What is the sum of all interior angles of a 32-sided regular polygon?

169°
180°
5,400°
5,580°

The points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin are

(2–√,−2–√,2−22–√)

(−2–√,2–√,2+22–√)

Using Lagrange multipliers we attempt to find the extrema of f(x,y,z)=x2+y2+z2 given that g(x,y,z)=x−y+z−2=0 and that h(x,y,z)=x2+y2−4=0.

Given,

∇f=⟨2x,2y,2z⟩

∇g=⟨1,−1,1⟩

∇h=⟨2x,2y,0⟩

Extrema satisfy the condition that ∇f=μ∇g+λ∇h for some λ,μ∈R.

This is to say,

2x=2λx+μ

2y=2λy−μ

2z=μ

If λ=1 then μ=0 and so z=0, the g constraint tells us that x=y+2, and the h constraint tells us that y2+(y+2)2=4, meaning that either y=0 or y=2. This provides us with two crucial points in addition to the g constraint:

(2,0,0)

(0,−2,0)

Now assume λ≠1, and so

x=μ2−2λ

y=−μ2−2λ=−x

Since x=−y, we have that x=±2–√, y=∓2–√. Using the g constraint, our two critical points are

(2–√,−2–√,2−22–√)

(−2–√,2–√,2+22–√)

And then it's east to determine which is the max and which is the min out of these four critical points.

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The possible variable terms for the given expression are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression is (2a+4b)⁸.

The expansion is

(2a+4b)⁸=256a⁸+4096a⁷b+2867a⁶b²+114688a⁵b³+286720a⁴b⁴+458752a³b⁵+458752a²b⁶+262144ab⁷+65536b⁸

Hence, in the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

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The slope and a point of a line are given then the equation of a line can be found. So the answer is true.

The equation of a line:

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The most popular form in algebra is the "slope-intercept" form. y = mx + b. This in effect uses x as a parameter and writes y as a function of x: y = f(x) = mx+b.

Here we have to get to know if the slope and a point on a line are given then we can find the equation of a line or not.

Let us assume m is the slope of a line and (x1, y1) is the point on a line.

By this, we get the equation:

y- y1 = m( x - x1)

Therefore from the slope and a point on a line, we can find the equation of a line.

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When two numbers have the same sign, the result will be the number with the larger absolute value. 25 + (-15) - (-10) = 30

To calculate 25 + (-15) - (-10), we must first look at the order of operations. We start with the parentheses, so we need to calculate -15 and -10 first. When two numbers have the same sign, the result will be the number with the larger absolute value. In this case, -15 and -10 both have negative signs, so the result will be -15.

Next, we move on to the addition and subtraction signs. We add 25 and -15 to get 10. Then we subtract -10 from 10, and the result is 30. So, 25 + (-15) - (-10) = 30.

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The statement "considered multiple regression which is a sample at 36 observations for a given eggs and fitted why the 95% approximate prediction interval for individual why is wider than the corresponding approximate 95% confidence interval for the conditional mean" is false.

Here we have given the statement and we need to identify whether this one is true or not.

As we all know that then Confidence interval is narrower than the prediction interval because Prediction intervals must account for both the uncertainty in estimating the population mean, plus the random variation of the individual values.

Therefore the prediction interval is always wider than a confidence interval.

And also here the prediction interval will not converge to a single value as the sample size increases.

Therefore, the statement is incorrect.

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The number of cans of soup bought is 8 and the number of frozen dinners purchased is 3.

s + f = 11 equation 1

350s + 650f = 4750 equation 2

Where:

The elimination method would be used to solve for the required values:

Multiply equation 1 by 350

350s + 350f = 3850 equation 3

Subtract equation 2 from equation 3 :

300f = 900

f = 900 / 300

f = 3

Substitute for f in equation 1 :

s + 3 = 11

s = 11 - 3

s = 8

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The radius reduced to 57.3% of its normal value.

The expression of Poiseuille's law for flow in a tube is:

Q = Δpπr⁴/8ηl

where:

Q = is the flow rate

P₁ = is the pressure at first end of vain

P₂ = is the pressure at the other end

η = is the viscosity of the concrete

r - radius of pipe

l = is the length

Re arrange the expression for the radius of the pipe,

r = (8Qηl/πΔP)¹/⁴

the flow rate in an artery has been reduced to 10.0%and the difference in blood pressure is increased by 20%.

so,

Q' = 0.100Q and

ΔP' = 1.20ΔP

SUbstitute the above points.

r' = (8( 0.100Qηl/π(1.20ΔP))¹/⁴

= 0.537(8Qηl/πΔP)¹/⁴

Combine the expression of radius before the flow and pressure changes and the expression derived or the new radius,

r' = 0.537r

Hence the radius reduced to 57.3% of its normal value.

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The measure of angle 1 is given as follows:

m < 1 = 150º.

