Write each logarithmic expression as a single logarithm.

1/2 (logx4 + logx y) - 3 logx z

Mean = Sum of all observations/Number of observations

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.

Given,

The set of scores =  0, 40, 60, 70, 75, 80, 85, 95, 95, 100

                           = 700/9

                           = 77.777

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The total Cost of a bench is 1.008x.

According to the statement,

We have to find that the cost of the bench.

So, For this purpose, we know that the

The cost function may be accustomed find the typical cost, which is that the average amount of cash it costs to provide a unit.

From the given information:

The owner of the outdoor furniture center decides to use the 120% markup. at the tip of the season, he wants to sell all the benches that are available. he sells the benches for 20% off.

Then

Since we've provided that

Let the price price be 'x'.Mark up % = 120%

So, price value would be 120x/100

Then

Discount % = 20%

Amount of discount is given by

20* 1.2x/1000.

24x

So, it becomes,

Amount after discount is given by

1.2x - 0.24x = 0.96x

Amount of sales tax would be

100+5/100*0.96x

105/100*0.96x

1.008x.

So, The total Cost of a bench is 1.008x.

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The quotient that best represents the rate of change in the mountain goat’s elevation is 2.27 feet/minute.

Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

The rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Mathematically, the rate of change can be calculated by using this formula;

Rate of change = Δy/Δx = Change in height/Change in time

Substituting the given parameters into the formula, we have;

Rate of change = Quotient = 50 feet/22 minutes

Rate of change = Quotient = 2.27 feet/minute.

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The numerical expression using commutative property of multiplication that is equivalent to 2⁸ is 2² x 2² x 2² x 2² = 256.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Now the given exponent is,

2⁸

Now, 8 can be written as using associative property of addition,

8 = 2 + 2 + 2 + 2

Thus we can write,

2⁸ = 2^( 2 + 2 + 2 + 2 )

Using exponential property

x^(a + b) = x^a . x^b

Thus we get,

2⁸ = 2^2 . 2^2 . 2^2 . 2^2

Thus numerical expression for 2^8 = 2^2 . 2^2 . 2^2 . 2^2

Solving we get,

2^8 = 4 x 4 x 4 x 4 = 256

Thus, the numerical expression using exponential property of multiplication that is equivalent to 2⁸ is 2² x 2² x 2² x 2² = 256.

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[tex]{\huge\color{red}{\boxed{\fcolorbox{green}{black}{꧁ANSWER ꧂}}}}[/tex]

A stem and leaf plot is a simple kind of graph that is made out of the numbers themselves.

It is a means of displaying the main features of a distribution.

If a stem and leaf plot is turned on its side.

it will resemble a bar graph or histogram and provide similar visual information.

Answer:

A stem and leaf plot is a simple kind of graph that is made out of the numbers by their selves.

answer: x=3

5(3x+2)+7=6+2(3x−8)

1: Simplify both sides of the equation.

5(3x+2)+7=6+2(3x−8)

(5)(3x)+(5)(2)+7=6+(2)(3x)+(2)(−8)(Distribute)

15x+10+7=6+6x+−16

(15x)+(10+7)=(6x)+(6+−16)(Combine Like Terms)

15x+17=6x+−10

15x+17=6x−10

2: Subtract 6x from both sides.

15x+17−6x=6x−10−6x

9x+17=−10

3: Subtract 17 from both sides.

9x+17−17=−10−17

9x=−27

4: Divide both sides by 9.

9x/9=-27/9

x=−3

The number of coupons send by new club to existing members are 64.

For the given conditions in the question.

Let the existing number be 'x'.

3 times the number means do the multiplication of number by 3.

= 3x.

3 times as many to potential members than to existing members.

Thus,

3x = 192

x = 192/3

x = 64

Thus, the number of existing members are found to be 64.

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[tex]23^8\cdot 23^n=(23^5)^3\implies \underset{same~base}{\stackrel{same~exponent}{23^{8+n}=23^{(5)(3)}}}\implies 8+n=(5)(3) \\\\\\ 8+n=15\implies n=7[/tex]

Answer:

-12

Step-by-step explanation:

putting value of n in the equation will give you the answer

Answer:

C I think would be the answer.

