Select ALL the ordered pairs that are solution to the following system. (There are several correct answers. Find them all.) Select the ordered pair that are solution to the following system:
2x + 3y>10
y≥ -3x + 2
(ordered pairs)
(15, -1) (0, 0) (-6, 1) (-2, 8) (15,-20) (0,4) (10, 30) (8,-2) (5, 5) (1, 10)​

Using petid as a primary key in the pet relation is generally a good way to uniquely identify each data record in the relation. However, in some cases, it may be necessary to include personid as part of the primary key of the pet relation.

This is because each pet should have a unique identifier, and petid is specifically designed to serve this purpose. This would be the case if a person can have more than one pet in the database, and if the same petid value is used for more than one pet (which would violate the uniqueness requirement of a primary key).

By including personid as part of the primary key of the pet relation, we ensure that each pet in the database has a unique identifier (i.e., a unique combination of petid and personid). This allows us to avoid any confusion that might arise if two or more pets in the database had the same petid value. It also allows us to link each pet to its owner via the personid attribute, which can be useful for querying and reporting on the data.

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The original number of roommates was 6, determined by comparing the original and new shares of rent per roommate and solving for the minimum number of roommates that satisfies the inequality.

Let's assume that there were 'x' original roommates in the apartment.

When the rent was shared equally among 'x' roommates, each roommate's share was:

[tex]6000/x[/tex]

After four roommates moved out, the remaining roommates continued to share the same rent of $6000 but each person's share increased by $250. So the new share per roommate is:

[tex](6000/x) + 250[/tex]

Since the number of roommates decreased by 4, the new number of roommates is:

[tex]x - 4[/tex]

We know that the new share per roommate is greater than the original share per roommate, so we can set up the following inequality:

[tex](6000/x) + 250 > 6000/x[/tex]

Simplifying the inequality, we get:

[tex]250 > 6000/x - 6000/x[/tex]

[tex]250 > 6000/x^2[/tex]

[tex]x^2 > 24[/tex]

[tex]x > 4.9[/tex]

Since the number of roommates must be a whole number, the minimum value for x is 6.

Therefore, there were originally 6 roommates in the apartment.

The solution involves setting up an inequality to compare the original share of the rent per roommate with the new share of the rent per roommate, and then solving for the minimum number of original roommates that satisfies the inequality.

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According to the above statement, she has a 1/6 chance of rolling a 7 on the dice.

A possibility is a ratio that expresses the possibility or likely that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

When using two six-sided dice, there are 36 possibilities that might occur.

By using two dice, there are six ways to arrive to the sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), & (6, 1).

The likelihood of rolling a 7 is thus 6/36 = 1/6.

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Mae Ling make $590 in a work week if she sold $4,500 worth of merchandise.

The given is:

We need to find how much she would earns in a work week

Mae Ling earns a weekly salary of $320

She earns a 6.0% commission on sales

She sold by $4,500 in that week

Add $320 to the product of 6.0% and $4,500

She made = 320 + (6.0% × 4,500)

6.0% = 6.0 ÷ 100 = 0.06

She made = 320 + (0.06 × 4,500)

She made = 320 + 270

She made = 590

She would make $590 in a work if she sold $4,500 worth of merchandise.

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The horizontal and vertical translations applied to ΔABC:

A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.

Given that,

[tex]\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right][/tex]   = ?

After using matrix operation it can be further solved as,

[tex]\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right][/tex]

Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

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The probability that a randomly chosen person has diabetes is 34.2 million / (0.105 * total population).

The probability that a randomly chosen person has diabetes is equal to the number of people who have diabetes divided by the total population:

probability = number of people with diabetes / total population

Substituting the given values:

probability = 34.2 million / (10.5% of the total population)

To calculate this, we need to convert the percentage to a decimal by dividing by 100:

probability = 34.2 million / (0.105 * total population)

Assuming the total population remains constant between 2018 and now, and that the percentage of people with diabetes has also remained constant, we can use this probability to estimate the current number of people with diabetes in the United States.

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The y-intercept is 5, and the slope is -4. As a result, the line's equation is y = -4x + 5, where -4 is the slope and 5 is the y-intercept.

A linear equation is an algebraic equation of the form y = mx + b, where the slope is m and the y-intercept is b, and only a constant and a first-order (linear) term are included.

