If A + B + C = π, express cos (A + B) in terms of angle C.​

Answer:

150.72

Step-by-step explanation:

area of a cylinder = top circle + bottom circle + lateral

lateral = perimeter of the circle * height = 2π*2 * 10 =40π

area of a circle = πr² = 4π

top & bottom =8π

total = 40π+8π =48π = 150.72

The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is [tex]$$150.8 \mathrm{~cm}^2$$[/tex].

The sum of the areas of all the faces or surfaces that surround a solid results in its total surface area. The tops and bottoms (bases) as well as the remaining surfaces make up the faces. The surface area of a solid without its bases is known as its lateral surface area.

The area of the cylinder is determined by adding the areas of the curving surface and its two circular bases.

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

Total surface area [tex]$S=2 \pi r h+2 \pi r^2$[/tex]

Substitute the values in the above equation, we get

[tex]$$\Rightarrow \mathrm{S}=2 \pi \mathrm{r}(\mathrm{r}+\mathrm{h})=2 \times 3.1416 \times 2 \times 12$$[/tex]

simplifying the equation, we get

[tex]$$\Rightarrow \mathrm{S}=150.8 \mathrm{~cm}^2$$[/tex]

[tex]$\Rightarrow \mathrm{S} \approx 1.51 \times 10^4 \mathrm{~mm}^2$$[/tex]

Therefore, the surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is [tex]$$\mathrm{S}=150.8 \mathrm{~cm}^2$$[/tex].

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Answer:

Step-by-step explanation: north-south and east-west lines are perpendicular

2.50 is the coupon amount and 0.08 is the cost for one copy from the equation y = 0.08x - 2.50.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

y = 0.08x - 2.50

Where x is the number of copies and y is the cost of printing x copies.

Now,

From the equation,

y = 0.08x - 2.50

2.50 is the coupon amount.

0.08 is the cost for one copy.

Thus,

2.50 is the coupon amount.

0.08 is the cost for one copy.

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The rationalization of the given surd gives the answer as √2/3

Rationalization is a process that finds application in elementary algebra, where it is used to eliminate the irrational number in the denominator.

Given here:  The surd 2/√18

Thus rationalizing we get as follows:

2/√18

=2×√18/√18×√18  ( multiplying both numerator and denominator by √18)

=2√18/√18² ( since 18²ˣ¹/₂=18)

=2√18/18

=2√3²×2 / 18  ( ∵ 18=3²×2)

=2×3×√2/18

=(6/18) × √2

=(1/3)×√2

=√2/3

Hence, The rationalization of the given surd gives the answer as √2/3

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The true statement about the solution to the system is (e) none of the above

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

Solving a linear system

You get a final statement of 5 = 0

This equation is false

This is so because 0 and 5 do not have the same value

This statement creates a contradiction, which means that there is no solution to the linear system.

This means that the sytsem of equation has no solution and the solution to the system does not exist

Hence, the system has no solution

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Histograms are a waste of time and provide no meaningful information about process variation are true statement

A machine should be calibrated closer to the lower spec limit than the upper spec limit if the cost of fixing output that is too high is greater than the cost of fixing output that is too low.

If the cost of fixing output that is too high is greater than the cost of fixing output that is too low then it make sense to calibrate the machine closer to the lower spec limit.

This way if the machine produces less output than is required, it can be fixed at a lower cost than if the machine had been set to the upper spec and produces output that is too high.

Histograms are a waste of time and provide no meaningful information about process variation

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21 + 25 = 46

21 + 12 = 33

46 + 33 = 79

therefore the answer is 79

Step-by-step explanation: thank you for listening

Answer:

We can't solve this problem if there is no context given. Since nothing is mentioned, it is safe to assume that PR and QR are line segments. Based on the nomenclature, it may be a collinear system of 3 points: P, Q and R. The equation should be:

PR = PQ + QR

Assume x is referred to line PQ

(9x - 31) = x + 43

9x - x = 43 + 31 = 74

8x = 74

x = 9.25

Answer:

5x - 4y = -20

y = x + 5

y = -x + 5

Step-by-step explanation:

The formula for slope-intercept form is y = mx + b, with b being the y-int.

If the equation does not have an x, y, or b, it is not a slope-intercept form.

5x - 4y = -20 (can be rearranged to y = 5/4x + 5)

y = 1, x = 5/4, b = 5

y = x + 5y

x = 1, y = 1, b = 5

y = -x + 5

x = -1, y = 1, b = 5.

Other answer choices does not have all three variables.

The probability that more heads are tossed using coin A than using coin B is [tex]$\frac{7}{8}$[/tex].

This is because there are 8 possible outcomes when both coins are tossed: (H, H), (H, T), (T, H), (T, T) for both coins A and B.

Out of these 8 possible outcomes, 7 of them have more heads from coin A than from coin B, so the probability is [tex]\frac{7}{8}[/tex].

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen. Probability is used to measure the likelihood of uncertain events, such as the outcome of a coin flip or the result of a dice roll.

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Answer:

7×(3+x)=21+7x or 7x+21

Step-by-step explanation: Simply multiply 7 by 3 and then 7 by x.

Answer:

t = 4 years

Step-by-step explanation:

Simple Interest = Prt where r = rate in decimal, t = time in years, P = principal

r = 5/100 = 0.05

Plugging in knowns
120 = 600 x 0.05 x t

120 = 30t

30t = 120

t = 120/30

t= 4 years

Answer: - $83.88

Step-by-step explanation:

$66.11 - $99.01 + $1.20 - $35.92 - $68.67+ $52.41 = $83.88

The 15th element of the geometric sequence generated by exponential function y = 200 · (- 1 / 2)ⁿ⁻¹ is 25 / 2048.

In this question we find the case of geometric sequence, that is, a set of values generated by a exponential function, whose definition is shown below:

y = a · rⁿ⁻¹, n ≥ 1

Where:

If we know that y₄ = - 25 and y₉ = 25 / 32, then the expression that generates the geometric sequence is:

- 25 = a · r³

25 / 32 = a · r⁸

- 1 / 32 = r⁵

r = - 1 / 2

a = - 25 / r³

a = - 25 / (- 1 / 2)³

a = - 25 / (- 1 / 8)

a = 200

y = 200 · (- 1 / 2)ⁿ⁻¹

And the 15-th term of the geometric series is:

y = 200 · (- 1 / 2)¹⁴

y = 25 / 2048

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Answer:

the answer to this question is 2.25

The difference is quite small, the effect was statistically significant. the explanation is that the sample size is very large.

As per the given data:

An engineer designs an improved light bulb.

The previous design had an average lifetime of 1200 hours.

The new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs.

Let us assume the null and alternative hypothesis

Null: The average lifespan of old and new designs is the same.

Alternative: The lifespans of new and ancient designs differ.

Because of the huge sample size, the p-value is lower. Reject the null hypothesis as a result, and the effect is now considered statistically significant.

Although the difference between 1200 hours and 1201 hours is quite tiny, the effect was statistically significant because of the high sample size.

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An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The new bulb has a lifetime of 1201 hours, using a sample of 2000 bulbs. Although the difference is quite small, the effect is statistically significant. The explanation is:

(a) that new designs typically have more variability than standard designs.

(b) that the sample size is very large.

(c) that the mean of 1200 is large.

(d) all of the above.

Your roommate shook 10 hands at the party you and your roommate hosted.

If each person at the party shakes hands with a different number of people, and each person did not shake hands with their own roommate, then the number of hands each person shakes will form a set of integers from 0 to 19, with no duplicates. Since there are 20 people at the party, the sum of the numbers from 0 to 19 is 20 * 19 / 2 = 190.

If we subtract the number of hands that each person shakes from this sum, we find that the number of hands that my roommate shook is equal to 190 - (0 + 1 + 2 + ... + 19) = 190 - (0 + 19) * 20 / 2 = 190 - 20 * (19 / 2) = 190 - 20 * 9.5 = 190 - 190 = 0. This is not possible, since each person must shake at least one hand. The only possible answer is 10, which satisfies the conditions.

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Answer:

A) 15:30

B) 8 km

Step-by-step explanation:

a) At 15:30, Bethan's journey line intersects the y-axis, indicating her arrival at home from school.

b) Siobhan's journey line starts and ends at 2 km on the x-axis, which represents the distance from her home. Therefore, Siobhan travels a total of 4 km to school and 4 km back, so she travels a total distance of 8 km each day.

For the given asymptotes, y - intercept = not defined and horizontal asymptote at y = 2.

[tex]F(x)=1/x+2[/tex] by x and simplify

[tex]F= \frac{1+2x}{x}[/tex]

Apply the limit x or x – to locate the horizontal asymptotes.

Apply the limit y or y – to determine the vertical asymptotes.

Divide the numerator by the denominator to determine the slant asymptote (if any).

Each point on a vertical line has the same x-coordinate. The line equation is x=c if two points share the same x-coordinate. The x-intercept of a vertical line x=c is the point (c,0). Except for the line x=0, vertical lines don't have a y -intercept.

By evaluating the function when the input variable, x, is 0, which is always equal to the constant b, the vertical intercept (y-intercept) can be found. There is a chance.

[tex]F= \frac{1+2x}{x}[/tex]

We can find y - intercept by setting x = 0,

⇒ y - intercept = not defined

horizontal asymptote at y = 2

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The eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) is -1.

The eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) can be calculated by using the formula:

λ = 1/sinθ (d/dθ cosθ)

This formula states that the eigenvalue is equal to the inverse of the sine of θ multiplied by the derivative of the eigenfunction cosθ with respect to θ.

To calculate the eigenvalue, we first take the derivative of the eigenfunction cosθ with respect to θ, which is -sinθ. Then, we multiply this value by the inverse of the sine of θ. This gives us an eigenvalue of -1.

In summary, the eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) is -1. This can be calculated by taking the derivative of the eigenfunction and multiplying it by the inverse of the sine of θ.

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The value of the consecutive interior angles formed by the parallel lines is : ∠CGF = 61°

For the stated question:

∠HGD = ∠CGF = 119° (vertically opposite angles)

And,

∠AFG + ∠CGF = 180° (consecutive interior angles)

∠CGF = 180° - 119°

∠CGF = 61°

Thus, the value of the consecutive interior angles formed by the parallel lines is : ∠CGF = 61°

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The smallest number of cars that can tailgate in a straight line at a football game is 12.

This can be determined by using a logic puzzle approach. If one car is in front of four cars, that's 5 cars in total. If one car is behind four cars, that's also 5 cars. And if three cars are between two cars, that's 5 sets of two cars, or 10 cars. The total number of cars is 5 + 5 + 10 = 20.

This logic puzzle approach is not applicable for all problems. It depends on the specific problem and the information provided. For certain types of problems, a different approach or method may be more appropriate. The key is to understand the problem, determine the necessary information, and select the best approach to solve it.

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Answer:



Step-by-step explanation:

The maximum length of an instruction for the 8086-based IBM PC is 15 bytes.

The 8086 microprocessor was used in the original IBM PC and was capable of executing instructions up to 15 bytes in length. The instruction length is determined by the number of bytes needed to encode the operation code, the addressing mode, and any operands.

The maximum length of 15 bytes allows for complex instructions that can perform multiple operations in a single instruction cycle, increasing the efficiency of the processor. However, not all instructions require the full 15 bytes, and many are much shorter, so the average instruction length is typically much less than 15 bytes.

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Assuming neither item has changed in price, the cost of a book is $13.

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

Firstly, you should convert the text of the problem into equations, thus you can write:

11b+8m=207 (1)

16b+9m=280 (2)

where: b=book and m= movie

From the substitution method, you can solve this question following the steps below:

The equation 1, you can re-write as: b=(207-8m)/11. This relation, you can apply in equation2. See below.

16b+9m=280

[tex]{16*\frac{(207-8m)}{11} }+ 9m=280 \\ \\ \frac{3312-128m}{11} + \frac{99m}{11} =\frac{3080}{11} \\ \\ 3312-128m+99m=3080\\ \\ -29m= -232\\ \\ m=8[/tex]

If m=8, you can find the value of the cost of a book from the relation (207-8m)/11. Then,

[tex]b=\frac{(207-8m)}{11}=\frac{207-8*8}{11} =\frac{207-64}{11} \\ \\b=\frac{143}{11} =13[/tex]

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If two hundred fifty people were surveyed to determine their favorite mode of transportation. The  number of people that chose walking is 35?

A survey is a research method used to collect information from a sample of individuals about their opinions, beliefs, behaviors, or other characteristics.

The purpose of a survey is to gather data to help understand a specific population or topic, and the results of a survey can be used to make decisions, inform policy, or guide further research.

From the question (image attached)

14 people - Walking

Total surveyed  =250

Therefore: 14/100 * 250

= 35

Hence 35 people were walking.

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The value of the given limit (at x =1) f(x)=18.

An output value that a function approaches for the specified input values is referred to as a limit. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. It is employed in the analysis process and constantly considers how the function will behave at a specific point.

A function may approach two different limits. One where the variable approaches its limit through values larger than the limit and the other where the variable approaches its limit through values smaller than the limit. In such a case, the limit is not defined but the right and left-hand limits exist.

we have given that,

[tex]lim_(x- > 1) f(x)-7x-1=10[/tex]

and find out the limit (x=1)f(x).

[tex]\lim_{x \to \1} f(x)-7x-1=10\\\\f(1)-7-1=10\\\\f(1)=10+8=18\\\\now \ the \ \lim_{x \to 1} f(x)\\f(1)=18.[/tex]

Hence, the value of limit x tends to 1 f(x)= 18.

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Based on the addition property of equality, from the equation x=12, we can generate the following equations and solutions:

The addition property of equality states that you can add the same value to both sides of an equation and still maintain an equivalent equation.

It states that if two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.

If x = 12, using the addition property of equality, the following equations can be generated.

x+3 = 15 (12+3)

x+7 = 19 (12+7)

x+3 = 32 (12+20)

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