Approximately 41% of films are rated PG. If 950 films were recently rated, how many films were rated PG.?

Answer:

Therefore, z = 1 + i.

Step-by-step explanation:

Given that the argument of z + 1 is pi/6 and the argument of z - 1 is 2*pi/3, we can use the fact that the argument of a complex number is equal to the angle between the positive x-axis and the line connecting the origin to the complex number in the complex plane.

Let's call the complex number z = a + bi. Then, z + 1 = a + (b + 1), and z - 1 = a - (b - 1).

Using the argument values given, we have:

arg(z + 1) = pi/6, so the line connecting the origin to z + 1 makes an angle of pi/6 with the positive x-axis.

arg(z - 1) = 2pi/3, so the line connecting the origin to z - 1 makes an angle of 2pi/3 with the positive x-axis.

From the above information, we can sketch the complex plane and find the location of the complex number z. We then have two equations for a and b in terms of the argument of the complex numbers:

a = (z + 1 + z - 1)/2 = 1

b = (z + 1 - z - 1)/2 = 1

Therefore, z = 1 + i.

Answer:

Step-by-step explanation:

Given:

Find the length of AC and CB:

Find CB:

Find the length of CD:

Find the length of AD:

Find the midpoint of AD:

Find the midpoint of CB:

Find the distance between the midpoints:

Answer:

Step-by-step explanation:

Answer:

slope is 5/4

Step-by-step explanation:

The equation of the line is written in the form

y = mx+b where m is the slope and b is the y intercept

y = 5/4x -7/4

The slope is 5/4 and the y intercept is -74

Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

Answer:

(-3, 0) and (-5, 0)

Step-by-step explanation:

[character limit thing]

The expansion will be 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

We can expand (2d+3)^6 using the binomial theorem, which states that:

(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn-1 * a^1 * b^(n-1) + nCn * a^0 * b^n

where nCk is the binomial coefficient, given by:

nCk = n! / (k! * (n-k)!)

Expanding (2d+3)^6 using this formula, we get:

(2d+3)^6 = 6C0 * (2d)^6 * 3^0 + 6C1 * (2d)^5 * 3^1 + 6C2 * (2d)^4 * 3^2 + 6C3 * (2d)^3 * 3^3 + 6C4 * (2d)^2 * 3^4 + 6C5 * (2d)^1 * 3^5 + 6C6 * (2d)^0 * 3^6

Simplifying each term using the binomial coefficient formula, we get:

(2d+3)^6 = 1 * 64d^6 * 1 + 6 * 32d^5 * 3 + 15 * 16d^4 * 9 + 20 * 8d^3 * 27 + 15 * 4d^2 * 81 + 6 * 2d * 243 + 1 * 1 * 729

Simplifying each term further, we get:

(2d+3)^6 = 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

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Answer: To calculate the average cost per widget, we need to consider both the fixed costs and the variable costs.

Fixed costs: $34,000

Variable costs per widget: $5.00

Total costs = Fixed costs + (Variable costs per widget × Number of widgets)

Total costs = $34,000 + ($5.00 × 7,000)

Total costs = $34,000 + $35,000

Total costs = $69,000

Average cost per widget = Total costs / Number of widgets

Average cost per widget = $69,000 / 7,000

Average cost per widget ≈ $9.86

Therefore, the average cost per widget of producing 7,000 Wild Widgets is approximately $9.86.

Step-by-step explanation: :)

Answer:

hold on..

Step-by-step explanation:

Answer:

x =  − 4

Step-by-step explanation:

I put your question in a math calculator and this is what I got. Good Luck

Answer:

(-3, -0.5)

Step-by-step explanation:

(-8 + 2) = -6 / 2 = -3

(-6 + 5) = -1 / 2 = -0.5

We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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Answer: 0 = 3

Step-by-step explanation: If y = 7 - 3x, we can plug that in for y in the equation 3x + y = 10 by writing it as 3x + 7 - 3x = 10.

                                                                    - 7            - 7

                                                               --------------------------

                                                               3x - 3x        = 3

                                                                       0          = 3

Answer:

1/3 (a+b)

Step-by-step explanation:

The required solution is 1/3ab.

It is required to find the solution.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Let the 2 numbers be a and b.

