 5x  + 4x

18 ≥ 9x

Divide both sides by 9.

2 ≥ x

-6x - 16 < 2x

Add 16 on both sides.

-6x < 2x + 16
Subtract 2x on both sides.

-6x - 2x < 16

-8x < 16

Divide both sides by 8.

-x < 2

Change sign.

x > -2

(1/2)x - 4 > -4

1/2x > -4 + 4

1/2x > 0

x > 0

Code = 4776

Thus,

The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

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Recall that the interior angles of a triangle add up to 180 degrees, then:

Now, recall that a right angle measures 90 degrees.

Then we can set the following equation:

Adding like terms we get:

Subtracting 105 degrees from the above equation we get:

Answer:

The Mean of the dispersion of z-scores will be 0, and the standard deviation will be 1. 

On the off chance that all of the scores within the populace are changed into z-scores, at that point the coming about the conveyance of z-scores will have a cruel (mean) of and a standard deviation of 1.

Usually, since the change of a crude score x to a z-score is given by:

z = (x - μ) / σ

where μ is the populace Mean.

and σ is the populace standard deviation.

When all scores within the populace are changed to z-scores, the Mean of the coming about dispersion of z-scores will be:

( Mean of z-scores)

= [(Mean  of crude scores) - μ] / σ

= (μ - μ) / σ =

So also, the standard deviation of the dissemination of z-scores will be:

(standard deviation of z-scores) = (standard deviation of crude scores) / σ = σ / σ = 1

In this manner,

The cruel of the dispersion of z-scores will be 0, and the standard deviation will be 1. 

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If all of the scores in the population are transformed into z-scores, the values for the mean and standard deviation for the complete set of z-scores will be a mean of 0 and a standard deviation of 1.

This is because the process of transforming scores into z-scores involves subtracting the mean of the population and dividing by the standard deviation, which effectively standardizes the data to have a mean of 0 and a standard deviation of 1. When all the scores in a population are transformed into z-scores, the mean of the complete set of z-scores will be 0 and the standard deviation will be 1. This is because z-scores represent the number of standard deviations a value is from the mean, and the transformation standardizes the distribution.

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Answer:

30.5

Step-by-step explanation:

35/2 is 17.5 add 13 is 30.5

Answer:

\(35 \div 2 + 13 \\ = 17.5 + 13 \\ = 30.5\)

Answer:

Kai is correct and Leila is incorrect. The movie is actually 10,800 seconds long.

Step-by-step explanation:

1 hour = 60 minutes

1 minute = 60 seconds

Therefore, 1 hour = 60 x 60 = 3600 seconds

So, the movie's length in seconds is:

3 hours x 3600 seconds/hour = 10,800 seconds

Leila says the movie is less than 10,000 seconds, which is not correct, since the movie is actually longer than 10,000 seconds.

Kai says the movie is more than 10,000 seconds, which is correct.

Answer:

After solving we get (f.g)(5)=-115

But the correct option is not given in the question.

Step-by-step explanation:

We are given:

\(f(x) = 4x+3\\g(x)=-2x+5\)

We need to find (f.g)(5)

First we will multiply f and g to find (f.g) i.e

\((f.g)(x)= f(x) \times g(x)\\(f.g)(x) = (4x + 3)(-2x + 5)\\(f.g)(x)=4x(-2x+5)+3(-2x+5)\\(f.g)(x)=-8x^2+20x-6x+15\\(f.g)(x)=-8x^2+14x+15\\\)

Now putting x=5

\((f.g)(x)=-8x^2+14x+15\\Put \ x=5\\(f.g)(5)=-8(5)^2+14(5)+15\\(f.g)(5)=-8(25)+70+15\\(f.g)(5)=-200+70+15\\(f.g)(5)=-115\)

So, after solving we get (f.g)(5)=-115

But the correct option is not given in the question.

The limits are important in calculus and mathematical analysis and can be used to define integrals, derivatives and continuity. The limit of the given function is 4.

In mathematics, the limit is defined as the value that a function approaches the output for the given input values. It is used in the analysis process and it always concerns about the behaviour of the function at a particular point.

