A student noticed different gas prices as she drove around town. Find the first quartile. Round your answer to the nearest cent. $3.31 $3.28 $3.42 $3.35 $3.31 $3.26 $3.38 $3.32 $3.34

Answer:

Values of x are ±4 and ±5

Step-by-step explanation:

Let y = [tex]x^{2}[/tex]

Which means: [tex]y^{2} = x^{4}[/tex]

Therefore:

A quadratic equation is formed:

[tex]y^{2} - 41y + 400 = 0[/tex]

The above quadratic equation can be simplified either by The Double Bubble Method or using the quadratic formula

Double Bubble Method:

[tex]y^{2} - 41y + 400 = 0[/tex]

The pair of factors of 400 that add together to give 41 are 25 and 16. Use these two factors to rewritre -41y:

[tex]y^{2} - 25y - 16y + 400 = 0[/tex]

Then do Factorization by grouping (i.e group the terms with common factors before factorizing):

[tex]y(y -25) - 16(y - 25) = 0[/tex]

[tex](y - 25)(y - 16) = 0[/tex]

The product of two expressions is zero, which means either of the two expressions is equal to Zero:

Either: [tex]y - 25 = 0[/tex]

Substituting [tex]y = x^{2}[/tex]:

          = [tex]x^{2} - 25 = 0[/tex]

         = [tex]x^{2} = 25[/tex]

         = [tex]\sqrt{x^{2}} = \sqrt{25}[/tex]

         ∴ x = ±5

 Or: [tex]y - 16 = 0[/tex]

Substituting [tex]y = x^{2}[/tex]

     [tex]= x^{2} - 16 = 0[/tex]

     [tex]= x^{2} = 16[/tex]

     [tex]= \sqrt{x^{2}} = \sqrt{16}[/tex]

    ∴ x = ±4

∴Values of x are ±4 and ±5

Answer:

8x3 + 2x − 5

Step-by-step explanation:

The numbers required in the word problem are

Let's call the numbers x and y

From the first equation, we have:

2x + y = 18

From the second equation, we have:

3x - y = 7

Solving simultaneously by substitution method

3x - y = 7

3x = 7 + y

x = (7 + y)/3

substitute this expression for x into the first equation:

2x + y = 18

2((7 + y)/3) + y = 18

14/3 + 3y/3 = 18

14/3 = 18 - 3y/3

14/3 = 18 - y

collecting like terms

y = 18 - 14/3

y = 18 - 4 2/3

y = 13 1/3

substituting to solve for y

x = (7 + y)/3

x = (7 + 13 1/3)/3

x = 10 4/3/3

x = 3 4/3

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Answer:

$14

Step-by-step explanation:

i multiplied 2.80 times 5 and got 14.

i hope this helped :)

The amount of Tylenol remaining after 8 hours is 47.1g

half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive.

R = A(0.5)^t/3

R = 300(0.5)^8/3

R = 300( 0.157)

R = 47.1

therefore after 8 hours 47.1 g of Tylenol is is left

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495.95

convert the percentage into a decimal

0.09

then do b=1-r

1 - 0.09 = 0.91

Now do 545 x 0.91

Answer: 495.95

Let's assume that the original price of the antique was x.

We know that the antique was sold at a profit of 9%, which means that the selling price is 109% of the original price:

[tex]Selling \: price = Original \: price + Profit[/tex]

[tex]£545 = x + 0.09x \\ £545 = 1.09x[/tex]

[tex]x = 500[/tex]

Answer:

10.305

Step-by-step explanation:

The phrase to describes the algebraic expression Three-fourths x + 2 is three-fourths of a number plus two.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given in question;

The algebraic expression;

Three-fourths x + 2

Now,

The phrase that describes the algebraic expression Three-fourths x + 2;

three-fourths of a number plus two.

Therefore, the phrase of expression will be three-fourths of a number plus two.

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Answer:

y=3x-2

Step-by-step explanation:

The value of t is,

⇒ t = 28

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

The circle is shown in figure.

Now, From the figure we can formulate;

t = 1/2 (3t - 28)

2t = 3t - 28

3t - 2t = 28

t = 28

Thus, The value of t is,

⇒ t = 28

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According to the equation, when 9 video games are rented, the total cost is $31.5 which is expressed in the equation as 3.5x.

