Round 68,425,389 to the nearest million. (Don't forget to include commas in the number.)

Answer:

A) SAS postulate

Step-by-step explanation:

Answer:

SAS

Step-by-step explanation:

you know that ST is equal and you also know two equal angles and one other equal side

The values of the given functions are as follows: [f∘g](x) = 1/2x - 8, [g∘f](x) = 1/2x - 1, [f∘g](x) = x^3 + 3x^2 + 3x + 1, [f∘g](x) = 8x^3 + 4x^2 + 1 and [g∘f](x) = 2x^3 + 2x^2 + 2.

To find [f∘g](x) and [g∘f](x), we need to substitute the values of g(x) in f(x) and then find the result for [f∘g](x) and vice versa.

If f(x) = 1/2x - 7 and g(x) = x + 6, then [f∘g](x) is calculated as follows:

f[g(x)] = f(x + 6) = 1/2(x + 6) - 7 = 1/2x - 8

Therefore, [f∘g](x) = 1/2x - 8.

If f(x) = 1/2x - 7 and g(x) = x + 6, then [g∘f](x) is calculated as follows:

g[f(x)] = g(1/2x - 7) = 1/2x - 7 + 6 = 1/2x - 1

Therefore, [g∘f](x) = 1/2x - 1.

If f(x) = x^3 and g(x) = x + 1, then [f∘g](x) is calculated as follows:

f[g(x)] = f(x + 1) = (x + 1)^3 = x^3 + 3x^2 + 3x + 1

Therefore, [f∘g](x) = x^3 + 3x^2 + 3x + 1.

If f(x) = x^3 and g(x) = x + 1, then [g∘f](x) is calculated as follows:

g[f(x)] = g(x^3) = x^3 + 1

Therefore, [g∘f](x) = x^3 + 1.

If f(x) = x^3 + x^2 + 1 and g(x) = 2x, then [f∘g](x) is calculated as follows:

f[g(x)] = f(2x) = (2x)^3 + (2x)^2 + 1 = 8x^3 + 4x^2 + 1

Therefore, [f∘g](x) = 8x^3 + 4x^2 + 1.

If f(x) = x^3 + x^2 + 1 and g(x) = 2x, then [g∘f](x) is calculated as follows:

g[f(x)] = g(x^3 + x^2 + 1) = 2(x^3 + x^2 + 1) = 2x^3 + 2x^2 + 2

Therefore, [g∘f](x) = 2x^3 + 2x^2 + 2.

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To answer this question we will use the following trigonometric identity:

Solving the first equation for cosθ we get:

Solving the second equation for sinθ we get:

Substituting

in the trigonometric identity we get:

Simplifying the above result we get:

Finally, recall that:

Therefore:

Therefore x is on the interval:

Answer:

where x is on the interval

Each person (Tammy, John, Allison, and Henry) paid $11.25 for a movie ticket.

To determine the cost of each movie ticket, we will divide the total amount paid by the number of people who bought tickets.

Total amount paid: $45
Number of people: Tammy, John, Allison, and Henry (4 people)

Step 1: Divide the total amount paid by the number of people.
$45 ÷ 4 = $11.25

So, Allison and each of her friends paid $11.25 for a movie ticket.

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There are 15,504 ways to randomly select a team of 5 people from a group of 20 people

If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:

C(20, n) = 20! / (n! * (20 - n)!)

where C(20, n) represents the number of ways to select n people from a group of 20 people.

For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:

C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504

Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.

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Answer:

Step-by-step explanation:

a. equation 2

b. equation 3

c. equation 1

d. equation 4

e. equation 5

To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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Answer:

$2.85

Step-by-step explanation:

Answer:

$22.23

Step-by-step explanation:

7.8 x 2.85 = 22.23 :D

Answer:

The measure of angle WVX is 140°.

Step-by-step explanation:

Let x be the measure of angle WVX.

\( \frac{14}{9} \pi = 2x\)

\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)

Answer:

angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.

so, the answer is 140 degrees.

Answer:

slope = - \(\frac{1}{2}\), y- intercept = 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = \(\frac{0-1}{2-0}\) = - \(\frac{1}{2}\)

The y- intercept is the value of y where the graph crosses the y- axis.

y- intercept = 1

If a contractor is constructing a pool with the labels ABCD and if AC = 5y + 6 and BD = 8y-3, then the  value of y which is 03 that ensures the pool is a rectangle.

The statement  states that  he is building a pool labeled ABCD on the plans. If AC = 5y + 6 and BD = 8y-3

We know that rectangle has 2 diagonals of equal length.

Diagonal 1 = Ac

Diagonal 2 = BD

AC = BD

5y+ 6 = 8y -3

9 = 3y

3 = y

3 value of y ensures the pool is a rectangle .

