on the coordinate plane, triangle PQR is rotated 180* clockwise about the origin O

Answer:

x < 1.175

Step-by-step explanation:

-0.4x + 1.27 > 0.8

-0.4x > -0.47

x < 1.175

If the base of an isosceles triangle is 50 cm and the length of one of its legs is 65 cm, the height of the isosceles triangle is 60 cm.

To find the height of the isosceles triangle, we need to use the Pythagorean theorem and the properties of isosceles triangles.

First, we draw a diagram of the triangle and label the known values. We know that the base is 50 cm and one of the legs is 65 cm. Since the triangle is isosceles, the other leg is also 65 cm.

Next, we can draw a perpendicular line from the top vertex to the base, which represents the height of the triangle. We can label this height as "h".

Now, we have a right triangle with a base of 50 cm, a hypotenuse of 65 cm, and a height of "h". We can use the Pythagorean theorem to find the value of "h":

h² + 25² = 65²

h² + 625 = 4225

h² = 3600

h = 60

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Answer:

62.5%

Step-by-step explanation:

The number of states do not use nuclear: 20 + 12 = 32

The number of states that do not use nuclear and use coal: 20

so 20/32 = 5/8 = 62.5%

Using simple interest his interest is $ 1165.50  

Simple interest is given by I = PRT/100 where

Given that Tucker deposits an amount of $7400 in an account that pays 3.15 % simple interest. Since he keep the amount in the account for 5 years without making any withdrawal or deposits, we need to find the amount of interest after 5 years.

Using the simple interest formula,

I = PRT/100

Given that

So, substituting the values of the variables into the equation, we have that

I = PRT/100

I = $ 7400 × 3.15 % × 5/100

= $ 74 × 315 × 5/100

= $ 116550/100

= $ 1165.50

So, his interest is $ 1165.50  

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The real values of "a" that make (x - a) a factor of the given polynomial are: a = 3, a = 2, and a = 3/14.

To find the values of "a" for which (x - a) is a factor of the given polynomial x⁴ + 3x³ - 6x² - 28x - 24, we can use the Remainder Theorem.

So, let's divide the given polynomial by (x - a) and set the remainder to zero to find the values of "a".

Using long division or synthetic division, we get:

       x³ + (a - 3)x² + (3a - 6)x + (6 - 28a)

   __________________________________________

x - a | x⁴ + 3x³ - 6x² - 28x - 24

Since the remainder is zero, we have;

x³ + (a - 3)x² + (3a - 6)x + (6 - 28a) = 0

Now, for (x - a) to be a factor of the given polynomial, the coefficients of x², x, and the constant term must be zero, because these are the coefficients of (a - 3)x², (3a - 6)x, and (6 - 28a), respectively.

So, we can set them to zero and solve for "a":

a - 3 = 0 (Coefficient of x²)

3a - 6 = 0 (Coefficient of x)

6 - 28a = 0 (Constant term)

Solving these equations, we get:

a - 3 = 0 => a = 3

3a - 6 = 0 => 3a = 6 => a = 2

6 - 28a = 0 => 28a = 6 => a = 6/28 => a = 3/14

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Answer: 81mi^2

Step-by-step explanation:

Area Formula for Square: side * side

9*9 = 81

Hence, the rectangular prism has a surface area of 272 square centimetres.

For instance, by multiplying the length and breadth of a rectangle, the area of the shape can be determined. Pi (roughly 3.14), multiplied by the square root of the radius, can be used to get a circle's area. Calculating the size of numerous forms and figures, including triangles, circles, squares, and polygons, involves the usage of area, a key topic in geometry. The size of a piece of land, a building's floor area, or the surface of such an object are just a few examples of the many real-world uses for it.

given

We must add up the areas of all six faces of a rectangular prism in order to determine its surface area.

In this instance, the dimensions are as follows: width (w), length (l), and height (h), all in centimetres.

You can compute the surface area (A) as follows:

A = lw + lh + lw

Inputting the values provided yields:

A is equal to 2 (4 x 4 cm) + 2 (4 x 15 cm) + 2. (4 cm x 15 cm)

[tex]A=32 cm^2 + 120 cm^2 + 120 cm^2[/tex]

A = 272 cm²

Hence, the rectangular prism has a surface area of 272 square centimetres.

