Do I have to do Greatest Common denominator or do I factor it, or do I have to do AC grouping bc A doesn’t equal 1

The point of intersection of f(x) and \(f^{-1}\)(x)   is (3, 3)

"It defines a relation between input and output values."

"In function, for each input there is exactly one output."

"The inverse function of x = f(m) is m =\(f^{-1}\) , where x, m are real values"

For given question,

A function  f(x) and its inverse function \(f^{-1}(x)\),  are both plotted on the same coordinate plane.

We know that the inverse function \(f^{-1}(x)\)   is the mirror image of the function f(x.)

This means, both the functions must be symmetric about the line y = x.

The curve of inverse function \(f^{-1} (x)\)  would cross the Y-axis at (0, 2), changes direction at (-1, -1) and crosses the X-axis at (-2, 0)

And both the functions intersect each other only on y = x

The point which satisfy the line y = x is (3, 3)

Therefore, the point of intersection of f(x) and\(f^{-1} (x)\) is (3, 3)

The complete question is : If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).

A.(0, –2)

B.(1, –1)

C.(2, 0)

D.(3, 3)

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Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.

What is division in mathematics?

Division is the process of splitting a number or an amount into equal parts.

To find the number of times Anna will need to fill the measuring cup, divide the number of cups of turnips by the size of the measuring cup:

78 cups/14 cups:

                            = 78/14

                              =5.57 measures

Hence, Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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The percent of the field goals did Samuel make will be 77.5%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Samuel made 31 out of 40 field goals during football practice. The percent of the field goals did Samuel make will be:

= 31 / 40 × 100

= 77.5%

The percentage is 77.5%.

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In your test plan, include the number of repetitions you will perform and a method for analyzing the data to account for random errors.

A test plan should account for the presence of systematic and random errors through the following steps:

1. Calibration: Calibration ensures that the instruments used in the experiment are accurate and consistent. By calibrating the equipment, you can minimize the impact of systematic errors on your results. Start your test plan by ensuring all instruments are calibrated and their measurements are reliable.

2. Randomization: Randomization is the process of randomly assigning subjects or samples to different experimental conditions. This helps to eliminate any potential bias or systematic errors caused by the arrangement of the experiment. In your test plan, make sure to include a method for randomizing the experiment to minimize the effect of systematic errors.

3. Repetition: Repeating the experiment multiple times can help reduce the impact of random errors. By performing the experiment multiple times and averaging the results, you can minimize the influence of random errors on your findings.

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Answer:

Complementary angles are two angles that add up to 90° in total measurement.

Example:

Angle 1 is 34°. It's complement would be 56°.

\(90 -34=56\)

Brainilest Appreciated.

Answer:

29

Step-by-step explanation:

23x2=46-17=29 so 29 the answer

The probability of at least one cloudy day in a five-day span is 0.7627 or approximately 0.76.

The probability of a sunny day in Virginia in July is 0.75, which means the probability of a cloudy day is 1 - 0.75 = 0.25.

Assuming the days are independent, the probability of at least one cloudy day in a five-day span can be calculated using the complement rule:

P(at least one cloudy day) = 1 - P(no cloudy days)

The probability of no cloudy days in a five-day span is the probability that all five days are sunny, which is \((0.75)^5\) = 0.2373.

Therefore, the probability of at least one cloudy day in a five-day span is:

P(at least one cloudy day) = 1 - P(no cloudy days) = 1 - 0.2373 = 0.7627

So the probability of at least one cloudy day in a five-day span is 0.7627 or approximately 0.76.

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The conversion 336g to m³ is impossible because they measure different units

From the question, we have the following parameters that can be used in our computation:

Convert 336g to m³

To convert a unit to another, the units must measure the same quantity

Take for instance:

Grams can be converted to kilograms because they both measure mass

Using the above as a guide, we have the following:

336g to m³  cannot be done because of the different quantities they represent

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The surface area of the composite rectangular prism is 434 cm²

The surface area of a rectangular prism is given by S.A = 2(lb + lh +bh) where l = length, b = base and h = height

Now, to find the surface area of the composite figure, we proceed as follows.

