1. Let the point \( P \) be \( (-1,3) \) and the point \( Q \) be \( (3,7) \). Find the following. a. \( \mathbf{v}=\overrightarrow{P Q} \) b. \( \|\mathbf{v}\| \) c. \( \overrightarrow{P Q}+\overrigh

Answer:

60m^2

Step-by-step explanation:

15.1×10.3=155.53

155.53÷2=77.765

2.8×6.5=18.2

77.765-18.2= 59.565

rounded to nearest 10th = 60m^2

In the triangle the value οf x is D) 27.

A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.

Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.

Here in the given triangle, using ratiο then

=> [tex]\frac{x+8}{10}=\frac{2x-5}{14}[/tex]

=> [tex]14\times(x+8)=10(2x-5)[/tex]

=> 14x+112=20x-50

=> 20x-14x=112+50

=> 6x = 162

=> x =[tex]\frac{162}{6}[/tex]

=> x = 27

Hence the cοrrect οption is D)27.

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We start by isolating the square root on one side of the equation:

3x - 3 = sqrt(3x^2 + 177)

Squaring both sides of the equation gives:

(3x - 3)^2 = 3x^2 + 177

Expanding the left-hand side gives:

9x^2 - 18x + 9 = 3x^2 + 177

Simplifying gives:

6x^2 - 18x - 168 = 0

Dividing both sides by 6 gives:

x^2 - 3x - 28 = 0

We can now solve for x using the quadratic formula:

x = (3 ± sqrt(3^2 + 4128)) / 2

x = (3 ± 7) / 2

Therefore, the solutions are x = -2 and x = 5, and their sum is -2 + 5 = 3.

Thus, the answer is (C) 3.

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Answer: To check if (3x + 2) is a factor of a trinomial, we can use long division or synthetic division. However, we can also use the factor theorem, which states that if f(c) = 0 for a polynomial f(x) and a constant c, then (x - c) is a factor of f(x).

In this case, we can use the factor theorem with c = -2/3 to check if (3x + 2) is a factor:

f(-2/3) = 0 if and only if 3(-2/3) + 2 = 0, which is true. Therefore, (3x + 2) is a factor of f(x) if and only if f(-2/3) = 0.

Using this method, we can check each trinomial:

6x² +19x+10: f(-2/3) = 0. Therefore, (3x + 2) is a factor of 6x² +19x+10.

6x²-x-2: f(-2/3) = 0. Therefore, (3x + 2) is a factor of 6x²-x-2.

6x² +7x-3: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 6x² +7x-3.

6х2 - 5x - 6: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 6х2 - 5x - 6.

12x²-x-6: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 12x²-x-6.

Therefore, the trinomials that have (3x + 2) as a factor are:

6x² +19x+10

6x²-x-2

Note: We could also use long division or synthetic division to confirm our results.

Step-by-step explanation:

The measure of angle A is 85^o.

A quadrilateral is any form of plane figure which is bounded by four straight sides. Examples include: square, rhombus, rectangle trapezium etc. Each example of quadrilateral has differentiating properties.

The given quadrilateral ABCD inscribed in the circle has the shape of a rhombus. So we have:

the measure of opposite internal angles of a rhombus are congruent, so that;

x + (2x + 1) + 148 + (2x + 1) = 360

5x + 150 = 360

5x = 360 - 150

5x = 210

x = 210/ 5

  = 42

x = 42^o

Thus measure of angle A = (2x + 1)

                              = 2*42 + 1

                              = 85^o

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Answer:

Its mostly a step by step process

Step-by-step explanation:

Just Put your full name and the date your depositing the money where the date is and how many bills your depositing how many coins if you don't have coins don't answer it the total amount would be 800 and the net deposit. I added a link just in case. Happy birthday btw.

The length of the legs are 2 units and 3.464 units

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

The triangle

The legs can be calculated using sine and cosine ratios

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

sin(30) = PQ/Hyp

cos(30) = RQ/Hyp

Substitute the known values in the above equation, so, we have the following representation

PQ/4 = 0.5

RQ/4 = 0.8660

So, we have

PQ = 4 * 0.5

RQ = 4 * 0.8660

Evaluate

PQ = 2

RQ = 3.464

Hence, one of the leg is 3.464 units

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a. False. If we form the table with aspirin in the first row (instead of placebo), the confidence interval is (1/2.33, 1/1.44) = (0.43, 0.69).

b. True. We may get a different odds ratio value if we treat marijuana use as the response variable than if we treat alcohol use as the response variable.

c. False. Interchanging two rows or interchanging two columns in a contingency table does have an effect on the value of the X2 or G-chi-squared statistics. Thus, these tests treat both the rows and the columns of the contingency table as nominal scale, and if either or both variables are ordinal, the test takes that information into account.

d. False. Income and gender are not necessarily independent in the 2 x 2 marginal table, even if they are conditionally independent given the type of job.

e. False. The estimated odds ratio between opinion on global warming and whether one is a Democrat or a Republican does not equal 2.96 x 2.08 = 6.2, it equals (2.96/2.08) = 1.42.

