How do you write an inequality in a word problem?

Answer:

D)  229.05

Step-by-step explanation:

f(75) = 0.81(75) + 168.3 = 229.05

To solve the system of equations y=4x-3 and y=-2x+9, we can set the two equations equal to each other and solve for x:

4x - 3 = -2x + 9

Adding 2x and 3 to both sides, we get:

6x = 12

Dividing both sides by 6, we get:

x = 2

Now that we have the value of x, we can substitute it into either of the original equations to find the corresponding value of y. Let's use the first equation:

y = 4x - 3

y = 4(2) - 3

y = 8 - 3

y = 5

Therefore, the solution to the system of equations is x = 2 and y = 5. The solution is the ordered pair (2, 5).

SSS" is when we know three sides of the triangle, and want to find the missing angles

The length of side x is 10 units

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

Segment AD bisects angle BAC.

Using the above as a guide, we have the following:

BD = DC

substitute the known values in the above equation, so, we have the following representation

x = 20 - x

Evaluate the like terms

2x = 20

Divide by 2

x = 10

Hence, the value of x is 10

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Answer: 23.56 in

Step-by-step explanation:

The perimeter of the 30-60-90 triangle with a shorter leg of 3.4 inches is 16.08 inches.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In a 30-60-90 triangle, the lengths of the sides are in the ratio of 1:√3:2, where the shortest side is opposite the 30-degree angle,

the medium side is opposite the 60-degree angle, and

the longest side is opposite the 90-degree angle.

So if the shorter leg of the triangle is 3.4 inches long, the other two sides can be found as follows:

Medium side =√3× shorter leg

= 1.732 × 3.4

= 5.88 inches

Longest side = (2 × shorter leg)

= (2 × 3.4)

= 6.8 inches

The perimeter of the triangle is simply the sum of the lengths of all three sides:

Perimeter = Shorter leg + Medium side + Longest side

= 3.4 + 5.88 + 6.8

= 16.08 inches

Therefore, the perimeter of the 30-60-90 triangle with a shorter leg of 3.4 inches is 16.08 inches.

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Answer:

-7.988 or -2E

Step-by-step explanation:

Answer:

20,000

Step-by-step explanation:

I'm assuming your class is using this model of the exponential decay function:

f(x) = a(1 - r)^x

In this case, the equation would be:

f(x) = 20,000(1 - .15)^x

or, when 1 - r is calculated:

f(x) = 20,000(.85)^x

The "a" value is basically the starting value, because on a graph, the starting value would be where x = 0. Anything to the 0th power is 1, and anything multiplied by 1 is the same thing, making "a" the same as the starting value, or the y-intercept.

Therefore, a = 20,000.

Hope this helps!

The amount that Ayaan will have in his tax-free savings account after 6 months of depositing $746 at 2.15% interest is $754.02.

The future value refers to the present value plus the interest.

The future value for this savings account can be computed using the simple interest system since there is no compounding of interest.

The initial deposit (present value) = $746

Interest rate = 2.15%

Savings period = 6 months

Future value = $754.02 ($746 + ($746 x 2.15% x 6/12)

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The correct answer is B. 2

The statement "If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x)." is incorrect.

The origin of the coordinate plane is the point (0, 0), and it is the center of rotation for many geometric transformations.

When a point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, x). This is because rotation by 90 degrees counterclockwise causes the x-coordinate to become the negative of the original y-coordinate and the y-coordinate to become the original x-coordinate.

To see this, imagine the point (x, y) on the coordinate plane and draw a line segment connecting the point to the origin. The length of this line segment is given by the Pythagorean theorem as the square root of x² + y². After rotating the point 90 degrees about the origin, the line segment will be perpendicular to the original line segment and have a length equal to y and -x.

In summary, rotating a point (x, y) at 90 degrees about the origin results in the point (-y, x) due to the change in the direction and length of the line segment connecting the point to the origin.

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The correct answer is option D. We can be 95% confident that the sample proportion is captured by the confidence interval.

The margin of error of plus or minus three percentage points at a 95% confidence level means that the true proportion of people who jog regularly in the population is estimated to be between 15% and 21%. We can be 95% confident that the true proportion of people who jog regularly falls within this interval.

Therefore, option B is correct. Option A is incorrect because it implies that the margin of error always holds true for any sample size, which is not the case. Option C is incorrect because it presents a range of values for the population, not for the estimate. Option E is incorrect because it refers to the proportion of samples that would find the same sample proportion, not the range of values within which the true proportion lies.

