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The quotient using a synthetic method of division is m³ - 10m² - 9m - 1

The quotient expression is given as

(m⁴ -7m³ -39m² - 28m - 3) divided by m + 3

Using a synthetic method of quotient, we have the following set up

 -3 |   1    -7    -39    -28    -3

      |__________

Bring down the first coefficient, which is 1:

 -3 |   1    -7    -39    -28    -3

      |__________

         1

Multiply -3 by 1 to get -3, and write it below the next coefficient and repeat the process

 -3 |   1    -7    -39    -28    -3

     |____-3__ 30__27__3____

          1    -10    -9    -1      0

So, the quotient is m³ - 10m² - 9m - 1

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Answer: The dance class has more students

Step-by-step explanation:

3 divided by 10 = 0.3

2 divided by 3 = 0.66

Since 0.66 is more than 0.3, we can say that more students entered the dance class than the music class.

Answer:

5, 6, 8, 11, 15, 20

5+1=6+2=8+3=11+4=15+5=20

18, 20, 24, 30, 38, 48

18+2=20+4=24+6=30+8=38+10=48

55, 54, 51, 46, 39, 30, 19

55-1=54-3=51-5=46-7=39-9=30-11=19

82, 81, 78, 73, 66

82-1=81-3=78-5=73-7=66

0+6=6+0

6=6

14+9=9+14

23=23

20x(4+3)=(20x4)+(20x3)

20x7=80+60

140=140

9+(6+5)=(9+6)+5

9+11=15+5

20=20

10x(4+6)=(10x8)+(10x2)

100=100

Step-by-step explanation:

Answer:

a)6

b)15 and -15

Step-by-step explanation:

a)5*5*5*5*5*5 there is 6 5's so, we  can show it as, [tex]5^{6}[/tex]

[tex]5^{6}[/tex]=[tex]5^{x}[/tex]

x=6

b) in this one you found one of the answers of y which is 15.

but [tex]15^{2}=-15^{2}\\so y=15\\and y=-15[/tex]

Answer:

The answer is down below

Step-by-step explanation:

a) 5×5×5×5×5×5=5^x

5×5×5×5×5×5=5⁶

b)y²=225

square both sides

√y²=√225

y=15

Answer:

It all depends on the linear system

Step-by-step explanation:

A system of linear equations usually has a single solution but sometimes it can have no solution (parrel lines) or infinite solutions (same line).

I hope this helped

The answer is Three.

One solution.

Infinitely many solutions.

No Solutions at all.

Check the picture below.

so we're really looking for the area of a sector of a circle with 63° and a radius of 3, twice.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =63\\ r=3 \end{cases}\implies A=\cfrac{(63)\pi (3)^2}{360} \\\\\\ A=\cfrac{63\pi }{40}\implies \stackrel{\textit{now let's double that}}{2\cdot \cfrac{63\pi }{40}}\implies \cfrac{63\pi }{20}\implies 9.9~cm^2[/tex]

The functions are classified as follows:

a) Linear.

b) Linear.

c) Linear.

d) Non-linear.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

Hence, from the definition, a function is classified as linear if the highest exponent of both x and y is of one.

A term x on the denominator has an exponent of -1, hence item d is not a linear function.

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The linear equations in the options are:

a) 5x - 9 + 7y = x - 4

b) 0.01x - 0.7y = 2.2

c) -3x = 4

We say that an equation is linear if the dependence with the veriables is only of first degree.

For example, equations of the form:

a*x + b*y = c

Are linear, because the variables x and y have an exponent of 1.

Then, the options that show linear equations are:

a) 5x - 9 + 7y = x - 4

b) 0.01x - 0.7y = 2.2

c) -3x = 4

The last option is non linear, because x is on the denominator.

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The given distribution is not a probability distribution.

The given distribution is not a probability distribution, since the sum of probabilities is not equal to 1. A probability distribution must satisfy two conditions: 1) the probabilities must lie inclusively between 0 and 1, and 2) the sum of probabilities must be equal to 1.

In this case, the sum of probabilities is 15+15+15 = 45, which is not equal to 1. Therefore, the given distribution is not a probability distribution. The other options are incorrect because they do not accurately describe the given distribution.

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Answer: x = 31 over 14 − 5y over 14

Step-by-step explanation: Move all terms that don't contain x to the right side and solve.

In the given cube, the required data is as follows:

Faces = 6

Edges = 12

Vertices = 8

A cube is a solid three-dimensional form with six square faces that all have the same length sides. It is one of the five platonic solids and is also referred to as a regular hexahedron.

Six square faces, eight vertices, and twelve edges make up the form.

Here in the question as asked,

Faces = 6

Edges = 12

Vertices = 8

Now to prove that we are correct,

V -E + F =2

= 8 - 12 + 6

=2

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Answer:

s is inversely proportional to t

Step-by-step explanation:

As s increases, t decreases.  They are inversely proportioanl when that happens.

To calculate the dosage strength of digoxin, which is supplied by the pharmacy in mg per tablet, the physician orders digoxin 0.25 mg po daily.

In other words, The physician ordered 0.25 mg of digoxin to be administered orally every day. The medication provided by the pharmacy is to be taken in tablet form. To calculate the amount of digoxin in each tablet, you need to divide the ordered dose by the amount of tablets.

The equation is:Dose Ordered / Tablets = Dose per tablet

Substitute the known values:Dose Ordered = 0.25 mgTablets = 1 tablet0.25 mg / 1 tablet = 0.25 mg per tablet.

Therefore, the dosage strength of the digoxin supplied by the pharmacy is 0.25 mg per tablet.

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The value of sin(D) is 7/25 after the application of the Pythagoras theorem.

The Pythagorean theorem is a fundamental theorem in geometry that describes the relationship between the sides of a right triangle. It claims that the hypotenuse's square length, which is the side that faces the right angle, is equivalent to the total of the squares of the lengths of the other two sides in a right triangle. The theorem can be formulated mathematically as:

c² = a² + b²

where, even the lengths for the remaining two sides (the legs) of the right triangle are a and b, and c is the length of the hypotenuse.

The Pythagorean theorem may be employed to determine the triangle's third side's length:

DE²= FD² + EF²

25² = 24² + EF²

625 = 576 + EF²

EF² = 49

EF = 7

Now, we can use the definition of sine to find sin(D):

sin(D) = opposite/hypotenuse = EF/DE = 7/25

Therefore, the value of sin(D) is 7/25.

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Answer:

We can solve the inequality for m to find the maximum number of muffins that can be purchased within the budget of $75:

75 ≥ 0.82m

Divide both sides by 0.82:

m ≤ 91.46

Since m must be a whole number, the maximum number of muffins that can be purchased is 91. Therefore, 91 customers could possibly get a muffin.

Step-by-step explanation:

The area of the circle to the nearest tenth is 28.3 square centimeters.

To find the area of a circle with a given radius, we use the formula

A = π[tex]r^2,[/tex]

where A is the area and r is the radius.

In this case, the radius is 3 cm, so we can substitute it into the formula to get:

A = 3.14 x [tex]3^2[/tex]

Simplifying this equation, we get the following:

A = 3.14 x 9

A = 28.26

To round this to the nearest tenth, we look at the digit in the hundredth place, 6. Since 6 is greater than or equal to 5, we round up the number in the tenth place, which is 2. Therefore, the final answer is:

A ≈ 28.3 [tex]cm^2[/tex]

So, the area of the circle to the nearest tenth is 28.3 square centimeters.

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The length of the arc with a central angle of 45° is 4.24 cm

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The length of an arc formed on a circle with a central angle Ф and radius r is:

Length of arc = (Ф/360) * 2πr

Given the circle radius is 5.4 cm and the central angle is 45°, hence:

Length of arc = (Ф/360) * 2πr = (45/360) * 2π(5.4) = 4.24 cm

The length of the arc is 4.24 cm

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The logical expressions for each sentence can be written as follows:
(a) t(Sam, Math 101)
This expression states that Sam has taken Math 101.
(b) ∀x∃y t(x, y)
This expression states that for every student x, there exists a math class y such that the student x has taken the math class y.
(c) ∀x∃y (t(x, y) ∧ y ≠ Math 101)
This expression states that for every student x, there exists a class y such that the student x has taken the class y and the class y is not Math 101.
(d) ∃x∀y (t(x, y) ∧ y ≠ Math 101)
This expression states that there exists a student x such that for every math class y, the student x has taken the math class y and the math class y is not Math 101.
(e) ∀x∃y∃z (t(x, y) ∧ t(x, z) ∧ x ≠ Sam ∧ y ≠ z)
This expression states that for every student x, there exists two different math classes y and z such that the student x has taken the math classes y and z and the student x is not Sam.
(f) ∃y∃z (t(Sam, y) ∧ t(Sam, z) ∧ y ≠ z ∧ ∀w (t(Sam, w) → (w = y ∨ w = z)))
This expression states that there exists two different math classes y and z such that Sam has taken the math classes y and z and for every math class w, if Sam has taken the math class w, then the math class w is either y or z.

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The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath. The function C(t) = 250sin(2I/5(t))+2450.

It shows the capacity of the lung of a person at any point of time t in milliliters (mL).

We not only need to find the one full cycle but also determine the period of function and it is given by:

T = 2I/(2I/5)

T = 5 seconds.

This means that the function completes one full cycle every 5 seconds.

To find the maximum value of the function over one full cycle, we need to find the maximum value of sin(2π/5(t)). The maximum value of sin(2π/5t) is 1, this happens at 2π/5(t) = π/2 + nπ, and n is considered as an integer.

So, the maximum value of the function occurs when sin(2I/5(t)) = 1, Substituting this into the original function, we get maximum value, Cm:

Cm = 250(1) + 2450

= 2700 mL.

The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath.

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Answer: The comparison "3.4 < 3.36" is reasonable because 3.36 is greater than 3.4.

The decimal point separates the whole number part of a number from the fractional part. In this case, 3.36 has a greater whole number part (3) than 3.4, and both have the same decimal part (0.36). So, 3.36 is greater than 3.4.

Therefore, the statement "3.4 < 3.36" is a true and reasonable comparison.

Step-by-step explanation:

After 3 seconds, the rider is still at their starting height of 0 metres.

The height of a rider after 3 seconds can be calculated using the equation h(t) = v₀t - (1/2)gt², where h(t) is the height of the rider in metres at time t, v₀ is the initial velocity in metres per second, and g is the acceleration due to gravity in metres per second squared.

Assuming v₀ is 0, since the rider is just starting, and g is 9.81, then the height of the rider after 3 seconds is h(3) = 0 - (1/2)(9.81)(3²) = -44.355. Since this is a negative number, the rider is still at their starting height of 0 metres after 3 seconds.

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Step-by-step explanation:

If the interest is not compounded, it means that Mabel will earn a simple interest of 11% per year on her principal amount of $30,000.

The formula for calculating simple interest is:

Interest = (Principal x Rate x Time)

Where:

Principal = $30,000

Rate = 11% = 0.11 (as a decimal)

Time = 2 years

So, substituting the values in the formula, we get:

Interest = (30,000 x 0.11 x 2) = $6,600

Therefore, Mabel will earn $6,600 in interest over a period of 2 years.

The equation of the line that is parallel to y = -(1/4)x + 5 and passes through (2, -3) is y = -(1/4)x - 5/2.

To find the equation of the line that is parallel to the line y = −(1/4)x + 5 and passes through the point (2, −3), follow these steps:Step 1: Determine the slope of the given line.The slope-intercept form of the equation of the line is y = mx + b where m is the slope of the line. y = −(1/4)x + 5 is already in slope-intercept form, so its slope is −1/4. Step 2: Determine the slope of the line that is parallel to the given line. The slope of a line parallel to another line is the same as the slope of the given line. Therefore, the slope of the line we need to find is also −1/4. Step 3: Determine the y-intercept of the line we need to find. We already know that the line passes through the point (2, −3). To determine the y-intercept of the line, substitute x = 2 and y = −3 into the slope-intercept form of the equation of the line. −3 = −(1/4)(2) + b b = −3 + 1/2 = −5/2 Therefore, the y-intercept of the line we need to find is −5/2. Step 4: Write the equation of the line in slope-intercept form. The equation of the line we need to find is y = mx + b where m = −1/4 and b = −5/2. y = −(1/4)x − 5/2 is the equation of the line that is parallel to y = −(1/4)x + 5 and passes through (2, −3).Answer: The equation of the line that is parallel to y = -(1/4)x + 5 and passes through (2, -3) is y = -(1/4)x - 5/2.

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The height of the mountain above sea level is 777.94 m.

The two engineers can calculate the height of the mountain by using the principle of trigonometry. Firstly, they must calculate the altitude of the mountain from the point A, which can be done by using the formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point A and d is the distance between point A and the mountain. In this case, the altitude from point A is h = tan(37°) * 1200 = 1645.58 m. Secondly, they can calculate the altitude from point B, which can be done by using the same formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point B and d is the distance between point B and the mountain. In this case, the altitude from point B is h = tan(45°) * 480 = 867.64 m. Finally, the height of the mountain above sea level can be calculated by subtracting the altitude from point B from the altitude from point A, i.e. h = 1645.58 m - 867.64 m = 777.94 m.

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Answer:

0.099, 0.18, 0.2, 0.698.

Step-by-step explanation:

The location at which a function is not differentiable is a Vertical tangent line

A function may not be differentiable at some points. Such points are known as non-differentiable points. Let's take a look at each of the given terms to figure out the non-differentiable points. Discontinuity: A discontinuity is when a function's graph is interrupted by a break or hole.

It occurs when a function is undefined at a certain point. It may be classified into three categories: removable, jump, and infinite. Functions may not be differentiable at removable discontinuities but are differentiable at jump and infinite discontinuities. A discontinuous point is not the same as a non-differentiable point because it may be differentiable at other points of the function.

Cusp: A cusp is a sharp corner formed by a curve. It happens when the slope of the function approaches infinity. The curve is not differentiable at the cusp. Horizontal Tangent Line: When the slope of a function approaches zero, it creates a horizontal tangent line. The function may or may not be differentiable at this point depending on the shape of the graph.

It may be differentiable or not differentiable. Therefore, it is not a non-differentiable point. Vertical Tangent Line: When a function's slope approaches infinity, it creates a vertical tangent line. The function is non-differentiable at this point. A vertical tangent line is always a non-differentiable point.

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The probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.

When sampling from either a small population without replacement, the hypergeometric distribution consists of a discrete probability distribution which determines the likelihood that an event occurs k times in n trials.

The given data:

Total market sample of rabbits = 100.

Randomly selected rabbits = 50.

Let the probability that the sample of 50 rabbits contains exactly 2 marked rabbits be P(E).

Then, using hypergeometric distribution;

P(E) = ⁵⁰C₂ / ¹⁰⁰C₂

Solve the probability using the combination.

P(E) = 25*49 / 50*49

P(E) = 25/50

P(E) = 1/2

Thus, the probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.

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Answer:

66.67%

Step-by-step explanation:

There are two ways to solve this problem depending on which way you like. Percentages are based on a 0-100 system and thus you can start by dividing 100/90. This will give you an amount of 1 family. We are looking for 60 families, so multiply that value by 60 to get how much of a percentage 60 families is.

The other way is to divide 90 by 60, and then multiply that result by 100 to give you a percent.

Regardless of your preferred method, both answers are the same.