The air temperature of a mountain drops by 2 ℃ for every 500 m of elevation. If the air temperature is 26 ℃ at the base of the mountain, at what elevation will the air temperature be 16 ℃ ?

We can use the power rule to find the derivative of f(x) = x^n + x^(n-1). The power rule states that the derivative of x^n is nx^(n-1).

So, the derivative of x^n is nx^(n-1)

And the derivative of x^(n-1) is (n-1)x^(n-2)

So the derivative of f(x) = x^n + x^(n-1) is:

f'(x) = nx^(n-1) + (n-1)x^(n-2)

Now, if we combine the exponents we have :

f'(x) = nx^n-1 + nx^n-2

And we can factor out x^n-2 from the second term, we have:

f'(x) = nx^n-1 + (n-1)x^n-2*x^2

Now, we can simplify the expression by canceling the x^n-2 factor.

f'(x) = nx^n-1 + (n-1)x

And finally, by simplifying the exponent and factoring the constants, we have:

f'(x) = (nx + n - 1) / x^(2-n)

So the derivative of f(x) = x^n + x^(n-1) is f'(x) = (nx + n - 1) / x^(2-n)

Answer: 1

Step-by-step explanation:

Explanation and steps in photo

The value that the probability of correctly classifying a type an insect equals the probability of correctly classifying a type b insect is 4.5 millimeters.

To find the value that the probability of correctly classifying a type A insect equals the probability of correctly classifying a type B insect, we need to find the point where the probability density functions of the two types of insects intersect.

For type A insects, the probability density function is given as -

f(x) = [tex](1/2)e^{-{x-3}^{2/2}}[/tex]

For type B insects, the probability density function is given as-

f(x) = [tex](1/4)e^{-{x-5}^{2/2}}[/tex]

We can set these two probability density functions equal to each other and solve for x as follows -

[tex](1/2)e^{-{x-3}^{2/2}}[/tex] =  [tex](1/4)e^{-{x-5}^{2/2}}[/tex]

Solving for x, we get:

x = 4.5

So the value that the probability of correctly classifying a type A insect equals the probability of correctly classifying a type B insect and is 4.5 millimeters. This means that if the length of the insect is 4.5 millimeters or less, it will be classified as type A, and if it is greater than 4.5 millimeters, it will be classified as type B.

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Answer: Given a line represented by the equation 3x + y = 9, the slope of the line is -3/1. Since we know that the slope of the line perpendicular to this line is the negative reciprocal of the original line's slope, we can find the slope of the perpendicular line by taking -1/-3 = 1/3.

To find the equation of the perpendicular line that passes through the point (1,-2), we can use the point-slope form of the line equation, which is: y - y1 = m(x - x1) where m is the slope of the line and (x1,y1) is a point on the line.

Therefore, the equation of the perpendicular line that passes through the point (1,-2) is:

y - (-2) = (1/3)(x - 1)

y + 2 = (1/3)x + (1/3)

y = (1/3)x - (2/3)

So the final equation of the perpendicular line is y = (1/3)x - (2/3)

Step-by-step explanation:

Assuming the horizontal lines are parallel, we will see that the measure of angle 4 is m∠4 = 39°

First, we assume that the two horizontal lines are parallel, that will mean that the measures of angle 4 and 7 are equal, beacause both of them are on the same quadrant.

Also, notice that angle 7 and 141° should add up to 180° (a plane angle) thus, we will get:

m∠7 + 141° = 180°

m∠7 = 180° - 141°

m∠7 = 39°

The measure of angle 4 is also that, so we conclude that:

m∠4 = 39°

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The type of transformation and scale factor as required are;

16) Rotation

17) Reflection

18) Dilation

19) n = 5

20)P = r = 4

There are different types of transformation as follows;

1) Translation: This type of translation is defined as moving the object in space by keeping its size, shape or orientation constant. In a translation, each point of the shape must be moved in the same direction and for the same distance

2) Dilation: This type of translation expands or contracts the object by keeping its orientation or shape the same. This is also known as resizing.

3) Rotation: This type of transformation has an object about a fixed point without changing its size or shape.

4) Reflection: This type of translation is called reflection because it flips the object across a line by keeping its shape or size constant.

16) This transformation is rotation based on the definitions above.

17) This type of transformation is a reflection as it is like the image was flipped across a line more like a mirror image.

18) This called dilation as the scale factor was adjusted to produce the new image.

19) Scale Factor = 6/3 = 2

Thus;

n = 10/2 = 5

20) Scale factor = 12/9 = 4/3

Thus;

P = r = 3 * 4/3

= 4

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(a) The missing value of y is 8

(b) The missing value of x is 144

Now, According to the question:

The ration table is:

X      Y

2      ?

4     16

5     20

?      36

We have to find the value of y

Now, According to the table :

The value of x is 2

So, value of y will be 8

x/y = 2/8 = 1/4

Next, x/y = 4/16 = 1/4

=> 5/20 = 1/4

Similarly, we are multiplying the first column by 1/4 to get the second column, we can set up the following equation for x.

1/4x = 36

x = 144

Hence,  the missing value of y is 8

(b) The missing value of x is 144.

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Both triangles are similar using angle-angle-angle similarity theorem and the similarity ratio is 2

Two figures are similar if they have the same shape and ratio of their corresponding sides are proportional.

Two triangles are similar if they have the same shape, all the three angles are congruent and the ratio of their corresponding sides are proportional.

Triangle TUV and triangle FGH are given.

∠U = ∠G = 54° (given)

∠T = ∠F = 50° (given)

∠V = ∠H = 76° (given)

Since all three angles of both triangles are equal, therefore both triangles are similar using angle-angle-angle similarity theorem

Similarity ratio = GF / UT = 26/13 = 2

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Answer:

g(- 1) = - 4

Step-by-step explanation:

g(- 1) means what is the value y when x = - 1

Locate - 1 on the x- axis, go vertically down to meet the line at (- 1, - 4 ) , so

when x = - 1 then y = - 4 , that is

g(- 1) = - 4

Answer:

[tex]g(x)=-4[/tex]

Step-by-step explanation:

1. Find the slope-intercept form of the equation

So to first solve this equation you need to find the slope of the line to find the slope you do [tex]\frac{rise}{run}[/tex] which means you count the number of boxes the line moves up or down which is 2 so that is the "rise" part of our equation. To find the run you find how much the equation moves left or right which is one. So the slope would be [tex]\frac{2}{1} x[/tex] or [tex]2x\\[/tex]. To find the y-intercept you look at where the line hits the y-axis which is at -2. So now you have your equation in a slope-intercept form which is [tex]g(x)=2x-2[/tex]

2. Find g(-1)

So... The slope-intercept form of the equation is [tex]g(x)=2x-2[/tex] that you replace the x in the g(x) with -1 so now you replace the x in the slope-intercept equation with -1. Then simplify!

[tex]g(-1)=2(-1)-2[/tex]

[tex]g(-1)= -2-2[/tex]

[tex]g(-1)=-4[/tex]

Answer:

see attached.

Step-by-step explanation:

The minimum value of the third side is 9 cm, and The maximum value of the third side is 6.7 cm.

The minimum value of the third side is when the triangle is a degenerate triangle, meaning that the third side is a line segment joining the two endpoints of the first two sides, which is equal to 3 cm + 6 cm = 9 cm.

The maximum value of the third side is when the triangle is a right triangle, and the two sides are the legs. According to the Pythagorean theorem, the third side (the hypotenuse) should be equal to the square root of 3² + 6² = 9 + 36 = 45, which is equal to 6.7 cm.

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--The given question is incorrect; the correct question is

"The length of two sides of a triangle are 3cm and 6cm. What could be the minimum and maximum value of its third side?"--

Approximately 99.7% falls within three standard deviations.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

Since the mean score is 50 and the standard deviation is 10, this means that approximately 68% of the students scored between 40 and 60, approximately 95% scored between 30 and 70, and approximately 99.7% scored between 20 and 80. Therefore, approximately 32% of students scored above 60.

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The trigonometric function can be used to calculate the distance (4124966.128 AU) between the star and also the sun.

d = 4124966.128

Given:

Step 1: To calculate the distance in astronomical units here between star and the Sun, apply the trigonometric function.

The sine function is used to calculate the distance in step two.

sin Ф = P/ H

where H is the hypotenuse and P is the perpendicular.

Step 3: Replace the above expression with the known terms.

sin (0.00001389 ) = 1/d

Step 4: Condense the previous expression.

d = 4124966.128

Thus, the distance of star from the sun is found as d = 4124966.128.

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The numeric value of the expression 36x + 42y - 18x + 6 when x = 0.25 and y = -1 is given as follows:

-31.5.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The expression in this problem is given as follows:

36x + 42y - 18x + 6.

We want to find the numeric value at:

x = 0.25 and y = -1.

Hence:

Then the numeric value is given as follows:

36(0.25) + 42(-1) - 18(0.25) + 6 = -31.5.

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“Although part of your  question is missing, you might be referring to this full  question: In the given triangle with base length =[tex]8\sqrt{3}[/tex] and angles at  vertices are 60°,90°, and 30° respectively find the length of side x ”

The length of side x in the given triangle is 4√3 units.

In the given triangle with a base length of 8√3 and angles at the vertices of 60°, 90°, and 30°, we can use trigonometry to find the length of side x.

Since we know that one angle is 90°, we can use the 30-60-90 triangle ratios to determine the other sides. The ratios for a 30-60-90 triangle are as follows:

Opposite side (x) / hypotenuse (8√3) = sin 30° = 1/2

Adjacent side (y) / hypotenuse (8√3) = cos 30° = √3/2

So, using these ratios, we can calculate the length of the opposite side (x):

x = (8√3) (1/2) = 4√3

Therefore, the length of side x in the given triangle is 4√3 units.

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Hey there!

Answer:

18 is 90% of 20.

Solution:

We already have our first value 18 and the second value 90. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1

[tex]18=90*y[/tex]

STEP 2

[tex]18=\frac{90}{100} *y[/tex]

Multiplying both sides by 100 and dividing both sides of the equation by 90 we will arrive at:

STEP 3

[tex]y=18*\frac{100}{90}[/tex]

STEP 4

[tex]y=18*100[/tex] ÷ [tex]90[/tex]

STEP 5

[tex]y=20[/tex]

Finally, we have found the value of Y which is 20 and that is our answer.

You can easily calculate 18 is 90 percent of what number by using any regular calculator, simply enter 18 × 100 ÷ 90 and you will get your answer which is 20.

Hope this helps! If you mark Brainliest, TYSM! :D

What is a percentage?

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

We can convert 90% into a fraction, making it 90/100 or 9/10.

Now that we have that fraction, we can multiply that by 20.

9/10 × 20 = 18

Therefore, 18 is 90% of 20.

For the equation 5^n = 5^11 × 5³ the value of n using the exponents rule is obtained as n = 14.

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The given equation is 5^n = 5^11 × 5³

Since, the base of the exponents is same, so apply the operations on the powers of the base.

The value of n can be found by following the exponent rule.

The exponent rule is - a^(b) × a^(c) = a^(b + c)

Write the equation according to the rule -

5^n = 5^(11 + 3)

Use the arithmetic operation of addition -

5^n = 5^(14)

n = 14

Therefore, the value of n is obtained as 14.

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The length of the rectangle is 17/24 feet greater than the width.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The length of a rectangle is 5/6 feet and the width is 1/8 feet.

So, The length of the rectangle is greater than the width is,

⇒ 5/6 - 1/8

⇒ (40 - 6)/48

⇒ 34/48

⇒ 17/24 feet.

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The measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.

The given data:

As, GE is the straight line.

Thus,

m∠EHF = 180 - 128 (sum of all angles of line is 180, linear pair)

            = 52°

Now,

m∠HEF = 180 - 52 / 2 (isosceles triangle)

m∠HEF = 64°

Thus, the measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.

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The diagram for the question is attached.

Answer: 2/7

Step-by-step explanation:

Go from point A to D by moving up 2 units and right 7 units. Since it slopes up it's a positive number.

Answer:

y = 2/3x - 2

y = 8/3x - 4

Step-by-step explanation:

If you graph it you will intersect at (1 , -1 1/3)

According to the universe in which light only moves at 3x10^8 meters/sec, it would take 3.333 x 10^-6 seconds to go 1 meter.  

The number is written in the form  [tex]a \times 10^b[/tex] where we have  [tex]1 \leq a < 10[/tex]

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

According to the universe in which light only moves at 3x10^8 meters/sec, it would take 3.333 x 10^-6 seconds to go 1 meter.  

Given that light travels 3x10^8 m/s.    So there . . .

The speed of light is in units of meters/sec.  

If it is 3x10^8 meters/sec, we can also write the inverse:

1 sec/3x10^8 meters

Do the division to find seconds per 1 meter:  

3.333 x 10^-9 seconds.

For Milky Way inhabitants,

It only requires 3.33 x 10^-9 second.

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The complete question is;

Light travels about 3 x 10^8 metres per second. Find the time it takes to travel 1 metre.

Regarding the likelihood of a student chosen at random joining a club and the interpretation of the likelihood, the correct answer is C. Because P(Robotics) = P, the student will be equally likely to join the robotics club or the zoology club (Zoology).

The random events are represented by probability. When there are numerous potential outcomes, it is the likelihood that the expected outcome will occur.

Probability is obtained by dividing the total number of outcomes by the expected number of outcomes.

Probability gives a quotient lying between zero and one as decimals, fractions, or percentages.

Club              Percent of Students

Garden Club            0.1

Robotics Club         0.2

Technology Club    0.5

Zoology Club          0.2

P(Robotics) = 0.2

P(Zoology) = 0.2

P(Robotics) = P(Zoology)

Thus, Option C is true about the probabilities.

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Answer:

1. 20... 2. 31... 3. -50

Step-by-step explanation:

1. 8+12=20

2. 13+18=31

3.-20+-30=-50

4. -15+3=-12

5. -80+20=-60

1. 8-12=-4

2. 13-18=-5

3. -20--30=-50

4. -15-3=-18

5. 80--20=60

The two coordinate values are simply swapped in the reflection over the line y=x: A'' = (4, 1) (4, 1)

The x-coordinate and y-coordinate of a point change positions when it is reflected across the line y = x.

The x- and y-coordinates shift positions and are negated when a point is mirrored across the line y = -x.

In light of this, the reflection of the point (x, y) across the line y = x is (y, x).

The first reflection's location across the vertical line x=-3 ensures that the y-coordinate is constant.

The point (-3, 4) on the line of reflection will become the halfway point between A and A' thanks to the x-coordinate of A':

(-3, 4) = (A +A')/2

2(-3, 4) (-3, 4)

-A = A' = (-6-(-7), 8 -4) = (1, 4) (1, 4)

The two coordinate values are simply swapped in the reflection over the line y=x: A'' = (4, 1) (4, 1)

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Sixty three is the product of nine and a number which is seven

Multiplying in math is the same as adding equal groups.

The number of items in the group grows as we multiply. Parts of a multiplication problem include the product, the two components, and the answer.

In the multiplication problem involving 63 as the product of 9 and another number

let the number be x

9 * x = 63

9x = 63

isolating x by dividing both sides by 9

9x / 9 = 63 / 9

x = 7

the number is 7

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Answer:

-792 is this right lmk

Step-by-step explanation:

free fire is one of mugi game

Answer:

The correct answer is

x= 4

y=-3

Answer:

  (x, y) = (4, -3)

Step-by-step explanation:

You want to solve this system of equations using substitution.

The substitution method requires that you find an expression for one of the variables that you can use to replace that variable in the other equation.

Here, we choose to use the second equation to write an expression for y. This makes the resulting coefficients be decimal values.

  5y = 9 -6x . . . . subtract 6x

  y = 1.8 -1.2x . . . . divide by 5

Substituting this for y in the first equation gives ...

  4x -3(1.8 -1.2x) = 25

  7.6x -5.4 = 25 . . . . . . . simplify

  7.6x = 30.4 . . . . . . . . add 5.4

  x = 4 . . . . . . . . . . divide by 7.6

  y = 1.8 -1.2(4) = 1.8 -4.8

  y = -3

The solution is (x, y) = (4, -3).

__

Additional comment

We could have used the first equation to write an expression for x. That would also make the coefficients be terminating decimal values. Using the first equation to write an expression for y leaves coefficients that are multiples of 1/3, not nice decimals. Similarly, solving the second equation for x would result in coefficients that are multiples of 1/6, also not nice decimals.

These "not nice" values can be used to get the same result. It just depends on what kind of arithmetic you want to do: fractions or decimals.

This set of coefficients would generally indicate that some other method would be more desirable to use: graphing, or matrix methods, for example. The attachment shows a matrix method.

The summation notation of the sum is:

[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]

The total amount is $84.

Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.

Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.

Let n represent the number of weeks

Thus, this can be written using summation notation as:

[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]

Thus, the total amount = 4¹ + 4² + 4³ = $84

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The greatest two-digit prime number with the property that the product of its digits is also a prime number is 37, since 3 x 7 = 21.

The greatest two-digit prime number with the property that the product of its digits is also a prime number is 37, since 3 x 7 = 21. Prime numbers are those numbers greater than 1 that are divisible only by 1 and itself. Two-digit prime numbers are those number between 10 and 99. The prime numbers between 10 and 99 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. The product of the digits of 37 is 3 x 7 = 21, which is also a prime number. Therefore, the greatest two-digit prime number with the property that the product of its digits is also a prime number is 37.

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