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Option A → If KLM ≅ PQR and PQR ≅ STU , then KLM ≅ STU, is the correct answer for the transitive property of congruence.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given is to write the transitive property of congruence.

The transitive property of congruence states that “ if two shapes are congruent to the third shape, then all the shapes are congruent to each other. So, we can conclude that option A is the correct answer.

Therefore, Option A → If KLM ≅ PQR and PQR ≅ STU , then KLM ≅ STU, is the correct answer for the transitive property of congruence.

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Step-by-step explanation:

well, we don't need to look for any fancy calculation tricks.

all we need to do is calculate the amounts in both cases and then calculate the difference.

bachelor's degree income in 30 years :

59,100×30 = $1,773,000

high school diploma income in 30 years :

35,250×30 = $1,057,500

the difference is

$1,773,000 - $1,057,500 = $715,500

a person with a bachelor's degree would earn

$715,500

more over a period of 30 years than a person with only a high school diploma.

this is not considering the changes of the income levels over the period of 30 years (that adds insult to injury ...).

The value of the expression 7₂ + 3₃ is 10₅.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

An expression is 7₂ + 3₃.

To find the value of the expression, first, add 7 and 3.

That means, 7 + 3 = 10.

Now add 2 and 3,

2 +3 = 5

So, the value of the expression is 10₅.

Therefore, the result is 10₅.

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The coefficient a in the factorization [ x²+a x y+b y²=(x+5 y)(x-4 y) ] is -1. The correct answer is C

Terms are the sum of the numbers or variables, factors are the sum of the numbers or variables multiplied, and coefficient is the number multiplied by the variable.

To find the coefficient a, we can expand the right side of the equation and compare it to the left side.

Expanding the right side gives us: [ (x+5 y)(x-4 y)=x²-4 x y+5 x y-20 y² ]

Simplifying the right side gives us: [ x²+x y-20 y² ]

Comparing this to the left side of the equation, we can see that the coefficient a is -1.

Therefore, the correct answer is c. ( -1 ).

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The  value of the inequality for the expression is:  x >  -8

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

To solve the inequality, we need to isolate the variable, x.

We begin by simplifying the expression inside the parentheses:

2(3x - 2) = 6x - 4

Now we can substitute this expression into the original inequality:

-52 < 6x - 4

Add 4 to both sides:

-48 < 6x

Divide both sides by 6:

-8 < x

So the solution to the inequality is x > -8.

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Answer:

c.

Step-by-step explanation:

the inner angle is half of the sum of both outer angles.

65 = 1/2 × (36 + x)

130 = 36 + x

x = 130 - 36 = 94°

1. Elimination

2. Variable

3. Equation

4. Solve

5. Equation

6. Variable

7. Substitution

My best estimate

Elimination , variable ,equation , Solve , equation, variable, substitution .

An equation is a mathematical statement that asserts that two expressions are equal. It consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=). The expressions on both sides of the equation can be numbers, variables, or a combination of both, and the equal sign indicates that the two expressions have the same value.

Equations are used in mathematics to represent relationships between quantities, to solve problems, and to describe various phenomena. They are used in many areas of science, engineering, and economics, as well as in everyday life.

For example, the equation "2x + 3 = 7" represents the relationship between an unknown quantity x and the value 7. By solving this equation, we can find the value of x that makes the equation true. In this case, the solution is x = 2.

Identify elimination as the best method for the problem.

Find a variable with equal or opposite coefficients in the system.

Add or subtract one equation from the other.

Solve the one-variable equation.

Substitute the value of that variable into the other equation.

Solve for the second variable.

Check your answer. Use substitution and/or graphing.

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Answer:

How to calculate 8 + 3(5 - 7)​

Use Pemdas

Pemdas

8 + 3(5 - 7)​

5 - 7

= -2

8 + 3 ⋅ -2

Pemdas

8 + 3 ⋅ -2

3 x -2

= -6

8 + -6

Pemdas

8 + -6

Step-by-step explanation:

You're welcome.

