Which of the following expressions is equivalent to 3^2x − 3?

Answer:

7m + 20 ≥ 150

Closest option is 7m + 20 > 150 which is the second choice

Step-by-step explanation:

The words "at least" indicate a ≥ inequality.

There is a fixed earning of $20 for entering the race. So this amount will be earned on regardless of how much Carol runs

For each mile she runs she earns $7. For running m miles, she earns 7m dollars

Total amount earned for running m miles = 7m + 20
This must be at least $150
So the correct inequality is
7m + 20 ≥ 150

I don't see this exact inequality in any of the answer choices but that is the correct answer.

The height of the trapezoid is h = 4, and the answer is B.

A trapezoid, also known as a trapezium, is a four-sided polygon with two parallel sides, also called the bases. The non-parallel sides are called legs, and they can have different lengths. The parallel sides are perpendicular to the legs.

There are two types of trapezoids:

Isosceles trapezoid: This type of trapezoid has two parallel sides of equal length and two legs of equal length.

Scalene trapezoid: This type of trapezoid has two parallel sides of different lengths and two legs of different lengths.

We can use the formula A = 1/2 * h * (b1 + b2) to solve for h. Substituting the given values, we get:

28 = 1/2 * h * (6 + 8)

28 = 1/2 * h * 14

28 = 7h

h = 4

Therefore, the height of the trapezoid is h = 4, and the answer is B.

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Answer:

To solve this problem, we need to set up an inequality that represents the situation where Joseph will have more than 125 books.

Let w be the number of weeks.

At the end of w weeks, Joseph will have 50 + 5w books (since he adds five books to his library every week).

To find the inequality that represents having more than 125 books, we can set up the following equation:

50 + 5w > 125

Simplifying this inequality:

5w > 75

w > 15

Therefore, the inequality that represents the situation where Joseph will have more than 125 books is:

5w + 50 > 125

The answer is B.

As a result, for purchases of $9500, the salesperson gets a royalty of $285.

Commission, also known as a sales bonus, is paid to employees in accordance with the amount of sales they make. Statement generation is offered without charge by SumUp Bills. Frequently, a fee is calculated as a percentage of the sale's value.

To find the commission that the salesperson receives for $9500 in sales, we can use the formula:

commission = rate x sales

where rate is the commission rate as a decimal, and sales is the amount of sales.

In this case, the rate is 3% or 0.03, and the sales is $9500.When these numbers are added to the algorithm, we obtain:

commission = 0.03 x $9500

Simplifying this expression, we get:

commission = $285

Therefore, the salesperson receives a commission of $285 for $9500 in sales.

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The amount of ice cream in a properly filled cone is approximately 167.46 cubic cm.

The volumes of a cone and a cylinder with the same base and height are proportionate to one another. A cone's volume is specifically one-third that of a cylinder with the same base and height.

The volume of a cone, which is given by:

V = (1/3)πr²h

Substituting the values of radius and height we have:

V = 1/3π(4)²(10)

V = 167.46 cubic cm.

Hence, the amount of ice cream in a properly filled cone is approximately 167.46 cubic cm.

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Step-by-step explanation:

V = P(1 - r)^t

where V is the value of the car after t years, P is the initial value of the car, r is the annual depreciation rate as a decimal, and t is the number of years.

Plugging in the values given in the problem, we get:

V = 42000(1 - 0.15)^7

V = 42000(0.85)^7

V = 42000(0.327)

V = $13734.00

Therefore, the car will be worth $13,734.00 after 7 years. Rounded to the nearest dollar, the value is $13,734.

Answer:

A) $12,800.00. B) $13,629.44. The value of a car purchased for $20,000 decreases at a rate of 12% per year. What will be the value of the car after 3 years? C) ...

Answer:

Malleability and ductility refer to a material's ability to be shaped, bent, or stretched without breaking. Malleability is a measure of how easily a material can be hammered, pressed, or rolled into different shapes, while ductility is a measure of how much a material can be stretched before it breaks. Metals and alloys are generally highly malleable and ductile, while concrete and glass are less so

Step-by-step explanation:

The area of the triangle is given as follows:

9.3 units².

The area of a triangle is obtained multiplying the triangle's base by the triangle's height and dividing by 2, that is:

A = bh/2.

Considering segment (-5,3) to (-5,6) as the base, the base length is given as follows:

b = 6 - 3 = 3.

The midpoint of the base segment is given as follows:

(-5,4.5).

The height is given by the distance between the third vertex and the midpoint, hence:

h = sqrt[(-5 - 1)² + (4.5-3)²]

h = 6.2.

Hence the area is of:

A = 0.5 x 6.2 x 3

A = 9.3 units².

