In the figure, AC=86. Find BC.

Answer:

slope = - \(\frac{1}{3}\)

Step-by-step explanation:

given f(4) = 6 and f(- 2) = 8 , then 2 points on the line are

(4, 6 ) and (- 2, 8 )

calculate slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (- 2, 8 )

m = \(\frac{8-6}{-2-4}\) = \(\frac{2}{-6}\) = - \(\frac{1}{3}\)

The negation of the given statement can be expressed as follows: ∀ integers a, b, and c such that a+b+c is even and a+b is not even and b+c is not even.

In other words, the negation states that there exist integers a, b, and c for which the sum of a, b, and c is even, but neither the sum of a and b nor the sum of b and c is even.

This means that there are specific values of a, b, and c that violate the implication in the original statement. In those cases, the sum of a+b+c is even, but neither the sum of a+b nor the sum of b+c is even. Essentially, the negation disproves the claim made in the original statement by providing counterexamples where the implication does not hold.

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Since {e1, e2, e3, e4} is both linearly independent and spans R4, it is a basis for R4.

To prove that the set {e1, e2, e3, e4} is a basis for R4, we need to show that it is linearly independent (li) and that it spans R4.

1. Linear Independence:

To prove that {e1, e2, e3, e4} is linearly independent, we need to show that the only solution to the equation c1e1 + c2e2 + c3e3 + c4e4 = 0, where c1, c2, c3, and c4 are constants, is c1 = c2 = c3 = c4 = 0.

Let's set up the equation and solve for c1, c2, c3, and c4:

c1(1, 0, 0, 0) + c2(0, 1, 0, 0) + c3(0, 0, 1, 0) + c4(0, 0, 0, 1) = (0, 0, 0, 0)

Simplifying the equation, we get:

(c1, c2, c3, c4) = (0, 0, 0, 0)

Since the only solution to the equation is c1 = c2 = c3 = c4 = 0, we can conclude that {e1, e2, e3, e4} is linearly independent.

2. Spanning R4:

To prove that {e1, e2, e3, e4} spans R4, we need to show that any vector (a, b, c, d) in R4 can be expressed as a linear combination of e1, e2, e3, and e4.

Let's consider an arbitrary vector (a, b, c, d):

(a, b, c, d) = a(1, 0, 0, 0) + b(0, 1, 0, 0) + c(0, 0, 1, 0) + d(0, 0, 0, 1)

Simplifying the equation, we get:

(a, b, c, d) = (a, b, c, d)

We can see that any vector (a, b, c, d) can be expressed as a linear combination of e1, e2, e3, and e4.

Therefore, since {e1, e2, e3, e4} is both linearly independent and spans R4, it is a basis for R4.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

yes 3 and 12 are both indeed factors of twelve

Using the arrangements formula, it is found that 907,200 arrangements can be formed using the letters in the word FORGETTING.

The number of possible arrangements of n elements is given by the factorial of n, that is:

\(A_n = n!\)

When there are repeating elements, with the number of times given by \(n_1, n_2, \cdots, n_n\), the number of arrangements is given by:

\(A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}\)

In this problem, the word FORGETTING has 10 letters, of which G and T repeat twice, hence the number of arrangements is given by:

\(A_{10}^{2,2} = \frac{10!}{2!2!} = 907,200\)

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Answer: b is the answer

Step-by-step explanation:

Answer:

Step One: We need to find a way to equate either the x terms of the y terms in each equation. ...

Step Two: Take equation b) from equation a) to eliminate the x component. ...

Step Three: substitute the value of y into either equation to find the value of x.

Step-by-step explanation:

Answer:

youre answer is here I hope it's right

x=24

If you arrived at a relative's house 45 seconds after leaving home, traveling 90 m, the speed was 2 meters per second.

To find out how fast you traveled, you need to use the formula for speed, which is distance divided by time. In this case, the distance is 90 meters and the time is 45 seconds.

