Rational exponents: Products and quotients Simplify the expression. (a^(-(1)/(2)))/(a^(-(1)/(8)))

The surface area of the pyramid. A drawing of a square pyramid. The length of the base is 4.5 meters is 74.25 square meters.

To find the area of ​​a pyramid, we need to find the area of ​​the square base and the areas of the four triangular faces, then add them together.

Calculate the area of ​​the base of the square:

The area of ​​the square is the length of one side multiplied by itself, so the area of ​​the base of the square is 4.5 x 4.5 = 20 .25 square meters.

Find the area of ​​each triangle face:

The area of ​​a triangle is the base times the height divided by 2, so the area of ​​each triangle face is 0.5 x 4.5 x 6 = 13.5 square meters.

Add the area of ​​:

The area of ​​the pyramid is the sum of the areas of the square base and the four triangular faces, so the area is 20.25 + 4 x 13.5 = 20.25 + 54 = 74.25 square meters.

The area of ​​the pyramid is therefore 74.25 square meters.

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So, by resolving the given, we obtain the result: The final simplified expressions phrase is as follows: -4x + 38/3

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Let's start by condensing the first expression:

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

Now, we may reformat the phrase as follows:

(2x - 2/3) + 4x + 9 - 10x + 5

Mixing related concepts gives us:

-4x + 38/3

The final simplified phrase is as follows:

-4x + 38/3

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Answer:

Step-by-step explanation:

Make a model

Answer: The answer is 9/25. (36%)

Step-by-step explanation:

Since we know that 7/25 workers walk and 2/25 walk, we can do simple addition to find the total Percentage. This equals 9/25. To find the percentage, do the following:

Write 9/25 into a percentage: Divide

9 / 25 x (100%) = 36%

0.36 (100%) = 36%

Therefore 36% is your answer.

Answer:

vertex = (2, - 10 )

Step-by-step explanation:

given a quadratic function in standard form

ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

x² - 4x - 6 ← is in standard form

with a = 1 and b = - 4 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{-4}{2}[/tex] = 2

substitute x = 2 into the function for corresponding y- coordinate

2² - 4(2) - 6

= 4 - 8 - 6

= - 10

vertex = (2, - 10 )

The correct answer is c. 1/x^2 - 2/x + 1.

To find f(g(x)), we need to plug in the function g(x) into the function f(x).

f(x) = x^2

g(x) = 1/x-1

So, f(g(x)) = (1/x-1)^2

Using the distributive property, we can expand this expression:

f(g(x)) = (1/x-1)(1/x-1)

f(g(x)) = 1/x^2 - 1/x - 1/x + 1

f(g(x)) = 1/x^2 - 2/x + 1

Therefore, the correct answer is c. 1/x^2 - 2/x + 1.

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The value of x is approximately 2,04,582.80.

An expression is a mathematical phrase that can contain numbers, variables, operators, and functions. It can be a combination of terms and can include operations such as addition, subtraction, multiplication, division, and exponentiation.

Given,

Value of old car = 1,50,000

Price of new car = 6,50,000

Number of monthly installments = 20

Amount of each installment = 21,000

Rate of interest offered = 9% p.a.

Let x be the down payment amount.

The total amount to be paid by Madhu for the new car will be equal to the sum of the down payment and the total of 20 monthly installments.

Total amount = x + 20 × 21,000

Since the rate of interest is 9% p.a., the effective rate of interest for 20 months can be calculated as follows:

Effective rate of interest for 20 months = (1 + 0.09/12)^20 - 1 = 0.86118985

So, the total amount to be paid by Madhu for the new car can be expressed as follows:

Total amount = x + 20 × 21,000 × 0.86118985

According to the problem, Madhu exchanged her old car valued at 1,50,000 with the new car priced at 6,50,000. Therefore, the down payment x can be calculated as follows:

x + 20 × 21,000 × 0.86118985 = 6,50,000 - 1,50,00

x + 20 × 21,000 × 0.86118985 = 5,00,000

x= 5,00,000 - 20 × 21,000 × 0.86118985

x ≈ 2,04,582.80

Therefore, the value of x is approximately 2,04,582.80.

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Answer: C

Step-by-step explanation:  8.95x2=17.9,  3/4x12.80=9.6,  17.9+9.6+5.85=33.35. 33.35+1.65=35

The percent of the clothe required to make doll outfit as per given cost price and selling price is equal to 59.91%.

Cost price of the material for one outfit = $9.38

Selling price of the outfit = $15

Selling price is greater than cost price

⇒Profit = Selling Price - Cost price

Substitute the value to get profit,

⇒ Profit = $15 - $9.38

⇒ Profit = $5.62

Percent Markup = (Profit / Cost price ) x 100

Substitute the value we get,

⇒Percent Markup = ($5.62 / $9.38) x 100

⇒Percent Markup = 59.9147%

⇒Percent Markup = 59.91

Therefore, the percent markup of the making doll outfit is approximately 59.91%.

