210, 206, 202, ... Find the 35th term.​

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

The greatest common divisor (gcd) of 144 and 89 can be expressed as a linear combination of 144 and 89 as follows: gcd(144, 89) = 1 = (-21) * 144 + 34 * 89.

To express the gcd (144, 89) as a linear combination of 144 and 89, we can use the extended Euclidean algorithm. This algorithm finds the gcd of two numbers and also provides coefficients that represent the linear combination.

We start with the given numbers: a = 144 and b = 89.

Apply the Euclidean algorithm to find the gcd:

Divide 144 by 89: 144 = 1 * 89 + 55

Divide 89 by 55: 89 = 1 * 55 + 34

Divide 55 by 34: 55 = 1 * 34 + 21

Divide 34 by 21: 34 = 1 * 21 + 13

Divide 21 by 13: 21 = 1 * 13 + 8

Divide 13 by 8: 13 = 1 * 8 + 5

Divide 8 by 5: 8 = 1 * 5 + 3

Divide 5 by 3: 5 = 1 * 3 + 2

Divide 3 by 2: 3 = 1 * 2 + 1

Divide 2 by 1: 2 = 2 * 1 + 0

The last non-zero remainder obtained is 1, which means the gcd is 1.

Now, we work backwards through the algorithm to find the coefficients:

From 3 = 1 * 2 + 1, we can express 1 as a linear combination of 2 and 3: 1 = 3 - 1 * 2

Substitute 2 = 5 - 1 * 3 from the previous step: 1 = 3 - 1 * (5 - 1 * 3) = 2 * 3 - 1 * 5

Continue substituting until we reach the original numbers:

1 = 2 * 3 - 1 * 5 = 2 * (5 - 1 * 3) - 1 * 5 = 2 * 5 - 3 * 5 = 2 * 5 - 3 * (8 - 1 * 5)

Repeat until we get the desired linear combination:

1 = 2 * 5 - 3 * (8 - 1 * 5) = 2 * 5 - 3 * 8 + 3 * 5 = (-3) * 8 + 5 * 5 - 3 * 8 = 5 * 5 - 6 * 8

Substitute 8 = 13 - 1 * 5: 1 = 5 * 5 - 6 * (13 - 1 * 5) = 11 * 5 - 6 * 13

Repeat the process until we reach the original numbers:

1 = 11 * 5 - 6 * 13 = 11 * (13 - 1 * 8) - 6 * 13 = 11 * 13 - 11 * 8 - 6 * 13 = (-17) * 8 + 11 * 13

Substitute 13 = 21

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Answer: 2/25 *25

Step-by-step explanation:

Answer:

Third step

Step-by-step explanation:

To find the average amount it fell every hour, you need to divide -13 1/5 by 4 2/5. Since you can't do it with a mixed number, you need to make it an improper fraction by multiplying the denominator by the number and adding the numerator.

Now you divide the new numbers. However, in the problem, it is multiplying, so that is what's wrong.

Therefore the third step is wrong.

Hope I helped!!!

How to add two positive integers:

You add the numbers like you normally would. There's no trick even though it seems like a trick question.

Example: 3+5 = 8

In that example, you can think of like starting at 3 on the number line. Then you move 5 units to the right to arrive at 8 on the number line.

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

How to add two negative integers:

Treat the negative numbers as their positive version of themselves. Next, you add those positive counterparts like normal. The last thing you do is make the result negative.

For example,

-9 + (-12) = -21

which we can think of like this

9+12 = 21

Then we just make everything negative to get that first equation mentioned.

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

How to add positive and negative integers:

This will depend on which has larger absolute value. In other words, which is further away from 0 on the number line.

In any event, you basically subtract the positive version of each number. Then the one furthest from 0 will determine if the result is positive or negative.

Examples:

-8 + 9 = 1

7 + (-12) = -5

In the first example, we can think of it like 9-8 = 1. I'm subtracting the two numbers 8 and 9, but doing so large - small and only focusing on the positive versions so far. Because 9 is further away from 0 compared to -8, this ultimately means the result is positive (since 9 is positive).

In the second example, we would say 12-7 = 5. Then note how -12 is farther away from 0 compared to 7. This means the negative side wins, so to speak, and the final result is negative.

Answer:

its the third one down also you do compasscharters to lol

Step-by-step explanation:

Answer:

3:1 and 15:5

Step-by-step explanation:

Not too sure

Answer:

I agree with Nico.