So, you can plug these values into the formula to find your speed:
Speed = Distance / Time
Speed = 90 meters / 45 seconds
Speed = 2 meters per second

Therefore, you traveled at a speed of 2 meters per second. This means that you covered 2 meters in just one second. This is a relatively fast speed, especially if you were walking or running.

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Answer:

the base is 2 and the height is 4 or swapped

Step-by-step explanation:

Based on the information provided in the histogram, the percent of students that type less than 30 words per minute is 30%.

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the number of students and whose width is equal to the words per minute.

Percentage of students who type less than 30 words per minute = (number of students that type less than 30 words per minute) / total number of students) x 100

[(10 + 5) / 50] x 100 = 30%

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The point of intersection is (6, 6).


To find the point where two lines intersect, we need to solve the system of equations:

y = 2x - 6 (equation 1)

y = 1/2x + 3 (equation 2)

We can solve this system by setting the two expressions for y equal to each other:

2x - 6 = 1/2x + 3

Multiplying both sides by 2 to eliminate the fraction, we get:

4x - 12 = x + 6

Subtracting x and adding 12 to both sides, we get:

3x = 18

Dividing by 3, we get:

x = 6

Now we can plug this value of x into either equation to find the corresponding y-coordinate. Let's use equation 1:

y = 2(6) - 6 = 6

Therefore, the point of intersection is (6, 6).

Answer:

The answer is  43.9822972 rad but you could just round and put 43.98

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Monopolistic Competition is a type of imperfect competition such that many producers sell products that are differentiated from one another and hence are not perfect substitutes. Therefore B. would be correct since Monopolistic Competition is Many sellers with a featured product that's differentiated to the buyer.

Answer:

22.41 + 8.9= 31.31

hope this helps <3

The option that shows that the derivative of a function as well as its intervals is decreasing is option C (Image attached).

A derivative is known to be a tool that help us to know the altering relationship that between two variables. The derivative formula is known to be ddx. xn=n.

Note that:

F¹(x) =  e^sinx - cosx - 1

Set:

F¹(x) > 0

e^sinx  > cosx - 1

0.633 < x < 4.155  and 6,916 < x < 9

So, if you look at the equation, the option that fits into the equation is option c:

Therefore, The option that shows that the derivative of a function as well as its intervals is decreasing is option C (Image attached).

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Answer:

13

Step-by-step explanation:

Step-by-step explanation:

Plot the point.

-1+3=2 and -2-5=-7

this is your new plot, (2,-7)

move the dot an equal distance across the x-axis, which is up and down.

After finding the ratio, the population of Illinois than Alaska is 20 times greater.

The population of Alaska is approximately 6.5 x \(10^5\) people.

The population of Illinois is about 1.3 x \(10^7\) people.

We have to find how many times greater is the population of Illinois than Alaska.

We will use their population ratio to determine how many times the population of Illinois is greater than the population of Alaska.

Ratio = Population of Illinois's /Population of Alaska

Ratio = 1.3 x \(10^7\)/6.5 x \(10^5\)

Now simplifying.

Ratio = 0.2 x \(10^2\)

Ratio = 20

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It will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

The current Hours of Service (HOS) rules for truck drivers stipulate that a truck driver cannot drive for more than 11 hours after 10 consecutive hours off duty.

Additionally, the driver is not allowed to drive beyond 14 hours after coming on duty.

The driver's shift includes both driving and non-driving time.

Therefore, it is necessary to consider the total amount of time spent on the job.

The truck driver will have to stop for rest breaks, refueling, or other reasons during the 450-mile journey to Pittsburgh, Pennsylvania. The driver is required to take a 30-minute break after eight hours of driving.

Therefore, the minimum number of clock hours (not driving hours) it will take the truck driver to travel the 450-mile distance from Charlotte, NC to Pittsburgh, PA is calculated as follows:

Time for the trip = (Distance ÷ Average Speed) + Breaks

Time for the trip = (450 ÷ 50) + (30 ÷ 60) × 2

Time for the trip = 9 + 1

Time for the trip = 10 clock hours

Therefore, it will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

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Answer:

please perimeter is a summation .

so how can the perimeter be 60^2?

