Solve the following system of linear equations 3x₁ + x₂ + 2x3= 6
4x₁ - 3x₂ + 5x3 = 8,
2x₁ + x₂ + 3x3 = 10​

The similarity statement is completed as below

Triangle MTA ~ triangle HTM ~ triangle HMA

A similarity statement is a statement in mathematics that expresses the affinity between two or more figures.

These figures are similar, meaning they have corresponding angles that are identical and sides that are equivalent in size ratio. The same shape is shared by them, although their sizes may be different.

The similar triangles are

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Answer:

(a) To write g as a set of ordered pairs, we can use the given function values as follows:

g = {(-2, -5), (0, 0), (2, 2), (4, -5)}

(b) The domain of g is the set of all input values for which the function is defined. In this case, the domain is {-2, 0, 2, 4}.

The range of g is the set of all output values that the function can produce. In this case, the range is {-5, 0, 2}.

The graph of the inequality y ≥ (x+2)^2 is added as an attachment

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

y is greater than or equal to (x+2)^2

Express the statement properly

So, we have

y ≥ (x+2)^2

The above expression is a an inequality of a quadratic function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the expression in a graphing tool and attach the display

See attachment for the graph

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An equation and solution that describe the situation is: B. The equation 1/8(x + 16) = 76 represents the situation, where x is the food bill.

In order to write a linear equation to describe this situation, we would a assign variable to the food bill, and then translate the word problem into a linear equation as follows:

Let the variable x represent the total amount of the food bill.

Since this group of 8 friends spent a total of $76, which included the food bill and a tip of $16, and decided to split the bill and tip evenly among themselves, a linear equation that can be used to model this situation is given by;

1/8(x + 16) = 76

(x + 16) = 76(8)

x + 16 = 608

x = 608 - 16

x = $592.

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Answer:

The probability that a randomly chosen college student does not take statistics is 0.76.

Step-by-step explanation:

The probability of an event happening and the probability of its complement (the event not happening) must add up to 1. Therefore, if the probability that a randomly chosen college student takes statistics is 0.24, then the probability that they do not take statistics is:

1 - 0.24 = 0.76

So the probability that a randomly chosen college student does not take statistics is 0.76 or 76%.

Check the picture below.

Answer:

The domain is (-infinity, infinity), or all real numbers.

The range is (-infinity, infinity), or all real numbers.

Answer: 11 miles

Step-by-step explanation: 1/5280 = x/58,080

The equation of the function g(x) is g(x) = f(x+3) + 4 and g(x) = log₂(x+3) + 4

To shift the function 3 units left, we replace x with x+3. To shift it 4 units up, we add 4 to the function.

Therefore, the expression for g(x) in terms of f(x) is:

g(x) = f(x+3) + 4

Substituting f(x) = log₂(x), we get:

g(x) = log₂(x+3) + 4

The equation of the function g(x) is g(x) = log₂(x+3) + 4.

The domain of g(x) is all x such that x+3 > 0, since the argument of the logarithm must be positive.  This gives x > -3.

The range of g(x) is all real numbers, since the logarithm takes on all real values.

The vertical asymptote is x = -3, since this is where the function becomes undefined (the argument of the logarithm becomes 0).

The horizontal asymptote is y = 4, since as x approaches infinity or negative infinity, the function approaches 4.

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"Although part of your question is missing, you might be referring to this full question: Work out the sum of the interior angles of a pentagon".

A pentagon is a polygon with five sides. We can use a formula to get the pentagon's interior angle total. According to the formula, (n-2) x 180 degrees can be used to calculate the total of any polygon's internal angles. This formula can be changed to n=5 for a pentagon, giving us (5-2) x 180 degrees = 540 degrees. Consequently, a pentagon's internal angles add up to 540 degrees.

The sum of the interior angles of a pentagon can also be computed by dividing it by the number of sides, and the result can then be subtracted from 180 degrees to determine each inner angle. So, a pentagon's internal angles are each (540/5)-180 degrees, or 108 degrees.

In conclusion, a pentagon's interior angles add up to 540 degrees, and each interior angle is 108 degrees. In order to solve mathematical problems involving polygons, it can be helpful to comprehend the formulas used to calculate these numbers.

