7. Fill in the blanks below to make each statement true.
a. Fewer than 15% of coins were
of the coins were quarters.
b. Exactly
c. Nickels, dimes, and quarters account for
of the total number of coins.

The bee's path can be modeled as a complex number sequence.

The bee started flying from the point facing east and flies a distance of 1 foot due east. For, once the bee reaches a point, turns counterclockwise, and flies two-thirds of the previous distance it flew to point

The first step is 1 + 0i. Each subsequent step is two-thirds of the previous step rotated by -90 degrees, which is equivalent to multiplying by -1/3 + i√3/3.

The bee's final position is the limit of this sequence, which is 0.5 + 0.5i√3. The distance from the starting point is |0.5 + 0.5i√3| = 0.5√(0.5² + (0.5√3)²) = √(0.25 + 0.75) = √(1).

Therefore, = √(1), and = 1.

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The total pay at the end of the week is $618.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

Thomas gets paid $15 per hour during regular time, hence for 40 hours he gets:

(15)(40) = 600

He works a total of 46 hours:

The additional time worked is 6 hours.

The payment for the additional hours is:

(1.5)(15) = 22.5

For 6 hours he gets:

(6)(22.5) = 135

Hence, the total income that he should get is 600 + 135 = 735.

He gets an deduction of $117, the final pay is:

735 - 117 = 618

Hence, the total pay at the end of the week is $618.

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Answer:

To solve this problem, we can use a system of equations. Let x be the number of shoes sold at $66.95 and y be the number of shoes sold at $84.95. We know that:

x + y = 240 (because 240 pairs of shoes were sold in total)

66.95x + 84.95y = 17,652 (because this is the total amount of money earned from shoe sales)

To find the number of each type of shoe sold, we can use substitution method, by solving one equation for one variable and substituting that expression into the other equation.

We can solve the first equation for y:

y = 240 - x

Then we can substitute this expression into the second equation and solve for x:

66.95x + 84.95(240 - x) = 17,652

66.95x + 21,068 - 84.95x = 17,652

-18x = -3,416

x = 176

So, 176 pairs of shoes were sold at $66.95. To find the number of shoes sold at $84.95, we can substitute this value of x into the first equation:

y = 240 - 176 = 64

So, 64 pairs of shoes were sold at $84.95.

In conclusion, we can recover the information and the manager can know that 176 pairs of shoes were sold at $66.95 and 64 pairs of shoes were sold at $84.95.

The units of a and b are m/sec³ and m/sec⁴

Given :v = at² + bt³

The dimension of velocity v = [L] [T]⁻¹

According to the Principle of Homogeneity of Dimension, "the terms combining the equation must have the same dimensions for the equation to have any physical meaning."

So, Dimensiona of v = Dimensions of at²

                       [L][T]⁻¹ = a[T]²

                 a = [L][T]⁻³ = m/sec³

Similarly, we can say

Dimension of v = Dimension of bt³

              [L][T]⁻¹ = b[T]³

       b = [L][T]⁻⁴ = m/sec⁴

Hence, the unit of a is m/sec³ and the unit of b is m/sec⁴

The question is incomplete, the complete question is

"During a short interval of time, the speed v in m/s of an automobile is given by v = at² + bt³ where the time t is in seconds the units of a and b are respectively:"

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We can make 5 pies with one pack of apples as the number of pies should be an integer.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A bushel of apples weighs about 42 pounds and there are four packs in a bushel.

So, The weight of one pack of apples is (42/4) = 10.5 pounds.

Now, It takes 2 pounds of apples to make one pie,

Therefore, We can make (10.5/2) = 5.25 pies but we can only make 5 pie from one pack of apples.

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The number of free variables in an augmented matrix depends on the size of the matrix. An augmented matrix with an [tex]$m \times n$[/tex] matrix on the left side has n free variables.

An augmented matrix is composed of two parts, the left side and the right side. The left side is an [tex]$m \times n$[/tex] matrix, where m is the number of rows and n is the number of columns. The right side is a column of constants. The number of free variables in an augmented matrix is equal to the number of columns in the left side matrix, which is n.

The number of free variables in an augmented matrix depends on the size of the matrix. An augmented matrix with an[tex]$m \times n$[/tex] matrix on the left side has n free variables.

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Correct option is B, function for the area of the circle in terms of the side of the square is A = [tex]\pi \frac{S^2}{4}[/tex].