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Answer:

19,306 = 10 + 90 + 30 + 60

Step-by-step explanation:

If to display charts and other educational material, your teacher has requested that two rows of strips be placed around the entire room. the total length of strips is: 4L + 4W.

To find the total length of strips required, we need to know the dimensions of the room. Let's assume that the room has a length of L and a width of W.

If we place two rows of strips around the entire room, one at the top and one at the bottom, the length of each strip will be equal to the perimeter of the room.

The perimeter of the room can be calculated as:

P = 2L + 2W

So, the length of strips required for one row around the room will be:

L1 = P = 2L + 2W

Since we need two rows of strips, the total length of strips required will be:

L2 = 2L1 = 2(2L + 2W) = 4L + 4W

Therefore, the total length is 4 times the length of the room plus 4 times the width of the room.

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Answer:

24% of 10,000 is 2,400.

Step-by-step explanation:

To find out what number is 24% of 10,000, we can multiply 10,000 by 24% (or 0.24):

Number = 10,000 x 0.24

Number = 2,400

Therefore, 24% of 10,000 is 2,400.

Answer:

 2,400  

Step-by-step explanation

:24% of 10,000 = 24% × 10,000 = 24/100 × 10,000 = (24 ÷ 100) × 10,000 = 24 × 10,000 ÷ 100 = 240,000 ÷ 100 =

In this case, the boxplot is option A, which shows the box extending from 130 to 165.5 mBq, with a line segment drawn through the box at 160.75 mBq. The whiskers extend from 114 to 201 mBq, with no outliers.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The problem asks us to construct a boxplot and identify the 5-number summary of a set of data. The data represents the amounts of strontium-90 (in millibecquerels, or mBq) in a sample of baby teeth from residents born after 1979. The data is as follows:

124, 127, 131, 135, 138, 142, 142, 143, 147, 150, 154, 156, 157, 160, 163, 168, 170, 171, 174, 181

To construct the boxplot, we need to first find the 5-number summary, which consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. We can find these values by putting the data in ascending order and then using the following formulas:

Q1 = median of the lower half of the data

Q2 = median of the entire data set

Q3 = median of the upper half of the data

Using these formulas, we find the 5-number summary to be:

Minimum value: 124 mBq

Q1: 138 mBq

Median: 150 mBq

Q3: 168 mBq

Maximum value: 181 mBq

We can now use this information to construct the boxplot. The horizontal axis represents the values in the data set, and the vertical axis represents the frequency or density of those values. The boxplot consists of a box that extends from Q1 to Q3, with a line segment drawn through the box at the median (Q2). Whiskers extend from the top and bottom of the box to the minimum and maximum values, respectively, unless there are outliers. Outliers are plotted as individual points beyond the whiskers.

Therefore, In this case, the boxplot is option A, which shows the box extending from 130 to 165.5 mBq, with a line segment drawn through the box at 160.75 mBq. The whiskers extend from 114 to 201 mBq, with no outliers.

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The sections of each course it should offer are 3 finite maths, 2 applied calculus and 2 computer methods

Let's use the following variables to represent the unknowns:

From the problem, we can write the following system of equations:

x + y + z = 7 (total number of sections)

40x + 40y + 10z = 220 (total number of students)

40000x + 60000y + 29000z = 298000 (total revenue)

Simplify

x + y + z = 7

4x + 4y + z = 220

40x + 60y + 29z = 298

We can solve this system of equations using substitution

So, we have

x = 7 - y - z

By substitution, we have

4(7 - y - z) + 4y + z = 22

This gives

28 - 4y - 4z + 4y + z = 22

So, we have

28 - 3z = 22

This gives

3z = 6

Divide

z = 2

Recall that

40x + 60y + 29z = 298

So, we have

40x + 60y + 29*2 = 298

40x + 60y + 58 = 298

This gives

40x + 60y = 240

Divide by 20

2x + 3y = 12

Also, recall that x = 7 - y - z

So, we have

2(7 - y - z) + 3y = 12

This gives

2(7 - y - 2) + 3y = 12

2(5 - y) + 3y = 12

Open brackets

10 - 2y + 3y = 12

Evaluating the like terms, we have

y = 2

Lastly. we have

x = 7 - y - z

x = 7 - 2 - 2

x = 3

Hence, the number of sections of Finite Math is 3

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The net price using the net price factor, complement method is $2958.75.

The complementary of the product of the market discount rates is represented by the net price factor, which is a decimal number. It is used to determine an item's final price after various trade discounts have been applied. By multiplying the complementary of the discount rates collectively and deducting the result from 1, we may determine the net price factor.

We use the complement method to calculate the net price using the net price factor.

