In a particular metal mixture there are:
1 part mercury to 5 parts copper,
3 parts tin to 10 parts copper,
You would need how many parts mercury to how many parts tin?

A) 1:3
B) 2:3
C) 6:13
D) 4:15

Just ten more days and I'll be in London!

Answer:

Just ten more days and I'll be in London!

The product of two rational numbers is 1 . A . Rational number because multiplying two rational numbers is equivalent to the ratio of 3 . Two integers which is 1 . a rational number .

The product of two rational numbers is always a rational number. This is because a rational number is defined as a number that can be expressed as the ratio of two integers.

When you multiply two rational numbers, you are simply multiplying two ratios, which is still a ratio and therefore a rational number.

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If you get a new job, outline the forms you will have to deal with to file your taxes. The form has to fill in Form W-9 sent by the employer and given use to file your taxes.

The company determines what information to include in the Form 1098 or Form 1099 based on the information provided on the Form W-9.

Information about taxpayers is gathered using Form W-9 to assist with informational reporting to the IRS.

Although it is utilised in other contexts as well, the Form W-9 is most frequently employed when working with businesses that employ independent contractors.

The form requests that a taxpayer enter their name, residence, tax bracket, and withholding specifications.

Therefore, from the following conditions are:

1. Outline the forms you will need to file your taxes if you get a new job. Form W-9 must be completed and returned to the employer in order to file your taxes.

A W-2 will be given to you detailing your profits. New employees are frequently required to complete a Form W-4 rather than a Form W-9 in order to supply their company with information about their taxpayers.

2. Gross income is all income from whatever source derived that is not excluded or deferred from income. AGI is gross income minus "for AGI" deductions. Taxable income is AGI minus "from AGI" deductions.

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The simplified form of the expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex] is  [tex]6\frac{1}{8}[/tex].

Given the expression in the question:

[tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex]

To simplify the given expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex], first, rewrite the expression using the negative exponent rule:

[tex]( \frac{1}{2^{\frac{1}{2} }} * 7^{\frac{1}{3} )^6[/tex]

Next, combine the fractions:

[tex]( \frac{7^{\frac{1}{3} }}{2^{\frac{1}{2} }} )^6[/tex]

Simplify the numnerator:

[tex]\frac{49}{(2^{\frac{1}{2} })^6}[/tex]

Simplify the denpminator:

[tex]\frac{49}{8}\\ \\6\frac{1}{8}[/tex]

Therefore, the simplified form is [tex]6\frac{1}{8}[/tex]

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Answer:

Answer is in the attached photo

Step-by-step explanation:

The solution is in the attached photo, do take note to find the value of y, we will have to make y the subject.

The probability that in a given week in September, it will rain on at most two days is 0.12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The probability that it rains on any given day in September = 0.3.

P ( rains ) = 0.3

And,

The probability that it will not rain on any given day in September.

P (no rain) = 1 - 0.3

P(no rain) = 0.7

Now,

The probability is that in a given week in September, it will rain on at most two days.

= P (x ≤ 2)

= P(no rain) + P(rain) + P(rain)

= 0.7 + 0.3 + 0.3

= 0.12

Thus,

The probability that in a given week in September, it will rain on at most two days is 0.12.

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Answer:

1. 18 + 35

2. 6 * 50

3. b - 25

4. x / 4

5. t + 11

6. 100 - k

Step-by-step explanation:

Tony can afford the car insurance, and he has enough money($426.33) left over each month to cover other expenses.

Automobile, truck, motorbike, and other types of road vehicles are covered by vehicle insurance. Its main purpose is to offer financial security against property loss or personal injury brought on by auto accidents, as well as against liability that can emerge from related events.

According to the information given,

Tony's yearly pay is $8,320

and his monthly pay is $693.

If we round his yearly pay to $8,000, his monthly car insurance will be 1/30 of that amount, or $266.67.

Since Tony's monthly pay is $693, and his monthly car insurance will cost $266.67, he can afford the insurance. He will have $426.33 remaining each month after paying for the insurance.

Therefore, Tony can afford the car insurance, and he has enough money left over each month to cover other expenses. However, this calculation assumes that Tony has no other major expenses or debts, and it is always a good idea to budget carefully and consider all potential costs before making a significant purchase.

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Option (c) is correct answer.

(C) DE = 12, DF = 16 and m∠D = 35

which states, length of DE is 12 units , length of DF is 16 units and m/D=35 degrees.

If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.

Property 1:

Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.

Property 2:

The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.

Now by property 1,

The pairs of  corresponding sides of similar triangles are proportional .

Therefore, in the given triangles,

[tex]\frac{AB}{DE} =\frac{AC}{DF} \\\\\frac{AB}{AC} =\frac{DE}{DF} \\\\\frac{9}{12} =\frac{DE}{DF} \\\\\frac{3}{4} =\frac{DE}{DF}[/tex]

Therefore, in the given options, option (c) satisfies the condition.

Hence, DE = 12 , and DF = 16.