From the image given at the end of the answer, we have that two Railroad tracks are transversal to the Olive Street.

Considering that Olive Street is transversal to the parallel lines, we have that the angle 2 forms a linear pair with the angle of 30º.

Linear pairs are supplementary angles, meaning that the sum of their measures is of 180º, hence the measure of angle 2 is given as follows:

m < 2 + 30º = 180º

m < 2 = 180º - 30º

m < 2 = 150º.

Now we have that angles 1 and 2 are alternate interior angles, as they are between the two parallel lines, on the opposite side of the transversal.

Alternate interior angles are congruent, meaning that the measure of angle 1 is given as follows:

m < 1 = 150º.

The diagram is given by the image shown at the end of the answer.

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The length of the wire attached to the pole is 20.62 feet

The pole is perpendicular to the ground in the direction of the point where the wire is attached to the ground to form a right angle triangle.

A leg of the triangle is 20 feet(length of the pole from the surface of the ground to the top)

The other leg is5 feet(distance from the base of the pole to the point where the wire is attached to the ground)

The third side of the right angle triangle is the hypotenuse(length of the wire)

Applying Pythagoras theorem;

Hypotenuse² = Opposite² + Adjacent²

= 20 feet ² + 5 feet²

= 400 + 25

Hypotenuse² = 425

Find the square root of both sides

Hypotenuse = √425

= 20.6155

Approximately,

Hypotenuse = 20.62 feet

In conclusion, the hypotenuse side of the right angle triangle is 20.62 feet

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Answer: (-11,0) (Please make sure this answer is correct, as I am not a master...)

Step-by-step explanation:

We can solve this a super simple way.

The midpoint is (-6,-3/2) and the coordinate B is (-1,3)

We notice that we change y by positive 5 and we change our x by negative 3/2, from M to B. So to get to A from M, we change y by -5 and change our x by positive 3/2...

So we have:

(-6-5,-3/2+3/2)

(-11,0)

So the coordinate of A is:

(-11,0) (Please make sure this answer is correct, as I am not a master...)

The answer of the given scientific multiplication is,  8.84 x 10^-1.

What is scientific multiplication?

Multiply the decimal numbers to multiply the numbers in scientific notation. Add the 10 power exponents after that. In scientific notation, place the new power of 10 with the decimal.

Given:

(6.8 x 10^2) x (1.3 x 10^-3)

We have to solve this using scientific multiplication.

First to multiply the decimals,

6.8 x 1.3 = 8.84

Now to solve

10^2 x 10^-3 = 10^(2-3) = 10^-1

⇒  (6.8 x 10^2) x (1.3 x 10^-3) = 8.84 x 10^-1

Hence, the answer of the given scientific multiplication is,  8.84 x 10^-1.

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This indicates that the probability is 0.4402% without replacement.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

n = 5

x = 1

p = 5/20 = 0.25

15C4 = 15! / 4! * 11! = 1365

P = (5C1 * 15C4) / 20C5

Replacing:

P = 5 * 1365/15504

P = 0.4402

Hence, This indicates that the probability is 0.4402% without replacement.

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Max Says that the product 30 x 10 by 4 has exactly four zeros is not true.

Multiplication is a method of finding the product of two or more numbers

We need to check whether product 30 x 10 by 4 has exactly four zeros

firstly we have to multiply thirty with ten

Now multiply 30×10=300

Which has two zeros and now we have to divide it by 4

300/4

Three hundred by four

75

Seventy five.

Hence, Max Says that the product 30 x 10 by 4 has exactly four zeros is not true.

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The answer is 18x10^4 using simple arithmetic calculations and exponential function.

What are arithmetic calculations?
Arithmetic calculations are mathematical operations that involve the addition, subtraction, multiplication, and division of real numbers. Arithmetic is used to solve problems and execute tasks in everyday life, and is an integral part of mathematics. It is also used to analyze data and solve equations. Arithmetic involves the use of numbers, symbols, and operations in order to solve problems. Examples of arithmetic operations include addition, subtraction, multiplication, division, and exponentiation. The order of operations is an important part of arithmetic, as it dictates which operations take precedence over others. Arithmetic is used in a variety of applications, such as in engineering, finance, education, and science. It can also be used to solve puzzles and games. Arithmetic calculations can be used to help people better understand the world around them, as well as to help them make better decisions in life.

Two exponential function having same base , then powers can be added or subtracted.

In given equation, base is of 10 and powers are 8 and -4.

now the power will be 4

and 3 and 6 get multiplied i.e. 18.

So, the answer is 18x10^4.

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The mapping diagram above does not represent a function since for each number in Set A (the input) where there are multiple mappings from Set B (the output).

In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set A) to an output variable (Set B).