For the given trade discount rates we have:

The complement of 35% is 65%

The complement of 30% is 70%

The complement of 5% is 95%

Multiply the values:

65% × 70% × 95% = 0.65 × 0.70 × 0.95 = 0.40825

The net price is obtained by:

1 - 0.40825 = 0.59175

Multiply the net price by the list price:

0.59175 × 5000 = $2958.75

Hence, the net price using the net price factor, complement method is $2958.75.

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The equation where F(x) = G has no solution (x). By graphing the functions, the answer has been discovered.

The creation of a relevant function's graph is the first step in the graphing process. If a curve reflects the function at a given point, the curve at that point satisfies the function equation.

We are given two functions as f(x) = (3x + 2) and g(x) = (3x - 5)

The graph of the given functions has been plotted and attached below.

In the graph, the red line represents the f(x) function and the blue line represents the g(x) function.

From the graph, it is clear that the two lines are parallel, therefore they will never meet.

Hence, there is no solution where F(x) = G(x).

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Question: Graph the following functions and determine where F(x) = G(x). Select all that apply.

f(x)=(3x+2) and g(x)=3x-5

.

just find the area of a circle which is

pi times 3.5 squared. 3.5 is the radius because 7 is the diameter

all of them are equivalent

Therefore, Lisa will need 52 square inches of purple paint to paint all sides of her letter L.

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces, including the base(s) and any lateral faces, that make up the object. Surface area is usually expressed in square units, such as square centimeters, square meters, square inches, or square feet, depending on the unit of measurement used. The surface area of an object is an important factor in many physical and mathematical calculations, such as calculating the amount of material needed to cover an object, the rate of heat transfer, and the amount of friction between surfaces.

by the question.

To find the total surface area that Lisa will need to paint purple, we need to first calculate the surface area of each piece of wood and then add them together.

The longer piece of wood has a surface area of:

2 x 7 = 14 square inches on one side

2 x 2 = 4 square inches on the other side

2 x 5 = 10 square inches on the third side

So, the total surface area of the longer piece is 14 + 4 + 10 = 28 square inches.

The shorter piece of wood has a surface area of:

5 x 2 = 10 square inches on one side

2 x 2 = 4 square inches on the second side

5 x 2 = 10 square inches on the third side

So, the total surface area of the shorter piece is 10 + 4 + 10 = 24 square inches.

To get the total surface area of the letter L, we add the surface areas of the two pieces of wood together:

28 + 24 = 52 square inches.

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The expression for the given Venn Diagrams are:

A Venn diagram employs circles or other shapes that overlap to show the logical connections between two or more groups of objects.

They frequently serve to visually group objects while highlighting how they differ and how they are similar.

The union of two sets A and B is a new set that contains all the elements that are in A or in B or in both. It is denoted by A ∪ B.

Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.

The intersection of two sets A and B is a new set that contains all the elements that are in both A and B. It is denoted by A ∩ B.

Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.

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The surface area of the shape is 110 square units.

The area of a two-dimensional figure is the area enclosed by its perimeter. The area of a closed figure is the number of unit squares that cover its surface. Area is measured in square units such as cm2 and m2. The area of a shape is measured in two dimensions.

The rectangle's surface area is:

Area = 10 × 9 = 90 unit square

The area of the triangle is:

Area = 0.5 × 10 × 4 = 20 unit square

The figure's area is as follows:

Total = 90 + 20

Total = 110 unit square

Hence, the shape's area is 110 unit square.

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The answers to each part context to similar triangles is given above.

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given are two similar triangles as shown in the image.

{ 1 } -

We can write the scale factor as -

{k} = ZX/AC

{k} = 39/13

{k} = 3

{ 2 } -

m∠X = m∠A = 67°

m∠X = 67°

{ 3 } -

ZW/CD = k

CD = ZW/k

CD = 36/3

CD = 12 units

{ 4 } -

Area of triangle ABC = 1/2 x 5 x 12 = 30 square units.

A{ΔABC} = 30 square units

{5} -

Ratio of area of triangle ABC to triangle XYZ = (30)/(15 x 36) = 1/18

A{ΔABC}/A{ΔXYZ} = 1/18

Therefore, the answers to each part context to similar triangles is given above.

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Therefore , the solution of the given problem of function comes out to be  height is 64 feet .

What is meant by the word function?

The study of mathematics includes histology, architecture, and both actual and fictitious geographic locations, as well as arithmetic, numerals, and their divisions. A function explains the relationships between different components, each of which has a corresponding result. A function is made up of a variety of components that, when put together, produce specific outputs for each input.

Here,

The highest spot on the ball's trajectory, which is at the vertex of the parabolic path, must be identified in order to calculate the maximum height the ball has ever attained.

The following equation describes the height of the projectile as a function of time:

s = -16t² + 64t

We can apply the following method to determine the parabola's vertex:

t = -b/2a

where b = 64 and a = -16.