Answer:

8+3(5-7)=-2

You will use the"Bracket Of Division Multiplication Addition and Subtraction(BODMAS)" method. Hence solve the one in the bracket first. So it's going to be 5-7 which is -2.Then you continue with the multiplication of 3 by the -2 you got making -6. Finally add the 8 to the -6 making 2.

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [2] + [3]

To write vector u as a linear combination of the vectors in set S, we need to find scalars a, b, and c such that:

u = a[1] + b[2] + c[-2]

Substituting the given values of u and the vectors in S, we get:

[3] = a[1] + b[2] + c[-2]

To solve for the scalars a, b, and c, we can set up a system of equations:

3 = a + 2b - 2c

Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:

a = 1, b = 1, c = 0

Substituting these values back into the equation, we get:

[3] = 1[1] + 1[2] + 0[-2]

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [1] + [2]

Similarly, for the second set of vectors, we need to find scalars d, e, and f such that:

u = d[2] + e[3] + f[-5]

Substituting the given values of u and the vectors in S, we get:

[8] = d[2] + e[3] + f[-5]

To solve for the scalars d, e, and f, we can set up a system of equations:

8 = 2d + 3e - 5f

Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:

d = 2, e = 2, f = 0

Substituting these values back into the equation, we get:

[8] = 2[2] + 2[3] + 0[-5]

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [2] + [3]

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Answer:

Using the rules of arithmetic, we can simplify the given expressions as follows:

-8 - (-6) = -8 + 6 = -2

-3 - (-7) = -3 + 7 = 4

6 - (-7) = 6 + 7 = 13

-2 - (-15) = -2 + 15 = 13

-12 - 3 = -15

-4 - 12 = -16

9 - (-5) = 9 + 5 = 14

Therefore, the simplified expressions are:

-2, 4, 13, 13, -15, -16, and 14.

The inequality is represented as t + b ≤ 102 , where t is the number of tacos and b is the number of burritos

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of tacos be = t

Let the number of burritos be = b

The total number of burritos or tacos be = 102

On simplifying , we get

t + b = 102

So , the maximum number of tacos and burritos to be sold is

t + b ≤ 102

Hence , the inequality is t + b ≤ 102

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18% of the total inventory was sold.

A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.

Given that, 30% of the inventory is sold over the weekend, on the second day only 15% of the inventory that was left in the store to be sold,

Let x be the total inventory,

Sold inventory = 30% of x,

The second day = x - 30% of x is sold

x -30% of x = 15% of x

x - 0.3x = 0.15x

x = 0.3x+0.15x

x = 0.18x

x = 18% of x,

Hence, 18% of the total inventory was sold.

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Answer:

Your answer:

6. x = 8

8. x = 3

Step-by-step explanation:

Basic calculation involving adding/subtracting and multiplying and dividing.

Formula for Area of a Rectangle:

Area = Length * Width.

6. Given information

A = 165 cm^2

length = 4x + 1

width = 5

(4x + 1) * 5 = 165 cm^2

5 * (4x + 1)= 165

20x + 5 = 165

20x = 160

x = 8

8. Given information

A = 40 cm^2

length = 7x - 1

width = 2

(7x - 1) * 2 = 40 cm^2

2 * (7x - 1)= 40

14x - 2 = 40

14x = 42

x = 3

The minimum number of people is not possible for the given situation operator has to revise the cost.

Let us consider the minimum number of people ride the Double Shot be x.

Cost per ride = $6.00

Revenue earned from the ride = $6.00x

Rental fee of the ride = ($200).

Safety inspection fee = ($65)

Cost of the rides  = 6x

⇒ Total Cost = $200 + $65 + ($6.00)x

Profit of at least $1,000 each day.

This implies,

Revenue ≥ Total Cost + Desired Profit

Substituting the expressions for revenue and total cost,

$6.00x ≥ $200 + $65 + ($6.00)x + $1,000

Simplifying the above expression we get,

$6.00x ≥ $1,265 + ($6.00)x

Subtracting ($6.00)x from both sides we get,

$0.00x ≥ $1,265

⇒No solution for x, because the number of riders cannot be negative.

⇒Operator must either increase the price per ride, decrease the costs, or revise their profit goal.

Therefore, for the given cost it is impossible to get the minimum number of people.

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The equation for the line of best fit is y = 5.43x + 76.41.

The correlation coefficient is 0.79

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the number of hours would be plotted on the x-axis of the scatter plot while the test scores would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the number of hours and test scores, a linear equation for the line of best fit is given by:

y = 5.43x + 76.41

In conclusion, the type of correlation between the variables is a strong positive correlation.

