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The solution to the system of equations 9x - 3y = 5 and 2x - 3y = 7 is (-2/7, -53/21)

An equation is an expression showing the relationship between numbers and variables.

Given the equations:

9x - 3y = 5     (1)

2x - 3y = 7     (2)

To solve by elimination method, subtract equation 2 from 1, hence:

7x = -2

Dividing by 2:

x = -2/7

Put x = -2/7 in equation 2:

2(-2/7) - 3y = 7

y = -53/21

The solution is (-2/7, -53/21)

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The number with the fewest  Decimal point will determine the number of significant figures in the calculated result.

The significant figures in the estimated result of an addition or subtraction calculation are determined by the decimal places of the measured values. This is so that the computed result can accurately reflect the precision of the measurement, which is shown by the decimal points in the measured values. Therefore, in the calculation with the fewest decimal places, the calculated result should have the same number of decimal places as the measured value. The result should have two decimal places, for instance, if one number has two decimal places and the other has four. By doing this, it is ensured that the result is not given a higher level of precision than the measured data utilized in the computation warrant.

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Answer: X = 17

Step-by-step explanation:

8.75 + 1.95x = 41.9

1.95x = 41.9 - 8.75

1.95x = 33.15

x = 33.15/1.95

x = 17

The measure of hypotenuse of the triangle whose sides are given would be = 17.80cm

The formula used to calculate the hypotenuse of a triangle is the Pythagorean formula= C²= a² + b²

Where c = hypotenuse = ?

a² = 11 cm

b² = 14 cm

Substitute the given values into the formula to find hypotenuse.

c² = 11² + 14²

c² = 121+196

c² = 317

C = √317

C = 17.80cm.

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Complete question:

One of the legs of a right triangle measures 11 cm and the other leg measures 14 cm.

Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

The range is not likely to vary, which is one of the claims regarding the new salary distribution that is supported.

Therefore,

Given that a small company's salary distribution of 27 employees has a mean of $35,000 and a standard deviation of $2,000,

When a highly unusual value, such as 120000, is taken into account for the 28th employee, we discover that the mean increases.

The new median would be the average of items 14 and 15, as the prior median was the 14th item. Thus, the median may alter.

Because the maximum has been raised up to 120000, the range will undoubtedly vary.

so that we can say

Range changes, median changes, and mean increases.

Thus, we determine that Option B is correct.

The complete question is:

The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th

28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported?

The median is not likely to change. I

The range is not likely to change. II

The mean is likely to increase. III

A) I only

B) III only

C) I and II only

D) I and III only

E) I, II, and III

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The result of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex] is[tex]$-56\frac{13}{20}$[/tex]

A mixed number is a combination of a whole number and a fraction, like [tex]3\frac{1}{2}[/tex], expressing numbers greater than one whole unit. It can be converted to an improper fraction.

To find the solution of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex]

We can first simplify the inner parenthesis

[tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right)=53\cdot(-1\frac{1}{10})=-53\frac{11}{10}$[/tex]

Then simplify the denominator, The denominator is the bottom part of a fraction, which represents the total number of parts in the whole. It is used to indicate the size of the fraction's unit or whole. It is also used to divide the numerator (top part of a fraction) by in order to determine the fraction's value.

[tex]$2\frac{3}{4} - 1\frac{2}{3} = \frac{11}{4} - \frac{5}{3} = \frac{44}{12} - \frac{20}{12} = \frac{24}{12} = 2$[/tex]

Now we can divide -53 and 11/10 by 2

[tex]$-53\frac{11}{10} \div 2 = -53\frac{11}{20} = -\frac{1133}{20} = -56\frac{13}{20}$[/tex]

So, the answer is [tex]$-56\frac{13}{20}$[/tex]

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The product of 7 and ⁵/₈ is less than 7 because ⁵/₈ is less than 1

We want to find the product of 7 and ⁵/₈.

Now, this will be expressed as;

7 * ⁵/₈.

Now, we are multiplying a whole number by a proper fraction that is less than 1 and as such, it means that the product will be lesser than 7 simply because ⁵/₈ is less than 1.

Thus;

7 * ⁵/₈ = 35/8

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Answer: 6.14for the tip

Step-by-step explanation:

Answer:

$6.14

Step-by-step explanation:

Well, first step is to divide 15.0% by $40.94.

Then you get 6.141

Translate that to money, rounding off, you get:

$6.14!

I hope this helps! Great to be of service to you!

The rate at which the candle burns is 1.5 inches per hour.

