Consider the points below. P(1, 0, 1), Q(-2, 1, 4), R(6, 2, 7) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. Need Help? (b) Find the area of the triangle PQR. SCALC9 12.4.029.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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The probability that the experiment results in exactly 6 successes is 0.2668.

To calculate the probability of exactly 6 successes in a binomial experiment with p=0.7 and n=7, we can use the binomial probability formula:

P(X = k) = (n choose k) * \(p^{k}\) * \((1-p)^{n-k}\)

where X is the random variable representing the number of successes, k is the number of successes we're interested in, and n is the total number of trials.

Substituting the values, we get:

P(X = 6) = (7 choose 6) * \(0.7^{6}\) * \((1-0.7)^{7-6}\)

= 7 * \(0.7^{6}\) * \(0.3^{1}\)

= 0.266827932

Therefore, the probability of exactly 6 successes in a binomial experiment with p=0.7 and n=7 is approximately 0.2668.

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Answer:

29.53 ≤ x + 5 ≤ 56.15

Step-by-step explanation:

A $5 in-store coupon for every person who buys a flea control product which ranges between $29.53 to $56.15. This means that if you bought a flea control product you would be given an additional $5 that means that for buying a flea product, $5 is given to you. If you have $x, and you bought a flea product you would have x + 5. The inequality that represents this situation is given as:

29.53 ≤ x + 5 ≤ 56.15

a = 1st zero or root of the quadratic

b = 2nd zero or root of the quadratic

\(x^2-8x+k=0\implies (x-a)(x-b)=0\implies x= \begin{cases} a\\ b \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -ax-bx=-8x\implies -a-b=-8\implies -b=a-8\implies b=8-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{3a+4b=29}\qquad \implies \qquad \stackrel{\textit{substituting from above}}{3a+4(8-a)~~ = ~~29}\implies 3a+32-4a=29 \\\\\\ -a+32=29\implies 32=a+29\implies \boxed{3=a}\hspace{5em}\stackrel{ 8~~ - ~~3 }{\boxed{b=5}}\)

\(~\dotfill\\\\ (x-3)(x-5)=0\implies x^2-8x+\stackrel{ \textit{\LARGE k} }{15}=0\)

True.

A 95% confidence interval for the population mean means that if we draw multiple samples from the same population and construct confidence intervals for the mean using each sample, then 95% of those intervals will contain the true population mean. This is because the confidence interval is computed based on the sample mean and the sample's standard deviation, which are random variables that are expected to vary from sample to sample. Therefore, we cannot be 100% certain that the true population mean is within any particular confidence interval, but we can be confident (95% confident, in this case) that most of the intervals we construct will contain the true mean. A 95% confidence interval for the population mean implies that if samples are drawn repeatedly and confidence intervals for μ are constructed, then 95% of the confidence intervals computed will contain the population mean. This means that you can be 95% confident that the true population mean lies within the calculated interval.

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Answer:

Answer:

Slopem=−49

As a decimal:

m = -0.444444

Step-by-step explanation:

Slope m with two points

Graph of the line for y = mx + b

Point Slope Form y - y1 = m(x - x1)

Slope Intercept Form y = mx + b

Standard Form Ax + By = C

y-intercept, when x = 0

x-intercept, when y = 0

Answer:

The relation is not a function.

Step-by-step explanation:

Since x=0 produces  y=3 and y=6, the relation (0,3),(1,4),(2,5),(0,6) is not a function.

The relation is not a function.

Answer:

option 4

2

Step-by-step explanation:

1 Litre = 1000 mililitre

so,

2 litres = 2000 mililitres

Answer:

To compare the deals, we need to find the price per milliliter of lemonade for each deal.

For the first deal, the price per milliliter is:

94p / 500ml = 0.188p/ml

For the second deal, the price per milliliter is:

£1.44 / 750ml = 0.192p/ml

Therefore, the first deal is better as it has a lower price per milliliter of lemonade.

Answer:

the answer is

He did not subtract correctly in one of the steps. D

step by step explination: just took the test.

put me as branliest

Answer:

He multiplied the dividend by 100 instead of 10.

Step-by-step explanation:

Have a great day!

(Edgeunity quiz)

Answer:

x=70º

Step-by-step explanation:

Triangle ABC, A/C=50º, B/C=40º

40º+50º=90º

Triangle XZY, Y/Z=20, Y/X=x

Since it is a right triangle it will add up to 90º.

So 90º-20=70

The missing angle x is 70

x= 70

The length of the unknown side of the triangle XYZ is 25 units.

Two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.

Given is Triangle ABC which is similar to triangle XZY.

Since both the triangles are congruent to each other, their corresponding sides will be in equivalent ratios. Therefore, we can write-

BC/YZ = AC/YX

40/20 = 50/x

x = (50 x 20)/40

x = 50/2

x = 25

Therefore, the length of the unknown side of the triangle XYZ is 25 units.