Because the area of a square is one of its sides multiplied by itself, the area equals the square of the radius of a circle multiplied by two. Because the radius of the circle is a known quantity, the area of the inscribed square can be calculated numerically.

An “inscribed” square in a square is one in which all of the vertices of the smaller square are on the borders of the bigger square. To do this, the vertices of the smaller square will split each side of the bigger square into two segments, one on each side.

If a square is used to inscribe a circle, the square's side length will match the circle's diameter. As a result, the radius of an inscribed circle is S/2 for a square with length S. hence, the area of a circle is expressed as the square's sides,

= [tex]\pi \frac{S^2}{4}[/tex]

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The statement [1,5] = { 1, 2, 3, 4, 5 is False.

In mathematics, there are two ways of representing a set of elements: by using curly braces {} or square brackets []. The curly braces {} are commonly used to represent sets, while square brackets [] are used to represent lists or arrays.

[1,5] is a list, which means it is ordered and has duplicates allowed. On the other hand, {1,5} is a set, which means it is unordered and has no duplicates allowed.

Therefore, [1,5] is not equal to {1, 2, 3, 4, 5} because the former is a list of two elements, while the latter is a set of five distinct elements.

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A hallway having 1000 doors at the end of the process the doors which are open are all the factors of 24 i.e, 24,48,72,96,120,144...

A hallway has 1000 doors named 1 from 1000

So he opens all the doors of the hallway so all the doors are opened.

He decides to close every other door starting with door number 2 so 1st door is open and from 2nd door every alternate door is opened so factor of 2 is all close,

2, 4, 6, 8, 10, 12, 14, 16, 18, 20..................1000.

Then he decides to close very open door and open every close door from door three so,

3 is open it will be closed

6 was close so open

9 was open so it will be close

12 was close the it is open

so on 15,21, 27,33......999 will all be closed,

and all 18, 24, 30.....will be all open

then he walks down the hall and changes every fourth door starting with door 4

so 4 will be open so on

4, 8, 16,20, 28,32, 36,40........so on 1000 will all be open

and 12,24,48,60.............will be closed.

So all the door with factor of 12 i.e.12,24,36,48,60,72...will closed.

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Answer:

1/21

Step-by-step explanation:

1/3 divided by 7

= 1/3 x 1/7

= 1/21

The value of the function when evaluated is 1/2

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

f(x)=2/√10-6

Express properly

So, we have the following representation

f(x)=2/√(10-x)

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

f(-6)=2/√10+6

Evaluate the like terms

f(-6)=2/√16

So, we have

f(-6) = 1/2

Hence, the function value is 1/2

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APX is congruent to WX and APZ is congruent to WZ

From step 2 and 3, we can conclude that APX is congruent to APZ.

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a. The different sequences possible are 1200.

b. The different sequences have all hip, knee, and shoulder surgeries scheduled consecutively are 720.

c. The different schedules begin and end with knee surgery is 6.

(a) To find the number of different sequences, we can use the permutation formula n!/(n-r)!

where n is the total number of surgeries and r is the number of surgeries of each type that we need to schedule.

For knee surgeries, n = 5 (total surgeries) and r = 3 (number of knee surgeries), so the number of different sequences for knee surgeries is 5!/(5-3)! = 5!/(2!) = 54 = 20.

Similarly, the number of different sequences for hip surgeries is 5!/(5-2)! = 5!/(3!) = 54*3 = 60.

Hence, the total number of different sequences is 20 * 60 = 1200.

(b) To find the number of different sequences with all hip, knee, and shoulder surgeries scheduled consecutively, we first need to find the number of sequences for each type of surgery.

For knee surgeries, n = 3 (number of knee surgeries) and r = 3 (number of knee surgeries), so the number of different sequences for knee surgeries is 3!/(3-3)! = 3!/(0!) = 3! = 6.

Similarly, the number of different sequences for hip surgeries is 2!/(2-2)! = 2!/(0!) = 2! = 2.

For shoulder surgeries, the number of different sequences is 5!

Hence, the total number of different sequences with all hip, knee, and shoulder surgeries scheduled consecutively is 6 * 2 * 5! = 720.

(c) In order to find the number of different schedules that begin and end with knee surgery, we first need to find the number of sequences for the middle surgeries.

There are 2 hip surgeries and 2 knee surgeries left to schedule, so the number of different sequences for these surgeries is (2+2-1)!/(2!2!) = 3!/(2!1!) = 3.

Hence, the total number of different schedules that begin and end with a knee surgery is 3 * 2 * 1 = 6.

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The complete question is -

A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries.

(a) How many different sequences are possible?

(b) How many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively?

(c) How many different schedules begin and end with knee surgery?

The GCFs of the given polynomials are 4, 7x² and 1

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Given are some polynomial, we need to find GCF,

a) 12x²-8x+4

12x² = 2×2×3×x×x

8x = 2×2×2×x

4 = 2×2

GCF = 2×2 = 4

b) 7x⁸-14x⁴+21x²

7x⁸ = 7×x×x×x×x×x×x×x×x

14x⁴ = 7×2×x×x×x×x

21x² = 7×3×x×x

GCF = 7×x×x

GCF = 7x²

c) 17x³+15x²-21x+3

17x³ = 17×x×x×x

15x² = 3×5×x×x

21x = 7×3×x

3 = 3×1

GCF = 1

Hence, the GCFs of the given polynomials are 4, 7x² and 1

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Answer: Option d.  0.26

Step-by-step explanation:

Since the addition of complementary angles = 90°

75° + x = 90°

x = 90° - 75 °

x = 15°  ( the complementary angle )

sine 15° = 0.25882

             = 0.26 correct to two decimal places

We know Ms. Langlois has 26 pencils.

We DO NOT know the amount of pencils that Mr.Cox has, we can use the variable "x" to represent Mr.Cox's number of pencils.

An expression is just an expression, not an equation, so it DOES NOT require a "="

The expression could be represented as 26+x

The area of the shaded region is equal to sin(2).

The shaded region is a sector of a circle with radius r and central angle 2. To find the area of the shaded region, we first need to find the radius of the circle, which is given by r2 = sin(2). Taking the square root of both sides, we get r = sqrt(sin(2)).

Next, we need to find the area of the sector, which is given by:

A = (r^2 * 2) / 2 = r^2

Substituting r = sqrt(sin(2)), we get:

A = (sqrt(sin(2)))^2 = sin(2)

Therefore, the area of the shaded region is equal to sin(2).

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QUESTION CORRECTION: Find The Area Of The Shaded Region. R² = Sin (2Ф).

two angles in the triangle are 60°, so the last one must be 60°, since all must add up to 180°, that means the triangle is equilateral

[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3}~ ~~ units^2[/tex]

Answer:

C.

Step-by-step explanation:

It is an equilateral triangle.

DB = 6, AB = 12, DC = height

[tex]DC=\sqrt{(CB)^{2}- (DB)^{2} } =\sqrt{144-36} =\sqrt{108}=\sqrt{(36)(3)} =6\sqrt{3}[/tex]

[tex]A=\frac{(DC)(AC)}{2} =\frac{(6\sqrt{3})(12) }{2} =\frac{72\sqrt{3} }{2} =36\sqrt{3}[/tex]

Hope this helps

The expression that has a term with a coefficient greater than 1 is

3) 5 + 3m.

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.

Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.

We know a coefficient is a constant term that is with a variable.

By observing the given options we conclude that the expression

5 + 3m has a coefficient which is 3 and it is greater than 1.

Q. Which expression has a term with a coefficient greater than 1?

1) m -5×3.

2) 5 + m.

3) 5 + 3m.

4) 5/6m + 3.

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The probability of winning the game with at least one Ace among the four draws is 0.736.

The probability of winning in this game is calculated as,

There are 4 Aces in a standard deck of 52 cards, so the probability of drawing an Ace on one draw is 4/52.

The probability of not drawing an Ace in 4 draws is (48/52) * (47/51) * (46/50) * (45/49) = 0.264.

The probability of winning is the complement of not winning, which is 1 - 0.264 = 0.736.

So, the probability of winning the game with at least one Ace among the four draws is 0.736.

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As per the given number nine billion is 8.9 x 10⁹ greater than one hundred million

Numbers are a fundamental part of our lives and the world around us. Understanding how to compare and perform arithmetic with large numbers is an important skill.

In this question, we are comparing two large numbers: nine billion and one hundred million.

The correct answer is (a) 8.9 x 10⁹.

The number nine billion can be written as

=> 9 x 10⁹,

where 10⁹ means 10 raised to the 9th power, or 10 multiplied by itself 9 times, which is equal to 1,000,000,000.

Meanwhile, one hundred million can be written as 100 x 10⁶, or 100 million.

To compare these two numbers, we subtract 100 million from nine billion, which gives us 8.9 x 10⁹.