We know that the proportional relation between the number of inches that the candle has burned away, b, and the time in hours, t, is:

b = 1.5*t

The rate at which the candle burns is the amount burned in one unit of time, in this case, hours, then:

So, after t = 1 (one hour)

b = 1.5

In one hour, the candle burns 1.5 inches.

That is the rate at which the candle burns, it should be written as:

rate = 1.5 inches burned per hour.

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The area of this inscribing circle is 36π cm².

The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.

The perimeter of a square is the sum of the lengths of all the sides.

We know area of a square is side².

Given, The area of this square is 144 cm².

We know 12×12 is 144.

Therefore, The length of the sides of this square is 12 cm.

We know a circle inscribed in a square has a diameter that is equal to the side of a square.

Therefore, The diameter of this circle is 12 and hence radius is 12/2 = 6 cm.

We also know that the area of a circle is πr².

Therefore, The area of this circle is π(6)² cm².

= 36π cm².

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Answer:

what to find in this question ?

Without any values of the functions f, g, h, and k, it is not possible to find the equation of each function. The equation of a function can be determined by analyzing the values of the function. Based on the given values, a possible equation can be found and then verified by plotting the points on a graph and seeing if they align with the equation.

It's important to note that the equation can be a linear or exponential equation but it's impossible to determine it without any values.

Kevin hiked up Lamb's Canyon with the goal of making it to the top.

Let x be the distance Kevin hiked up the canyon.

For hiking: 3 hr = x / h

For running: 2 hr = (x + 1.8) / r

Solving the two equations for x yields:

x = (3h * r) / (h + r)

Therefore, Kevin hiked (3h * r) / (h + r) mi up the canyon.

Distance = (x mph) * (3 hr)

Distance = (x + 1.8 mph) * (2 hr)

(x mph) * (3 hr) = (x + 1.8 mph) * (2 hr)

Solving for x, we get x = 2.4 mph.

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The first five terms of the arithmetic sequence are given as follows:

3, -1, -5, -9, -13.

An arithmetic sequence is a sequence for which the difference between consecutive terms is constant, being called common difference d.

The recursive definition is given as follows:

f(n) = f(n - 1) + d.

For this problem, the definition is given as follows:

f(n) = f(n - 1) - 4.

Meaning that the common difference is of 4, and hence each term is obtained subtracting the first term by 4, starting with the first term given by f(1) = 3.

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The correct order of bond lengths P, Q, and R in the above diagram is P > Q > R. The correct option is A.

The bond length is the distance between the centers of two bound atoms. Consider the fact that a homonuclear diatomic molecule's bonded atoms are separated by half their element's atomic radius (sometimes referred to as the covalent or bonding atomic radius).

Less percentage of s character in a bond means the length of orbitals of the molecule is more, and also the bond length is more.

Therefore, the correct option is A. P > Q > R.

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The question is incomplete. Your most probably complete question is given below:

Which is the correct order of bond lengths P, Q, and R in the above diagram?

P > Q > R

R > Q > P

Q > P > R

Q > R > P

The correct option regarding the probabilities for Sandy's is given as follows:

A. Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

For the theoretical probability, the outcomes are considering without any experiment, while for an experimental probability the outcomes are taken from previous experiment.

This means that for a large number of trials, these probabilities should be very close, meaning that the correct option is given by option A.

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Its A...............

Step-by-step explanation:

Answer:

x ≤ - 2 ; 0 ≤ x ≤ 7    

Step-by-step explanation:

x ≤ - 2

0 ≤ x ≤ 7

Answer:

|-28|

Step-by-step explanation:

-28 is the least value in the expression given

According to the information, the probability that the next pice of fruit out of the bag will be an apple is 0.66.

To calculate the probability that the next piece of fruit out of the bag will be an apple we have to perform the following mathematical operation:

We have to calculate how many fruits there are in the bag.

So, we have 4 apples and 2 peaches, so we have 6 fruits in total. Now, we have to divide the number each fruit in the bag by the total number of fruits as shown.

4 / 6 = 0.66

2 / 6 = 0.33

According to the above, the probability that the next pice of fruit out of the bag will be an apple is 0.66.

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The total monthly revenue when 200 units were sold is $28800 and the monthly revenue when 800 units were sold is $52800.

