I need help finding

The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]

Given,

Write the expression as a sum and/or difference of logarithms with all variables to the first degree.

[tex]In\sqrt{8t^4v^2}[/tex]

Convert to exponential form

= [tex]In(8t^4v^2)^\frac{1}{2}[/tex]

Simplify using exponent rule with same exponent [tex](ab)^n = a^n . b^n[/tex]

= [tex]In (8^\frac{1}{2} . (t^4)^\frac{1}{2}(v^2)^\frac{1}{2} )[/tex]

Apply laws of logarithms to simplify the expression.

= [tex]In 8^\frac{1}{2} + In(t^4)^\frac{1}{2} + In(v^2)^\frac{1}{2}[/tex]

Express the logarithm of a power of an expression as the power times the logarithm of the expression.

= [tex]\frac{1}{2} . In8 + In(t^4)^\frac{1}{2} + In(v^2)\frac{1}{2}[/tex]

=[tex]\frac{1}{2} . In8 + \frac{1}{2} . In(t^4) + \frac{1}{2} .In(v^2)[/tex]

Multiply the monomials

[tex]\frac{In8}{2} + \frac{1}{2} . 4 . In t + \frac{1}{2} . 2 . In v[/tex]

= [tex]\frac{In8}{2} + 2 . In t + \frac{1}{2} . 2 . In v[/tex]

= [tex]\frac{In8}{2} + 2 . In t + In v[/tex]

Hence, The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]

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when w = 18 then z =2

take ratio,

k = 18/2

k = 9

when w =45 then z = 5

take ratio

k = 45/5

k = 9

now it is clear that the constant of proportionality is k = 2

so, the relation between w and z is

w = k z

put k = 9

w = 9z

so, the relation between w and z is w = 9z

The degree of the second term in the polynomial;

is 19

The scale factor which is being used by this drawing is 1 : 12.

A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, river, planets in our solar system, etc.

Mathematically, the scale factor of a geometric figure can be calculated by using tis formula:

Scale factor = Dimension of image/Dimension of original figure

Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.

Conversion:

1 inch = 1 foot

12 inches = 1 foot

Therefore, the scale factor for this drawing is 1 : 12.

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Answer:

Step-by-step explanation:

gee girls generation

The relative frequency of an event is the quotient of the division between the event and the total number of the sample

From the given table

Add the numbers of males to find their total

Then add the numbers of females and males to find the total of the sample

Now, divide the number of males by the total to find the relative frequency

Round it to 2 decimal places, then

The relative frequency of the male students = 0.49

Answer:

  B: (3, 4, 5)

Step-by-step explanation:

You want to know which segment lengths could be used to form a triangle.

The triangle inequality requires the sum of the two short sides of a triangle exceed the length of the longest side.

A: 1+2 = 3 . . . not a triangle

B: 3+4 > 5 . . . forms a triangle

C: 1+10 < 100 . . . not a triangle

D: 1+2 < 5 . . . not a triangle

E: 1+3 = 4 . . . not a triangle

F: 1+20 < 100 . . . not a triangle

__

Additional comment

The above expression of the triangle inequality seems to be the one most commonly used in algebra and geometry courses.

The triangle inequality can also be seen to be expressed as ...

  a + b ≥ c . . . . . . where a, b, c are side lengths in any order

The "equal to" case allows triangles of zero height. (They look like a line segment.) Using that formulation, triples A and E in your answer list will also be considered to form a "triangle."

The measure of the given polygon's angle is 2340°

Polygons are two-dimensional closed objects in geometrical mathematics where n number of line segments cross each other to generate n number of vertices. A triangle is a polygon with three sides, for instance.

In an n-sided polygon, there are n inner angles.

The total of all interior angle measurements in a polygon is always constant and is denoted by the notation "n" for the number of sides in the polygon.

the formula is ;

Sₙ = ( n - 2 ) 180°

Here in question n is given as 15

Thus Sₙ = ( n - 2 ) 180° becomes

Sₙ = ( 15 - 2) 180

13 × 180

= 2340 °

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Answer:

it is really A 156 i took the test and got an 100%

Step-by-step explanation:

The value of y when y = y = 0.25sin(4(x+2π))-4. and x = 2pi is -4.

Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions.The Amplitude is the height from the center line to the peak (or to the trough).The Phase Shift is how far the function is shifted horizontally from the usual position.The Vertical Shift is how far the function is shifted vertically from the usual position.

