maths question to purely maths tutor

Answer:

Step-by-step explanation:

SOLUTION

Write out the equation

The root of the equation is

Equate the factors to zero

Hence, the root of the equation is

(-6,0) and (2,0)

The vertex of the equation will be obtained using

Then

Then

Plotting this point using the scale 2unit on both axes, the image of the graph will be

Ordered pair, when graphed, would be on the same line as (1, -2) and

(-2, 4) are (3,-6).

As given in the question,

Equation of the line passes through the point (1.-2) and (-2,4) when graphed is :

(y +2)/(x-1) = (4+2)/(-2-1)

⇒y +2 = -2(x -1)

⇒y =-2x

Ordered pair satisfied the equation of the line passes through the point (1.-2) and (-2,4) when graphed is :

A. (-2,6)

x=-2 ⇒y=4

Not satisfied.

B. (3,6)

x=3⇒y=-6

Not satisfied.

C.(3,-6)

x=3⇒y=-6

Satisfied.

D. (1,2)

x=1⇒y=-2

Not satisfied.

Therefore, ordered pair, when graphed, would be on the same line as (1, -2) and (-2, 4) are (3,-6).

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Answer and Explanation:

1B: {x | -7 ≤ x ≤ 8}

2A: [-4, 3]

2B: {y | -4 ≤ y ≤ 3}

The range of a function is its set of y-values.

Set builder notation (roster method) is a way to define the values within a set.

1. Length of rectangular area = 120 yards

Width of rectangular area = 120 yards

2. Maximum area = 14,400 square yards.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Total fencing Peter has = 480 yards

Now,

We can say that the total fencing he has in terms of length L and width W of the rectangle will be;

⇒ L + L + W + W = 480

⇒ 2(L+W) =480

Divide both sides by 2 to get

⇒ L+W = 240

Subtract W from both sides so we get L in terms of W;

⇒ L= 240 - W

Since, The area of a rectangle is Length times width.

So, Area = (L × W)

⇒ Area  = (240-W) W

⇒ Area  = 240W - W²

Now, By comparing the equation with an quadratic equation

ax² + bx + c , we get;

⇒ a = -1 and b = 240

Since, Area is maximum when;

W = -b/2a

W = - 240/-2

W = 120

So, for W = 120 yards area is maximum.

Hence, Length of yards = 240 - 120 = 120 yards.

(b) Maximum area of the rectangle can be found by substitute this

W = 120 in the Area equation;

So, the maximum area ,

A = 240 (120) - 120²

A = 28800 - 14400

A = 14400

Hence, Maximum area = 14,400 square yards.

Thus,

1. Length of rectangular area = 120 yards

Width of rectangular area = 120 yards

2. Maximum area = 14,400 square yards.

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The set of irrational numbers is the union of the set of rational numbers Q in the real numbers R. Therefore, the correct answer option is C. union.

An irrational number is a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11.

A rational number simply refers to a type of number which comprises fractions, integers, terminating or repeating decimals such as 4.

In Mathematics, the union of the set of all irrational numbers (Q') and the set of all rational numbers (Q) are generally referred to as a set of real numbers (R).

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Complete Question:

The set of irrational numbers is the ______ of the set of rational numbers Q in the real numbers R

Select one:

A. complement

B. ratio

C. union

D. Intersection

The shortest straight path they must run back to the starting line is the square root of 34 miles.

The distance run by the runners forms a right triangle. A right triangle is a polygon that has three sides. The length, base and the hypotenuse. The hypotenuse is the longest side of the right triangle.

The miles run north is the length, the miles run west is the base and the shortest straight path to the starting line is the hypotenuse.

In order to determine the hypotenuse, the Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

3²  + 5²

= 9 + 25

= 34

c = √34

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Answer:

3^8

Step-by-step explanation:

9^4 = 9*9*9*9

9 = 3*3

9^4 = (3*3)*(3*3)*(3*3)*(3*3)

9^4 = 3*3*3*3*3*3*3*3 = 3^8

or, more simply

9 = 3^2

9^4 = (3^2)^4

we use (x^y)^z = x^(y*z)

(3^2)^4 = 3^(2*4) = 3^8

The probability that both of them go back to prison is 4.48%.

The state recidivism rate is given by 22%.

So, the probability that both of the prisoners will go back to prison will be:

Hence, the probability that both of them go back to prison is 4.48%.

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The ending balance Statement of Changes in Owner's Equity for this data is given by: $222,000.

