1. In which quadrant does the following point lie? (-2,1/2)​

The system of equation has no solution.

Two or more expressions with an Equal sign is called as Equation.

The system of solution is

y=2x+6...(1)

2y=4x-2...(2)

Multiply equation 1 with 2

2y=4x+12...(3)

Subtract equation 2 and 3

2y-2y=4x-2-4x-12

0=-14

Hence, the system of equation has no solution.

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number of tickets?

The two equations can be set equal to each other and solved for x:

30x + 20 = 20x + 50

10x = 30

x = 3

Therefore, they sold the same number of tickets after 3 days

The two positive numbers are 1 and 1, depending on the given information.

Let first number be x. So, the second number is 1/x. Now, their sum is minimum, so representing the expression for given information -

Sum (x) = x + 1/x

Rewriting the expression -

Sum (x) = x + [tex] {x}^{-1} [/tex]

Finding the derivative

Sum' (x) = 1 + (-1) [tex] {x}^{-2} [/tex]

Sum' (x) = 1 + (-1)/[tex] {x}^{-1} [/tex]

Sum' (x) = (x² - 1)/x²

Now, to find the minimum -

x² - 1/x² = 0

Multiplying x² on Right Hand Side of the equation

x² - 1 = 0

Rewriting the equation

x = ± 1

As the numbers are positive, so x will be 1.

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Answer:

d. 35

Step-by-step explanation:

y = 35x + 40

The slope is 35 as 'm' is the slope of the equation

LMK IF IT WAS RIGHT!!

Answer:

D (35)

Step-by-step explanation:

Sarah can pour 1 gallon from one batch of Green Team juice .

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that Sarah mixes 6 quarts of green apple juice with 3 quarts of kiwi juice and 3 quarts of spinach juice.

6 quarts apple juice and 8 cups cranberry juice.

3 quarts = 0.5 gallons

8 cups = 0.5 gallons.

Total juice got here is 0.5 + 0.5 = 1 gallon.

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Z-scores are used to standardize a raw score by converting it into the number of standard deviations it is above or below the mean.

The formula to convert a raw score into a z-score is:

z = (X - Mean) / Standard Deviation

Where X is the raw score, Mean is the mean of the population, and Standard Deviation is the standard deviation of the population.

For z = 2.00:

z = (X - Mean) / Standard Deviation

X = (z * Standard Deviation) + Mean

X = (2.00 * 38.2) + 202 = 238.4 + 202 = 440.4 (rounded to nearest whole number = 440)

For z = -2.00:

z = (X - Mean) / Standard Deviation

X = (z * Standard Deviation) + Mean

X = (-2.00 * 38.2) + 202 = -76.4 + 202 = 125.6 (rounded to nearest whole number = 126)

So for z = 2.00, the corresponding test score is 440, and for z = -2.00, the corresponding test score is 126.

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Answer: 3 13/24

Step-by-step explanation:

When the term "evaluate" is in a question you are being asked to perform the operation, in this case subtraction of fractions.

Note that these are mixed number fractions, meaning there is a whole number with a fraction.

7 1/6 - 3 5/8

Step 1: Convert the mixed fractions to improper fractions.

For 7 1/6 take 7 x 6 = 42. Take 42 + 1 = 43

7 1/6 becomes 43/6

For 3 5/8 take 3 x 8 = 24. Take 24 + 5 = 29

3 5/8 becomes 29/8

Step 2: Arrange the improper fractions into the subtraction problem.

43/6 - 29/8

Step 3: Find the least common denominator for 6 and 8, which is 24.

43/6 (4/4) - 29/8 (3/3) =

172/24 - 87/24 = 85/24

Step 4: Turn the improper fraction into a mixed fraction.

Divide 85 by 24, which equals 3 13/24.

The equivalent expression is x + 3 + 4/(x - 1)

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x² + 2x + 1) / (x - 1)

Now,

x² + 2x + 1

= x² + (1 + 1)x + 1

= x² + x + x + 1

= x(x + 1) + 1(x + 1)

= (x + 1)(x + 1)

= (x + 1)²

Now,

(x² + 2x + 1) / (x - 1)

= (x + 1)² / (x - 1)

Now,

x + 3 + 4/(x - 1)

((x - 1)x + 3(x - 1) + 4) / (x - 1)

= (x² - x + 3x - 3 + 4) / (x - 1)

= (x² + 2x + 1) / (x - 1)

Thus,

x + 3 + 4/(x - 1) is the equivalent expression.