We can have all of them in one equation:

y = A sin(B(x + C)) + D

amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

So, for the given question we have amplitude is 0.25, period is 2π/4, phase shift is 2π, vertical shift is -4

So,

y = 0.25sin(4(x+2π))-4.

when x = 2π

y = 0.25sin(16π)-4

y = 0-4

y = - 4

Therefore,  y = 0.25sin(4(x+2π))-4, and its y - value when x = 2π is -4.

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The way that expresses the number of ways those textbooks could be distributed among the students is ⁵C₂.

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr

Combination formula will be:

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time

In this case, each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. This will be illustrated as ⁵C₂.

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There are ten ways (which are ⁵C₂ = 10) to distribute those textbooks could be among the students in this situation.

Combinations indicate the choosing of items from a predetermined list of items.

The combination is given by the relation, ⁿCₓ = n!/{x!(n-x)!}

The quantity is given by n. and x is equal to how many objects are taken at once.

Each of the five students in this situation wants to purchase a specific textbook, but there are only 2 books available.

The expression for the number of possible distributions of such textbooks among the students is

⇒ ⁵C₂

⇒ 10

Hence, there are ten ways to distribute those textbooks could be among the students.

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The range is the set of y-values of the points given.

The points given are:

{(3, 4), (7,-2), (11, -8)}

The range would be:

4, -2, and -8

Range = {4,-2,-8}

Option C

The two numbers whose sum is 50 and three times the first is 5 more than twice the second are 21 and 29.

What do you mean by sum?

A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.

Let the two numbers be X and Y.

There are two condition given in the question through which we can form a system of equation containing two equations.

First condition: The sum of the numbers is 50.

Therefore,

X + Y = 50

Second Condition: Three times the first is 5 more than twice the second

Therefore,

3X = 2Y + 5

We get the system of equation:

X + Y = 50

3X = 2Y + 5

Solving this system of equation

3X - 5 = 2(50 - X)

3X - 5 = 100 - 2X

X = 105/5

X = 21

Putting the value of X in one of the equation:

Y = 50 - X

Y = 50 - 21

Y = 29

Therefore, two numbers are 21 and 29

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The equation of the line is  y-2x= 6.

Here the problem we are dealing with is related to the slope of the line, where, a slope of a line is the alter in the y coordinate about the alter in the x coordinate. The net change in the y-coordinate is spoken to by Δy and the net change in the x-coordinate is spoken to by Δx. The equation for the slope of a straight line is given by y − y1 = m(x − x1), where m is the slope and (x1,y1) are the points that pass through it,whereas the slope-intercept form of the line is given by y = mx + b, where b is the y-intercept. Since if two lines are parallel at that point it said the slope of both those lines are equal  i.e m₁= m₂

Since it is given that the coordinates (-2,2) and the slope of the parallel to it, m=2

so the equation for the line is

=>y − y1 = m(x − x1)

=>y − 2 = 2(x +2)

=>y − 2 = 2x+4

=>y-2x= 6

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Find the eqaution of the line that passes through the coordinates -2,2 parallel to the line whose slope is -1.

The solution:

Given the functions:

Required:

To find the value of g(f(4))

Step 1:

Substitute 4 for x in f(x).

Step 2:

Substitute -64 for x in g(x).

Therefore, the correct answer is 9 [option C]

The average rate of change of the function at the interval x = -3 to x = 5 has a value of (b) 0

From the question, we have the following points

Parabola going through (-3, -1) and (5, -1).

Also from the question, the interval is given as

x = −3 to x = 5

This interval can also be represented as

(a, b) = (-3, 5)

The points in the question can be expressed as

f(a) = f(-3) = -1

f(b) = f(5) = -1

The value of the average rate of change of the graph at the interval is then calculated as

Rate = [f(b) - f(a)]/[b - a]

Substitute the known values in the above equation

So, we have the following equation

Rate = [f(5) - f(-3)]/[5 + 3]

So, we have the following equation

Rate = [-1 + 1]/[5 + 3]

Evaluate the above quotient

Rate = 0

Hence, the average rate of change of function f is (b) 0

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Answer:

y= -7x-11

Step-by-step explanation:

m= -7 (gradient)

b= -11 (y-intercept)

write in the form of y=mx+b

y=-7x-11

ANSWER

Amount = $3102.75

Interest = $1598.75

EXPLANATION

The annuity pays 6.6% compounded monthly.

The formula for an Amount compounded at a rate of r after t years is given as:

where P = principal (amount deposited) = $1,504

r = rate = 6.6% = 0.066

n = 12 (12 months in a year)

t = number of years = 11 years

Therefore, the amount in the account after 11 years is:

That's the amount in the account after 11 years.

This means that the amount of interest after 11 years is the amount after 11 years minus the amount that was there initially:

Interest = 3102.75 - 1504

Interest = $1598.75

step 1

Find the slope

we need two points

take the points (0,3) and (1,0)

m=(0-3)/(1-0)

m=-3

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-3

b=3

substitute

step 3

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=-3

point (0,3)

y-3=-3(x-0)

step 4

standard form

AX+By=C

we have

y=-3x+3

Answer: The line parallel to y = -2x + 5 that passes through the point(1,1)

Has the same slope, m but a different y intercept (0,b)

So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b

y = mx + b

m = -2

1 = -2(1) + b

1 = -2 + b

Add 2 to both sides of the equation to solve for b

1 + 2 = b

3 = b

The line is

y = -2x + 3

Step-by-step explanation:

Based on the location of 0 in the bottom distribution (meaning no difference in the means), the best conclusion is:

A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.

In mathematics, distribution describes the probability that a system or a data set will take on a specific value or set of values.

Probability distribution shows how data values are distributed.  It is also known as statistical distribution because it demarcates values into common and uncommon (left and right), making a bell-shaped normal distribution.

Thus, when there is no difference in the means, the best conclusion of the statistical distribution is Option A.

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A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.

B- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are not statistically different.

C- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are statistically different.

D- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are statistically different.

Solution:

Given the graph:

Using two points on the line to find the slope, m:

Thus, the y-intercept and slope, m of the line respectively are:

Answer:

look my photo. hope it can help

The price of the lined jacket at discount heaven is 32.

To find the price of the lined jacket at the house of denim we use the rule of three.

Then the discount is:

Hence, the price of the lined jacket at house of denim is:

Therefore, the price of the lined jacket at house of denin is $31.73.

-5/4 can be shown as -1 1/4, and plotted on the number line as the first quarter tick past -1. Its opposite, 1 1/4, is the same way, the first quarter tick past 1.

Answer: On the plot line 5/4 is 5 tic marks passed 0 so -5/4 would be 6 tic marks before. Hope this helps

If this is wrong I am deeply sorry.

Answer: x<2 or (−∞,2)

Step-by-step explanation:

Answer:

y = 4·0.5^x

Step-by-step explanation:

If x is increased by 1, y is multiplied by 0.5.

x | y

0 | 4

1 | 4·0.5

2 | 4·0.5·0.5

3 | 4·0.5·0.5·0.5

The cost of the meal before the sales tax and tip= $689

Sales tax = 8%

The family then tipped 20% on the ammount after the sales was added

PART A

The amount of the sales tax can be calculated as follows

Amount of sales tax = sales tax * the amount of the meal

Amount of sales tax = 8% x $689

Amount of sales tax = 8/100 x 689

Amount of sales tax = 0.08 x 689

Amount of sales tax = $55.12

Therefore, the amount of sales tax is $55.12

PART B

What is the total amount paid by the family after adding the tax sales and 20% tipping

The cost of the meal = $689

Amount of sales tax = $55. 12

20% tipping on the amount after the sales tax was added

Amount of the meal after the sales has been added = $689 + $55.12

Amount of the meal after the sales tax has been added = $744. 12

20% tipping of the total amount = 20% x 744.12

= 20/100 x 744.12

= 0.2 x 744.12

= $148.82

The total amount paid by the family = 689 + 55.12 + 148.82

The total amount = $892.94

Therefore, the family paid a total amount of $892.94

The inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car is 25y + 750 ≥ C.

If the car costs a total of $4500 number of yards you will have to mow is 150 yards at least.

In mathematics, a statement of an order relationship between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to) is called an Inequality.

Given:

Price of the car paid by your parents = $750

You have a summer job mowing yards for $25 per yard.

We have to determine an inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.

So, the required inequality is

25y + 750 ≥ C

Now, the Cost of the car given is $4500.

Substituting this in the inequality to find the number of yards,

25y + 750 ≥ 4500

Subtracting 750 from both sides

25y  ≥ 3750

Dividing both sides by 25,

y  ≥ 150

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we know that

The formula of simple interest is equal to

In this problem

we have

I=$170

P=$8,500

r=4%=4/100=0.04

t=?

substitute given values in the formula

therefore

0.5 years=6 months