According to given question we have,

Product =a× b=ab

1/3 of product =1/3ab

Therefore, the required solution is 1/3ab.

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Answer:

12,746

Step-by-step explanation:

To find this answer, we need to divide by 8

Since we know that South Dakota sells 8X less than Michigan, we have to use the opposite sign (which in this case is division.)

Now, we use the equation 101,968/8 which gets us an answer of…

12,746!

Answer:

The percentage of beads on clearance that are plastic is 90%

Step-by-step explanation:

9/10 = 90/100

The answer has to be out of 100. So, you would multiply 9 times 10 to get 90 and 10 times 10 to get 100

90/100 = 90%

Hope this helps :)

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

D

Step-by-step explanation:

First, to find the length of the side FH we will use the Pythagorean theorem which states \(a^2+b^2=c^2\). We can say that FH = a, FG = b, and HG = c. Since we know the values of b and c, we will rearrange the formula to solve for a \(a = \sqrt{c^2-b^2}\). That will be \(\sqrt{18^2-12^2)\) which gives us 13.4 for the missing side.

Now to solve for the angles we will use simple trigonometry. Since we know that \(sin(\theta) = \frac{opposite} {hypotenuse}\), we can do inverse trigonometry for the missing angles \(sin^{-1}(\frac{opposite}{adjacent}) = \theta\). For angle H, we can do \(sin^{-1}(\frac{12}{18})\) which gives us 41.8 degrees. For angle G we can do \(sin^{-1}(\frac{13.4}{18})\) and we get 48.1 degrees. We could also use inverse cos and trig to solve it.

Looking at the answer choices, only answer choice D is correct.

Answer:

$24

Step-by-step explanation:

First, find the cost to cover one pair of shoes.

Cost to cover one pair of shoes = surface area of the shoe box × cost per square inch

= 2(LW + LH + HW) × 0.02

L = 14 in.

W = 8 in.

H = 4 in.

Plug in the values

Cost to cover one pair of shoes = 2(14*8 + 14*4 + 4*8) × 0.02

= 2(112 + 56 + 32) × 0.02

= 2(200) × 0.02

= 400 × 0.02 = 8

Cost to cover one pair of shoes = $8

Cost to cover 3 pairs of shoes = 3*8 = $24

The vertex of the graph is a maximum at (-2, 4)

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a quadratic function

From the graph, we can see that the graph has a maximum value

This maximum value represents the vertex of the graph

And it is located at (-2, 4)

So, we have

Maximum = (-2, 4)

Hence, the maximum value of the function is (-2, 4)

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Answer:

333234

Step-by-step explanation:

333234$ for the next 4 years and the ecvation is 69$+-2$

Answer:

[see below]

Step-by-step explanation:

-7n is getting subtracted from 15.

7n is 'the product of 7 and n'

15-7n could be 'the difference of fifteen and the product of 7 and n'. The correct answer choice would be the one closest to this/

Hope this helps.

Answer: 12/5 which simplifies to 2 2/5.

Step-by-step explanation: Check attachment.

g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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Answer:

  61.03°

Step-by-step explanation:

You want the angle opposite the side of length 7 in the triangle with other sides of lengths 4 and 8.

The law of cosines relates the angles of a triangle to the side lengths. For triangle ABC with opposite sides a, b, c, the relation is ...

  c² = a² +b² -2ab·cos(C)

Solving for angle C, we have ...

  cos(C) = (a² +b² -c²)/(2ab)

  C = arccos((a² +b² -c²)/(2ab))

In this triangle, that means ...

  C = arccos((4² +8² -7²)/(2·4·8)) = arccos(31/64)

  C ≈ 61.03°

The angle of interest is about 61.03°.

__

Additional comment

We get the same result from a triangle solver. See the second attachment. (The angle we want is angle B in that attachment.)

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Answer:

11

Step-by-step explanation:

for each full cup of sugar, you need 3 one-third measuring cups.

we have 3 full cups so 3×3=9

and another 2 for the 2/3, 9+2=11

so a total of 11 scoops

Answer:

Answer:

yes I just checked it

Step-by-step explanation:

Answer:

His average speed is 50.5 miles per hour

Step-by-step explanation:

I divided 141.4 miles by 2.8 hours and got 50.5 miles per hour

Explanation:

This problem is a simple percent chage problem. The absoluge change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.