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The correct answer is: The confidence interval from the first simulation is (0. 149, 0. 195), and the confidence interval from the second simulation is (0. 180, 0. 230). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 149 and 0. 195. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 180 and 0. 230.

The confidence interval is a range of values that is likely to contain the true proportion of wins with the new game strategy based on the sample data.

A 95% confidence interval means that if the simulation is repeated many times, the proportion of wins with the new game strategy will fall within this range 95% of the time.

The correct interpretation of the confidence intervals is that for the first simulation, we are 95% confident that the true proportion of wins with the new game strategy is between 0.149 and 0.195.

This means that if we were to repeat the simulation many times, we would expect the true proportion of wins to fall between these values in 95% of the trials.

Similarly, for the second simulation, we are 95% confident that the true proportion of wins with the new game strategy is between 0.180 and 0.230.

Therefore, the correct answer is an option (b).

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The volume of the Cylinder is 24.11 cubic feet.

Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.

The radius of the cylinder is half the diameter of the circular base, so:

r = 2.6/2 = 1.3 feet

The volume of the cylinder is given by:

V = πr²h

Substituting the values given:

V = 3.14 × 1.3² × 4.4 ≈ 24.11 cubic feet

Rounding to the nearest hundredth:

V ≈ 24.11 cubic feet

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The correct answer is B. The graph shows the amount of water in a sink after several minutes, so it is a decreasing function.

Graph is a mathematical structure used to represent connections or relationships between objects. It consists of nodes, which are connected by edges. Graphs are used in computer science and other fields to represent networks of communication, data organization, computational devices, the flow of computation, and other objects. Graphs are also used to represent the abstract connections between objects in a more visual way. Graph theory is the study of graphs and their properties.

Option B, y = -3/2x + 5, is a linear function with a negative slope, which is the correct representation for this situation. This equation can be used to find the amount of water in the sink after any given number of minutes.

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The maximum profit is $165 per day when the business owner hires 40 employees.

To find the maximum profit, we need to find the vertex of the quadratic function f(x)= -0.1x2 + 8x +5. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -0.1 and b = 8.

x = -8/(2*-0.1) = -8/(-0.2) = 40

Now, we can plug in the x-value of the vertex into the function to find the maximum profit:

f(40) = -0.1(40)2 + 8(40) + 5 = -0.1(1600) + 320 + 5 = -160 + 320 + 5 = 165

Therefore, the maximum profit is $165 per day when the business owner hires 40 employees.

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Both the limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1. So, The function is continuous at x=1.

To determine if the function is continuous at x=1, we need to evaluate the left and right limits of the function at x=1 and see if they are equal.

Left limit as x approaches 1:

\lim_{x\to 1^-}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}

Right limit as x approaches 1:

\lim_{x\to 1^+}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}

Since both limits are indeterminate forms of 0/0, we can use L'Hopital's Rule to evaluate them.

Taking the derivative of the numerator and denominator of the original function, we get:

\lim_{x\to 1^-}\frac{4x-5}{1} = -1

\lim_{x\to 1^+}\frac{4x-5}{1} = -1

Both limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1.

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The sale price of a pair of dress shoes originally at $69.98 with a 25% discount will be $52.49.

To find the sale price, you need to calculate the discount amount and subtract it from the original price.

Step 1: Find the discount amount by multiplying the original price by the discount percentage.
$69.98 x 0.25 = $17.49

Step 2: Subtract the discount amount from the original price to get the sale price.
$69.98 - $17.49 = $52.49

Therefore, the sale price of the dress shoes will be $52.49.

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The values of sec x, csc x, and cot x are:

sec x = sqrt(61)/6

csc x = -sqrt(61)/5

cot x = -6/5

What is the Pythagoras Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right-angled triangle.

We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the terminal side and the x- and y-axes. Then, we can use the definitions of the trigonometric ratios to find the values of sec x, csc x, and cot x.

Let r be the length of the hypotenuse:

r = sqrt(6^2 + (-5)^2) = sqrt(61)

Then, we have:

cos x = adjacent/hypotenuse = 6/sqrt(61)

sin x = opposite/hypotenuse = -5/sqrt(61)

From these, we can find:

sec x = hypotenuse/adjacent = sqrt(61)/6

csc x = hypotenuse/opposite = -sqrt(61)/5 (Note that csc x is negative because sin x is negative in the third quadrant)

cot x = adjacent/opposite = -6/5

Hence, the values of sec x, csc x, and cot x are:

sec x = sqrt(61)/6

csc x = -sqrt(61)/5

cot x = -6/5

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