The slope and y-intercept of the linear equation 4x + y = 5,

we need to solve for y and put the equation in slope-intercept form, y = mx + b,

where the slope is m and the y-intercept is b

4x + y = 5

Subtract 4x from both sides:

y = -4x + 5

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The currect option is (b) H0: p = 0.5; Ha: p > 0.5

p represents the population proportion.

A null hypothesis is a statement from the population parameter which is either rejected or accepted (fail to reject) upon testing. It is expressed using the equality sign.

An alternate hypothesis is also a statement from the population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected. It is expressed using any of the inequality signs.

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. a commentator believes that more than half of all adults favor such a ban. the null and alternative hypotheses you would use to test this claim are

a) H0:p^=0.5;Ha:p^>0.5

(b) H0:p=0.5;Ha:p>0.5

(c) H0:p=0.5;Ha:p<0.5

(d) H0:p=0.5;Ha:p≠0.5

(e) H0:p>0.5;Ha:p=0.5

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Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.

The 12.4% calculation made by Dr. Raynor is referred to as a confidence interval. A confidence interval is a range of numbers that is likely to contain a population parameter. In this case, the population parameter is the percentage of students in the school with concerning behaviors that impact their performance in the classroom. To calculate the confidence interval, Dr. Raynor first determined the sample proportion, which is 12.4%. Then, she used the following formula to calculate the confidence interval:

Confidence Interval = (Sample Proportion ± Margin of Error)

In this case, the margin of error was 2.2%, which is calculated by multiplying the sample proportion by 1.96 (1.96 being the critical value for a 95% confidence interval). Thus, the confidence interval of 10.2% to 14.6% was determined. This confidence interval means that Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.

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The profit generated from selling x boxes of pencils is a linear function of x, with a slope of $0.80 and a y-intercept of -$12.60

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range) with the property that each input is related to exactly one output.

Let us first define the demand function as D(x), where x is the number of boxes of pencils sold. We know that the manager can sell 10 boxes of pencils at a price of $2.19 per box, which means that the revenue generated from this sale is:

10 * $2.19 = $21.90

Similarly, when the price is $1.70, she can sell 24 boxes of pencils, which gives a revenue of:

24 * $1.70 = $40.80

Now, we can use these two data points to find the equation of the demand function. Since we assume that the demand is linear, we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept. In our case, y represents the revenue generated by selling x boxes of pencils.

To find the slope, we use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the two data points we have.

m = ($40.80 - $21.90) / (24 - 10)

m = $18.90 / 14

m = $1.35

To find the y-intercept, we can use either of the two data points and solve for b:

$21.90 = $1.35 * 10 + b

b = $7.40

Therefore, the demand function for the pencils is:

D(x) = $1.35x + $7.40

This means that for each additional box of pencils sold, the revenue generated increases by $1.35. The y-intercept of $7.40 represents the revenue generated when no pencils are sold, which includes fixed costs such as rent, utilities, and wages.

We also have the cost function C(x) = 0.55x + $20, which represents the total cost of buying x boxes of pencils. The profit function P(x) is defined as the difference between the revenue and the cost:

P(x) = D(x) - C(x)

Substituting the expressions for D(x) and C(x), we get:

P(x) = ($1.35x + $7.40) - (0.55x + $20)

Simplifying this expression, we get:

P(x) = $0.80x - $12.60

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The value of MN is 3.05

Along with arithmetic, geometry is one of the earliest subfields of mathematics. It is concerned with spatial characteristics like the separation between objects, their shape and size, and their relative positions.

Since MN=NK,

draw an isosceles triangle (two sides are equal).

Mark the angle N as 110 degrees.

Now, draw a line from N to the opposite side at a right angle. This line will divide MK=5 in half since MN = NK.

It will also divide angle N into half. So, we will end up with a right triangle with one side 5/2 = 2.5 and the opposite angle 55 degrees.

sin(55) = opposite / hypotenuse = 2.5 / MN = 0.82

MN = 2.5 / 0.82 = 3.05

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The function with a greater stretch factor is the function graphed and the value is 3 times greater

The function with a greater stretch factor is the function which has a greater number multiplying the function

The given equation is a(x) = 1/3 x³ while the function graphed is b(x) = x³+ 2

The stretch factor is determined by the coefficients which are

a(x): 1/3 and b(x): 1

comparing this numbers

= b(x) / a(x)

= 1 / 1/3

= 3

this shows that b(x) which is 1 is greater by 3 times.

