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Answer: 21

Step-by-step explanation:

The vector that satisfies the equation v = 2u - 3w, where u = (5, -4) and w = (4, -2), is v = (-2, -2).

A vector is a mathematical quantity that represents a magnitude (length) and direction in space, usually represented as an ordered set of numbers or coordinates, used to describe physical quantities and geometric objects.

An equation is a mathematical statement that indicates the equality of two expressions or quantities, often containing variables, used to describe relationships and solve problems in various fields of mathematics and science.

According to the given information:

To find the vector that satisfies the given equation:

v = 2u - 3w

we need to first calculate the vectors u and w using the given points:

u = (5 - 0, 1 - 5) = (5, -4)

w = (4 - 0, 3 - 5) = (4, -2)

Substituting these values into the equation:

v = 2u - 3w

v = 2(5, -4) - 3(4, -2)

v = (10, -8) - (12, -6)

v = (-2, -2)

Therefore, the vector that satisfies the given equation is (-2, -2).

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The point on the number line that has a value that is the opposite of 15 must be -15

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

Point = 15

The opposite of 15 is

Opposite = -15

This means that the point must have a value of -15

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The probability that the randomly selected person attending the concert is an adult or has purchased the ticket in advance is 188/250.

We have,

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given a table which shows when the tickets for a concert are sold and the types of tickets that are sold.

The probability of A or B can be calculated as,

P(A or B) = P(A) + P(B) - P(A and B)

Let A denote the people is an adult.

Let B denote the people who has purchased the ticket in advance.

P(A) = 148/250

P(B) = 140/250

P(A and B) = 100/250

Probability that a randomly selected person attending the concert is an adult or has purchased the ticket in advance is,

P(A or B) = 148/250 + 140/250 - 100/250

              = 288/250 - 100/250

              = 188/250

Hence the required probability is 188/250.

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Answer: y + 6 = -4 (x+2)

Step-by-step explanation:

Answer:

9 Prizes

Step-by-step explanation:

She begins with 420 tickets.

She goes on 2 rides for 75 tickets each so 420-75-75= 270

She then attends the concert for 180 tickets so 270-180= 90

Now she is left with 90 tickets. 10 tickets = 1 prize therefore you can do 90/10 = 9

9 PRIZES

The time it will take for the money in the account to reach $4,000 is about 15.407 years.

To solve for the number of years it takes for the amount in the account to reach $4,000, we need to solve the equation:

[tex]4000 = 2000e^{0.045t[/tex]

Dividing both sides by 2000, we get:

[tex]2 = e^{(0.045t)[/tex]

To solve for t, we can take the natural logarithm of both sides:

[tex]ln 2 = ln e^{(0.045t)[/tex]

Using the property that ln [tex]e^x = x[/tex], we can simplify this to:

[tex]ln 2 = 0.045t[/tex]

Dividing both sides by 0.045, we get:

t = (ln 2)/0.045

Using a calculator, we can evaluate this expression to get:

[tex]t = 15.407[/tex]

Therefore,  it will take about 15.407 years for the amount in the account to reach $4,000.

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The sum of the measures of the interior angles of the pentagon is given as follows:

540º.

Hence the angle measures are given as follows:

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

A pentagon has five sides, that is, n = 5, hence the sum is given as follows:

S(5) = 180 x (5 - 2)

S(5) = 540º.

Then the value of x is obtained as follows:

x + 40 + 80 + x + 50 + x + 5 + 125 = 540

3x + 300 = 540

3x = 240

x = 80º.

Then the angle measures are given as follows:

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The equation that shows the point-slope form of the line which passes through (3, 2) is: y - 2 = (x - 3).

The equation of any straight line on a coordinate plane can be expressed in point-slope form as:

y - b = m(x - a), where (a, b) is a point and m is the slope of the line.

Given the point a line goes through as (3, 2), which also has a slope (m) of 1, to find the equation of the line in point-slope form, substitute a = 3, b = 2 and m - 1 into y - b = m(x - a):

y - 2 = 1(x - 3)

y - 2 = (x - 3)

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The length of the missing side is 3 < x < 13.

We have, two measurement of triangle is 9 and 6 unit.

Also, we know that the length of third side of a triangles lies in between the sum of sides and difference of sides.

So, Sum of sides = 9 + 6= 13 unit

Difference of side= 9-6 = 3 unit

Then, the measure of third side is 3 < x < 13.

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a) There are 720 different ways to arrange all six tables in a row. b) There are also 15 other methods to select four of the six tables.

A combination is a technique for calculating the number of alternative arrangements in a set of objects where the order of the selection is irrelevant.

Given this,

Mrs. Smith wants to arrange six activity tables side by side in her classroom.

After aligning all six tables in a straight line, we can use the factorial function to compute the product of all positive integers up to a specified value. We could write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

As a result, there are 720 different ways to arrange all six tables in a row.

