A culture of bacteria has an initial population of 74000 bacteria and doubles every 3 hours. What is the population of bacteria in the culture after 13 hours, to the nearest whole number?

A collegiate basketball player hits 80% of his free throw attempts. Assuming free throw attempts are independent, he will try 100 free throws this season the answers are as follows:

a) The mean of X is 80.

b) The standard deviation of X is 4.

c) The probability that the basketball player makes at least 90 of these attempts is approximately is 0.0062.

d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is 0.0064.

As per the question given,  

a) The mean of X is given by the formula: mean = n * p, where n is the number of trials and p is the probability of success on each trial. In this case, the player attempts 100 free throws with a probability of success of 0.8, so the mean is:

mean = 100 * 0.8 = 80

Therefore, the correct answer is 80.

b) The standard deviation of X is given by the formula: standard deviation = sqrt(n * p * (1 - p)). Substituting the values, we get:

standard deviation = sqrt(100 * 0.8 * 0.2) = 4

Therefore, the correct answer is 4.

c) To find the probability that the player makes at least 90 free throws, we can use the normal approximation to the binomial distribution. The mean is 80 and the standard deviation is 4, so we can standardize the value of X as follows:

z = (90 - 80) / 4 = 2.5

Using a standard normal distribution table, we can find the probability that Z is greater than 2.5, which is approximately 0.0062.

Therefore, the correct answer is 0.0062.

d) If the player attempts only 10 free throws, the number of successful attempts X follows a binomial distribution with n=10 and p=0.8. The probability that he makes at most 4 of these attempts is:

P(X <= 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Using the binomial distribution formula, we can calculate each of these probabilities and sum them up. Alternatively, we can use a binomial probability table or a calculator to find the cumulative probability.

Using a binomial probability calculator, we get:

P(X <= 4) = 0.0064 (rounded to four decimal places)

Therefore, the correct answer is 0.0064.

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The orthocenter of ▲ABC is the point (27/4, 17/4)

What is Orthocenter in coordinate geometry?

Any triangle's three altitudes are contemporaneous line segments (they intersect in a single point), and this point is known as the triangle's orthocenter.

To find the orthocenter of ▲ABC, we need to first find the altitude lines of the triangle, which are the perpendicular lines from each vertex to the opposite side. The point where these three lines intersect is the orthocenter.

The slope of this line is:

BC = (-1 - (-4)) / (-1 - 5)

BC = 3/2

Using point-slope form, the equation of the line BC is:

[tex]y -y_{b} = m_{BC} (x - x_{b} )[/tex]

y - (-4) = (3/2)(x - 5)

y = (3/2)x - 17/2

To find the altitude from vertex A to BC, we need to find the equation of the line passing through A and perpendicular to BC. The slope of this line is the negative reciprocal of the slope of BC:

[tex]m\ altitude_A = -2/3[/tex]

The point-slope form of the equation of the altitude from A is:

[tex]y -y_{A} = m_{BC} (x - x_{A} )[/tex]

y - 5 = (-2/3)(x - 5)

y = (-2/3)x + 25/3

Similarly, we can find the equations of the altitudes from vertices B and C to the opposite sides AC and AB, respectively:

Altitude from B to AC:

[tex]m_{AC} = \frac{(y_{C} -y_{A})}{(x_{C} -x_{A})} \\\\m_{AC} = \frac{-3}{2}[/tex]

AC = 2/3

y - (-4) = (2/3)(x - 5)

y = (2/3)x - 2/3

Altitude from C to AB:

[tex]m_{AB} =\frac{(y_{B}- y_{A})}{(x_{B}- x_{A})} \\[/tex]

= (-4 - 5) / (5 - 5)

= undefined

x = -1

Now, we need to find the point of intersection of these three altitudes, which is the orthocenter. To do this, we can solve the system of equations formed by the three altitude lines:

y = (3/2)x - 17/2

y = (-2/3)x + 25/3

y = (2/3)x - 2/3

Substituting the third equation into the first two equations, we get:

(2/3)x - 2/3 = (-2/3)x + 25/3

(4/3)x = 9

x = 27/4

Substituting x = 27/4 into any of the three equations, we get:

y = (2/3)(27/4) - 2/3 = 17/4

Therefore, the orthocenter of ▲ABC is the point (27/4, 17/4).