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Here are the general steps for using the u-substitution method to evaluate a definite integral:

1. Identify a part of the integrand that looks like the derivative of another function.

This is usually denoted as u, and u should be a function that is easy to integrate.

2. Replace the selected part of the integrand with u. In other words, substitute u for the expression inside the integral.

3. Take the derivative of u with respect to the variable of integration, and then multiply by dx to obtain du.

4. Replace dx with the expression in terms of du, using the relationship you found in step 3.

5. Rewrite the entire integral in terms of u and du, and simplify as much as possible.

6. Evaluate the integral using u and the limits of integration. Replace u with the original expression, and then evaluate the expression at the upper and lower limits of integration.

7. Substitute the values obtained in step 6 into the original equation to get the final answer.

The u-substitution method is a powerful technique for evaluating definite integrals.

The general idea behind the u-substitution method is to replace a complicated expression inside the integral with a simpler expression, which is equal to the original expression.

Here are the general steps for using the u-substitution method to evaluate a definite integral:

Let's take an example to illustrate these steps:

Evaluate the definite integral ∫[tex](2x + 1)^(3/2) dx from x = 1 to x = 2.[/tex]

Let u = 2x + 1.

Replace 2x + 1 with u in the integral to get ∫[tex]u^{3/2} dx.[/tex]

Take the derivative of u with respect to x to get du/dx = 2, and then multiply by dx to obtain du = 2dx.

Replace dx with 1/2 du.

Rewrite the entire integral in terms of u and du to get ∫[tex]u^{3/2} (1/2) du.[/tex]

Evaluate the integral using u and the limits of integration to get (2/5) [tex]u^{5/2}[/tex] from 3 to 5.

Substitute the values obtained in step 6 into the original equation to get the final answer, which is[tex](2/5) [(5^{5/2}- 3^{5/2}].[/tex]

Therefore, the value of the definite integral ∫[tex](2x + 1)^{3/2}[/tex]dx from x = 1 to x = 2 is approximately 6.243.

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Answer:

11.502

Step-by-step explanation:

The formula C6*D6 can be found in the cell E6. Option A is the correct answer.

A spreadsheet cell is a square region in a grid that can hold text, numbers, or formulas as well as other types of data. A unique cell address, which comprises of a column letter and a row number, is used to identify each cell. For instance, cell C4 is the cell in the third column and fourth row, and cell A1 is the top-left cell in the spreadsheet. Users can enter data, format cells, and use formulas to conduct calculations on the cells in a spreadsheet, among other tasks.

The formula C6*D6 can be found in the cell E6. Option A is the correct answer.

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The loan that will have a lower balance and the amount is D. The Stafford loan will have a lower balance by $274.54 at the time of repayment.

First, find the future balance of the PLUS Loan by the formula :

= Principal x ( 1 + monthly interest rate ) ^ number of months

= $ 11, 443.63 x ( 1 + 0. 005458 ) ⁶

= $ 11, 443.99

Then, find the future balance of the unsubsidized Stafford Loan with the same formula :

= 10, 720 x (1 + 0. 004958) ¹⁸

= $ 11, 169.46

This shows that the unsubsidized Stafford Loan would have a lower balance and the difference would be :

=  $11, 443.99 - $11, 169.46

=  $ 274.54

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Skewness measures the magnitude, degree, and direction of asymmetry in a distribution. It is an important tool for describing and understanding the shape of data distributions.

Skewness is a measure of the asymmetry of a distribution. It is a statistical measure that indicates the degree to which a distribution deviates from the symmetry of a normal distribution. Skewness can be either positive or negative, or it can be zero, indicating no skewness.

Magnitude, The magnitude of skewness is determined by the degree of asymmetry in the distribution. The larger the magnitude of skewness, the more asymmetrical the distribution is. A small magnitude indicates a distribution that is close to symmetric.

Degree, The degree of skewness is the extent to which the distribution deviates from symmetry. Positive skewness indicates a distribution with a longer right tail than left, while negative skewness indicates a distribution with a longer left tail than right.

Direction, The direction of skewness is the direction of the longer tail of the distribution. If the tail is to the right, the distribution is positively skewed, and if the tail is to the left, the distribution is negatively skewed.

