21. You are placing a circular drawing on a square piece of poster board. The poster board is 15 in wide. The part of the poster board not covered by the the function drawing will be painted blue. If the radius of the drawing is r, A = 225 - 3.14r^2 gives the area to be painted blue.
a. Graph the function.
b. What x-values make sense for the domain? Explain why.
c. What y-values make sense for the range? Explain why​
(i need help)

Answer:

x = 4√5 ≈ 8.94 (2 d.p.)

y = 8√5 ≈ 17.89 (2 d.p.)

Step-by-step explanation:

To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.

[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]

From inspection of the given right triangle RST:

Substitute the values into the formulas:

[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]

Solve the equation for x:

[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]

[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]

[tex]\implies 80=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]

[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]

[tex]\implies x=4\sqrt{5}[/tex]

Solve the equation for y:

[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]

[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]

[tex]\implies 320=y^2[/tex]

[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]

[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]

[tex]\implies y=8\sqrt{5}[/tex]

The measure of angle A and B is 29° and 61° respectively

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

tan(tetha) = opp/adj

cos(tetha) = adj/hyp

The opposite is 6 and the adjascent = 11

Therefore tan (tetha) = 11/6 = 1.833

tetha = tan^-1( 1.833)

= 61°( nearest degree)

The sum of angle in a triangle is 180°

therefore,

angle A = 180-( 61+90)

= 180-151

= 29°

therefore the measure of angle A and B is 29° and 61° respectively.

learn more about trigonometric ratio from

https://brainly.com/question/24349828

#SPJ1

The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.

The word PENCIL has 6 letters, here we have to use permutation method.  If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,

So there are 5! = 120 ways to arrange them.

Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is

4 x 5! = 4 x 120 = 480

Therefore, the correct option is (B) 480.

Learn more about permutation here

brainly.com/question/28720645

#SPJ4

Answer:

Same equation just using the assocaitive property

Step-by-step explanation:

For example, 8 + (2 + 3) = (8 + 2) + 3 = 13

Hope this helps! =D

Answer:

[tex]f(x) = 500( {.89}^{x} )[/tex]

The value of x is approximately 10.57 and the value of y is approximately 15.25.

In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.

The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.

In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:

105 + (7y + 1) + (7x + 1) + (4y + 14) = 180

Simplifying and solving for x and y, we get:

7x + 4y + 122 = 180

7x + 4y = 58 ......(1)

Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:

105 + (4y + 14) = 180 ......(2)

(7y + 1) + (7x + 1) = 180 ......(3)

Simplifying and solving for y in equation (2), we get:

4y + 119 = 180

4y = 61

y = 15.25

Substituting this value of y in equation (3) and solving for x, we get:

(7x + 1) + (7*15.25 + 1) = 180

7x + 106 = 180

7x = 74

x = 10.57

Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.

To know more about equation visit:

https://brainly.com/question/15298662

#SPJ1

The best prediction possible for the number of times the spinner will not land on yellow is 18.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Assuming that the spinner is fair and all outcomes are equally likely, we can calculate the probability of the spinner not landing on yellow in one spin by adding up the probabilities of all other outcomes, which are green, blue, and red.

The probability of the spinner not landing on yellow in one spin is:

P(not yellow) = P(green) + P(blue) + P(red)

= 1/6 + 1/3 + 1/6

= 1/2

Therefore, the expected number of times the spinner will not land on yellow in 36 spins is:

E(not yellow) = 36 x P(not yellow)

= 36 x 1/2

= 18

So the best prediction possible for the number of times the spinner will not land on yellow is 18. However, it's important to note that this is just a prediction based on probabilities, and the actual number of times the spinner doesn't land on yellow in 36 spins may vary.

To learn more about probability from the given link:

https://brainly.com/question/30034780

#SPJ1

The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

For similar question on beta measures:

https://brainly.com/question/30023263

#SPJ11

Answer:

-2

Step-by-step explanation:

The explanation is in the picture

Step-by-step explanation:

x = -4     ( the value of the x-coordinate of the vertex is the axis of symmetry for normal up or down opening parabolas)

The area of the cement part is 24 m².

Area is the region bounded by a plane shape.

To calculate the area of the part with cement. we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 24 m².

Learn more about area here: https://brainly.com/question/28470545

#SPJ1

Answer:

  2

Step-by-step explanation:

You want the average rate of change of f(x) = -x² -2x +6 on the interval [-7, 3].