And, to select four of the six tables, we can use the combination function, which computes the number of ways to select k things from n different items, regardless of their order. We could write:

⁶C₄ = 6! / (4! x 2!)

= (6 x 5 x 4 x 3 × 2 × 1) / [(4 x 3 x 2 x 1) × (2 × 1)]

= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)

= 15

As a result, there are 15 different methods to select four of the six tables.

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The number of stamps that Jessica and Bonita have altogether if the percent increase in stamps with Bonita is 15% more is 2150.

Given that,

Bonita has 15 percent more stamps than Jessica.

Let x be the number of stamps that Jessica has.

Then,

Number of stamps that Bonita has = x + 150

x + 150 = x + 15% of x

x + 150 = x + (0.15)x

x + 150 = 1.15x

0.15x = 150

x = 1000

Hence the number of stamps that Jessica has = 1000

Number of stamps that Bonita has = 1150

Total number of stamps = 1000 + 1150 = 2150

Hence the total number of stamps is 2150.

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The class width is 0.3877.

In order to analyze data, it is often helpful to group it into categories, or intervals, and then determine how frequently each interval occurs. This process is known as frequency distribution.

To calculate the class width, you need to determine the range of each interval. The range is the difference between the upper and lower limits of the interval. For example, the first interval is 160-179, so the range is 179-160=19.

In mathematical terms, the formula for class width is:

Class Width = (Range of all intervals) / (Number of intervals)

In your case, the range of the intervals are:

19, 19, 19, 19, and 19

And the number of intervals is:

53 + 24 + 93 + 27 + 48 = 245

So, the class width can be calculated as follows:

Class Width = (19+19+19+19+19) / 245

Class Width = 95 / 245

Class Width = 0.3877

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Complete Question:

The data given below is for 245 randomly selected 10-minute intervals, where the number of people entering the atrium of a large mall were recorded. Calculate the class width.

Number of Guests         Frequency

160 - 179                                 53

180- 199                                 24

200 - 219                              93

220 - 239                              27

240 - 259                             48

Answer:

25%

Step-by-step explanation:

Answer:

The statement that best defines a circle is:

C. The set of all points that are the same distance from a given point called the center.

A circle is a geometric shape consisting of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. Therefore, a circle is defined as the set of all points that are the same distance (equal to the radius) from a given point (the center).

Answer: The answer should be B

paint 1 house in = 6 days

paint ? house in = 222 days

= 222 ÷ 6 = 37 houses

Answer: A painter can paint 37 houses in 222 days

The Mean Absolute Deviation of the given data set, 58, 38, 54, 48, 26, 36 is 10

From the question, we are to calculate the mean absolute deviation of the given data set

The given data set is:

58, 38, 54, 48, 26, 36

First, we will determine the mean of numbers

Mean = (58 + 38 + 54 + 48 + 26 + 36) / 6

Mean = 260 / 6

Mean = 43.33

To calculate the MAD, we will determine the absolute deviation of each data from the mean

|58 - 43.33| = 14.67

|38 - 43.33| = 5.33

|54 - 43.33| = 10.67

|48 - 43.33| = 4.67

|26 - 43.33| = 17.33

|36 - 43.33| = 7.33

Now, we will calculate the mean of the absolute deviations

MAD = (14.67 + 5.33 + 10.67 + 4.67 + 17.33 + 7.33) / 6

MAD = 60/6

MAD = 10

Hence, the MAD is 10

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The total selling price, as per the percent rule, is $9,000.

You must first determine the selling price of each toy in order to determine the overall selling price.

As per the percent rule, the cost price plus the markup equals the selling price.

The cost price of each toy is $24, so the markup is 25% of $24, which is $6.

Therefore, the selling price of each toy is $24 + $6 = $30.

To find the total selling price, you need to multiply the selling price of each toy by the number of toys sold.

The store bought 300 toys, so the total selling price is 300 x $30 = $9,000.

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Answer: $4,580

Step-by-step explanation:

First, we need to calculate the monthly payment for the 15-year, fixed-rate loan at the original rate of 5.05%. We can use the formula for the monthly payment of a mortgage loan:

P = L[c(1 + c)^n]/[(1 + c)^n - 1],

where P is the monthly payment, L is the loan amount, c is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of payments (which is the number of years multiplied by 12).

Plugging in the given values, we get:

L = $137,000

c = 0.0505/12 = 0.0042083 (rounded to 7 decimal places)

n = 15 x 12 = 180

P = $1,071.18

Next, we need to calculate the monthly payment at the lower rate of 4.81% if the buyers purchase four points. Each point costs 1% of the loan amount, so four points will cost 4% of the loan amount.