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The integer 8 represents the amount lost each time the pass was used.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that, every time Ezequiel rides the bus, money is deducted from the value of the pass.

He rode 9 times and $72 was deducted from the value of the pass.

Let x be the integer that represents the amount deducted each time.

The amount deducted after 9 times is 9x.

9x = 72

We have to divide 72 into 9 parts to know the value of x.

x = 72 / 9 = 8

Hence Ezequiel lost $8 each time the pass was used.

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The graph of the linear inequality  [tex]y\geq -3x+4[/tex] is given below.

What is linear inequality?

The expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. A linear inequality, which is an inequality including at least one linear algebraic expression, is when a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1. There are numerous ways to depict various kinds of linear inequalities.

Given linear inequality is [tex]y\geq -3x+4[/tex] for which y region will be in the positive range.

Hence, the graph of the given linear inequality is given below.

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Referring to the given kite, the length of the other diagonal. DF, is 21 cm.

A kite is a quadrilateral shape, meaning it has four sides. The two pairs of adjacent sides are of equal length, while the opposite sides are not.

The shape of a kite is typically described as having two pairs of congruent adjacent sides that are connected by two diagonal lines that intersect at a right angle. The diagonal lines of a kite are perpendicular to each other, and the shorter diagonal bisects the longer diagonal.

Let's denote the point of intersection of the two diagonals as O.

Since the two diagonal intersect at a right angle, diagonal DF is perpendicular to diagonal EG.

DG = 13 cm

FG = 20 cm

OG = 1/2 EG = 1/2 x 24 = 12 cm

Using the Pythagorean Theorem:

OD = √(DG² - OG²)

     = √(13² - 12²) = 5 cm

OF = √(FG² - OG²)

     = √(20² - 12²) = 16 cm

DF = OD + OF

     = 5 + 16 = 21 cm

The picture in your question is missing, most likely it was like on the attached picture.

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Answer: c

Step-by-step explanation: I got it right

Answer:

Step-by-step explanation:

You want to know the number of points and the number of turns when Tony and his cousin will have the same score. Tony has 12 points and earns 10 points per turn; his cousin has 0 points and earns 14 points per turn.

The attachment shows a table of points and turns. It shows the score will be tied at 42 points after 3 turns.

Tony's points can be described by ...

  p = 12 +10t . . . . . . . . 12 points in addition to 10 per turn

Cousin's points can be described by ...

  p = 0 + 14t . . . . . . . . . 14 points per turn added to the current score of 0

These will be equal when ...

  p = p

  12 +10t = 0 +14t . . . . substitute for p in both cases

  12 = 4t . . . . . . . . . . subtract 10t

  3 = t . . . . . . . . . . divide by 4

  p = 14·3 = 42 . . . . the scores after 3 turns

Donald and Reynold work at the same rate, the it also takes 8 hours for Donald to make 4 baked zitis.

We know that Reynold can make 4 baked zitis in 8 hours, then his rate of work is:

R = (4 zitis)/(8 hours) = 0.5 zitis per hour.

Whit Donald's help they can make 4 zitis in 4 hours, if we define D as Donald's rate we can write:

(R + D)*4 hours = 4 zitis.

Replacing R we get:

(0.5 zitis/hour + D)*4 hours = 4 zitis

(0.5 zitis/hour + D) = (4 zitis)/(4 hours)

(0.5 zitis/hour + D) = 1 ziti/hour

D = 1 ziti/hour - 0.5 zitis/hour = 0.5 zitis/hour

So Donald works at the same rate than Reynold, then it will take 8 hours for Donald to make 4 baked zitis.

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Answer:

  (b)  area = 29 units²

Step-by-step explanation:

You want the area of the irregular shape shown in the figure.

The area of a rectangular shape is the product of its length and width:

  A = LW

The given shape can be considered to be a 6 unit square with some pieces removed. The area of the remaining shape is the area of that square less the areas of the removed pieces.

The piece removed from the upper left corner is a 2-unit square. Its area is ...

  A = (2 units)(2 units) = 4 units²

The piece removed from the lower right side is 3 units by 1 unit, so its area is ...

  A = (3 units)(1 units) = 3 units²

The area of the square before those pieces were removed was ...

  A = (6 units)(6 units) = 36 units²

Then the area of the remaining shape after the pieces are removed is ...

  Area = 36 units² -4 units² -3 units² = (36 -7) units² = 29 units²

The area of the figure is 29 units².

