Answer the question please

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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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 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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Answer:

Step-by-step explanation:

again , you know that the two angles add up to 180°

you know that by the complementary angle rule.

set the two equations equal to 180 and solve for x

180= eq1 + eq2

To calculate the interest and the total amount , we use Simple interest formula S.I = ( P× r × t ) / 100.

Simple interest is a method of calculating the interest that is charged on fixed deposits , savings accounts and the loans .

The money you put in the bank is called the principal, the bank pays you interest.

The interest is computed as a certain percent of the principal; called the rate of interest. The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent.

The variable for time, t, represents the number of years the money is left in the account.

The formula to calculate simple interest is :

S.I = ( P× r × t ) / 100

where P is principle , r = rate of interest and t is term of loan in year.

To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable.

To find the total amount ,

Amount = Principle + Interest

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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 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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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.

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:

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

Answer: 85

Step-by-step explanation:

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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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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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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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!

The  Bayes's theorem help us to take an better prediction of even with the help of another occuring event.

Bayes' theorem, in probability hypothesis, a method for reexamining expectations considering important proof, otherwise called restrictive likelihood or opposite likelihood. The hypothesis was found among the papers of the English Presbyterian clergyman and mathematician Thomas Bayes and distributed after death in 1763.

Bayes' theorem expresses that the contingent likelihood of an occasion, in view of the event of another occasion, is equivalent to the probability of the subsequent occasion given the principal occasion duplicated by the likelihood of the main occasion.

This theorem gives us an idea to take better prediction of the event.

Option(a)  to help you make a better decision is correct answer.

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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;

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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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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Answer:

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

Step-by-step explanation:

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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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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The quotient of division 2/( √13+√11) is (√13-√11).

A quotient is a quantity that is obtained by dividing two integers. The answer is D.

What is a quotient?

A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.

In order to find the quotient of the fraction, we need to take the rationalize of the fraction.

= 2/(√13 + √11)

= 2/(√13 + √11) x (√13 - √11)/(√13 - √11)

= 2(√13 + √11)/(√13)^2 - (√11)^2

= 2(√13 - √11)/13-11

= 2(√13-√11)/2

= (√13-√11)

Hence the answer is, the quotient of division 2/( √13+√11) is (√13-√11).

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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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Answer:

A.2

Step-by-step explanation:

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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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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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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