ABC has vertices A(-3,2). B(3,2), and C(0, – 3). Is ABC scalene, isosceles, or equilateral?
Is ABC scalene, isosceles, or equilateral?

Answer:

\(y(x)=-\frac{3}{4}-\frac{1}{2}x-\frac{1}{2}x^2+\frac{2}{3}e^{-2x}+\frac{1}{12}e^x\)

Step-by-step explanation:

\(y''+y'-2y=x^2,\: y(0)=0,\: y'(0)=0\\\\\mathcal{L}\{y''\}+\mathcal{L}\{y'\}-2\mathcal{L}\{y\}=\mathcal{L}\{x^2\}\\\\s^2Y(s)-sy(0)-y'(0)+sY(s)-y(0)-2Y(s)=\frac{2}{s^3}\\ \\s^2Y(s)+sY(s)-2Y(s)=\frac{2}{s^3}\\ \\(s^2+s-2)Y(s)=\frac{2}{s^3}\\ \\Y(s)=\frac{2}{s^3(s^2+s-2)}\\ \\Y(s)=\frac{2}{s^3(s+2)(s-1)}\)

Perform the partial fraction decomposition

\(\frac{2}{s^3(s+2)(s-1)}=\frac{A}{s}+\frac{B}{s^2}+\frac{C}{s^3}+\frac{D}{s+2}+\frac{E}{s-1}\\\\2=s^2(s+2)(s-1)A+s(s+2)(s-1)B+(s+2)(s-1)C+s^3(s-1)D+s^3(s+2)E\\\\2=s^{4} A + s^{4} D + s^{4} E + s^{3} A + s^{3} B + 2 s^{3} D - s^{3} E - 2 s^{2} A + s^{2} B + s^{2} C - 2 s B + s C - 2 C\\\\2=s^{4} \left(A + D + E\right) + s^{3} \left(A + B + 2 D - E\right) + s^{2} \left(- 2 A + B + C\right) + s \left(- 2 B + C\right) - 2 C\)

Solve for each constant

\(\begin{cases} A + D + E = 0\\A + B + 2 D - E = 0\\- 2 A + B + C = 0\\- 2 B + C = 0\\- 2 C = 2 \end{cases}\)

\(-2C=2\\C=-1\)

\(-2B+C=0\\-2B+(-1)=0\\-2B-1=0\\-2B=1\\B=-\frac{1}{2}\)

\(-2A+B+C=0\\-2A+(-\frac{1}{2})+(-1)=0\\-2A-\frac{1}{2}-1=0\\-2A-\frac{3}{2}=0\\-2A=\frac{3}{2}\\ A=-\frac{3}{4}\)

\(A+D+E=0\\-\frac{3}{4}+D+E=0\\D+E=\frac{3}{4}\\D=\frac{3}{4}-E\)

\(A+B+2D-E=0\\-\frac{3}{4}+(-\frac{1}{2})+2(\frac{3}{4}-E)-E=0\\-\frac{3}{4}-\frac{1}{2}+\frac{3}{2}-2E-E=0\\-\frac{3}{4}+1-3E=0\\\frac{1}{4}-3E=0\\\frac{1}{4}=3E\\\frac{1}{12}=E\)

\(D=\frac{3}{4}-E\\D=\frac{3}{4}-\frac{1}{12}\\D=\frac{9}{12}-\frac{1}{12}\\D=\frac{8}{12}\\D=\frac{2}{3}\)

Take the inverse transform and find the solution to the IVP

\(Y(s)=\frac{-\frac{3}{4}}{s}+\frac{-\frac{1}{2}}{s^2}+\frac{-1}{s^3}+\frac{\frac{2}{3}}{s+2}+\frac{\frac{1}{12}}{s-1}\\ \\y(x)=-\frac{3}{4}-\frac{1}{2}x-\frac{1}{2}x^2+\frac{2}{3}e^{-2x}+\frac{1}{12}e^x\)

Answer:0.8p+1 and 1+0.8p

Step-by-step explanation:

0.5p+0.3p=0.8p

7-6=+1

0.8p+1

and

Swap both numbers

(0.5p+7)+(0.3p-6)=1+0.8p

Answer:

x=-7±√97/4

Step-by-step explanation:

-7±√97

______

    4

Answer:

\( \dfrac{580}{9} \)

Step-by-step explanation:

\( \dfrac{1}{5}x + \dfrac{1}{4}x = 29 \)

\( \dfrac{4}{20}x + \dfrac{5}{20}x = 29 \)

\( \dfrac{9}{20}x = 29 \)

\( x = 29 \times \dfrac{20}{9} \)

\( x = \dfrac{580}{9} \)

Answer: \( \dfrac{580}{9} \)

Answer:

0.104 = 10.4% probability that at least 2 drive without a seatbelt.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they drive without a seatbelt, or they do not. The probability of a person driving without a seatbelt is independent of any other person. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

20% of the people in Fiji drive the car without seatbelt.

