What is the explicit formula for the sequence: .25,5,1,2

4) Where the hypotenuse is 100 and the adjacent side is x and α = 45°, the x = 70.71

5) Where the opposite side is 100, and  α = 45°, the hypotenuse is 141.42

6) Where the hypotenuse is 88 and β = 45°, x (the opposite side) is 62.23

7) Therefore, the length of each leg of the 45°-45°-90° triangle with a hypotenuse length of 26 is approximately 18.33 units.

8) Therefore, the approximate length of the hypotenuse of the 45°-45°-90° triangle with a leg length of 50 centimeters is 70.71cm.

9) Where the Base is 11 and α = 30°, Hypothenus (x) = 22 and Opposite (y) = 19.05

10) Where the hypotenuse  is 8√3, and β = 45°, opposite (x) = 11.99 and adjacent (y) = 6.93

11) Where the adjacent is 5√3  and α = 30°, opposite (x) = 14.99 and Hypothenus (y) = 17.32

12) where hypotenuse = 30, and the β = 60°, the adjacent (x) = 15 and the opposite (y) = 25.98

13) where opposite is 36.372 and the β = 60°, the hypothenus (x) = 41.99 and the adjacent (y) = 20.99

14) where the hypotenuse is 90.316 and  β = 60°, the opposite (x) = 78.22 and the adjacent (y) is 45.16

15) An equilateral triangle has an altitude length of 27 feet, and the length of a side is 15.588 feet.

16) the length of a side of the equilateral triangle is 22 feet.

The basic rule applied here (from 4-14) is the principle of SOHCAHTOA.


The principle of SOHCAHTOA is a mnemonic device used to remember the three basic trigonometric ratios in a right triangle:

Sine (sin) = opposite/hypotenuse

Cosine (cos) = adjacent/hypotenuse

Tangent (tan) = opposite/adjacent

In SOHCAHTOA, each letter represents one of the ratios:

"S" stands for sine, which relates the opposite side to the hypotenuse.

"O" stands for opposite, which is the side opposite to the angle of interest in the right triangle.

"H" stands for the hypotenuse, which is the longest side of the right triangle and is opposite to the right angle.

"C" stands for cosine, which relates the adjacent side to the hypotenuse.

"A" stands for adjacent, which is the side adjacent to the angle of interest in the right triangle.

"T" stands for the tangent, which relates the opposite side to the adjacent side.

By using SOHCAHTOA, we can quickly and easily find any of the three basic trigonometric ratios, given two sides of a right triangle and an angle.


In 4) This is an example of a right triangle, where one of the angles is 90 degrees. In a right triangle, the side opposite the 90-degree angle is called the hypotenuse, while the other two sides are called the adjacent and opposite sides.

In this case, the hypotenuse is given as 100 units, and the angle between the hypotenuse and adjacent side (x) is given as 45 degrees. To find the length of the adjacent side, we can use the trigonometric function cosine, which relates the adjacent side to the hypotenuse and the angle between them:

cos(α) = adjacent/hypotenuse

Substituting the given values, we get:

cos(45°) = x/100

Simplifying, we get:

x = 100 * cos(45°)

Using the identity cos(45°) = √2/2, we get:

x = 100 * √2/2

Simplifying further, we get:

x = 50√2

To find the approximate value of x in decimal form, we can use a calculator or approximate the value of √2 as 1.414. Then, we get:

x ≈ 50 * 1.414 = 70.71

Therefore, x is approximately equal to 70.71 units.

In 8) Where we needed to find the length of the hypotenuse of a 45°-45°-90° triangle with a leg length of 50 centimeters.

In a 45°-45°-90° triangle, the two legs are congruent, and the length of the hypotenuse is √2 times the length of each leg.

