Given f (x) = 2x² - 4x + 9 and g(x) = 4x +1:
Find (fog)(-1)

f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1,  f(x) = 1 is a constant function, f(x) = 2 is a constant function

A constant function is a mathematical function whose output value is the same for every input value

From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies  that for every unit increase in x, the value of y increases by 1.

Also,  f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.

In the same way,  f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.

The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.

The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.

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Answer:

C

Step-by-step explanation:

Tangent of an angle is the opposite side over the adjacent side.

Tangent of angle beta is 8/15

(a) The probability that exactly 5 of the 6 Americans donated money to a charitable cause ≈ 0.2787.

(b) The probability that less than 2 of the 6 Americans donated money to a charitable cause ≈ 0.0225

(c) The probability that no more than 5 of the 6 Americans donated money to a charitable cause is approximately 0.7772.

To solve these probability problems, we can use the binomial probability formula.

In this case, the probability of success (p) is 0.81 (since 81% of Americans donated money), and the sample size (n) is 6.

a. To obtain the probability that exactly 5 of them donated money to a charitable cause, we can use the binomial probability formula:

P(X = 5) = (n choose k) * p^k * (1 - p)^(n - k)

P(X = 5) = (6 choose 5) * 0.81^5 * (1 - 0.81)^(6 - 5)

P(X = 5) = 6 * 0.81^5 * 0.19^1

P(X = 5) ≈ 0.2787

Therefore, the probability that exactly 5 of the 6 Americans donated money to a charitable cause is approximately 0.2787.

b. To obtain the probability that less than 2 of them donated money to a charitable cause, we can calculate the probabilities of 0 and 1 successes and add them together:

P(X < 2) = P(X = 0) + P(X = 1)

P(X < 2) = (6 choose 0) * 0.81^0 * (1 - 0.81)^(6 - 0) + (6 choose 1) * 0.81^1 * (1 - 0.81)^(6 - 1)

P(X < 2) = 0.19^6 + 6 * 0.81 * 0.19^5

P(X < 2) ≈ 0.0006 + 0.0219

P(X < 2) ≈ 0.0225

Therefore, the probability that less than 2 of the 6 Americans donated money to a charitable cause is approximately 0.0225.

c. To obtain the probability that no more than 5 of them donated money to a charitable cause, we can calculate the probabilities of 0, 1, 2, 3, 4, and 5 successes and add them together:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X ≤ 5) = (6 choose 0) * 0.81^0 * (1 - 0.81)^(6 - 0) + (6 choose 1) * 0.81^1 * (1 - 0.81)^(6 - 1) + (6 choose 2) * 0.81^2 * (1 - 0.81)^(6 - 2) + (6 choose 3) * 0.81^3 * (1 - 0.81)^(6 - 3) + (6 choose 4) * 0.81^4 * (1 - 0.81)^(6 - 4) + (6 choose 5) * 0.81^5 * (1 - 0.81)^(6 - 5)

P(X ≤ 5) ≈ 0.19^6 + 6 * 0.81 * 0.19^5 + 15 * 0.81^2 * 0.19^4 + 20 * 0.81^3 * 0.19^3 + 15 * 0.81^4 * 0.19^2 + 6 * 0.81^5 * 0.19^1

P(X ≤ 5) ≈ 0.0006 + 0.0219 + 0.0979 + 0.2095 + 0.2387 + 0.2086

P(X ≤ 5) ≈ 0.7772

Therefore probability that no more than 5 of the 6 Americans donated money to a charitable cause is approximately 0.7772.

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Answer:

See below for proof.

\(S_{500}=125250\)

Step-by-step explanation:

Given arithmetic series:

Therefore:

\(S_n=1+2+3+...+(n-2)+(n-1)+n\)

\(S_n=1+(1+1)+(1+2)+...+(1+n-3)+(1+n-2)+(1+n-1)\)

\(S_n=1+(1+1)+(1+2(1))+...+(1+(n-3)(1))+(1+(n-2)(1))+(1+(n-1)(1))\)

Let:

Therefore:

\(S_n=a+(a+d)+(a+2d)+...+(a+(n-3)d)+(a+(n-2)d)+(a+(n-1)d)\)

Reverse the order:

\(S_n=(a+(n-1)d)+(a+(n-2)d)+(a+(n-3)d)+...+(a+2d)+(a+d)+a\)

Add the two expressions for Sₙ:

\(2S_n=(2a+(n-1)d)+(2a+(n-1)d)+(2a+(n-1)d)+...+(2a+(n-1)d)\)

Therefore, the term (2a + (n – 1)d) has been repeated n times:

\(2S_n=n(2a+(n-1)d)\)

Divide both sides by 2:

\(S_n=\dfrac{1}{2}n(2a+(n-1)d)\)

\(S_n=\dfrac{1}{2}n(a+a+(n-1)d)\)

Replace  a with  a₁  (first term) and a + (n – 1)d  with  aₙ (last term):

\(S_n=\dfrac{1}{2}n(a_1+a_n)\)

To find the sum of the series 1 + 2 + 3 + ... + 500, substitute the following values into the formula:

Therefore:

\(\implies S_{500}=\dfrac{1}{2}(500)(1+500)\)

\(\implies S_{500}=250(501)\)

\(\implies S_{500}=125250\)

Answer:

a) 201s / 1000

b) 7s / 125 + s / 10 + 7s / 5 + s / 30 + s / 2

Step-by-step explanation:

Total de miembros de la familia = 4

Ganancia de la madre = s / 1000 por mes

Ganancia del papa = s / 40 por semana

Ganancia por venta de huevos = s / 10

Ganancia total por mes = s / 1000 + s / 40 * 4 + s / 10 = s / 1000 + s / 10 + s / 10 = 201s / 1000  

Gasto-

Servicio - S / 250 * 4 = 4s / 250

ropa - 4S / 40

servicios de agua - 4S / 30

Electricidad - 4S / 100

paquete de teléfono, internet y cable - S / 120

gas - S / 40

alimento para pollos - S / 15 cada mes

higiene personal 4S / 20

4 mascarillas de tela - 4S / 10

4 litros de alcohol - 4 S / 8

3 litros de lejía - 3S / 5

Gastos totales = 2s / 125 + s / 10 + 2s / 15 + s / 25 + s / 120 + s / 40 + s / 15 + s / 5 + 2s / 5 + s / 2 + 3S / 5

Gasto total = 7s / 125 + s / 10 + 7s / 5 + s / 30 + s / 2

The distance between two parallel planes is given by the absolute value of the difference between the constant terms in their equations divided by the square root of the sum of the squares of the coefficients of x, y, and z.

In this case, the constant term in the equation 2x − 5y + z = 4 is 4, and the constant term in the equation 4x − 10y − 2z = 2 is 2. Therefore, the absolute value of their difference is |4 - 2| = 2.  The coefficients of x, y, and z in the two equations are 2, -5, 1 and 4, -10, -2, respectively. The sum of the squares of these coefficients is 30 + 41 = 71. Therefore, the distance between the two planes is 2/√71.

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A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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Answer:

all above, 9 and 14 ....

Step-by-step explanation:

Search up what corresponding means

Answer:x+65=180 /  x+y+z=115

Step-by-step explanation:

Answer:

it lies on 4 faces hope it helps

Answer:

The answer is four.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The change in the amount of water in the pool is the difference between the amount of water that enters and leaves the pool

Change in volume of water in the pool after 112 minutes is \(\underline{-117\frac{1}{3}}\) gallons

Reason:

The given parameters are;

The volume volume of entering the pool = 10 3/4 gallons per minute

The volume of water leaving the pool = 12 1/3 gallons per minute

Required:

The change in the amount of water in the pool after 112 minute

Solution:

The volume of water, V₁, that enters the pool in 112 minute is given as follows;

The volume of water, that enters the pool, V₁ = 1,204 gallons

The volume of water, V₂, that  leaves the pool in 112 minute is given as follows;

The volume of water, that that leaves the pool, V₂ = 1,381\(.\overline 3\) gallons

The change in the amount of water in the pool after 112 minutes, ΔV, is given as follows;

ΔV = V₁ - V₂

Change in volume of water in the pool after 112 minutes, ΔV = \(\underline{-117\frac{1}{3}}\) gallons

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The sample distribution is a collection of the parameters of all possible samples of a particular size taken from a particular population. The correct answer is option E.

A sampling distribution refers to a probability distribution of a statistic which comes from selecting random samples of a given population. Also known as a finite-sample distribution, it represents the distribution of frequencies on how spread apart various outcomes will be for a specific population.

As sample sizes increase, the sampling distributions approach a normal distribution. With infinite numbers of successive random samples, the mean of the sampling distribution is equal to the population mean (µ). The mean of the sampling distribution of a sample proportion is np, the sample size times the probability of success for each trial (or observation).

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Answer:

triangle

Step-by-step explanation:

The cross section must be a vertical cross section that includes the vertex of the pyramid.

Answer: triangle

Answer:

mate....where is red shaded region....

probably this will help ..... ;)

find the probability that a randomly selected point within the circle falls in the red shaded area

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The empirical probability of the red car moving a specific number of times in 8 rolls of the die can be estimated by rolling the die many times and counting the number of times the red car moves a specific number of times, then dividing this count by the total number of rolls.