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The cost of each large van is 22,323.53 and each small van is 36,117.65.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the cost of a large van and y be the cost of a small van.

The total cost of the vans for Location A is $228,500.

Location A buys 7 large and 2 small vans.

So we have a linear equation,

7x + 2y = 228,500

The total cost for Location B is $153,000.

Location B buys 2 large and 3 small vans.

So we have a linear equation,

2x + 3y = 153,000

Multiplying the first equation with 3 and the second equation with 2,

21x + 6y = 685,500

4x + 6y = 306,000

Subtracting,

17x = 379,500

x = 22,323.53

Substituting in one of the equation,

y = 36,117.65

Hence the cost of each large and small van are 22,323.53 and 36,117.65 respectively.

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We can determine the radius of the container using the formula for a sphere's surface area because it resembles an orange and has a surface area of roughly 50.3 square inches:

A sphere's surface area equals [tex]4 r^2[/tex].

where r denotes the sphere's radius.

50.3 sq. = 4πr²

By multiplying both sides by 4, we obtain:

r² = 50.3 sq. / (4π)

r² ≈ 4

When we square the two sides, we obtain:

r ≈ 2

Hence, the spherical container has a radius of around 2 inches.

The volume of the container can now be calculated using the following formula:

A sphere's volume equals [tex](4/3)r^3[/tex].

Container volume = (4/3) X(23)

The container's volume is 33.5 cubic inches.

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Answer:

First off that is my name.

y=-0.5x+5 is the first equation. I don't know the second.

Sorry

Step-by-step explanation:

The metric system of measurement is based on the number 10.

This system is also known as the International System of Units (SI) and is used in most countries around the world. In the metric system, various units of measurement are defined as multiples or fractions of a base unit, which is defined for each quantity being measured. For example, the base unit for length is the meter, and the base unit for mass is the kilogram. Prefixes such as kilo-, centi-, and milli- are used to indicate multiples or fractions of the base unit, based on factors of 10. For example, a kilometer is 1000 meters, a centimeter is 1/100 of a meter, and a milligram is 1/1000 of a gram. This makes the metric system easy to use and convert between units, as well as consistent and universally recognized.

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The points are plotted and labeled in the graph.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

A graph of the coordinate plane.

The points are (0, 2), (-3, 4), (4, -6), (6, -2), (5, 5), (-3, -5), (0, -4), (4, 0), (5, 0), and (3, -6).

The points are plotted and labeled in the graph.

The required graph is given in the image below.

Therefore, all the coordinates are plotted in the graph.

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A time complexity cheat sheet is a reference guide that provides an overview of the time complexity of common algorithms and operations in computer science.

Time complexity is a measure of the amount of time an algorithm takes to solve a problem, expressed in terms of the input size of the problem. It is typically denoted using Big O notation, which provides an upper bound on the amount of time an algorithm takes.

A time complexity cheat sheet can be useful for quickly determining the time complexity of an algorithm or operation, as well as for comparing the time complexity of different algorithms. Some common time complexities that may be included in a time complexity cheat sheet are:

O(1): Constant time complexity. An algorithm with O(1) time complexity takes a fixed amount of time, regardless of the input size.

O(log n): Logarithmic time complexity. An algorithm with O(log n) time complexity takes time proportional to the logarithm of the input size.

O(n): Linear time complexity. An algorithm with O(n) time complexity takes time proportional to the input size.

O(n log n): Log-linear time complexity. An algorithm with O(n log n) time complexity takes time proportional to the input size multiplied by the logarithm of the input size.

O(n^2): Quadratic time complexity. An algorithm with O(n^2) time complexity takes time proportional to the square of the input size.

O(2^n): Exponential time complexity. An algorithm with O(2^n) time complexity takes time proportional to two raised to the power of the input size.

Other time complexities may also be included, depending on the complexity of the algorithm or operation. A time complexity cheat sheet can be a helpful tool for understanding and analyzing algorithms, but it is important to remember that time complexity is not the only factor to consider when evaluating the performance of an algorithm.

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An algebraic expression representing the amount Xavier will have in his savings account after w weeks is 43 + 15w.

Algebraic expressions consist of numbers, variables, and the mathematical operations, especially addition, subtraction, division, and multiplication.

An algebraic expression does not have the equation symbol (=) unlike an equation because it is not a complete mathematical statement.

