Solve each of the following system of linear equations
x_1+〖3x〗_2=1

2x_1+〖5x〗_2=3

Answer:

Sure In this context, a weak negative linear relationship between the number of hours worked and the amount of donations collected means that as the number of hours worked by Thor each week increases, the amount of donations collected by the organization each week decreases, but the relationship is not very strong.

When we say that the correlation between two variables is weak, we mean that there is a low degree of association between them. In this case, the negative correlation suggests that there is a tendency for the amount of donations collected to decrease as the number of hours worked increases, but the relationship is not very strong, meaning that there is a lot of variability in the data and it is difficult to make strong predictions or conclusions based on this relationship alone.

It is important to note that correlation does not necessarily imply causation, so a weak negative linear relationship between the number of hours worked and the amount of donations collected does not necessarily mean that one variable causes the other. Other factors may be influencing the amount of donations collected by the organization each week, and further analysis would be required to determine the nature and strength of these relationships.

Step-by-step explanation:

This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.

The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.

The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

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Answer:

Step-by-step explanation:

If (x + a) is a factor of x³ + 8x² + 4ax - 3a, then we know that dividing x³ + 8x² + 4ax - 3a by x + a will give a quotient of x² + (8 - a)x + (4a - 3), and a remainder of 0.

We can write this as:

x³ + 8x² + 4ax - 3a = (x + a)(x² + (8 - a)x + (4a - 3))

Expanding the right-hand side, we get:

x³ + 8x² + 4ax - 3a = x³ + (8-a)x² + (4a-3)x + ax² + (8-a)ax + (4a-3)a

Collecting like terms, we get:

x³ + 8x² + 4ax - 3a = x³ + (a+8)x² + (5a-3) x + a(4a-3)

Comparing the coefficients of x², x and the constant term, we get the following equations:

a + 8 = 8   --> a = 0

5a - 3 = 0   --> a = 3/5

4a^2 - 3a = 0 --> a(4a-3) = 0

Therefore, we have:

a³ - 4a² + 3a = a(a² - 4a + 3) = a(a-1)(a-3) = 0

So, a can be 0, 1, or 3

Therefore, the possible values of a are 0, 1, and 3.

Therefore, a function equivalent to y = x² - 8x + 10 is: y = (x - 4)² + 4.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range), with the property that each input is associated with exactly one output. Functions are often denoted using function notation, such as f(x) or g(y), where the letter in parentheses represents the input and the expression to the right of the parentheses represents the output. Functions are used in many areas of mathematics, science, and engineering to model real-world phenomena and to solve problems. They are essential tools for analyzing data, making predictions, and creating mathematical models of physical and natural systems.

Here,

The function y = x² - 8x + 10 is a quadratic function, which has a U-shaped graph. To find a function that is equivalent to this function, we can start by completing the square, which involves adding and subtracting a constant term to create a perfect square trinomial. We can then write the function in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Completing the square, we get:

y = x² - 8x + 10

= (x² - 8x + 16) - 6 + 10 // Add and subtract (8/2)² = 16 to create a perfect square

= (x - 4)² + 4

Now we can see that the vertex of the parabola is at (4, 4). We also see that the coefficient of the squared term is 1, which means the parabola opens upward.

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Point C is located at -1 3/8

Hope that helps!

Trigonometric functions have some interesting symmetry properties

If tan x= -2.5, then tan (-x)= 2.5 and If sin x= 0.4 then sin (-x)= -0.4

If cos x = 0.9 then cos (-x)= 0.9  If tan x = 1.5 then tan (pi+x)= -1.5

Trigonometric functions are mathematical functions that are widely used in various fields, including mathematics, physics, and engineering. The most commonly used trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

Trigonometric functions have some interesting symmetry properties. For example, the sine and tangent functions are odd functions, which means that sin(-x) = -sin(x) and tan(-x) = -tan(x). On the other hand, the cosine function is an even function, which means that cos(-x) = cos(x).

These symmetry properties have important implications in many applications of trigonometric functions. For example, if we know the value of sin(x), we can immediately determine the value of sin(-x) by using the odd symmetry property. Similarly, if we know the value of cos(x), we can determine the value of cos(-x) by using the even symmetry property.

