844,758,200,030 rounded to the nearest billion.

The total number of people in the population is 2940.To find the total number of people, we need to determine the ratio of big spenders to the total population.

Given that the ratio of big spenders to tightwads is 5 to 2, we can consider it as 5x to 2x, where x is a common factor.

We are told that there are 2100 big spenders, which represents the 5x portion of the ratio. So we can set up the equation:

5x = 2100

To solve for x, we divide both sides of the equation by 5:

x = 2100 / 5

x = 420

Now that we know the value of x, we can find the total population by adding the big spenders (5x) and the tightwads (2x):

Total population = [tex]5x + 2x = 7x[/tex]

Substituting the value of x:

Total population [tex]= 7 * 420 = 2940[/tex]

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The range of the absolute value function y = |x| is all non-negative numbers, which can be expressed as [0, ∞).

The absolute value function is a type of mathematical function that measures the distance between a given number and zero. It is denoted by two vertical bars surrounding the number or expression.

The range of the absolute value function is the set of all non-negative numbers. This is because the absolute value of any number is always a positive number or zero.

For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3.This means that the output of the function can never be negative and can range from zero to infinity.

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The range of the absolute value function below is C. f(x) < 1.

The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function. Domain→ Function →Range.

The range of a function is the set of all its outputs. Example: Let us consider the function f: A→ B, where f(x) = 2x and each of A and B = {set of natural numbers}.

The function y=|ax+b| is defined for all real numbers. So, the domain of the absolute value function is the set of all real numbers. The absolute value of a number always results in a non-negative value.

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What is the range of the absolute value function below?

f(x) > -4

f(x) > -1

f(x) < 1

f(x) < 4

The missing value 'x' in the two-way relative frequency table is 0.36.

To convert the two-way table to a two-way relative frequency table, we need to calculate the relative frequencies for each category. Relative frequency is calculated by dividing the frequency of a particular category by the total count in that row or column.

Let's denote the missing value as 'x'. To find the value of 'x', we need to ensure that the sum of the relative frequencies in each row and each column adds up to 1.

First, let's calculate the relative frequencies for each category:

Likes hockey: The total count in this row is 12 + 18 = 30.

Relative frequency of "Likes hockey" = 12/30 = 0.4

Relative frequency of "Doesn't like hockey" = 18/30 = 0.6

Likes baseball: The total count in this column is 12 + 14 = 26.

Relative frequency of "Likes baseball" = 12/26 ≈ 0.4615

Relative frequency of "Doesn't like baseball" = 14/26 ≈ 0.5385

To ensure that the relative frequencies add up to 1, we can set up the following equations:

0.4 + x = 1 (sum of relative frequencies in the "Likes hockey" row)

0.4615 + 0.5385 + x = 1 (sum of relative frequencies in the "Likes baseball" column)

Simplifying the equations, we have:

x = 0.6 (1 - 0.4) = 0.6 * 0.6 = 0.36

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Ken will receive a total dividend payment of $75 for that quarter.

We have to given that,

Ken owns 500 shares of LaceNBrace, which makes hockey equipment.

And, He receives a notice stating the company will be paying $0.15 dividend per share.

Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:

= $0.15 per share x 500 shares

= $75

Therefore, Ken will receive a total dividend payment of $75 for that quarter.

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The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

Now, For the greatest distance that can be filmed by a drone with a maximum altitude of 0.12 km, we can use the Pythagorean theorem.

Let's a right triangle with one leg being the radius of the Earth 6378 km and the other leg being the maximum altitude of the drone 0.12 km.

Hence, The hypotenuse of this triangle represents the line of sight from the drone's camera to the horizon.

Hence, By Using the Pythagorean theorem, we can solve for the length of the hypotenuse:

h² = 6378² + 0.12²

h = √40684000.145

h = 6374.5 km

Therefore, The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

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The inequality that describes the situation is x ≤ 16

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

There must be no more than 16 people on the field at the same time.