The amount Xavier already has in his savings account = $43

The planned weekly savings = $15

The period of savings = w

43 + 15w

Thus, using an algebraic expression, after w weeks, Xavier will have 43 + 15w in his savings account.

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Using Distributive Property, the two expressions that is equal to 72 are

3(10+14) and 4(5+13).

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. The operations includes sum, Difference, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

Now,

The expressions using distributive property can be

3(10+14)=3*10+3*14

            =30+42

            =72

4(5+13)=4*5+4*13

            =20+52

           =72

Hence,

            the two expressions that is equal to 72 are 3(10+14) and 4(5+13).

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Answer:

It should be = 20/68 = 0.294117647

The elevation of the diver after the dive can be found to be 42 feet below sea level or - 42 feet.

If the diver's elevation is -30 feet relative to sea level, and she dives down 12 feet, we can find her new elevation by adding the change in depth to her initial elevation:

New elevation = Initial elevation + Change in depth

New elevation = - 30 feet + ( - 12 feet )

New elevation = - 42 feet

Therefore, the diver's new elevation after the dive is -42 feet relative to sea level.

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The full question is :

A divers elevation is -30 feet below sea level. She dives down 12 feet. What is her elevation after the dive?

The value of each of the following:

(a) 0.0837 ml

(b) 460.68 m

(c) 84 L

(d) 100￠

The denominator of a percentage (also known as a ratio or fraction) is always 100. Ram, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test.

For 6 1/5 % of 1.35 ml

⇒ 6 1/5 % = 31/5 %

⇒ 31/5 % of 1.35 ml

= 31/(5×100) × 1.35 ml

= 0.0837 ml

For 56 7/8 % of 810 m

⇒ 56 7/8 % = 455/8 %

⇒ 455/8 % of 810 m

= 455/(8×100) × 810 m

= 460.68 m

For 0.56% of 15 000 L

⇒ 0.56% of 15 000 L

= 0.56/100 × 15 000 L

= 84 L

For 2000% of 5￠​

⇒ 2000% of 5￠​

= 2000/100 × 5￠​

= 100￠​

Hence, the answers are as follows:

(a) 0.0837 ml

(b) 460.68 m

(c) 84 L

(d) 100￠

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The measure of angle B is given as follows:

<B = 295º.

Angles A and B in the context of this problem are reflex angles, meaning that the sum of their measures is of 360º.

The measures are given as follows:

Hence the measure of angle B is obtained as follows:

65 + <B = 360

<B = 360 - 65

<B = 295º.

The diagram modeling the situation is given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation:

To find the diagonal of a rectangular lot, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side, also known as the diagonal of the rectangle) is equal to the sum of the squares of the lengths of the other two sides.

So, for a rectangular lot 165 feet long and 90 feet wide, the length of the diagonal can be calculated as follows:

d = √(165^2 + 90^2) = √(27225 + 8100) = √35325 = 189 feet

The diagonal fence for the lot would require 189 feet of fencing. To round this to the nearest foot, we would round up to 190 feet, since 189.5 is closer to 190 than 189.

Therefore, 190 feet of fencing are needed to make a diagonal fence for the lot.

Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

An inferential statistic is one that makes inference or predictions about a population based on a sample.

From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

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One cubic foot is equal to approximately 28.3168 liters. So to convert cubic feet to liters, you can multiply the number of cubic feet by 28.3168.

Unit conversion is the process of converting a value expressed in one unit of measurement to an equivalent value expressed in another unit of measurement. For instance, to convert 10 feet to meters, you would use the conversion factor 1 foot = 0.3048 meters.

For example, if you have a volume of 5 cubic feet, you can convert it to liters as follows:

5 cubic feet * 28.3168 liters/cubic foot = 141.584 liters

Therefore, 5 cubic feet is equivalent to 141.584 liters (approximately).

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Answer: x intercept: -4, y intercept: 2 (look at the image for the solution)

Step-by-step explanation:

Answer:

x intercept: -4, y intercept: 2

Step-by-step explanation:

The diameter of the circular garden round to the nearest tenth will be 19.1 inches.

In a circle, an infinite number of diameters can be drawn. A diameter is a straight line passing through the center and joins two points of the circumference of a circle. The length of a diameter is twice the length of the radius.

The circumference of a circle is given by C = πd, where d is the diameter of the circle and π can be taken as 3.14.

Substitute C = 60 and π = 3.14 into the above formula and find d.

60 = 3.14×d

d = 60/3.14

≈ 19.108

≈ 19.1

Therefore, the obtained answer is 19.1 inches.

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