The height is stated that it is 8 (next to the symbol indicating a right angle).

Hope that helps!

Step-by-step explanation:

Answer:

Any number other than 4

Step-by-step explanation:

I think we should first determine what value would make the equation true.

13 = 2x + 5

13 - 5 = 2x

8 = 2x

4 = x

Let's try plugging in 5 for x.

13 = 2 (5) + 5

13 = 10 + 5

13 = 15

Obviously this isn't true. 13 has never equaled

Let's try plugging in 3 for x.

13 = 2(3) + 5

13 = 6 + 5

13 = 11

This can't be true either.

So the two values that make this false are  5 and 3.

In short, this equation has only one value that makes it true. It's 4. Any number other than 4 makes it false.

Answer:

A

Step-by-step explanation:

:)

Answer:

−y−1=3

Step-by-step explanation:

Which equation can be used to find the solution of (1/4)^y+1=64?

This can be solved by power of indices

(1/4)^(y+1)=64

(4^-1)^(y + 1)= 4^3

Note

(x^a)^b = x^ab

Hence:

4^(-1)(y + 1)= 4^3

4^-y - 1 = 4^3

Divide both sides by 4

−y−1=3

Hence, the equation that can be used to find the solution of (1/4)^y+1=64 is

−y−1=3

Answer:

-y-1=3

Step-by-step explanation:

took the test and got it correct

The probability that the student will get at least three questions correct is 0.1719

To solve this problem, we can use the binomial distribution formula, which gives the probability of getting exactly k successes in n independent Bernoulli trials, where each trial has a probability p of success:\(P(k successes) = (n choose k) p^k (1-p)^{n-k}\)

In this case, n = 10 (the number of questions), p = 0.5 (the probability of getting a correct answer by guessing), and we want to find the probability of getting at least three questions correct. This means we need to add up the probabilities of getting exactly 3, 4, 5, ..., 10 questions correct.

\(=P(at least 3 correct) = P(3 correct) + P(4 correct) + ... + P(10 correct)\)

\(= (10 choose 3) (0.5^3) (0.5^7 )+ (10 choose 4) (0.5^4) (0.5^6) + ... + (10 choose 10) (0.5^{10} )(0.5^0)\)

\(= 0.1719\)

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Answer:

Kim and Zara are correct.

Step-by-step explanation:

Correct simplification:

-3(x+4) - 2(5x-6)

-3x + (-12) - 10x + 12

-3x - 12 - 10x + 12

- 13x

Answer:

around 190

Step-by-step explanation:

Answer:

He needs to learn the disciplinary principal

Step-by-step explanation:

The principal is necessary to generate this amount of monthly income is $497.

Given that, Jack wants to retire with $1,000 per month.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = \(Amount=Principal(1+\frac{R}{100})^{nt}\)

⇒ 1000 =P\((1+0.06)^{12}\)

⇒ 1000=P×2.012

⇒ P=1000/2.012

⇒ P=$497

Hence, the principal is necessary to generate this amount of monthly income is $497.

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The general form of such a model that predicts the volume of sales (Y) as a function of advertising (X) in which sales increase as advertising increases, but at a decreasing rate is given by  Y^ = b0 + b1X + b2X². Option C.

The general form of the model that fits the description of the sales model that is given in the problem is C. Y^ = b0 + b1X + b2X². Where Y^ represents the predicted or estimated value of Y. b0, b1, and b2 are the coefficients of the model, and they represent the intercept, the slope, and the curvature of the relationship between X and Y, respectively.

In this model, the variable X has a quadratic relationship with the variable Y because of the presence of the squared term X². This indicates that the effect of X on Y is not linear but curvilinear, which means that the effect of X on Y changes as X increases. Specifically, the effect of X on Y increases initially but then levels off or diminishes as X becomes larger. Answer option C.

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The theorem (¬P → ¬(P^Q)) can be proven using a conditional derivation and an indirect derivation, where we assume the antecedent (¬P) and derive the consequent (¬(P^Q)) within that assumption.

To prove the theorem (¬P → ¬(P^Q)), we start by assuming the antecedent (¬P) and aim to derive the consequent (¬(P^Q)). We use a conditional derivation, which involves assuming the antecedent and attempting to derive the consequent within that assumption.