The new rate after purchasing four points is:

5.05% - 0.24% = 4.81%

The new loan amount after purchasing four points is:

$137,000 - (4% x $137,000) = $131,920

Using the same formula for the monthly payment, but with the new values for the loan amount and monthly interest rate, we get:

L = $131,920

c = 0.0481/12 = 0.0040083 (rounded to 7 decimal places)

n = 15 x 12 = 180

P = $1,030.98

The monthly savings due to the lower interest rate is:

$1,071.18 - $1,030.98 = $40.20

To calculate the cost of the four points, we need to divide the upfront cost of the points by the monthly savings:

Cost of four points = ($40.20 x 180)/0.0024 = $3,015

Therefore, the cost of the four points is $3,015, which is closest to $4,580.

The four points that the homebuyers are purchasing to lower their rate from 5.05% to 4.81% will cost them D. $5,480.

The points purchased for loans are charges that the borrower pays upfront to lower their interest rates.

Each point equals a percentage of the loan amount.

For example, four points on a $137,000 loan are 4 percent of the loan amount, or $5,480.

The loan amount for the purchase of the condominium = $137,000

Fixed interest rate = 5.05%

Loan period = 15 years

Loan option rate = 4.81%

Hence, Four points =  $137,000 x 4%

                              = $5,480

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Answer: The monthly payment for the sailboat is $348.14, and the total interest paid over the 12-year period is $13,080.16.

Step-by-step explanation: To calculate the monthly payment and interest for the sailboat, we can use the formula for the present value of an annuity due:

PV = PMT * [(1 - (1 + r)^(-n)) / r] * (1 + r)

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.

First, we need to calculate the present value of the sailboat after the down payment:

PV = $35,000 - (0.2 * $35,000) = $28,000

Next, we can plug in the values and solve for PMT:

$28,000 = PMT * [(1 - (1 + 0.0875/12)^(-12*12)) / (0.0875/12)] * (1 + 0.0875/12)

Simplifying this equation, we get:

PMT = $348.14

Therefore, your monthly payment for the sailboat would be $348.14.

To calculate the total interest paid, we can multiply the monthly payment by the total number of payments (12 years * 12 months/year = 144 payments) and subtract the principal amount:

Total Interest = (PMT * n) - PV

Total Interest = ($348.14 * 144) - $28,000

Total Interest = $13,080.16

Therefore, you would pay a total of $13,080.16 in interest over the 12-year period.

I'm assuming you mean y = [3x+5], wherein the brackets signify the biggest integer function (also known as the floor function).

What exactly are function and example?

A function was a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter something for x, you will only get a single result for y. Because x represents the input value, we can say as y represents a function of x.

To graph this formula, we must plot points which satisfy the conditions, where y is the largest integer that is equal or less than to 3x+5.

Let's begin by examining some specific x values:

When x equals -2, y equals [3(-2)+5]. = [-1] = -1

When x equals -1.5, y equals [3(-1.5)+5]. = [-0.5] = -1

When x equals -1, y equals [3(-1)+5]. = [2] = 2

y = [3(-0.5)+5] for x = -0.5. = [3.5] = 3

When x = 0, y equals [3(0)+5]. = [5] = 5

When x equals 0.5, y equals [3(0.5)+5]. = [6.5] = 6

When x equals 1, y equals [3(1)+5]. = [8] = 8

When x equals 1.5, y equals [3(1.5)+5]. = [9.5] = 9

When x equals 2, y equals [3(2)+5]. = [11] = 11

We can draw points on a chart and link them to construct a line using these values:

        |

  12    |

        |

  11    |             x=2

        |

  10    |

        |

   9    |             x=1.5

        |

   8    |             x=1

        |

   7    |

        |

   6    |             x=0.5

        |

   5    |             x=0

        |

   4    |

        |

   3    |

        |

   2    |             x=-1

        |

   1    |

        |

   0____|_____________

       -2   -1   0   1   2

It's worth noting that the graph is made up of a succession of horizontal lines with "jump" points wherein 3x+5 is a number.  The graph meets the x-axis at the following locations: (-5/3), where the biggest integer was -2, and each subsequent intersection happens at x & (-5/3) + (1/3) & (-4/3), (-5/3) + (2/3) & (-1/3), (-5/3) + (3/3) & 0, (-5/3) + (4/3) & (1/3), and so on.

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The factors are (x+6) (x-6), 3(x+4) (x-4), (x+3) (x+3) and 4(x+3)(x-5)

Given that are polynomial, we need to find their factors,

a) x²-36 =

We know that a²-b² = (a+b) (a-b)

So, x²-36 = x²-6² = (x+6) (x-6)

b) 3x²-12 =

3(x²-4²) = 3(x+4) (x-4)

c) x² + 6x + 9

= x² + 3x + 3x + 9

= x(x+3) + 3(x+3)

= (x+3) (x+3)

d) 4x² - 8x - 60

= 4(x²-2x-15)

= 4(x²-5x+3x-15)

= 4{x(x-5) +3(x-5)}

= 4(x+3)(x-5)

Hence, the factors are (x+6) (x-6), 3(x+4) (x-4), (x+3) (x+3) and 4(x+3)(x-5)

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The volume of the oblique rectangular prism  is 629.1 unit² .