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The Mean Value Theorem is satisfied for c = 3 on the closed interval [0,3]. This can be expressed as:

The Mean Value Theorem (MVT) of differential calculus states that for any differentiable function f(x) on the closed interval [a,b], there exists a point c between a and b such that the slope of the tangent at c is equal to the average rate of change of f(x) over [a,b]. Mathematically, this can be expressed as:

f'(c) = [f(b) - f(a)] / (b - a)

In the given function f(x) = x^3 - 3x^2, we need to find all values of c that satisfy the conclusion of the MVT on the closed interval [0,3].

First, we need to find the derivative of f(x):

f'(x) = 3x^2 - 6x

Then, we need to evaluate the average rate of change of f(x) over [0,3]:

[f(3) - f(0)] / (3 - 0) = (27 - 0) / 3 = 9

Therefore, we need to find all values of c between 0 and 3 such that f'(c) = 9.

Setting f'(c) = 9, we get:

3c^2 - 6c = 9

c^2 - 2c - 3 = 0

(c - 3)(c + 1) = 0

Thus, the two possible values of c that satisfy the conclusion of the MVT are c = 3 and c = -1. However, we need to check if these values actually lie in the closed interval [0,3]. Since -1 is not in [0,3], the only value of c that satisfies the conclusion of the MVT on [0,3] is c = 3.

Therefore, the conclusion of the Mean Value Theorem is satisfied for c = 3 on the closed interval [0,3]. This means that there exists a point c between 0 and 3 where the slope of the tangent to the graph of f(x) is equal to the average rate of change of f(x) over [0,3].

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Answer:

Step-by-step explanation:

take length as x,

perimeter= 28cm

Answer:

28cm

Step-by-step explanation:

7+7+7+7

The required value of the x to the nearest tenth is given as x = 8.8. Option C is correct.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal 180°

Here,
Since the question seems to be incomplete, the complete question has been attached at the last of the solution,

Now, A triangle is shown in the image attached,

To evaluate the measure of x, we apply the sine rule,
8.2/(sin(180-126-28)) = x/sin28
8.2/sin26 = x/sin28
x = 8.2sin28/sin26
x = 8.8

Thus, the required value of the x to the nearest tenth is given as x = 8.8. Option C is correct.

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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:

To solve it, you need to use compound interest. Let me show you how.

Let P be the initial amount that Terry invested. Then after 4 years, the amount in the account is:

P × (1 + 0.037)^4

After withdrawing $2000, the remaining amount is:

P × (1 + 0.037)^4 - 2000

This amount is then moved to another account earning 4.5% p.a. compounded annually. After 3 more years, the amount in the account is:

(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3

We are given that this amount is equal to $5635.66. So we can write an equation:

(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3 = 5635.66

Simplifying the equation, we get:

P × 1.1597 - 2000 = 5635.66 / 1.1406

Adding 2000 to both sides, we get:

P × 1.1597 = 5635.66 / 1.1406 + 2000

Dividing both sides by 1.1597, we get:

P = (5635.66 / 1.1406 + 2000) / 1.1597

Using a calculator, we get:

P ≈ 5000.01

Therefore, Terry initially invested about $5000.01.

Step-by-step explanation:

the angle BAD is 75 degrees and  we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD .

To work out angle BAD, we need to use the properties of angles in a circle and the tangent-secant theorem. Here are the steps to solve the problem:

Identify the relevant angles First, we need to draw a diagram to visualize the problem. We have a circle with center O, points A, B, C, and D on the circumference, and tangent ED. Angle ODB is given as 25 degrees. We need to find angle BAD. We can label the angles in the diagram as follows:

Angle AOB = 2x (angle at the center is twice the angle at the circumference)

Angle BCD = x (angles in the same segment are equal)

Angle OBD = 90 degrees (tangent and radius are perpendicular)

Angle OED = 90 degrees (tangent and radius are perpendicular)

Angle ABD = y (we need to find this angle)

Angle BAD = z (we need to find this angle)

Use the sum of angles in a triangle

We notice that triangle ABD is a right triangle, with right angle at B. Therefore, angles ABD and BAD are complementary. That is, ABD + BAD = 90 degrees. Use the tangent-secant theorem

We can use the tangent-secant theorem to find the value of angle ABD. The tangent-secant theorem states that if a tangent and a secant intersect at a point on a circle, then the angle between the tangent and the secant is equal to the half the difference of the intercepted arcs. In our diagram, ED is a tangent, and BD is a secant. Therefore, angle ODB = 25 degrees is half the difference of the intercepted arcs AD and AB. That is, angle ABD = (2x - x)/2 = x/2.