Therefore, if one leg of the triangle has a length of 50 centimeters, then the other leg also has a length of 50 centimeters, and the hypotenuse has a length of:

hypotenuse length = leg length x √2

hypotenuse length = 50 cm x √2

To simplify the expression, we can multiply the numerator and denominator of the fraction by √2:

hypotenuse length = 50 cm x √2 x √2 ÷ √2

hypotenuse length = 50 cm x 2 ÷ √2

hypotenuse length = 100 cm ÷ √2

To rationalize the denominator, we can multiply the numerator and denominator of the fraction by √2:

hypotenuse length = 100 cm ÷ √2 x √2 ÷ √2

hypotenuse length = 100√2 ÷ 2

hypotenuse length = 50√2

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle with a leg length of 50 centimeters is 50√2 centimeters or 70.71cm.

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A graph of the equation -5 < x < -3 is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Next, we would rewrite the given compound inequality in pairs as follows;

-5 < x < -3 ≡ x > -5 or x < -3

In this scenario, we would use an online graphing calculator to plot the inequality as shown in the graph attached below.

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Answer:

500 Milliliters

Step-by-step explanation:

Because a liter is 100x a milliliter so 0.5x100=500

let's firstly convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{ccll} miles&minutes\\ \cline{1-2} \frac{3}{2}&\frac{9}{4}\\[1em] x&34 \end{array}\implies \cfrac{~~ \frac{3 }{2 } ~~}{x}~~ = ~~\cfrac{~~ \frac{9}{ 4} ~~}{34}\implies \cfrac{3}{2x}=\cfrac{9}{(4)(34)}\implies \cfrac{3}{2x}=\cfrac{9}{136} \\\\\\ (3)(136)=18x\implies \cfrac{(3)(136)}{18}=x\implies \cfrac{68}{3}\implies \stackrel{ miles }{x=22\frac{2}{3}}[/tex]

Step-by-step explanation:

11/2 is equivalent to 21/4 is

equivalent to 9/4

The unit rate will be:

3/2 miles= x

9/4 min 1 min

Now use this unit to find how far the car will travel in 26 minutes

2/3 mile •26 min= 52/3 miles or 17 and 1/3

miles

1 min

Since 1 hour is equal to 60 minutes, we can

multiply the unit rate by 60 to find the distance traveled in 1 hour.

2/3 mile• 60 min = 120/3 = 40 miles

traveled in 1 hour

1 min

After answering the presented question, we can conclude that equation Therefore, the solution to the given system of equations is (x, y) = (2, 2).

An equation is a mathematical statement that proves the equality of two expressions connected by the equal symbol '='. 2x - 5 Equals 13, for example. Expressions include 2x-5 and 13. The character '=' joins the two expressions. A mathematical formula with two algebraic expressions on either side of an equal sign (=) is known as an equation. It demonstrates the relationship of equivalence between the left and right formulas. In every formula, LHS = RHS (left side = right side).

[tex]4x + y = 10 ...(1)\\y = 2x - 2 ...(2)\\y = 2x - 2 ...(2)\\y + 2 = 2x ...(2)\\x = (y+2)/2 ...(3)\\4x + y = 10 ...(1)\\4[(y+2)/2] + y = 10 \\[/tex]

[tex]2(y+2) + y = 10 \\3y + 4 = 10\\3y = 6\\y = 2 \\y = 2x - 2 ...(2)\\2 = 2x - 2 \\4 = 2x \\x = 2 \\[/tex]

Therefore, the solution to the given system of equations is (x, y) = (2, 2).

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Answer:

52 : 39 56 : 42 60 : 45

64 : 48 68 : 51

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Volume = L  X  W  X  H    For a CUBE, all of the dimesions L, W, and H are the same ...so this becomes   volume =L  x  L   x  L  =   L^3

Volume = L^3

64 = L^3             take the cube root of both sides of the equation:

L = 4 meters  

Answer:

6,400,500 = 660,000(0.66)^t

Step-by-step explanation:

The letter of the 3D figure which matches the statement of the student with regards to the surface areas of the figures are;

The net of this triangular prism covers the smallest total surface area; B

The lateral surface area is 96.6 unit²; C

The total surface area is 111.6 units²; C

The lateral surface area is 85.56 unit²; A

The total surface area is 103.96 unit²; A

The net of this triangular prism covers the largest lateral surface area; C

The surface area of a three dimensional, (3D), figure is the area of the boundary surface that surrounds the space occupied by the figure.

