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Q6: Let 8 be an angle in standard position lying in QII. If cos 0 = -a, where a € [0,1), find sin 0 in terms of a. 1 1 Q7: Simplify the expression + 1 cosx 1+cosx Q8: Find the possible value(s) of x

Trey's rectangular prism will require more material to be constructed.

To determine which rectangular prism will require more material to construct, we need to calculate the surface area of each prism.

The surface area of a rectangular prism is given by the formula,

SA = 2×l×w + 2×l×h + 2×w×h

where l, w, and h are the length, width, and height of the prism, respectively.

For Trey's prism, the length is 12, the width is 7, and the height is 4. Therefore, the surface area of Trey's prism is:

SA of Trey = 2(12 x 7) + 2(12 x 4) + 2(7 x 4) = 336

For Matt's prism, the length is 10, the width is 6, and the height is 3. Therefore, the surface area of Matt's prism is,

SA of Matt = 2(10 x 6) + 2(10 x 3) + 2(6 x 3) = 192

Comparing the surface areas, we see that Trey's prism requires more material to construct since its surface area is larger than Matt's prism. Therefore, Trey's rectangular prism requires more material to construct than Matt's rectangular prism.

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Answer:

5

Step-by-step explanation:

180-108=72 interior + exterior angle add to 180

360/72=5

Answer:

Number of polygon sides = 360 / (180 - ONE INTERIOR ANGLE)

Number of polygon sides = 360 / (180 -108)

Number of polygon sides = 360 / 72

Number of polygon sides = 5

Source: http://www.1728.org/polygon.htm

Step-by-step explanation:

The economic and political circumstances that President Obama thinks might make terrorist groups attractive to many people in the world are the economic disparity between the rich and the poor, the political instability in many regions of the world, and dissatisfaction with the current political circumstances.

According to President Obama, there are several economic and political circumstances that might make terrorist groups attractive to many people in the world. The first circumstance is the economic disparity between the rich and the poor. Many people who are attracted to terrorist groups come from poor and underdeveloped countries where there is a lack of economic opportunities. These individuals may be drawn to terrorist groups because they see it as a way to achieve financial stability and gain power.

Another circumstance is the political instability in many regions of the world. Many terrorist groups take advantage of the instability and lack of government control in certain areas to gain support and recruit new members. Additionally, many people who are dissatisfied with their current political circumstances may be drawn to terrorist groups because they believe it is a way to bring about change and fight against perceived injustices.

Overall, the economic and political circumstances that President Obama believes might make terrorist groups attractive to many people in the world are the economic disparity between the rich and the poor, political instability, and dissatisfaction with the current political circumstances.

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Using mathematical operations, the quantity of YumYum cupcakes required by my siblings and 1, with each wanting 7 halves of it, is 14 cupcakes.

The total quantity of cupcakes required by the 4 siblings can be determined using the mathematical operations of division and multiplication.

Division operation consists of the dividend, the divisor, and the quotient while multiplication involves the multiplier, the multiplicand, and the product.

The number of siblings = 4

The quantity of YumYum cupcakes required by each = 7 halves

7 halves = 3.5 (7 ÷ 2)

Thus, since each sibling requires 3.5 cupcakes, using mathematical operations, the total quantity = 14 cupcakes (3.5 x 4)

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What is the total quantity of YumYum cupcakes required?

If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.

Determining the Value of PT

It is given that,

T is the midpoint of PQ ........ (1)

PT=3x+3 ......... (2)

TQ=7x-9 .......... (3)

From (1), the distance from P to T and the distance from T to Q will be equal.

⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]

Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,

3x + 3 = 7x - 9

or 7x - 9 = 3x + 3

or 7x - 3x = 9 + 3

or 4x = 12

or x = 12/4

⇒ x = 3

Substitute this obtained value of x in equation (2)

PT = 3(3) + 3

PT = 9 + 3

PT = 12 units

Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.

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Answer: should be the last answer! to the right.

Step-by-step explanation:

You have 30 coins and the d are dimes and q are quarters

Answer: ≈ 572.55526

Step-by-step explanation:

A = πr2 = π(13.52) ≈ 572.55526

The area of the tire is 572.27 sq meters having a radius of 27 inches.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

If the diameter of the circle is 27 meters then the radius of the circle is

(27/2) = 13.5 meters.

So, the area of a tire with a radius of 13.5 meters is,

= π(13.5)² sq meters.

= 3.14×182.25 sq meters.

= 572.27 sq meters.

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answer:

\({ \tt{ \cos(100x) + \frac{4}{3} = 0}} \\ { \tt{ \cos(100x) = - \frac{4}{3} }} \\ { \tt{100x = { \cos }^{ - 1} ( - \frac{4}{3} )}} \\ { \tt{invalid \: answer}}\)

Answer:

3

Step-by-step explanation:

Midpoint means EF and FG are both 8 the whole thing is 19 so 19 - 16 = 3

Answer:

C

24Step-by-step explanation:

Trust me on this one.

