In an isosceles triangle △ABC with base of AB=8, points K and L are marked on sides AC and BC accordingly, such that KL∥ AB. It turns out that △BLK and △AKB are also isosceles triangles. What can be the length of CL?

Answer:

C. 5 is solution of the inequality: B>2.1

Answer:

  1.39 km/h

Step-by-step explanation:

Let the initial position of ship B represent the origin of our coordinate system. Then the position of ship A as a function of time t is ...

  A = -120 +20t . . . (east of the origin)

and the position of B is ...

  B = 15t . . . (north of the origin)

Then the distance between them is ...

  d = √(A² +B²) = √((-120 +20t)² +(15t)²) = √(625t² -4800t +1440)

And the rate of change is ...

  d' = (625t -2400)/√(625t² -4800t +14400)

At t = 4, the rate of change is ...

  d' = (625·4 -2400)/√(625·16 -4800·4 +14400) = 100/√5200 = 1.39 . . . km/h

The distance between the ships is increasing at about 1.39 km/h.

Answer:

[tex]\huge\boxed{a=\dfrac{16}{3}=5\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\triangle ZYW\sim\triangle WYX\ (AAA)\\\\\text{Therefore corresponding sides are in proportion}\\\\\dfrac{YX}{YW}=\dfrac{YW}{ZY}\\\\\text{substitute}\\\\YX=a;\ YW=4;\ ZY=3\\\\\dfrac{a}{4}=\dfrac{4}{3}\qquad\text{multiply both sides by 4}\\\\4\cdot\dfrac{a}{4}=4\cdot\dfrac{4}{3}\qquad\text{cancel 4}\\\\a=\dfrac{16}{3}[/tex]

Answer:

  the order of points remains the same

Step-by-step explanation:

Assuming the distortion is isomorphic, the order of points on any line or other continuous curve will remain the same.

Answer:

- Was the car speeding?

Yes, the car was speeding as its current speed of 57.65 mph was more than the speed limit of that freeway.

- Do you agree with Nico or with Katya?

I agree somewhat with both Nico and Katya, but, I agree more with Nico.

- Explain your reasoning.

Like I said, I agree more with Nico's method of rounding the speed to the nearest whole number. This is because in this question, the standard speed we want to compare the calculated speed with is given as a whole number. Hence, it is more proper to estimate the calculated speed to its nearest whole number too.

Step-by-step explanation:

Speed during a travel is given as distance travelled divided by time taken

Speed = (Distance/time)

Distance = 98 miles

Time = 1.7 hours

Speed = (98/1.7) = 57.6470588235 = 57.65 mph = 58 mph

- Was the car speeding?

The speed limit for the road is 55 mph and the current speed of the car = 57.65 mph

Since 57.65 > 55

The car was overspeeding.

- Nico says it's okay to round what his calculator says to the nearest whole number. Katya says that because the calculator displays eight numbers after the decimal point, they shouldn't round. She says they should write down exactly what the calculator shows. Do you agree with Nico or with Katya?

I agree somewhat with both Nico and Katya as the both methods of recording the speed ate right, depending on what the speed is required for.

Although, I agree more with Nico's method as it seems like a better fit for the situation described in the question.

- explain who you agree with and provide the reasons why.

Like I said earlier, I agree more with Nico's method of rounding the speed to the nearest whole number. This is because in this question, the standard speed we want to compare the calculated speed with is given as a whole number. Hence, it is more proper to estimate the calculated speed to its nearest whole number too.

Katya's method of writing the calculated speed as is will be correct in cases where extreme accuracy is required, not an estimate. For this question, the estimate will do.

Hope this Helps!!!

Answer:

Yes, the car was speeding as its current speed of 57.65 mph was more than the speed limit of that freeway.

Step-by-step explanation:

Nico and Katya i agree with.

Answer:

b(20) = 3 means that for 20 boxes of cards sold, 3 badges were earned.

Step-by-step explanation:

The number of badges earned based on the number of boxes of cards sold means that badges earned are a function of the number of boxes of cards sold.

b(20) means the number of badges earned for selling 20 boxes of cards.

b(20) = 3 means that for 20 boxes of cards sold, 3 badges were earned.

Answer:

Someone who sells 20 boxes of cards earn 3 badges.

