Parent-teacher interviews were held on
Thursday. Of those parents who
attended, 1/6 attended in the morning,
1/3 attended in the afternoon,
and the rest attended in the evening.
a) What fraction of the parents
attended in the evening?
b) Thirty parents attended the
interviews. How many parents
attended in the evening?

The probability that a sample of size 16 will have a sample mean greater than 82.5 is 0.006 or 0.6%.

We will use the standard normal distribution (also known as the z-distribution) which is a normal distribution with a mean of 0 and a standard deviation of 1.

We first need to convert the sample mean of 82.5 to a z-score. To do this, we use the following formula:

z = (x - μ) / σwhere x is the sample mean, μ is the population mean, and σ is the population standard deviation.

So, the z-score of 82.5 is:

z = (82.5 - 80) / 10 = 2.5

Now we can use the z-score to find the probability using a standard normal table or calculator. The probability of a sample mean greater than 2.5 is the area under the curve to the right of 2.5.

Using a calculator or standard normal table, we can find that the probability that a sample of size 16 will have a sample mean greater than 82.5 is 0.006 or 0.6%.

So the probability that a sample of size 16 will have a sample mean greater than 82.5 is 0.006 or 0.6%.

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Answer:

The sales tax is 91 cents.

Step-by-step explanation:

15.10 x 0.06= $0.906 (approx. 0.91)

Answer:

A side of a square is represented by 2.5x-3 and a side of an equilateral triangle is represented by 2x-2.

If the perimeter of the square and the equilateral triangle are the same, then we can set the perimeter of the square equal to the perimeter of the triangle:

4(2.5x-3) = 3(2x-2)

Expanding the equation and combining like terms we get:

10x - 12 = 6x - 6

Subtracting 6x from both sides we get:

4x - 12 = -6

Adding 12 to both sides we get:

4x = 6

Dividing both sides by 4 we get:

x = 3/2

With x = 3/2, we can find the perimeter of the square by plugging it back into the equation for the side of the square:

4(2.5(3/2) - 3) = 4(3.75 - 3) = 4(.75) = 3

And we can find the perimeter of the equilateral triangle by plugging it back into the equation for the side of the triangle:

3(2(3/2) - 2) = 3(3 - 2) = 3(1) = 3

So the perimeter of the square is 3 units and the perimeter of the equilateral triangle is also 3 units.

The value that is added on the left-hand side to make the equation equal is -1/100.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows: multiplication, division, addition, and subtraction.

Given [1/-2  - 3/4  of -8/15],

to add a number so the sum equals the product of -7/50 and 11/14

let the number be x

according to the question,

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

taking LHS

[1/-2  - 3/4  of -8/15] = -1/2 - (3(-8)/60)

[1/-2  - 3/4  of -8/15] = -1/2 + 24/60

[1/-2  - 3/4  of -8/15] = (-30 + 24)/60

[1/-2  - 3/4  of -8/15] =-6/60 = -1/10

RHS

-7/50*11/14 = -77/700 = -11/100

substitute the values

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

-1/10 + x = -11/100

x = -11/100 + 1/10

x = (-11 + 10)/100

x = -1/100

Hence -1/100 is added to make the equation equal.

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The inequalities whose symbol will be reversed are -4.5c > 9 and -21/5 ≤ -5/2d

A relationship between two expressions or values that are not equal to each other is called inequality.

Given are given some inequality,

We know that, when anytime you are multiplying or dividing an inequality by a negative, you must reverse the inequality symbol

-4.5c > 9 will have its inequality symbol reversed

-21/5 ≤ -5/2d will have its inequality symbol reversed

Hence, the correct options are -4.5c > 9 and -21/5 ≤ -5/2d

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A unique solution occurs in a set of linear simultaneous equations if and only if (a) the number of unknowns and equations are equal, (b) all equations are consistent, and (c) there is no linear dependency between any two or more equations, that is, all equations are independent.

If a pair of linear equations is consistent with a unique solution, then their lines intersect.