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Answer:

5:1

Step-by-step explanation:

d_a = 20

d_b = 5

Equation for the circumference of a circle:

C = pi*d

C_a = pi * d_a

C_a = pi*20

C_b = pi * d_b

C_b = pi * 5

Ratio of C_a to C_b = C_a/C_b

C_a/C_b = (pi * 20)/(pi * 4) = 5:1

In summary, A, B, E are valid linear programming relationships, while C, D, F are not.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

A. -1A+2B less than or equal to 70: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

B. 2A -2B= 50: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

C. 1A-2B^2 less than or equal to 10: This relationship is not acceptable for a linear programming model because it contains a quadratic term, B^2. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

D. 3(square root of) A + 2B greater than or equal to 15: This relationship is not acceptable for a linear programming model because it contains a square root function. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

E. 1A+1B=6: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

F. 2A+5B+1AB less than or equal to 25: This relationship is not acceptable for a linear programming model because it contains a product of variables, AB. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

Therefore, In summary, A, B, E are valid linear programming relationships, while C, D, F are not.

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The loan that will have a lower balance is;

Option B: The PLUS Loan will have a lower balance by $70.47 at the time of repayment.

To determine which loan will have a lower balance at the time of repayment, we need to calculate the total amount of interest that will be accrued on each loan.

1) For the unsubsidized Stafford loan:

The loan amount is $3,725.

The annual interest rate is 4.65%, compounded monthly. This means the monthly interest rate is 4.65%/12 = 0.3875%.

The loan will be repaid in 6 months, so there will be 6 monthly compounding periods.

Using the formula for compound interest, the balance of the loan at the time of repayment will be:

balance = principal x (1 + monthly interest rate)^number of compounding periods

balance = $3,725 x (1 + 0.003875)^6

balance = $3,901.95

So the balance of the unsubsidized Stafford loan at the time of repayment will be $3,901.95.

2) For the PLUS loan:

The loan amount is $3,725.

The annual interest rate is 5.65%, compounded monthly. This means the monthly interest rate is 5.65%/12 = 0.4708%.

The loan will be deferred until graduation, which is in 6 months, so there will be 6 monthly compounding periods.

Using the formula for compound interest, the balance of the loan at the time of repayment will be:

balance = principal x (1 + monthly interest rate)^number of compounding periods

balance = $3,725 * (1 + 0.004708)^6

balance = $3831.47

So the balance of the PLUS loan at the time of repayment will be $3831.47

Difference in balance = $3,901.95 - $3831.47

= $70.47

Therefore, the PLUS loan will have a lower balance at the time of repayment, by an amount of $70.47

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The diagonal distance from the airplane to the runway is approximately 5230.8 ft.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to measurements of angles and distances.

The angle of depression of 18° is the angle between the airplane's line of sight and the horizontal line representing the runway. We can label the altitude of the airplane as 1560 ft:

Now we can use trigonometry to find the diagonal distance from the airplane to the runway. In particular, we can use the tangent function:

tan(18°) = opposite / adjacent

In this case, the opposite side is the altitude of the airplane (1560 ft), and the adjacent side is the diagonal distance we're trying to find (x). Therefore:

tan(18°) = 1560 / x

To solve for x, we can multiply both sides by x and then divide both sides by tan(18°):

x = 1560 / tan(18°)

Using a calculator, we find that:

x ≈ 5230.8 ft

Therefore, the diagonal distance from the airplane to the runway is approximately 5230.8 ft.

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(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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Answer:

Determine Your Budget.

Check Your Credit.

View Multiple Rentals.

Consider Roommates.

Consider a Cosigner.

Gather Your References.

Check Out the Neighborhood.

Check All the Websites.

The required choice is true of an observational study B, C, and D.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
Option a is not true of an observational study. In an observational study, the researcher cannot control the variables of interest, unlike in a true experiment where the researcher can manipulate the variables.

Option b is true of an observational study. Since the researcher cannot control the variables of interest, the study is entirely based on observing the subjects and collecting data.

Option c is true of an observational study. The data collected in an observational study is similar to the data collected in a true experiment, and the same statistical methods can often be used to analyze both types of data.

Option d is true of an observational study. Since the researcher cannot control the variables of interest, they have to take advantage of natural variation in the variables to draw conclusions.

Thus, Options B, C, and D are correct.

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Answer:

5 or -2

Step-by-step explanation:

|2x-3| can equal either (2x-3) or -(2x-3) thus

(2x-3) = 7

2x = 10

x = 5

-(2x-3) = 7

-2x = 4

x = -2

Answer: it’s 5 or -2, |2x-3| can equal either (2x-3) or -(2x-3) thus(2x-3) = 72x = 10x = 5-(2x-3) = 7-2x = 4x = -2

Step-by-step explanation: hope this helps0^0

The sum of 106 and h can be written as an expression in the following way:   106 + h

This expression represents the sum of the two numbers, 106 and h. We can simplify this expression by combining like terms, but since h is a variable and 106 is a constant, we cannot combine them. Therefore, the expression remains as 106 + h.

In conclusion, the sum of 106 and h is represented by the expression 106 + h.