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Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160).

1) Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160). Alternative hypothesis: The mean height of top-rated roller coasters is not 160 feet (Ha: u ≠ 160). The claim is the null hypothesis.

2) Sample mean = (325+188+306+107+208+167+105+78+140+232+230+170+170+205+305+135+200+200+100+223+135+195+80+90+120+210+82+161+245+88+70+116+121+146+149+124)/36 = 164.97 feet. The test statistic z = (x - μ) / (σ / √n) = (164.97 - 160) / (71.6 / √36) = 1.21.

3) The p-value is the probability of observing a test statistic as extreme as the one computed from the sample, assuming the null hypothesis is true. Using a standard normal distribution table, the p-value is 0.1131.

4) At α = 0.05, the p-value (0.1131) is greater than a. Therefore, we fail to reject the null hypothesis.

5) Based on the statistical analysis, we do not have sufficient evidence to reject the claim that the mean height of top-rated roller coasters is 160 feet.

6) Hypothesis testing is a statistical method used to make decisions based on the analysis of sample data. It is used to determine whether a claim or hypothesis about a population is supported by the evidence provided by the sample data.

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we can be sure that 6c + 3d will have a higher value than 4c + 2d if c and d are positive decimal numbers.

A variable in mathematics is a symbol or letter that is used to indicate a quantity in a mathematical statement or equation that can have many values. It is a symbol that may be used to represent an arbitrary or undefined integer in algebraic expressions and equations.

Both expressions have the same common factor of 2, so we can simplify them as follows:

4c + 2d = 2(2c + d)

6c + 3d = 3(2c + d)

Since c and d are positive decimal numbers, we know that both 2c + d and 3(2c + d) are positive. Therefore, the expression with the higher value will be the one with the larger coefficient, which is 3 in the second expression.

So, we can be sure that 6c + 3d will have a higher value than 4c + 2d if c and d are positive decimal numbers.

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Yes, the project consists on single set of ordered pairs numbered 1 through 30 on coordinate planes for all class students is a suitable one.

Ordered pair is a composition of the x- coordinate (i.e., abscissa) and the y coordinate (i.e, ordinate), that's two values written in a fixed order within. In mathematics, an ordered pair ( pair means two objects) so, (a, b) is a pair of objects in particular order. The order in the pair is very significant, that is ordered pair (a, b) is different from the ordered pair (b, a). Now, Ms. todd provide a project to students which consists a single set of ordered pairs numbered 1 through 30, for all students in her class. We can easily graph a ordered pair on coordinate plane. Coordinate plane is a 2-D graph made using x-coordinate and y-coordinate. There is two axis x-axis and y-axis. So, first they collect all possible ordered pairs from 1 to 30 like ( 1,1),( 1,2),(1,3),..........(1,30), (30,1),.....,(30,30) ... etc. In this coordinate plane consists 30 numbers value on y-axis and 30 on x-axis. Then, draw on graph. Hence, it is suitable.

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Answer: Luis will spend a total of $22,868.48 on his lease.

Step-by-step explanation: To calculate the total cost of Luis's lease, we need to multiply the monthly cost by the number of months in the lease:

Total cost = monthly cost x number of months

The number of months in 4 years is 4 x 12 = 48 months.

Therefore, the total cost of Luis's lease is:

Total cost = $475.86/month x 48 months

Total cost = $22,868.48

So Luis will spend a total of $22,868.48 on his lease.

The change in the perimeter is:

= 36m

The side lengths of a triangle are 3 meters,4 meters, and 5 meters.

We have to find the perimeter of the triangle.

Now,

Perimeter of a triangle is sum of all sides.

We have the side's length are:

[tex]P_1[/tex] = 3 + 4 + 5 = 12 meters.

Now, In the second case we have to multiplied the side length by 4.

Side's length are:

3 = 3 × 4 = 12

4 = 4 × 4 = 16

5 = 4 × 5 = 20

Perimeter of a triangle is sum of all sides.

[tex]P_2[/tex] = 12 + 16 + 20

[tex]P_2[/tex] = 48 meters

Now, the change in the perimeter is:

[tex]P_2 - P_1[/tex] = 48 - 12 = 36m

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According to the banker's rule, Amber can afford to borrow a maximum of $96,900.

