5 people were asked how many books they own, and the results are shown
below. Michael owns 97 books and wants to know whether he owns more books
than most other people.
a) Which average should he use to compare?
b) What is the value of this average for the five numbers shown below?
225
142
29
103
61

The solution to the system of linear equations 2x + 3y = 3 and 7x -  3y = 24 is (3 , -1).

A linear equation is an algebraic equation of the form y = mx + c, involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

2x + 3y = 3

7x - 3y = 24

By addimng both the linear equation,

9x = 27

x = 27/9

x = 3

Substitute the value of x in either of the equations

2 (3) = 3y = 3

6 + 3y = 3

3y = -3

y = -1  

Therefore, the solution to this system of linear equations is (3 , -1).

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The distance between the points (22,11) and (6,11) in the coordinate plane is 16 units.

According to the question,

We have the following information:

The two points in the coordinate plane = (22,11) and (6,11)

Now, we know that the following formula is used to find the distance between two points in the coordinate plane:

Distance between two points = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }[/tex]

We have the following values:

x1 = 22 and y1 = 11

x2 = 6 and y2 = 11

Distance between two points = [tex]\sqrt{(11-11)^{2} +(6-22)^{2} }[/tex]

Distance between two points = [tex]\sqrt{(-16)^{2} }[/tex]

Distance between two points = 16 units

Hence, the distance between the points (22,11) and (6,11) in the coordinate plane is 16 units.

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It takes 12 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.

What is the distance?

Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Given that,

The distance to uncle's house = 728 miles

The time taken to drive to uncle's house = 14 hours

So,

speed = (728)/14 = 52 miles/hour

Then the time to drive 624 miles(to Atlanta) is calculated by,

time t = (624)/52 = 12 hours.

Hence,  It takes 12 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.

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The equation that can be used to to determine the  number of trees can be presented as follows;

t = 41790 ÷ 210  + 5

An equation is a mathematical statement that consists of mathematical expressions joined by an equals to sign.

The number of orange trees MacDonald removes from his farm = 5 teres

The number of oranges produced by each of the remaining trees = 210

The number of oranges in the harvest = 41790 oranges

The initial number of orange trees is therefore;

The number of orange trees that produce the 41790 oranges is therefore;

41790  ÷ 210 =  199

The number of orange trees remaining after the 5 trees have been removed =  199 trees

The initial number of trees is therefore;
t = 5 + 41790 ÷ 210 = 204

The initial number of trees, t = 204 trees

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The value of 5.37/3 is 1.79.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given term is 5.37 divided by 3,

The mathematical expression for 5.37 divided by 3,

= 5.37/3

= 1.79

The value of 5.37 divided by 3 is 1.79.

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If the coefficient of determination is a positive value, then the correlation coefficient can be negative or positive, which means the value of the correlation coefficient is between -1 and +1. If the variable x increases, the variable y also increases, and if the variable x decreases, then the variable y also decreases.

The coefficient of determination is a statistical measurement which examines how differences in one variable can be explained by the difference in a second variable, when predicting the outcome of a given event. The coefficient of determination is a number between 0 and 1 that measures how well a statistical model predicts an outcome. This provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.

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Dyan must show harm to recover damages as he claims to have access to a stock-trading algorithm that will multiply an investment many times over.

What is algorithm?

In arithmetic and computing, an algorithm could be a finite sequence of rigorous directions, generally wont to solve a category of specific issues or to perform a computation. Algorithms ar used as specifications for acting calculations and processing.

Main body:

As he has the access to to a stock-trading algorithm , it becomes his obliged duty to help the customer with his recovery damages.

Hence , Dyan must show harm to recover damages

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Answer:

A.2

Step-by-step explanation:

Options A,B are true and the other 3 C,D,E are false.

What is matrix?

The arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns are known as matrices, which is the plural version of the word matrix. They are rectangular arrays with defined operations for addition, multiplication, and transposition. The constituents of the matrix are its numbers or entries. Vertical entries in matrices are referred to as columns, whereas horizontal entries are known as rows. A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for operations like subtraction, addition, and multiplication. The number of rows and columns in a matrix determines its size, sometimes referred to as its order.

A) If Ax=λx for some vector x, then x is an eigenvector of A

if x not equal to 0 then the statement is true.

B) A steady-state vector for a stochastic matrix is actually an eigenvector:

As it is an egien vector the statement is true.

C) If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues.:

the statement is false.

D) The eigenvalues of a matrix are on its main diagonal:

It's only true for the trigonal matrix.

E) An eigenspace of A is just a null space of a certain matrix:

the statement is false.

Hence we have determined the true and false statement from the given option.

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Some other names for the unit rate are:

A general proportional relation is written as:

y = k*x

You can see that it goes through the origin because when we evaluate in x = 0, we get:

y = k*0 = 0

So it passes through (0, 0).

The value "k" has several names, unit rate is the one given here, but it is generally called the "constant of proportionality"

It is also called the slope (like in a linear equation with an y-intercept equal to 0).

Or the rate of change or gradient, which are equivalent terms that particularly in the case of linear equations are equal to the slope (but not for other functions).