Answer:

15 to 20 minutes

Step-by-step explanation:

Answer:

10-15

Step-by-step explanation:

i took the test

Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;

60° + 70° + y = 180°

130° + y = 180°

y = 180° - 130°

y = 50°

Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.

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Answer: \(4^0\)

Step-by-step explanation:

\(4^5*4^-^7/4^-^2\)

Rewriting this;

\(\frac{4^5*4^-^7}{4^-^2}\)

When you multiply by the same base, you add exponents.

\(\frac{4^5^+^(^-^7^)}{4^-^2}\)

\(\frac{4^5^-^7}{4^-^2}\)

\(\frac{4^-^2}{4^-^2}\)

When you divide by the same base, you subtract exponents.

\(4^-^2^-^(^-^2^)\)

\(4^-^2^+^2\\4^0\)

Answer:

No

Step-by-step explanation:

A parallelogram has opposite angels equal and opposite sides equal. in this case, only a single pair of angels are equal.

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE

As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.

So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.

Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.

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The complete question is given below:

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:

"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."

When a fair die is rolled once, the events A and B are:

A = {2, 4, 6} (the event of rolling an even number)

B = {1, 3, 5} (the event of rolling an odd number)

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.

The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if we roll a fair six-sided die, the probability of rolling a 3 is 1/6, because there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

When a fair die is rolled once, there are six possible outcomes: 1, 2, 3, 4, 5, or 6.

The event A of rolling an even number consists of the outcomes 2, 4, and 6. Therefore, we can represent A as:

A = {2, 4, 6}

The event B of rolling an odd number consists of the outcomes 1, 3, and 5. Therefore, we can represent B as:

B = {1, 3, 5}

Note that these events are mutually exclusive, which means that they have no outcomes in common. Specifically, an event cannot be both even and odd at the same time. Therefore, we can say that:

A and B are mutually exclusive events such that A ∩ B = ∅

In summary, when a fair die is rolled once, the events A and B are:

A = {2, 4, 6} (the event of rolling an even number)

B = {1, 3, 5} (the event of rolling an odd number)

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Answer:

6647.6 liters

Step-by-step explanation:

The volume of a cylinder with end area r and length (or height) h is

V = πr²h

If we substitute 2.3 m for r and 400 m for h, we get:

V = π(2.3 m)²(400 m) = 6647.6 m³ or 6647.6 liters

Explanation (100 words): To find the linearization, we need to use the formula for linear approximation:L(x) = f(a) + f'(a)(x - aFirst, we find f(a) by substituting a = 0 into the given function:


The linearization of y = (81 + 2x^2)^(-1/2) at a = 0 is L(x) = 1 - x^2/81.

Explanation (100 words): To find the linearization, we need to use the formula for linear approximation:L(x) = f(a) + f'(a)(x - aFirst, we find f(a) by substituting a = 0 into the given function:

f(0) = (81 + 2(0)^2)^(-1/2) = 81^(-1/2) = 1/9

.Next, we find f'(x) by differentiating the given function with respect to x:f'(x) = d/dx [(81 + 2x^2)^(-1/2)] = (-1/2)(81 + 2x^2)^(-3/2)(4x) = -4x/(2√(81 + 2x^2)) = -2x/(√(81 + 2x^2)).Now, we substitute a = 0 and simplify to get the linearization:

L(x) = f(0) + f'(0)(x - 0) = 1/9 + (-2(0))/(√(81 + 2(0)^2)) = 1/9 - 0 = 1/9.

Therefore, the linearization of y = (81 + 2x^2)^(-1/2) at a = 0 is L(x) = 1 - x^2/81.

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The Cp (Process Capability Index) for the process is 1.4.

To calculate the Cp (Process Capability Index) for a process, we need to compare the process spread with the specification limits. Cp is defined as the ratio of the tolerance width to the process spread.

Cp = (Upper Specification Limit - Lower Specification Limit) / (6 * Standard Deviation)

Given that the process has a CpK (Process Capability Index on the Upper Side) of 2.4 and a CpK on the Lower Side of 1.4, we can use the relationship between Cp and CpK to find the Cp value.

Cp = min(CpK Upper, CpK Lower)

Cp = min(2.4, 1.4)

Therefore, the Cp for this process would be 1.4.

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Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

The mass of 133Xe is calculated by dividing the decay rate (15.3 exa Becquerels) by the decay constant (0.0000015309 s^-1) and multiplying by the molar mass of xenon (133 g/mol).

To calculate the mass of 133Xe, we need to use the formula: Mass = Decay rate / Decay constant.

The decay rate is given as 15.3 exa Becquerels, and the decay constant is given as 0.0000015309 s^-1.

We can convert the decay rate to Becquerels by multiplying it by 10^18.

Dividing the decay rate by the decay constant gives us the number of seconds it takes for one disintegration event.