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Answer:

\(22\)

Step-by-step explanation:

Similar shapes must have corresponding sides in a constant proportion. Therefore, we can set up the following equation and solve for \(?\):

\(\frac{28}{42}=\frac{?}{33}\) (divide corresponding sides)

\(\frac{28}{42}=\frac{?}{33},\\\\?=\frac{28\cdot 33}{42}=\boxed{22}\)

The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

(-3,6)

Step-by-step explanation:

As  graph shows x=-3 and y=6  

Answer:

-3 to +6 is the answer to the question

The equation holds true, confirming that (-5, 2) is indeed the solution to the given equation.

To complete the missing value in the solution to the equation x - 5y = -15, we substitute the given x-value (-5) into the equation and solve for y.

Substituting x = -5 into the equation, we have:

-5 - 5y = -15

Next, we simplify the equation by combining like terms:

-5y = -15 + 5

-5y = -10

To isolate y, we divide both sides of the equation by -5:

y = (-10) / (-5)

Simplifying further, we have:

y = 2

Therefore, the missing value in the solution to the equation is y = 2.

In the ordered pair form, the solution is represented as (-5, 2), where -5 corresponds to the x-value and 2 corresponds to the y-value.

This means that when x is equal to -5, and y is equal to 2, the equation x - 5y = -15 is satisfied. Plugging in these values into the equation:

-5 - 5(2) = -15

-5 - 10 = -15

-15 = -15

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The total area of the figure is 250 sq units. So, option B is the correct option.

The area of the rectangle with a length of 25 and a height of 5 is given by:

A=25×5=125 sq units

The two triangles and a rectangle that are atop the first rectangle are shown below:

Let’s calculate the area of the triangles:

The two triangles have a base of 25 units (the same as the length of the first rectangle)

and heights of 2 units (8-6) each,

so the area of one triangle is:(1/2)×25×2=25 sq units

Therefore, the area of both triangles is:2×25=50 sq units.

Now let’s calculate the area of the rectangle:

To calculate the area of the rectangle, we need to find its length and height.

We know that the two triangles and the rectangle are a top the first rectangle,

so the length of the rectangle is also 25 units.

The height can be found by subtracting the height of the triangles (2 units) from the height of the first rectangle (5 units), so the height of the rectangle is : 5 - 2 = 3 units

Therefore, the area of the rectangle is: A = 25×3 = 75 sq units.

Now we can find the total area of the figure by adding up the areas of the first rectangle, the two triangles, and the second rectangle:

Total area = 125+50+75 = 250 sq units

Therefore, the total area of the figure is 250 sq units.

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Question:

The figure is made up of 2 rectangles and 2 right triangles.

What is the area of the figure?

A. 173 \(units^2\)

B. 250 \(units^2\)

C. 277 \(units^2\)

D. 325 units^2

The complete statement is BC = TR. The correct option is d. TR

From the question, we are to complete the given statement

From the given information,

ΔABC = ΔSTR

That is, ΔABC and ΔSTR are similar triangles

If ΔABC and ΔSTR are similar triangles,

Then,

AB = ST

BC = TR

AC = SR

Hence, the complete statement is BC = TR. The correct option is d. TR

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Answer:

5

Step-by-step explanation:

The number of apples bought by him is 113.

A grouping of variables, symbols, and/or numbers used to represent a mathematical quantity or relationship is known as an expression in mathematics. Expressions might be straightforward with just one number or variable or complex with many terms, operations, and functions.

Let's assume that Sam bought x number of apples.

He bought them at 60 cents each, which means the total cost of buying these apples was:

Cost price = 60x cents

He sold all but 5 of these apples at R1.00 each, which means the total revenue he earned from selling them was:

Revenue = (x - 5) x R1.00 = R(x - 5)

Sam made a profit of R5.00, which means his revenue was more than his cost price by R5.00. We can write this as:

Revenue - Cost price = R5.00

Substituting the values of revenue and cost price from above, we get:

R(x - 5) - 60x = 500 cents

Rearranging and simplifying this equation, we get:

40x = 500 + 5R

Substituting R = R1.00, we get:

40x = 500 + 5 = 505

Solving for x, we get:

x = 12.625

Since Sam cannot buy a fraction of an apple, we round up x to the nearest integer:

x = 13

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Answer:

840

Step-by-step explanation:

7000×2×6 ÷ 100. since it is 2%

= 840

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

Answer:

Greater probability of gray than black = 3/25

Step-by-step explanation:

Given:

Total block = 5 x 5 = 25

Number of black blocks = 6

Number of gray blocks = 9

Find:

Greater probability of gray than black

Computation:

Greater probability of gray than black = Probability of gray - Probability of black

Greater probability of gray than black = 9/25 - 6/25

Greater probability of gray than black = 3/25

Displacement is calculated as the shortest distance between starting and final point which prefers a straight-line path over curved paths.

Displacement is the distance between two different positions of an object in m motion. So, it depends on the initial position and its final position. Also, displacement is the minimum distance between the starting and final positions.

Suppose a body is moving in two different directions x and y then the Resultant Displacement will be S=√x²+y²

Example 1: The path distance from the garden to a school is 5 m west and then 4 m south. A builder wants to build a short-distance path for it. Find the displacement length of the shortest path.