Solve for x

To find x, we can use the fact that the angles in a triangle add up to 180 degrees. Therefore, x + 2x + 90 = 180 (sum of angles in triangle AOB). Solving for x, we get x = 30 degrees.

Find angle ABD and angle BAD

Using the result from step 3, we get ABD = x/2 = 15 degrees. Using the result from step 2, we get BAD = 90 - ABD = 75 degrees.

Therefore, the angle BAD is 75 degrees. In summary, we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD. We noticed that ABD and BAD are complementary, and we used the tangent-secant theorem to find ABD. Then, we solved for x using the fact that the angles in a triangle add up to 180 degrees. Finally, we used the results from steps 2 and 3 to find BAD.

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In a normal distribution, the mean and the 'median' are equal.

In a normal distribution, the mean represents the central tendency of the data, while the median represents the middle value. In a perfectly symmetrical normal distribution, the mean and median are exactly the same value. This is because the normal distribution is a bell-shaped curve that is symmetric around the mean. However, in skewed distributions, the mean and median can differ, with the mean being pulled towards the tail of the distribution. Overall, the equality of the mean and median in a normal distribution is a reflection of the symmetry of the data.

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Answer:160

Step-by-step explanation:

A man brought some glasses at 12 each and 5 broke so he sold remaining at 16 each and made profit of rupees 160. Find number of glasses he bought

The upper quartile score on the final exam is 83.

Upper quartile, represented as Q₃, also known as third quartile is the value in a data set such that 75% of the points in the data set are below this value, after arranging in an ascending order.

Given data set is the scores for the final exam in an 8th grade math class.

58, 72, 74, 92, 84, 40, 74, 81, 76, 83.

First arrange the data in an ascending order.

40, 58, 72, 74, 74, 76, 81, 83, 84, 92.

Median is the middle element.

Median = (74 + 76) / 2 = 75

Upper quartile is the median of the second half.

Consider the second half.

76, 81, 83, 84, 92.

Median = 83

Third quartile = 83

Hence 83 is the upper quartile score on the final exam.

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Answer:

64

Step-by-step explanation:

The right triangle ABC with right angle at vertex B has the length of the segment is; 4√2 unit.

The Pythagorean theorem state that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.

We can find the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can find that side BC is equal to the length of side AB.

The side lengths are 8/2 = 4

Now, Another side length that is x

So , the equation formed is;

xcos45 = 4

x/√2 = 4

x = 4√2

Hence the length of the segment is; 4√2 unit.

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Since the chance that the interval contains the actual value of the population parameter is what we put the confidence level 1 - alpha near to 1 when creating confidence intervals for parameters. false

Parameters are a value or set of values that can be used to define or characterize a certain system, model, or process. It is a variable that can be changed to affect how the system or process to which it is connected functions. In mathematics, a parameter is a variable that is used to describe the overall properties of a function or equation. In computer programming, it refers to a value or variable that is passed to a function or procedure. The function or method can then use these parameters to perform a specific operation or calculation.A parameter in statistics is a number that characterizes a population or a sample of data. They help to specify the characteristics.

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Answer:

The solution is (x = 6, y = -3)

Step-by-step explanation:

[tex]\sf \frac{x}{y + 1} = - 3 \: \: ........(1) \\ \\ \sf \frac{y}{x - 3} = - 1 \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \sf x + 3y = - 3 \: ........(1) \\ \\ \sf x + y = 3 \: \: \: \: \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \: \: \: \sf x + 3y = - 3 \: \: \: \: \: | \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf x + y = 3 \: \: \: \:\: \: \: \: | \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Six triangles are needed for each hexagon.

To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Each hexagon requires six triangles to make it, so two hexagons would need double that amount. Since the pattern blocks come in the shapes of triangles, you can easily construct the hexagons by placing the triangles together. Each triangle has two sides that fit together and two sides that overlap, so the six triangles will create a complete hexagon when they are all put together. Once you have two hexagons constructed, they will fit together to make a larger shape, depending on how you place them. With this method, you can easily make two hexagons out of pattern blocks.

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