The ending balance is given by the difference between all the amounts that were on the account, and were added, by all amounts that were removed from the account.

The amounts that were added to the balance are given as follows:

The amounts that were removed from the balance are given as follows:

Hence the ending balance is calculated as follows:

6,000 + 200,000 + 15,000 + 10,000 + 56,000 - 5,000 - 60,000 = $222,000.

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Answer: True

Step-by-step explanation:

The equation of the function of the agency revenus in terms of x is R(x) = (50 + x) * (100 - 3x)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

From the question, the given parameters are given as

Number of people = 50

Amount charged per person = $100

The above means that the total charges is

Total = Number of person * Amount charged per person

Rewrite as

Revenue =  Number of person * Amount charged per person

From the question, we have

The charges for each traveller reduces by $3 for each additional person

Let the number of added person be x

So, we have

Revenue =  (Number of person + x) * (Amount charged per person - 3x)

Substitute the known values in the above equation

So, we have

R(x) = (50 + x) * (100 - 3x)

Hence, the agency's revenue R as a function of x is R(x) = (50 + x) * (100 - 3x)

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If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ .

The volume of  the cube with side length "a" can be calculated using the formula

Volume = a³ ,

For Example : if the side length of the cube is 2m , then the volume of the cube will be

Volume = 2³  = 8m³ .

In the question ,

it is given that ,

the  side length of the cube is x⁻² inches ,

So, substituting the value of side length in the Volume formula , we get

volume = (x⁻²)³

= x⁻⁶         ....(as (xᵃ)ᵇ = (x)ᵃˣᵇ = xᵃᵇ )

Therefore , If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ inches³ .

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ANSWER

637.5π mm³

EXPLANATION

The volume of a cylinder is the product of its base area and its height. In this problem, the radius of the base of the cylinder is 5 mm, and its height is 25.5 mm. The volume is,

Hence, the volume is 637.5π mm³.

The value of x is 10 .

In the question ;

from the given figure , we can see that MS=SL   and KR=RL which means

that R and S are the mid points of sides ML and KL respectively .

The Mid Point Theorem states that

If the line segment adjoining the mid points of any of the sides of the triangle then the line segment is said to be parallel to the third  side and is half of the length of the third side .

which means RS parallel  to KM   and KM/2=RS  ( ... by mid point theorem)

Substituting the values of RS=2x-10 and KM=2x, we get

2x/2=2x-10

2x = 2(2x-10)

2x = 4x -20

4x-2x=20

2x=20

x=10

Therefore , the value of x is 10 .

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(a) (c) The Kelly family earns more than the Moore family.

(b) (a) The Kelly family earns more than the Moore family.

Each of the 100 equal groups into which a population can be divided according to the distribution of values of a particular variable is called percentile.

Percentile is computed using the following formula,

P = n/N X 100

Where, n =ordinal rank of a given value

N = number of values in the data set,

P = Percentile

In (a) part , Kelly family's percentile is 77th percentile and Moore family's percentile is 24th percentile.

therefore option (c) i.e. The Kelly family earns more than the Moore family is correct .

In (b) part , Moore family's income is less than Kelly's family income.

therefore option (a) i.e. The Kelly family earns more than the Moore family is correct.

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Answer:

  x = 770

Step-by-step explanation:

You want the solution to the equation 6(915 - x) = 100 + x.

It often works well to simplify the equation first. Here, that means eliminating parentheses using the distributive property:

  6(915) -6(x) = 100 +x

  5490 -6x = 100 +x . . . . . . . . carry out the multiplication

  5490 -6x +6x = 100 +x +6x . . . . . add 6x to both sides

  5490 = 100 +7x . . . . . . . . . . collect terms

  5490 -100 = 100 +7x -100 . . . . . . subtract 100 from both sides

  5390 = 7x . . . . . . . . . . . . . . collect terms

  5390/7 = (7x)/7 . . . . . . . . . . . . . . . . divide both sides by 7

  770 = x . . . . . . . . . . . . . . . . carry out the division

The solution to the equation is x = 770.

__

Check

  6(915 -770) = 100 +770 . . . . use the value of x in the equation

  6(145) = 870 . . . . true

__

Additional comment

After eliminating parentheses, this is a 3-step linear equation, so is solved in the usual way. First, the variable terms are collected on one side of the equal sign. Then the constant terms are collected on the other side of the equal sign. Finally, the equation is divided by the coefficient of the variable.