Assuming that the probability of the red car moving is independent and equal for each roll, the number of times the red car moves in 8 rolls can be modeled using a binomial distribution.

Let's say that the probability of the red car moving in a single roll is p, and we want to find the empirical probability of the red car moving k times in 8 rolls.

To find the empirical probability, we would need to roll the die 8 times and record how many times the red car moves. We can repeat this process many times to collect a large sample of outcomes and estimate the probability based on the proportion of times the red car moves k times in 8 rolls.

For example, if we roll the die 8 times and observe that the red car moves 4 times, we would record that as 4 occurrences of the red car moving in 8 rolls. We can repeat this process many times and record the number of occurrences for each possible value of k (from 0 to 8).

Then, we can calculate the empirical probability of the red car moving k times in 8 rolls as:

The empirical probability of k red car moves = (number of occurrences of k red car moves) ÷ (total number of trials)

For each value of k, we would calculate this empirical probability based on the collected sample.

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Answer:

3x + 6.

Step-by-step explanation:

That would be x + x +2 + x + 4

= 3x + 6.

Verify this  by adding 7 9 and 11:

7 + 9 + 11 = 27

3(7) + 6 =  21 + 6 = 27.

The answer to whether or not the triangles are similar depends on the given information, so it could be either option C or D.

If the given information includes the measures of two angles of each triangle, and the two pairs of angles are congruent, then we can conclude that the triangles are similar by the AA theorem. On the other hand, if the given information includes the measures of two sides and the included angle of each triangle, and the two pairs of sides are proportional and the included angles are congruent, then we can conclude that the triangles are similar by the SAS theorem.

If the question includes a diagram or gives information about the measures of angles or sides, we can apply the triangle similarity theorems to determine if the triangles are similar. However, if there is not enough information provided, then we cannot definitively determine if the triangles are similar and options A or B would be correct. It is important to note that there are other similarity theorems that can be used to prove similarity, such as the SSS (Side-Side-Side) theorem and the AAA (Angle-Angle-Angle) theorem, but these theorems are not applicable in all cases. It is also important to remember that similarity does not imply congruence, as similar figures have the same shape but not necessarily the same size.

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Answer:

Y = 4/3

Step-by-step explanation:

Solve for Y:

3 Y = 4

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 3 Y = 4 by 3:

(3 Y)/3 = 4/3

Hint: | Any nonzero number divided by itself is one.

3/3 = 1:

Answer: Y = 4/3

Answer:

The probability that a randomly selected resident of the Gold dorm is a senior is 0.1562

Step-by-step explanation:

The given percentage of each class of student is presented as follows;

Priority A (seniors) = 22%, ∴ P(s) = 0.22

Priority B (juniors) = 29%, ∴ P(j) = 0.29

Priority C (freshmen and sophomores) = (100 - 22 - 29)% = 49%, ∴ P(fs) = 0.49

The percentage of the seniors that elect to live at the Gold dorm, = 71%, ∴ P(sG) = 0.71

The percentage of the juniors that live at the Gold dorm = 19%, ∴ P(jG) = 0.19

The percentage of the freshmen and sophomores that live in the Gold dorm = 5%, ∴ P(fsG) = 0.05

The probability that a randomly selected resident of the Gold dorm is a senior = P(s∩sG) = P(s) × P(sG)

∴ P(s∩sG) = 0.22 × 0.71 = 0.1562

Therefore;

The probability that a randomly selected resident of the Gold dorm is a senior = P(s∩sG) = 0.1562.

Question:

Simplify the radical expressions

\(1.\ \sqrt{63\)     \(2.\ \sqrt{48\)    \(3.\ \sqrt{75\)      \(4.\ \sqrt{99\)      \(5.\ \sqrt{92\)

\(6.\ \sqrt[3]{24}\)      \(7.\ \sqrt[3]{81}\)      \(8.\ \sqrt{128}\)     \(9.\sqrt[3]{40}\)     \(10.\ \sqrt[3]{135}\)

Answer:

\(\sqrt{63}= 3 \sqrt7\)

\(\sqrt{48} = 4\sqrt{3}\)

\(\sqrt{75} = 5\sqrt{3}\)

\(\sqrt{99} = 3 \sqrt{11\)

\(\sqrt{92} = 2\sqrt{23\)

\(\sqrt[3]{24} = 2 \sqrt[3]{3}\)

\(\sqrt[3]{81} =3\sqrt[3]{3}\)

\(\sqrt{128} = 8 \sqrt{2}\)

\(\sqrt[3]{40} = 2 \sqrt[3]{5}\)

\(\sqrt[3]{135} =3\sqrt[3]{5}\)

Step-by-step explanation:

\(1.\ \sqrt{63\)    

Express 63 as 9 * 7

\(\sqrt{63}= \sqrt{9 * 7\)

Split:

\(\sqrt{63}= \sqrt{9} * \sqrt7\)

\(\sqrt{63}= 3 * \sqrt7\)

\(\sqrt{63}= 3 \sqrt7\)

\(2.\ \sqrt{48\)    

Express 48 as 16 * 3

\(\sqrt{48} = \sqrt{16*3}\)

Split

\(\sqrt{48} = \sqrt{16}*\sqrt{3}\)

\(\sqrt{48} = 4*\sqrt{3}\)

\(\sqrt{48} = 4\sqrt{3}\)

\(3.\ \sqrt{75\)    

Express 75 as 25 * 3

\(\sqrt{75} = \sqrt{25*3}\)

Split

\(\sqrt{75} = \sqrt{25}*\sqrt{3}\)

\(\sqrt{75} = 5\sqrt{3}\)

\(4.\ \sqrt{99\)  

Express 99 as 9 * 11

\(\sqrt{99} = \sqrt{9} * \sqrt{11}\)

Split

\(\sqrt{99} = 3 \sqrt{11\)

\(5.\ \sqrt{92\)

Express 92 as 4 * 23

\(\sqrt{92} = \sqrt{4} * \sqrt{23\)

\(\sqrt{92} = 2* \sqrt{23\)

\(\sqrt{92} = 2\sqrt{23\)

\(6.\ \sqrt[3]{24}\)    

Express 24 as 8 * 3

\(\sqrt[3]{24} = \sqrt[3]{8} * \sqrt[3]{3}\)

Express 8 as 2^3

\(\sqrt[3]{24} = \sqrt[3]{2^3} * \sqrt[3]{3}\)

\(\sqrt[3]{24} = 2 \sqrt[3]{3}\)

\(7.\ \sqrt[3]{81}\)

Express 81 as 27 * 3

\(\sqrt[3]{81} =\sqrt[3]{27}*\sqrt[3]{3}\)

Express 27 as 3^3

\(\sqrt[3]{81} =\sqrt[3]{3^3}*\sqrt[3]{3}\)

\(\sqrt[3]{81} =3\sqrt[3]{3}\)

\(8.\ \sqrt{128}\)    

Express 128 as 64 * 2

\(\sqrt{128} = \sqrt{64} * \sqrt{2}\)

\(\sqrt{128} = 8 \sqrt{2}\)

\(9.\sqrt[3]{40}\)

Express 40 as 8 * 5

\(\sqrt[3]{40} = \sqrt[3]{8} * \sqrt[3]{5}\)

\(\sqrt[3]{40} = \sqrt[3]{2^3} * \sqrt[3]{5}\)

\(\sqrt[3]{40} = 2 \sqrt[3]{5}\)

\(10.\ \sqrt[3]{135}\)

Express 135 as 27 * 5

\(\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}\)

Express 27 as 3^3

\(\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}\)

\(\sqrt[3]{135} =3\sqrt[3]{5}\)

3 positive 1 positive

Step-by-step explanation:

D goes 3 units right and it get to 3 Positive and then two units down gets you to 3 Positive and 1 Positive 3,1

True, the joint probability of Y1 and Y2 taking on the value 1 simultaneously is 1/3.

The first dummy random variable is defined as follows:

Let X be the random variable representing the number on the first dice. Then, the dummy random variable Y1 is defined as:

Y1 = 1 if X is either 1, 2, or 3

Y1 = 0 otherwise

Similarly, the second dummy random variable is defined as:

Let Z be the random variable representing the number on the second dice. Then, the dummy random variable Y2 is defined as:

Y2 = 1 if Z is either 3, 4, 5, or 6

Y2 = 0 otherwise

Since Y1 and Y2 are independent, their joint probability distribution can be computed by multiplying their marginal probabilities.