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To describe the number of vocabulary words that are understood by the first-graders is better to use the mode.

Based on this, the factor to be considered to know the number of words first-graders know is the mode because this is the most common number of words and the most accurate information.

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The equation that represents the distance traveled by the second car is 60(t + 1.33).

Let t = travel time of the 2nd car when it overtakes the 1st

:

Find the travel time of the 1st car to go 80 mi; time = dist/speed

time = 80%2F60

time = 1.33 hrs for the 1st car to go 80 mi

therefore

(t+1.33) = travel time of the 1st car when it is overtaken

:

When the 2nd overtakes the 1st, they will have traveled the same distance

Write a distance equation, dist = speed * time

:

2nd car dist = 1st car dist

70t = 60(t+1.33)

70t = 60t + 80

70t - 60t = 80

10t = 80

t = 8 hrs travel time of the 2nd car to overtake the 1st

:

;

Confirm this by finding the actual distances, should be equal

70*8 = 560 mi

60*9.33 ~ 560 mi

Hence , the equation that represents the distance traveled by the second car is 60(t + 1.33).

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The probability that X will be between 21 and 25 is increased.

The probability that a continuous random variable with a uniform distribution takes on a value between two specific points (a, b) is given by:

P(a X b) = (b - a) / (max - min)

where X is the random variable, max and min are the distribution's upper and lower bounds, and (b - a) is the length of the interval between two specific points.

In this case, the uniform distribution of X is from 20 to 28, so:

max = 28 min = 20

And we want to know how likely it is that X will have a value between 21 and 25:

P(21 < X < 25) = (25 - 21) / (28 - 20) = 4 / 8 = 0.5

As a result, the probability that X will be between 21 and 25 is increased.

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There is no significant difference in interaction means.

The ANOVA table is used to test the null hypothesis that the means of two or more groups are equal. In this case, we are testing the means of four levels of Factor A and three levels of Factor B. The table shows the Sum of Squares (SS) for each source, the Mean Squares (MS), and the F-value for each source.

To determine if there is a significant difference in Factor A and Factor B means, we must calculate the critical values to test for equal means. We can do this by dividing the Mean Square (MS) of each factor by the Error Mean Square (MS Error). For Factor A, we have MS Factor A/MS Error = 60/400 = 0.15. For Factor B, we have MS Factor B/MS Error = 40/400 = 0.1. We can then compare these values to the critical value for a 0.05 significance level, which is 3.89. Since both of our values are below this critical value, we can conclude that there is no significant difference in Factor A and Factor B means.

Finally, to determine if there is a significant difference in interaction means, we must calculate the F-value for the Interaction source. This is done by dividing the Mean Square of the Interaction source (MS Interaction) by the Error Mean Square (MS Error). In this case, we have MS Interaction/MS Error = 110/400 = 0.275. We can then compare this value to the critical value for a 0.05 significance level, which is 3.89. Since our value is below this critical value, we can conclude that there is no significant difference in interaction means.

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The value of the given exponent numerical expression will be negative 32.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

[tex]\rightarrow \left ( -128 \right )^{\frac{5}{7}}[/tex]

We know that 128 can be written as,

128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

128 = 2⁷

Then the value of the expression is given as,

[tex]\rightarrow \left ( (-2)^7\right )^{\frac{5}{7}}\\\\\rightarrow \left ( -2\right )^{\frac{7 \times 5}{7}}\\\\\rightarrow \left ( -2 \right )^5[/tex]

Simplify the expression, then we have

⇒ (-2)⁵

⇒ - (2)⁵

⇒ - 32

The value of the given exponent numerical expression will be negative 32.

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the probability that x is 4 is given by the formula  P(x) = [tex](1 - p)^(x-1) * p[/tex]

The formula for the probability of a geometric distribution is [tex]P(x) = (1 - p)^(x-1) * p[/tex]

Given the probability of success (p) is 0.3, the probability of x being 4 would be:[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]

P(x) = 0.0729 or 7.29%

The geometric distribution is a probability distribution for the number of failures before the first success in a series of independent trials.

In this problem, the probability of success (p) is 0.3 and the probability of failure (1-p) is 0.7.