Based on the mapping diagram shown above, we can reasonably infer and logically deduce that the inputs (4, 3), (-2, 3), (8, 6), and (4, 7) are ordered pairs which does not represent a function because they indicate multiple mappings in Set B (the output).

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There are 20 numbers in the set.

Given,

Set of numbers is 120

one number is increased by 300

and, mean increases to 135.

To find the how many numbers are in the set?

Now, According to the question:

Let the number of numbers be 'n'

Then, (sum of numbers)/n = 120

or, old sum = 120n

if one number is increased by 300, the new sum = (old sum + 300)

Then, (new sum)/ n= 135

or new sum = 135n = old sum + 300 = 120n + 300

The equation will  be:

135n = 120n + 300

15n = 300

n = 20

Hence, There are 20 numbers in the set.

In the question:

The mean of a set of numbers is 120. if one number is increased by 300, the mean increases to 135.

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Answer:

The answer is (-4x² + x + 2)

Step-by-step explanation:

(2x² - 4x + 3) + (5x - 6x² - 1)

open the brackets

2x² - 4x + 3 + 5x - 6x² - 1

rearrange the priority order

2x² - 6x² - 4x + 5x + 3 - 1

combine like terms

-4x² + x + 2

Thus, The answer is (-4x² + x + 2)

Answer:

Step-by-step explanation:

The answer as I believe is H.

I just used the rise/run method, so you’ll go six up and 5 to the left ( the answer is negative because you’re moving to the left).

Hope this helps

Answer:

Any line that is in the form

y =

Step-by-step explanation:

See the graph below.  Perpendicular means that the lines meet at 90°.  You will see the black line graphed that is x = 2.  Then you will see two graphs in red.  y = 6 and y = -1.  any line in the form y = some number will be perpendicular to x = 2.

Do not reject H(0). There is not sufficient evidence to a manufacturer of transistors claims that its transistors will last an average of different than 1000 hours. at 0.01 significance level.

In the given question, a manufacturer of transistors claims that its transistors will last an average of 1000 hours.

To maintain this average, 25 resistors are tested each month.

We may assume that the distribution of the lifetime of a transistor is normal.

We have to calculate a sample that has a mean of 1010 and a standard deviation of 60.

So let us consider

X : Life time of a transistor

So we have

N=25

x=1010

s=60

Since sample size n(25≤30) is small and population standard is unknown so we use t statistic for hypothesis testing.

Now our null and alternate hypotheses are given as:

H(0): μ=1000

H(1): μ≠1000 (two tailed test)

Under Null hypothesis our test statistic is;

t=(x-μ)/(s/√n)

t=(1010-1000)/(60/√25)

t=0.83

Critical Value:

t(α,(n-1))=t(0.01, 24)

t(α,(n-1))=2.80

We have given level of significance α=0.01 and also we find the t-score 0.83 and degree of freedom=24

p value

The Excel formula is used to calculate the p value is:

P value =2×(1- (t(24) > 0.83))

P value =2×(1-0.7926)

P value =2×0.2074

P value =0.4147

Since p value=0.42 greater than α=0.01 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected and we claims that its transistors will last an average of 1000 hours.

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Answer:

240 = 150 + 120 + x

240 = 270 + x

x = 30

150 - 30 = 120 learned math only

120 - 30 = 90 english

30 = both subject

Step-by-step explanation:

The number of students who learn math only is 120 and those who learn both subjects are 30.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that in a class of 240 students 150 learn math and 120 learn English.

The number of students learning both subjects will be,

240 = 150 + 120 + x

240 = 270 + x

x = 30

The number of students learning math only,

150 - 30 = 120 learned math only

120 - 30 = 90 English

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Answer:

A

Step-by-step explanation:

y=-2 when x=-4 y=-4 when x=-8

what's given: 4. what's given:2

-4k=-2. -8k=-4

-4/4. -2/4. -8/8. -4/8

k=0.5. k =0.5

0.5(2) =1. 0.5(2)=1

Answer:

Step-by-step explanation:

You want to identify the proportional relations in the given tables and equations, and you want to find and use the constant of variation given that y=35 when x=7.

A proportional relation is one that has an equation of the form ...

  y = kx

One variable is a constant multiple of the other. If the relation cannot be put in this form, it is not a proportional relation.

The value of k in the above equation can be found as ...

  k = y/x . . . . . . . divide both sides by x

This is a constant if the relation is proportional.

  y/x = -8/-4 = -4/-2 ≠ 18/6 . . . . . not a proportional relation

  y/x = -4/-5 ≠ 10/2 . . . . . not a proportional relation

  y/x = -12/-3 = 24/6 = 32/8 = 4 . . . . . a proportional relation

You are looking for equations of the form y = kx. The only ones having that form are ...

The others represent inverse proportions and a linear (not proportional) relation.

As we saw above, the constant of variation is ...

  k = y/x = 35/7

  k = 5

Then the value of x can be found from ...