The surface areas and the lateral surface areas of the nets and the prisms are presented as follows;

Figure A;

Surface area = 2×(1/2)×4.6×4 + 3×6.2×4.6 = 103.96

The lateral surface area = 3×6.2×4.6 = 85.56

Figure B;

Surface area = 2×(1/2)×4×3.8 + 2×4.3×6 + 4×6 = 90.8

The lateral surface area = 2×4.3×6 + 4×6 = 75.6

Figure C;

Surface area = 2×(1/2)×5×3 + 5×7 + 3×7 + 5.8×7 = 111.6

The lateral surface area = 5×7 + 3×7 + 5.8×7 = 96.6

Therefore;

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Answer:

1.65 inches

Step-by-step explanation:

3.63/2.2= 1.65

Check

2.2 x 1.65 x 1/2 = 1.815

Repeat for the other half of the triangle

2.2 x 1.65 x 1/2 = 1.815

Add

1.815 + 1.815= 3.63

Answer:

1.65"

Step-by-step explanation:

I did the test

Hope this helps :)

The ratio is [tex]\frac{3}{2}[/tex] in its simplest form.

If the probability of choosing an even card is [tex]\frac{3}{5}[/tex] , then the probability of choosing an odd card is 1- [tex]\frac{3}{5}[/tex] = [tex]\frac{3}{2}[/tex].

Let e be the number of even cards Alisha has, and let o be the number of odd cards. Then, we have:

[tex]\frac{e}{e+0}[/tex]

which simplifies to:

5e=3(e+o)

Expanding the right side gives:

5e=3e+3o

Simplifying further gives:

2e=3o

Dividing both sides by 2 gives:

e= [tex]\frac{3}{2}[/tex]o

[tex]\frac{3}{2}[/tex]

Probability is a branch of mathematics that deals with the study of random events or experiments. It involves the analysis of the likelihood or chance of an event occurring, usually expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event is certain to occur.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{6}{x}=\cfrac{x}{8}\implies 48=x^2\implies \sqrt{48}=x\implies \sqrt{4^2\cdot 3}=x\implies 4\sqrt{3}=x[/tex]

The factors that would most likely reduce the monthly premium a policyholder who pays for automobile insurance is -

Option A: I, II

What is insurance?

Insurance is a legal agreement, evidenced by a policy, under which a policyholder receives financial security or compensation from an insurance provider against losses. In order to make payments to the insured more manageable, the company pools the risks of its clients.

The factors that can affect the monthly premium a policyholder pays for automobile insurance include the type of vehicle, driving record, and other personal factors.

Out of the options given, buying a minivan  and maintaining an accident-free driving record over time would most likely reduce the monthly premium a policyholder pays for automobile insurance.

Minivans are generally considered safer and less expensive to repair than other types of vehicles, and having an accident-free driving record indicates that the policyholder is a lower risk for filing a claim in the future.

Paying a speeding ticket and taking a job with a longer commute by car are unlikely to reduce the monthly premium a policyholder pays for automobile insurance.

Paying a speeding ticket indicates a violation of traffic laws and a higher risk for accidents, and a longer commute by car increases the risk of accidents and damages.

Therefore, the answer is buying a minivan and maintaining an accident-free driving record over time.

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Answer: option a (I, II)

Step-by-step explanation: Person above is correct!

The decrease in reserve rate from 5% to 2% would increase the amount of money that results from fractional reserve banking on a $25,000 deposit in a bank.

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

If the Federal Reserve decreases the reserve rate from 5% to 2%, it means that banks are required to hold a lower percentage of deposits as reserves and can lend out more money. This can lead to an increase in the amount of money that results from fractional reserve banking.