The length of the oblique rectangular prism = 6 unit

The width of the oblique rectangular prism = 9 unit

Using trigonometry the height will be

tan θ = perpendicular / base

Perpendicular = h

Base = 9

h/9 = tan (59)

h = 1.66 (9)

h = 11.6 unit

The height of the oblique rectangular prism = 11.6 unit  

The volume of the oblique rectangular prism = l × b ×h

The volume of the oblique rectangular prism = 6 × 9 ×11.6

The volume of the oblique rectangular prism = 629.1 unit²

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Answer:

To convert radians to degrees, we use the conversion factor which is:

1 radian = 180/π degrees

To convert 11π/12 radians to degrees, we can multiply by the conversion factor:

11π/12 radians × 180/π degrees/radian = 990/π degrees

This is the exact value in degrees. If we want a decimal approximation, we can use a calculator to evaluate:

990/π degrees ≈ 315.944 degrees

Therefore, 11π/12 radians is approximately equal to 315.944 degrees.

Answer:

0 they cancel each other out..

Step-by-step explanation:

The expression -4x + 4x simplifies to zero:

-4x + 4x = (-4 + 4)x = 0x = 0

Therefore, the result is zero.

Option 1, 3 and 6 are the proper subsets of the set U = {a, c, e, g, i, k}.

The subsets of U that do not include all of its components are the correct subsets of U. Given that it doesn't include any items of U, Option 1, A = empty set, is a valid subset of U. In the case of option 2, B = "a, c, e, g, i, k" is the set U itself and is not a legitimate subset of U because it contains all of U's components.

Now, option 4, D = {b, d, f, h}, is not a subset of U as it contains elements that are not in U. Option 5 is not correct as it includes both A and B, which is not a proper subset of U. In option 6, both 1 and 3 are given, hence, it is correct.

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Complete question - If U = {a, c, e, g, i, k} then which of the following are proper subsets of U?

Choose one  4 points

1. A = emptyset

2. B = {a, c, e, g, i, k}

3. C = {a, c, e, g}

4. D = {b, d, f, h}

5. Set A, set B and set C

6. Set A, and set C

1/5 ÷3 is equal to 1/15

I hope this helps

Answer:

Step-by-step explanation:

yees

Property of logarithms: The property of logarithms that we used in this problem states that if loga(b) ≥ loga(c), then b ≥ c. This property is true for any base of the logarithm. Note that the inequality symbol flips when you move from the logarithmic expression to the exponential expression.

Solving linear inequalities: To solve a linear inequality like ax + b > c, you need to isolate the variable on one side of the inequality. This involves adding or subtracting terms and possibly multiplying or dividing by constants. You need to be careful when multiplying or dividing by a negative number, as this flips the inequality symbol.

Domain restrictions: When solving logarithmic inequalities, you need to make sure that the argument of the logarithm is positive. This means that the expression inside the logarithm cannot be zero or negative. You need to check for domain restrictions and make sure that any values that make the argument zero or negative are not included in the solution.

Check the solution: After solving the inequality, it's always a good idea to check the solution to make sure that it satisfies the original inequality. You can plug in the solution to the inequality and make sure that both sides of the inequality are still true. If not, you may have made a mistake in solving the inequality.

To solve log2(7x-3) ≥ log2(x+12), you can start by using the fact that if loga(b) ≥ loga(c), then b ≥ c:

Using this property, you can rewrite the inequality as:

7x - 3 ≥ x + 12

Simplifying the inequality by subtracting x and adding 3 from both sides, you get:

6x ≥ 15

Dividing both sides of the inequality by 6, you get:

x ≥ 2.5

Therefore, the solution to the inequality is x ≥ 2.5 which is option C.

Note that when you use the property of logarithms to simplify an inequality, you need to make sure that the argument of the logarithm is positive. In this case, both arguments are positive as long as x > 3/7 and x > -12, respectively. However, these conditions are automatically satisfied when x ≥ 2.5, so there is no need to check them separately.

The correct option about the two data set's distribution is B) The distributions are somewhat similar.

Given that,

For data set 1,

Mean = 54 and MAD = 4

For data set 2,

Mean = 60 and MAD = 2

Means to MAD ratio = (60 - 54) / (2 - 4) = 6 / -2 = -3

So means to MAD ratio is -3, not 3.

Now, it is clear that the distributions are not fully similar.

But it appears to be somewhat similar since Mean absolute deviation is somewhat similar, which is close.

Hence the correct option is B.

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