Answer:

0% (0/40)

Step-by-step explanation:

I feel like this is a trick question. since chicken is not indicated on the graph, I believe chicken is nobodies favorite food

Step-by-step explanation:

a.

\(f(2) = 0\)

b.

\(f(x) = 4 \\ f(5) = 4 \\ x = 5\)

c.

[—3,2] union [3.4, 4]

Answer:

y = -3x - 1

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Point (-1, 2) (1, -4)

We see the y decrease by 6 and the x increase by 2, so the slope is

m = -6 / 2 = -3

Y-intercept is located at (0, - 1)

So, the equation is y = -3x - 1

The missing terms between -320 and 5 in the geometric sequence are -40 and -5.

Explanation:

To find the missing terms in a geometric sequence, we need to determine the common ratio (r) first. The common ratio can be found by dividing any term by its preceding term.

Let's consider te given terms: -320 and 5. To find the common ratio, we divide 5 by -320:r = 5 / (-320) = -1/64

Now that we know the common ratio (r = -1/64), we can find the missing terms.

To find the first missing term, we multiply the preceding term (-320) by the common ratio:-320 * (-1/64) = 5

So, the first missing term is 5.

To find the second missing term, we multiply the preceding term (5) by the common ratio:5 * (-1/64) = -5/64

Hence, the second missing term is -5/64 or -0.078125.

In summary, the two missing terms between -320 and 5 in the geometric sequence are -40 and -5.

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In this problem, Alice's shopping duration, represented by the random variable H, can take values 1, 2, or 3 with equal probability.

The number of books she buys, represented by the random variable B, depends on her shopping duration. The joint distribution, marginal distribution, conditional distribution, and conditional expectation are calculated. The solution involves the chain rule, conditional probability, and Bayes' Theorem.

a) To find the joint distribution of B and H, we can use the chain rule. The joint distribution is given by P(B=b, H=h) = P(B=b | H=h) * P(H=h). Since P(B=b | H=h) = h^(-1) for b=1,...,h and P(H=h) = 1/3 for h=1,2,3, we have P(B=b, H=h) = (1/3) * (h^(-1)).

b) The marginal distribution of B can be obtained by summing the joint probabilities over all possible values of H. P(B=b) = Σ[P(B=b, H=h)] for h=1,2,3. Simplifying this expression, we get P(B=b) = Σ[(1/3) * (h^(-1))] for h=1,2,3. The marginal distribution of B is a probability mass function that assigns probabilities to each possible value of B.

c) To find the conditional distribution of H given that B=1, we use the definition of conditional probability. P(H=h | B=1) = P(H=h, B=1) / P(B=1). Using the joint distribution from part a), we have P(H=h | B=1) = [(1/3) * (h^(-1))] / P(B=1). To calculate P(B=1), we sum the joint probabilities over all possible values of H when B=1.

d) To find the expected number of hours Alice shopped conditioned on the event that she bought either 1 or 2 books, we use conditional expectation and Bayes' Theorem. Let E denote the expected number of hours conditioned on this event. We have E = E[H | B=1 or B=2]. Using the law of total expectation, we can express E as the sum of the conditional expectations E[H | B=1] and E[H | B=2], weighted by their respective probabilities. These conditional expectations can be calculated using the conditional distribution of H given B=1 (from part c).

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Answer:

first function

Step-by-step explanation:

there is a common difference between consecutive terms , that is

13 - 10 = 16 - 13 = 19 - 16 = 22 - 19 = 3

this indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 10 and d = 3 , then

\(a_{n}\) = 10 + 3(n - 1) = 10 + 3n - 3 = 7 + 3n

The price before tax is $4.50 and the tax is %10, then the tax is

then, the total price is the sum of the tax and the price before the tax, that is,

then, the total price is $4.95 and the tax is $0.45