At a certain instant, the base of a triangle is 5 inches and is increasing at the rate of 1 inch per minute. At the same instant, the height is 10 inches and is decreasing at the rate of 2.5 inches per minute. Is the area of the triangle increasing or decreasing? Justify your answer.

Answers

Answer 1

Using differentiation, the area of the triangle is decreasing at the given time.

Is the area of the triangle increasing or decreasing?

The formula for the area of a triangle is:

A = (1/2)bh

where b is the base and h is the height.

Differentiating both sides of the equation with respect to time t, we get:

[tex]\frac{dA}{dt} = (1/2)[(\frac{db}{dt}) h + b(\frac{dh}{dt}) ][/tex]

Substituting the given values, we get:

[tex]\frac{dA}{dt} = (1/2)[(1)(10) + (5)(-2.5)] = (1/2)(10 - 12.5) = -1.25[/tex]

Since the derivative of the area with respect to time is negative (-1.25), the area of the triangle is decreasing at the given instant.

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Related Questions

What was your recommended intake of carbohydrates (grams), and how far were you from it? Show the mathActual Intake Recommended Intake Percentage159.00 115-166 100%

Answers

The actual intake of carbohydrates is 138% as compare to recommended intake.

Recommended intake of carbohydrates or any other nutrient are,

Based on the information provided,

Consumed 159 grams of carbohydrates,

Recommended intake is between 115 and 166 grams.

Calculate the percentage of actual intake compared to the recommended intake, use the following formula,

Percentage = (Actual Intake / Recommended Intake) x 100%

Substituting the values in the formula we have,

⇒Percentage = (159 / 115) x 100%

⇒Percentage ≈ 138.3%

Therefore,  the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.

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Se depositan $ 8.000 en un banco que reconoce una tasa de interés del 36% anual, capitalizable mensualmente. ¿Cuál será el monto acumulado en cuatro años?

Answers

Answer:

Se depositan $ 8.000 en un banco que reconoce una tasa de interés del 36% anual, capitalizable mensualmente. ¿Cuál será el monto acumulado en cuatro años?

Step-by-step explanation:

Para resolver este problema, podemos utilizar la fórmula del interés compuesto:

A = P*(1 + r/n)^(n*t)

Donde:

A: el monto acumulado después de t años

P: el capital inicial

r: la tasa de interés anual

n: el número de veces que se capitaliza el interés por año

t: el tiempo en años

En este caso, tenemos:

P = $8.000

r = 36% = 0.36

n = 12 (ya que la tasa de interés se capitaliza mensualmente)

t = 4 años

Sustituyendo estos valores en la fórmula, obtenemos:

A = $8.000*(1 + 0.36/12)^(124)

A = $8.000(1 + 0.03)^48

A = $8.000*(1.03)^48

A = $16.751,83

Por lo tanto, el monto acumulado en cuatro años será de $16.751,83.

Question is on the picture

Answers

By answering the presented question, we may conclude that She spends equation 40% of her time at work and 15% of her time on other hobbies. She spends 20% of her time napping.

What is equation?

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion  [tex]"2x + 3 = 9"[/tex] states that the word  [tex]"2x + 3"[/tex] Corresponds to the number "9".

The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.

For example, in the equations [tex]"x2 + 2x - 3 = 0[/tex]  ," the variable x is lifted to the powercell. Lines are utilized in many areas of mathematics, include algebra, arithmetic, and geometry.

Abby, according to the picture, spent:

She spends 25% of her time in school.

She spends 40% of her time at work and 15% of her time on other hobbies.

Therefore, Furthermore, she spends  [tex]20[/tex] of her time napping.

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I will mark you brainiest!

A concave polygon can never be classified as a regular polygon.

A) True
B) False

Answers

Answer:

False.

Step-by-step explanation:

A concave polygon can never be a regular polygon as it can never be equiangular. Each side of a regular polygon must be the same length, and all interior angles must also be equal.

PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.

Answers

Answer: 24

Step-by-step explanation:

To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.

Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.

The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.

Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19

Radius of the circle = 4.19/60 = 0.07

Angle of sector = 360 - 60 = 300 degrees

Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041

The area of the triangle can be found using the formula:

Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24

Therefore, the total area of the composite figure is:

0.0041 + 24 = 24.0041

Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.