What is an equation?

A formula known as an equation uses the equals sign (=) to express how two expressions are equal. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have left hand side equal to right hand side in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as an expression.

Given,

The cost of renting a video game = $3.50

The total cost of rentals for the month  = $31.50

The equation given is:

    3.5x = 31.5

The term 3.5x in the equation represents the total cost of a month when the number of video games rented is x.

In this case x = 31.5/3.5 = 9

Therefore, according to the equation, when 9 video games are rented, the total cost is $31.5 which is expressed in the equation as 3.5x.

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To sit comfortably, the students need a total of 6 tables. The correct option is 3.

There are 32 students in a classroom. In 5th grade. Now to sit comfortably, the students need 6 tables. In each table, a total of 6 students can fit. In 5 tables, only 30 students can sit but two students will remain table less. With 1 extra table, 2 students can sir and each student from a table can sit in the las bench, i.e., 6th table.

The number of pupils in the classroom is 32. in grade five. The pupils now require 6 tables in order to sit comfortably. A total of 6 pupils can fit at each table. Only 30 pupils can fit at 5 tables, however 2 students will be tableless. With one extra table, two students can sit at the sixth table and each student from a table can use the last bench. Therefore, students need a total of 6 tables.

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Answer:

Step-by-step explanation:

reflict means to put the point in the other way but in the same point.

Answer: Choose Option D (look at the image for the solution and make sure to give me brainliest)

Step-by-step explanation:

The snow on the lawn after 5 hours is 14.50 inches.

The snow on the lawn after tt hours is 12 + 0.5tt inches

The equation that represents the amount of snow after a number of hours is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of the equation is:

Total snow = snow on the lawn + (rate at which the snow falls x number of hours)

Snow after 5 hours = 12 + (0.5 x 5)

= 12 + 2.5 = 14.50 inches

Snow after tt hours = 12 + (0.5 x tt)

= 12 + 0.5tt inches

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In order to guide learners to move from the concrete level to the semi-concrete and finally to the abstract level in relation to their understanding of the more than/less than concept, I would use a step-by-step approach.

At the concrete level, I would introduce the concept of more than/less than with a hands-on activity. For example, I would have students compare the number of counters or blocks and have them determine which group has more or less. This would help them develop a fundamental understanding of the concept.At the semi-concrete level, I would introduce the concept of more than/less than with written numerals. I would have students compare numbers on paper, such as 4 and 6, and have them determine which number is more or less. I would also ask them to use concrete objects to represent the numbers, such as using four counters for 4 and six counters for 6.At the abstract level, I would introduce the concept of more than/less than with larger numbers. I would ask students to compare numbers such as 12 and 15, and determine which number is more or less. I would also ask them to use abstract symbols, such as 12 + and 15 -, to represent the numbers.By using this step-by-step approach, students will be able to move from the concrete level to the semi-concrete and finally to the abstract level of understanding the more than/less than concept. This will help them develop a strong foundation of the concept, which will allow them to solve more complex problems in the future.

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Answer:

84 square inches

Step-by-step explanation:

The shaded region comprises of two same trapeziums:

∴Area of shaded region = 2 × (Area of a trapezium)

    = 2 × [tex]\frac{1}{2}[/tex] × (Sum of parallel sides) × (perpendicular height of trapezium)

    = [tex]\frac{2}{2}[/tex] × (4 + 8) × (6)

    = 84 square inches

1. Cosx = 5/√(41)

2. An equation {tan(x) + cot(x)}/{tan(x)} =csc²(x)

Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

Given:

1. tanx = -4/5

and tanx = perpendicular/adjacent leg

So, P = -4 and A = 5

So, H = √(-4)² + (5)²

H = √(41)

So, Cosx = 5/√(41)

2. A trigonometric identity,

{tan(x) + cot(x)}/{tan(x)}

Simplifying,

= {tan(x)/tan(x) + cot(x)/{1/tan(x)}

= 1 + cot²(x)

= csc²(x)

Therefore, Cosx = 5/√(41)

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The height of the kite is 56 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

[tex]sin(30)=\frac{h}{112}[/tex]

h = 56 feet

Therefore, the height of the kite is 56 feet.