The unique solution of a linear equation denotes the existence of just one point at which the L.H.S. and R.H.S. of an equation become equal when substituted. A linear equation with one variable always has a unique solution.

A one-of-a-kind solution is the sole solution. In your case, if (x0,y0) solves your problem, it is said to be unique if the following condition is true: if (x1,y1) solves the equation, it implies x0=x1,y0=y1.

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Answer: 6 books

Step-by-step explanation:

42 divided by 7 equals 6, which is how many books he read each month, considering the books per month are proportional.

Answer: 6 books a month

Step-by-step explanation: If Roberto reads the same amount of books a month, then the answer is simple to achieve.

42 / 7 = 6

42 books divided over 7 months equals 6 books a month.

The answer to the equation would be the simplified equation of y = 3 / 8x - 4.

A mathematical statement that proves two mathematical expressions are equal is what an equation in algebra is defined as in its most basic form.

The equation given is a linear equation which means that it would normally take the form of :

y = MX + c

By taking the form, 3x - 8y = 32, the equation is in the form:

MX - y = c

This can be changed to become :

3x - 8y = 32

3 x - 32 = 8y

3 / 8 x - 32 / 8 = y

y = 3 / 8x - 4

Therefore, The answer to the equation would be the simplified equation of y = 3 / 8x - 4.

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The complete question is:

What is the solution of equation 3x - 8y = 32?

Answer: 7

Step-by-step explanation:

Multiple all terms by the same value to eliminate fraction denominators.

2.5 = W/2.8

14 * 2.5 = 14 * w/14/5

Cancel multiplied terms that are in the denominator.

14 * 2.5 = 14 * w/14/5

14 * 2.5 = 5w

Multiply the numbers.

14 * 2.5 +5w

35 = 5w

Answer: The inequality 4x ≤ 34 can be used to find the numbers of boxes of cookies, x, Freeman can buy with $34. The statement "x is a whole number less than or equal to 8.5" describes all the possible numbers of boxes of cookies Freeman can buy with $34.

Because 34 ÷ 4 = 8.5, Freeman can buy 8 boxes of cookies at most. Since x is the number of boxes, x is a whole number so Freeman can buy 8 boxes of cookies or less.

Step-by-step explanation:

This tip can be used for C. Multiple-choice questions.

The tip "If your answer is not among the choices, try writing it in a different form" is most applicable to multiple-choice questions on the math section of the PSAT.

This is because multiple-choice questions typically give a set of answer choices to select from, and if the student's calculation or solution does not match any of the choices, they can try to rewrite it in a different form that may match one of the choices.

For example, if the question asks for the solution of an equation in simplified radical form and the student's answer is in decimal form, the student can try converting their answer to simplified radical form.

This tip is not as useful for Grid-in questions, Matching sections, or Fill-in-the-blank questions since the answer is not given in multiple choices and the student needs to write the answer themselves.

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Complete question is given as:

Read the following tip. "If your answer is not among the choices, try writing it

in a different form." For which questions on the math section of the PSAT

could you use this tip?

A. Grid-in questions

B. Matching sections

4

C. Multiple-choice questions

D. Fill-in-the-blank questions

Answer:

multiple choice questions

Step-by-step explanation:

This is a sequence of numbers where each number is determined by the number that comes before it.

a(1) = 1, a(2) = 2, a(3) = -1, a(4) = -4, a(5) = 7

b(1) = 1, b(2) = -1, b(3) = -3, b(4) = -5, b(5) = -7

c(1) = 1, c(2) = 3, c(3) = 7, c(4) = 15, c(5) = 31

d(1) = 1, d(2) = 2, d(3) = 5, d(4) = 26, d(5) = 677

f(1) = 1, f(2) = 3, f(3) = 6, f(4) = 11, f(5) = 18

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Answer:

b = 3. (x + 3)(x2 - x ⋅ 3 + 32) = 0 Simplify. Tap for more steps... (x + 3)(x2 - 3x + 9) = 0

hope you like it : )

The final statement is: a) the ball hits the ground after 2 seconds b) the highest point is 5 m 3) It takes t=1 to reach the highest point.