Represent the number of people with x

So, we have

There must be no more than 16 x

No more than means

Less than or equal to

So, we have

x ≤ 16

Hence, the inequality that describes the situation is x ≤ 16

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Answer:

Mr Jones: $399.69
Mr Williams: $290.31

Step-by-step explanation:

Calculate the total investment: $2000 + $1450 = $3450.

Calculate Mr Jones' share: ($2000 / $3450) * $690 ≈ $399.69.

Calculate Mr Williams' share: ($1450 / $3450) * $690 ≈ $290.31.

Hence, Mr Jones will receive approximately $399.69 in profit, while Mr Williams will receive approximately $290.31 in profit.

The situation that can be modelled with the inequality is if Trevor and Brain works x hour, Trevor's earnings is at least $30 more than Brian. (second option)

The first step is to determine inequality signs and what they mean.

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The given inequality is:

$12x - $30 ≥ $10

If the inequality is rearranged, it becomes:

$12x ≥ $10x + $30

This can be interpreted as if both of them work x hours, Trevor's income is at least $30 more than Brian's.

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Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Answer:

D) 210 degrees

Step-by-step explanation:

The angle 210 degrees is equal to 7π/6 radians.

This is a coterminal angle of 31π/6, because it is the same angle, just measured from a different starting point.

Answer:

37

Step-by-step explanation:

106+37+x= 180( being sum of angle of triangle)

143+x= 180

x= 180-143

= 37

•°•x= 37°

Answer:

37

Step-by-step explanation:

106+37+x-180

x-180-143

x+-37

The correct transformation that describes why rectangles ABCD and A′B′C′D′ are similar is Rectangle ABCD was dilated by a scale factor of 5 to form rectangle A′B′C′D′.

Dilation is a transformation that changes the size of an object while maintaining its shape. In this case, the coordinates of rectangle ABCD were multiplied by a scale factor of 5 to obtain the coordinates of rectangle A′B′C′D′.

This means that each side length of rectangle ABCD was multiplied by 5 to get the corresponding side length of rectangle A′B′C′D′.

The reflection across the y-axis and the rotation of 90° counterclockwise would result in different shapes and orientations, not maintaining the similarity between the two rectangles.

The dilation by a scale factor of 15 or 1/5 would also change the proportions and not result in a similar rectangle.

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The measurement of a crayon and half a pencil dreambox will depend on the specific dimensions of the dreambox. As there is no information provided about the exact size or shape of the dreambox.

To measure the crayon and half pencil dreambox, you would typically need a measuring tool such as a ruler or tape measure. Here are the steps to measure it:

1. Determine the length measurement: Place the dreambox on a flat surface and measure the length from one end to the other using the measuring tool. Make sure to align the measuring tool properly to get an accurate measurement.

2. Measure the width: Measure the width of the dreambox by placing the measuring tool perpendicular to the length measurement. Again, ensure that the measuring tool is aligned correctly to obtain an accurate width measurement.

3. Measure the height: Measure the height of the dreambox by placing the measuring tool vertically from the bottom to the top of the dreambox. Ensure that the measuring tool is aligned properly for an accurate height measurement.

By following these steps and using a measuring tool, you can obtain the measurements of the crayon and half pencil dreambox accurately.

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The graph of the inequality is on the image at the end.

Here we want to find the graph of the inequality:

y < -x + 3

To graph this, we need to graph the line:

y = -x + 3

With a dashed line (because the points in the line aren't solutions for the inequality)

And we can see that y is smaller than the line, then we need to shade all the region below that dashed line.

The graph of the inequality is the one you can see in the image at the end.

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Answer:

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

Let the radius be r.

Use circumference formula and find the value of r:

Find the area using the circle area formula:

The matching choice is (B).

Answer:

Step-by-step explanation:

Total volume of figure is,

V = 10,488 inches³

We have to given that,

The figure shown in image is made with cuboid and triangular prism.