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Answer:

x = 13.85 cm

Step-by-step explanation:

Forming the equation,

→ (16)² = (x)² + (8)²

Now the value of x will be,

→ (16)² = (x)² + (8)²

→ 256 = x² + 64

→ x² = 256 - 64

→ x = √192

→ x = 13.8564

→ [ x = 13.85 ]

Hence, value of x is 13.85.

The power output of a  motor for a ski tow rope is  6925.333 Watt.

We are know that,

Speed = v = 2.0m/s

Mass = m = 60kg

Number of skier = N = 25

The slope formed angle = Ф = 32°

The acceleration due to gravity = 9.8m/s²

Thus, to calculate the power of motor for a ski tow rope then we use formula, and (we know that F = mg)

P = (Nmg)(vcosФ)

Where , P is the power and putting the all given values in above equation,

P =[(25× 60kg ×9.8m/s²)×(2.0km/hr)×{(1m/s})/(3.6km/h)} cos32°

P = 8166.66×0.848 Watt

P = 6925.333 Watt

Therefore, the power output of a  motor for a ski tow rope would be  6925.333 Watt.

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If the theater club fulfills its sales target, 40 student tickets can be sold in total when the drama club members need to sell 100 tickets.

Given that,

The drama club members need to sell 100 tickets. If the drama club fulfils its sales target, will tickets cost $5 each and be sold to students. Tickets cost $10 for non-students. The total amount of ticket sales that the drama club must get is at least $800. The number of student tickets, s, and the number of non-student tickets, n, that the members must sell are represented by the system of inequalities.

s+n≤100

5s+10n≥800

We have to find if the theater club fulfills its sales target, how many student tickets can be sold in total.

We know that,

Take the system of inequality

s+n≤100

5s+10n≥800

By solving the inequality we get s=40 and n=60

Therefore, if the theater club fulfills its sales target, 40 student tickets can be sold in total.

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Answer:

A.

Step-by-step explanation:

The given number 8 is not a prime number.

Given that,
To justify whether the number 8 is a prime number or not.

A prime number is a whole number bigger than one with just the number one and itself as factors.

Here,
A prime number is given as 1,2, 3,5, 7, 11, 13, and so on,
From the above series, it is determined that 8 is not a prime number.

Thus, the given number 8 is not a prime number.

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Any number that represents something other than zero is considered to be positive.

In the given question we have to explain a positive number in math.

Any number that represents something other than zero is considered to be positive. When referring to the amount of money in your bank account, a positive figure would undoubtedly make you feel good as well.

The natural, or counting, numbers 1, 2, 3, 4 and 5 are examples of positive numbers, as are fractions like 8/5 or 32/45 and decimals like 49.4.

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Answer:

12

Step-by-step explanation:

= 6:3(3+3)

= 6/3 x 6

= 12

The amount compounded at a rate of 8% over a period of 6 years is  $8,551.56

The compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The formula for compound interest can be derived from the formula for simple interest. The formula for simple interest is the product of the principal, time period, and rate of interest (SI = ptr/100). Before looking into to derivation of the formula for compound interest, let us understand the basic difference between simple interest, compound interest computation. The principal remains constant over a period of time, for simple internet computation, but for compound interest computation the interest is added to the principal, for compound interest computation.  The compound interest formula is given below:

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

Applying the formula of compound interest here;

A = 5300(1 + 0.08/12)^12 * 6

A =  $8,551.56

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The recommended statistic is statistic II because this statistic is unbiased and has the smallest standard deviation of three.

Unbiased statistic is more accurate than biased statistic because which on sampling distribution mean equal to population parameter.

Standard deviation is value of dispersed of observed value sampling around population parameter. Smaller standard deviation can be equated with a smaller deviation of data. Which in unbiased statistic means lots of value closer to population parameter.

If even statistic is unbiased but standard deviation high (statistic III) it not recommended because lots of value is not close enough to population parameter.

Thus, the recommended statistic is unbiased statistic and have smallest standard deviation which is statistic II.

Your question is incomplete, but most probably your full question was (image attached)

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Answer:

6,942 steps left!

Step-by-step explanation:

OK so this is easy so we know that if 1 / 19 = 0.052 we minus that by - 3 because - 3 is our exponent that gives us 3.052 so now we just take 3.052 - 10,000 which gives us exactly 6942 you two steps so he needs 6942 steps left

Answer:

3,141 steps

Step-by-step explanation:

Let x be equal to the number of steps he needs to reach his goal

10,000 = [tex](\frac{1}{19} )^{-3}[/tex]+ x

10,000 = 6,859 + x

3,141 = x

Answer: 85

Step-by-step explanation:

The scale factor of the dilation of triangle DEF is 3/10

Given,

Triangle DEF's scale factor of dilation is equal to the ratio of its corresponding sides to those of triangle D'E'F':

f = D'F'/DF = D'E'/DE = E'F'/EF scale factor (1)

The comparable triangles OD'F' and ODF can be used to calculate the ratio D'F'/DF because their sides must be proportional:

D'F'/DF = OF'/OF = OD'/OD (2) (2)

According to the figure, we understand:

If F'F = 7 and OF' = 3, then

OF = OF' + F'F → OF = 3 + 7 → OF = 10

Then substituting in (2):

(2) DF/DF = 3/10 = OD/OD

Also substituting in (1):

(1) f = 3/10 = E'F'/EF = D'E'/DE

That is,

The scale factor of the dilation of triangle DEF is 3/10

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The question is incomplete. Completed question is given below;

What is the scale factor of the dilation of triangle DEF?