The upper and lower limits are used to define the definite integrals whereas the indefinite integrals are defined without using the limits and it have an arbitrary constant while integrating the function.

The limit of the given function is:

limₓ → -1  (2x² + 3x + 5)

(2 × (-1)² + 3 × (-1) + 5)

(2 × 1 + (-3) + 5) = ( 2 - 3 + 5)

= 4

So the limit of the given function is 4.

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Your question is incomplete most probably your full question was:

Evaluate the given limit lim ₓ → -1  (2x² + 3x + 5)

(a) We can represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel as f(24.9).

(b) We can represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel as f(49.71).

(a) We have to determine how can we represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel.

We can create the a table and function to describe that statement but F(24.9) is the best representation of Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel.

(b) We have to determine how can we represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel.

We can create the a table and function to describe that statement but F(49.71) is the best representation of Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel.

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The complete question is:

In the previous modules we developed formulas, tables, and graphs to represent how two varying quantities change together. For example, we considered how Kristin's height above the ground changed as her total distance traveled increased while riding a Ferris wheel.

We even assigned letters to represent the possible varying values each quantity can assume.

• Let d represent the distance Kristin has traveled (in meters) around the Ferris wheel starting at the bottom.

• Let h represent Kristin's height above the ground (in meters).

Note that the way we are thinking about this relationship is that we vary Kristin's distance traveled and observe what happens to her height above the ground.

What if you want to communicate information about her position after she traveled some number of feet? You could write it out in words, like "Kristin was 16.3 meters above the ground when she had traveled 23.7 meters around the Ferris wheel". However, that's a lot to have to write out, especially if you want to talk about multiple values. You could also draw a table or create a graph, but mathematicians developed a tool called function notation to help them represent values in a covarying relationship.

[Note: We will define the exact meaning of "function" later in this investigation. For now, just think of "function" as meaning the same thing as "relationship".]

First, we pick a letter to represent the name of the relationship. Let's call this relationship "f". Now, instead of saying "the relationship between Kristin's height above the ground (in meters) and her total distance traveled (in meters)" we can simply say "relationship f".

Also, we can use f(d) to represent values of Kristin's height above the ground (values of h). We read this as "f of d", and the parentheses here are just part of the notation. They do NOT indicate multiplication.

For example, f(13) represents Kristin's height above the ground (in meters) when she has traveled 13 meters around the Ferris wheel.

a. How can we represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel?

(Hint: you should use function notation.) Preview syntax error Enter an algebraic expression (more..]

b. How can we represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel? x Preview

If a 10 percent cut in price causes a 15 percent increase in sales, then it is likely that the product has an elastic demand. This means that customers are highly responsive to changes in price and are willing to purchase more of the product when it is cheaper.

In this scenario, the decrease in revenue from the price cut may be offset by the increase in sales volume. However, it is important to consider the potential long-term effects on the product's brand value and profitability.

If a 10 percent cut in price causes a 15 percent increase in sales, then:

1. Calculate the new price after the 10 percent cut:
New price = Original price x (1 - 0.10)

2. Calculate the new quantity sold after the 15 percent increase in sales:
New quantity sold = Original quantity sold x (1 + 0.15)

In this scenario, the price elasticity of demand is greater than 1, indicating that the product has elastic demand. This means that a decrease in price will result in a proportionally larger increase in quantity demanded, leading to higher revenue for the seller.

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Cases (iii) and (iv) are left as exercises, meaning the proof for those cases is not provided in the given information. To fully establish the Characterization Theorem, the proof for these remaining cases needs to be completed.

Theorem 2.5.1 (Characterization Theorem):

If S is a subset of R that contains at least two points and has the property that if x, y ES and x < y, then (x, y)C S, then S is an interval.Proof.

There are four cases to consider:

(i) S is bounded,

(ii) S is bounded above but not below,

(iii) S is bounded below but not above, and

(iv) S is neither bounded above nor below.

Case (i): Let a = inf S and b = sup S.

Then SC[a, b] and we will show that (a, b)C S. If a < z < b, then there exist x, y

ES such that x < z < y. Since x < y and S has property (1), we have (x, y)C S.