Since, WE know that,

Volume of cuboid is,

V = b × h × l

And, Volume of triangular prism is,

V = 1/2 × b × h × l

Substitute all the values, we get;

Volume of cuboid is,

V = b × h × l

V = 18 x 23 x 16

V = 6624 inches³

And, Volume of triangular prism is,

V = 1/2 × b × h × l

V = 1/2 x 21 x 23 x 16

V = 3864 inches³

Thus, Total volume of figure is,

V = 6624 inches³ + 3864 inches³

V = 10,488 inches³

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The average weight of the 50 students is 37 kilograms.

In mathematics, a continuous series is a sequence of numbers that has no gaps between any of its values. In order to find the average weight of a continuous series of 50 students, we can divide the sum of their weights by the total number of students.

Let us assume that the weight of each student is measured in kilograms. If the sum of the weights of 50 students is 1,850 kilograms, then the average weight can be calculated as follows:

Average weight = Total weight / Number of studentsIn this case, the total weight is 1,850 kilograms and the number of students is 50. Therefore, we can substitute these values into the formula and simplify as follows:

Average weight = 1,850 / 50Average weight = 37 kilograms It is important to note that this calculation assumes that all of the weights are evenly distributed among the students and that there are no outliers or extreme values that would skew the average.

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Answer:

0.482 is the probability of the fair die of getting at most 1 five.

Step-by-step explanation:

Getting at most 1 five means there can be 1 five or 0 five.

Condition 1:

Condition 2:

We sum up the favorable outcomes ( 0 five and 1 five) and divide it by the total outcomes to find the probability.

P = ( Number of favorable outcomes) / (Total number of outcomes)

p = (3125 +625)/6^5 => 3750 / 7776 => 0.482

p = 0.482

Therefore the probability is 0.482.

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The equation matches the graph is -2cosx.

The graph of the function y = -2cos(x) represents a cosine function that has been reflected vertically and stretched by a factor of 2.

The cosine function is a periodic function that oscillates between -1 and 1. The negative sign in front of the function (-2cos(x)) reflects the graph across the x-axis. This means that all the positive values of the cosine function become negative, and vice versa.

So, the coefficient of -2 stretches the graph vertically by a factor of 2. This means that the amplitude of the graph doubles, and the oscillations are more spread out vertically.

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5/6 is the probability that the number landed on an odd or is greater than 4

Probability is defined as the likelihood or chance that an event will occur.

If a number cube is rolled, the sample space will be:

(S) = {1, 2, 3, 4, 5, 6}

n(S) = 67

If it lands on a odd number, the number of events will be:

(E) = {1, 3, 5}

n(E) = 3

If it lands on a number greater than 4 the number of events will be:

(E) = {5, 6}

n(E) = 2

Pr(even or greater then 4) = 3/6 + 2/6

Pr(even or greater then 4) = 5/6

The probability that the number landed on an odd or is greater than 4 is 5/6

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Answer: 4/6 or 2/3

Step-by-step explanation:

Even number=3/6 or 1/2 chance

Greater than 4=2/6 chance or 1/3 chance

Union basically means either or

So: 1/2+1/3 or 3/6+2/6 or 5/6

This doesn't always work though, so we use trial and error

1 2 3 4 5 6

1 3 5 are the ones not even

13 are the ones not greater than 4

Answer:

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{\boxed{ x = 1}}[/tex]

Step-by-step explanation:

Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.

To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.

Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.

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

Step1: Subtract [tex]\bold{2x}[/tex] from both sides

Step 2: Subtract 3 from both sides

Step 3: Divide both sides of the equation by 6

So the solution to the equation [tex]\bold{8x + 3 = 2x + 9}[/tex] is [tex]\bold{x = 1}[/tex].

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

The ordered pair solutions for the system of equations are:

(4, 5) and (-1, 0).

We have,

To find the ordered pair solutions for the system of equations, we need to solve the equations simultaneously.