Step-by-step explanation:

Answer:

152.3

Step-by-step explanation:

area of a parralellogram is L×B

since a degree is given

it will make it

sin 65×14×12

sin 65=0.9063

so 0.9063×14×12

=152.3

Answer: -6.4

Step-by-step explanation:

(0.4)(8)(-2)

3.2*-2

-6.4

Answer:

5000

Step-by-step explanation:

500×2=1000

1000=1.00

1000×5=5.00

Answer:

The writer worries about being left out.

Step-by-step explanation:

The answer is option A

Step-by-step explanation:

Thirteen less than a number is written as

n - 13

Equate it to 42

We have

n - 13 = 42

Hope this helps you

The probabilities are solved and:

(a) A and B are independent.

(b) C and D are not independent.

(c) E and F are independent.

Given data:

To determine if two events are independent or not, determine if the probability of their intersection is equal to the product of their individual probabilities.

(a)

A = {X is even}, B = {X is divisible by 5}

The probability of event A is P(A) = 50/100 = 1/2, as there are 50 even numbers from 1 to 100.

The probability of event B is P(B) = 20/100 = 1/5, as there are 20 numbers divisible by 5 from 1 to 100.

To determine if A and B are independent, compare P(A ∩ B) with P(A) * P(B).

The probability of the intersection A ∩ B is the probability of choosing a number that is both even and divisible by 5. From 1 to 100, there are 10 such numbers: 10, 20, 30, ..., 90. Therefore, P(A ∩ B) = 10/100 = 1/10.

P(A) * P(B) = (1/2) * (1/5) = 1/10.

Since P(A ∩ B) = P(A) * P(B), A and B are independent events.

(b)

C = {X has two digits}, D = {X is divisible by 3}

The probability of event C is P(C) = 90/100 = 9/10, as there are 90 two-digit numbers from 1 to 100.

The probability of event D is P(D) = 33/100, as there are 33 numbers divisible by 3 from 1 to 100.

To determine if C and D are independent, compare P(C ∩ D) with P(C) * P(D).

The probability of the intersection C ∩ D is the probability of choosing a number that is both two digits and divisible by 3. From 1 to 100, there are 30 such numbers: 12, 15, 18, ..., 99. Therefore, P(C ∩ D) = 30/100 = 3/10.

P(C) * P(D) = (9/10) * (33/100) = 297/1000.

Since P(C ∩ D) ≠ P(C) * P(D), C and D are not independent events.

(c)

E = {X is a prime}, F = {X has a digit 5 prime number}

The probability of event E is P(E) = π(x)/100 = π(100)/100 = 25/100 = 1/4, as there are 25 primes from 1 to 100.

The probability of event F is P(F) = 4/100 = 1/25, as there are 4 prime numbers (5, 25, 55, and 75) that have the digit 5.

To determine if E and F are independent, compare P(E ∩ F) with P(E) * P(F).

The probability of the intersection E ∩ F is the probability of choosing a prime number that has the digit 5. From 1 to 100, there is only one such number: 5. Therefore, P(E ∩ F) = 1/100.

P(E) * P(F) = (1/4) * (1/25) = 1/100.

Since P(E ∩ F) = P(E) * P(F), E and F are independent events.

To learn more about probability, refer:

https://brainly.com/question/17089724

#SPJ4

Answer:

247

49

Step-by-step explanation:

a) f•g (4) =

f•g (x) =  f(g(x)) = (x + 9)^2 + 6(x + 9)

f•g (4) =  (4 + 9)^2 + 6(4 + 9)

= 13^2 + 6(13)

= 247

B) g•f (4) =

g•f (x) = g(f(x)) = x^2 + 6x + 9

g•f (4) = 4^2 + 6(4) + 9

= 16 + 24 + 9

= 49

Answer:

[tex]\huge\boxed{A=3\sqrt{255}\ in^2\approx47.91\ in^2}[/tex]

Step-by-step explanation:

We have two sides

[tex]a=12in;\ b=14in[/tex]

and the preimeter

[tex]P=34in[/tex]

We can calculate the length of the third side:

[tex]c=P-a-b[/tex]

substitute

[tex]c=34-12-14=8\ (in)[/tex]

Use the Heron's formula:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)[/tex]

where

[tex]p=\dfrac{P}{2}[/tex]

substitute:

[tex]p=\dfrac{34}{2}=17\ (in)\\\\A=\sqrt{17(17-12)(17-14)(17-8)}=\sqrt{(17)(5)(3)(9)}\\\\=\sqrt{9}\cdot\sqrt{(17)(5)(3)}=3\sqrt{255}\ (in^2)\approx47.91\ (in^2)[/tex]

Answer:

Selling price = $190003.206 and total interest paid is $135640.794

Step-by-step explanation:

The down payment of house = $25404

Monthly payment = $834 per month.