__

Additional comment

Quite often, the area of an irregular shape is more easily found by subtracting missing areas than by dividing up the existing shape into pieces whose area formulas you know.

The second attachment shows division of the area into smaller rectangles. Working clockwise from upper left, their areas are 1×2, 3×4, 3×1, 3×4, for a total of 2+12+3+12 = 29 square units.

The length of the hypotenuse is 11.31 cm

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

A right, isosceles triangle has its legs to be 8cm

Represen the length of the hypotenuse of the isosceles right triangle  with x

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

x = Leg√2

substitute the known values in the above equation, so, we have the following representation

x = 8 * √2

This gives

x = 11.31

HEnce, the hypotenuse is 11.31 cm

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The correct weight of butter is 1/32 pounds. Olivia will use 1/32 pound of butter in each batch of muffins.

Olivia has 1/8 pound of butter that she needs to divide equally among 4 batches of muffins. To find out how much butter is used each batch of muffins, we can divide the total amount of butter by the number of batches. So, the amount of butter in each batch of muffins is: 1/8 ÷ 4 batches = 1/32 pound. So, Olivia will use 1/32 pound of butter in each batch of muffins. A pound (lb) is a unit of weight or mass commonly used in the United States and other countries that follow the customary system of measurement.

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In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.

A millimeter, abbreviated mm, is the smallest unit for length in the metric, or Standard International, system of measurement. It is used to measure small lengths and for precise measurements. Millimeters can be converted to either units within the metric system or the customary system of measurement.

Divide 8500 kilometers by which 500 km equals 17.5 millimeters.

Therefore, In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.

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Answer: 7 + [tex]\frac{B}{5}[/tex] = 3

Step-by-step explanation:

Its pretty simple, just do as the words say. :) the only issue could be "of a number and 5", so you go in order, letting B be the number, it's B/5

Answer: A. [tex]92cm^{3}[/tex]

Step-by-step explanation:

[tex]V= \frac{4}{3} \pi r^{3}[/tex]

[tex]V=\frac{4}{3}\pi 2.8^{3}[/tex]

[tex]4/3=1.33333333333[/tex]

calculate in calculator

[tex]1.33333333333\pi 2.8^3=91.9523225755[/tex]

round to nearest ones (9 tells 1 to go to 2)

Therefore, A. 92cm^3

Answer:

Step-by-step explanation:

Method 1: Counting the number of committees with exactly one engineer:

There are 2 ways to choose the engineer, and 10 ways to choose the remaining 9 computer scientists. Hence, there are 2 * 10 = 20 different committees with exactly one engineer.

Method 2: Using the combinations formula:

There are 12 people in total, and we need to choose 10 of them for the committee. We can use the combinations formula to calculate the number of different ways to choose 10 people from 12: C(12, 10) = (12!) / (10! * (12-10)!) = (12!) / (10! * 2!) = 66.

So, there are 66 different ways to create a committee of 10 people with at least one engineer represented.

Answer:

Step-by-step explanation:

You want to know the meaning of D(2.60) = 159 if D(p) tells you the number of toys demanded at price p in hundreds.

Compare D(p) to D(2.60) and you see that p=2.60. The problem statement tells you p is the price. This means ...

The problem statement tells you that D(p) is the number of toys in hundreds. When D(p) is 159, the demand is 159 hundred toys.

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Using the value of principal, annual rate and time, the simple interest is $375

Simple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.

The formula for simple interest is:

I = P * r * t

where:

I is the interest amount

P is the principal amount

r is the interest rate (expressed as a decimal)

t is the time period (in years)

In the given problem, we can calculate the simple interest by substituting the values into the formula

A = P(1 + rt)

A = 250(1 + 0.05(10))

A = 375

The simple interest is $375

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The statement that is true is:

b.) A high correlation can indicate a relationship but cannot prove causation.

Correlation measures the strength and direction of the relationship between two variables, but it does not necessarily imply causation. A high correlation means that there is a strong linear relationship between the two variables, but it does not indicate whether one variable causes the other. There can be other factors that influence the relationship. Therefore, it is important to use other methods, such as experiments or observational studies, to determine causation. Correlation is useful for identifying associations between variables, but it cannot be used as evidence of a causal relationship.