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Answer:

181

Step-by-step explanation:

To simplify this expression, we need to apply the order of operations (PEMDAS):

First, we evaluate the expression inside the parentheses: 9 ÷ 3 = 3.

Then, we add 6 + 3 = 9.

Finally, we divide 1,629 by 9 to get the answer:

1,629 ÷ 9 = 181.

Therefore, 1,629 ÷ (6 + 9 ÷ 3) simplifies to 181.

Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.

A percentage that corresponds to one tenth of an amount. One percent, represented by the symbol 1%, is equivalent to one hundredth of something; hence, 100 percent represents the complete object, and 200 percent represents twice the amount given.

According to the table:

The total number of Yellow Trains is 450.

The total number of all modes of transportation is 4730.

To calculate the percentage of the total that Yellow Trains make up, we can use the following formula:

percentage = (part/whole) x 100

Substituting the values we have:

percentage = (450/4730) x 100

percentage = 0.095 x 100

percentage = 9.5%

Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.

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The new account balance at the end of 2 years is $517.

Simple interest

5 yearsUsing this formula I= (P+r×t)

Where: I=Interest=?

P=Principal=$400

r=Interest rate=3.5%

t=Time=5 years

Hence: I= ($400×0.035 x 5) which makes I= $70

2 years

I=Interest=?

P=Principal=$470

r=Interest rate=5%

t=Time=2 years

I=($470+0.05×2) which makes I=$47

New balance:

New balance=$400+$70+$47

New balance=$517

Inconclusion the new account balance at the end of 2 years is $517.

I. The correct statement is: m<AOB = m<BOC

The measures of the angles are:

II. m<BOC = 53 degrees.

III. m<AOC = 106 degrees.

When a segment bisects an angle, it forms two equal angles. Therefore, we have following which explains how to find the measure of the given central angle.

I. <AOC is bisected by segment OB into: AOB and BOC, which are equal. Therefore:

m<AOB = m<BOC

II. m<AOB = 53 degrees, therefore,

m<BOC = 53 degrees.

III. m<AOC = 2(53)

m<AOC = 106 degrees.

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Answer:

Step-by-step explanation:

Let's begin by calculating Jim's total cost for creating one painting:

Cost of paint and canvas + Cost of brushes = $44 + $1 = $45

This means that Jim makes a profit of $45 - $45 = $0 per painting sold until he breaks even.

To determine how many paintings Jim needs to sell to break even, we can set up an equation:

Total Cost = Total Revenue

Let's say Jim sells x paintings. Then his total revenue would be:

Total Revenue = $45x

His total cost would be the cost of materials plus the cost of brushes multiplied by the number of paintings:

Total Cost = $45 + $1)x = $46x

Setting these equal, we get:

$46x = $45x

Solving for x, we get:

x = 45

So Jim needs to sell 45 paintings to break even.

Once he has sold 45 paintings, he will have earned:

Total Revenue = $45 x 45 = $2025

So Jim will have earned $2025 after selling 45 paintings.

Answer:

Step-by-step explanation:

To break even, Jim's total revenue from selling his paintings should be equal to his total cost of producing them, including the cost of materials and the cost of the brushes. Let's call the number of paintings he needs to sell to break even as "x".

The cost of producing each painting is $44 + $1 = $45.

The revenue from selling each painting is $45.

So, Jim's total revenue from selling x paintings would be:

Total revenue = Price per painting x Number of paintings sold

Total revenue = $45 x x

Total revenue = $45x

Jim's total cost of producing x paintings would be:

Total cost = Cost per painting x Number of paintings produced + Cost of brushes

Total cost = $45 x x + $1

Total cost = $45x + $1

For Jim to break even, his total revenue must equal his total cost:

Total revenue = Total cost

$45x = $45x + $1

Solving for x:

$45x - $45x = $1

0 = $1

This is a contradiction, meaning that the situation is impossible. It is impossible for Jim to break even by selling his paintings at the given prices. If he sells each painting at $45, which is the same price he paid to produce it, he will not make any profit. In fact, he will lose $1 for every painting he sells due to the cost of the brushes.

If Jim wants to break even or make a profit, he will need to increase the selling price of his paintings or find ways to reduce the cost of producing them.

So overall, you can expect to make a profit of $166.67 if you play the game 100 times.

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

To determine how much you expect to win or lose if you play the game 100 times, we need to calculate the expected value of each round and then multiply it by the number of rounds.

Let X be the random variable that represents the amount you win in one round of the game. The possible outcomes of X are winning $14, winning $12, or losing $10. We can calculate the expected value of X using the following formula:

E(X) = P(win $14) × $14 + P(win $12) × $12 + P(lose $10) × (-$10)

To calculate the probabilities, we can use the fact that there are 5 red balls, 3 green balls, and 4 yellow balls in the bag. The probability of drawing a red ball is therefore 5/12, the probability of drawing a green ball is 3/12, and the probability of drawing a yellow ball is 4/12.