01106115 Ex-1 Find the height of a tree if the angle of elevation Of its top Changes from 25 to 50° as the Observer advanced 15 meters toward
it's base​

Answers

Answer:

  about 11.5 m

Step-by-step explanation:

You want the height of a tree when the angles of elevation to its top are 25° and 50° from points 15 m apart.

Tangent

The tangent relation between angles and sides in a right triangle is ...

  Tan = Opposite/Adjacent

In the attached diagram, this means ...

  tan(25°) = TX/AX

  tan(50°) = TX/BX

Solution

The difference between AX and BX is known, so we can rearrange this to ...

  AX -BX = 15 = TX/tan(25°) -TX/tan(50°)

  15·tan(25°)·tan(50°) = TX(tan(50°) -tan(25°) . . . multiply by tan(25°)tan(50°)

  TX = 15·tan(25°)·tan(50°)/(tan(50°)-tan(25°) ≈ 11.5 . . . . meters

The height of the tree is about 11.5 meters.

__

Additional comment

The value of the height can be computed by finding each tangent only once if we use ...

  TX = 15/(1/tan(25°) -1/tan(50°))

You recognize 1/tan(x) = cot(x) = tan(90°-x), so this is ...

  TX = 15/(tan(65°) -tan(40°))

Suppose Set A contains 98 elements and Set B contains 93 elements. If Sets A and B have 35 elements in common, what is the total number of elements in either Set A or Set B.

Answers

The total number of elements in either Set A or Set B is 156.

How are sets and subsets different from one another?

A set is a collection of unique items, but a subset is a set that contains only components that belong to another set, termed the superset. In other words, set A is a subset of set B if all of its items are also found in set B.

Given that, Set A contains 98 elements and Set B contains 93 elements.

Total number of elements in either Set A or Set B = number of elements in Set A + number of elements in Set B - number of common elements

Total number of elements in either Set A or Set B = 98 + 93 - 35

Total number of elements in either Set A or Set B = 156

Hence, the total number of elements in either Set A or Set B is 156.

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Conduct a survey with a minimum of 20 people. Complete the designed questionnaire in 1.2. Remind participants why you are doing survey and that their information will be kept confidential. Submit 20 original completed questionnaires.

Answers

Some of the tips which is used to conduct a survey are:

Determine the purpose of the survey and define the population of interest.Design the questionnaire and ensure that the questions are clear and concise.Select a sample from the population and distribute the questionnaire to the participants.Remind participants why you are conducting the survey and assure them that their responses will be kept confidential.

What is the need to conduct a survey (questionnaire)?

Conducting a survey is an important tool for gathering information from a large and diverse group of people. Its allows allow researchers to obtain data from a representative sample of the population, which can then be used to make informed decisions, identify trends, and measure changes over time.

Also important, its can provide insight into people's attitudes, beliefs, and behaviors, which can be valuable in developing marketing strategies, designing programs and policies, and making important decisions.

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A weight is attached to a spring that is oscillating up and down. It takes 2 seconds for the spring to complete one cycle, and the distance from the highest to the lowest point is 5 in. What equation models the position of the weight at time t seconds?

Answers

The equation that models the position of the weight at time t seconds is y(t) = 2.5 sin (πt) + 2.5

The equation that models the position of the weight at time t seconds is

y(t) = 2.5 sin (πt) + 2.5

The position of the weight at time t seconds can be modeled by a sinusoidal function of the form

y(t) = A sin (ωt + φ) + C

where

A is the amplitude of the oscillation (half the distance between the highest and lowest points), which is 2.5 in.

ω is the angular frequency of the oscillation, which is 2π divided by the period (the time for one complete cycle), which is 2 seconds. So, ω = 2π/2 = π radians/second.

φ is the phase angle, which depends on the initial position of the weight. We can assume that the weight starts at the highest point (the crest), so φ = 0.

C is the vertical shift, which is the midpoint of the oscillation (half the distance between the highest and lowest points added to the starting point). So, C = 2.5 + 0 = 2.5 in.

Putting it all together, we get

y(t) = 2.5 sin (πt) + 2.5

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Solve the polynomial equation by factoring and then using the zero-product principle.
4x = 864x
Rewrite the equation in factored form.
(Blank)= 0

What is the solution pair?