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The above question is incomplete, the complete question is:

Keri is making a doll clothes for a holiday craft show. The wholesale cost of the materials for one outfit is $9.38. If she sells an outfit for $15, what is the percent of the markup?

Therefore, -3/5x + 4/5 is the expression that represents the outcome of applying the distributive principle to 1/5(3x+4).

An expression in mathematics is a grouping of digits, variables, and mathematical signs (like +, -, +, +, and =) that denote a mathematical relationship or computation. Expressions can be made up of a single number or variable or they can be intricate arrangements of different words and mathematical processes.

given

According to the distributive principle, a(b + c) = ab + ac. We can distribute the 1/5 to both terms inside the parentheses in order to apply the distributive principle to the expression 1/5(3x+4):

1/5(-3x + 4) = 1/5(-3x) + 1/5(4) (4)

If we simplify, we get:

1/5(-3x) + 1/5(4) = -3/5x + 4/5

Therefore, -3/5x + 4/5 is the expression that represents the outcome of applying the distributive principle to 1/5(3x+4).

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The decimal (base-10) equivalent of the binary (base-2) value (111)_(2) is (7)_(10).

To convert a binary (base-2) value into its decimal (base-10) equivalent, we need to multiply each digit in the binary value by the corresponding power of 2, and then add the results together.

Here is how to do it step-by-step for the given binary value (111)_(2):

1. Start with the rightmost digit (the least significant bit) and work your way to the left:
(1 * 2^0) + (1 * 2^1) + (1 * 2^2)

2. Simplify the powers of 2:
(1 * 1) + (1 * 2) + (1 * 4)

3. Multiply the digits by the powers of 2:
1 + 2 + 4

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Answer:

36

Step-by-step explanation:

bbecause yes and because a put in my quiz and they put me a A

Answer:

10 tonnes = 6 trucks, 5 tonnes = 2 trucks

Step-by-step explanation:

Total number of trucks = 8

Let number of trucks carrying 10 tonnes = x

then number of trucks carrying 5 tonnes = 8 - x

We can represent this situation as follows:

10x + 5(8 - x) = 70 tonnes

10x + 40 - 5x = 70

5x + 40 = 70

5x = 30

x = 6

Number of trucks with 10 tonnes capacity = 6

Number of trucks with 5 tonnes capacity = 2 (i.e; 8-x = 8-6)

Hope it helps.......

Answer:

Step-by-step explanation:

A cylinder has a base diameter of 12 foot and a height of 12 foot what is its volume in cubic feet to the nearest 10s place

The volume of a cylinder can be calculated using the formula:

V = πr^2h

where:

V is the volume of the cylinder

π is a mathematical constant, approximately equal to 3.14159

r is the radius of the base of the cylinder

h is the height of the cylinder

We are given the diameter of the base, which is 12 feet. The radius (r) is half of the diameter, so we have:

r = 12/2 = 6 feet

The height (h) is also given as 12 feet.

Substituting the values we have into the formula, we get:

V = π(6)^2(12) ≈ 1357.17

Rounding to the nearest 10's place, the volume is approximately 1360 cubic feet. Therefore, the volume of the cylinder is 1360 cubic feet to the nearest 10's place.

The vertex of the function is (-3, -20), the axis of symmetry is x = -3, the x-intercepts are (-8.44, 0) and (1.44, 0), the y-intercept is (-11), the range is (-∞, -20], and the domain is (-∞, ∞).

To find the vertex, axis of symmetry, x-intercept, y-intercept, range, and domain of the function f(x) = x² + 6x - 11, we can use the following formulas:

- Vertex: (-b/2a, f(-b/2a))

- Axis of symmetry: x = -b/2a

- X-intercept: Solve f(x) = 0

- Y-intercept: f(0)

- Range: All real numbers for a parabola that opens up or down

- Domain: All real numbers


Using these formulas, we can find the following:

- Vertex: (-3, -20)

- Axis of symmetry: x = -3

- X-intercept: (-8.44, 0) and (1.44, 0)

- Y-intercept: (-11)

- Range: (-∞, -20]

- Domain: (-∞, ∞)


Therefore, the vertex of the function is (-3, -20), the axis of symmetry is x = -3, the x-intercepts are (-8.44, 0) and (1.44, 0), the y-intercept is (-11), the range is (-∞, -20], and the domain is (-∞, ∞).

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Answer: y = 5/6x

Step-by-step explanation:

It is a direct variation.

The scores of students were normally distributed.

a)Approximately 68% of the students scored between 40 and 62 .

b) The approximately 95% of the students scored between 29 and 73.