Figure is attached;

The following inequalities are equivalent to the inequality 5 < -y + b.

y< b - 5 and b - 5 > y

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

5 < -y + b

Adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged

5 < -y + b

Add y on both the sides, we get

5+y < b

subtract 5 on both sides

y< b - 5

 Interchange the expressions .So inequality symbol changes

b - 5 > y

So, the following inequalities are equivalent to the inequality 5 < -y + b.

y< b - 5 and b - 5 > y

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An equilateral right angled triangle is not possible because a triangle can only consist of 180°. Since a right angle is 90°, there is no way that a triangle can be have three right angles. 180° ≠ 270°

An isosceles acute triangle is possible because two angles can be acute and have the same degree values and the last angle can have a different value of another acute angle. The two angles that are acute would have the same value for their corresponding sides.

A scalene obtuse triangle is possible because one angle can be obtuse and the other ones can be acute. All the sides can be different.

I hope this helps you! Have an amazing rest of your day!

Answer:

What is the question?! I don't understand, sry?!

Step-by-step explanation:

The required difference in the speed of Grayson ans Maya is 2 miles per hour.

Speed is characterized as. The pace of progress of position of an article toward any path. Speed is estimated as the proportion of distance to the time in which the distance was covered. Speed is a scalar amount as it has just bearing and no extent.

Grayson biked 45 miles in 3 hours

His speed = 45/3 = 15 miles/hour

Similarly,

Maya biked 26 miles in 2 hours

So, his speed = 26/2 = 13 miles /hour

Difference in their speed = 15-13 = 2 miles per hour

Thus, Speed of Grayson is 2 miles/hour greater than Maya.

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The probability that both are red is 0.0791.

Given,

Total marbles: 37 + 15 = 52

According to the number of red cards out of all the cards, there is a 15/52 possibility that a red card will be pulled during our initial pull.

Depending on how many red/total marbles are still in there, there is a 14/51 probability that the second marble pulled will also be red.

Our two fractions are multiplied together from here,

15/52 * 14/51

We can start by simplifying a little bit; the numbers 14 and 52 share a 2;

15/26 * 7/51

Our result is 35/442

Depending on whether you choose to maintain it in fractional, ratio, or percentage form, the result of dividing is around 0.0791, which rounds to 7.91%.

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The value of expected time ex(b)=1 day approximately if b is the number of days a busy student delays Laundry.

The basic anticipated value formula is (P(x) * n): the probability of an occurrence multiplied by the number of times the event occurs.

The expected value (also known as the expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average in probability theory. The anticipated value is the arithmetic mean of a large number of independently chosen random variable outcomes.

Let b be the number of days a busy student puts off doing laundry.

The given information is tabulated as below:

Days(b)                      1              2

Probability, p(b)       2/3          1/3

The expected time is given as,

E(b)=∑i=1ᵇp(b)

=(1×(2/3))+(2×(1/3))

=4/3

=1.3333

Therefore, the value of ex(b):

1.3333 day ≈ 1 day

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Yes the room is square with the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet .

Given:

Elena has received grant money to open a local community center. she will do many of the improvements herself to the old building she rents. while touring the building to make her project list, she uses a tape measure to check whether floors, doorways, and walls are square, meaning that they meet at right angles. a elena measures the lobby of the building for new laminate flooring. the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet.

with sides 30, 16 and hypotenuse 34 the figure forms a right angled triangle.

According to pythagoream theorem:

30^2+16^2 = 34^2

900+16^2 = 34^2

900 + 256 = 1156

1156 = 1156

Therefore Yes the room is square with the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet .

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As per the given total number of chocolates, and the number of chocolates given to his friends and the left chocolates , the number of friends at Jack's party were equal to 16.

As given in the question,

Total number of chocolates given by Jack's mother is equal to 50

Number of chocolates given by Jack to his friends = 3

Number of chocolates left with Jack = 2

Let 'x' represents the number of friends

Requires equation to show the relation we have,

3x + 2 = 50

⇒ 3x = 50 - 2

⇒ 3x = 48

⇒ x = 48/ 3

⇒ x= 16 friends

Therefore, for the given total number of chocolates, and the number of chocolates given to his friends and the left chocolates , the number of friends at Jack's party were equal to 16.

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The number of layers of cubes present in the rectangular prism of volume 102/3 in³ is 7.

Volume is defined as the space occupied within the boundaries of any three-dimensional solid.

To calculate the number of layers of cubes in the prism, we use the formula below.

n = V/9l³............Equation 1

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, there are 7 layers in the rectangular prism.

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