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The equation b = 3.99a has a slope of 3.99 and the y intercept is 0.

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

The standard form of a linear equation is:

y = mx + b

Where y, x are variables and b is the y intercept

Given an equation:

b = 3.99a

Comparing with the standard linear equation:

The slope is 3.99 and the y intercept is 0.

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Answer:

36°

Step-by-step explanation:

2x+3x=5x

5x=180°

x=180°:5=36°

The area of the figure nearest hundredth will be 84.13 square feet.

The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The figure is the combination of the rectangle and the semicircle. Then the area of the figure is the addition of the rectangle and the semicircle. Then we have

A = L x W + (π / 8) D²

A = 14 x 5 + (3.14/ 8) (14 - 4 - 4)²

A = 70 + 0.3925 x 36

A = 70 + 14.13

A = 84.13 square feet

The area of the figure nearest hundredth will be 84.13 square feet.

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The missing diagram is given below.

Completely factorize the polynomial using any methods that are appropriate, then look for shared factors and the polynomial's roots. Next, double-check your work to confirm accuracy.

Follow these steps to determine a polynomial's factorization:

Completely factor the polynomial using any relevant techniques, including grouping, utilizing the difference of squares or cubes, or using the quadratic formula.

By multiplying them all together, you can verify that each factor is accurate. The final figure must match the initial polynomial.

Look for shared factors among the polynomial factors. If the polynomial has common components, remove them from the equation and rewrite it as the product of the common factors and the other factors.

The polynomial's roots can be verified by setting each factor to zero and calculating the variable. The roots ought to correspond to the original polynomial.

Verify your work a second time to make sure all relevant elements have been identified and taken into consideration.

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Answer: 4cos(pi/6x)+3

Step-by-step explanation:

If Elish was required to write a 600 word Literature essay and word count on her computer showed that she had typed 240 words Elish still needs to complete 3/5 of the essay.

To find the fraction of the essay that Elish still needs to complete, we need to determine how many words she has left to write. We can do this by subtracting the number of words she has already written from the total required word count:

Words left to write = Total word count - Words already written

Words left to write = 600 - 240

Words left to write = 360

Now, to find the fraction of the essay that Elish still needs to complete, we can express the remaining words as a fraction of the total word count:

Fraction of essay left to complete = Words left to write / Total word count

Fraction of essay left to complete = 360 / 600

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 120:

Fraction of essay left to complete = (360 ÷ 120) / (600 ÷ 120)

Fraction of essay left to complete = 3 / 5

This means that she has completed 2/5 of the essay so far (which is the equivalent fraction of 240/600).

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There are two quadratic functions as A. 2b(b - 7) + b = 0 and B. (4a + 2)(2a - 1) + 1 = 0.

The quadratic function is defined as a function containing the highest power of a variable is two.

A. 2b(b - 7) + b = 0 is a quadratic function because it can be simplified to the form of ax² + bx + c = 0 where a, b, and c are constants and x is the variable. In this case, a = 2, b = -13, and c = 0.

B. (4a + 2)(2a - 1) + 1 = 0 is also a quadratic function because it can be simplified to the form of ax² + bx + c = 0. In this case, a = 8, b = -2, and c = 1.

C. 2y + 2(3y - 5) = 0 is not a quadratic function because it can be simplified to the form of mx + b = 0 where m and b are constants and x is the variable.

D. 8 - 5x = 4(3x - 1) is not a quadratic function because it can be simplified to the form of mx + b = 0 where m and b are constants and x is the variable.

Thus, the correct answer would be options A. 2b(b - 7) + b = 0 and B. (4a + 2)(2a - 1) + 1 = 0.

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The opposite sides of FGHJ are parallel.

A quadrilateral is a four-sided polygon, having four edges and four corners.

FGHJ is a quadrilateral.

From the figure we can observe that opposite sides are equal which means the quadrilateral is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

The line segment FG≅JH

GH≅FJ

The sides are congruent and parallel.

Hence, the opposite sides of FGHJ are parallel.

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