By property 2 we know that , corresponding angles of similar triangles are equal.

hence, /A=/D

therefore, /D=35.

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The polygon DEFG is translated 3 units left to get F'(1, 6)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size.

Polygon DEFG has coordinates D(2, 5), E(3, 1), F(4, 6), and G(6, 6). The polygon is translated 3 units left to get F'(1, 6)

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The average rate of change of the function f(x) over the interval (-1, 2) is; 3.

As evident in the task content; the given function is as represented by the graph of f(x).

Hence, the average rate of change of the function over the given interval; (-1, 2) is;

= ( f (2) - f (-1) ) / (2 - (-1))

where; f (2) = 5 and f (-1) = -4.

Therefore, the average rate of change is;

= (5 - (-4)) / (2 - (-1))

= 9 / 3.

= 3.

Ultimately, the difference quotient of f (x) over the given interval is; 3.

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y=mx+b

m=slope

b= y-intercept

x=6

y=-5

-5= -1/3(6)+b

-5= 2+b

-2       -2

      -7    =  b

y= -1/3x-7

Answer:

y=-1/3x-3

Step-by-step explanation:

Answer: To calculate the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

20Y1:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share

Common Stock: $6,000 / 50,000 shares = $0.12 per share

20Y2:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share (cumulative preferred stock means that if the company misses a dividend, they still have to pay it in the future, so the dividends per share remain the same)

Common Stock: $45,000 / 50,000 shares = $0.90 per share

20Y3:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share

Common Stock: $0 (there is no information about dividends for the common stock in 20Y3)

So, the dividends per share for each year would be:

20Y1:

Preferred Stock: $2.00 per share

Common Stock: $0.12 per share

20Y2:

Preferred Stock: $2.00 per share

Common Stock: $0.90 per share

20Y3:

Preferred Stock: $2.00 per share

Common Stock: $0.00 per share

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The pair of opposite angles formed by two intersecting straight lines are known as Vertical Angles.

In the given figure, there are two pairs of vertical angles~

That are :

[tex]\qquad \sf  \dashrightarrow \: \angle1 \: \: and \: \: \angle3[/tex]

and

[tex]\qquad \sf  \dashrightarrow \: \angle2 \: \: and \: \: \angle4[/tex]

Also, vertical opposite angles are equal in measure.

You cannot construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm, as the sum of the lengths of the two smaller sides is not greater than the length of the larger side.

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

The lengths for this problem are given as follows:

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On solving the provided question, we can say that first angle is 37.9° . second angle will be 52.1°.

An angle is a fοrm in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a pοint in the middle known as the angle's vertex. In the plane where the rays are placed, twο rays can produce an angle.

An angle is alsο produced when two planes intersect. They're knοwn as dihedral angles. In plane geοmetry, an angle is the form that two rays or lines with a commοn termination might take. The Latin word "angulus," which means "hοrn," is where the English word "angle" comes from. The two rays, also knοwn as the sides of the angle, have a common termination knοwn as the vertex.

x = first angle

Complementary angle is 14.2 degrees more than the cοmplementary angle.

First angle  = x

Second angle = x + 14.2°

Complementary angle

x+x+14.2=90

2x+14.290

2x 90 14.2

2x = 75.8 x = 37.9

First angle is 37.9°.

Second angle will be:

x+14.2°

⇒37.9°+ 14.2°

⇒52.1°

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The decimal number is -5.690134489..... irrational number. Therefore, option C is the correct answer.

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.

Here,

-9.121212121212......

This decimal number is non terminating, but repeating

So, the decimal number is rational number

-1.5000000000.....

This decimal number is non terminating, but only zeros are repeating

So, the decimal number is rational number

-5.690134489.....

This decimal number is non terminating and non repeating

So, the decimal number is irrational number

-9.121212121212....

This decimal number is non terminating, but repeating

So, the decimal number is rational number

Therefore, option C is the correct answer.

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The required value of C is 3 which makes 16x² - 24x + C a perfect square.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

The expression is given in the question, as follows:

16x² - 24x + C

(4x)² - 24x + C

As we know that the factoring identity:

(a - b)² = a² - 2ab + b²

After comparing, we have a = 4x and 2ab = 24x

Solving for b:

2(4x)b = 24x

b = 24x/8x

b = 3

So 16x² - 24x + 3 = (4x - 3)²

This means the required value of C is 3 which makes a perfect square.

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Answer: 8^5

Step-by-step explanation: 8^6 is 8*8*8*8*8*8, so when you divide by 8 it cancels one of the 8s. Therefore you are left with 8*8*8*8*8 or 8^5.

The value of x in the given equation using laws of exponents is; x = 512

The different laws of exponents include;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

We have the equation as;

x^(2/3) = 64

We can write 64 as (∛512)²

This can be further expressed as;

512^(2/3)

Thus, we have;

x^(2/3) = 512^(2/3)

Thus, by identity rule;

x = 512

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Step-by-step explanation:

A set is a collection of distinct elements, and a subset is a collection of elements taken from a larger set. In this case, the set is {10, 15, 14, 20, 11}.