This means that \(p = 0.2\)

3 people are randomly selected

This means that \(n = 3\)

Find the probability that at least 2 drive without a seatbelt?

This is:

\(P(X \geq 2) = P(X = 2) + P(X = 3)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{3,2}.(0.2)^{2}.(0.8)^{1} = 0.096\)

\(P(X = 3) = C_{3,3}.(0.2)^{3}.(0.8)^{0} = 0.008\)

\(P(X \geq 2) = P(X = 2) + P(X = 3) = 0.096 + 0.008 = 0.104\)

0.104 = 10.4% probability that at least 2 drive without a seatbelt.

Answer:

44 inches and 24 inches

Step-by-step explanation:

Let \(l,b\) denotes length and breadth of a rectangle.

\(lb=1056\)

A square of 3 inches is cut from each corner, and an open box is made by turning up the ends and sides.

New length \(=l-6\) inches

New breadth \(=b-6\) inches

Height of box \(=3\) inches

Volume of box = length × breadth × height

\((l-6)(b-6)3=2052\)

\(lb-6l-6b+36=684\\6(l+b)=408\\l+b=68\\b=68-l\)

Put \(b=68-l\) in \(lb=1056\)

\(l(68-l)=1056\\l^2-68l+1056=0\\l^2-44l-24l+1056=0\\l(l-44)-24(l-44)=0\\(l-24)(l-44)=0\\l=24,44\)

At \(l=24,b=\frac{1056}{24}=44\) inches

At \(l=44,b=\frac{1056}{44}=24\) inches

Answer:

She saved $27

Step-by-step explanation:

Search "what is 30% of $90"

It says 27 US$

Answer:

8(9).894 is the correct answer

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

52

Step-by-step explanation:

Answer:52

Step-by-step explanation:

Let x represent the weight of Jessica’s dog

Let y represent the weight of Emma’s dog

The dogs weigh 38 pounds altogether.It means that

x + y = 38

Emma’s dog weighs 10 pounds more than Jessica’s dog. It means that

y = x + 10

Substituting y = x + 10 into the first equation, then

x + x + 10 = 38

2x + 10 = 38

The equation that can be used to find the weight of Jessica’s dog is

2x + 10 = 38

The function family of f(x) = 5x - 2 is the linear function and the comparison of the graphs of y = x and f(x) = 5x - 2 is that:

The function is given as:

f(x) = 5x - 2

Linear functions are represented as:

y = mx + c

The equation f(x) = 5x - 2 take the form of a linear function.

And the parent function of a linear function is y = x

Hence, the function family of f(x) = 5x - 2 is the linear function

The comparison of the graphs of y = x and f(x) = 5x - 2 is that:

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When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.

A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.

The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.

When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.

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Answer:

5

Step-by-step explanation:

Answer:

62 %

Step-by-step explanation:

186   out of 300

186/300 = .62    this represents 62%

Answer:

The first is 12

The second is 25.35

Step-by-step explanation:

The second is confusing so sorry if I got that wrong

Please give brainelest

9514 1404 393

Answer:

  1856

Step-by-step explanation:

The numbers given do not have a common difference, but they do have a common ratio:

  58/29 = 116/58 = 2

The general term of a geometric sequence with first term a1 and common ratio r is ...

  an = a1×r^(n-1)

For this sequence, a1=29 and r=2, so the general term is ...

  an = 29×2^(n-1)

Then the 7th term is ...

  a7 = 29×2^(7-1) = 29×64 = 1856

The 7th term is 1856.

_____

If you prefer, you can double each term until you have 7 of them.

 29, 58, 116, 232, 464, 928, 1856, ...

Complete question :

The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29.Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.

