let be a regular pentagon, and let be the midpoint of side . what is the measure of angle in degrees?

The required solution of the given initial value problem is y(t) = -2e^(-7t/2).

The given differential equation is 2y'' + 13y' - 7y = 0,

with initial conditions y(0) = -2,

y'(0) = -9.

For solving the initial value problem, we follow the steps given below:

Step 1:

Write the auxiliary equation.

For the given differential equation, the auxiliary equation is:

2m² + 13m - 7 = 0

Step 2:

Solve the auxiliary equation for m.

Solving the above quadratic equation by factoring, we get:

(2m - 1)(m + 7) = 0

So, m = 1/2 or m = -7

Step 3:

Write the general solution of the differential equation.

The general solution of the given differential equation is:

y(t) = c1e^(-7t/2) + c2e^(t/2)

Step 4:

Apply initial conditions.

Substituting y(0) = -2 in the general solution, we get: -2 = c1 + c2  ...

(1)Differentiating the general solution w.r.t. t, we get:

y'(t) = (-7/2)c1e^(-7t/2) + (1/2)c2e^(t/2)

Substituting y'(0) = -9 in the above equation, we get:

-9 = (-7/2)c1 + (1/2)c2  ...

(2)Solving equations (1) and (2) simultaneously, we get:

c1 = -2 and c2 = 0

Substituting the values of c1 and c2 in the general solution, we get:

y(t) = -2e^(-7t/2)

Therefore, the required solution of the given initial value problem is y(t) = -2e^(-7t/2).

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Ŝ\(_{1}\), the slope estimator is:

A: \(\beta\)\(_{1}\) X is a random variable
D: When the LINE assumptions are met, the mean of Ê, is \(\beta\)\(_{1}\), the slope in the population regression model.


The slope estimator Ŝ\(_{1}\) is a random variable because it is a function of the random sample data. When the LINE assumptions are met, the mean of Ŝ\(_{1}\) is equal to the slope in the population regression model, \(\beta _{1}\). This means that Ŝ\(_{1}\) is an unbiased estimator of \(\beta _{1}\). However, the variance of Ŝ\(_{1}\) is dependent on the predictor variable values (X) and the distribution of Ŝ\(_{1}\) is not necessarily Normal.

"

Complete question

What can we say about Ŝ1, the slope estimator? Please select all that apply. It's possible that there is only one correct answer.

A: B 1 X is a random variable

B: When the LINE assumptions are met, the variance of Ê, is not dependent on the predictor variable values (X).

C: When the LINE assumptions are met, Ê, has a Normal distribution.

D: When the LINE assumptions are met, the mean of Ê, is B1, the slope in the population regression model.

"

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The sum of the numerator and denominator of the decimal is found as 111.

As for the given question;

The decimal number is given as;

0.12 bar

Decimal to fraction conversion

100(0.12 bar) = 12(0.12 bar)

99.(0.12bar) = 100(0.12bar) - (0.12 bar)

99.(0.12bar) = 12 × 0.12bar - 0.12bar

99.(0.12bar) = 12

0.12 bar = 12/99 (lowest fraction)

Thus, in the result the numerator is found as 12 and the denominator is found as 99.

Add = 12 + 99

Add = 111

Thus, the sum of the numerator and denominator of the decimal is found as 111.

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Answer:

\(m=-3\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in the 2 coordinates into the slope formula to find slope m:

\(m=\frac{5-(-1)}{-5-(-3)}\)

\(m=\frac{5+1}{-5+3}\)

\(m=\frac{6}{-2}\)

\(m=-3\)

Answer:

\(x = 14 - 3\)

Step-by-step explanation:

*The key word 'less than' means to subtract.

x + 3 = 14 is incorrect. Kiran isn't adding weight to his backpack.

In other words, the backpack didn't increase in pounds.

3(x) = 14 is incorrect. Multiplying is irrelevant to this problem, it's not saying Kiran's backpack is 3 times a number equal to Clare's backpack weight.

x = 143 is incorrect. This equation is unrealistic.

x = 14 - 3 is correct. This equation is explaining that Kiran's backpack is 3 pounds less than Clare's backpack (14)

The volume of the container is 444 m³

The region occupied by a cuboid is known as the volume of the cuboid. We can find the volume of a cuboid by calculating the product of the length breadth and height of the cuboid.