By replacing these numbers, we obtain:

t = -64/(2*(-16)) = 2

Thus, after two seconds, the utmost height is reached.

We can enter t = 2 into the calculation to get the height at this point:

s = -16(2)² + 64(2) = 64 feet

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Answer:

33.02 centimeters of cloth

Step-by-step explanation:

Since 1 inch is equal to 2.54 cemtimeters then all you need to do is multiply 13x2.54 and you have your answer of 33.02

Each of the 40 students would occupy 8.75 m²

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

The class must seat 40 students along with the teachers Table and shelves which will occupy 350m². The space each student would occupy is:

Space for each student = Total space / Total number of students = 350 m² / 40 student = 8.75 m²

Each student would occupy 8.75 m²

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The two fractions' sum is therefore (a + b) / (a² × b²).

A sum, usually referred to as a summation, is the product of combining two or more quantities or numbers. A summation always has an even term count. It could be two terms simply, or it might total 100,000 or a million. Many terms can be included in some summations.

We require a common denominator in order to add these two fractions.

The first fraction's denominator is a² × b, and the second fraction's denominator is a × b².

Get the supreme strength of each component that exists in either denominator, then utilize the result of these factors to determine the least frequent multi of these two denominators:

LCM (a² × b, a × b²) = a² × b²

The two fractions can now be rewritten using the following common denominator:

1/(a² × b) + 1/(a × b²) = (1 × b + 1 × a) / (a² × b²)

If we condense this phrase, we get:

1/(a² × b) + 1/(a × b²) = (a + b) / (a² × b²)

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The exact values are;

Sin 2x = 7/8

Cos 2x = 7/4

Tan 2x = 1

Trigonometric ratios are mathematical functions that relate the angles and sides of a right-angled triangle. The three primary trigonometric ratios are:

Sine (sin) - the ratio of the length of the opposite side to the length of the hypotenuse.

Cosine (cos) - the ratio of the length of the adjacent side to the length of the hypotenuse.

Tangent (tan) - the ratio of the length of the opposite side to the length of the adjacent side.

Given that sinx = 7/16

opposite = 7

Hypotenuse = 16

Adjacent is now;

b^2 = 16^2 - 7^2

b = 14

Thus;

Sin 2x = 14/16 = 7/8

Cos 2x = 2(14/16) = 28/16 = 7/4

Tan 2x = 2(7/14) = 14/14 = 1

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The oven will heat up by 18 degrees in 1 minute at this rate.

What is expressions ?

Expressions can be simplified, evaluated, or manipulated using mathematical rules and operations. They are used in a variety of mathematical contexts, such as algebra, geometry, calculus, and more.

We can start by finding the rate of temperature increase per minute. Since the temperature rose 3 degrees in 1/6 of a minute, we can multiply both sides by 6 to find the rate per minute:

3 degrees ÷ (1/6 minute) = 18 degrees per minute

So the oven heats up at a rate of 18 degrees per minute. To find how much the oven will heat up in 1 minute, we simply multiply the rate by the time:

18 degrees per minute × 1 minute = 18 degrees

Therefore, the oven will heat up by 18 degrees in 1 minute at this rate.

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Answer:

Step-by-step explanation:

Let the sweater price be x

Let the shirt price be y

x + 4y=38

4x+5y=86
4x+16y= 152

11y=66

y=6

Substitute into x+4y=38,

x+4x6=38

x=14

Based on the 2009 season, the Texas Rangers have a winning percentage of .533. The probability that the Rangers win 4 of their next 5 games is 18.8%.

We can use the binomial distribution formula to find the probability that the Texas Rangers win exactly 4 of their next 5 games:

P(4 wins) = (5 choose 4) * (.533)^4 * (1-.533)^1

= (5! / (4! * 1!)) * (.533)^4 * (.467)^1

= 5 * 0.533^4 * 0.467^1

= 18.8%

where "choose" is the binomial coefficient, which represents the number of ways to choose a subset of size k from a set of size n, and is given by:

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

So the probability that the Rangers win 4 of their next 5 games is 18.8%,.

Therefore, the answer is B.

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The value of m if the ratio of their heights is equal to 1:m is 4/3.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Area of A=144cm²

Area of B=256cm²

Ratio of heights= 1:m

Now,

The ratio of the areas of two similar solids is equal to the square of the ratio of their corresponding heights. So, we have:

(area of A) / (area of B) = (height of A)^2 / (height of B)^2

Substituting the given values, we get:

144 / 256 = 1^2 / m^2

9 / 16 = 1 / m^2

Multiplying both sides by m^2, we get:

9m^2 / 16 = 1

Multiplying both sides by 16/9, we get:

m^2 = 16/9

Taking the square root of both sides (and noting that m must be positive since it is a length), we get:

m = 4/3

Therefore, by the given ratio answer will be 4/3.

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