Assume ¬P (Conditional Assumption)

Suppose P^Q (Indirect Assumption)

From 1 and 2, we have P by conjunction elimination

From 3, we have ¬P by reiteration

From 2 and 4, we have a contradiction (P and ¬P)

Therefore, ¬(P^Q) by indirect derivation (proof by contradiction)

Therefore, ¬P → ¬(P^Q) by conditional derivation

By using a conditional derivation and an indirect derivation, we have shown that ¬P → ¬(P^Q) is true. The proof relies on assuming the antecedent, deducing a contradiction, and concluding the consequent.

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When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

Answer:

y = -3x + 800

Step-by-step explanation:

You start out with 800 eggs and go down 3 eggs with each customer

The function for the number of eggs left y after x customers is

y = 800 - 3x

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Number of eggs the diner starts in a week = 800

The number of eggs each customer gets = 3

Now,

The number of y eggs after x customers.

y = 800 - 3x

Thus,

The function is y = 800 - 3x.

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Answer:

using pythagoras theorem

a^2+b^2=c^2

8^2+x^2=(x+2)^2

64+x^2=x^2+2*x*2+2^2

64+x^2=x^2+4x+4(here x^2 of left hand side and x^2 of right hand side gets cancel)

64=4x+4

64-4=4x

60/4=x

15=x

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

Factors of 96:  1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 , 120

Highest number between the two sets of factors which is common is 24

Due to length restriction we kindly invite to check the explanation for further details about the analysis of three quadratic equations and inherent rigid transformations.

Herein we find the graph of the parent quadratic equation f(x) = x² and two proposed resulting functions, whose difference with the former one have to be explained in terms of the kind of rigid transformations they have.

By comparing them, we find that both functions g(x) and h(x) are the result of a rigid transformation of the form f'(x) = k · f(x), where the transformation is a simple vertical dilation for k > 1, simple vertical contraction for 0 < k < 1, vertical contraction and reflection around the x-axis for - 1 < k < 0 and vertical dilation and reflection around the x-axis for k < - 1.

Function g(x) is the result of dilating f(x) by a factor of 3 and function h(x) is the result of dilating and reflecting f(x) around the x-axis by a factor of - 3.

The tables for each quadratic function are summarized below:

g(x):

 x             - 2             - 1               0             1                2

g(x)            12               3              0             3               12

f(x):

 x             - 2             - 1               0             1                2

g(x)          - 12            - 3               0           - 3            - 12

Lastly, we prepare the graph with the three functions in the image attached below.

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The correlation coefficient {r} = 0.01 represents the worst correlation.

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data

Given are the correlation values as given in the image.

The correlation coefficient {r} = 0.01 represents the worst correlation. It is shows that the data is scattered to a very large extent and the dependency between the two variables is not mathematically structured according to some rule.

Therefore, the correlation coefficient {r} = 0.01 represents the worst correlation.

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Step-by-step explanation:

Angles EXTERNAL to a circle are equal to 1/2 the difference of the intercepted arcs

   arcs are     17x   and  360 - 17x

75 = 1/2(17x - ( 360-17x)

75 = 1/2 ( 17x - 360 + 17x)

 150 = 34x-360

  510 = 17x

   x =30  

Answer:

Step-by-step explanation:

                          \(\boxed{x^2-y^2=(x+y)(x-y)}\)

\(c^2-(d+2)^2=\\(c+(d+2))(c-(d+2))=\\(c+d+2)(c-d-2)\)

Answer:

119.3

Step-by-step explanation:

Rounding up the given number 1199.28856995 to the nearest ten will result in 1200

When rounding 1199.28856995 to the nearest ten, we look at the digit in the tens place, which is 9.

Since 9 is greater than or equal to 5, we round up the digit in the hundreds place by adding 1.

Thus, 1199.28856995 becomes 1200, the nearest multiple of ten. This is because rounding to the nearest ten means finding the number that is closest to the original number while having a 0 in the units place.

In this case, 1200 is closer to 1199.28856995 than 1190 would be.

This concept of rounding helps simplify numbers while keeping a reasonable level of accuracy.

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Um I'm not sure but I think 3gallons I'm not sure

Answer:

5 gallons

Step-by-step explanation:

The x component of the vector is 16.24m

The components of a vector in two dimension coordinate system are the parts of vectors generated along the axes(x and y) and are considered to be x-component and y-component. It can be represented as, (Vx, Vy), where V is the vector.

The x component of a vector V is Vcos¢

where¢ is the angle of vector

the positive equivalent angle of - 96.3 is 83.7°

x component= 148cos 83.7

Vx= 16.24m

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