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Answer:

(x+2)(x−5)(x−4)

Step-by-step explanation: These are the possible roots of the polynomial function. ± 1 , ± 40 , ± 2 , ± 20 , ± 4 , ± 10 , ± 5 , ± 8 Substitute − 2 and simplify the expression. In this case, the expression is equal to 0 so − 2 is a root of the polynomial. Tap for more steps... 0 Since − 2 is a known root, divide the polynomial by x + 2 to find the quotient polynomial. This polynomial can then be used to find the remaining roots. x 3 − 7 x 2 + 2 x + 40 x + 2 Divide x 3 − 7 x 2 + 2 x + 40 by x + 2 . Tap for more steps... x 2 − 9 x + 20 Write x 3 − 7 x 2 + 2 x + 40 as a set of factors. ( x + 2 ) ( x 2 − 9 x + 20 )

y=-1.5x+2.5 is the linear function with the y-intercept of 2. 5 for the line passing through (4. 5, -4. 25).

An expression that quantifies a line's direction and steepness is called its slope or gradient. This allows one to see how quickly the dependent variable is changing as the independent variable does. Given the points are (4. 5, -4. 25) and the y-intercept is 2.5.

First, find the slope of the equation. For this substitute (x₁, y₁) value and (x₂, y₂) values in the formula m=(y₂-y₁)/(x₂-x₁). We get,

[tex]\begin{aligned}m&= \frac{(y_2 - y_1)}{(x_2 - x_1)} \\&=\frac{(2.5 - (- 4.25))}{(0 - 4.5)}\\&= -1.5\end{aligned}[/tex]

Substitute, the value of slope and y-intercept in the general equation y=mx+c. We get, y=-1.5x+2.5.

The required answer is y=-1.5x+2.5.

The complete question is -

What is a linear function in the form y=mx+b for the line passing through (4.5, -4.25) with y-intercept 2.5?

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Answer:

The product of (x+7)^2 is (x+7)(x+7) = x^2 + 14x + 49

Step-by-step explanation:

Answer:

x ≈ 2.8

Step-by-step explanation:

using the sine ratio in the right triangle

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{PQ}{OQ}[/tex] = [tex]\frac{1.8}{x}[/tex] ( multiply both sides by x )

x × sin40° = 1.8 ( divide both sides by sin40° )

x = [tex]\frac{1.8}{sin40}[/tex] ≈ 2.8 ( to the nearest tenth )

Answer:2.8

Step-by-step explanation:

By using sine ratio , sine40°=opposite/hypotenuse

or, sine40°= 1.8/

or, x= 1.8/sine40°

or,x= 2.8003.......

or,x =2.8

A. greater than 180°. A major arc is an arc of a circle that has a measure greater than 180°.

Arc is a curved line which is part of the circumference of a circle or other curved shape. In mathematics, an arc is defined as a continuous segment of a circle. It is a line that joins two points on a circle's circumference. The length of an arc is proportional to the circle's circumference and is measured in radians or degrees. An arc can also be a part or section of a different type of curve such as an ellipse or parabola.

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Answer:

A. The graph of the stock value would start at a low point on the left side of the graph and gradually increase in value as it moves to the right. The line representing the stock value would start to level off and then suddenly drop, representing the quick decrease in value. The line would then level off again and stay the same for the rest of the day.

B. If the stock gradually decreased during the middle of the day, the line on the graph would start at a high point, gradually decrease in value, and then level off.

Answer: Option D

Step-by-step explanation: Given: -2x + 14 + 10x = 34

-2x + 10x + 14 = 34

8x + 14 = 34

8x = 34 - 14

8x = 20

divide both sides by 8

8x/8 = 20/8

x = 5/2

The given statement "the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population." is FALSE

In inferential statistics, sample data is analysed as opposed to the entire population since, in some cases, it is impossible to analyse the population of an entire country. As a result, inferential statistics uses analysis of sample data to make conclusions about the entire population. The population's sample data are chosen, and after analysis, the results can be utilised to draw conclusions about the entire population.

Hence, the given statement "the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population." is false

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$20 more money the band members need to raise.

What is the total amount?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A car that has been totaled in an accident is irreparably damaged.

Here, we have

Given: Band members are selling magazines to raise $150 for a school dance.

= 150 - (25 + 45 + 10 +25 + 15 + 10)

= 150 - 130

= 20

Hence, $20 more money the band members need to raise.

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