=> Volume of cuboid = Length × Breadth × Height

Here we have

Plant container which can be divided into two parts

The first part is a cuboid with dimensions of 15 m × 4 m × 3 m  

Volume of cuboid = 15 m × 4 m × 3 m = 180 m³  

The lower part is a cuboid with dimensions of 8 m × 11 m × 3 m  

Volume of the cuboid = 8 m × 11 m × 3 m = 264 m³  

From the above calculations,

The volume of the container = 180 m³ + 264 m³ = 444 m³  

Therefore,

The volume of the container is 444 m³

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Given:

We're given a four-sided figure.

Value of ∠ADB = 9x + 20

Value of ∠DBC = 15x + 2

To find:

The value of x for which ABCD must be a parallelogram.

Step-by-step solution:

For ABCD to be a parallelogram, Alternate angles (Z angles) should be equal:

Thus,

∠ADB = ∠DBC

9x + 20 = 15x + 2

18 = 6x

x = 3

Final answer:

Thus we can say that the value of x should be 3 for ABCD to be a parallelogram.

Answer:

m≤1

Step-by-step explanation:

Move the variable to the left,

m-5m≥-4

Collect like terms so you would have,

-4m≥-4

Then divide and switch the sign because you divided,

m≤1

Answer:

Fraction of the garden used =  \(\frac{5}{8}\)

Step-by-step explanation:

The fifth graders to plant a butterfly garden.

We are given that

Clover grows in ½ of the garden

Daisies grow in ¼ of the garden

Coneflowers grow in ⅛ of the garden

milkweed grows in ⅛ of the garden

The fifth graders notice that the butterflies land on the clover and milkweed.

We are asked to find out the fraction of the garden that the butterflies used.

Fraction of the garden used = clover + milkweed

Fraction of the garden used =  \(\frac{1}{2} + \frac{1}{8}\)

The LCM of 2 and 8 is 8

Fraction of the garden used =  \(\frac{4 +1}{8}\)

Fraction of the garden used =  \(\frac{5}{8}\)

Therefore, the butterflies used \(\frac{5}{8}\) fraction of the garden.

Answer:

I can't read it.

Step-by-step explanation:

The difference quotient for the function \(f(x) = -\frac{1}{5x-12}\)  is \(\frac{5}{(5x+5h-12)(5x-12)};\) h≠0

Option B) is the correct answer.

Given that;

We know that difference quotient is expressed as;

\(\frac{f(x+h)-f(x)}{h}\)

Next, substitute x+h for x.

Hence;

\(f(x+h) = -\frac{1}{5(x+h)-12}\)

Now,

\(\frac{f(x+h)-f(x)}{h} = \frac{-\frac{1}{5(x+h)-12}-(-\frac{1}{5x-12}) }{h} \\\\= \frac{5}{(5x-12)(5h+5x-12)}\\\\= \frac{5}{(5x+5h-12)(5x-12)};\)h≠0

The difference quotient for the function \(f(x) = -\frac{1}{5x-12}\)  is \(\frac{5}{(5x+5h-12)(5x-12)};\) h≠0

Option B) is the correct answer.

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The equation that represents the number of pages Ben can read per minute is p = (3/4)m.

The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.

If x and y are in direct proportion then

=>  x ∝ y

=>  x = ky  [ where k is constant ]

Here we have,

Ben reads 6 pages in 8 minutes

9 pages can be read in 12 minutes

30 pages can be read in 40 minutes

And the number of minutes = m

Number of pages = p

If observe the given data,

When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages

=> p ∝ m

=> p = km --- (1)  

[ where k is constant ]  

From the given data,

At p = 6 pages, m = 8 minutes

=> 6 = k(8)

=> k = 6/8 = 3/4

From (1)

=> p = (3/4)m

Therefore,

The equation that represents the number of pages Ben can read per minute is p = (3/4)m

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The greatest common factor of their product is 2

From the question, we have the following parameters that can be used in our computation:

GCF of 2x - 4 = 2

GCF of 4 * 8  = 4

Using the above as a guide, we have the following expressions

GCF of 2x - 4 = 2

GCF of 4 * 8  = 2  * 2

Write out the common factors

GCF = 2

This means that the GCF is 2

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Answer:

139.18 is the answer, I even double checked

Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

Complementary angles are defined as two angles whose sum is 90 degrees.