We have a nationwide test taken by high school students, Mean score, μ = 51

Standard deviations, s = 12

The scores were normally distributed, that is

X~ N(M= 51, s = 12)

Lower bound of confidence interval= 40

Upper bound of CI = 62

As we know according to empirical rule the percentage of data falls within one,two and three

standard deviations are 68%,95% and 99.7%

respectively.

a) Mean + standard deviations = 51 + 12 = 63 close to 62

= Upper bound

For 2 standard deviations, 51 + 2×12 = 75

Mean - standard deviations= 51 - 12 = 39 close to 40 = lower bound

For 2 standard deviations, 51 - 2×12 = 27

Thus, data falls within one standard deviation

that is under 68% and so, approximately 68% of students scored between 40 and 62.

b) Similarly, the empirical rule demonstrates that 95% of scores falls within two standard deviation.

mean - 2× standard deviations= 51 - 2× 11

= 51 - 22 = 29

mean + 2× standard deviations= 51 + 2×11

= 51 + 22 = 73

Therefore, approximately 95% of students scored

between 29 and 73.

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Complete question:

On a nationwide test taken by high school students, the mean score was 51 and the standard deviation was 11

The scores were normally distributed. Complete the following statements.

(a) Approximately ?% of the students scored between 40 and 62 .

(b) Approximately 95% of the students scored between ? and ?

The equation of the line in slope-intercept form is y = -x + 1

To write an equation for the line in point-slope form, we can use the formula y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

Since the x-intercept and y-intercept are both 1, we know that the line passes through the points (1,0) and (0,1).

To find the slope of the line, we can use the formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates of the two points, we get:

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

Now we can plug in the slope and one of the points into the point-slope form equation:

y - 0 = -1(x - 1)

Simplifying, we get:

y = -x + 1

This is the equation of the line in point-slope form.

To write the equation in slope-intercept form, we can use the formula y = mx + b, where m is the slope of the line and b is the y-intercept.

We already found the slope to be -1, and the y-intercept is given as 1. So we can plug these values into the slope-intercept form equation:

y = -1x + 1

Simplifying, we get:

y = -x + 1

This is the equation of the line in slope-intercept form.

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Marco will need 2025 pounds of marble.

The ratio is defined as the relationship between two similar magnitudes in terms of the number of times the first includes the second.

Let's say that Marco mixes 1 bag of quartz with x pounds of marble. Then the ratio of quartz to marble in this bag is:

135 pounds quartz : x pounds marble

3 pounds quartz : x/45 pounds marble

Now we know that the ratio of quartz to marble in one bag is 3: (x/45). Since the ratio stays the same for every bag, we can set up a new proportion using the total amount of quartz and marble:

135 pounds quartz : x pounds marble = total pounds quartz : total pounds marble

We know the total pounds of quartz is 135. Let's call the total pounds of marble "m".

Substituting these values into the proportion, we get:

135 : x = 135 : m/45

To solve for x, we can cross-multiply and simplify:

135(m/45) = 135x

3m = 45x

m = 15x

So, Marco will need 15 times as many pounds of marble as he has of quartz, or:

m = 15 × 135 = 2025 pounds of marble.

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Given:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

The interest earned on a deposit of $18,000 for five years at 5% APR compounded semiannually.

To calculate the interest earned on a deposit of $18,000 for five years at 5% APR compounded semiannually, we will use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

Plugging in the given values:

A = 18,000(1 + 0.05/2)^(2*5)

A = 18,000(1.025)^10

A = 23,386.28

To find the interest earned, we subtract the initial investment from the final amount:

Interest earned = A - P

Interest earned = 23,386.28 - 18,000

Interest earned = $5,386.28

Therefore, the interest earned on a deposit of $18,000 for five years at 5% APR compounded semiannually is $5,386.28.

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d

2/3 is the same as 4/6 and 25/100 is the same as 1/4. -1.3 is transferred to the beginning of the equation

The exact value of cos(5π/12), using the cosine summation identity, is (√6 - √2)/4.

The exact value of cos(5π/12) can be found using the cosine sum identity, which is:

cos(a + b) = cosa · cosb - sina · sin b

In this case, we can rewrite 5π/12 as (π/4) + (π/6) and use the identity:

cos(5π/12) = cos[(π/4) + (π/6)] = cos(π/4) · cos (π/6) - sin(π/4) · sin (π/6)

Using the values of cos(π/4) = √2/2, cos(π/6) = √3/2, sin(π/4) = √2/2, and sin(π/6) = 1/2, we can plug them into the equation:

cos(5π/12) = (√2/2) · (√3/2) - (√2/2) · (1/2) = √6/4 - √2/4 = (√6 - √2)/4

Therefore, the exact value of cos(5π/12) is (√6 - √2)/4.