The surfcae area of the composite figure S.A = S' + S - A where

So, S' =  2(LB + LH + BH) where

So, S' =  2(LB + LH + BH)

= 2(10 × 7 + 10 × 5 + 7 × 5)

= 2(70 + 50 + 35)

= 2(120 + 35)

= 2(155)

= 310 cm²

Also,  S =  2(lb + lh + bh) where

So, S' =  2(lb + lh + bh)

= 2(8 × 3 + 8 × 4 + 3 × 4)

= 2(24 + 32 + 12)

= 2(56 + 12)

= 2(68)

= 136 cm²

Also, A = bh where

So, A = bh

= 3 × 4

= 12 cm²

S.A = S' + S - A

= 310 cm² + 136 cm² - 12 cm²

= 434 cm²

So, the surface area is 162 cm²

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What is Null hypothesis?

The null hypothesis assumes that any difference between the selected attributes in a set of data is attributable to chance. For example, if the predicted earnings for the gambling game are genuinely zero, then any discrepancy between the data's average earnings and zero is due to chance.

(a) The appropriate null and alternative hypotheses for this setting are:

Null hypothesis: The actual mean systolic pressure (μ) of the individual is not greater than 130 (μ ≤ 130).

Alternative hypothesis: The actual mean systolic pressure (μ) of the individual is greater than 130 (μ > 130).

(b) Type I error occurs when the null hypothesis is rejected when it is actually true. In this case, it means that the device recommends that the person seeks medical attention when they do not actually need it. The consequence of this error is that the person may undergo unnecessary medical tests or treatments, which can be costly, time-consuming, and can cause anxiety or other negative effects.

Type II error occurs when the null hypothesis is not rejected when it is actually false. In this case, it means that the device does not recommend medical attention when the person actually needs it. The consequence of this error is that the person may not receive the necessary medical attention and treatment, which can lead to serious health problems, including organ damage or failure, stroke, or heart attack.

(c) In this scenario, the cost of making a Type II error is likely to be much higher than the cost of making a Type I error. The reason is that failing to detect high blood pressure in a person can have serious health consequences. Therefore, it is better to make the Type I error probability smaller and the Type II error probability larger. This means that the device should be adjusted to have a higher threshold for recommending medical attention, which would decrease the likelihood of a false alarm, even if it increases the likelihood of missing some cases where medical attention is needed.

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The initial assertion that forms the null hypothesis frequently rests on research from the past or expert knowledge. According to the alternative hypothesis, a population parameter is either less, larger, or different from the value predicted by the null hypothesis.

A type I error (false-positive) occurs when a researcher rejects a null hypothesis that is actually true in the population; if the researcher does not do this When a null hypothesis is rejected even when it is false in the population, this is known as a type II error (false-negative).

Parameter Hypothesis testing is a second sort of statistical inference.

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126 yards

Step-by-step explanation:

Nine times fourteen is one hundred and twenty six

The first four terms of the sequence are 6, -24, 96 and -384

How to determine the first four terms?

The sequence is given as:

an=6(-4)^n-1

When n = 1, we have:

a(1)=6(-4)^(1-1)

This gives

a(1) = 6

When n = 2, we have:

a(2)=6(-4)^(2-1)

This gives

a(2) = -24

When n = 3, we have:

a(3)=6(-4)^(3-1)

This gives

a(3)=96

When n = 4, we have:

a(4)=6(-4)^(4-1)

This gives

a(4)=-384

Hence, the first four terms of the sequence are 6, -24, 96 and -384

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The transitive closures for the given relations are:

a. \( \{(a, c), (b, d), (c, a), (d, b), (e, d), (c, c), (d, d), (e, b)\} \)

b. \( \{(b, c), (b, e), (c, e), (d, a), (e, b), (e, c)\} \)

To find the transitive closure of a given relation, we need to determine all possible pairs that can be reached through a series of intermediate pairs. Let's calculate the transitive closures for the given relations:

a. \( \{(a, c),(b, d),(c, a),(d, b),(e, d)\} \)

To find the transitive closure, we need to identify all pairs that can be reached from the given pairs through a sequence of intermediate pairs. Let's analyze the given pairs:

- (a, c): No additional pairs can be formed from this pair.

- (b, d): No additional pairs can be formed from this pair.

- (c, a): This pair allows us to form the pair (c, c), which means c can reach itself.

- (d, b): This pair allows us to form the pair (d, d), which means d can reach itself.

- (e, d): This pair allows us to form the pair (e, b) because (e, d) and (d, b) are present.

After considering all the pairs, we have the following transitive closure:

\( \{(a, c), (b, d), (c, a), (d, b), (e, d), (c, c), (d, d), (e, b)\} \)

b. \( \{(b, c),(b, e),(c, e),(d, a),(e, b),(e, c)\} \)

Let's analyze the given pairs to determine the transitive closure:

- (b, c): No additional pairs can be formed from this pair.