  49 = 5x

  49/5 = x = 9.8

The total number of fishes present in the lake on my 1 is 840.

The given data for the question-

September is equivalent to a percentage of tagged fish in May.

3/42 = 60/x

x = 60 *42 / 3

x = 840

Thus, the total number of fishes present in the lake on my 1 is 840.

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The ratios of calories Robyn burned on Thursday to the number of calories she burned for the week is 3 : 20.  

Ratio, in math, is a term that is used to compare two or more numbers. In other words, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

Therefore, the ratios of calories Robyn burned on Thursday to the number of calories she burned for the week can be calculated as follows:

Let's represent it in fractions,

calories burn on Thursday / calories burn for the week

calories burn on Thursday = 360

calories burn for the week = 488 + 551 + 610 + 360 + 391 = 2400

Hence,

360 / 2400 = 36 / 240 = 12 / 80 = 3 / 20

Therefore, the ratio is 3:20

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If the bookstore sells 15 pencils, the ratios of pens to pencil written as fraction is 2 / 3.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

Therefore, proportional relationship can be represented as follows:

y ∝x

y = kx

where

Therefore,

4 = 6k

k = 4 / 6

k = 2 / 3

Therefore, let's find the number of pen sold when the bookstore sells 15 pencils.

y = 15 × 2 / 3

y = 30 / 3

y = 10

Therefore, if the bookstore sell 15 pencils the ratio of pen to pencil is 10 / 15 = 2 / 3

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After 7 years  the laptop computer will be worth $200 or less.

Given:

A laptop computer is purchased for $1400 .

Each year, its value is 75%  of its value the year before.

After how many years will the laptop computer be worth $200  or less = ?

1400(0.75)t≤ 200

0.75t  ≤ 1/7

ln(0.75t) ≤ ln(1/7)

tln(0.75) ≤ ln(1/7)

t ≥ ln(1/7)/ln(0.75)

t ≥ 6.76

The natural log of a number between 0 and 1 is negative, and dividing by a negative switches the sign.

So, after 7 years, the laptop computer will be worth $200 or less.

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Translation is one of the four types of mathematical transformations that may be applied to a function graph.

(x, y) = (x + a, y + b)

In mathematics, a translation is the up, down, left, or right movement of a form. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more routes have been altered. There is no change in the form because it is just being moved from one location to another.

When the shape is moved towards the left by k units, then replace x with x - k.

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

When the shape is moved down by k units, then replace y with y - k.

Example: What are the new coordinates when the translation (x, y) → (x - 2, y + 3) is applied to the point (2, 5).

Solution:

The coordinates of old point (preimage) are (x, y) = (2, 5). Now, applying the given translation to this point,

x - 2 = 2 - 2 = 0

y + 3 = 5 + 3 = 8

Thus, the coordinates of the translated point (image) are (0, 8).

This was the example of translation.

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Concept: Proportion, to find the km/h return journer

3 hours to 84 km/hr = 3.5 hours to x km/hr

(since its inverse proportion, multiply the 1st to 2nd and 3rd to 4th)

Inverse proportion: as the other quantities increase, the other one decreases

3 : 84 = 3.5 : x

3(84) = 3.5x

252 = 3.5x                (divide 3.5 both sides)

x = 72

Step-by-step explanation:

- [(2x - cos x) / (2y - cos y)] of the following expressions represents sin x + sin y = x² + y², using the concept of differentiation.

One method is to determine a function's derivative by differentiation. Finding the instantaneous rate of change of a function depending on one of its variables is a technique known as differentiation in mathematics.

Differentiation refers to the process of calculating a function's derivative. The derivative, when applied to two variables x and y, is the rate at which x changes in relation to y. To calculate the immediate rate of change of quantities, differentiation is used.

sin x + sin y = x² + y²

Differentiating w.r.t x

d/dx (sin x + sin y) = d/dx (x² + y²)

or, cos x + cos y dy/dx = 2x + 2y dy/dx

or, cos y dy/dx - 2y dy/dx = 2x - cos x

or, dy/dx (cos y - 2y) = 2x - cos x

or, dy/dx = (2x - cos x) / (cos y - 2y)

or, dy/dx = - [(2x - cos x) / (2y - cos y)]

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The rate at which Submarine B descends is 29.8 feet per hour.

The rate refers to the average speed of an object in motion from one point to another.

The rate can be determined by dividing the distance by the time.

The rate or average speed is the quotient between distance and time.

The distance descended by Submarine A = 193.5 feet (126 + 4 ½ x 15)

The time Submarine B descends = 6.5 hours

Submarine B's rate of descent = 29.77 feet (193.5/6.5) per hour

= 29.8 feet

Thus, we can conclude that Submarine B descends at the rate of 29.8 feet every hour, whereas, Submarine A descends 15 feet per hour.

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