The given equations are:

f(x) = x² - 2x - 3

f(x) = x + 1

Since both equations are equal to f(x), we can set them equal to each other:

x² - 2x - 3 = x + 1

Now, let's solve this quadratic equation:

x² - 2x - 3 - x - 1 = 0

x² - 3x - 4 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula.

Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation,

a = 1, b = -3, and c = -4.

Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(1)(-4))) / (2(1))

x = (3 ± √(9 + 16)) / 2

x = (3 ± √25) / 2

x = (3 ± 5) / 2

We have two possible solutions:

When x = (3 + 5) / 2 = 8 / 2 = 4

When x = (3 - 5) / 2 = -2 / 2 = -1

Therefore, the ordered pair solutions for the system of equations are:

(4, f(4)) and (-1, f(-1))

Now, let's substitute these values into either equation to find the corresponding y-values (f(x)):

For x = 4:

f(4) = 4 + 1 = 5

So, one solution is (4, 5).

For x = -1:

f(-1) = -1 + 1 = 0

So, another solution is (-1, 0).

Therefore,

The ordered pair solutions for the system of equations are:

(4, 5) and (-1, 0).

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Answer:

1900

Step-by-step explanation:

Use a proportion:

16 is to 950 as 32 is to x.

16/950 = 32/x

32/16 = x/950

x/950 = 2

x = 1900

Answer: 1900

Hello!

7/8 - 2/3

= 7*3/8*3 - 2*8/3*8

= 21/24 - 16/24

= 5/24

The laptop computer will be worth $700 or less after 6 years.

To determine the number of years it takes for the laptop computer to be worth $700 or less, we can set up an equation based on the given information.

Let's denote the initial value of the laptop as V0 = $2900. Each subsequent year, its value will be 70% of its value the previous year.

So, the value of the laptop after one year would be V1 = 0.7 * V0 = 0.7 * $2900 = $2030.

In general, the value of the laptop after n years can be represented as Vn = [tex]0.7^n[/tex] * V0.

We want to find the value of n when Vn ≤ $700. Thus, we can set up the following inequality:

[tex]0.7^n[/tex] * V0 ≤ $700

Substituting the value of V0, we get:

[tex]0.7^n[/tex] * $2900 ≤ $700

Dividing both sides of the inequality by $2900, we have:

[tex]0.7^n[/tex] ≤ $700 / $2900

[tex]0.7^n[/tex] ≤ 0.2414

To solve for n, we can take the logarithm (base 0.7) of both sides:

n ≤ log0.7(0.2414)

Using logarithmic properties, we can rewrite this as:

n ≤ log(0.2414) / log(0.7)

Using a calculator, we find:

n ≤ 6.54 (rounded to two decimal places)

Since n represents the number of years, it must be a whole number.

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The value of x and y from the given triangle are 52.3 feet and 42.84 feet respectively.

Given that, an engineer sketches a right triangle to show that the screen in a movie theater is 30 ft high and that the vertical viewing angle from the from row is 35 degree.

We know that, sinθ = Opposite/Hypotenuse

sin35° = 30/x

0.5736 = 30/x

x = 30/0.5736

x = 52.3 feet

We know that, tanθ = Opposite/Adjacent

tan35°=30/y

0.7002=30/y

y = 30/0.7002

y = 42.84 feet

Therefore, the value of x and y from the given triangle are 52.3 feet and 42.84 feet respectively.

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Answer:

0.7 Radians

Step-by-step explanation:

0.7 radians is equal to 40.107°. Therefore, 0.7 radians is greater than 40°.

Answer:

1:72

Step-by-step explanation:

The scale of a drawing is the ratio of the length in the drawing to the real length.

Drawing length: 7 inches

Real length: 42 ft × 12 in. / ft = 504 in.

Scale:

7 in. to 504 in.

Divide both numbers by 7:

1 in. to 72 in.

Scale: 1:72

B. No

Step-by-step explanation:

tho im not 100% sure i think this is the answer because there is enough data to be able to calculate the average of the data to represent the city.

h9pe that helps