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a) The mean number of cases in groups of 17,199 children is 0.187.

b) The probability of 0 or 1 case in a group of 17,199 children is 0.832.

c)  The probability of more than one case in a group of 17,199 children is 0.168.

d) The expected number of cases is 3.214 and the actual number of cases is 4

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

For example, if you flip a fair coin, the probability of it landing heads up is 0.5, because there are two equally likely outcomes (heads and tails), and one of them is heads. Similarly, if you roll a fair six-sided die, the probability of rolling a 3 is 1/6, because there are six equally likely outcomes (rolling a 1, 2, 3, 4, 5, or 6), and only one of them is a 3.

a. Assuming that the tumor occurs as usual, the mean number of cases in groups of 17,199 children can be calculated as:

mean = (probability of a single case) x (number of children) = 0.000011 x 17,199 = 0.187

So the mean number of cases in groups of 17,199 children is 0.187.

b. The probability of 0 or 1 case can be found using the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the mean rate of occurrence. In this case, the Poisson distribution can be used to find the probability of 0 or 1 case in a group of 17,199 children, given the mean of 0.187.

The probability of 0 or 1 case can be calculated as follows:

P(0 or 1 case) = P(0 case) + P(1 case)

= (e⁽⁻⁰°¹⁸⁷⁾ * 0.187⁰) / 0! + (e⁽⁻⁰°¹⁸⁷⁾ * 0.187¹) / 1!

= 0.832

Therefore, the probability of 0 or 1 case in a group of 17,199 children is 0.832.

c. The probability of more than one case can be found as:

P(more than one case) = 1 - P(0 or 1 case)

= 1 - 0.832

= 0.168

Therefore, the probability of more than one case in a group of 17,199 children is 0.168.

d. To determine whether the cluster of four cases is attributable to random chance, we can compare the actual number of cases with the expected number of cases based on the mean rate of occurrence.

The expected number of cases in a group of 17,199 children can be found by multiplying the mean rate of occurrence (0.187) by the number of groups:

expected number of cases = 0.187 x 17199 = 3.214

Since the expected number of cases is 3.214 and the actual number of cases is 4.

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Answer:

60 (C)

Step-by-step explanation:

65+55=120

180-120=60

An equation of the line that passes through the points (0, 6) and (-6, 6) is y = 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 6)/(-6 - 0)

Slope (m) = 0/-6

Slope (m) = 0.

At data point (0, 6) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 0(x - 0)

y - 6 = 0

y = 6

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The expressions using scratch addition is 516

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

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87

Using the Scratch method of Addition. we add the numbers one after the other

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

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 103 + 29 + 59 + 67 + 37 + 55 + 79 + 87

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 132 + 59 + 67 + 37 + 55 + 79 + 87

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 191 + 67 + 37 + 55 + 79 + 87

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 258 + 37 + 55 + 79 + 87

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 295 + 55 + 79 + 87

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 350 + 79 + 87

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 429+ 87

45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 516

HEnce, the solution is 516

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1) The opposite face of the black circle is, Plus +.

2) The volume of the sliced cylinder is 96π cubic cm.

We have to given that;

Three different views of identical cubes are shown at right.

Now, From first and third dice,

Star is just opposite to symbol ~.

Hence, From second and third dice,

The opposite face of the black circle is, +

2) For the volume of the sliced cylinder, we need to first find the volume of the full cylinder and then subtract the volume of the smaller cylinder that's left after the slice is made.

Hence, The volume of the full cylinder is given by:

V = πr²h

Where r is the radius of the base and h is the height of the full cylinder.

Using the given values, we can find:

V = π(4²)(18)

V = 288π cubic cm

Now, let's find the volume of the smaller cylinder. The shorter height of 12 cm tells us that the slice removed 6 cm from the top of the cylinder. So the height of the smaller cylinder is,

18 - 6 = 12 cm.

The radius remains the same at 4 cm.

Thus, the volume of the smaller cylinder is:

V = π(4²)(12)

V = 192π cubic cm

Finally, we can find the volume of the sliced cylinder by subtracting the volume of the smaller cylinder from the volume of the full cylinder;

⇒ V = (288π) - (192π)

⇒ V = 96π cubic cm

Therefore, the volume of the sliced cylinder is 96π cubic cm.