- (b, e): This pair allows us to form the pair (b, c) because (b, e) and (e, c) are present.

- (c, e): No additional pairs can be formed from this pair.

- (d, a): No additional pairs can be formed from this pair.

- (e, b): This pair allows us to form the pair (e, c) because (e, b) and (b, c) are present.

- (e, c): No additional pairs can be formed from this pair.

After considering all the pairs, we have the following transitive closure:

\( \{(b, c), (b, e), (c, e), (d, a), (e, b), (e, c)\} \)

Therefore, the transitive closures for the given relations are:

a. \( \{(a, c), (b, d), (c, a), (d, b), (e, d), (c, c), (d, d), (e, b)\} \)

b. \( \{(b, c), (b, e), (c, e), (d, a), (e, b), (e, c)\} \)

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In "Caged Bird" by Maya Angelou, the free bird is an extended metaphor for a free person, and the caged bird is an extended metaphor for an oppressed person.

Throughout her collection of autobiographies, Angelou makes frequent use of the poem by Paul Laurence Dunbar's description of a bird trying to escape its prison as a metaphor. The caged bird signifies Angelou's incarceration as a result of racism and injustice, much like components in a prison story.

The free bird represents individuals who exist in our world without being constrained by prejudice of any kind, including racial, social, and psychological bias.

The chance exists for the free bird to move through life and take in all that it has to offer. She is implying that the caged bird's dreams will never come true in the line "but a caged bird stands on the tomb of dreams" (the caged bird represents someone without freedom). Since your dreams cannot genuinely be real, it is a metaphor.

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Answer:

3/19

Step-by-step explanation:

First, make 4 a fraction. Now, flip 4/1 to 1/4 for the following instruction: Do 12/19 x 1/4 = 12/76. Now divide both the denominator and numerator by 4 which equals 3/19.

Answer:  3/19 gallon

Step-by-step explanation:  1/4 of 12 is 3.

Just keep the denominator.

This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

Amount is a numerical value that refers to the total sum of money or other type of payment due. It is used to quantify the size of a transaction, the cost of goods or services, or any other type of financial transaction. Amounts can be expressed in a variety of different currencies, and they can be negative (owing) or positive (owed).

To calculate the amount of work required to pump all the water from the rectangular swimming pool into a drain at the top edge, we must first calculate the volume of the water in the pool. Volume is calculated by multiplying the length, width, and depth of the pool, which in this case is 20 ft x 20 ft x 8 ft = 3,200 cubic ft. Since the pool is filled to 1 ft below the top, the volume of water is 3,200 ft3 - 20 ft3 = 3,180 ft3.

Next, we must calculate the weight of the water, which is the volume multiplied by the weight density of water (62.4 lb/ft3). The weight of the water in the pool is 3,180 ft3 x 62.4 lb/ft3 = 197,952 lbs.

Finally, to calculate the amount of work required to pump the water from the pool into a drain at the top edge, we must multiply the weight of the water (197,952 lbs) by the height of the drain (8 ft). This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

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a. At point (2, 2, 1) the vector \(\bar{C} = - 2\bar{a}y+4\bar{a}z\)

b. At (2, 2, 1) the value of D = 23

Given that,

For \(\bar{A}=x \bar{a} x+y \bar{a} y+z \bar{a} z \)\) and \(\( \bar{B}=2 x \bar{a} x+3 y \bar{a} y+3 z \bar{a} z \)\).

Here, A and B are vectors

We know that,

a. At (2, 2, 1) we have to find \(\bar{C}=\bar{A} \times \bar{B}\).

C is a vector by using matrix,

\(\bar{C}=\left[\begin{array}{ccc}\bar{a}x&\bar{a}y&\bar{a}z\\x&y&z\\2x&3y&3z\end{array}\right]\)

Now, determine the matrix,

\(\bar{C} = \bar{a}x(3yz - 3yz) - \bar{a}y(3xz - 2xz)+\bar{a}z(3xy - 3xy)\)

\(\bar{C} = - \bar{a}y(xz)+\bar{a}z(xy)\)

At point (2,2,1) taking x = 2 , y = 2 and z = 1

\(\bar{C} = - \bar{a}y(2\times 1)+\bar{a}z(2\times 2)\)

\(\bar{C} = - 2\bar{a}y+4\bar{a}z\)

b. At (2, 2, 1) we have to find \(D=\bar{A} .\bar{B}\)

\(D=\bar{A} .\bar{B}\)

\(D = (x \bar{a} x+y \bar{a} y+z \bar{a} z )(2 x \bar{a} x+3 y \bar{a} y+3 z \bar{a} z)\)

D = 2x² + 3y² + 3z²

At point (2,2,1) taking x = 2 , y = 2 and z = 1

D = 2(2)² + 3(2)² + 3(1)²

D = 23.

