Tien has three employees working for her in Saskatoon. Each employee is paid
minimum wage for an 8 hour day. They are also paid a commission of 12% on all sales
they make. If the three employees made sales of $785.96, $452.87, and $616.42, how
much must Tien pay in total for the day

Answer:

Step-by-step explanation:

Answer:

y = 40°

z = 140°

x = 100°

Information:

(i) Sum of interior angles of a triangle sum ups to 180°

(ii) On a straight line, the angles sum up to 180°

(iii) One exterior angle is equal to two opposite interior angles.

Here the exterior angle theorem applies.

∠z = 120° + 20°

∠z = 140°

Find the angle C. Here angles lie on a straight line.

∠? + 120° = 180°

∠? = 180° - 120° = 60°

80°, 60° and y are interior angles of a triangle.

y + 80°+ 60° = 180°

y = 180° - 140°

y = 40°

∠? = 40° (vertically opposite angle)

Now,

y + x + 40° = 180°

40° + x + 40° = 180°

x = 100°

The distance between the two given points coordinates is; Option C: √85

Formula for the distance between two coordinates is;

d = √((x₂ - x₁)² + (y₂ - y₁)²)

We are given the coordinates as;

(-2, 3) and (5, -3). Thus;

d = √((-2 - 5)² + (-3 - 3)²)

d = √(49 + 36)

d = √85

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The value that remains under the radical is 2

The correct expression in the question is:

1250^4

This can be rewritten as:

[tex]\sqrt[4]{1250}[/tex]

Express 1250 as product

[tex]\sqrt[4]{(2 * 5^4)}[/tex]

Expand the expression

[tex]\sqrt[4]{2} * \sqrt[4]{5^4}[/tex]

Simplify

[tex]\sqrt[4]{2} * 5[/tex]

Evaluate the product

[tex]5\sqrt[4]{2}[/tex]

Hence, the value that remains under the radical is 2

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The correct statement is that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. Option D

6x + y = 2 2x − 3y = −10    System A

-x − y = −3 −x − y = −3 System B

Let;s solve for x and y in system A

6x + y = 2

Make 'y' the subject

y = 2-6x

Substitute in the other equation

-x -y = -3

-x - (2-6x) = -3

-x -2+6x = -3

Collect like terms

5x = -3+2

x = -1/5

Substitute in y = 2-6x to find 'y'

y = 2- 6(-1/5)

y = 2+ 6/5

y = [tex]\frac{10+ 6}{5}[/tex]

y = 16/5

For system B

-x-y = -3

Make y subject, we have

-x + 3 = y

y = -x + 3

Substitute in the other equation, we have

2x − 3y = −10

2x - 3(-x+3) = -10

2x + 3x -9 = -10

Collect like terms

5x -9 = -10

5x = -10 + 9

x = 1/5

Substitute into y = -x + 3 to find 'y'

y = -(1) + 3

y = 2

Thus, the correct statement is that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. Option D

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:

LM

Step-by-step explanation:

Usually these problems would already be in order, so since PQ are the first 2 letters of polygon PQRS, then for LMNO, it's LM.

Answer: 3

Step-by-step explanation:

By the intersecting chords theorem,

[tex](KM)(16)=(4)(12)\\\\KM=3[/tex]

Answer:

If it is assumed that the change was constant from 2009 and 2012 , then change of population is 142 .

Step-by-step explanation:

In the question, it is given that the population of a small town increased from 1442 to 1868 between 2009 and 2012 .

It is asked to find the change of population if it is assumed that the change was constant from 2009 and 2012 .

Step 1 of 2

Population in 2012 is given to be 1868 and

Population in 2009 is given to be 1442 .

Duration of year is given by 2012-2009 which is 3 years.

Change in population is given by 1868-1442 which is 426 .

Step 2 of 2

Change in population per year is given by dividing the change in population and the duration of years it took to happen the change.

Hence, change in population per year is

[tex]$\frac{426}{3}=142$[/tex]

Hence, the population was changed by 142 per year from 2009 to 2012 .

Answer:

Step-by-step explanation:

from the sign on the picture it is a rigth triangle

we use pythagoras

x² = 12² - 7²

x² = 144 - 49

x² = 95

x = √95

(x = 9.75)

Answer:

x = [tex]\sqrt{95}[/tex]

Step-by-step explanation:

In this problem, we need to use the Pythagorean theorem.

Pythagorean theorem is a theorem where you can find a side length in a right triangle.

The hypotenuse (The longest side) squared equals the other two side lengths added together after being squared.

In numbers, this will be: (12)^2 = (7)^2 + (x)^2.

144 = 49 + x^2.

95 = x^2

x = [tex]\sqrt{95}[/tex]

We cannot simplify [tex]\sqrt{95}[/tex], so that is the final answer.