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The questions have been answered below based on the concept of apportionment.

Here, we have,

Apportionment is the challenge of distributing a certain number of items among groups of varying sizes. The Mathematics of Apportionment discusses the mathematical concepts and methods used to allocate identical things fairly among parties with differing claims.

In question 1, the quantity that does not vary from state to state when we apportion congress representatives to different states is called the standard quota.

In question 2, the standard quota is found by dividing the state's population by the standard divisor.

In question 3, the modified divisor in Webster's method is found by dividing the state's population by the modified divisor.

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The value of m + n for the given quadratic equation is 8.

What is a quadratic equation?

A quadratic equation is a polynomial equation of the form:

[tex]ax^{2} +bx+c=0[/tex]

where x is the unknown variable, and a,b and c are constants. The highest power of the variable x in a quadratic equation is 2, hence the term "quadratic". The constants a,b and c are known as the coefficients of the quadratic equation.

According to the given information:

Let's denote the roots of the quadratic equation [tex]2x^{2} -mx+n=0[/tex] as r1 and r2, with r1 and r2 being the roots of the equation.

Given that the sum of the roots is 6 and the product of the roots is 10. This gives us the following equations:

r1 + r2 = 6 ------ (1)

r1*r2 = 10 ------- (2)

We can use these equations to solve for the values of m and n.

The sum of the roots r1 + r2 is also equal to [tex]\frac{-m}{2}[/tex] by Vieta's formulas, which state that the sum of the roots of a quadratic equation [tex]ax^{2} +bx+c=0[/tex] is given by [tex]\frac{-b}{a}[/tex]. Therefore, we can write:

[tex]\frac{-m}{2}[/tex] = 6

Solving for m, we get:

m = -2*6 = -12  ----------(3)

The product of the roots r1*r2 is also equal to n/2 by Vieta's formulas, which states that the product of the roots of a quadratic equation [tex]ax^{2} +bx+c=0\\[/tex] is given by [tex]\frac{c}{a}[/tex]. Therefore, we can write:

n/2 = 10

Solving for n, we get:

n = 2 * 10 = 20  ------------(4)

Now, we can find the value of m+n by substituting the values of m and n from equations (3) and (4) respectively:

m + n = -12 + 20 = 8

So, the value of m+n is 8.

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Answer:

0

Step-by-step explanation:

If we have the function f(x)=sqrt((x-8)/3), where 8 is less than or equal to x which is less than or equal to 16, we can evaluate f(8) as follows:

f(8)=sqrt((8-8)/3)

=sqrt(0/3)

=0

Hope this helps!

The framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.

Explanation :

The statement that best explains that Article III of the constitution gives congress the ability to create lower courts inferior to the supreme court from "time to time" is that the framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.

As there will be more framers of the constitution which gave them as a  congress the power to create lower courts as they wanted that the congress should have authority over the courts and to control them.

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complete question:

Which statement best explains why Article lll of the constitution gives Congress the ability to create lower courts inferior to the Supreme Court “from time to time”?

Answer:

180 square inches

5 x 6 = 32.5

32.5 x 4 = 130

5 x 5 = 25

25 x 2 = 50

130 + 50 = 180

Step-by-step explanation:

first find the area of all the sides (length times width)

width = 5

length = 6.5

5 x 6.5 = 32.5

32.5 is the area for one side. there are 4 others identical to it

32.5 (one side) x 4 (the amount of sides identical) = 130

then you need to find the area for the bottom/top side

5 = length

5= width

5(L) x 5(W) = 25

25 is the area for the bottom. the top is identical to it

25(bottom side) x 2 (the amount of sides identical)

now add all of the sides up

130 + 50 = 180

Answer:

Step-by-step explanation:

The equation given is:

120 + 1814x = 180 - 134x

We can simplify this equation by adding 134x to both sides:

120 + 1948x = 180

Next, we can subtract 120 from both sides:

1948x = 60

Finally, we can solve for x by dividing both sides by 1948:

x = 60/1948

Therefore, the solution is:

x = 0.0308 (rounded to four decimal places)

Answer:

To solve the equation, we need to first convert the mixed numbers to improper fractions:

120 + 18 1/4 x = 180 − 1 3/4 x

120 + 73/4 x = 180 - 7/4 x (converting mixed numbers to improper fractions)

Multiplying both sides by 4 to eliminate the fractions, we get:

480 + 73x = 720 - 7x

Combining like terms, we get:

80x = 240

Dividing both sides by 80, we get:

x = 3

Therefore, the solution for x is 3.