Therefore, At (2, 2, 1) D = 23

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The question is incomplete the complete question is -

For \(\bar{A}=x \bar{a} x+y \bar{a} y+z \bar{a} z \)\) and \(\( \bar{B}=2 x \bar{a} x+3 y \bar{a} y+3 z \bar{a} z \)\).

Find the following at (2,2,1)

a. \(\bar{C}=\bar{A} \times \bar{B}\)

b. \(D=\bar{A} .\bar{B}\)

Answer:

24s+ 200 ≥ 500

Step-by-step explanation:

Let s be the number of sales

200 + 24s is the amount that they will make

They want to make at least 500 so the  amount they make must be greater than or equal to 500

200 + 24s≥ 500

Changing the order on the left side

24s+ 200 ≥ 500

Answer:

\(y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}\)

Step-by-step explanation:

Given

\(y=c_1e^x +c_2e^{-x\)

\(y(1) = 0\)

\(y'(1) =e\)

Required

The solution

Differentiate \(y=c_1e^x +c_2e^{-x\)

\(y' = c_1e^x - c_2e^{-x}\)

Next, we solve for c1 and c2

\(y(1) = 0\) implies that; x = 1 and y = 0

So, we have:

\(y=c_1e^x +c_2e^{-x\)

\(0 = c_1 * e^1 + c_2 * e^{-1}\)

\(0 = c_1 e + \frac{1}{e}c_2\) --- (1)

\(y'(1) =e\) implies that: x = 1 and y' = e

So, we have:

\(y' = c_1e^x - c_2e^{-x}\)

\(e = c_1 * e^1 - c_2 * e^{-1}\)

\(e = c_1 e - \frac{1}{e}c_2\) --- (2)

Add (1) and (2)

\(0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2\)

\(e = 2c_1e\)

Divide both sided by e

\(1 = 2c_1\)

Divide both sides by 2

\(c_1 = \frac{1}{2}\)

Substitute \(c_1 = \frac{1}{2}\) in \(0 = c_1 e + \frac{1}{e}c_2\)

\(0 = \frac{1}{2} e+ \frac{1}{e}c_2\)

Rewrite as:

\(\frac{1}{e}c_2 = -\frac{1}{2} e\)

Multiply both sides by e

\(c_2 = -\frac{1}{2} e^2\)

So, we have:

\(y=c_1e^x +c_2e^{-x\)

\(y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}\)

\(y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}\)

Answer:

  47

Step-by-step explanation:

Given 3 persons per horse, 4 sheep per cow, 3 ducks per person, you want to know if the total number of people, horses, sheep, cows, and ducks can be any of 41, 47, 59, 61, or 66.

Using {d, p, h, s, c} for numbers of {ducks, people, horses, sheep, cows}, the given ratios are ...

We can combine the first and last of these to d : p : h = 9 : 3 : 1.

In terms of horses, the total number of horses, people, and ducks will be ...

  h(1 + 3 + 9) = 13h

In terms of cows, the total number of sheep and cows will be ...

  c(1 + 4) = 5c

Then the total Hamlet population will be (13h +5c).

We need to find the number on the given list that cannot be expressed as this sort of sum.

In the attachment, we do that by subtracting multiples of 13 from the offered choice, and seeing if any remainders are divisible by 5. The cases where subtracting a multiple of 13 gives a multiple of 5 are highlighted.

Only 47 cannot be a total of people, horses, sheep, cows, and ducks.

Based on the above analysis, the numbers that could not possibly be the total number of people, horses, sheep, cows, and ducks in Hamlet are: 41, 47, 59, and 61.

To determine which of the given numbers could not possibly be the total number of people, horses, sheep, cows, and ducks in Hamlet, we need to check if they satisfy the given ratios between these animals and people.