The average rate of change of f(x) on the interval [a, b] is computed as ...

  m = (f(b) -f(a))/(b -a)

For the given function f(x), this is ...

  m = (f(3) -f(-7))/(3 -(-7)) = (-9 -(-29))/10 = 20/10 = 2

The average rate of change of f(x) on the interval [-7, 3] is 2.

__

Additional comment

The derivative of the function is f'(x) = -2x -2. The midpoint of the interval is x = (-7 +3)/2 = -2. The value of the derivative at the midpoint is equal to the average rate of change on the interval:

  -2(-2) -2 = 4 -2 = 2 . . . . average slope between x=-7 and x=3.

<95141404393>

Systematic sampling is a type of probability sampling method where every nth item in a population is selected for inclusion in the sample.

For example, if a researcher wanted to select a systematic sample of 100 students from a school population of 1,000 students, they would randomly select one of the first 10 students (1/10th of the population) and then select every 10th student thereafter until they reach 100. Systematic sampling is often used when the population is too large to enumerate and it is more efficient than simple random sampling. However, it is important to ensure that the sampling interval is not biased in any way, otherwise the sample may not be representative of the population.

Learn about more inclusion here:

https://brainly.com/question/22302092

#SPJ11

Systematic sampling is a relatively easy and quick method of sampling, as it requires less effort and time than other methods such as stratified or cluster sampling.

The starting point is truly random, and that the interval selected does not create any bias in the sample.

Systematic sampling is a method of selecting a sample from a population using a system or a pattern.

It involves selecting every nth item or person from the population after a random starting point has been determined.

To perform systematic sampling, the first item or individual in the sample is randomly selected from the population.

Then, the remaining items or individuals are selected at regular intervals, such as every 10th or 20th item or individual.

The interval is calculated by dividing the population size by the desired sample size.

A researcher wants to select a sample of 100 from a population of 1000, the interval would be. [tex]1000/100 = 10.[/tex]

The researcher would randomly select the first item or individual from the population, and then select every 10th item or individual thereafter until the desired sample size is reached.

For similar questions on Systematic sampling

https://brainly.com/question/28505229

#SPJ11

The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.

Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.

So, we can write this as a fraction:

$18.00 / $30.00

To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.

$18.00 / $30.00 = 0.6

Another way to say this is that Maggie spent 60% of the money she had in her wallet.

To know more about decimal here

https://brainly.com/question/9543292

#SPJ4

Answer: A

Explanation:

Answer:

Your answer should be A

we get the quotient as 161 and remainder as 11.So the missing numbers are:R = 11

9, 1, 6

First divide the greater number by the smallest number and then divide the smaller number by the remainder. We continue the process until we get 0 remainder. The divisor is the HCF of the given numbers.

To divide 5,472 by a two-digit number, we can use long division method as follows:

34) 5 4 7 2( 34

   -    4 0

     ______

       1 4 7

  -    1 3 6

      _______

            1 1

Therefore, we get the quotient as 161 and remainder as 11.

So the missing numbers are:

R = 11

9, 1, 6

Learn more about HCF here

https://brainly.com/question/29114178

#SPJ1

Answer: If you want me to evaluate its 18x - 2

Hope it helped :D

The tax on the belt buckle is $1.56

What is Rate?

In general terms, a rate is a measure of the relationship between two quantities that are measured in different units. A rate expresses how much of one thing there is per unit of another thing. For example, miles per hour is a rate that expresses how many miles are traveled in one hour.

To calculate the tax on the belt buckle, we need to multiply the price of the belt buckle by the sales tax rate:

Tax = Price x Tax rate

In this case, the price of the belt buckle is $25 and the sales tax rate is 6.25%. To convert the tax rate from a percentage to a decimal, we need to divide it by 100:

Tax rate = 6.25% ÷ 100 = 0.0625

Now we can calculate the tax on the belt buckle:

Tax = Price x Tax rate

= $25 x 0.0625

= $1.56

Therefore, the tax on the belt buckle is $1.56. The total cost of the belt buckle including tax would be $25 + $1.56 = $26.56.

To learn more about Rate visit the link:

https://brainly.com/question/119866

#SPJ1

A student willing to participate in a debate competition is required to fill out a registration form.

Form filling in two types of data i.e.,

Quantitative data is data that can be counted or measured in numerical values. The two main types of quantitative data are discrete data and continuous data. Height in feet, age in years, and weight in pounds are examples of quantitative data. Qualitative data is descriptive data that is not expressed numerically.