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This equation has two solutions: λ = 0 and λ = -1

The determinant of a matrix is given by the formula:

det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)

In the given matrix, the values of a11, a22, and a33 are λ, (λ+1), and λ respectively. The values of a12, a13, a21, a23, a31, and a32 are all 0. Substituting these values into the formula for the determinant gives:

det(A) = λ((λ+1)λ - 0) - 0(0 - 0) + 0(0 - 0) = λ^3 + λ^2

To find the values of λ for which the determinant is zero, we can set the determinant equal to zero and solve for λ:

λ^3 + λ^2 = 0
λ^2(λ + 1) = 0

This equation has two solutions: λ = 0 and λ = -1. Therefore, the values of λ for which the determinant is zero are 0 and -1. The answer can be written as a comma-separated list as follows:

λ = 0, -1

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The formula for the nth term of the sequence is:

an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3

To find the formula for the nth term of the sequence 4, 15, 44, 109, 228, 419,... using polynomial fitting, we need to follow the following steps:

1. Identify the degree of the polynomial: Since the sequence has 6 terms, the degree of the polynomial is 5.

2. Create a system of equations: Use the given terms of the sequence to create a system of equations with the polynomial coefficients as unknowns.

3. Solve the system of equations: Use any method to solve the system of equations to find the values of the polynomial coefficients.

4. Write the formula for the nth term: Use the values of the polynomial coefficients to write the formula for the nth term of the sequence.

The system of equations is:
a5n^5 + a4n^4 + a3n^3 + a2n^2 + a1n + a0 = an

Plugging in the values of the terms of the sequence, we get:
a5(1)^5 + a4(1)^4 + a3(1)^3 + a2(1)^2 + a1(1) + a0 = 4
a5(2)^5 + a4(2)^4 + a3(2)^3 + a2(2)^2 + a1(2) + a0 = 15
a5(3)^5 + a4(3)^4 + a3(3)^3 + a2(3)^2 + a1(3) + a0 = 44
a5(4)^5 + a4(4)^4 + a3(4)^3 + a2(4)^2 + a1(4) + a0 = 109
a5(5)^5 + a4(5)^4 + a3(5)^3 + a2(5)^2 + a1(5) + a0 = 228
a5(6)^5 + a4(6)^4 + a3(6)^3 + a2(6)^2 + a1(6) + a0 = 419

Solving this system of equations, we get:
a5 = 1
a4 = -5
a3 = 9
a2 = -7
a1 = 3
a0 = 3

Therefore, the formula for the nth term of the sequence is:
an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3

So, the formula for the nth term of the sequence 4, 15, 44, 109, 228, 419,... using polynomial fitting is an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3.

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The expressions ordered from least to greatest are: -2 < b < (a + c)

In maths, an expressiοn is a cοmbinatiοn οf numbers, variables, functiοns (such as additiοn, subtractiοn, multiplicatiοn οr divisiοn etc.)

Expressiοns can be thοught οf as similar tο phrases. In language, a phrase οn its οwn may include an actiοn, but it dοesn't make a cοmplete sentence.

According to the question:

-1 < a < 0

2 < b < 3

4 < c < 5

Now, we have the expression a + c

= (-1 < a < 0) + (4 < c < 5)

= (-1 + 4) < (a + c) < (0 + 5)

= 3 < (a + c) <  5

Thus, we have the expressions ordered from least to greatest are:

-2 < 2 < b < 3 < (a + c) <  5

-2 < b < (a + c)

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Complete question:

The rate of consumption of fuel of Matt's car is 37 miles per gallon (mpg).

Matt's car can travel a total distance of 555 miles.
The fuel required to travel the total distance is 15 gallons by Matt's car.
Hence the rate of consumption of fuel of Matt's car can be measured in mpg (miles per gallons) as = Total distance travelled / Total gallons required to travel that distance
(that is, total distance travelled divided by the total amount of gallons to travel the same)
Thus the mpg of Matt's car is = 555 miles / 15 gallons
= 37 miles per gallon
(that is 37 mpg)

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The correct answer is option C. Only Table 1 and Table 3 represent a function.

Each input value should be paired with only one output value, as stated in the definition of a function. Therefore, we must verify that each input value is paired with only one output value in order to determine which tables represent a function.

For each input value, Table 1 contains unique output values and unique input values. As a result, a function is represented by Table 1.

For the same input value (input 1), there are two distinct output values in Table 2. As a result, there is no function represented in Table 2.

For each input value, Table 3 contains unique output values and unique input values. As a result, a function is represented by Table 3.

For the same input value (input -2) in Table 4, there are two distinct output values. Subsequently, Table 4 doesn't address a capability.

Consequently, c is the correct response because Tables 1 and 3 only depict functions.

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Complete Question:

Which table(s) represent(s) a function? A. Table 1 only B. Table 2 only C. Tables 1 and 3 only D. Tables 1, 3, and 4 only