The banker's rule is a guideline used by some lenders to determine the maximum amount that an individual can borrow based on their annual income.

According to the banker's rule, the maximum amount that can be borrowed is typically a multiple of the borrower's annual income.

The exact multiple used in the banker's rule may vary depending on the lender and the borrower's financial situation, but a common multiple used is 3.

Therefore, to calculate the amount that Amber can afford to borrow using the banker's rule, we can multiply her annual income by 3.

Given that Amber makes $32,300 annually, we can calculate the amount that can be borrowed using the banker's rule as follows:

Maximum amount that can be borrowed = Annual income * Banker's rule multiple

Maximum amount that can be borrowed = $32,300 * 3

Maximum amount that can be borrowed = $96,900

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Using Ariana's method to  work out 135 ÷  12 1/2 without a calculator will gives us:  54/5 or 10.8.

Ariana's method for division involves breaking down the divisor into a more manageable fraction and adjusting the dividend accordingly. Here's how we can use this method to solve 135 ÷ 12 1/2 without a calculator:

Step 1: Rewrite the mixed number as an improper fraction:

12 1/2 = 25/2

Step 2: Determine the reciprocal of the fraction:

25/2 → 2/25 (reciprocal)

Step 3: Rewrite the division problem as multiplication by the reciprocal:

135 ÷ 12 1/2 = 135 x 2/25

Step 4: Simplify the expression:

135 x 2/25 = (27 x 5) x 2/25 = 54/5

Therefore, 135 ÷ 12 1/2 = 54/5 or 10.8 when rounded to one decimal place.

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The estimated probability that the golfer will hit at least 4 times in his next 10 attempts is approximately 40%. So correct option is B.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It involves quantifying the chance or likelihood of an event happening, and it is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to happen.

Probability is often used in real-world situations to predict the likelihood of future events, make informed decisions, and understand patterns in data. It has many applications in various fields such as finance, physics, biology, and engineering.

To simulate the situation, we can use the table of random numbers to generate 10 digits, and count the number of times a digit is less than or equal to 3, which represents a hit for the golfer.

Using the table, we get the following sequence of digits:

26 53 48 69 55 23 44 72 89 55

Counting the number of hits, we get 4 hits out of 10 attempts. Therefore, the estimated probability that the golfer will hit at least 4 times in his next 10 attempts is approximately 40%.

So, the answer is B. Possible answer: 40%.

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The result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].

Rotation is a transformation in geometry that involves turning or spinning an object around a fixed point called the center of rotation. The center of rotation remains stationary while all the points of the object move along circular paths, at the same angle and distance from the center.

To rotate a point [x/y] counterclockwise by 90 degrees, we can use a 2x2 matrix of the form:

[ 0 -1 ]

[ 1 0 ]

To multiply this matrix by a point [x/y], we can use the following matrix multiplication:

[ 0 -1 ] [ x ] [ -y ]

[ 1 0 ] [ y ] = [ x ]

So, if we have a point [x/y] and we want to rotate it 90 degrees counterclockwise, we can multiply it by the matrix [ 0 -1 ; 1 0 ] to get the new point [-y/x].

To rotate a point 90 degrees counterclockwise using a matrix, we need to represent the point as a column matrix and then multiply it by the 2x2 rotation matrix.

Assuming that the point is [x, y] = [-5, 2], we can represent it as a column matrix:

| -5 |

| 2 |

To rotate the point counterclockwise by 90 degrees, we can use the following 2x2 rotation matrix:

| 0 -1 |

| 1 0 |

Multiplying the rotation matrix by the column matrix representing the point gives:

| 0 -1 | | -5 | | 2 |

| 1 0 | ×| 2 | = | -5 |

So the result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].

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Before doing calculations we can predict rectangular prism A has greater surface area to volume ratio than that of rectangular prism B.

The surface area of rectangular prism A is 136 square inches and that of B is 170 square inches. And  the ratio of surface area to volume of rectangular prism A is 1.4167 square inches/ cubic inches (approximately) and that of B is 1.1334 square inches/ cubic inches (approximately).