Since zEP(x, y), it follows that zES.

Thus (a, b)C S.

Now if a S and b S, then S =[a, b].

If a S and b S, then S=(a, b).

The other possibilities lead to either S = (a, b) or S = [a, b].

Case (ii): Let b = sup S.

Then SC (-[infinity]o, b] and we will show that (-oo, b)C S. For, if z < b, then there exists y

ES such that z < y < b.

Since b is the least upper bound of S and yES, it follows that y 6S. But then (z, y)C (-oo, b) and (z, y)C S.

Thus (-oo, b)C S. Now if S contains its smallest element a, then S = [a, b]. Otherwise, S=(a, b).

Cases (iii) and (iv) are left as exercises.

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Answer: 28282

Step-by-step explanation:

I think

Answer:

-1 1/2 if you need a mixed number then choose -1 1/2

Answer: There are many possible fractions, here is all of them.

-3/2 = -6/4 = -9/6 = -12/8

= -15/10 = -18/12 = -21/14 = -24/16

= -27/18 = -30/20 = -33/22 = -36/24

= -39/26 = -42/28 = -45/30 = -48/32

= -51/34 = -54/36 = -57/38 = -60/40

= -63/42 = -66/44 = -69/46 = -72/48

= -75/50 = -78/52 = -81/54 = -84/56

= -87/58 = -90/60 = -93/62 = -96/64

= -99/66 = -102/68 = -105/70 = -108/72

= -111/74 = -114/76 = -117/78 = -120/80

= -123/82 = -126/84 = -129/86 = -132/88

= -135/90 = -138/92 = -141/94 = -144/96

= -147/98 = -150/100 = -153/102 = -156/104

= -159/106 = -162/108 = -165/110 = -168/112

= -171/114 = -174/116 = -177/118 = -180/120

= -183/122 = -186/124 = -189/126 = -192/128

= -195/130 = -198/132 = -201/134 = -204/136

= -207/138 = -210/140 = -213/142 = -216/144

= -219/146 = -222/148 = -225/150 = -228/152

= -231/154 = -234/156 = -237/158 = -240/160

= -243/162 = -246/164 = -249/166 = -252/168

= -255/170 = -258/172 = -261/174 = -264/176

= -267/178 = -270/180 = -273/182 = -276/184

= -279/186 = -282/188 = -285/190 = -288/192

= -291/194 = -294/196 = -297/198 = -300/200

Step-by-step explanation:

If you have any questions feel free to ask

The function for the given compound interest will be A = 3000(1+6/4)  and A = 5000(1+7.2)  .

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate is raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

$3000 deposit that earns 6% annual interest compounded quarterly.

A = P (1 + r/4)4

A = 3000(1+6/4)

$5000 deposit that earns 7.2% annual interest compounded monthly.

A = P (1 + r)

A = 5000(1+7.2)  

Hence the function for the given compound interest will be A = 3000(1+6/4)  and A = 5000(1+7.2)  .

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Answer:

4.5

so I did 9 /2 = 4.5

Answer:

4.5 or 9/2 or 4 1/2

Step-by-step explanation:

You divide 9 by 2, to get 4.5 in number form. 9/2 for improper fraction form and 4 1/2 for whole number fraction.

No , we cannot have a triangle with 2cm , 3cm and 5cm , because the sum of two sides is not greater than the other sides .

What is a Triangle ?

A triangle can be defined as the closed figure , that is made up of three line segments .

The Condition for any three sides to form a triangle : the sum of any two sides of triangle should be greater than the third side .

The sides of triangle are given to be : 2cm , 3cm and 5cm ;

on adding the two sides ,

we get ;

⇒ 2 + 3 = 5 > 5 ; False

⇒ 3 + 5 = 8 > 2 ; True

⇒ 2 + 5 = 7 > 3 ; True

All the conditions are not met ,

Therefore , the given sides cannot form a triangle .

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Answer:

Approximately \(0.032\) (or, equivalently, \(3.2\%\),) assuming that the availabilities of the \(12\) jurors are independent from one another.

Step-by-step explanation:

The question states that the probability that a given juror is unavailable is approximately \(0.25\).