Answers

In response to the stated question, we may state that As a result, the equation's answer is x = 0.

What is equation?

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

4x = 864x is the provided equation.

This equation may be simplified by deleting 4x from both sides:

[tex]860x = 0[/tex]

This equation may now be rewritten in factored form:

[tex]860x = 0 \sx(860) = 0[/tex]

We know from the zero-product principle that if the product of two elements is zero, then at least one of them must be zero. As a result, we may set each component to zero and solve for x:

x = 0 or 860 = 0 (which is impossible) (which is impossible)

As a result, the equation's answer is x = 0.

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The triangle shown has an area of 46 square centimeters. Find the measure of the base (segment AB ). Triangle A B C. A line goes from point C to point D on side A B. Side A C is 11 centimeters, C B is 9 centimeters, and A B is question mark.

Answers

By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.

What precisely is a triangle?

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

the length of the base AB,

Area = (1/2) * base * height

[tex]CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\[/tex]

We also know that the area of the triangle is:

[tex]46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\[/tex]

[tex]8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\[/tex]

[tex]AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\[/tex]

Therefore, the length of the base AB is approximately 20.88 centimeters.

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A Triangle has a height that is half of 28 yards and an area of 56 yards^2. What is the length of the base of the trangle?

Answers

The length of the base of the triangle is 8 yards whose height is half of 28 yards.

What is triangle?

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

According to question:

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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Find the mean of 8,2,2 graphically.

Answers

The mean of the numbers 8, 2 and 2 when solved graphically is 4

How to determine the mean of numbers

The numbers in the dataset are given as

8, 2 and 2

The mean is also known as the average and is calculated by adding up all the values in a dataset and then dividing the sum by the total number of values.

To find the mean of 8, 2, and 2 graphically, we can use a number line.

First, we mark the three numbers on the number line:Next, we find the midpoint of the three numbers on the number line, which represents the mean:

The midpoint between 2 and 8 is 5, and the midpoint between 2 and 2 is also 2.

Therefore, the mean of 8, 2, and 2 is the average of the midpoints

Mean = (8 + 2 + 2)/3

Mean = 4

Hence, the mean is 4

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Identify the values of the variables. Give your answers in simplest radical form.

Answers

The value οf v=3√2 and  w=√3/√2.

What is Pythagοras theοrem?

If a triangle has a straight angle (90 degrees), the hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides, accοrding tο the Pythagοras theοrem.

Keep in mind that BC² = AB² + AC²in the triangle ABC signifies this. This equatiοn uses the variables base AB, height AC, and hypοtenuse BC. It is impοrtant tο nοte that the hypοtenuse, οr lοngest side, οf a right-angled triangle is.

Here fοr sin(30)= v/3√2

1/2 = v / 3√2

v = 3√2

cοs(30)= w/3√2

w=3√2*√3/2

w=√3/√2

Hence the value οf v=3√2 and  w=√3/√2.

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Please check the image for directions, Five stars, and like. Thank you

Answers

The measure of HI based on the given diagram is 70 units.

What is a triangle mid segment?

A triangle mid segment is the line joining the midpoint of any two sides of the triangle which is parallel to the third side and is also half of the length of the third side.

HI = 3x + 5

EF = -3x + 55

So,

HI = 1/2(EF)

3x + 5 = 1/2(-3x + 55)

3x + 5 = (-3x + 55) / 2

cross product

2(3x + 5) = -3x + 55

open parenthesis

6x + 10 = - 3x + 55

6x + 3x = 55 - 10

9x = 45

divide both sides by 9

x = 45/9

x = 5

Therefore, the measure of HI and EF are;

HI = 3x + 5

= 3(5) + 55

= 15 + 55

= 70

EF = -3x + 55

= -3(5) + 55

= -15 + 55

= 40

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Evaluate the logarithmic expression without using a calculator. Answer exactly. log 2 ( 1/16 ) + 4 =

Answers

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}[/tex]

[tex]\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4[/tex]

PLEASE HELP ME YOU WILL BE MARKED BRAINLIEST!!!1

Answers

The experimental probability of winning the contest based on the data of all 3 games is 0.432.