Assuming a fractional reserve ratio of 10%, which means that banks are required to hold 10% of deposits as reserves, here's how the change in the reserve rate can affect the amount of money that would result from a $25,000 deposit in a bank:

Initially, the bank would hold $2,500 (10% of $25,000) as reserves and can lend out $22,500 ($25,000 - $2,500).

After the decrease in the reserve rate to 2%, the bank would only be required to hold $500 (2% of $25,000) as reserves and can now lend out $24,500 ($25,000 - $500).

If this process continues through multiple rounds of lending and deposits, the total amount of money that can be created through fractional reserve banking can increase significantly.

However, it's important to note that the actual impact of a change in the reserve rate on the money supply depends on a variety of other factors, such as the demand for loans and the willingness of banks to lend out money.

Therefore, the decrease in reserve rate from 5% to 2% would increase the amount of money that results from fractional reserve banking on a $25,000 deposit in a bank.

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a. To calculate the gross salary per pay period, we need to divide the yearly salary by the number of pay periods in a year:

Gross salary per pay period = Yearly salary / Number of pay periods per year

Since there are 26 pay periods in a year (bi-weekly paychecks), we have:

Gross salary per pay period = $67,000 / 26 = $2,576.92

Therefore, the DON's gross salary per pay period is $2,576.92.

b. To compute the net salary per pay period, we need to take into account federal and state taxes, Social Security, and Medicare deductions, as well as any other pre-tax or post-tax deductions, such as health insurance premiums or retirement contributions.

Assuming a standard tax withholding rate of 20%, Social Security and Medicare deductions of 7.65%, and health insurance premiums of $200 per pay period, we can calculate the net salary per pay period as follows:

Net salary per pay period = Gross salary per pay period - Taxes - Social Security and Medicare - Health insurance

Net salary per pay period = $2,576.92 - ($2,576.92 x 0.20) - ($2,576.92 x 0.0765) - $200

Net salary per pay period = $2,576.92 - $515.38 - $197.02 - $200

Net salary per pay period = $1,664.52

Therefore, the DON's net salary per pay period is $1,664.52.

It takes Carlos 2 minutes longer than Ariel to sing the song.

To find out how much longer it takes Carlos to sing the song, we need to find the difference between the time it takes Ariel and Carlos to sing the song.

Time taken by Ariel = 5.92 minutes

Time taken by Carlos = 7.73 minutes

So, we have

Difference = 7.73 - 5.92 = 1.81 minutes

Rounding to the nearest whole number, we get:

Difference = 2 minutes (rounded to the nearest whole number)

Therefore, the time taken is approximately 2 minutes longer

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The number of intersection points is (a) 1 point or 2 points.

Given that

Line AB and circle P lie on the same plane.

And, we have

AP = 6 mm

BP = 8 mm

The intersection points can be 0, 1, or 2.

Since the radius of circle P is 6mm, any intersection point must also be 6mm away from P.

Next, we have the following test cases

Hence, the answer is (A) 1 point or 2 points.

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Answer:

B. 0.25x² + 0.8x - 8 = 0

C. 5x² + 7x = 15

Step-by-step explanation:

Let's try by solving all equations;

(x + 3)² = 36

x² + 3² = 36

x² + 9 = 36

x² = 36 - 9

x² = 27

x = √27

x ≈ 5.2

No quadratic

What about others

0.25x² + 0.8x - 8 = 0

Hmm.... that can only be solved by quadratic

[tex] \sf { \fbox{0.25x² + 0.8x - 8 = 0} \: can \: only \: be \: solved \: by \: quadratic}[/tex]

Also, 5x² + 7x = 15

[tex] \sf { \fbox{5x² + 7x = 15} \: can \: only \: be \: solved \: by \: quadratic}[/tex]

(x + 8)(x + 9) = 0

x² + 9x + 8x + 72 = 0

x² + 17x + 72 = 0

(x + 8)(x + 9) = 0

Not truly quadratic but can be solved with quadratic.