For the complement of that event, the probability that this particular juror is available would be \(1 - 0.25 = 0.75\).

Assume that the availabilities of the \(12\) jurors are independent from one another. The number of available jurors would be a binomial variable with \(n = 12\) and \(p = 0.75\) (\(12\!\) independent observations, each with a \(0.75\) probability of being "available".)

Hence, the probability that all \(12\) jurors are available would be:

\((0.75)^{12} \times (0.25)^{0} \approx 0.032 = 3.2\%\).

A 24-hour clock will read:

To determine the time on a 24-hour clock after a certain number of hours, we can use modular arithmetic.

(a) 100 hours after the clock reads 2:00:

To find the time, we add 100 hours to 2:00 and take the result modulo 24 (to account for the 24-hour cycle):

Time = (2 + 100) mod 24 = 102 mod 24 = 6

(b) 45 hours after the clock reads 12:00:

Similarly, we add 45 hours to 12:00 and take the result modulo 24:

Time = (12 + 45) mod 24 = 57 mod 24 = 9

(c) 168 hours after the clock reads 19:00:

Again, we add 168 hours to 19:00 and take the result modulo 24:

Time = (19 + 168) mod 24 = 187 mod 24 = 19

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The researcher should use a sample size of approximately 312 middle school students to conduct the research.

To determine the sample size needed for the researcher to create a 95% confidence interval with a margin of error of 0.5 days, we can use the formula:

\(\[ n = \left(\frac{Z \cdot \sigma}{E}\right)^2 \]\)

Where:

- \(\( n \)\) is the sample size

- \(\( Z \)\) is the z-score corresponding to the desired confidence level (for 95% confidence, Z is approximately 1.96)

- \(\( \sigma \)\) is the known standard deviation of the population

- \(\( E \)\) is the desired margin of error

Plugging in the values, we get:

\(\[ n = \left(\frac{1.96 \cdot 4.5}{0.5}\right)^2 \]\)

To solve the equation for the required sample size, we can substitute the given values into the formula:

\(\[ n = \left(\frac{1.96 \cdot 4.5}{0.5}\right)^2 \]\)

Calculating this expression gives us:

\(\[ n = \left(\frac{8.82}{0.5}\right)^2 \]\)

\(\[ n = (17.64)^2 \]\)

\(\[ n \approx 311.1696 \]\)

Therefore, the researcher should use a sample size of approximately 312 middle school students to conduct the research.

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Answer:

2.  43 degrees

3.  35 degrees

Step-by-step explanation:

Srr the attached worksheet.

Answer:

The linear equation to represent the amount of money m that Mark has earned this summer after working h hours at the grocery store is:

Step-by-step explanation:

Mark has already earned some amount x. Lets find it using the number of hours worked and the total amount after this:

This amount represents an initial value or the y-intercept of the line and the payment per hour represents the slope of same line.

We know the equation of line in slope-intercept form:

Plug in the values and variables to get the linear equation for the earned amount:

Mark's m earned this summer after working h hours at the grocery store is represented by the linear equation: m = 9.5h + 140.

Given

Earning per hour = $9.50,

Worked hours = 16,

Total earning = $292,

Mark has earned some amount initially for mowing lawns.

Linear equation of amount of money m after working h hours

Mark has already earned some amount x.

Lets find it using the number of hours worked and the total amount after this:

16 × 9.50 + x = 292

Simplifying the above equation then we get,

152 + x = 292

x = 292 - 152

x = 140

This amount represents the line's initial value or y-intercept, and the payment per hour represents the slope of the same line.

The slope-intercept equation of a line is as follows:

y = mx + b, where y is the line, m is the slope, and b is the y-intercept

To obtain the linear equation for the earned amount, enter the values and variables as follows:

∴ m = 9.5h + 140

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Answer:

the equation doesn't have z as an exponent so i can't answer it

Step-by-step explanation:

Z = 5/8

-3 = 2 - 8z

-3= -8z +2

Solution

To write r > -10/3 on a number line,

Step 1: Draw a number line and include -10/3 on it

Step 2: Draw an arrow to the right with the small circle at its initial