Answer:

Step-by-step explanation:

Domain is the set of all possible inputs (x) for the function f(x)

The range is the set of all possible values for that domain

This function is 4x + y = 3 which can be re-written as y = 3-4x

Plug in each of the domain values and you will get the range

For -2 : y = 3-4(-2) = 3 + 8 = 11

For 1:  y = 3-4(1) = -1

For 5: y = 3-4(5) = -17

So range is {-17, -1, 11}  

Answer:

Second graph

Step-by-step explanation:

See attached image.

The first graph is the exponential function.

The exponential function serves as the  positive-valued function with respect to real variable. and  the values denoted as X which is exponential is  all real numbers.

Analyzing the first graph, moving down the graph, we can see that  x value increases.

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Answer:

First Graph

Step-by-step explanation:

Edge

Answer:

=========

We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.

Find the slope of line 1 by converting the equation into slope-intercept from standard form:

Info:

Its slope is 3/k.

Find the slope of line 2, using the slope formula:

We have both the slopes now. Find their product:

So when k is 18, the lines are perpendicular.

a. The required sample size when pn and qn are unknown then n = 1844

b. The required sample size when about 10% of Californians are left-handed is n = 664

c. There would have been no effect on parts a and b if entire US has been chosen

According to statement

a. No estimate of proportion is given so we will assume:  

{p} = {q} = 0.5

For 99% confidence, z = 2.576

E = 0.03  

Hence, Required sample size  

n = (0.5)*(0.5)*(2.576/0.03)^2  

n = 1844

b. {p} = 0.10

{q} = 1 - {p}

{q} = 1 - 0.10

{q} = 0.90  

For 99% confidence, z = 2.576

E = 0.03

Hence,  Required sample size  n = (0.1)*(0.9)*(2.576/0.03)^2  = 664

c. There would have been no effect on parts a and b if entire US has been chosen because minimum sample size required is not dependent on population size.

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Answer:

The greatest common factor of 72 and 162 is 18.

Step-by-step explanation:

In my opinion, one of the easier ways to find the greatest common factor of two numbers is to get the prime factors of both and multiply the common ones. The prime factorization of 72 is 2*2*2*3*3, and the prime factorization of 162 is 2*3*3*3*3 (you can make a factor tree for both of these numbers to verify this). The common primes factors for both of these numbers are 2, 3, and 3 (both 72 and 162 have one 2 and at least two 3s). 2*3*3 is 18, which is the greatest common factor.

Answer:

a monomial, a constant

Step-by-step explanation:

It has only 1 term, so it's a monomial.

Also, the term is a constant.

Answer:

The third option.

Step-by-step explanation:

[tex](\frac{4xy^3}{x^2})^2\\\\=(\frac{4y^3}{x})^2\\\\=\frac{16y^6}{x^2}[/tex]

Hence the 3rd option.

Answer:

Answer A is correct

Step-by-step explanation:

Let us use completing square method for this.

[tex]x^{2} -5x -10=0\\\\x^{2} -5x=10\\\\x^{2} -5x+\frac{25}{4}=10+ \frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{10*4}{1*4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40}{4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40+25}{4} \\\\(x+\frac{5}{2}) ^{2} =\frac{65}{4} \\\\(x+\frac{5}{2}) = \±\sqrt{\frac{65}{2} }\\\\(x+\frac{5}{2}) =\±\frac{\sqrt{65}}{4}\\\\x=\±\frac{\sqrt{65}}{4}-\frac{5}{2}[/tex]

∴ [tex]x=-\frac{5}{2} \±\frac{\sqrt{65}}{4}[/tex]

The values of the trigonometric functions are

[tex]sin \theta = \frac{12}{13}[/tex]

[tex]cos \theta = \frac{5}{13}[/tex]

[tex]tan \theta = \frac{12}{5}[/tex]

 [tex]cot\theta = \frac{5}{12}[/tex]

[tex]csc\theta = \frac{13}{12}[/tex]

From the question, we are to determine the values of the given trigonometric functions

From the given information,

[tex]sec \theta =\frac{13}{5}[/tex]

∴ [tex]\frac{1}{cos \theta} =\frac{13}{5}[/tex]

[tex]cos \theta = \frac{5}{13}[/tex]

Thus,

Adjacent = 5

Hypotenuse = 13

Opposite = ?

Using the Pythagorean theorem

|Opp|² = |Hyp|² - |Adj|²

|Opp|² = 13² - 5²

|Opp|² = 169 - 25

|Opp|² = 144

|Opp| = √144

|Opp| = 12

∴ Opposite = 12

Thus,

By using SOH CAH TOA

[tex]sin \theta = \frac{12}{13}[/tex]

[tex]tan \theta = \frac{12}{5}[/tex]

[tex]cot\theta = \frac{1}{tan\theta}[/tex]

∴ [tex]cot\theta = \frac{5}{12}[/tex]

[tex]csc\theta = \frac{1}{sin\theta}[/tex]

∴ [tex]csc\theta = \frac{13}{12}[/tex]

Hence, the values of the trigonometric functions are

[tex]sin \theta = \frac{12}{13}[/tex]

[tex]cos \theta = \frac{5}{13}[/tex]

[tex]tan \theta = \frac{12}{5}[/tex]

 [tex]cot\theta = \frac{5}{12}[/tex]

[tex]csc\theta = \frac{13}{12}[/tex]

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Step-by-step explanation:

it isnot looking well here so go on geogebra. org/calculator and you will see. have a nice day :))

Answer:

C on Edge 2022

Step-by-step explanation:

Just did it and got it right

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal. The correct option is C.