The length of the diagonal of the cube is x = 3√2 inches

Given data ,

Let the length of the diagonal of the cube be x

Now , the side length of the cube is = 3 inches

From the Pythagoras theorem , we get

x = √s² + s²

On simplifying , we get

x = √ ( 3² + 3² )

x = √18

On simplifying , we get

x = 3√2 inches

Hence , the diagonal is 3√2 inches

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The similar triangle is solved and the width of the river is R = 33.88 m

Given data ,

Let the base of the larger triangle be = 59 m

Let the base of the smaller triangle be = 35 m

Now , height of smaller triangle = 20.1 m

And , width of the river = height of the larger triangle

From the similar triangles , we get

59 / 35 = R / 20.1

Multiply by 20.1 on both sides , we get

R = 33.88 m

Hence , the width of river is 33.88 m

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Changing the base from 5/7 to 7, the end behavior of the function would be given as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The function for this problem is given as follows:

f(x) = 4(5/7)^x.

Changing the base to 7, it would have an absolute value greater than 1, hence the function would be increasing with the end behavior given as follows:

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The confidence interval of the given data is (117, 107).

Given that:

Sample mean X = 112

Standard deviation σ = 45

Sample size n = 81

Confidence level = 99.7%

Z Score = (x − μ )/σ

Z score = 0.9944

Confidence interval = X±z (σ/√n)

= 112±0.9944(45/√81)

= 112±0.9944(5)

= 112±4.972

= 112+4.972 or 112-4.972

= 116.972 or 107.028

= (117, 107)

Therefore, the confidence interval of the given data is (117, 107).

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Answer: [tex]\frac{8}{15}[/tex]

Step-by-step explanation: In total, Patty placed 45 slips of paper in a bag(10+9+8+7+6+5). Out of those 45 slips of paper, only 24 had even numbers on them(10+8+6), resulting in the fraction [tex]\frac{24}{45}[/tex]. If you divide both 24 and 45 by 3, the fraction can be simplified to [tex]\frac{8}{15}[/tex].

The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in  [tex]A_2[/tex]  [tex]B_2[/tex] , where   [tex]A_2[/tex]  is the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] , and  [tex]B_2[/tex]  is the product of  [tex]B_2[/tex]  and   [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] .

A vector is a mathematical construct with a length and a direction. It is frequently used to symbolise tangible properties like force, velocity, and acceleration. There are numerous techniques to multiply, add, and manipulate vectors. The characteristics and interactions of vectors in higher dimensions are described using vector calculus.

[tex]A_2B_2=A_2.B_2\\\\A_2=A.A\\\\A.A=[1.1+2.2+5.5+4.4][/tex]

=1+4+25+16

=46

[tex]B_2=B.B\\\\B_2=B.B\\\\B.B=[-1.-1+1.1+1.1+10.10][/tex]

=1+1+1+100

=103

[tex]A_2B_2=46.103\\\\A_2B_2=4738[/tex]

Therefore, [tex]A_2B_2=4738[/tex]

The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in  [tex]A_2[/tex]  [tex]B_2[/tex] , where   [tex]A_2[/tex]  is the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] , and  [tex]B_2[/tex]  is the product of  [tex]B_2[/tex]  and   [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] .

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A website is selling barbecue grills for $94, but mentions that they originally cost $200 the discount, as a percentage, is 53%.

The discount is the difference between the original price and the discounted price.

Discount = $200 - $94 = $106

To find the percentage discount, we need to calculate what percentage of the original price the discount represents:

Percentage discount = (Discount/Original price) x 100%

Percentage discount = ($106/$200) x 100%

Percentage discount = 53%

Therefore, the discount, as a percentage, is 53%.

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