Rectangular prism A has dimension as,

length = 3 inches , breadth = 4 inches and height = 8 inches

Rectangular prism B has dimension as,

length = 5 inches , breadth = 5 inches and height = 6 inches

The surface area of rectangular prism can be calculated using the formula = 2( length*breadth + length*height + height*breadth)

Therefore, surface area of rectangular prism A = 2{ (3*4) + (3*8) + (4*8)} square inches =136 square inches (that is, 136 [tex]inches^{2}[/tex])

Surface area of rectangular prism B = 2{ (5*5) + (5*6) + (5*6)} square inches =170 square inches (that is, 170 [tex]inches^{2}[/tex])

The volume of rectangular prism can be calculated using the formula = length * breadth * height (in cubic unit)

Therefore, volume of rectangular prism A = (3)(4)(8) cubic inches =96 cubic inches (that is, 96 [tex]inches^{3}[/tex] )

Volume of rectangular prism B = (5)(5)(6) cubic inches =150 cubic inches (that is, 150 [tex]inches^{3}\\[/tex] )

Therefore, ratio of surface area to volume of rectangular prism A = (136/96) square inches/ cubic inches = 1.4167 square inches/ cubic inches (approximately)

Ratio of surface area to volume of rectangular prism B = (170/150) square inches/ cubic inches = 1.1334 square inches/ cubic inches (approximately)

Thus,  ratio of surface area to volume of rectangular prism A is greater than that of rectangular prism B.

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The approximate area of the sketch for the new lamp is : A = 70

We have,

A trapezium is one pair of parallel sides and one pair of non-parallel sides.

from the diagram we can extract the necessary information needed to find the area of the trapezium.

for the first trapezium (lamp shade)

a = 4 in

b = 6 in

h = 6 in

A1 = a+b/2 * h

   = 5 * 6 = 30

For the area of the second trapezium (lamp base)

a = 4 in

b = 6 in

h = 4 in

A2  =a+b/2  * h

      = 5 * 4 = 20

For the area of the third trapezium (lamp base)

a = 6 in

b = 4 in

h = 4 in

A3 = a+b/2  * h

     =  5 * 4 = 20

The total Area of the trapezium (lamp)

A =  A1 +  A2  + A3

A = 30 + 20 + 20

A = 70

In conclusion, The approximate area of the sketch for the new lamp is :

A = 70

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Answer:

x = -3

Step-by-step explanation:

[tex]-4x-5-11x=40\\-15x=40+5[/tex]

[tex]x=\frac{45}{-15}[/tex]

[tex]x=-3[/tex]

Hope this helps.

its 12.67 because like look at it this way

The probability of winning a giveaway with 73 entries and 2 winners is the fraction 2/73.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 73

the event of winning = 2

probability of winning the giveaway = 2/73

This means that each winner has a 2/73 chance of winning the giveaway.

Therefore, the probability of winning a giveaway with 73 entries and 2 winners is the fraction 2/73.

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Answer:

Step-by-step explanation:

I do believe you should most definitly add units

The simplification that accurately explains the statement 73 = 713A is A = 73/713

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

7 3 = 7 1 3 A.

Express properly

So, we have

73 = 713A

Divide both sides of the equation by 713

So, we have

A = 73/713

Hence, the simplification that accurately explains the statement is A = 73/713

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The fewest number of minutes it will take Jeremy and Michael to solve 10 Rubik's cube is 16 with a speed such that Jeremy solve one in 4 minutes and Michael solves 5 in 12 minutes.

To solve the following word problem,

Time taken by Jeremy to solve one cube = 4 minutes = 240 seconds

Time taken by Michael to solve 5 cubes = 12 minutes

Time taken by Michael to solve 1 cube = [tex]\frac{12}{5}[/tex] minutes = 144 seconds

Since one solves the cube alone, they do it individually,

For the first 12 minutes,  Michael solves 5 cubes and Jeremy solves 3 cubes ([tex]\frac{12}{3}[/tex])

Then, to solve 2 or more cubes Michael takes 288 seconds

And if Michael and Jeremy each solve one cube it takes them 144 seconds and 240 seconds respectively.

Therefore, the second situation is responsible for solving in the least time which comes out to be 12 minutes + 4 minutes (240 seconds) is 16 minutes.

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