So we have:

E(X) = (5/12) × $14 + (4/12) × $12 + (3/12) × (-$10)

E(X) = $5/3

This means that on average, you expect to win $5/3 per round. Over 100 rounds, you can expect to win:

100 × $5/3 = $166.67

However, it's important to note that this is just an average - in reality, you may win more or less than this amount depending on the luck of the draw.

Therefore, overall, you can expect to make a profit of $166.67 if you play the game 100 times.

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Answer:

Step-by-step explanation:

D, 57,500

Answer:

there were 15 almonds in the snack pack.

Step-by-step explanation:

Let's use variables to represent the unknown quantities. Let's call the number of almonds in the snack pack "a", and the number of cashews in the snack pack "c".

we can use the following equations to represent the problem:

c = 2a (the number of cashews is twice the number of almonds)

c - 10 = a + 5 (there are 5 more cashews than almonds after Sylvia eats 10 cashews)

Substituting the first equation into the second equation, we get:

2a - 10 = a + 5

Solving for "a", we get:

a = 15

So there were 15 almonds in the snack pack.

I think the radius would be 2

The solution to the matrix is x1 = (-555 - 356x3)/90, x2 = (138 + 89x3)/10 and x3 = free variable

To find the solution to this matrix, we need to perform row operations to put it into row echelon form or reduced row echelon form. We can do this by adding multiples of one row to another row, multiplying a row by a nonzero scalar, and swapping two rows.

Here are the row operations we can use to put this matrix into row echelon form:

1. Add 5 times the first row to the third row to eliminate the 5 in the (3,1) entry:

0 0 -9 6

0 -1 -4 4

25 35 11 38

2. Multiply the second row by -1 to make the pivot in the second row, second column equal to 1:

0 0 -9 6

0 1 4 -4

25 35 11 38

3. Add 9 times the second row to the first row to eliminate the -9 in the (1,3) entry:

0 9 0 -30

0 1 4 -4

25 35 11 38

4. Add -25 times the second row to the third row to eliminate the 25 in the (3,1) entry:

0 9 0 -30

0 1 4 -4

0 10 -89 138

5. This matrix is now in row echelon form. We can solve for the variables by back-substitution. Starting with the last row:

0 10 -89 138 | x3

We have:

10x2 - 89x3 = 138

Solving for x2, we get:

x2 = (138 + 89x3)/10

Substituting this expression for x2 in the second row, we have:

Copy code

0 1 4 -4 | (138 + 89x3)/10

Solving for x1, we get:

9x1 + 4(138 + 89x3)/10 = -30

Simplifying and solving for x1, we get:

x1 = (-555 - 356x3)/90

So the solution to the matrix is:

x1 = (-555 - 356x3)/90

x2 = (138 + 89x3)/10

x3 = free variable

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The length of ML in the line segment is 35 units.

The figure below has the following length as follows:

LN = 79 units

Let's find ML in the line segment as follows:

LM + MN = LN

Hence,

LM = 5y - 5

MN = 4y + 12

Therefore,

LN = 5y - 5 + 4y + 12

79 = 5y - 5 + 4y + 12

79 = 9y + 7

79 - 7 = 9y

72 = 9y

divide both sides by 9

y = 72 / 9

y = 8

Therefore,

ML = 5(8) -5

ML = 40 - 5

ML = 35 units

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Answer:

B

Step-by-step explanation:

urheheyfthxhzhditoiytdyifxzydzyfuyrzuysriduyrsute

The area of a circle with a diameter of radius 14 inches is given as follows:

A = 153.86 inches².

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr².

The radius, representing the distance between the center and a point on the circumference of the circle, has the measure defined as half the diameter, hence it is given as follows:

r = 7 inches.

Hence the area of the circle with radius of 7 inches is given as follows:

A = 3.19 x 7²

A = 153.86 inches².

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The length of PR is 4.8 units.

In geometry, a trapezoid, also known as a trapezium in some countries, is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs. The angle between the bases of a trapezoid determines its height.

Trapezoids can be classified into several types based on their properties, such as:

Isosceles trapezoid: a trapezoid with congruent legs.

Right trapezoid: a trapezoid with a right angle between one of its legs and one of its bases.

Scalene trapezoid: a trapezoid with no congruent sides.

Since QR is parallel to NO, we have:

∆PNQ ~ ∆PRO (by AA similarity)

So we can write:

PR/PQ = PO/PN

PR/7.2 = 6/9

PR = 7.2 × 6/9

PR = 4.8

Therefore, the length of PR is 4.8 units.

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