Given,

 The equation for monthly revenue, [tex]R(x)= 170x - 0.13x^{2}[/tex]      [tex](0 < x < 800)[/tex]

      where [tex]x[/tex] is the number of units sold

(a)  Total number of units sold, [tex]x = 200[/tex]

                Monthly revenue, [tex]R(200)= 170x- 0.13x^{2}[/tex]

                                                           [tex]= 170*200 - 0.13*200^{2}[/tex]

                                                           [tex]= 34000 - 0.13* 40000[/tex]

                                                           [tex]= 34000 - 5200[/tex]

                                                           [tex]= 28800[/tex]

         Hence , monthly revenue = $28800

(b)   Total number of units sold, [tex]x = 800[/tex]

                    Monthly revenue, [tex]R(800)= 170x- 0.13x^{2}[/tex]

                                                               [tex]= 170*800 - 0.13*800^{2}[/tex]

                                                               [tex]= 136000 - 0.13*640000[/tex]

                                                               [tex]= 136000- 83200[/tex]

                                                               [tex]= 52800[/tex]

         Hence , monthly revenue = $52800

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The solved for x round to the nearest tenth is x≈ 14.

What is meant by round ?

Remember Sine of an angle is = opposite side /hypotenuse

So let the hypotenuse be  x :

sin(54°) = opposite side / x

sin(54°) = 12 / x

To solve for x, divide sin(54°) by 12:

x = 12 / sin(54°)

x≈14

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Answer:

y intercepts : (0, -5)

Step-by-step explanation:

Answer:

(0,-5)

Step-by-step explanation:

Answer:

The exponential model representing the amount of Iodine-125 remaining in the tumor after t days would be:

Iodine-125(t) = 0.6 * e^(-0.0115t)

To find the amount of Iodine-125 that would remain in the tumor after 60 days, we would plug in t = 60 into the model:

Iodine-125(60) = 0.6 * e^(-0.0115(60))

= 0.6 * e^(-0.69)

= 0.6 * 0.5032

= 0.3019

So after 60 days, there would be approximately 0.3019 grams of Iodine-125 remaining in the tumor.

If I helped you, could you please make my answer best?

The given triangle is obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The triangle's longest side measures 15 units in length.

Compare the sum of the squares on the other two sides to the square that is the length of the longest side.

The square of the longest side is 15², which equals 225.

9² + 10² = 181 square units make up the sum of the squares on the other two sides.

Thus, 181 < 15².

As a result, the triangle is an obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.

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Answer:

Diameter is 8

Circumference is 8pi ~= 25.13

Step-by-step explanation:



The diameter is double the radius. So the given radius is 4 and double is 8.

The Circumference is given by C = pi•d or C = 2pi•r

Both of these equations will give the circumference.

C = pi•d

= pi•8

= 8pi ~= 25.13

OR

C = 2pi•r

= 2pi•4

= 8pi ~= 25.13

For finding the diameter, I multiply the radius by 2:

Diameter = 2 × radius

                = 2 × 4

                = 8

So the diameter is 8. As for the circumference, we can use two ways : either multiply pi times the diameter, or multiply 2 times pi times the radius.

The formulas are

C = πd              and C = 2πr

To find the circumference, stick in 8 for d:

C = π × 8

C = 25.13 units

Using mathematical operations, Ara's remaining pounds of apples are 1.405 pounds.

The four basic mathematical operations are addition, subtraction, division, and multiplication.

In this situation, we applied the mathematical operations of multiplication, addition, and subtraction to determine the difference (or the quantity of apples left) between the quantity brought to the market and the quantity sold.

The total quantity of apples = 35¹/₂ pounds

The quantity sold in the morning = ¹/₂  of 35¹/₂ pounds = 17.75 pounds

The quantity sold in the afternoon = ⁴/₁₉ of 35¹/₂ pounds = 7.47 pounds

The quantity sold in the evening = ¹/₄ of 35¹/₂ pounds = 8.875 pounds

The total quantity sold = (¹/₂ + ⁴/₁₉ + ¹/₄) = ³⁶/₃₈ of 35¹/₂ pounds = 34.095 pounds

The remaining pounds of apples = 1.405 pounds (35.5 - 34.095)

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The probability that the next fruit out of the bag is an apple is P = 4/5

We want to fnind the probability of randomly selecting an apple from the bag, where we assume that all the fruits have the same probability of being randomly selected.

Remember that the probability is equal as the quotient between the number of apples and the total number of fruit on the bag.

Originally, there are:

The checkout person takes 2 plums and 1 peach, so now there are:

For a total of 4 + 1 = 5 fruits

Then the probability of randomly grabing an apple is:

P = 4/5

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