Total number of years = 30 years = 30*12 = 360 months.

Interest rate compounded monthly = 4.5 % * 1/12 = 0.375% per month or 0.00375.

Now we have to calculate the selling price of house and total interest paid.

Loan amount = Present value of monthly payments.

[tex]\text{Loan amount} = \frac{ Monthly \ payment \times [1- (1+r)^{-n}]}{r} \\= \frac{ 834 \times [1- (1+ 0.00375)^{-360}]}{0.00375} \\= 164599.206[/tex]

Selling price of house = 25404 + 164599.206 = 190003.206

Interest amount = total amount of installment – loan amount

Interest amount = 834*360 – 164599.206 = 135640.794 dollars.

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▹ Answer

a. 4

▹ Step-by-Step Explanation

|4² - 34| ÷ 4 × 6² - 12² - 14

|16 - 34| ÷ 4 × 6² - 12² - 14

|16 - 34| ÷ 4 × 36 - 144 - 14

|-18| ÷ 4 × 36 - 144 - 14

18 ÷ 4 × 36 - 144 - 14

18/4 × 36 - 144 - 14

9/2 × 36 - 144 - 14

9 × 18 - 144 - 14

162 - 144 - 14

ANSWER = 4

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

28 miles

Step-by-step explanation:

to fin the actual distance you must multiply the didtance on the map by the map scale

3.5*8=28

Answer:

A.   [tex]\frac{x^2-3x+6}{x^2 - 2x}[/tex]

Step-by-step explanation:

1. Move all of numerators above the corresponding common denominator

2. Multiply inside the parentheses then remove any remaining parenthesis to get your final answer to get your fraction.

Answer:

[tex] \dfrac{x^2 - 3x + 6}{x^2 - 2x} [/tex]

Step-by-step explanation:

[tex] \dfrac{x}{x - 2} - \dfrac{3}{x} = [/tex]

[tex] = \dfrac{(x)x}{(x)(x - 2)} - \dfrac{(x - 2)(3)}{(x - 2)(x)} [/tex]

[tex] = \dfrac{x^2}(x - 2)} - \dfrac{3x - 6}{(x - 2)(x)} [/tex]

[tex] = \dfrac{x^2 - (3x - 6)}{x^2 - 2x} [/tex]

[tex] = \dfrac{x^2 - 3x + 6}{x^2 - 2x} [/tex]

Answer:

  0 +256i

Step-by-step explanation:

According to Euler's formula, ...

  (4 cis π/8)^4 = (4^4) cis (4×π/8) = 256 cis π/2 = 0 +256i

_____

"cis" is an abbreviation sometimes used for "cosine + i×sine". It simplifies writing the expression. Engineers sometimes simplify it further, writing 4∠(π/8) for the expression in this problem statement.

Answer:

Proofs for Pythagoras Theorem usually use visual/geometry approaches. I don't post pictures in my answers, so I will present a linear algebra approach. You can see it in the blog posted by Professor Terence Tao.

Note that there are several elegant proofs using animations and drawings, but this is just personal.

I've seen this some time ago, it is really interesting proof.

It states that [tex]a^2+b^2=c^2[/tex] is equivalent to the statement that the matrices

[tex]%\begin{pmatrix}a & b \\ -b & a%\end{pmatrix}%[/tex]    [tex]\begin{pmatrix}a& b \\-b & a\\\end{pmatrix}[/tex] and [tex]\begin{pmatrix}c & 0\\0 & c \\\end{pmatrix}[/tex] have the same determinant.

The determinant of the first matrix is [tex]a^2+b^2[/tex]

The determinant of the second matrix is [tex]c^2[/tex]

Once the linear transformations associated with these matrices differ by rotation, we claim that

[tex]a^2+b^2=c^2[/tex]

Answer:

Probability (N more than 2) = 0.3773

Step-by-step explanation:

Given:

Average number of crashes (N) = 2.2

Find:

Probability (N more than 2)

Computation:

Probability (N more than 2) = [1-P(N=0)-P(N=1)-P(N=2)]

Probability (N more than 2) = [1 - e⁻²°² - 2.2e⁻²°² - (2.2²e⁻²°²)/2]

Probability (N more than 2) = 0.3773

Answer:

$833

Step-by-step explanation:

Since there are 9 people, we need to determine the cost of accommodation and flights for all 9 people:

9(273) + 9(184) = 2457 + 1656 = 4167 for 9 people

We then subtract that amount from the amount of money she won:

5000 - 4167 = 833

Answer:

B. 1788

Step-by-step explanation:

The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by

length * height * width

The volume for current object is :

12 * 28 * 5

= 1788 cubic yards.

