What is the meaning of life?

Answer:

Step-by-step explanation:

tan is the same thing as sin/cos. therefore,

\(tan(-\frac{\pi}{2})=\frac{sin(-\frac{\pi}{2}) }{cos(-\frac{\pi}{2}) }\)

\(sin(-\frac{\pi}{2})=-1\) and \(cos(-\frac{\pi}{2})=0\) so

\(tan(-\frac{\pi}{2})=-\frac{1}{0}\) which is undefined. On the graph, this is represented by an asymptote. So your answer is true.

Answer:

Step-by-step explanation:

The answer is true!

Colin's new mean score, after getting 6 runs on Sunday, is approximately 20.09.

To calculate Colin's mean score, we need to sum up all his scores and divide by the number of scores.

a) Mean score:

16 + 11 + 25 + 27 + 11 + 25 + 20 + 26 + 29 + 35 = 215

Total scores: 10

Mean score = 215 / 10 = 21.5

Colin's mean score is 21.5.

b) To calculate his new mean score after getting 6 runs on Sunday, we need to add the new score to the previous total and divide by the new number of scores.

New total scores = 215 + 6 = 221

New number of scores = 10 + 1 = 11

New mean score = 221 / 11 = 20.09 (rounded to two decimal places)

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Answer:

Step-by-step explanation:

:)

Answer:

The answer is 6.75

Step-by-step explanation:

Answer:

The y-intercept of the link is -23.

Step-by-step explanation:

(attached)

answer

the last one unshaded from 75 moving towards 76

Step-by-step explanation:

it says h is greater than 75.5 so it should not be shaded ......sorry my keyboard dosent have those mathematical symbols

The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .

What is probability?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

A highway construction site's cycle time for trucks transporting concrete is evenly spread over the range of 50 to 70 minutes, thus a = 50 and
b = 70
f(x) = 1/[b - a] = 1/[70 - 50] = 1/20 = 0.05, thus a uniform distribution.
Let P(cycle time is less than 65 minutes if it is known that the cycle time exceeds 55 minutes) be:
P(60 < X < 65) = ₆₀∫⁶⁵ f(x) dx =  ₆₀∫⁶⁵ (0.05) dx = 0.05*[65 - 60] = 0.05*5
= 0.25
Thus, the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .

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The number line highlighted such that  all the numbers that can be values of x so |x| < 7 is attached accordingly.

A number line is a graphic depiction of numbers on a straight line in mathematics. A number line has numbers that are consecutively set at identical distances throughout its span. It may be stretched in any direction indefinitely and is commonly depicted horizontally.

Number lines are significant because they show numbers in context. Primarily because they allowed negative numbers to be expressed in a meaningful fashion.

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\(\huge \tt༆ Answer ༄\)

The respective terms used for the lines are ~

Step-by-step explanation:

a is tangent

b radius

c diameter

d chord

The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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Answer:

Given expression is \(\frac{1}{\text{cosec}A-1}-\frac{1}{\text{cosecA+1}}\) = 2tan²A

We have to prove this identity.

\(\frac{1}{\text{cosec}A-1}-\frac{1}{\text{cosecA+1}}=\frac{(\text{cosecA+1})-(\text{cosecA-1})}{(\text{cosecA-1})(\text{cosecA+1})}\)

                              = \(\frac{(\text{cosecA}-\text{cosecA})+(1+1)}{cosec^2A-1}\)

                              = \(\frac{2}{cosec^{2}A-1}\)

                              = \(\frac{2}{cot^{2}A}\) [From the identity, (cosec²A - 1) = cot²A]

                              = 2tan²A [From the identity, cotA = \(\frac{1}{\text{tan}A}\)]

Hence the given equation is proved.

Answer:

8/9

Step-by-step explanation:

The probability that the number chosen is a multiple of 9 is 1/9, so the probability that it isn't a multiple of 9 is 1 - (1/9) = 8/9

The percentage of all men between 66.5 inches and 71.5 inches is 99.99%

The mean of the heights of adult men in inches = 69

The standard deviation of the adult men in inches = 2.5

The percentage of all men between the heights of 66.5 inches and 71.5 inches can be calculated using the normal distribution.

P(66.5 < x < 71.5)

The standard form for these random samples using the formula,

Z = (X - μ) ÷ σ

where Z is the standard form

X is the random sample

μ is the mean

σ is the standard deviation.