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here: The height is given by y=10x-5x²

When height y=0 therefore

0=10x-5x²

5x²=10x

5x=10

x=2

The ball hits the ground after 2 seconds and the highest point is at t=1

with maximum height=5 m

Hence, the graph reaches its maximum point at (1,5)

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The value of Sin(θ/2) is √(17/20)      

From trigonometric ratios, the half-angle formula is given by  

When the θ/2 is in the 1st or 2nd quadrants, the result of Sin(θ/2) will be positive. When θ/2 is in the 3rd or 4th quadrants, the result Sin(θ/2) will be negative.  

Here we have cosθ = -7/10  

By the given formula,

Sin(θ/2) = ± √((1 + 7/10)/2)    

= ± √((17/10)/2)    

= ± √(17/20)    

Given that 90º < θ < 180°, θ/2 will lies in 1st or 2nd quadrants  

Sin(θ/2) = + √(17/20)      

Therefore,

The value of Sin(θ/2) is √(17/20)      

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Answer: 388872

Step-by-step explanation: take 396000 divide it by 98.2%

The four numbers that Rhys wrote down are 7 , 7 , 5 , 2 .

What is mean ?

mean can be defined as the ratio of sum of the observations and total number of observations.

Given ,

Rhys wrote down four whole numbers.

The mode of the four numbers is 7

The median of the four numbers is 6

The range of the four numbers is 5

The mode is 7 so atleast for 2 times it may be repeated.

so,

let another two numbers be x , y .

the numbers could be

7,7,x,y.

so given median = 6

so,

the elements will be arranged in either ascending order or descending order,

so,      7 , 7 , 5 , 2 .

median = 7+5 / 2 = 6

which satisfies the condition

Range = Greatest number - smallest number

= 7 - 2 = 5

Hence, the range also satisfies.

Therefore , the four numbers that Rhys wrote down are 7 , 7 , 5 , 2 .

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On solving the provided question we can say that area of trapezium = a+b/2 X h = 7+5/2 X 4 = 6X 4 = 24 sq units

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is known as Trapezium in the United Kingdom and other English-speaking countries. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's base is defined as its parallel sides. An identical one set of opposite sides that are parallel to one another define a trapezoid, a convex quadrilateral. When drawn on paper, the two-dimensional trapezoid shape resembles a table. A polygon with four sides and four vertices is referred to as a quadrilateral in Euclidean geometry.

here,

area of trapezium = a+b/2 X h

7+5/2 X 4

6X 4 = 24 sq units

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Answer:

f(x) increases from -9 to -0.5 and from 3 to 5.

Step-by-step explanation:

See the attached graph.

The probability of having a 10-digit number whose sum of digits is divisible by 10 is around 52 %. To find the probability that the sum of the digits of a 10-digit number is divisible by 10, we can first find the number of 10-digit numbers whose digits sum to a multiple of 10 and then divide by the total number of 10-digit numbers.

To find the number of 10-digit numbers whose digits sum to a multiple of 10, we can consider the possible values that the units digit can take. The units digit must be 0 or 5 to make the sum of the digits a multiple of 10.

For the units digit to be 0, the sum of the remaining 9 digits can be any multiple of 9 (since 9 is a factor of 10). There are 9 possible digits (0-9) to choose from for each remaining digit, so there are 9^9 ways to arrange the remaining 9 digits. For the units digit to be 5, the sum of the remaining 9 digits can be any multiple of 9 plus 5.

There are 9 possible digits (0-9) to choose from for each remaining digit, and there are 9 ways to choose the position of the 5.

Therefore, the total number of 10-digit numbers whose digits sum to a multiple of 10 is

[tex](9^9 + 9*9^8) / 10^10 = (478296875 + 43046721) / 10000000000 = 478296875/10000000000 + 43046721/10000000000 = 0.478296875 + 0.043046721 = 0.521343596[/tex]

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The x value for the point located 2/3 the distance from A to B is 2.67. This can be found by calculating the midpoint between A and B, which is (2, 1.5), and then taking 2/3 of the x component (2).