Answer:

0.10868

Step-by-step explanation:

Given that :

Mean (m) = 3.02

Standard deviation (s) = 0.29

Sample size (n) = 20

Probability of 3.10 GPA or higher

P(x ≥ 3.10)

Applying the relation to obtain the standardized score (Z) :

Z = (x - m) / s /√n

Z = (3.10 - 3.02) / 0.29 / √20

Z = 0.08 / 0.0648459

Z = 1.2336940

p(Z ≥ 1.2336) = 0.10868 ( Z probability calculator)

Answer:

90

Step-by-step explanation:

90 degrees minus 35 degrees equals 65 degrees

I'll help.

The answer to your question is True!!

So,the value of the 30th percentile of the given data will be =P30=4

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, assessed at x, is the likelihood that X will have a value less than or equal to x in probability theory and statistics.

Using the Cumulative Distribution Function to Calculate Probabilities

F(x) is a cumulative distribution function that calculates the likelihood that the random variable X is smaller than or equal to x:

To get the cumulative probability that X is less than or equal to 1, multiply P(X=0) by P(X = 0) by (P=1):

First, we will determine the value of the cumulative probability P(X<=x):

x         f(x)       P(X<=x)

1       0.02          0.02

2       0.01          0.03

3       0.2          0.23

4       0.17           0.4

5       0.39           0.79

6       0.2           0.99

7 0.01 1

30th percentile will be the x value,

below which less than or equal to 30% of the data falls.

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Answer:

47, 17

Step-by-step explanation:

Let the numbers be x and y. Then, x+y=64 and x-y=30. Adding these equations, we get 2x=94, and thus x=47.

It follows that y=17.

Answer: a

Step-by-step explanation: C is in quadrant 1 and quadrant 1 is (+,+)

The coordinate of the point C will be (b, c). Then the correct option is A.

The polygon which is having five sides and each side are congruent. And each internal angle of the Pentagon will be of 108 degrees.

The pentagon ABCDE with the coordinate of A, B, C, D, and E are given below.

If a line intersect the shape and the shape look identical on both sides of line, then the line is known as axis of symmetry.

In a regular pentagon, there are five line of symmetry.

In the figure, the y-axis is the axis of symmetry and the axis of symmetry is passing through the point D.

The point C is in the first coordinate, then the abscissa and ordinate will be positive.

Then the coordinate of the C will be (b, c).

Then the correct option is A.

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Arithmetic operation - The answer will be 60 minutes.

What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

For one minute the word typed is 90 words
1 page contains 540 words 10 pages will have 5400 words.
So, 5400 words will be type in 5400/90 = 60 minutes
Hence it will take 60 minutes to type 10 pages.

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Answer:

think answer is 0.5 each

Answer:

\(Ratio = 0.74\)

Step-by-step explanation:

Represent

- Andy with A

- Christopher with C

\(A = 3.5L\)

\(C = 2580mL\)

Required

Determine the ratio of C to A

Ratio is represented as thus:

\(Ratio = C:A\)

Rewrite as fraction

\(Ratio = \frac{C}{A}\)

This gives

\(Ratio = \frac{2580mL}{3.5L}\)

Convert L to mL

\(Ratio = \frac{2580mL}{3.5*1000mL}\)

\(Ratio = \frac{2580mL}{3500mL}\)

\(Ratio = \frac{2580}{3500}\)

\(Ratio = 0.73714285714\)

\(Ratio = 0.74\) --- Approximated

Answer:

732 samples ;

752 samples

Step-by-step explanation:

Given :

α = 90% ; M.E = 0.03 ; p = 0.58 ; 1 - p = 1 - 0.58 = 0.42

Using the relation :

n = (Z² * p * (1 - p)) / M.E²

Zcritical at 90% = 1.645

n = (1.645² * 0.58 * 0.42) / 0.03²

n = 0.65918769 / 0.0009

n = 732.43076

n = 732 samples

B.)

If no prior estimate is given, then p = 0.5 ; 1 - p = 1 - 0.5 = 0.5

n = (Z² * p * (1 - p)) / M.E²

Zcritical at 90% = 1.645

n = (1.645² * 0.5 * 0.5) / 0.03²

n = 0.67650625 / 0.0009

n = 751.67361

n = 752 samples

Answer:

-0.3, -0.12, -0.03, 0.15

Step-by-step explanation:

-0.3 is the least because 0.3 = 0.30 and 0.30 is greater than 0.12, -0.12 is the second one because it is 0.12 behind 0 and is greater than -0.03. 0.15 is the last one because it is the only positive number therefore is the greatest one.

really hope this helps and isn't confusing but I'm pretty sure this is correct!