A rectangle ABCD is transformed to from other rectangle ABCD such the corresponding sides of the ABCD are unequal but proportional.which is transformation of ABCD could result in ABCD? A.dilation B.rotation C.reflection D.transformation

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer: 5(f+7)

Step-by-step explanation: I know you didn't ask for an explanation but here:

First what you want to do is find what both terms have in common, the LCM, (least common multiple), is the only thing common between them, which is 5, so divide 35 by 5, which is 7, and since you divided by 5, you put it outside, and put f and 7 together.

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

a) The parametric equations of the line are: x(t) = −2 + 3t, y(t) = 4 − 2t, z(t) = 3 + 4t and The symmetric equation of the line are: (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) The line intersects yz-plane at (0, 8/3, 17/3)

The given points on the line are:

(x₁, y₁, z₁) = (−2, 4, 3)

(x₂, y₂, z₂) = (1, 2, 7)

The direction ratios of this line are:

⟨a, b, c⟩ = ⟨x₂ − x₁, y₂ − y₁, z₂ − z₁⟩

             = ⟨1 + 2, 2 − 4, 7 − 3⟩

             = ⟨3, −2, 4⟩

a) Parametric equations of the line:

These are given by:

x(t) = x₁ + at = −2 + 3t

y(t) = y₁ + bt = 4 − 2t

z(t) = z₁ + ct = 3 + 4t

Symmetric equation of the line:

This is given by:

              (x − x₁)/a = (y − y₁)/b = (z − z₁)/c

              (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) When a line intersects the yz-plane, its x-coordinate is zero.

Using the parametric equations of the part (a):

                                   x = 0

                          −2 + 3t = 0

                                  3t = 2

                                    t = 2/3

Substitute this in the parametric equations corresponding to y and z as well:

                                   y = 4 −2t

                                      = 4 − 2(2/3)

                                      = 8/3

                                   z = 3 + 4t

                                      = 3 + 4(2/3)

                                      = 17/3

Hence, the required point is: (x, y, z) = (0, 8/3, 17/3)

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Answer:

B. 46.

Step-by-step explanation:

First we set up the equation A(n)=-172 and substitute the given equation for A(n), giving us -172=8+(n-1)(-4). Simplifying, we get -180=(-4n+12), or -4n=-192, or n=48. However, n represents the number of terms in the sequence, and since the sequence starts with n=1, we need to subtract 1 from our answer to get the term number corresponding to A(n)=-172. Therefore, the answer is B) 46.

Answer:

try growwithjo or mrandmrsmuscle on yt!!! they are fun and effective workouts.

Answer:

Kelly got a higher percentage score.

Step-by-step explanation:

35 / 52 = 0.673

47 / 68 = 0.691

Answer:

5/12 cup of water per plant

To determine the shaded portion in the following figures on the image attached

Count the number of shaded portions and divide by the number of unshaded portions. =

(a)

(b)

(c)

(d)

Answer:

yes

Step-by-step explanation:

Answer:

A. 3. ASA

B. 1. SSS

C. 2. SAS

D. AAS

Answer:

3 inches is 150 and 1/2 is 25

Step-by-step explanation:

Answer: a. The independent variable in the equation C(a) = 5a is a. It represents the number of art classes Amir attends.

b. The dependent variable in the equation C(a) = 5a is C(a). It represents the cost Amir incurs as he attends art classes. The dependent variable is dependent on the independent variable because the cost will change as the number of classes attended changes.

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Answer:

Step-by-step explanation:

Answer:

volume=base×length×height

surface area=2(length×base+base×height+length×height)

9514 1404 393

Answer:

  C.  $1,315.06

Step-by-step explanation:

Saving 103.19 per month for 12 months would give Ricky the amount of ...

  12 × $103.19 = $1238.28

The amount of interest earned on this amount in one year is ...

  I = Prt = $1238.28·0.031·1 = $38.39 . . . . rounded to nearest cent

Then the balance after 2 years will be ...

  $1238.28 +2 × $38.39 = $1315.06

Answer:

c

Step-by-step explanation:

Answer:

e = 16

Step-by-step explanation:

-5/6e - 2/3e = -24

-5/6e + -2/3e = -24

-3/2e = -24

e = 16

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{MN}\\ o=\stackrel{opposite}{18} \end{cases} \\\\\\ MN=\sqrt{ 30^2 - 18^2} \implies MN=\sqrt{ 576 }\implies MN=24 \\\\[-0.35em] ~\dotfill\\\\ \cos(M )=\cfrac{\stackrel{adjacent}{24}}{\underset{hypotenuse}{30}} \implies \cos(M)=\cfrac{4}{5}\)

The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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Answer: 48

Step-by-step explanation:

The Area of rectangle is 48 unit².

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area. The area of a plane figure is the space enclosed by its boundary. The number of unit squares that cover the surface of a closed form is the figure's area.

We have the graph from which we can write

width of rectangle = 8 unit

Length of rectangle= 6 unit

So, the area of rectangle

= lw

= 8 x 6

= 48 unit²

Thus, the Required Area is 48 unit².

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Answer:

$260.65

Step-by-step explanation:

189/100=1.89

1.89x15=28.35

289-28.35=260.65

Have a good day:)

Answer:

$245.65

Step-by-step explanation:

1. Determine how much is being spent.

- You are paying for only 85% of the bike since it is discounted by 15%.

2. Multiply 0.85 and 289.

- If you are only paying for 85% of the bike, that is what needs to be found.