Answer: 1778

Step-by-step explanation:

because Ik I had the question

Answer:

  a.  It has exactly two odd vertices

  b.  A C E D B A D C

Step-by-step explanation:

(a) There will not be an Euler path if the number of odd vertices is not 0 or 2. Here, the graph has exactly two odd vertices: A and C.

__

(b) We are required to produce a path of the form {A, _, _, D, B, _, D, _}.

Starting at A, there is only one way to get to node D as the 4th node on the path: via C and E. Node B must follow. From B, there is exactly one way to cover the remaining three edges that have not been traversed so far.

The Euler path meeting the requirements is ...

  A C E D B A D C

It is shown by the arrows on the edges in the graph of the attachment.

Answer:

Option D

Step-by-step explanation:

x is given to be 4 in this case, so all we would have to is plug it into the following function -

[tex]f ( x ) = \left \{ {{x - 2, x < 4 } \atop {x + 2, x \geq 4 }} \right[/tex]

Through substitution, you would receive the following function -

[tex]f ( x ) = \left \{ {{2, 4 < 4 } \atop 6, 4 \geq 4 }} \right[/tex]

Now the graph proves that this function is closer to 4, and thus proves that the y - coordinate is about 2 at the same time. However, the graph is cut off, so the limit doesn't exists.

Answer:

Step-by-step explanation:

Answer:

[tex] P(14.8< X<16.5)= \frac{16.5-11.1}{19.2-11.1} -\frac{14.8-11.1}{19.2-11.1}= 0.667-0.457= 0.210[/tex]

The probability that it will require between 14.8 and 16.5 minutes to perform the task is 0.210

Step-by-step explanation:

Let X the random variable "completion times for a job task" , and we know that the distribution for X is given by:

[tex] X \sim Unif (a= 11.1, b= 19.2)[/tex]

And for this case we wantto find the following probability:

[tex] P(14.8< X<16.5)[/tex]

And for this case we can use the cumulative distribution given by:

[tex] F(x) =\frac{x-a}{b-a} , a\leq X \leq b[/tex]

And using this formula we got:

[tex] P(14.8< X<16.5)= \frac{16.5-11.1}{19.2-11.1} -\frac{14.8-11.1}{19.2-11.1}= 0.667-0.457= 0.210[/tex]

The probability that it will require between 14.8 and 16.5 minutes to perform the task is 0.210

Answer:

[tex] P(X=7)[/tex]

And using the probability mass function we got:

[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]  

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=15, p=0.23)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

And we want to find the following probability:

[tex] P(X=7)[/tex]

And using the probability mass function we got:

[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]  

Hey there! :)

Answer:

≈ $41330

Step-by-step explanation:

Begin by finding the area of the racetrack by subtracting the area of the smaller circle from the larger one.

Calculate the areas of the circles using: A = πr²

Larger circle:

A = π145²

A = 21025π = 66018.5 ft²

Smaller circle:

A = π80²

A = 6400π = 20096 ft²

Subtract the smaller from the larger of the areas:

66018.5 - 20096 = 45922.5 ft²

Divide this by 100 to solve for the amount of asphalt needed:

45922.5 / 100 = 459.225.

Since asphalt costs $90 dollars per 100 ft², then:

459.225 · 90 = $ 41330.25 ≈ $41330 rounded.

Answer:

4/5 gallon per wall

Step-by-step explanation:

We can find the unit rate

1/5 gallon

------------------

1/4 wall

1/5 ÷ 1/4

Copy dot flip

1/5 * 4/1

4/5 gallon per wall

Answer:

4/5 gallon of paint

Step-by-step explanation:

1/5 gallon of paint is needed to cover 1/4 of the wall.

To cover the whole wall:

1/4 × 4 = 1 (whole)

1/5 × 4 = 4/5

Answer: b) 180° rotation & reflection over x-axis

Step-by-step explanation:

Rotation of 180° changes the signs of both x and y.

(x, y) → (-x, -y)

Reflection over the x-axis changes the sign of y.

(-x, -y) → (-x, y)

 (x, y)        (-x, y)  

 (0, 1)   →    (0, 1)

 (1, -1)   →   (-1, -1)

 (5, 3)   →   (-5, 3)