That leaves us with only B and C as the answer

Answer:

Step-by-step explanation:

The first question is 3 * 2x which equals 6x + 15. That's your answer

Answer:

[tex]\tt \: Hope \: it \: helps \: you \\[/tex]

The vertices are (0,3) and (0,-3). The center of the ellipse is (0,0). the equation of the ellipse is (x²)/9 + (y²)/5 = 1.

The center of the ellipse is at the midpoint of the foci, which is (0,0).

The distance between the center and each focus is 2, so we know that c = 2.

The length of the major axis is 6, so we know that a = 3.

The formula for the distance between the center and each vertex is a, so we can find the vertices at (0,3) and (0,-3).

The formula for the minor axis is b² = a² - c², so we have b² = 5. Therefore, b = √(5).

The equation of the ellipse is (x - h)²/a² + (y - k)²/b² = 1, where (h,k) is the center. Plugging in our values:

(x - 0)²/3² + (y - 0)²/5 = 1

Simplifying:

(x²)/9 + (y²)/5 = 1

So the equation of the ellipse is (x²)/9 + (y²)/5 = 1.

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Since HM = NK and ∠FGH = ∠KGH = 45°, we have FG = KH by the hypοtenuse-leg (HL) cοngruence theοrem.

A triangle is geοmetric shape that is fοrmed by the three straight line segments that cοnnect tο fοrm the three sides. These sides enclοse  regiοn in  plane, and  three pοints where  line segments intersect are called vertices.

We are given that HF GK, and ZF and ZK are right angles.

Tο prοve: FG KH

We will use the fοllοwing steps tο prοve the statement:

Draw perpendiculars frοm F and G tο HK, and label the pοints οf intersectiοn as M and N, respectively.

Since ZF is a right angle, we have ∠FMH = 90°.

Similarly, since ZK is a right angle, we have ∠GNK = 90°.

We are alsο given that HF GK, sο triangle HFG is cοngruent tο triangle KFG by the hypοtenuse-leg (HL) cοngruence theοrem.

Therefοre, FH = GK and ∠HFG = ∠KFG.

Since ∠FMH = 90° and FH = GK, we have HM = NK.

Alsο, since ∠HFG = ∠KFG, we have ∠FGH = ∠KGH.

Using angle additiοn pοstulate, we have ∠FGH + ∠KGH = ∠FGK = 90°.

Thus, ∠FGH = ∠KGH = 45°.

Finally, since HM = NK and ∠FGH = ∠KGH = 45°, we have FG = KH by the hypοtenuse-leg (HL) cοngruence theοrem.

Therefοre, FG KH, which cοmpletes the prοοf.

Hence, we have prοved that FG KH.

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If the given zeros are 4 and -2+√5, then the polynomial function of the least degree with integral coefficients that has these zeros can be obtained by using the fact that if a polynomial has a root at x=a, then it has a factor of (x-a).

Therefore, the polynomial function with these zeros can be written as:

(x - 4)(x - (-2+√5))(x - (-2-√5))

Expanding the factors using the difference of squares, we get:

(x - 4)((x + 2) - √5)((x + 2) + √5)

Simplifying the expression further, we get:

(x - 4)((x + 2)^2 - 5)

Expanding the square, we get:

(x - 4)(x^2 + 4x - 1)

Therefore, the polynomial function of the least degree with integral coefficients that has the zeros 4 and -2+√5 is:

f(x) = (x - 4)(x^2 + 4x - 1)

Expanding the factors, we get:

f(x) = x^3 + 4x^2 - x - 16

In this particular case, a 2-year old child should receive a dosage of approximately 16.15mL of the drug. This figure is calculated by using the following formula: (adult dosage/150) x (child's weight in kg).

Dosage is a term used to describe the amount of medicine or drug prescribed for a particular individual to take at a given time. It is usually prescribed by a doctor or healthcare provider based on the patient's age, weight, and medical condition. Dosage may vary from person to person depending on their health condition and other factors.

The appropriate dosage of a drug for a 2-year old child is calculated by taking into account the weight, age and health status of the child. Before administering any medications, it is important to consult with a doctor or a pharmacist to ensure that the appropriate dosage is used.

The adult dosage of 257mL is divided by 150 to obtain the base dosage of 1.71mL. This is then multiplied by the child's weight in kilograms (which is usually around 9 kg) to obtain the final dosage of 16.15mL.

It is important to note that the dosage should be rounded to the nearest hundredth. Therefore, the recommended dosage for the 2-year old child in this case would be 16.2mL. It is important to ensure that the dosage is not rounded up, as this could lead to an overdose of the drug, which could have serious consequences.

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Answer:

About a 7.3 percent Decrease

Step-by-step explanation:

First, calculate the diffrence between the two numbers:

122-113=9

Then, divide this number by the original number, it being 122, and then multiply that number by 100.

the simplified version of this number to the tenths place is 7.38%

The missing measure of the angle on the triangle will be 45°.

An angle is the measure of the space between two intersecting lines or planes. It is usually measured in degrees or radians. A degree is a unit of measurement for angles, where a full circle is 360 degrees, while a radian is a unit of measurement for angles defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (more than 90 degrees and less than 180 degrees), or straight (exactly 180 degrees).

The missing angle will be:

= 180° - (76° + 59°)

= 180° - 145°

= 35°

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The equation of the graph is y = 0, which means that the graph is a horizontal line at y=0.

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written with an equals sign (=) separating the two expressions. For example, the equation "2x + 1 = 7" asserts that the expression "2x + 1" is equal to the expression "7". Equations can contain variables, which are symbols that represent unknown values. In the example equation, "x" is the variable that we want to solve for. Equations can be used to solve problems and find solutions to unknown values. There are various techniques and methods to solve equations depending on their complexity and nature.

Since the graph is on a semi-log scale, we know that the vertical axis is a logarithmic scale and the horizontal axis is a linear scale. Therefore, the equation of the graph is of the form:

y = a * bˣ

where a and b are constants to be determined.

We are given two points on the graph: (1,0) and (0.5,0). Let's use these points to find the values of a and b.

Using the point (1,0):

0 = a * b¹

0 = a * b

Using the point (0.5,0):

0 = a * b^0.5

0 = √(a)

Therefore, we have:

a = 0

b can be any non-zero number

So the equation of the graph is:

y = 0 * bˣ

which simplifies to:

y = 0

So the equation of the graph is y = 0, which means that the graph is a horizontal line at y=0.

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The correct statement regarding the mean of the data-set when the score of 47 is removed is given as follows:

The mean increased by about 6.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The observations for this problem are given as follows:

100, 95, 47, 83, 87, 89, 89.

There are 7 observations, and their sum is given as follows:

100 + 95 + 47 + 83 + 87 + 89 + 89 = 590.

Hence the mean is of:

590/7 = 84.29.

Removing the observation of 47, there will be 6 observations, with a sum of 590 - 47 = 543, hence the mean is of:

543/6 = 90.5.

Meaning that the mean increases by about 6.

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Answer (0,0)

Step-by-step explanation:

Method 1)

look at the graph to see where the two lines intersect, which is at (0,0).

Method 2)

 [tex]\frac{4}{3} x[/tex] =  -2x ............................set the 2 equations equal

[tex]\frac{10}{3} x[/tex] = 0.................................set the equation to 0 (by adding 2x to both sides)

x = 0.....................................solve for x (by dividing both sides by [tex]\frac{10}{3}[/tex]

Note: you can use y =  [tex]\frac{4}{3} x[/tex]  OR y = -2x

y= -2x

y = -2(0)...............................plug in the x

y = 0.....................................solve

(x,y)

(0,0)......................................plug in x and y value