Given ratios:

3 people for each horse

4 sheep for each cow

3 ducks for each person

Let's evaluate each option:

a) 41:

To satisfy the ratios, the number of horses would need to be a multiple of 3. However, 41 is not divisible by 3, so it is not possible.

b) 47:

Again, the number of horses would need to be a multiple of 3 to satisfy the ratios. 47 is not divisible by 3, so it is not possible.

c) 59:

Similarly, 59 is not divisible by 3, so it is not possible.

d) 61:

Once again, 61 is not divisible by 3, so it is not possible.

e) 66:

In this case, the number of horses would be 66 / 3 = 22. If we have 22 horses, we would need 22 * 3 = 66 people, which satisfies the ratio. However, we also need to check the other ratios. If we have 22 horses, we would need 22 * 4 = 88 sheep and 66 * 3 = 198 ducks. The number of cows can be any number since there is no ratio involving cows. Therefore, 66 is possible as the total number.

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The value of k for the given expression is, 2.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 8 (k + 10) = 48k

Now, We can solve the expression for k as;

⇒ 8 (k + 10) = 48k

Divide by 8,

⇒ k + 10 = 48k/8

⇒ k + 10 = 6k

Subtract k,

⇒ 10 = 6k - k

⇒ 10 = 5k

⇒ 5k = 10

Divide by 5;

⇒ k = 10/5

⇒ k = 2

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The efficient outcome in the market for milk portrayed in the figure would be where the marginal cost (MC) curve intersects with the demand (D) curve, which is at a price of $3 per gallon.

To determine which price yields an efficient outcome in the market for milk, we need to find the equilibrium price. The equilibrium price is where the supply and demand curves intersect, which represents the point at which the quantity demanded equals the quantity supplied.

                                At this price, the quantity of milk produced and consumed will be at the socially optimal level where the marginal benefit (MB) equals the MC, resulting in a Pareto efficient outcome. It is important to note that this assumes no externalities or market failures are present in the market for milk.

1. Identify the supply and demand curves in the figure. The demand curve typically slopes downward, while the supply curve slopes upward.
2. Locate the point where the supply and demand curves intersect.
3. Find the price corresponding to this point on the vertical axis (price axis).

The equilibrium price found in step 3 is the price that yields an efficient outcome in the market for milk.

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Answer:

? = 4.29

Step-by-step explanation:

Remark

Let  x be the question mark. You get the proportionality by using the dimensions of the little triangle to the dimensions of the large triangle.

Equation

14/(14+ 4) = 15/(x + 15)                   Combine like terms on the left

14/18 = 15/(x + 15)                          Cross multiply

14*(x + 15) = 18 * 15                        Simplify the right

14(x + 15) = 270                             Divide by 14

x + 15 = 270 / 14

x + 15 = 19.29                               Subtract 15 from both sides

x = 19.29 - 15

x = 4.29    

The maximum possible revenue the banquet hall will receive from the dinner is $2535.

What is total revenue?

The total of all inbound funds that the business has received from the sale of goods or services. Overall revenue is computed by multiplying the average sales price per item or unit by the number of items or units sold.

Here, we have

Given: a banquet hall charged $30 per person and 60 people attended the soccer banquet. This year, the hall's manager has said that every. 10 extra people that attend the banquet, will decrease the price by $1.50 per person.

The decrease in price for 1 person is $1.50.

Let x more number of people attended price will be:

(30 - 0.15x)

Revenue will be: (60+x)(30 - 0.15x)

R(x) = (60+x)(30 - 0.15x)

R(x) = 30×60 - 0.15x×60 + 30x - 0.15x²

R'(x) = - 0.15×60 + 30 - 0.3x

- 0.15×60 + 30 - 0.3x = 0

x = 70

R(70) = (60+70)(30 - 0.15×70)

R(x) = 2535

Hence, the maximum possible revenue the banquet hall will receive from the dinner is $2535.

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The true statement among the given options is:

c) Statements 1 and 3

Let's analyze each statement individually:

If n is a multiple of 8, then n is a multiple of 4. This statement is true because 8 is a multiple of 4, meaning any number that is divisible by 8 will also be divisible by 4. If n is a multiple of 18, then n is a multiple of 2.

This statement is also true since 18 is divisible by 2. Hence, any multiple of 18 will also be divisible by 2. However, statement 2 is not true:

If n is a multiple of 18, then n is a multiple of 9. This statement is false because not all multiples of 18 are multiples of 9. For instance, the number 18 itself is a multiple of 18 but not a multiple of 9. Therefore, the correct answer is c) Statements 1 and 3.

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Answer:

I think 57+2x−3gx  

2

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