1. Calculate the midpoint between A and B: (0 + 4) / 2 = 2 and (0 + 3) / 2 = 1.5

2. Take 2/3 of the x component of the midpoint: 2/3 * 2 = 2.67

The  value x for the point located 2/3 the distance from A to B can be found using a few simple steps. First, we need to calculate the midpoint between A and B. This can be done by adding the x and y components of the two points and then dividing by 2. For our points A and B, this gives us the midpoint (2, 1.5). Now, we need to take 2/3 of the x component of the midpoint (2). This gives us 2/3 * 2 = 2.67. This means that the x value for the point located 2/3 the distance from A to B is 2.67. This process can also be used to determine the y value for the point, which is 1.

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When a variable can be substituted with a number to produce a true number statement, that number is the solution to the equation.

x = 10m - 1800° ACB / A(10A5 - 540° CB): 10A5 + 540° CB ≠ 0.

m/A = A {5x+18}° (3x + 10) C B

m/A = A5x + 18° (3x + 10 )CB : x = 10m - 1800° ACB / A(10a5 + 540° CB;

10A5 + 540° CB ≠ 0

m / A = A5x + 18° (3x + 10)CB

A5x + 18°(3x + 10)CB = m/A

A5x. 10 + 18° (3x + 10)CB.10 = m/A .10

18°(3x + 10)CB . 10 : 180° CB(3x + 10)

m/A.10 : 10m/A

A5x. 10 + 180° CB(3x + 10 ) 10m/A

A5x. 10 + 180° CB(3x + 10) = 10m/A

A5x.10+180° CB (3x + 10) : 10A5x + 540° CB x + 1800° CB

A5x . 10 + 180° CB(3x + 10)

=10A5x + 180° CB(3x + 10)

180° CB(3x + 10); 540° CBx + 1800° CB

= A5x . 10 + 540° CBx + 1800° CB

10A5x + 540 ° CBx + 1800° CB = 10m / A

Move 180° CB to the right side

10A5x + 540° CBx = 10m / A -1800° CB

Factor 10A5x + 540° CBx : x(10A5 + 540° CB)

10A5x + 540° CBx

= x( 10A5 + 540° CB)

x(10A5 + 540° CB) = 10m /A - 1800° CB

x(10A5 + 540° CB) / 10A5 + 540° CB = 10m / A / 10A5 + 540° CB - 1800° CB / 10A5 + 540° CB: 10A5 + 540° CB ≠ 0

Simplify

x = 10m - 1800° ACB / A(10A5 - 540° CB): 10A5 + 540° CB ≠ 0.

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Answer:

x = 3

Step-by-step explanation:

If B is the midpoint of the line A to C then that means A to B and B to C are equal to one another.

Therefore, to find x you would set the 2 line equations equal to each other:

4x + 2 = 3x + 5

Move the terms around. Start by subtracting the 3x from both sides.

4x - 3x + 2 = 5

Then subtract the 2 from both sides.

4x - 3x = 5 - 2

Then combine like terms.

4x - 3x is x. 5 - 2 is 3.

So that leaves you with:

x = 3

The smallest side in the triangle is side opposite angle T

The smallest side in the triangle is calculated using the idea of sum of angles in a triangle is 180 degrees

Because of this idea, we have the equation

9x + 40 + x + 74 + 7x - 36 = 180

collecting like terms

9x + x + 7x + 40 + 74 - 36 = 180

17x + 78 = 180

17x = 180 - 78

17x = 102

dividing through by 17

17x / 17 = 102 / 17

x = 6

angle C = 9x + 40 = 9 * 6 + 40 = 94

angle A = x + 74 = 6 + 74 = 80

angle T = 7x - 36 = 7 * 6 - 36 = 6

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Step 1 (x+1) (x+2)/(x+5) (x+1) (x+2)/(x+2) (x+2) * Step 2 (x+5/x+2) * ( x+2/x+5) Step 3 (x+5/x+2) ( x+2/x+5z  Step 4 The solution is 1, so there.