SNSWER

. x = 2

F. x = -1

EXPLANATION

e can rewrite this equation as a quadratic frunction equal to zero.

First apply the binomial squared on the left side:

This is to write it in standard form. Now we have the equation:

We can add 3x on both sides of the equation:

And subtract 6 from both sides:

Now we can use the quadratic formula to solve this for x:

In our equation a = 1, b = -1 and c = -2:

Therefore the solutions to the given equation are x = 2 and x = -1

well, one uses 75% and that other uses 76%,  so hmmmm those values aren't equal however the statements are talking about the same type of group.

let's reword them

a)

75% of the HCLT will be paid by folks making < 120K

b)

HCLT is paid in 76% by folks making < 120k

a) we know that 75% of the HCLT is paid by those folks

b) we only know that many folks pay for the HCLT, but 76% of it is paid by folks making < 120k, namely 76% of the HCLT is paid by them.

pretty much the same group is referred on both statements.

Space available for the art show is 2/3 or 66.6%.

A number that represents a rational number is called a common fraction. Additionally, that same quantity can be expressed as a decimal, a percent, or a negative exponent.

The art room is divided into a total of three divisions, as can be seen from the information given. There is 2/3 of the total amount of space available for the art section because the artwork will only be presented on 2 of the 3 available parts. With 33.3% of the art room currently filled and unavailable, only 66.6% of the space is available for the art to be displayed on.

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The probability of event A is 0.0012 and the probability of event B is 0.0288

There are 7 people and 4 prices.

A) The probability that Ann wins the first prize is 1/7, assuming that all 7 people have the same probability of winnig.

Then Jim is second, now the probability is 1/6 (because we don't count Ann anymore).

Soo wins the third one, with a probability 1/5.

Kira wins the last one, with a probability of 1/4.

The joint probability is the product of all the individual ones:

P(A) = 1/7*1/6*1/5*1/4  = 0.0012

B) Now we just want that Soo, Ann, Ravi, and Hans win, but the order does not matter.

So we have the same probability than above, but now we need to include the permutations of the 4 elements, so we add a factor 4!.

P(B) = 4!*0.0012 = 4*3*2*1*0.0012 = 0.0288

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In order to simplify the expression, start by solving the subtraction of fractions in the form

then,

Using the normal approximation to the binomial distribution, there is a 0.0060 = 0.60% probability that at least 12 sales will result from mailing to the 30 prospects.

The z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution in the context of this problem are given as follows:

n = 30, p = 0.2.

Hence the mean and the standard deviation for the approximation are given as follows:

Using continuity correction, the probability that at least 12 sales will result from mailing to the 30 prospects is P(X > 11.5), which is one subtracted by the p-value of Z when X = 11.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (11.5 - 6)/2.19

Z = 2.51

Z = 2.51 has a p-value of 0.9940.

1 - 0.9940 = 0.0060.

Hence the probability is of 0.0060 = 0.60%.

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The area of the shaded section, in terms of the radius R, is:

A = 0.67*R^2

On the image we can see a circle where a section with an angle of 120° is not shaded and the rest is shaded.

Remember that the area of a circle of radius R is:

A = pi*R^2

Where pi = 3.14

Particularly, for a section defined by an angle x the area is:

A = (x/360°)*pi*R^2

In this case we have:

x = 360° - 120° = 240°

Then the area, in terms of the radius, is:

A = (240°/360°)*3.14*R^2 = 0.67*R^2

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -8}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(-2~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -8}{2}=-2\implies x-8=-4\implies \boxed{x=4} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3}{2}=1\implies y-3=2\implies \boxed{y=5}[/tex]

Answer: 33/10

Step-by-step explanation:

=3.3 X 10/10

= 33/10

Answer done. 33/10 #

Answer:

x>5

Step-by-step explanation:

2x>10

x>5

Based on the statement about Thomas's income rising along with his stress income, the correlation and cause is C. Positive correlation; common underlying cause.

Positive correlation between two variables means that they move in the same direction. When one of the variables increases, the other variable increases as well. When one variable decreases, the other variable decreases too.

The income level of Thomas is increasing at the same time the stress is increasing so this is a positive correlation.

A higher Income level might lead to more work and responsibilities which is most likely the common underlying cause for the positive correlation.

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L = 2w - 5

Plug this in for perimeter equation:

2l + 2w = 56

4w - 10 + 2w = 56

6w = 66

W=11

now find length

L = 22 - 5

L = 17