P(Y1=1, Y2=1) = P(Y1=1) * P(Y2=1)

To compute P(Y1=1), we need to find the probability that X is either 1, 2, or 3. Since each face of a fair dice has an equal probability of appearing, we have:

P(X=1) = P(X=2) = P(X=3) = 1/6

Therefore,

P(Y1=1) = P(X=1 or X=2 or X=3) = P(X=1) + P(X=2) + P(X=3) = 3/6 = 1/2

Similarly, to compute P(Y2=1), we need to find the probability that Z is either 3, 4, 5, or 6. Again, since each face of a fair dice has an equal probability of appearing, we have:

P(Z=3) = P(Z=4) = P(Z=5) = P(Z=6) = 1/6

Therefore,

P(Y2=1) = P(Z=3 or Z=4 or Z=5 or Z=6) = P(Z=3) + P(Z=4) + P(Z=5) + P(Z=6) = 4/6 = 2/3

Thus,

P(Y1=1, Y2=1) = P(Y1=1) * P(Y2=1) = (1/2) * (2/3) = 1/3

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Using division, we can find that the best statement that describes the given expression is:

Add 8 to half the difference of 6 and 2, then subtract 1.

One of the fundamental mathematical operations is division, which entails breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 pupils are required to be split into groups of five for a sporting event? The division operation can quickly and easily fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will be a total of 6 groups, each with 5 pupils. Use the beginning number, 30, which is obtained by multiplying 6 by 5, to check this response.

8 + fraction 1 over 2 x (6 − 2) − 1.

The above is expressed mathematically as:

8 + 1/2(6 - 2) - 1

Therefore, the statement that describes this expression from the options given correctly is :

Add 8 to half the difference of 6 and 2, then subtract 1.

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We can use division to determine that the following statement best captures the meaning of the given expression:

To make up the difference between 6 and 2, add 8 and then take away 1.

Division, which involves dividing a larger number into smaller groups with the same number of components, is one of the basic mathematical operations. For instance, if 30 students must be divided into groups of five for a sporting event, how many groups will be formed. Such problems can be rapidly and readily resolved by the division operation. In this instance, we need to multiply 30 by 5. The outcome is 30 x 5 = 6.

There will be 6 groups in total, each with 5 students. To verify this response, use the starting number, 30, which is produced by dividing

6 by 5.

1 x (6 x 2) + 8 plus fraction 1 over 2 = 8.

The following can be represented mathematically:

8 + 1/2(6 - 2) - 1

Therefore, from the available possibilities, the statement that accurately represents this expression is:

To make up the difference between 6 and 2, add 8 and then take away 1.

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Thus, the equation of the plane determined by the intersecting lines L1 and L2 is: -2x + 14y + 18z - 48 = 0.

To find the plane determined by the intersecting lines L1 and L2, we need to find a normal vector to the plane.

First, we'll find two direction vectors for the lines L1 and L2.

For L1:

x = -1 + t

y = 2 + 4t

z = 1 - 3t

Taking the differences of these equations, we obtain two direction vectors for L1:

v1 = <1, 4, -3>

For L2:

x = 1 - 4s

y = 1 + 2s

z = 2 - 2s

Again, taking the differences of these equations, we obtain two direction vectors for L2:

v2 = <-4, 2, -2>

Since the plane contains both lines, the normal vector to the plane will be perpendicular to both direction vectors, v1 and v2.

To find the normal vector, we can take the cross product of v1 and v2:

n = v1 x v2

n = <1, 4, -3> x <-4, 2, -2>

Using the cross product formula, the components of the normal vector n can be calculated as follows:

n = <(4 * -2) - (-3 * 2), (-3 * -4) - (1 * -2), (1 * 2) - (4 * -4)>

n = <-8 - (-6), 12 - (-2), 2 - (-16)>

n = <-2, 14, 18>

So, the normal vector to the plane determined by the intersecting lines L1 and L2 is n = <-2, 14, 18>.

Now we can write the equation of the plane using the normal vector and a point on the plane (which can be any point on either L1 or L2).

Let's choose the point (-1, 2, 1) on L1.

The equation of the plane can be written as:

-2(x + 1) + 14(y - 2) + 18(z - 1) = 0

Simplifying:

-2x - 2 + 14y - 28 + 18z - 18 = 0

-2x + 14y + 18z - 48 = 0

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Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

\(\implies 6 \times 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

\(\implies (0.06) \cdot (0.154)=0.00924\)

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

Answer option A

\(\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}\)

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

\(\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)\)

Therefore, this is a valid answer option.

Answer option B

\(\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}\)

Multiply the numbers 6 and 154:

\(\implies 6 \times 154 = 924\)

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

\(\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924\)

Therefore, this is a valid answer option.

Answer option C

\(\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}\)

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

\(\implies 6 \cdot 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

\(\implies 0.924\)

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

\(\boxed{6 \cdot 154 \cdot (0.00001)}\)

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

\(\implies 6 \cdot 154 \cdot (0.00001)=0.00924\)

Therefore, this is a valid answer option.

Answer option E

\(\boxed{0.00924}\)

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

Answer:

12+45=57 good job for me y

Step-by-step explanation:

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