The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)

given

The formulas (x2+ 7x+10/x2+ 4x+4) should be factored. (x²+ 3x+2/x²+ 6x+5)

(x2+ 2x+x+ 2/x2+ 5x+x+5) = (x2+ 5x+2x+ 10/x2+ 2x+2x+4)

taking typical

=[x(x+5) +2(x+5)/ x(x+2) +2(x+2) ] x((x+5) +1(x+5)/x((x+2) +1(x+2)

Making commons collaborative

=[(x+2) (x+5)/ (x+2) (x+2)] [ (x+2)(x+1)/ (x+1) (x+5)]

Cancelling

= [ (x+5)/ (x+2)]

* [ (x+2)/ (x+5)]

=[ (x+5)/ (x+2)] [ (x+2)/ (x+5)]

Once more canceling =1

Step 1 (x+1) (x+2)/(x+5) (x+1) (x+2)/(x+2) (x+2) * Step 2 (x+5/x+2) * ( x+2/x+5) Step 3 (x+5/x+2) ( x+2/x+5z  Step 4 The solution is 1, so there.

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The geometric mean—also known as the compounded annual growth rate—is used to determine average growth rates.

The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.

The geometric mean is a calculation that averages all values and determines the number's root. You must determine the nth root of the product of each integer in a set of n numbers. To summarise your data, utilise this descriptive statistic.

In finance, the geometric mean—also known as the compounded annual growth rate—is used to determine average growth rates.

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A document-term matrix is a data set that has asymmetric discrete or asymmetric continuous features because it represents a collection of documents.

Each document is represented by a row in the matrix. The matrix is populated with numerical values that represent the frequency of each term in each document.

The features in a document-term matrix are asymmetric because the number of terms (columns) in the matrix can be very large, while the number of documents (rows) is typically much smaller.

This results in a sparse matrix, with many cells having a value of zero, which means that the majority of the terms do not appear in most of the documents.

Additionally, the terms in the matrix can be discrete, as they represent specific words or phrases, but the frequency values can be continuous, as they represent the number of occurrences of each term in each document.

In conclusion, a document-term matrix is an example of a data set that has asymmetric discrete or asymmetric continuous features because it represents a collection of documents, where each document is represented by a row in the matrix.

Each column represents a specific term or word, and the number of terms (columns) in the matrix can be very large, while the number of documents (rows) is typically much smaller.

The terms in the matrix can be discrete, as they represent specific words or phrases, but the frequency values can be continuous, as they represent the number of occurrences of each term in each document.

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A systematic sample is a sampling method in which members from a population are selected in a regular and systematic way.

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Elements in set A is 7.

Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.

RECALL: The number of proper subsets of a set with nn elements is 2^n-12

N

−1.

Let n = number of elements of the set.$

Then,Then, 2^n-1 = 127

2^n = 127+1

2^n=128

2^n = 2^7

N=7

$The set has 7 elements.

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According to the given information in the question the element in set A is  7.

Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.

RECALL: The number of proper subsets of a set with nn elements is 2^n-12

N

−1.

Let n = number of elements of the set.$

Then, Then, 2^n-1 = 127

2^n = 127+1

2^n=128

2^n = 2^7

N=7

$The set has 7 elements.

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The non-rigid transformations are translation and reflection

A non-rigid transformation is a type of transformation that modifies an object's shape while maintaining its size. An object's position is altered by translation and reflection, but its size remains unchanged. Reflection is the act of sunlight reflecting off of any outside surface. The light allows us to see things.

Things happen to our eyes when the daylight enters. The cells take an image of it when they have seen it, which is subsequently sent to the retina and the brain. The laws governing the observation of light are uncommon, and the angle of frequency is always equal to the point of observation.

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