What is experimental probability ?

Experimental probability is a measure of the likelihood of an event occurring based on the results of an experiment or observation. It is determined by dividing the number of times the event occurred by the total number of trials or observations. The more trials or observations conducted, the more accurate the experimental probability will be. Experimental probability is often used in situations where the probability of an event cannot be determined theoretically or where the theoretical probability is difficult to calculate. It is also commonly used in scientific experiments, market research, and other fields where the results of an experiment or observation can be used to make predictions or inform decisions.

Finding the experimental probability of winning the contest :

In this case, the event is winning the contest by choosing a marble from a bag, and the trials are the three games played by Hal.

Total number of players in all three games = 123 + 155 + 172 = 450

Total number of winners in all three games = 52 + 63 + 65 = 180

Experimental probability of winning the contest = Number of winners / Total number of players = 180/450 = 0.432

Therefore, the experimental probability of winning the contest based on the data of all 3 games is 0.432.

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How does f(t) = 7 change over the interval from t = -4 to t = -3?
f(t) decreases by 7
f(t) increases by 600%
f(t) decreases by 7%
f(t) increases by 700%

Answers

Answer:

None of the options provided in the question accurately describe the behavior of f(t) = 7 over the interval from t = -4 to t = -3.

Step-by-step explanation:

he function f(t) = 7 is a constant function that does not depend on the value of t. Therefore, f(t) = 7 remains the same over the interval from t = -4 to t = -3. In other words, there is no change in the value of f(t) over this interval.

I don’t understand please help me with this

Answers

Answer:

Greg bought a pack of X jumbo stickers during the back - to - school sale at Crafty's craft store. He ( uses 4  ( -4 ), ( you didn't give options ). There were 8 stickers left in the pack.

Hope this helps!

Step-by-step explanation:

PLS HELP FAST + BRAINLIEST!!

Answers

You just collect like terms
2x - 5 + x + x + 3
= 4x - 2 which you can simplify to 2x - 1

x - 5 + x - 5 + 3x - 1 + 3x - 1
=8x - 12 and you can simplify further to 2x -3

for the square you can just times the length by 4 as the sides are equal
4(3x - 2y) = 12x -8y and you can simplify this to 3x -2y

the figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?

Answers

The statement that best describes the mode of selection depicted in the figure is (b) Directional Selection, changing the average color of population over time.

The Directional selection is a type of natural selection that occurs when individuals with a certain trait or phenotype are more likely to survive and reproduce than individuals with other traits or phenotypes.

In the directional selection of evolution, the mean shifts that means average shifts to one extreme and supports one trait and leads to eventually removal of the other trait.

In this case, one end of the extreme-phenotypes which means that the dark-brown rats are being selected for. So, over the time, the average color of the rat population will change.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

The figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?

(a) Disruptive Official, favoring the average individual

(b) Directional Selection, changing the average color of population over time

(c) Directional selection, favoring the average individual

(d) Stabilizing Selection, changing the average color of population over time

A parent donated 36 fruit cups and 24 bananas to fifth grade. The teacher wanted to make field trip snack bags with the donated food and wondered about the ways snacks could be packed. To be fair the teacher wants to make sure that all bags are exactly the same.

A) What is the greatest number of snack bags that the teacher can make, if each bag is identical? How do you know ?

B) What other numbers of snack bags could she make? How do you know?

2) Another parent also donated 24 bananas, so there are 48 bananas total. Now what is the greatest number of snack bags can that can be made?

3) The teacher realized that she miscounted and had only 30 fruit cups. How many snack bags can she make with 48 bananas and fruit cups?

4) What do the different numbers of snack bags that can be made have to do with the number of fruit cups and number of bananas?

Answers

A) To find the greatest number of snack bags the teacher can make, we need to determine the greatest common factor of 36 and 24. The prime factorization of 36 is 2^2 x 3^2, and the prime factorization of 24 is 2^3 x 3. The greatest common factor is 2^2 x 3, which is 12. Therefore, the teacher can make 12 identical snack bags.

B) Other numbers of snack bags that could be made would be factors of 12, such as 1, 2, 3, 4, or 6. This is because the teacher can only make an integer number of identical bags using the given number of fruit cups and bananas.