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Answer:

yall its AAAAAAAA

Step-by-step explanation:

TRUST ME

The factorized expression of the expression is 3(x + 8y)

A factorized expression is an expression written in a simpler form

The expression is given as:

3x + 24y

Factor out 3 in the expression

3x + 24y = 3(x + 8y)

Hence, the expressions when multiplied that give the expression are 3 and x + 8y

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There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

It is given that at least two of them should have the same remainder when divided by 15.

Division algorithm.

Let aa be an integer and d a positive integer. Then there are unique integers q and r with \(0\leq r < d\) such that \(a=dq+r\)

q is called the quotient and r is called the remainder

q=a div d

r=a mod d

Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.

Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

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It provides character details that indicate Mrs. This function Faxon's interaction with this character serve in the given excerpt. Therefore, the correct option is option A.

An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt. It provides character details that indicate Mrs. This function Faxon's interaction with this character serve.

Therefore, the correct option is option A.

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Reason: The line goes downhill when moving to the right, and when we're between x = -1 and x = 1. You can think of it like a roller coaster.

Answer:

253

Step-by-step explanation:

Based on the information provided, last week Kaylee had a total of 13 + 32 + 53 = 98 customers. The proportion of customers who paid with cash is 13/98. If she is expecting 1900 customers next week, we can estimate that about (13/98) * 1900 = 253 customers would pay with cash. Rounded to the nearest whole number, we get 253 customers.

You did not show the diagram that was made but from what I already know, I'm pretty sure that the answer is:

1.)  Energy is used up.

2.) Both - Oxygen is used up, and Carbon dioxide is used up.

3.) Glucose is broken down

Answer:

D. Carbon dioxide is used up.

Step-by-step explanation:

The statement "global warming leads to a poleward displacement of midlatitude cyclone tracks" is generally supported by scientific evidence and is widely accepted by the scientific community.

This is because the increase in global temperatures due to global warming affects atmospheric circulation patterns, leading to shifts in weather systems, including midlatitude cyclones.

On the other hand, the statement "global warming is unrelated to midlatitude cyclone tracks" is not supported by scientific consensus.

The statement "greenhouse gas emissions have little to do with the atmospheric greenhouse effect" is incorrect. Greenhouse gas emissions, such as carbon dioxide and methane, are major contributors to the greenhouse effect, which is responsible for trapping heat in the Earth's atmosphere.

Lastly, the statement "the conveyor belt model is inconsistent with greenhouse theory" is also incorrect. The conveyor belt model, also known as the thermohaline circulation, describes the movement of ocean currents that play a significant role in distributing heat around the globe. While it is not directly related to the greenhouse effect, it is not inconsistent with greenhouse theory and operates independently to transport heat in the ocean.

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Given:

The given system of equations is

\(4x-y=2\)

\(4x-y=5\)

To find:

The solution of the given system of equations.

Solution:

We have,

\(4x-y=2\)         ...(i)

\(4x-y=5\)         ...(ii)

Left hand sides of both equations are equal. So, after equalization of (i) and (ii), we get

\(2=5\)

This statement is false for any value of x and y. It means the given system of equation has no solution.

Therefore, the correct option is C.

We can add and subtract 4.5 in the left side to complete squares, then we can rewrite the quadratic equation as:

(x + 13)^2 = 4.5

Here we want to rewrite the quadratic equation:

x^2 + 26x + 164.5 = 0

To rewrite it in the desired way, we need to complete squares, remember that the perfect square trinomial is:

(a + b) = a^2 + 2ab + b^2

We can rewrite the given quadratic as:

x^2 + 26x + 164.5 = 0

x^2 + 2*13*x + 164.5 = 0

The missing term to complete squares is 13^2 = 169, so we can add and subtract 4.5 on the left side of that eqation to get:

x^2 + 2*13*x + 164.5 + 4.5 - 4.5 = 0

x^2 + 2*13*x + 169 - 4.5 = 0

(x + 13)^2 = 4.5

That is the equation we wanted to get.

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For the given statement, we have to correctly rejecting the null hypothesis.

According to the statement

we have to find the outcome when hypothesis test evaluating a treatment that has a very large and robust effect.

For this purpose, we know that the

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

And according to the given statement it is clear that the by this we have to rejected this hypothesis.

because this treatment and the large effects are not possible for the independent values of the hypothesis.

In other words, we can say that the we have to correctly rejecting the null hypothesis.

So, For the given statement, we have to correctly rejecting the null hypothesis.

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Answer:

Answer:

x=0

Step-by-step explanation:

The 7th term of the arithmetic sequence is 11.  The common difference in the arithmetic sequence can be found by using formula: an = a1 + (n - 1)d

We can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

Using the information given in the problem, we can write two equations:

a3 = a1 + 2d = 5

a11 = a1 + 10d = 18

We can solve for a1 and d by subtracting the first equation from the second:

8d = 13

d = 1.625

Substituting this value of d into the first equation, we can solve for a1:

a1 + 2(1.625) = 5

a1 = 1.75

Now we can use the formula for the nth term to find the 7th term:

a7 = 1.75 + 6(1.625)

a7 = 11

Therefore, the 7th term of the arithmetic sequence is 11.

Answer: c. 11

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The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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