Solution: Distance to the west x = 5 m

Distance to the south y = 4 m.

Displacement is given by S=√x²+y²

s = 6.403 m.

The builder can build a path for a displacement length of 6.7 m.

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The formula to solve the displacement is written as Δx  = xf − xi

The term displacement is defined as  the change in the position of any point or object. It has a direction and magnitude, so it is a vector quantity and it is shown with an arrow that points from the starting position to the final position.

In order to find the displacement by determining the object’s initial and final position.

Therefore, the displacement formula is written as,

=> Δx  = xf − xi

Here xf refers the final position,

And the variable xi is the initial position, and

Then the term Δx is the change in the position of the object.

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Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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Answer:

Will usually be labelled?

Answer: It should say either in the equation itself, or in the directions

Step-by-step explanation:

If the instructions don't say which variable you're solving for, you can figure it out by looking at the equation

For example, we have this equation

\(9x+3=21\)

In this equation, there is only one variable to solve for, and that variable is x

\(y=15-\sqrt{16}\)

In this equation, there is only one variable to solve for, and that variable is y

However, if you're given an equation with more than one variable, most of the time, you have to solve for both!

Answer:

2.8%, and 3.2%

Step-by-step explanation:

Buyer's real estate agent:

9522.80 ÷ 340100.00 = 0.028 = 2.8%

Seller’s real estate agent:

10883.20 ÷ 340100.00 = 0.032 = 3.2%

The correct answer is option c A stem plot of the data would be skewed right.

A median that is larger than the mean in a set of exam scores suggests that the data is skewed to the right (or positively skewed), meaning that there are more scores at the high end of the distribution. This results in a longer tail on the right side of the distribution, which is often seen in data that contains outliers or extreme values. In this case, a stem plot of the data would be skewed to the right, showing a long tail on the right side of the plot.

Option a (a stem plot of the data would be symmetric) is incorrect because a symmetric distribution would have a median and mean that are equal, which is not the case here.

Option b (a stem plot of the data would be skewed left) is incorrect because a skewed left distribution would have a median that is smaller than the mean, which is not the case here.

Option d (the data set must be so large that it would be better to draw a histogram rather than a stem plot) is incorrect because the size of the data set does not affect the skewness of the data or the choice of a plot to use.

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Answer:

150

Step-by-step explanation:

300-150

True. Since the square matrix that represents the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same. This property is a fundamental characteristic of orthogonal matrices and holds true for all orthogonal matrices.

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False While it is true that the square matrix that represents the DCT coefficient is orthogonal, it does not mean that its inverse and transpose are the same.

the inverse of an orthogonal matrix is its transpose. However, the transpose of the matrix does not necessarily mean that it is the same as the inverse of the matrix. In the statement is false because the inverse and transpose of an orthogonal matrix are not always the same.


The Discrete Cosine Transform (DCT) coefficient matrix is an orthogonal matrix. In the case of orthogonal matrices, the inverse matrix is indeed equal to the transpose of the original matrix. This is because the product of an orthogonal matrix and its transpose results in the identity matrix.

Since the square matrix representing the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same.

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The critical numbers of a function occur at the points where the derivative is either zero or undefined. To find the critical numbers of the function f(x) = \(-2x^3 + 27x^2 - 84x + 10,\) we need to find its derivative f'(x) and set it equal to zero.

Differentiating f(x) with respect to x, we get f'(x) = \(-6x^2 + 54x - 84\). Setting f'(x) equal to zero and solving for x gives us:

\(-6x^2 + 54x - 84 = 0\)

Dividing the equation by -6, we have:

\(x^2 - 9x + 14 = 0\)

Factoring the quadratic equation, we find:

(x - 2)(x - 7) = 0

So the critical numbers occur at x = 2 and x = 7.

Therefore, the values of A and B are A = 2 and B = 7.

To determine whether these critical numbers correspond to local maxima or minima, we need to evaluate the second derivative f''(x) of the function.

Differentiating f'(x) = \(-6x^2 + 54x - 84\), we obtain f''(x) = -12x + 54.

Substituting x = 2 into f''(x), we get:

f''(2) = -12(2) + 54 = 30

Substituting x = 7 into f''(x), we get:

f''(7) = -12(7) + 54 = 6

Since f''(2) > 0, it implies a concave up shape, indicating a local minimum at x = 2. On the other hand, f''(7) < 0 indicates a concave down shape, suggesting a local maximum at x = 7.

Therefore, f(x) has a local minimum at A (x = 2) and a local maximum at B (x = 7).

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The volume of the cone has a value of 410.67 cubic meters

From the question. the height and the radius of the cone are given as

Height = 7 feet

Radius = 8 feet

The volume of the cone can be calculated using the following volume formula

Volume = 1/3πr^2h

Substitute the known values in the above equation

So, we have

Volume = 1/3 * 22/7 * 8 * 7^2

Evaluate the products

Volume = 410.67

Hence, the volume is 410.67 cubic meters

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