Answer:

9 x x

Step-by-step explanation:

commutative property just means you can switch the numbers around

Answer:

Step-by-step explanation:

1. 170, 13 7/8, 13.5, 64/5

2. Plant D = 5.2 in Plant B =5.3 in Plant C = 5.5in Plant A =5.92

3. Chelsea, Finn, Erin, Mitchell

Answer:

[tex]x = 14[/tex]

Step-by-step explanation:

[tex](6-x)-(x-5)-(4-x)=-\frac x2 \text{ // Distribute}\\\to 6 - x - x + 5 - 4 + x = -\frac x2 \text{ // Simplify}\\\to 7 - x = -\frac x2 \text{ // Multiply by 2}\\\to 2(7 - x) = 2(-\frac x2) \text{ // Distribute}\\\to 14 - 2x = -x \text{ // Add 2x}\\\to 14 = x[/tex]

Answer:

Step-by-step explanation:

so 2.4 nails per second, multiply it by 60 (60 seconds in a minute) =144 so 144 nails per minute. 144 nails per minute times 60 minutes is 8640 nails per hour. If it’s running for 3 days non-stop it would be 72 hours, so 8640 multiplied by 72 (hours) 622,080 nails would be the total in 3 days.

Answer: P = 4x + 2, A = x² + x - 6

Step-by-step explanation:

       Perimeter is the distance around a shape, or all the sides added together. We will create an equation, plug in the known values, and then solve. The first step is to distribute, then we combine like terms.

   P = 2l + 2w

   P = 2(x + 3) + 2(x - 2)

   P = 2x + 6 + 2x - 4

   P = 4x + 2

       The area of a rectangle is found by multiplying the width by the length. We will use the FOIL method.

A = (x + 3)(x - 2)

A = x² + x - 6

First ➜ x * x = x²

Outside ➜ x * -2 = -2x

Inside ➜ 3 * x = 3x

Last ➜ 3 * -2 = -6

Add together ➜ x² + 3x - 2x - 6 = x² + x - 6

Based on the change in the temperature of the city over the 4-week period, the expression to show the average change in temperature each week is -20 / 4

When the expression is simplified, the result if -5°C which means that the temperature reduced by 5°C every week.

The average temperature change of the city each week can be found by:

= Total change in temperature / Number of weeks

Solving gives:

= -20 / 4

= -5°C

This means each week for the 4-week period, the temperature of the city decreased by 5°C.

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Using the calorie count C for a serving of food C=4h+7f+5​p, the formula for f is derived to be f =( C - 4h - 5p ) / 7

Given data

C = 4h + 7f + 5​p

C is the calorie count

h is the number of grams of carbohydrate

f is the number of grams of fat

p is the number of grams of protein

solving for f in the given equation

C = 4h + 7f + 5​p

make f the subject of formula

C - 4h - 5p = 7f

7f = C - 4h - 5p

dividing through by 7

f =( C - 4h - 5p ) / 7

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Answer:

[tex] \frac{2}{x {}^{4} } [/tex]

Step-by-step explanation:

[tex]1. \: \frac{32}{16} \times \frac{x {}^{3} }{x {}^{7} } \\ 2. \: 2 \times \frac{x {}^{3} }{x {}^{7} } \\ 3. \: 2x {}^{3 - 7} \\ 4. \: 2x {}^{ - 4} \\ 5. \: 2 \times \frac{1}{x {}^{4} } \\ 6. \: \frac{2}{x {}^{4} } [/tex]

The equation which can be used to find x is, [tex]\bold{\frac{1}{x} =\frac{1}{14} +\frac{1}{10} }[/tex]

The time taken by Franklin to make a 200 sq. foot cement patio = 14 hours

The time taken by Scott to make a 200 sq. foot cement patio = 10 hours.

Let x be the number of hours it would take Franklin and Scott to make the patio together.

Then x = 14 x 10 / (14 + 10)

⇒ 1 / x = (14+10)/(14 x 10)

⇒ 1/x = 1/14 +1/10

This is the equation to find the number of hours taken by Franklin and Scott together.

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Answer:

C

Edge2020

Step-by-step explanation:

The volume of the square pyramid that has a side length of 7 and a height of 21 is calculated as: 343 units³.

A square pyramid is a type of pyramid that has a square base and four triangular faces.

The volume of a square pyramid can be calculated using the formula expressed as:

Volume (V) = 1/3(a²)(h), where a is the length of a side and h is the height of the square pyramid.