Categorical data is a collection of information that is divided into groups. i.e., if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical.

a. What is your date of birth?

Quantitative.

b. Have you participated in any debate competition previously?

Categorical.

c. If yes, how many debate competitions have you participated so far?

Quantitative.

d. Have you won any of the competitions?

Categorical.

e. If yes, how many have you won?

Quantitative.

Learn more about Quantitative data at:

https://brainly.com/question/14810759

#SPJ4

The given question is incomplete, complete question is:

A student willing to participate in a debate competition required to fill a registration form. State

whether each of the following information about the participant provides categorical or quantitative

data.

a. What is your date of birth?

b. Have you participated in any debate competition previously?

c. If yes, how many debate competitions have you participated so far?

d. Have you won any of the competitions?

e. If yes, how many have you won?

Please write answer in two parts. A. Main answer (correctly paraphrased, addressing all aspect of the question) B. Explanation (Step-by-step explanation)

Answer:

Yo, when you adding or subtracting mixed numbers with the same denominators, the numerators stay chill, they don't change, bro.

But the denominators, they also stay the same, man. It's like keeping things consistent, ya feel me? So the answer is A, dude. Numerators stay put, denominators stay put. It's all good vibes, bro! ✌️

Answer: 1. 48.356 2. 75.3982236862

Step-by-step explanation:

Radias*2 pi

Answer:

2.36 miles

Step-by-step explanation:

radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles

Answer:

I would say convenience sampling. It's hard to tell. Sampling every other person is like systematic sampling, BUT convenience sampling would be to sample people that are easy to reach.

Answer:

≈ $26

Step-by-step explanation:

13% = 0.13

199.99 x 0.13 = $25.9987

So, 13% markup is ≈ $26

The expression used  to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.

Let us consider 'l' be the length of the rectangular prism.

'w' be the width of the rectangular prism .

'h' be the height of the rectangular prism.

From the attached figure we have,

Length of the rectangular prism l = 3 units

Width of the rectangular prism w = 2 units

Height of the rectangular prism h = 5 units

Surface of the rectangular prism = 2(lw + wh + hl )

Substitute the values in the formula we get,

⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )

⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)

⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15

Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.

Learn more about surface area here

brainly.com/question/14322585

#SPJ4

The above question is incomplete, the complete question is:

Which expression can be used to find the surface area of the following rectangular prism?

Attached figure.

The approximate p-value is 5.1250%.

P-value is the probability of obtaining a test statistic as or more extreme than what was actually observed, given that the null hypothesis is true.

Two-sided significance test, with a significance level of 2%. you then randomly sample 420 items from the production line, and find that 22 of the items are defective.

The approximate p-value for this two-sided significance test, with a significance level of 2%, is 5.1250%.

This is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This was calculated using a binomial test, which takes into account the sample size and the expected rate of defects.

This p-value indicates whether or not the observed rate of defects is significantly different from the expected rate.

In this case, the p-value is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This can be calculated using a binomial test.

For similar question on p-value :

https://brainly.com/question/31591314

#SPJ11

The standard deviation of the ACT scores is approximately 4.2.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.

According to the given information:

To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.

Given:

Mean (μ) = 21.4

Percentage of scores above 26 = 15%

Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.

Z-score formula:

Z = (X - μ) / σ

Where:

Z = Z-score

X = Value (in this case, 26)

μ = Mean (21.4)

σ = Standard deviation (to be found)

We can rearrange the formula to solve for σ:

σ = (X - μ) / Z

Substituting the given values:

X = 26

μ = 21.4

Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)

Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:

σ = (26 - 21.4) / 1.04

σ = 4.4 / 1.04

σ ≈ 4.2 (rounded to the nearest tenth)

So, the standard deviation of the ACT scores is approximately 4.2.

To know more about standard deviation visit:https://brainly.com/question/23907081

#SPJ1

The amount that each charity gets is $25.

The charity raise simply define as we raise funds in the form of small amounts of money from a huge crowd of people within a specific period of time.

For example, if 100 people donate $50 each to your crowdfunding campaign in two weeks, you will be able to raise $5000.

To find the amount that each charity got, we have to divide the total charity amount raised in the proportion given, i.e., 1/6.

Each charity gets 1/6 of the total amount raised, which is $150.

So, we need to divide $150 by 6:

$150 ÷ 6 = $25

Therefore, each charity received $25.

To know more about charity

https://brainly.com/question/30667130

#SPJ4