The degree of the polynomial is 14

The polynomial is given as:

y^2+7x^14-10x^2

Here, we assume that the variable of the polynomial is x

The highest power of x in the polynomial y^2+7x^14-10x^2 is 14

Hence, the degree of the polynomial is 14

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Answer: the expected value of Tom's payoff is m²

Step-by-step explanation:

Given the data in the question,

E[x] = mp                                        

where p = 1/2

Now Tom gets payoff pounds until a tail first appears = 2m pounds

so

E[x] = m × 1/2 × 2m

E[x] = m²

Therefore the expected value of Tom's payoff is m²

The other two factors are (x-3), and (x+4)

given that

polynomial p(x) = (x+5)(x-)(x+)

p(x) = \(x^{3}\) + 6\(x^{2}\) -7x - 60

So,

\(x^{2}\) +x -12 =0

\(x^{2}\) + 4x -3x -12 = 0

x(x+4) - 3(x + 4) = 0

(x -3)(x+4) = 0

the other two factors are (x-3), and (x+4).

Polynomial: A polynomial is a function that can be written in the form of

p(x)= \(a_{n}\)\(x^{n}\) + \(a_{n-1}\)\(x_{n-1}\)+..........+\(a_{1}\)x +\(a_{0}\) each ai is a real number, an≠0 and n≥0

Zero: A zero of a polynomial is an x-value for which the polynomial equals zero. This means that if x = c is a zero, then p(c) = 0 The zeros correspond to the x-intercepts of the polynomial

Multiplicity: The multiplicity of a zero, x = c, is the number of times the factor (x−c) appears in the fully factored form of the polynomial. This is equal to the exponent on the factor.

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Answer:

a₄ = 50

Step-by-step explanation:

work back from the seventh term a₇ using the reverse of the term to term rule , that is

divide by 2 then subtract 3

a₇ = 442

a₆ = 442 ÷ 2 - 3 = 221 - 3 = 218

a₅ = 218 ÷ 2 - 3 = 109 - 3 = 106

a₄ = 106 ÷ 2 - 3 = 53 - 3 = 50

Answer:

\(a_{4}=50\)

Step-by-step explanation:

\(a_{4} = 50\)

a₇ = 442

a₆ = 442 ÷ 2 - 3 = 221 - 3 = 218

a₅ = 218 ÷ 2 - 3 = 109 - 3 = 106

a₄ = 106 ÷ 2 - 3 = 53 - 3 = 50

The equation of the parabola is y = (x + 2)² - 2, and the value of f(-1) is -1 after plugging x = -1 in the function.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

From the graph the vertex form of the parabola:

(-2, -2)

h = -2

k = -2

The vertex form of the parabola:

y = a(x - h)² + k

y = a(x + 2)² - 2

Plug x = 0

y = 2

a = 1

y = (x + 2)² - 2

Or

f(x) = (x + 2)² - 2

f(-1) = (-1 + 2)² - 2

f(-1) = -1

Thus, the equation of the parabola is y = (x + 2)² - 2, and the value of f(-1) is -1 after plugging x = -1 in the function.

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Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)

Step-by-step explanation:

(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):

(6/x)/(6/x+2)

I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->

(6 +2x)/x

Do the classic keep, change, flip. \(\frac{6}{x} * \frac{x}{6+2x}\)

This simplifies to: \(\frac{6}{6+2x}\)

(b) Domain is all real numbers except for what makes the denominator equal to 0.     6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.

We have 98 % confidence that the true mean time a student sleeps per night is between 6.2928 hours and  7.1832 hours.

Mean = (8.6 + 8.3 + 7.6 + 6 + 7.1 + 5.6 + 5.1 + 6)/ 8 =  6.7875

Standard deviation = √Σ(x - mean)²/n

Σ(x - mean)² = (8.6 - 6.7875)^2 + (8.3 - 6.7875)^2 + (7.6 - 6.7875)^2 + (6 - 6.7875)^2 + (7.1 - 6.7875)^2 + (5.6 - 6.7875)^2 + (5.1 - 6.7875)^2 + (6 - 6.7875)^2

Standard deviation  : \(\sqrt{11.82875}/8\)

s = 0.42991

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

sample standard deviation

number of samples

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 8 - 1 = 7

Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99

Looking at the t distribution table,

z = 2.998

Margin of error = 2.998 × 0.42/√8

                        = 0.4452

The lower limit of this confidence interval is

6.738 - 0.4452 = 6.2928

The upper limit of this confidence interval is

6.738 + 0.4452 = 7.1832

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Answer:

Step-by-step explanation:

                                                   error

Answer:

x ≈ 75.2

Step-by-step explanation:

using the tangent ratio in the right triangle

tan62° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{40}\) ( multiply both sides by 40 )

40 × tan62° = x , then

x ≈ 75.2 ( to the nearest tenth )

Answer:

Therefore, the Panthers had a better overall record for the season, with a total of 212 points earned compared to the Cowboys' total of 173 points.

Step-by-step explanation:

To compare the measures of center, we can calculate the mean and median points earned by each team:

Panthers: Mean = 212/15 = 14.13 points, Median = 14 points

Cowboys: Mean = 173/15 = 11.53 points, Median = 10 points

Based on these calculations, we can see that the Panthers have a larger mean value of about 14.13 points compared to the Cowboys' mean value of about 11.53 points. However, the median value for both teams is less useful for comparison since they are only one point apart. Therefore, we can conclude that the Panthers had the better overall record for the season based on both the total points earned and their larger mean value.

So, the answer is Panthers; they have a larger mean value of about 14.8 points (Option C is incorrect as the mean value of Panthers is approximately 14.13 and not 14.8).