Given:

Side length (a) = 7 units

Height of the square pyramid = 21 units

Substitute

Volume (V) = 1/3(7²)(21)

Volume (V) = 1/3(49)(21)

Volume (V) = 1(49)(7)

Volume = 343 units³

Therefore, the volume of the square pyramid that has a side length of 7 and a height of 21 is calculated as: 343 units³.

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the temperature will be 2.5 degrees per second.

We are given the data:

Seconds       Temperature (°F)

0                            75

10                          100

20                         125

30                         150

We need to find the temperature in degrees per second.

So, we get that:

Seconds       Temperature (°F)                    degrees / sec

0                            75                                            Nil

10                          100                           (100 - 75) / (10 - 0) = 2.5

20                         125                         (125 - 100) / (20 - 10) = 2.5      

30                         150                         (150 - 125) / (30 - 20) = 2.5            

Therefore, the temperature will be 2.5 degrees per second.

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Answer:

x - y - 1 = 0

Step-by-step explanation:

Using y-intercept

b = y - m × x

b = 7 - (1) × (8) = -1

y = mx + b/Flip expression, subtracting from all sides

assuming x ≠ 0 for x = 1

assuming y = 0

y = x - 1

x - y - 1 = 0

The circle below has a sector 120° shaded. 120° 22. Then area of sector is 200.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Area of sector=theta/360*πr^2

Given π = 7,

theta=120 degrees

d=22, so r=11.

Area of sector=210/360*7*7^2

=0.583*7*7*7

=200.08

Therefore area of sector is 200.

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The final cost of the book is 9.12

A sales tax is one that is levied on both the selling of products and services to businesses and on the purchases of those same goods and services by consumers. It's a form of consumption tax, which means it charges consumers for their purchases. Because sales taxes are typically passed on to customers at the moment of sale, it is classified as a consumption tax.

Solving the question:

Cost of the book = 9.95

Sale tax rate = 9%

Sale tax amount on 9.95 = 9.95/(9/100) = 9.12

Therefore, the final cost of the book is  = 9.12

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The final cost of the book is 9.12

A sales tax is one that is levied on both the selling of products and services to businesses and on the purchases of those same goods and services by consumers. It's a form of consumption tax, which means it charges consumers for their purchases. Because sales taxes are typically passed on to customers at the moment of sale, it is classified as a consumption tax.

Solving the question:

Cost of the book = 9.95

Sale tax rate = 9%

Sale tax amount on 9.95 = 9.95/(9/100) = 9.12

Therefore, the final cost of the book is  = 9.12

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Answer: The answer for this question is x=1

Step-by-step explanation: -3(2x-3)=-6x+9 first you multiply -3x with 2x and -3 to get -6x+9=-6x+9 then subtract nine from both sides to leaves -6x=-6x then you divide -6 on both sides and you get x=1.

Any value of x makes the equation true. All real numbers

Interval Notation: (−∞,∞)

Because if you solve it

-3(2x-3)=-6x+9

distribute

-6x + 9 = -6x + 9

subtract 9 from both sides

-6x = -6x

simplify

0 = 0

If we expand the expression [tex]log_{10}[/tex] m⁴ n⁻², then we will get

4m-2n.

Given that the expression is [tex]log_{10}[/tex] m⁴ n⁻²

We are required to find the expansion value of the expression.

The change of base formula is basically the formula which will give us the answer of a log with a different base by using only log calculations with a base of 10.

The expression or function is [tex]log_{10}[/tex] m⁴ n⁻².

(We know that log mn=log m +log n)

So,

[tex]log_{10}[/tex] m⁴ n⁻² =4m-2n  (log [tex]a^{b}[/tex]=b log a)

Hence if we expand the expression [tex]log_{10}[/tex] m⁴ n⁻², then we will get

4m-2n.

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A possible real world scenario is that the product of your score in mathematics test and 16 is 8 more than the product of your score in mathematics test and 14

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

16x = 14x + 8

In the above equation, the variable of the equation is x while the number 8 is a constant

A possible real world scenario is that:

The product of your score in mathematics test and 16 is 8 more than the product of your score in mathematics test and 14

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694 divided by 41 is  16 remainder 38.

A division is a process of splitting a specific amount into equal parts.

given:

694÷41 is equal to 10+3+2+1

Now, performing the division

41  | 694  | 1 6

     - 41

__________

        284

         246

-___________

         38

So, when 694 is divided by 41 gives remainder 38.

Hence,  694 divided by 41 is  16 remainder 38.

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Answer:

D

Step-by-step explanation:

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