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Answer:

A.  Correct

B.  Correct

C.  Not correct

D.  Correct

E.  Not correct

Step-by-step explanation:

We are told that Michael's race numbers are:

5.25 miles

45.75 minutes

Divide the miles by the minutes to get mIchael's running rate:

0.114754098 mi/min

This result matches option B. " Michael's average pace was about 0.11 miles per minute."

======

Check all the answer options:

A. Michael's unit rate of minutes per mile was about 8.7.  

  Take 0.11475409 mi/min and invert it to find min/mile:

      1/(0.11475409 mi/min) = 8.71 min/mile

This is a correct statement.

B. Michael's average pace was about 0.11 miles per minute.

From above:  This is a correct statement.

C. Michael's unit rate of minutes per mile was about 6.9.

Take the given numbers:   (45.75 minutes)/(5.25 miles) = 8.71 min/mile

This is not a correct statement.

D. Michael's average speed during the race was about 6.9 miles per hour.  

Take the calculated rate of 0.11475409 mi/min and covert it to miles/hour:

  Use the conversion factor (60 min/1 hr)

   (0.11475409 mi/min)*((60 min/1 hr)) = 6.89 miles/hr

This is a correct statement.

E.  Michael ran about 8.7 miles in 1 minute.

We know from above that he runs at 6.89 miles per hour.  Running 8.7 miles in 1 minute  would mean he is running at (8.7)*(60) = 413 miles/hour.    

Perhaps he had some good energy bars, but the data do not support this conclusion.

This is not a correct statement.

Answer:

1. SAS

2. Not congruent

Step-by-step explanation:

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

The solution is,

1. SAS

2. AAS

3. SAS

4. Not congruent.

Two triangles are congruent if all three pairs of corresponding sides are equal. Two pairs of corresponding sides and the corresponding angles between them are equal.

here, we have,

we know that,

To identify which triangles are congruent measure the angles and sides of each of the triangles and compare them.

Meaning of congruent:

In mathematics, the word congruent is used if two figures have the same size and shape, although their orientation can be different.

Two triangles are congruent:

In the case of triangles two factors should be considered:

1) Lengths of each side are equal.

2) Angles are equal.

This means that to determine if the triangles are congruent, we must measure each side and angle and make sure these are the same in each triangle.

now, we have,

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second and, similar for 2 & 3 by AAS & SAS.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

Hence, 1. SAS

2. AAS

3. SAS

4. Not congruent.

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If a cuboid weighs 100N and has sides 5cm by 10cm, then the area of cuboid is 0.005m².

Weight of the cuboid = 100N

Sides of the cuboid = 5cm by 10cm

A solid structure or a three-dimensional shape in geometry is called a cuboid. It is similar to a cube in that a cuboid can become a cube by changing the angles between faces or the lengths of the edges. A convex polyhedron with the same polyhedral graph as a cube is referred to as a cuboid in mathematics.

Calculating the area of the Cuboid -

= 5cm × 10cm

= 50cm²

Converting -

Area of Cuboid

= 50/10000 m²

= 0.005 m²

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Answer: C

Step-by-step explanation:

A)  The mean of 2018 scores: μ₂₀₁₈ = 75

 The mean of 2019 scores: μ₂₀₁₉ = 75

 The standard deviation of 2018 scores: s₂₀₁₈ = 2.07

 The standard deviation of 2019 scores: s₂₀₁₉ = 5.26

B) The primary difference is that variation is higher in the 2018 season than the 2019 season.

A)

We know that the mean is nothing but the sum of all scores divided by the number of scores.

Thus the mean for 2018 scores is:

μ₂₀₁₈ = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8

μ₂₀₁₈ = 75

Similarly the mean for 2019 scores is:

μ₂₀₁₉ = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8

μ₂₀₁₉ = 75

We know that the formula for the standard deviation is:

[tex]s=\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1} }[/tex]

where s sample standard deviation

n the size of the sample

[tex]x_i[/tex] each value from the sample

[tex]\bar{x}[/tex] the sample mean

Using this formula, the standard deviation for 2018 scores is:

s₂₀₁₈ = [tex]\frac{\sqrt{ (73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 +(74-75)^2 + (76-75)^2} }{7}[/tex]

s₂₀₁₈ = 2.07

And the standard deviation for 2019 scores is:

s₂₀₁₉ = [tex]\frac{\sqrt{ (70-75)^2 + (69-75)^2 + (74-75)^2 + (76-75)^2 + (84-75)^2 + (79-75)^2 +(70-75)^2 + (78-75)^2} }{7}[/tex]

s₂₀₁₉ = 5.26

B)

We cwn observe that both the two years have the same mean but the 2019 scores have higher variation as compared to 2018 scores.