To convert this to mass, we need to know the molar mass of xenon, which is 133 g/mol. Multiplying the number of disintegration events per second by the molar mass gives us the mass of 133Xe in grams.

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The correct answer is Option 2.

The result of applying the square root property of equality to this equation is,

⇒ x + b/2a = ± √b² - 4ac / 2a

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ (x + b/2a)² = (b² - 4ac) / 4a²

Now, We can take the square root property of equality to this equation as,

⇒ (x + b/2a)² = (b² - 4ac) / 4a²

⇒√ (x + b/2a)² = √ (b² - 4ac) / 4a²

⇒ x + b/2a = ± √(b² - 4ac) / 2a

Thus, The result of applying the square root property of equality to this equation is,

⇒ x + b/2a = ± √b² - 4ac / 2a

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Answer:

\(36.77150\), or 37 (rounded)

Step-by-step explanation:

1. \(\sqrt{97} = 9.84885\)

2. \(9.84885\) + \(8.169178744\) = \(18.01803\)

3. \(\frac{18.01803}{0.49}\)

4. = \(36.77150\)

You can simplify 36.77150 to 37

... Hope this helped! Have a wonderful New Year!

The value of the equation is A = 36.77

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = ( √97 + 2.014³ ) / 0.49   be equation (1)

On simplifying the equation , we get

√97 = 9.8488578

2.014³ = 8.169178744

Substituting the values in the equation , we get

A = ( 9.8488578 + 8.169178744 ) / 0.49

A = 18.018036544 / 0.49

A = 36.77150

Therefore , the value of A is 36.77

Hence , the equation is A = 36.77

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Answer:

(6,7,8,8,9,11)

Step-by-step explanation:

Hopefully this helps:)

Answer:

2006-6, 2005-7, 2004-8, 2002-8, 2003-9, 2001-11

91 divided by 7 is 13 so k is 13

Step-by-step explanation:

Answer:

x 13      y 84

Step-by-step explanation:

a) To find an expression for a2k in the power series p(x) = 1 + ª₂x² + ª₁x²¹ +ª₆x⁶ + ···, where the coefficients a2k are positive, and p"(x) = p(x) for all x in the interval [0, 1], we can differentiate p(x) twice and equate it to p(x). Solving the resulting differential equation, we find a2k = (2k)! / (k!(k+1)!).

b) The function fn(x) is defined as fn(x) = 1 + ayn + aytan(πxn), where a, y, and n are constants. We need to show that the sequence {fn} converges with respect to the maximum norm in the space C([0, 1]). Using the properties of trigonometric functions and analyzing the convergence of f(1), we can establish the convergence of fn(x) in the given interval.

a) To find the expression for a2k, we differentiate p(x) twice to obtain p''(x) = 2ª₂ + 21ª₁x²⁰ + 6ª₆x⁵ + ···. Since p"(x) = p(x), we can equate the terms with the same powers of x. This leads to the equation 2ª₂ = ª₂, 21ª₁ = ª₁, and 6ª₆ = ª₆. Solving these equations, we find a2k = (2k)! / (k!(k+1)!), which gives the expression for a2k valid for every k in N.

b) The function fn(x) = 1 + ayn + aytan(πxn) is defined with constants a, y, and n. We need to show that the sequence {fn} converges in the space C([0, 1]) with respect to the maximum norm. By analyzing the properties of trigonometric functions and evaluating the limit of f(1) as n approaches infinity, we can demonstrate the convergence of fn(x) in the interval [0, 1].

The details of evaluating the convergence and providing a rigorous proof of convergence with respect to the maximum norm in C([0, 1]) would require further calculations and analysis, including the limit of f(1) as n tends to infinity.

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The minimum possible area of each cardboard piece = 72.25 in²

The equation for a circle in standard form is (x - x1)2 + (y - y1)2 = r2, where (x, y) is an arbitrary point on the circle's circumference, r is the circle's radius, and (x1, y1) is the circle's center.

The equation of the circle can be expressed in standard form as

(x - h)² + (y - k)² = r²

The circle's radius (r) and center (h,k) are shown here.

Drink coasters in the shape of circles are produced by a corporation. the following calculation can be used to determine a roller coaster's size:

x² + y² = 18.06

Inches are used as the unit of measurement. This equation can be expressed as,

x² + y² = (280/16)

x² + y² = (17/4)²

If we compare it to the circle's equation, we obtain,

h=0

k=0

r=17/4 inch

The circular coaster's radius is 17/4. Its diameter is,

D = 2 x (17/4)

D = 17/2

Each coaster is now cut from a square piece of cardboard. The square cardboard piece's side will be equal to the diameter of the circular coaster.

a=d=17/2 inch

The square of the square's side is the area of the square. The area of a square piece of cardboard is therefore,

A=a^2

A=(17/2)^2

A=75.25inch^2

The minimum possible area of each cardboard piece = 72.25 in²

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