Complementary angles sum up to 90 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

Therefore, the sum of the angles is 180 degrees.

Let's find the angles that are supplementary or complementary to the highlighted angles.

Therefore,

Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

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Answer:

can you tell me a little bit more?

Answer:

X= 2 and y = 3

Step-by-step explanation:

Answer:

The circumfrence is 150pi.

Step-by-step explanation:

While a circle, symbolically, represents many different things to many different groups of people including concepts such as eternity, timelessness, and totality, a circle by definition is a simple closed shape. It is a set of all points in a plane that are equidistant from a given point, called the center. It can also be defined as a curve traced by a point where the distance from a given point remains constant as the point moves. The distance between any point of a circle and the center of a circle is called its radius, while the diameter of a circle is defined as the largest distance between any two points on a circle. Essentially, the diameter is twice the radius, as the largest distance between two points on a circle has to be a line segment through the center of a circle. The circumference of a circle can be defined as the distance around the circle, or the length of a circuit along the circle. All of these values are related through the mathematical constant π, or pi, which is the ratio of a circle's circumference to its diameter, and is approximately 3.14159. π is an irrational number meaning that it cannot be expressed exactly as a fraction (though it is often approximated as 22/7) and its decimal representation never ends or has a permanent repeating pattern. It is also a transcendental number, meaning that it is not the root of any non-zero, polynomial that has rational coefficients. Interestingly, the proof by Ferdinand von Lindemann in 1880 that π is transcendental finally put an end to the millennia-old quest that began with ancient geometers of "squaring the circle." This involved attempting to construct a square with the same area as a given circle within a finite number of steps, only using a compass and straightedge. While it is now known that this is impossible, and imagining the ardent efforts of flustered ancient geometers attempting the impossible by candlelight might evoke a ludicrous image, it is important to remember that it is thanks to people like these that so many mathematical concepts are well defined today.

Answer:

598

Step-by-step explanation:

800x0.93^4

Answer:

x = 23 and y = 20

Step-by-step explanation:

Therefore, the value of δx for this problem is 2.

To find the value of δx, we first need to understand what l4 means in the context of this function.
l4 refers to the fourth subinterval of the interval [2,10]. To find the value of l4, we need to divide the interval [2,10] into smaller subintervals.
Let's first find the total number of subintervals. We can do this by subtracting the lower limit from the upper limit and dividing by the desired length of each subinterval:
Total number of subintervals = (10 - 2) / δx
We want to find the fourth subinterval, so we need to determine the value of δx that gives us four subintervals.
(10 - 2) / δx = 4
Solving for δx, we get:
δx = (10 - 2) / 4 = 2
Therefore, the value of δx for this problem is 2.

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Answer:

(1/2)(6)(4) = 12 square inches

2 inches = 5 feet, so 4 square inches = 25 square feet.

12/4 = s/25, so s = 75 square feet

a. The angle fact that Mohammed can use to find angle g is alternate angles

b) The angle fact that he then use to find angle h is alternate interior angles.

When two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent, according to the alternate angle theorem. To demonstrate: If a transversal cuts two parallel lines, the alternate interior angles are equal.

When two parallel lines are intersected by a transversal, the angles formed inside them are equal to their alternate pairs. These are known as alternate interior angles.

In this case, it should be noted that the angles will be 137° based on the illustration.

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The measure of angle DHG in triangle ΔABC, with H as the incenter, is 90 degrees.The measure of angle DHG can be found using the properties of an incenter.

Step 1: Draw the triangle ΔABC and locate point H, the incenter.
Step 2: Draw the angle bisectors from each vertex of the triangle to point H, creating three smaller angles:

∠DHA, ∠AHB, and ∠BHC.
Step 3: Since H is the incenter, the angle bisectors meet at right angles, forming a right triangle DHG.
Step 4: In a right triangle, the measure of the right angle is 90 degrees.
Therefore, the measure of angle DHG is 90 degrees.
The measure of angle DHG in triangle ΔABC, with H as the incenter, is 90 degrees.

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The probability that the batch is accepted if it contains five defectives will be 0.812.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Here,

P(A)=(1-5/100)*(1-5/99)*(1-5/98)*(1-5/97)

=0.812

If the batch has five defects, there is a 0.812 percent chance that it will be approved.