Thus, the variation in scores was higher in 2019.

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Find the complete question below.

The solution is, the situation can be modeled as y = 52 - 8x.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.

So, the total area to be painted is (28 + 3 × 8) = 52 square meters.

Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as

y = 52 - 8x ................ (1) (Answer)

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The statement must be true are A, B and D.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We are Given that Triangle DKL is congruent to Triangle PVX

We know that when two triangles are congruent then Acc. to CPCT [ Corresponding Parts of Congruent Triangle]

the corresponding parts are also congruent keeping in mind the vertices and the segments are in same comparison as given in the congruent triangles.

(a) Triangle LKD is congruent to Triangle XVP.

(b) Triangle VPX is congruent to Triangle KDL.

(c) Triangle VPX is not congruent to Triangle DLK as according to CPCT, V vertex is not congruent to D, P vertex is not congruent to L and X vertex is not congruent to K.

(d) Angle D is congruent to angle P.

(e) Thus Segment DL is not congruent to Segment PV ( as according to CPCT, Segment DL is congruent to PX and not PV.)

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The second year's interest rate is 1.80%.

Compound interest is defined as Since compound interest accrues and is added to the accrued interest from earlier periods, borrowers are expected to pay interest on interest in addition to principal.

We are aware that the compound interest formula is,

A = P(1 + r/100)ⁿ.

Where A is the amount, P is the principle, r is the rate, and n is the number of years.

Given, Katy places $2000 over a three-year period in a savings account.

For the first year, the account offers compound interest at a 2.5% annual rate.

∴ A = 2000(1 + 2.5/100)¹.

A = 2000(1.025). (1.025).

A = 2050.

It now earns x% for the second year.

∴ 2050(1+x/100)² = 2124.46

(1+x/100)² =2124.46/2050

1+x/100 =√(2124.46/2050)

x/100 = √(2124.46/2050) -1

x = (√(2124.46/2050) -1)*100

x = 1.80%.

the interest is 1.80 percent

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The statement "interpolation is used to determine values beyond a given set of data points" is true

The given statement is " interpolation is used to determine values beyond a given set of data points"

The interpolation is a method in statistics that used to determine or estimate the unknown values in the given set of values. So it is usually used to estimate the price and the potential yield of security

In the interpolation, we use the values from the given set of the data point and estimate the unknown values or values beyond the given set of data points

Therefore, the given statement is true

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Answer:

the domain is: {−3,0,1,6}

the range is:{2,3,4,−6,4}

the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Explanation:

In the relation:

{(−3,2),(0,3),(1,4),(1,−6),(6,4)}:

The domain:

Is the set of all the first numbers of the ordered pairs.

In other words, the domain is all of the x-values.

So in this case the domain is:

{−3,0,1,6}

The range:

Is the set of the second numbers in each pair, or the y-values.

So in this case the range is:

{2,3,4,−6,4}

A relation is a function if it has only One y-value for each x-value.

So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Step-by-step explanation:

There is No relation between the variables ggg and hhh.

To determine if the given table shows a proportional relationship between the variables ggg and hhh, we need to check if the ratio of hhh to ggg is constant for all values of ggg.

Let's calculate the ratios of hhh to ggg for each value of ggg:

For ggg = 333, hhh/ggg = 999/333 = 3.

For ggg = 666, hhh/ggg = 363636/666 = 546.

For ggg = 999, hhh/ggg = 818181/999 = 819.

Since the ratios of hhh to ggg are not constant, the given table does not show a proportional relationship between the variables ggg and hhh.

Therefore, the answer is "No, the table does not show a proportional relationship between the variables ggg and hhh."

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Answer:

Step-by-step explanation:

Find common denominator.

1/x + x-1/9x = 1  => 9/9x + x-1/9x = 1  (The common denominator is 9x.)

Combine like terms.

9 + x - 1 / 9x = 1  =>  x + 8/ 9x = 1

Cancel out 9x from denominator. What you do to one side, you do to the other.

(9x)(x + 8/9x) = 1(9x)  =>  x + 8 = 9x

Solve for x.

8 = 8x  =>  x = 1  (subtract x from both sides at the beginning and then simplify.)