For x = 66.5,

z =  (66.5 - 69) ÷ 2.5

= -2.5 ÷ 2.5

= -1

For x = 71.5,

z = (71.5 - 69) ÷ 2.5

= 2.5 ÷ 2.5

= 1

The standardized form of those random samples are

P(66.5 < x < 71.5) = P( -1 < z < 1)

which can be written as

= P(-1 < z < 0) + P(0 < z < 1)

By using the z-table we can find the value of z

P(-1 < z < 1) = 0.15866 + 0.8413

= 0.99996

Then, the percentage of heights between 66.5 and 71.5 is

= 0.99996 x 100

= 99.99 %

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Answer:

Step-by-step explanation:

Negative four is at least six less than a number

Sum of a negative two & nine times a number is less than seventy nine

Combined inequality:

Answer:

5w^3+8w^2-14w-5

Step-by-step explanation:

To find the indefinite integral of ∫(5/x - 5/(5√x)) dx, we will integrate each term separately. The indefinite integral of (5/x - 5/(5√x)) with respect to x, on the domain of positive real numbers, is given by 5 ln |x| - 2√x + C.

The integral of 5/x with respect to x is given by:

∫(5/x) dx = 5 ln |x| + C1,

where ln represents the natural logarithm and C1 is the constant of integration.

The integral of -5/(5√x) can be simplified as follows:

∫(-5/(5√x)) dx = -∫(1/√x) dx = -2√x + C2,

where C2 is the constant of integration.

Putting the results together, we have:

∫(5/x - 5/(5√x)) dx = 5 ln |x| - 2√x + C,

where C = C1 + C2 is the combined constant of integration.

Therefore, the indefinite integral of (5/x - 5/(5√x)) with respect to x, on the domain of positive real numbers, is given by 5 ln |x| - 2√x + C.

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\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=196\pi \end{cases}\implies \begin{array}{llll} 196\pi =4\pi r^2\implies \cfrac{196\pi }{4\pi }=r^2 \implies 49=r^2 \\\\\\ \sqrt{49}=r\implies 7=r~\hfill \underset{diameter}{\stackrel{2(7)}{14}} \end{array}\)

Answer:

x=111ft

Step-by-step

sin 24 = 45/x

+ the parallel lines

45 +x+24

x= 45/sin 24

The actual distance of your from the stage is 111 feet.

The angle formed by the line of sight and the horizontal plane for an object below the horizontal is called angle of depression.

The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.

According to the given question

We have

Angle of depression = 24degrees.

Let d be the actual distance of your from the stage.

Now in right angle triangle ABC

We have

AC = 45 feet

And, ∠ABC = 24 degrees

Now the Sine of an angle ∠ABC is given by

\(sin24 = \frac{AC}{AB}\)

⇒\(sin24=\frac{45}{d}\)

⇒ \(0.406=\frac{45}{d}\)

⇒ \(d =\frac{45}{0.406}\)

⇒\(d = 110.64 feet\) or \(111feet\)

Hence, the actual distance of your from the stage is 111 feet.

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Answer:

3

Step-by-step explanation:

If it took the mechanic 3 hours to diagnose the problem with Jackson's car, it would cost him $165. The situation does not represent a proportional relationship because the cost depends on the number of hours spent, which is not directly proportional to the initial fee.

7b. To calculate the cost if it took the mechanic 3 hours to diagnose the problem, we need to consider the initial fee of $60 and the additional cost per hour of $35.

  - The initial fee is $60.

  - The cost per hour is $35.

  - The number of hours spent by the mechanic is 3.

  To find the total cost, we multiply the number of hours by the cost per hour and add the initial fee:

  Total cost = (Number of hours * Cost per hour) + Initial fee

              = (3 * $35) + $60

              = $105 + $60

              = $165.

  Therefore, if it took the mechanic 3 hours to diagnose the problem, it would cost Jackson $165.

7c. This situation does not represent a proportional relationship because the cost does not vary directly with the number of hours. In a proportional relationship, the two variables would change at a constant rate or ratio. However, in this case, there is an initial fee of $60 regardless of the number of hours, and the additional cost is $35 per hour spent. The cost increases as the number of hours increases, but it is not directly proportional. If it were a proportional relationship, the cost per hour would remain constant. Here, the initial fee contributes a fixed amount to the total cost, while the hourly rate adds an additional variable component. Therefore, the situation does not exhibit a proportional relationship.

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Answer:

-4

Step-by-step explanation:

-4 is a negative integer

Answer:

F

(

x

)

=

x

2

−

7

x

+

C

Step-by-step explanation:

The value of function f (3) is -1.

Here,

The function is given as;

f (x) = 2x - 7

We have to find the value of f (3).

What is Function?

A function is defined as a relation between a set of inputs having one output each.

Now,

The function is given as;

f (x) = 2x - 7

To find the value of f (3), put x = 3 in the function, we get;

f (3) = 2 * 3 - 7

      = 6 - 7

      = -1

Hence, The value of function f (3) is -1.

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Based on the fact that Polygon R is a scaled copy of Polygon Q, the value of x can be found to be 8

The face that Polygon R is a scaled copy of polygon  Q means that you can find the value of x by first finding the scale factor that Polygon Q was reduced by to make Polygon R.

To find the scale factor, take the congruent sides of Polygon Q and R that are given, and divide the larger number by the smaller:

Polygon Q height = 14

Polygon R height = 7

Scale factor:

= 14 / 7

= 2

The value of x is therefore:

= Length of Q / scale factor

= 16 / 2

= 8

The length in Q was divided as Q is the larger polygon.

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Answer:

5

Step-by-step explanation:

The operation “x := x - 5” subtracts 5 from x. Begin with 25 and subtract 5 until it’s 8 or smaller. That’s 5 because 8 < 10 = 5+5 (the previous iteration) and 5 <= 8.

The coterminal angles in the given range is;

For angle

The regression equation for the given sample observations is Y = 12.071 - 1.087X.

By analyzing the given sample observations, we can determine the regression equation that represents the relationship between the variables X and Y.

The regression equation is derived through statistical analysis and allows us to estimate the value of Y based on the given values of X. In this case, the regression equation is Y = 12.071 - 1.087X.

This equation indicates that for every unit increase in X, the value of Y decreases by 1.087 units.

To determine the regression equation, statistical techniques such as linear regression are applied to find the best-fitting line that represents the relationship between the variables.

The coefficients in the equation, 12.071 and -1.087, represent the intercept and slope of the line, respectively.

They provide insights into the relationship and can be used to make predictions or analyze the impact of changes in X on the value of Y.

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Answer:

0.04

Step-by-step explanation:

The rate of flow is 0.043 gallons per minute.

Divide by 0.264 to obtain litres from gallons and multiply by 0.264 to obtain in gallons from litres.

According to the given question

Water flows through a pipe at a rate of 7 cubic meters per month.

We know 1 cubic meter is = 1000 litre

∴ 7 cubic meters per is

= (7 × 1000) litre

= 7000 litre

= (7000 × 0.264) gallons

= 1848 gallons per month

Now 1 month is

= ( 1 × 30 × 24 × 60 ) minutes.

=43200 minutes

So in 43200 minutes 1848 gallons of water flows through that pipe

∴ In a unit minute or per minute it the rate of flow will be

= 1848/43200 gallons per minute

= 0.043 gallons per minute.

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The slope of a plot of ln k versus 1/t equal to: −E_a/R

The Arrhenius equation is one that describes the relation between the rate of reaction and temperature for many physical and chemical reactions.

Arrhenius equation is expressed as:

k = \(Ae^{-E_{a}/RT }\)

Taking natural log on both sides,

ln k = ln \(Ae^{-E_{a}/RT }\)

In k = In A - E_a/RT

In k = In A - (E_a/R * (1/T))

This equation is in the form of y = mx + c

The plot of ln k vs 1/T gives a straight line with negative slope.

Slope = −E_a/R

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The correct option is (d) i.e. the correct notation of given series is ∑2n where n=1 is the lower notation and n=10 is the higher notation.

What is Series?

A series in mathematics has constant term differences. By multiplying the number of times the average of the final and first terms, we may determine the sum of the terms in an arithmetic series.

Given series : 2 + 4 + 6 + 8 + ... for 10 terms

Here, we can see that the first term is 2 and the difference btw the two terms is 2.

Similarly, the notation for lower limit is 1 and the notation for higher limit is 10 which is given.

We can write the given series as ∑2n.

When we put n=1, we get 2 which is the first term.

hence, verified too.

So, The notation of given series is ∑2n where n=1 is the lower notation and n=10 is the higher notation.

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The length of a rectangle is 14 meters when the width is 4 meters and the perimeter is 36 meters.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

We have been given that,

The formula P = 2L + 2W represents the perimeter of a rectangle.

To determine the length when the width is 4 meters and the perimeter is 36 meters.

The perimeter of a rectangle = 2(L+W)

Here W =  4 meters

⇒ 36 = 2L + 2(4)

⇒ 36 = 2L + 8

⇒ 2L = 28

⇒ L = 14

Therefore, the length of a rectangle is 14 meters.

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Answer: you start bye doing th

Step-by-step explanation:

Then you start too do