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There are 10000 micrometers are in a centimeter.

What is micrometers?

 Micrometers are commonly used to determine the thickness or diameter of microscopic objects such as microorganisms and colloidal particles. The International Bureau of Weights and Measures' symbol for a micrometre is m. The micrometer is a length unit derived from SI that equals 106 metre (SI standard prefix "micro-" = 106) and is equivalent to one millionth of a metre or one thousandth of a millimetre.

Here we know that ,

1 centimeter = 10000 micrometers.

If we want to convert 1 centimeter into micrometer we need to multiply by 10000.

Hence there are 10000 micrometers are in a centimeter.

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Answer: a+b=b+a is a clear example of commutative property.

Step-by-step explanation: The commutative property applies to addition and multiplication. The property states that terms can “commute,” or move locations, and the result will not be affected. This is expressed as a+b=b+a for addition, and a×b=b×a for multiplication. The commutative property does not apply to subtraction or division.

Answer:

9

Step-by-step explanation:

2/3 = 2/3 × 3/3 = 6/9

7/9 = 7/9 × 1/1 = 7/9

The expression for the area under the curve y = x^3 from 0 to 1, as a limit, is A = 1/4.

(a) To find an expression for the area under the curve y = x^3 from 0 to 1 using Definition 2, we need to approximate the area using a sum and then take the limit as the number of approximating rectangles approaches infinity.

Let's divide the interval [0, 1] into n equal subintervals. The width of each subinterval will be Δx = 1/n. We can choose any point within each subinterval as the representative x-value for that subinterval. Let's choose the right endpoint of each subinterval as our representative x-value.

The right endpoint of the ith subinterval will be x_i = iΔx = i/n, where i ranges from 1 to n. The corresponding y-value for each x_i is y_i = (i/n)^3.

The area of each rectangle can be approximated as the product of the width and height of the rectangle, which is ΔA_i = Δx  y_i = (1/n)  (i/n)^3.

The total area under the curve can be approximated by summing up the areas of all the rectangles:

A = Σ(ΔA_i) = Σ[(1/n)  (i/n)^3] for i = 1 to n.

(b) The formula given in Appendix E states that the sum of the cubes of the first n integers is [n(n+1)/2]^2. Therefore, we have:

1^3 + 2^3 + 3^3 + ... + n^3 = [n(n+1)/2]^2.

Using this formula, we can rewrite the expression for the area under the curve as a limit:

A ≈ Σ[(1/n)  (i/n)^3] for i = 1 to n

= (1/n^4)  [1^3 + 2^3 + 3^3 + ... + n^3]

= (1/n^4)  [n(n+1)/2]^2.

Taking the limit as n approaches infinity, we have:

A = lim(n→∞) [(1/n^4) [n(n+1)/2]^2]

= lim(n→∞) [(n^2(n+1)/2)^2 / n^4]

= lim(n→∞) [(n^4 + 2n^3 + n^2) / 4n^2]

= lim(n→∞) [(1 + 2/n + 1/n^2) / 4]

= (1 + 0 + 0) / 4

= 1/4.

Therefore, the expression for the area under the curve y = x^3 from 0 to 1, as a limit, is A = 1/4.

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To calculate the earnings per share, we need to divide the company's profit by the number of outstanding shares. The given information includes the company's profit of $117,667,008 and the share price of $56.97.

To determine the earnings per share, we need to know the number of outstanding shares. Since the number of outstanding shares is not provided in the given information, it is not possible to calculate the earnings per share with the given data alone.

The earnings per share (EPS) is calculated by dividing the company's profit by the number of outstanding shares. It represents the portion of the company's profit that is allocated to each outstanding share. By dividing the profit by the number of shares, we can determine how much profit is attributable to each individual share.

However, without the number of outstanding shares, we cannot calculate the exact earnings per share. The market capitalization and current share price do not provide enough information to determine the number of shares outstanding. Additional information, such as the number of shares issued by the company, is needed to calculate the earnings per share accurately.

In summary, the earnings per share cannot be determined with the given information alone. The calculation requires the number of outstanding shares, which is not provided. The earnings per share is a measure of the company's profitability allocated to each share, obtained by dividing the company's profit by the number of outstanding shares. To calculate the earnings per share accurately, the number of shares outstanding must be known.

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