To calculate the number of subsets, we can use the formula for the number of subsets of a set with n elements, which is 2^n. So, the number of subsets of the set {10, 15, 14, 20, 11} is 2^5 = 32.

To calculate the number of proper subsets, we need to exclude the empty set (Ø) and the set itself from the total number of subsets. So, the number of proper subsets is 32 - 2 = 30.

Therefore, there are 32 subsets and 30 proper subsets of the set {10, 15, 14, 20, 11}.

The value of the quadratic like equation is given as y = 1 and y = 81.

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be favoured over the cross-multiplication method and the elimination method for straightforward equations without a lot of complicated calculations.

The equation is:

[tex]y^{\frac{1}{2} } - 4y^{\frac{1}{4} } + 3 = 0[/tex]

Using the exponent property we can write the equation as follows:

[tex](y^{\frac{1}{2} })^{\frac{4}{4} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{\frac{4}{2} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{2} - 4y^{\frac{1}{4} } + 3 = 0[/tex]

Now suppose the value of [tex]y^{\frac{1}{4} } = x[/tex].

x² - 4x + 3 = 0

x² - 3x - x + 3 = 0

x(x - 3) -1 (x - 3) = 0

(x - 1)(x - 3) = 0

x = 1

x = 3

Now, back substituting the value of [tex]y^{\frac{1}{4} } = x[/tex].

[tex]y^{\frac{1}{4} } = 1\\\\y^{\frac{1}{4} } = 3\\[/tex]

Raise to four on both sides of the equation we have:

y = 1

y = (3)⁴

y = 81

Hence, the value of the quadratic like equation is given as y = 1 and y = 81.

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Answer:

Step-by-step explanation:

(a) Using de Moivre's Theorem, we have that:

z^n = cos(nθ) + i sin(nθ)

1/z^n = cos(-nθ) + i sin(-nθ)

So, we can find z^n + 1/z^n as:

z^n + 1/z^n = (cos(nθ) + i sin(nθ)) + (cos(-nθ) + i sin(-nθ)) = 2 cos(nθ)

And z^n - 1/z^n as:

z^n - 1/z^n = (cos(nθ) + i sin(nθ)) - (cos(-nθ) + i sin(-nθ)) = 2i sin(nθ)

(b) To express the equation 2z^4 - 5z^3 + 7z^2 - 5z + 2 = 0 in terms of cos(θ), we can substitute z with cos(θ) + i sin(θ):

2(cos(4θ) + i sin(4θ)) - 5(cos(3θ) + i sin(3θ)) + 7(cos(2θ) + i sin(2θ)) - 5(cos(θ) + i sin(θ)) + 2 = 0

Expanding the right hand side using the trigonometric identities, we get:

2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0

Note that the real and imaginary parts are separate, so we can simplify this equation to a real equation by equating the real and imaginary parts to 0.

(c) To solve the equation 2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0, we can use numerical methods or analytical methods such as the roots of unity.

Once the roots are found, they can be represented on an Argand diagram by plotting the real and imaginary parts of each root as a point in the complex plane. The magnitude of each point represents the magnitude of the complex number, and the argument (angle) represents the argument of the complex number.

Answer:

Step-by-step explanation:

To determine whether an ordered pair is a solution to a system of equations or inequalities, we need to substitute the values for x and y into each equation or inequality and see if the resulting expression is true. If it is true for all of the equations or inequalities, then the ordered pair is a solution to the system.

Here's the step-by-step process for each ordered pair:

(1,3):

Substitute x = 1 and y = 3 into y < 4x - 1: 3 < 4(1) - 1 = 3 < 3, which is true.

Substitute x = 1 and y = 3 into y > x: 3 > 1, which is true.

Since both inequalities are true, the ordered pair (1,3) is a solution to the system y < 4x - 1 and y > x.

(0,0):

Substitute x = 0 and y = 0 into y < 4x - 1: 0 < 4(0) - 1 = -1, which is false.

Substitute x = 0 and y = 0 into y > x: 0 > 0, which is false.

Since at least one inequality is false, the ordered pair (0,0) is not a solution to the system y < 4x - 1 and y > x.

The value of x are:

1)

81/2

2)

33/4

3)

13

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

First question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

45/20 = x/18

9/4 = x/18

x = 18 x 9 / 4

x = 9 x 9/2

x = 81/2

Second question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

22/8 = x/6

11/4 = x/6

x = 6 x 11 / 4

x = 66/4

x = 33/4

Third question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

21/15 = (5x - 16)/(3x - 4)

7/5 = (5x - 16)/(3x - 4)

7(3x - 4) = 5(5x - 16)

21x - 28 = 25x - 80

80 - 28 = 25x - 21x

52 = 4x

x = 13

Thus,

The value of x is 81/2, 33/4, and 13.

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Answer:

Nintendo's revenue was $21 billion

Step-by-step explanation: