Express the given in terms of the logarithms of prime numbers:

Step-by-step explanation:

So 2 * 4 = 8

8 * 4 = 32

32 * 4 = 128

128 * 4 = 512

512*4=2048

2048*4=8192

8192*4=32768

32768*4=131072

131072*4=524288

524288*4=2097152

2097152*4=8388608

8388608*4=33554432 and that would probably be your final answer

The required function f when f"(x) = x^-2, x > 0, f(1) = 0, f(2) = 0 is f(x) = - ln x  + (ln 8) x/7 + (ln 8)/7

In tthis question we have been given the second derivative of function

f"(x) = x^-2, x > 0, f(1) = 0, f(2) = 0

We need to find a function f(x).

Consider f"(x) = x^-2

Integrating above expression with respect to x we get,

f'(x) = -1/x + C

againg integrating above expression with respect to x we get,

f(x) = - ln x + Cx + D

Now we need to find C and D.

Given that f(1) = 0

- ln (1) + C + D = 0     

C + D = 0                       ........... (1)

And f(8) = 0

- ln 8 + 8C + D = 0   

8C + D = ln 8                ..............(2)

subtracting equation (1) from equation (2),

C = (ln 8)/7

Subtituting above value of C in equation (1) we get,

D = -(ln 8)/7

So, f(x) = - ln x  + (ln 8) x/7 + (ln 8)/7

Therefore, the required function : f(x) = - ln x  + (ln 8) x/7 + (ln 8)/7

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From the triangle, the values of a and b are 5.1 units and 4.4 units respectively

You should know that a triangle is a polygon with three sides, three vertices, three angles  whose sum of angles is 180⁰

Using the trig ratio of Cosine

CosY=Adjacent/Hypothenuse

cos31=w/6

Cross multiplying we have

6*cos31=w

w=5.1 units

Then to find b, note that /VW/=/VY/=5.1

<VYX=<VWX............... base angles of isosceles triangle  WVY

Using cosine again from trig.

Cos31=b/5.1

5.1*cos31=b

simplify to get b=4.4 units

Therefore b= 4.4 units  

a=90-31       (remaining 2 angles of a right angled triangle)

a=59⁰

In conclusion, the value of a=59⁰ and the value of b=4.4 units

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The measure of minor arc is 108°

Pentagon:

                  A pentagon is a geometrical shape, which has five sides and five angles. Here, “Penta” denotes five and “gon” denotes angle.

If a pentagon is regular, then all the sides are equal in length, and five angles are of equal measures. If the pentagon does not have equal side length and angle measure, then it is known as an irregular pentagon.

The sum of all the interior angles for a regular pentagon is 540°.

hence,

           Value of each interior angle = 540°/5

                                                       = 108°

From figure,

                    we have to find ∠AED

we can see ∠AED is one of the internal angle of pentagon.

so,

         ∠AED = 108°

The measure of minor arc is 108°

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The mixed fraction in simplest improper fraction is 31/5.

For the stated mixed fraction;

6 1/5

To convert this in improper fraction;

= (6x5 + 1)/5

= (30 + 1)/5

= 31/5

This, the mixed fraction in simplest improper fraction is 31/5.

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The area of the floor of the scale drawing and the scale factor are 72 in² and 1/2 respectively.

Actual Length = 28 feets

Actual width =  38 feets

Model width = 14 inches

The scale factor = 14/28 =1/2

The length of the model can  be calculated thus :

Actual Length × scale factor

Model width = 38 × 1/2= 19 inches

The Area of a rectangle can be calculated using the relation :

Area = Length × width

Area of floor = 19 inches × 14 inches = 266 inch²

Therefore, the area of the floor of the scale drawing is 266 in²

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Answer:

To determine how long it would take a 12-inch candle to burn down, we need to first determine the relationship between the length of the candle and the time it takes to burn down. Since the candles are the same thickness and make, we can say that the time it takes for a candle to burn down is directly proportional to its length. This means that we can write an equation to represent the relationship between the length of the candle and the time it takes to burn down as follows:

t = k * l

where t is the time it takes for the candle to burn down, k is the proportionality constant, and l is the length of the candle.

We can use the information given in the problem to find the value of k. We know that an 8-inch candle burns down in 4 hours, so we can substitute these values into the equation above to find the value of k, as follows:

4 = k * 8

Solving for k, we get:

k = 0.5

Now that we know the value of k, we can use the equation above to determine how long it would take a 12-inch candle to burn down. Substituting the values for t, k, and l into the equation, we get:

t = (0.5) * (12) = 6

This means that it would take a 12-inch candle 6 hours to burn down.

Answer:

Look at pic 2 for the measurements. I rounded to the thousandth, because some required rounding to the hunderedth and others required to the nearest mile and others were unspecified.

Step-by-step explanation:

We should first draw a diagram. Since you said a diagram is shown, I will assume that the diagram looks something like pic 1. I do not know which variables correspond to which lengths, so I used random variables, but the diagram I drew should help you figure out which variables I used correspond to your actual problem.

If so, we can use our trigonometric functions and Pythagorean theorem to solve for all the lengths

We must solve for x and y in the diagram, and we can do so by using sine and cosine. We know the orange angle of the triangle whose legs are x and y is 36 degrees. We also know the hypotenuse of that triangle is of length 20 nm. Thus, [tex]sin(36) = \frac{x}{20}[/tex] and [tex]cos(36) = \frac{y}{20}[/tex].

We can multiply both sides of both of these functions by 20 to get: [tex]x = sin(36) * 20[/tex] and [tex]y = cos(36) * 20[/tex]. These are approximately x = 11.756 nautical miles and y = 16.180 nautical miles

We can solve for the length of a by adding 40 to y and getting a = 16.180 + 40 = 56.180 nautical miles

We can solve for the length of z by using the Pythagorean theorem and the leg lengths of a and x. We can do [tex]\sqrt{(40 + 20cos(36))^2 + (20sin(36))^2}[/tex] and get z = [tex]\sqrt{3294.427191}[/tex] = 57.397 nautical miles

Thus, we get the measurements in pic 2 as the distances you are asked to solve for.

The lengths are 56.180 nautical miles and 57.397 nautical miles

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse.

Given that, A ship sails 40 nautical miles (nm) due west from point A and then changes course and sails 20 nautical miles in a direction that is 54° west of due north.

We can use our trigonometric functions and Pythagorean theorem to solve for all the lengths

We must solve for x and y in the diagram, and we can do so by using sine and cosine. Furthermore, we also know the hypotenuse of that triangle is of length 20 nm. Thus,  and.

We can multiply both sides of both of these functions by 20 to get:  and. These are approximately x = 11.756 nautical miles and y = 16.180 nautical miles.

We can solve for the length of a by adding 40 to y and getting a = 16.180 + 40 = 56.180 nautical miles

We can solve for the length of z by using the Pythagorean theorem and the leg lengths of a and x. Likewise, we can do √40+(20cos(36°)²)+(20sin36°)²) and get z = 57.397 nautical miles.

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Answer:

h (7, - 16 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

let the coordinates of h be (x, y )

here (x₁, y₁ ) = g (15, 4 ) and (x₂, y₂ ) = h (x, y )

use the midpoint formula on g, h and equate to the coordinates x (11, - 6 )

[tex]\frac{15+x}{2}[/tex] = 11 ( multiply both sides by 2 )

15 + x = 22 ( subtract 15 from both sides )

x = 7

and

[tex]\frac{4+y}{2}[/tex] = - 6 ( multiply both sides by 2 )

4 + y = - 12 ( subtract 4 from both sides )

y = - 16

then

coordinates of h = (7, - 16 )

Answer:

-----------------------------------

Perpendicular lines have opposite-reciprocal slopes.

Given line has a slope of - 1/3, so the perpendicular slope is 3.

The matching choice is B.

Answer:

[tex]\textsf{B.} \quad y=3x+2[/tex]

Step-by-step explanation:

If two lines are perpendicular to each other, their slopes are negative reciprocals.

The negative reciprocal of a number is -1 divided by the number.

Given equation:

[tex]y=-\dfrac{1}{3}x+4[/tex]

The slope of the given equation is -¹/₃

Therefore, the slope of the perpendicular line is:

[tex]\implies -1 \div -\dfrac{1}{3}=-1 \times -3=3[/tex]

Therefore, the equation of the line that is perpendicular to the given equation is:

The shadow of a 400ft tall building is increasing at a rate of 100ft /hr

The angle of elevation of the sun is decreasing at a rate of 0.25 rad/hr

The height of the building is 400 ft tall

We need to find the rate at which the shadow is increasing

d/dθ = 1/4 rad/hr at θ = π/4

400/x = tan θ

x = 400/ tan θ

Upon derivation with t

dx/dt = 400 sec²θ/tan ²θ dθ/dt

at θ = π/4 and dθ/dt = 0.25 rad/hr

dx/dt = 400 (2x3)x0.25

dx/dt = 100ft/hr

Therefore, the shadow is increasing at the rate of 100ft/hr

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The sample with more observations and/or more variability in the data will generally have a larger chi-square test statistic.

Chi-square test statistic is a measure of how well a set of observed data fits a theoretical model. The larger the sample size and the more variability in the data, the more likely it is that the theoretical model won't fit the data perfectly. Therefore, the larger sample size and variability in the data will lead to a larger chi-square test statistic.

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Answer: 30

Step-by-step explanation:

6 divided by 1/5 is the same as 6/1 * 5/1

6/1 * 5/1 = 30/1

=30

30/5 = 6

Answer:

30

Step-by-step explanation:

There are a couple of ways to do this.  One way is the traditional way.

[tex]\frac{6}{1}[/tex]÷[tex]\frac{1}{5}[/tex]  Then multiply by the reciprocal

[tex]\frac{6}{1}[/tex] x [tex]\frac{5}{1}[/tex] = [tex]\frac{30}{1}[/tex] = 30

Another way that is more intuitive:

[tex]\frac{6}{1}[/tex]÷[tex]\frac{1}{5}[/tex]  Get a common denominator of 15

[tex]\frac{90}{15}[/tex]÷[tex]\frac{3}{15}[/tex] = [tex]\frac{\frac{90}{3} }{\frac{15}{15} }[/tex]= [tex]\frac{30}{1}[/tex] = 30

If the value of the base is y, then y^(3x+2) = 5x(2x-4)

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b^x= n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log8 base 2.

Also if 10² = 100 , then 2 = log100 base 10.

representing the unknown base to be y

then, log 5x(2x-4) base y = 3x+2

from the law of logarithm

log a base b = x, then b = a^x

Similarly log 5x(2x-4) base y = 3x+2

then 5x(2x-4) = y^(3x+2)

Therefore the exponential equation of the logarithm is 5x(2x-4) = y^(3x+2)

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The value that 50% of the data, as shown in the box plot, lie above and what it is called is: B. 50.5, the median

A box plot that displays the data set has the value of the median indicated at the point where a vertical line divides the rectangular box.

The median can be referred to as the second quartile (Q2) or 50th percentile of the data set.

The median value shows that 50% of the data set is above it while 50% is below it also.

The box plot in the given image shows that the vertical line crosses the rectangular box at 50.5.

50.5 is therefore the median, and this means that 50% of the data lie above 50.5.

Therefore, the answer is:

B. 50.5, the median

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Answer:

A, 74°

Step-by-step explanation:

Both of the angles are named y, so this means they are the same/have the same value!

Remember, all triangles equal 180°

To find y...

First, we subtract 32° from 180° to see what the Y angles total up to!

180° - 32° = 148°

the two y angles on the left side of the triangle equal 148°, but what does just one of them equal?

Divide by 2 to find out!

148° ÷ 2 = 74°

one y angle = 74°

y = 74°

Answer:

16 is the third quartile

Answer:

a)

Step-by-step explanation:

additions do not work in general that way when we consider a mixture of positive and negative numbers.

e.g.

x = 3, y = -5

|3 + -5| >= |3| + |-5|

|-2| >= 3 + 5

2 >= 8

is definitely not true.

so, for positive/negative number mixtures a) is wrong.

b) works because

if x >= y, then |x - y| >= |x| - |y|. equal when x and y > 0. larger when x and/or y < 0. correct

if x < y, then |x - y| >= |x| - |y|. larger when x and y > 0.

equal when x and/or y < 0.

c) and d) work because the signs don't change anything. either the result is positive anyway, or if negative just gets converted to the positive result.

Answer:

Relation 1 & 2 are functions

Relation 3 & 4 are not functions

Step-by-step explanation:

For a relation to be a function every x must have one and only one y

This is not true for relation 3 which has 2 y's at x = m and 2 y's at x = v

This is also not true for relation 4 which has 2 y's at x = 4

Answer:

A. 13/15​

B. 13/10​

C. 22/21

D. ​−3/20​

Step-by-step explanation:

Just make the denominators equal to each other and solve. Ask your teacher for extra help

The requirement is represented by the inequality y≥3x, and he caught at least 21 fish last year.

In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. Inequality originates from a lack of equilibrium. To solve an inequality, isolate the variable on one side from the other constants. To do so, use opposing procedures to modify the inequality. To begin, separate the x by multiplying each side by two. Whatever you do on one side must equally be done to the other.

Here,

Let y is fishes caught in this year and x be the fishes caught in last year.

y≥3x

63≥3x

x≥21

The inequality that represent the condition is y≥3x and he caught at least 21 fishes last year.

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Answer:

Step-by-step explanation:

a. 40 because 25 percent is 1/4th and 160 times 1/4=40

b. 78  because 200 times 39/100 is 78

c. 48 because 32 times 150/100=48

d. 26 because if it is 50 percent it is 1/2 of a number so just multiply

e. 15

f. 70 percent, simplify both numbers to the lowest number possible equal to 21/30 so 7/10 and that is 70 percent

five out of of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise

If you were to attribute this film, that means you'd say that (something) caused the success of the movie Rocky. This question is basically asking what do you think made this movie a big hit? Personally, I'd say it's because of how the storyline and plot turned out. It's very intriguing and it doesn't just make the movie about boxing. The film adds some love between the protagonist and some other character, and not only that, but the movie teaches you something. Because Rocky lost to Apollo, Rocky didn't care. At least he still had Adrian. So, the movie teaches you that, even if you do lose, at least you still have something and/or someone with you.

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The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

Answer:

is your a nswer in it's simplest form

Step-by-step explanation:

Abdullah and Amna bought a car for $9000, Abdullah paid 45% of the $9000 and Amna paid

the rest.

b) Write down the ratio of the payments Abdullah: Amna in it's simplest form.

Abdullah paid 45% means Amna paid 55% (100% - 45% = 55%), so the Abdullah : Amna ratio is 45 : 55, let's simplify by dividing the two parts by 5 and we will have the ratio in its simplest form.

45 : 55

let's simplify

9 : 11 is your answer