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.

Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. The congruency statement that applies to the trapezoids is CDEF ≅ NMOP.

Hence, the correct option is C.

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Since we know that <C is congruent to <E, we can say that: A. the two triangles are similar by SAS.

In Geometry, two triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Ratio = BC/AC = 6/3 = 2.

Ratio = FE/DE = 4/2 = 2.

Thus, the ratio of their corresponding sides are equal in magnitude i.e BC/AC ≡ FE/DE.

Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.

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56 units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$

Properties of triangles are:

A triangle has three sides and three angles.

The sum of the angles of a triangle is always 180 degrees.

The exterior angles of a triangle always add up to 360 degrees.

The sum of consecutive interior and exterior angle is supplementary.

Given:

Height: ha = 7

Height: hb = 24

Height: hc = 25

Sum to sides is:

25 +7 + 24 =56 units.

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The equation which is equivalent to the given simple interest formula is

[tex]P=\frac{A}{1+rt}[/tex].

What is an equivalent equation?

Equivalent equations are algebraic equations that have identical solutions.

According to the given question.

We have a simple interest formula.

[tex]A=P(1+rt)[/tex]

Now, the equivalent equation for the above formula can be given as

[tex]A=P(1+rt)[/tex]

⇒[tex]P=\frac{A}{1+rt}[/tex]

Hence, the equation which is equivalent to the given simple interest formula is [tex]P=\frac{A}{1+rt}[/tex].

Thus, option A is correct.

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Answer:

Step-by-step explanation:

The  airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let a represent the rate of the airplane with no wind. and b the rate of the wind, hence:

(a - b)3.2 = 640

a - b = 200   (1)

Also:

(a + b)2 = 640

a + b = 320    (2)

The solution to equation 1 and 2 is:

a = 260, b = 60

The  airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.

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Answer:

The answer is B: x = 0 and x = 4

Step-by-step explanation:

The zeroes of a function are the x-intercepts, or the x values of the points that are on the x-axis. (The x-axis is the numbered horizontal line.)

One of the zeroes passes through the origin, which is (0,0). The other point is right before the number 5 on the x axis, which means that the point is (0, 4). If you look at the x-values of the ordered pairs of the zeroes, that's the answer.

(x, y)

dy/dx by implicit differentiation is cos(πx)/sin(πy)

Since we have the equation

(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.

So, [(sin(πx) + cos(πy)⁸ = 17]

d[(sin(πx) + cos(πy)⁸]/dx = d17/dx

d[(sin(πx) + cos(πy)⁸]/dx = 0

Let sin(πx) + cos(πy) = u

So, du⁸/dx = 0

du⁸/du × du/dx = 0

Since,

= dsin(πx)/dx + dcos(πy)/dx

= dsin(πx)/dx + (dcos(πy)/dy × dy/dx)

= πcos(πx) - πsin(πy) × dy/dx

So, du⁸/dx = 0

du⁸/du × du/dx = 0

8u⁷ × [ πcos(πx) - πsin(πy) × dy/dx] = 0

8[(sin(πx) + cos(πy)]⁷ ×  (πcos(πx) - πsin(πy) × dy/dx) = 0

Since 8[(sin(πx) + cos(πy)]⁷ ≠ 0

(πcos(πx) - πsin(πy) × dy/dx) = 0

πcos(πx) = πsin(πy) × dy/dx

dy/dx = πcos(πx)/πsin(πy)

dy/dx = cos(πx)/sin(πy)

So, dy/dx by implicit differentiation is cos(πx)/sin(πy)

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Answer:

c

Step-by-step explanation:

y = [tex]\frac{5}{2}[/tex] x + 2 → (1)

2y = 5x + 4 ( divide through by 2 )

y = [tex]\frac{5}{2}[/tex] x + 2 → (2)

the 2 equations are the same and will have infinitely many solutions

Answer:

3300

Step-by-step explanation:

This can be worked out using PEMDAS:

First you solve in the PARENTHESIS:

(4 × 10³) – (7 × 10²)

Then, you look at the EXPONENTS:

(4 × 10³) = (4 × 1000)

(7 × 10²) = (7 × 100)

After that, look at the MULTIPLICATION:

(4000) - (700)

Since there is only subtraction left, subtract it:

3300

Answer:

Parenthesis:

4 *1000 = 4000

7*100= 700

4000-700=3300

Step-by-step explanation: