Can someone please help me with this please please thank you

The simplification of the logarithm expression are as shown below

A logarithm expression is a mathematical statement that involves logarithms. It is an expression that contains logarithmic functions, such as log, ln, logₐ, etc. These expressions can include logarithms with different bases, numbers in logarithm form, and exponents.

The logarithm expressions can be simplified as follow:

1. since logₐa = 1,

log₄4 = 1

2. Since logₐ1 = 0,

log₁₀1 = 0

3.  since logₐ(M × N) =  logₐM -  logₐN and logₐa = 1

log₃4 × 3 = log₃4 + log₃3 = log₃4 + 1

4. since logₐxⁿ = n logₐx and logₐa = 1

log₄4³ = 3 log₄4 = 3 × 1 = 3

5. since logₐxⁿ = n logₐx and logₐa = 1

logₓx⁰ = 0 logₓx = 0 × 1 = 0

6. since logₐxⁿ = n logₐx and logₐa = 1

logₓx³ =  3 logₓx = 3 × 1 = 3

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The area of the plate of the microscope with a circumference of

100mm is 2500/π mm².

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed as 2πr.

Given the data in the question;

First, we determine the radius of the plate.

Circumference C = 2πr

100 = 2πr

r = 100/2π

r = 50/π

Now, calculate the area of the plate.

A = πr²

A = π ( 50/π )²

A = π × 2500/π²

A = 2500π / π²

A = 2500/π mm²

Therefore, the area of the plate is 2500/π mm².

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The value of the variable, h is 60 degrees

The properties of a trapezium are expressed as;

If the size of the angles of the trapezium are 2h, 2h, h and h

Then, it is represented as;

Add all the angles

2h + 2h + h + h

Equate the angles to the sum of the interior angles of a trapezium, we get

2h + 2h + h + h  = 360

Now, add the like terms

6h = 260

Divide both sides by the coefficient of h, we get;

6h/6 = 630/6

h = 60 degrees

Hence, the value is 60 degrees

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Answer:

3 laps every 12 minutes

Step-by-step explanation:

The formula would you put in cell location h10 to find the numerical derivative at position 10 of column k of the data found in j is =DERIVXY(h10, k10, j)

The term called derivative is defined as the process to determine the rate of change of a quantity with respect to another changing quantity

Here we have to write the formula for the cell location h10 to find the numerical derivative at position 10 of column k of the data found in j.

As from the definition, the general form derivative function is written as,

=> =DERIVXY(x, y, p, [options])

where x a vector of the points x-coordinates and y corresponding vector of the points y-values and p the point at which to compute the derivative.

Here we have the values of x as h10, y as k10 and p as j

Then the formula is written as,

=> =DERIVXY(h10, k10, j)

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Estimation done by Mia is not accurate, as the accurate estimated sum of the given expression 5/8 + 1/9  is equal to ( 1/2).

Estimation done by Mia is not accurate:

Replaced 5 /8 with 1.

But accuracy represents:

0 < (1 /4 ) < ( 1 /2 ) < (5 /8 ) < ( 3 / 4 ) < 1

( 5 / 8 ) is more close to ( 1 /2 ).

Estimated value of ( 5 / 8 ) is ( 1 / 2 )

0 < ( 1 / 9 ) < ( 1 / 4 )

So , estimated value of ( 1 / 9 ) is 0

Estimated sum = ( 1 / 2 ) + 0

                         = ( 1 / 2 )

                         ≠ 1

Therefore, accurate estimated sum of 5/8 + 1/9  is equal to ( 1 /2 ).

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The range of h include the following: A. -4 ≤ h(x) ≤ 6.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Generally speaking, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown, we can reasonably and logically deduce the following:

Range = [-4, 6]

In mathematical notation, the range of this graph can be rewritten as -4 ≤ h(x) ≤ 6.

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For the given table of values the equation that could be the function rule is option 4: y = 3x - 2.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The table of input and output values are given for the function.

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[-2 - (-11)]/[0 - (-3)]

(-2 + 11)/(0 + 3)

9/3

3

So, the slope point is obtained as m = 3.

The equation becomes - y =3x + b

To find the value of b substitute the values of x and y in the equation -

-11 = 3(-3) + b

-11 = -9 + b

b = -11 + 9

b = -2

So, the value for b is -2.

Now, the equation becomes -

y = 3x - 2

The graph is plotted for the function.

Therefore, the equation is y = y = 3x - 2.

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The length of DH (diagonal) in the rectangular prism is approximately 3.5 inches.

A rectangular prism has three dimensions: length, width, and height. The diagonal of a rectangular prism is the distance between two opposite corners of the prism.

To find the diagonal of a rectangular prism, you can use the Pythagorean theorem, which states that the square of the diagonal is equal to the sum of the squares of the length, width, and height.

In this case, the length is 1.5 inches, the width is 1 inch, and the height is 3 inches. So, you can use the formula:

d² = 1.5² + 1² + 3²

d² = 2.25 + 1 + 9

d² = 12.25

Then take the square root of the d²

d = √12.25

d ≈ 3.5 inches.

Therefore, the measure of the diagonal of the rectangular prism is approximately 3.49 inches.

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Answer:

3.5

Step-by-step explanation:

I took the quiz

Answer:2.75 (or 11/4, they are equal).

Step-by-step explanation: The graph of f(x) is continuous on the closed interval and differentiable on the open interval. Now we need to find the average slope over the interval, which is [0-3]/[5-(-4)] = -3/9 = -1/3. The goal is to find a place where f'(c) = -1/3, so basically anywhere where the derivative equals -1/3. First we need to find the derivative of the function which can be rewritten as (5-x)^(1/2). Differentiating this using the chain rule gives you -1/(2*sqrt(5-x)). Set this equal to -1/3. The numerator is -1, so really we just need to find where the denominator, 2sqrt(5-x), is equal to 3. Divide by 2 and get sqrt(5-x) = 3/2. Square both sides and get 5-x = 9/4. Subtract 5 and get -x = -2.75, so x = 2.75. This means c = 2.75.

If each child consumed the same quantity, then each would need to drink (63)x(4/n) of a gallon.

The US fluid ounce is equal to 1/128 of a US gallon since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint. The US gallon is accepted to be equivalent to around 3.785 L or 231 in inches, but the Imperial gallon is accepted to be equal to 4.54609 L. The liter is the unit of volume used by the great majority of people in the world. a volume measurement equal to eight pints.

An imperial gallon (Britain, Canada) is exactly 4.54609 liters. (US) 3.785 liters or around 231 cubic inches for liquids (a "U.S. liquid gallon")

Here gallon of lemonade to share = 63

let each children has 1 gallon of lemonade

so gallon=63

so portion =63/1

Formula = gallon to share x (4 parts of gallon shape / number of gallon)

which means if each one have n gallon then portion = (63)x(4/n)

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Each child would need to eat 63*4/n of a gallon if they all consumed the same amount.

Since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint, one US fluid ounce is equivalent to 1/128 of a US gallon. The Imperial gallon is acknowledged to be equal to 4.54609 L, but the US gallon is accepted to be about 3.785 L or 231 in. The vast majority of people in the world measure volume in litres. a volume that is eight pints in size.

In Britain and Canada, an imperial gallon equals precisely 4.54609 litres. 3.785 litres (US) or around 231 cubic inches (a "U.S. liquid")

Here, six thirty kids were sharing a gallon of lemonade.

each youngster should drink a gallon of lemonade.

Gallon = 63.

Hence part = 63/1

It indicates that the fraction is equal to 63*4/n if each has n gallons.

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Note: The complete question would be as bellow,

six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?

The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = 4 x² - x + 5

A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.

The general mathematical representation of a function is y = f(x).

f(x)=x²- 5x+7

g(x)=3x² + 4x - 2

(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)

(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)

(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2

(f + g)(x) = 4 x² - x + 5

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The population of interest and the sample size include the following:

Population: all potential customers of the parlor.

Sample size: 8.

In Statistics and science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.

In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.

In this scenario, we can logically deduce that sample is the eight customers that were selected and questioned by an employee at the local ice cream parlor.

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=============================================

Work shown for problem 1

[tex](f - g)(\text{x}) = f(\text{x}) - g(\text{x})\\\\(f - g)(\text{x}) = (2\text{x}^2+\text{x}-3)-(\text{x}-1)\\\\(f - g)(\text{x}) = 2\text{x}^2+\text{x}-3-\text{x}+1 \\\\(f - g)(\text{x}) = 2\text{x}^2-2\\\\[/tex]

This leads to choice D as the final answer.

The domain is the set of all real numbers since the result is a polynomial. Any polynomial function has the domain "all real numbers". This is because we don't have anything like a division by zero error. We also don't have to worry about square roots of negative values.

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

Work shown for problem 2

[tex](f * g)(\text{x}) = f(\text{x}) * g(\text{x})\\\\(f * g)(\text{x}) = (2\text{x}^2+\text{x}-3) * (\text{x}-1)\\\\(f * g)(\text{x}) = \text{x}(2\text{x}^2+\text{x}-3)-1(2\text{x}^2+\text{x}-3)\\\\(f * g)(\text{x}) = 2\text{x}^3+\text{x}^2-3\text{x}-2\text{x}^2-\text{x}+3\\\\(f * g)(\text{x}) = 2\text{x}^3-\text{x}^2-4\text{x}+3\\\\[/tex]

This leads to choice A as the final answer.

The domain is the set of all real numbers for the exact same reasoning as problem 1.

The equation represented as f(x) = x + 1/x + 2 is a function

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

f(x) = x + 1/x + 2

The above equation is a rational equation whose numerator and denominator are linear functions

Equations with these properties are always functions

This is so because their x values do not have multiple y values

Hence, the equation f(x) = x + 1/x + 2 is a function

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Answer:

x = greater than or equal to 3.5         x = 3≥

Step-by-step explanation:

any number that is greater than or is 3.5 will make 2x greater than 5 + 2 which equals 7

The amount of wood that they need to complete the supports is given as follows:

130.10 cm.

First we must obtain the side lengths of the right triangle.

The equal side lengths of the right triangle are obtained applying the Pythagorean Theorem, hence:

x² + x² = 92²

2x² = 92²

x² = 4232

x = square root of 4232

x = 65.05 cm.

They have two sides of 65.05 cm, hence the amount of wood needed is obtained as follows:

2 x 65.05 = 130.10 cm.

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The area of triangle A(F) D is 42.44 units²

The formula to calculate the area of a triangle with base b and height h is given by:

Area = 1/2(bh)

In ΔA(F) D, the base is (F)D and A(F) is the height

Using trigonometric ratio:

sin 30° = A(F) /AD  (opposite/hypotenuse)

0.5 = A(F) /14

A(F)  = 7 units

(F)D = √(14²-7²) = 7√3 units (Pythagoras theorem)

Area of  ΔA(F) D = 1/2 × (F) D × A(F)

Area of  ΔA(F) D = 1/2 × 7√3 × 7

Area of  ΔA(F) D = (49√3)/2

Area of  ΔA(F) D = 42.44 units²

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The mileage rate of 75 miles per gallon is equal to 19.8 miles/liter or 31.9 km/liter. The result is obtained by converting the value of each unit.

The conversion value of

Some hybrids achieve mileage ratings as high as 75 miles per gallon of gasoline. Determine that quantity in:

Multiply the number with the conversion value of each!

In miles per liter,

75 miles/gallon = 75 × 1/3.785 miles/liter

75 miles/gallon = 19.8 miles/liter

In kilometers per liter,

75 miles/gallon = 75 × 1.609 × 1/3.785 km/liter

75 miles/gallon = 31.9 km/liter

Hence, 75 miles per gallon is equal to 19.8 miles/liter or 31.9 km/liter.

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the total FBT liability for this benefit is $329 ($700 x 47% = $329).

Fringe Benefits Tax (FBT) is imposed by the Australian Taxation Office (ATO) on certain non-cash benefits provided to employees. If a company provides a weekend stay in Sydney valued at $1,000 as a Christmas gift in December 2022, the FBT liability is calculated as follows:

The taxable value of the benefit is calculated by deducting the expenses that are not subject to FBT, i.e. $300 (flight) from the total value of the gift, i.e. $1,000. This leaves a taxable value of $700 ($1,000 - $300 = $700).

The FBT liability is then calculated by multiplying the taxable value, i.e. $700, by the FBT rate which is currently 47% (as of 2021). This results in an FBT liability of $329.

Therefore, the total FBT liability for this benefit is $329 ($700 x 47% = $329).

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The total number of visitors to the zoo that day=3980.

Given:

cost of each ticket for an adult=$25

cost of each ticket for an adult=$10

Total ticket sales one day=$47,750.

⇒$25+$10=47,750

⇒25+10=47,750-----(1)

Also,

c=6a+270

6a-c=-270------(2)

multiplying eq(2) with 10 we get:

60a-10c=-2700----(3)

Adding eq(1) and eq(3) we get

25a+10c=47,750

60a-10c=-2700

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

85a=45050

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

To calculate a value just divide 45050 by 85 we get

a=45050/85

a=530

Now to get the value of c substitutes a value.

c=60(530)+270

c=3450

Number of Adult visitors=530

Number of children visitors=3450

Total Number of visitors=3980.

Therefore, the total number of visitors to the zoo that day=3980.

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Therefore, the method (addition or subtraction) used to combine or separate the terms is the primary distinction between adding and subtracting linear expressions.

Another difference is that when we subtract linear expressions, we get a smaller expression, whereas when we add them, we get a larger one.

A mathematical expression that results from the linear combination of variables and constants is known as a linear expression.

Linear expressions can be combined or separated using two distinct operations: adding and subtracting.

By keeping the same variable while adding the coefficients (the numerical part) to linear expressions, like terms are combined. If we wanted to add 2x and 3x, for instance, we would get 5x.

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Answer:

the average height is 5 feet 0 inches

Step-by-step explanation:

To find the average height of Maria, Marla, Mandy and Marilyn, we need to add up their individual heights and divide by the number of people in the group.

First, we need to convert all the heights to a common unit of measurement. Since inches are the smallest unit of measurement, we will convert all the heights to inches.

Maria: 5 feet 3 inches = 63 inches

Marla: 4 feet 11 inches = 59 inches

Mandy: 5 feet 2 inches = 62 inches

Marilyn: 4 feet 8 inches = 56 inches

Now we can add up the heights:

63 inches + 59 inches + 62 inches + 56 inches = 240 inches

To find the average, we divide the total height by the number of people:

240 inches / 4 people = 60 inches

So the average height of these four friends is 60 inches or 5 feet, which is the same as 5 feet 0 inches.

Therefore, the average height of these four friends is 5 feet 0 inches.

Answer:

-13F

Step-by-step explanation:

since its negative, you could find the answer by doing 35-22

then, just adding a negative symbol in front!

this is because you are finding the difference by subtracting, and by doing this i find it a lot easier to get your answer

so, 35-22 is equal to 13. so, 22-35 is -13

i hope that makes sense

honestly, you can just use a calculator to figure it out too! just put 22-35

Answer:

Step-by-step explanation:The exponent of a number shows how many times the number is multiplied by itself.

According to the rules of exponents,

We know that, am ÷ an = am − n

(5m ÷ 5−3) = 55

5m−(−3) = 55

5m + 3 = 55

The bases are the same on both the sides, so their exponents must be equal.

∴ m + 3 = 5

⇒ m = 5 − 3

⇒ m = 2

Paying off the lowest outstanding balance credit card first will not be beneficial over paying off the one with the highest. Instead, it's beneficial to pay the highest outstanding balance first.

Actually, paying the one with the highest interest rate is logically the right thing to do because you can shorten the amount that you spend on interest or charges by month, but paying the lowest outstanding balance credit card first makes more sense if you could transfer the highest interest balance into a low or maybe no interest rate that is being offered to another card, only if you are so certain that you will pay the remaining balance or on before its due. 

It should be remarked that paying off the lowest outstanding balance credit card first cannot be beneficial over paying off the one with the highest interest rate.

It's significant to pay the one that has the highest interest rate. This is because it'll assist in shortening the amount the person will pay as interest.

In conclusion, it's important to pay the highest Interest rate.

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The volume of the solid is approximately 32π/3 cubic units.

The volume of the solid obtained by rotating the region bounded by the curves y = 4 - 1/2x, y = 0, x = 0, and x = 1 about the x-axis can be found using the method of disks/washers. The formula for the volume is given by:

V = π * ∫[a,b] (R^2 - r^2) dx

where R is the outer radius (4 - 1/2x), r is the inner radius (y = 0), a and b are the limits of x (x = 0 and x = 1), and dx represents a small slice of the solid.

Evaluating the definite integral:

V = π * ∫[0,1] (16 - x^2 - x^2) dx = π * ∫[0,1] (16 - 2x^2) dx = π * (16x - 4/3 x^3) evaluated at x = 1 - x = 0 = π * (16 - 4/3) = 32π/3 cubic units.

So the volume of the solid is approximately 32π/3 cubic units.

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If Steven made $4,800 this month, the value of his sales for the month is $51,000.

Steven's base monthly salary on sales of $17,000 = $2,700

First sales commission above $17,000 sales = 10%

Second bonus commission above $25,000 sales = 5%

Total earnings for the month = $4,800

First sales commission = $800 ($25,000 - $17,000 x 10%)

Additional bonus commission = $1,300 ($4,800 - $2,700 - $800)

$1,300 = 5%

Sales above $25,000 = $26,000 ($1,300/5%)

Sales value = $51,000 ($25,000 + $26,000)

Thus, we can assert that Steven generated Sales of $51,000 to earn a total of $4,800 for the month.

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About 40 meters the submarine’s depth be if it continues its dive for another 110 meters. So the option A is correct.

Since it is essentially a ratio problem, we can use the information given and apply the Rule of Three assuming that the submarine is moving at a constant speed.

In this rule, the depth after 110 meters is obtained by simply multiplying the ratio's diagonal values and dividing by the last value.

70min = 25 m

110min = x m

x = (110 × 25)/70

x = 2750/70

x = 39.28

x = 40(approx)

We can see that at 110 minutes, the depth would have been approximately 40 meters, but since the submarine travelled further during this time, we must add this measurement to the original 25 meters to determine the submarine's total depth.

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The length of a  rectangular rug is 84 yards and the width is 36 yards

Let 'l' represents the length of the  rectangular rug and 'w' represents the width of a  rectangular rug.

The length of the rug is 12 yards more than two times the width.

So, we get an equation,

l = 12 + 2w

Also, a  perimeter of  a rectangular rug is 240 yards

We know that the formula for the perimeter of rectangle:

P = 2(w + l)

Using this formula the  perimeter of  a rectangular rug would be,

P = 2 × [w + (12 + 2w)]

240 = 2 (12 + 3w)

120 = 12 + 3w

108 = 3w

w = 118/3

w = 36

And the length would be,

l = 2 + 2( 36)

l = 84 yards

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The complete question is:

A rectangular rug has perimeter 240 yards. The length is 12 yards more than twice the width. Find the length and width of the rug.