Therefore, the probability that x is 4 is given by the formula  [tex]P(x) = (1 - p)^(x-1) * p[/tex]

Plugging in the values of p and x, we get:

[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]

This simplifies to

P(x) = 0.0729 or 7.29%

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Answer: $200,000

Step-by-step explanation:

The price of her home is $200,000.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The closing costs run from 2% to 7% of the purchase price.

Approximate closing costs would range from $4,000 to $12,000.

Price of her home = x

This means,

2% of x =  4000

(2/100)x = 4000

(1/50)x = 4000

x = 4000 x 50

x = 200,000 ____(1)

7% of x = 12,000

(7/100)x = 12,000

x = (12,000 x 100)/7

x = 171428.57

x = 171429 _____(2)

Now,

From (1) and (2) we can say that,

x = $200,000

Thus,

$200,000 is the price of her home.

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The complete question:

The closing costs run from 2% to 7% of the purchase price.

Becky was told that based on the price of her home, her approximate closing costs would range from $4,000 to $12,000. How much was the price of her home?

Options C and D are subsets of R³, which are {(-5x,4x,3x)| x arbitary} and {(x,y,z)| x+y+x=0}

A) Correct. We have to check whether the potential subspace containing the zero vector is a great place to start on these sorts of problems. No zero vector so this is not a subspace.

B) This is a subspace. The set of solutions of a homogeneous linear system is always a subspace it is known as a "null space" of some corresponding linear transformation.

Let, [tex]M=\left[\begin{array}{ccc}2&9&0\\8&0&-5\\\end{array}\right][/tex]  then the set in B) is just Null(M). Again, Nullspaces are always subspaces.

Alternatively, you could solve the corresponding system Mx=0 and find the elements of that set  [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex]  for any choice of z∈R. So this

can be a set in the span of   [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex]

C) Correct. we can see a subspace because the elements are just multiples of (−5,3,4) and again spans are subspaces.

D) Correct. This can be a  subspace for the same reasons as part B.

E) Correct. Not a subspace. An easier counter-example: (1,1,1) is in there. But (−1)(1,1,1)=(−1,−1,−1) is not.

F) Not a subspace. (0,0,0)  is not in there.

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The number of white balls is equally likely to be any number between 1 and n−1.

Let W be the number of white balls in the bin after the nth iteration. W can be any number between 1 and n−1. We can calculate the probability of obtaining a specific number of white balls in the bin by considering the number of possible sequences of choices. There are 2^n possible sequences of choices as each choice is either a white ball or a black ball. The number of sequences in which W white balls are selected is (W choose 1)*(n−W choose 1), which is equal to W*(n−W). Therefore, the probability of W white balls in the bin after the nth iteration is P(W) = (W*(n−W))/(2^n).

Since P(W) is equal for all values of W between 1 and n−1, it follows that the number of white balls is equally likely to be any number between 1 and n−1.

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1,3

Step-by-step explanation:

Answer:

y = (2/3)x + 10

Step-by-step explanation:

To find the equation of the line in slope-intercept form, y=mx+b, we need to know the slope and the y-intercept. The slope, or m, is rise over run. To find slope, we need to look at 2 points. For this question, I will be using the points (0,10) and (30,30). The rise, or change in y value, is 20, while the run, or change in x value, is 30. This means our rise over run in 20/30, or 2/3. Now that we have established the slope, or m, let's find the y-intercept, or b. To do this, you just need to look at where the line passes through the y-axis. In the image, you can see the line passes through the y-axis as x=10, making our y-intercept, or b, 10. Using this information, we can now find the equation of the line:

y = mx + b

m = slope, 2/3

b = y-intercept, 10

y = (2/3)x + 10

So, the equation of the line is y = (2/3)x + 10

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Compare the number of times customers who saw either version of the menu ordered the item.

In order to understand if setting the menu item apart in a text box increased the likelihood the item is ordered, researchers should first compare the number of customers who saw version A of the menu to the number of customers who saw version B of the menu. This will allow the researchers to determine if there is any difference in the number of customers who saw each version of the menu. Once this comparison is made, the researchers should then compare the number of times that customers who saw version A of the menu ordered the item to the number of times that customers who saw version B of the menu ordered the item. This will allow the researchers to see if the item was ordered more frequently with version A of the menu. Lastly, the researchers should compare the percentage of times that customers who saw version A of the menu ordered the item to the percentage of times that customers who saw version B of the menu ordered the item. This will allow the researchers to determine if there was a significant difference in the likelihood of the item being ordered with the different versions of the menu.

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Because it is typically too expensive and too time consuming, researchers often select a sample, a group of people that are representative of the larger population.

A sample is a smaller group of individuals selected from a larger population for the purpose of studying and making inferences about the population. Sampling is used when studying the entire population is not feasible due to limitations in time, resources, or practicality. The goal is to select a sample that accurately represents the population in terms of key characteristics such as age, gender, education level, etc. The sample must be representative of the population, meaning that it should accurately reflect the characteristics of the population. This is important because any biases or inaccuracies in the sample can lead to incorrect inferences about the population. A well-selected sample should also have a large enough size to provide meaningful results, yet not be so large that it becomes difficult to manage or too expensive to study.

In conclusion, sampling is a crucial step in research because it enables researchers to study a portion of the population, rather than the entire population, in order to make inferences about the larger group.

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A. The total value of the loan with quarterly compounded interest is $52,400.

B. The total value of the loan with monthly compounded interest is $52,010.04

Part A: Total value of the loan with the quarterly compounded interest

To find the total value of the loan, we'll use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (loan + interest)

P = principal amount (initial loan) = $20,000

r = interest rate = 7% = 0.07

n = number of times compounded per year = 4 (quarterly)

t = number of years = 10

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/4)^(4 * 10)

A = $20,000 * (1.0175)^40

A = $20,000 * 2.620075

A = $52,401.51

Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.

Part B: Total value of the loan with the monthly compounded interest

To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:

A = P * (1 + r/n)^(nt)

Where:

n = number of times compounded per year = 12 (monthly)

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/12)^(12 * 10)

A = $20,000 * (1.005833)^120

A = $20,000 * 2.600502

A = $52,010.04

Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04

The difference between the two loans is $52,401.51 - $52,010.04 = $391.47

The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.

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The variable type for the type of flooring in a room is Qualitative Discrete. This type of variable takes on unmistakable classes and can't be estimated on a mathematical scale.

Let us consider that the type of flooring in a room may be rug, tile, or hardwood, and there is no way to quantify the type of flooring on a mathematical scale.

The variable type for the type of cooking served in a café is likewise Qualitative Discrete. This variable takes on unmistakable classes like Italian, Chinese, and Mexican, and it is basically impossible to gauge the type of food on a mathematical scale.

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The domain and range of a function is discussed above.

An function in mathematics defines a relationship between one variable (the independent variable {x})  and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.

Given is the graph of the function as shown in the image.

Domain represents the set of values along the {x} - axis or the possible values of {x} for which f{x} exists.

Range represents the set of values along the {y} - axis or the possible existing values of f{x} for a specific value of {x}.

Therefore, the domain and range of a function is discussed above.

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To force the output to show the decimal point and trailing zeros of a decimal number use the showpoint, manipulator.

The showpoint function is a manipulator that sets the show point flag, which instructs an output stream to write a decimal point for floating-point output, even if the point is superfluous. This is done by setting the showpoint flag, which is done by setting the show point flag (only zeros appear after the decimal point). More specifically, the calls to the functions.

The distinction between a whole number and the fractional component of a number is denoted by the use of a symbol known as a "decimal point," which can be either a point or a dot. A different name for it is the Decimal Mark. The representation of the decimal point is the (.). In addition to using whole numbers, we frequently work with decimals.

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Answer: 43516

Step-by-step explanation:

C =(Current Salary). C x .012( 12%)=516

C + 516 = 43516

8. The length VX is not equal to the length WY. Then the incorrect option is A.

9. The measure of the angle ∠DEG will be 33°.

One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.

8. The base of the pyramid is a square. Then we have

WX = XY = YZ = ZW

VW = VX = VY = VZ

The length VX is not equal to the length WY. Then the incorrect option is A.

9. The measure of the angle ∠HBC = 33°. Then the measure of the angle ∠DEG is given as,

∠HBC = ∠DEG (Because they are alternate extiroir angles)

∠DEG = 33°

The measure of the angle ∠DEG will be 33°.

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Option B is correct, WX is perpendicular to ZY and WX is parallel to AB.

Coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

To find the solution of this problem.

Firstly let us understand the parallel and perpendicular lines.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane.

Two geometric objects are perpendicular if they intersect at a right angle. The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.

As we check all the options, WX is perpendicular to ZY and WX is parallel to AB.

Hence, Option B is correct, WX is perpendicular to ZY and WX is parallel to AB.

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The annual interest is $22.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

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