With 48 bananas and 36 fruit cups, the greatest common factor is 12, as shown in part A. Therefore, the teacher can make 12 identical snack bags with 48 bananas and 36 fruit cups.
With only 30 fruit cups, the greatest common factor between 30 and 48 is 6. Therefore, the teacher can make 6 identical snack bags with 30 fruit cups and 48 bananas.
The different numbers of snack bags that can be made are related to the greatest common factor between the number of fruit cups and bananas. The greatest common factor determines how many identical bags the teacher can make, as each bag must have the same number of fruit cups and bananas. If the greatest common factor is 1, then the teacher can only make one bag with all the fruit cups and bananas. If the greatest common factor is larger, then the teacher can make multiple bags with an equal number of fruit cups and bananas.

In the New York State Numbers Lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $750, which is a profit of $749. If you lose, you lose $1. Your probability of winning is 0.001.

Answers

The expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.

What is outcome?

The term "outcome" generally refers to the result or effect of an action, process, or event. It refers to what happens as a consequence of a particular decision, activity, or circumstance.

According to question:

To calculate the expected value, we multiply the possible outcomes by their probabilities and then sum them up.

Let's start with the possible outcomes:

If you win, you make a profit of $749, so the outcome is $749.

If you lose, you lose $1, so the outcome is -$1.

The probabilities are:

Probability of winning is 0.001.

Now we can calculate the expected value:

Expected value = (0.001 * $749) + (0.999 * -$1)

Expected value = $0.748 - $0.999

Expected value = -$0.251

Therefore, the expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.

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Use implicit differentiation to find an equation of the tangent line to the curve sin(x+y)=8x−8y at the point (π,π)

Answers

The equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).

To discover the equation of the tangent line to the curve sin( x y) = 8x- 8y on the point( π, π), we want to apply implicit differentiation to discover the pitch of the tangent line at that point.

We begin through differencing both sides of the equation with reference to xcos( x y)( 1 dy/ dx) = eight- 8dy/ dx

After, we can simplify the expression by isolating the terms beholding dy/ dx on one aspect

cos( x y) cos( x y) dy/ dx = 8- 8dy/ dx

8 cos( x y)) dy/ dx = 8- cos( x y)

dy/ dx = ( 8- cos( x y))( 8 cos( x y))

Now we're suitable to discover the pitch of the tangent line at the factor( π, π) by plugging in x = π and y = π into the expression we simply derived

dy/ dx = ( 8- cos( 2π))( 8 cos( 2π))

dy/ dx = ( 8- 1)/( 8 1)

dy/ dx = 7/ nine

Thus, the pitch of the tangent line to the curve sin( x y) = 8x- 8y at the factor( π, π) is7/9.

To find the equation of the tangent line, we can use the point- slope form of the equation

y- y1 = m( x- x1)

In which m is the pitch we simply set up, and( x1, y1) is the point( π, π). Plugging in the values, we get

y- π = ( 7/ nine)( x- π)

Simplifying, we get

y = ( 7/ nine) x-( 2π/ nine)

Thus, the equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).

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2(x-6)²

could you please explain this to me, thanks!

Answers

Answer:

expand the square

2(x-6) (x-6)

2(x(x-6)-6(x-6)

2(x²-6x-6(x-6)

2(x²-6x-6x+36)

2(x²-12x+36)

2x²-24x+72

Step-by-step explanation:

hope this helps

When a researcher wants to report the average cost of college tuition from the 1950s until present time, he or she enlists _______ statistics.a) Inferentialb) Descriptivec) Correlationald) Predictive

Answers

Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features.

When a researcher wants to report the average cost of college tuition from the 1950s until present time, descriptive statistics are the appropriate method to use. Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features. By using descriptive statistics, the researcher can calculate measures of central tendency, such as the mean, median, and mode, to determine the typical or average cost of college tuition over time. Additionally, measures of variability, such as the range and standard deviation, can be calculated to understand the spread of the data. Descriptive statistics are commonly used in many fields, including business, economics, psychology, and education, and can provide valuable insights into trends, patterns, and distributions within a dataset.

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Parts A-D. What is the value of the sample mean as a percent? What is its interpretation? Compute the sample variance and sample standard deviation as a percent as measures of rotelle for the quarterly return for this stock.

Answers

The sample mean is 2.1, the sample variance is 212.5% and the standard deviation is 14.57%

What is the sample mean?

a. The sample mean can be computed as the average of the quarterly percent total returns:

[tex](11.2 - 20.5 + 13.2 + 12.6 + 9.5 - 5.8 - 17.7 + 14.3) / 8 = 2.1[/tex]

So the sample mean is 2.1%, which can be interpreted as the average quarterly percent total return for the stock over the sample period.

b. The sample variance can be computed using the formula:

[tex]s^2 = sum((x - mean)^2) / (n - 1)[/tex]

where x is each quarterly percent total return, mean is the sample mean, and n is the sample size. Plugging in the values, we get:

[tex]s^2 = (11.2 - 2.1)^2 + (-20.5 - 2.1)^2 + (13.2 - 2.1)^2 + (12.6 - 2.1)^2 + (9.5 - 2.1)^2 + (-5.8 - 2.1)^2 + (-17.7 - 2.1)^2 + (14.3 - 2.1)^2 / (8 - 1) = 212.15[/tex]

So the sample variance is 212.15%. The sample standard deviation can be computed as the square root of the sample variance:

[tex]s = \sqrt(s^2) = \sqrt(212.15) = 14.57[/tex]

So the sample standard deviation is 14.57%.

c. To construct a 95% confidence interval for the population variance, we can use the chi-square distribution with degrees of freedom n - 1 = 7. The upper and lower bounds of the confidence interval can be found using the chi-square distribution table or calculator, as follows:

upper bound = (n - 1) * s^2 / chi-square(0.025, n - 1) = 306.05

lower bound = (n - 1) * s^2 / chi-square(0.975, n - 1) = 91.91

So the 95% confidence interval for the population variance is (91.91, 306.05).

d. To construct a 95% confidence interval for the standard deviation (as percent), we can use the formula:

lower bound = s * √((n - 1) / chi-square(0.975, n - 1))

upper bound = s * √((n - 1) / chi-square(0.025, n - 1))

Plugging in the values, we get:

lower bound = 6.4685%

upper bound = 20.1422%

So the 95% confidence interval for the standard deviation (as percent) is (6.4685%, 20.1422%).

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One 12 ounce can of soda has 150 calories. If Josiah drinks the big 24 ounce size from the local mini-mart, how many calories does he get?

Answers

Answer:

Step-by-step explanation:

       12 ounces = 150 calories, so

12 x 2 ounces = 150 x 2 calories,

      24 ounces = 300 calories

x P(x)
0 0.1
1 0.05
2 0.1
3 0.75


Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

Answers

Answer: To find the standard deviation of a probability distribution, we need to first calculate the mean or expected value of the distribution, which is given by:

E(X) = Σ [xi * P(xi)]

where xi is the ith outcome and P(xi) is its probability.

So, for the given distribution:

E(X) = (0 * 0.1) + (1 * 0.05) + (2 * 0.1) + (3 * 0.75) = 2.4

Next, we need to calculate the variance of the distribution, which is given by:

Var(X) = Σ [(xi - E(X))^2 * P(xi)]

So, for the given distribution:

Var(X) = (0 - 2.4)^2 * 0.1 + (1 - 2.4)^2 * 0.05 + (2 - 2.4)^2 * 0.1 + (3 - 2.4)^2 * 0.75 = 0.69

Finally, the standard deviation of the distribution is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(0.69) ≈ 0.83

Therefore, the standard deviation of this probability distribution is approximately 0.83, rounded to 2 decimal places.

Step-by-step explanation:

Increase £16470.45 by 3.5%
Give your answer rounded to 2 DP

Answers

Step-by-step explanation:

"increase" means to take the original 100% and put an additional 3.5% of these 100% on top of it.

so, we have to calculate

100% + 3.5% of £16470.45

100% of £16470.45 = £16470.45 × 100/100

3.5% of £16470.45 = £16470.45 × 3.5/100

the sum is therefore

£16470.45 × (100/100 + 3.5/100) =

= £16470.45 × (1 + 0.035) = £16470.45 × 1.035 =

= £17,046.91575 ≈ £17,046.92

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