Use unit multipliers to convert:
481 centimeters
to meters

Answer: 20%

Step-by-step explanation:

In functions, value of x = 45 and y = 45

What is function in math?

6)  x = 15

 y = 49

3x = 3 * 15 = 45

y - 4 = 49 - 4 = 45

7)  3x + 23 = 4x

    4x - 3x = 23

     x = 23

    y =  4 * 23 =   92°

8) y + 12 = 5x °

  3x + 50  =

According to the question

     y + 12 = 3x  + 50

      5x   = 3x + 50

      2x = 50

        x = 25

y + 12 = 5x °

y = 5 * 25 - 12

y = 125 - 12 =   113

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The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

C) $3.77

Step-by-step explanation:

Answer:

The Answer is 16

Step-by-step explanation:

The three angles enclosed in a triangle, made by its sides, are called its internal angles. The sum of internal angles of a triangle is

180

o

. Based on its internal angles, a triangle can be classified as acute angled, right angled and obtuse angled.

Your Welcome! :)

The sum of the measure of angle of a triangle = 180° .

Given two angles = 92° and 72°

_________________________

92° + 72° = 164°

180° - 164° = 16° (Ans)

The overall change for the week in the Dow Jones Industrial Average was -304.

To calculate the overall change for the week, we need to sum up the daily changes. Given the daily changes of 16, -28, -288, -17, and 13, we add them together:

16 + (-28) + (-288) + (-17) + 13 = -304.

The negative sign indicates a decrease or loss in value. Therefore, the overall change for the week in the Dow Jones Industrial Average is -304, indicating a net decrease in value over the course of the week.

It's worth noting that the overall change could also be represented as a percentage change or as a percentage gain/loss based on the starting value of the index. However, based on the given information of daily changes, the total change for the week is -304.

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The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Jimmy may purchase \(820\) roses for $\(0.80\) each, which is an inequality.

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in lieu of the equals sign. That is an illustration of inequality. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

Throughout the recent past, wealth disparity in India has grown, with the wealthy gap ranking among the widest among various comparable nations. According to household polls, inequality may have decreased slightly along with the recent slowdown in growth.

\(r = (5000 - [(5000 * 0.3) + (4000 * 0.6) + (300 * 0.25)])0.8\)

\(r = (5000 - [1500 + 2400 + 75])0.8\)

\(r = (5000 - 3975)0.8\)

\(r = 1025(0.8)\)

\(r = 820\)

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Answer:

\(\$56.25\)

\(\$9\)

8

\(8.2\ \text{pounds}\)

Step-by-step explanation:

Jonah earns $12.50 per hour

He works for 4.5 hours

Amount he earned

\(12.5\times 4.5=\$56.25\)

Amount Jonah earned is \(\$56.25\).

Items worth is $41.23

Amount paid is $50.23

Extra amount paid

\(50.23-41.23=\$9\)

Jessica paid \(\$9\) extra.

Length of cloth available is 20 m

Length of one long-sleeved blouse is 2.5 m

Number of blouses that can be made

\(\dfrac{20}{2.5}=8\)

Number of blouses that can be made from the material is 8.

Potatoes weight is 3.2 pounds

Oranges weight is 2.3 pounds

Onions weight is 2.7 pounds

Total weight of the purchase

\(3.2+2.3+2.7=8.2\ \text{pounds}\)

The weight of the purache is \(8.2\ \text{pounds}\).

Answer:

Jonah - 56.25

Jessica - 9

Josie - 8

Jeremy - 8.2

Step-by-step explanation:

I got this answer correct on my test for edmentum

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

The given equation is 4x+2 = 12.

To solve for x using the change of base formula, we need to isolate x on one side of the equation. We start subtracting 2 from LHS and RHS:

4x+2-2 = 12-2

4x = 10

Next, we use the change of base formula, which states log base a of b is equal to log base c of b divided by log base c of a. In this case, we want to find x, which is the exponent that 4 is raised to in order to get 10.

Rewrite equation:

x = log base 4 of 10

Use the change of base formula, we can present this as:

x = \(log base 10 of 10 / log base 10 of 4\)

Simplifying:

x = 1.442114

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

In conclusion, using the change of base formula, the answer to the equation 4x+2 = 12 is roughly 1.442114. This method can be used to solve a variety of problems in the sciences, engineering, and financial sectors, as well as exponential and logarithmic equations.

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Answer:

Below

Step-by-step explanation:

f(1)    -  2 = a(1) + b

        - 2 = a + b             (1)

f(5)     10 = a (5) + b

          10 = 5a + b            (2)

Multiply first underlined equation by -5  to get

      10 = -5a  - 5b       add this to the second equation (this will eliminate 'a')

      20 = - 4 b       so   b = -5

then the first equation becomes   - 2 = a +  (-5)

             which shows a = 3

so your function is just    f(x) = 3x  -5

Answer:

64

Step-by-step explanation:

first, we'll start with the value inside the parenthesis, which is 2³

2³ means to multiply 2 by itself 3 times

so it would be

2×2×2=8

which then means that the expression is now (8)²

now we need to do (8)², which is to multiply 8 by itself twice

8*8=64

hope this helps!

The formula for the function's inverse is

(a) f⁻¹(y) = Iny/In(0.7)

(b) f⁻¹(y) = [Iny - In(4.5)]/In(2.7)

(a) The function is;

f(x) = 0.7ˣ where y = f(x).

So y = 0.7ˣ

Taking In on both side,

Iny = x In(0.7)

Divide by In(0.7) on both side, we get

x = Iny/In(0.7)

f⁻¹(y) = Iny/In(0.7)

(b) The function is;

f(x) = 4.5(2.7)ˣ where y = f(x).

So y = 4.5(2.7)ˣ

Divide by 4.5 on both side, we get

y/4.5 = (2.7)ˣ

Taking In on both side,

In(y/4.5) = In(2.7)ˣ

Iny - In(4.5) = xIn(2.7)

Divide by In(2.7) on both side, we get

x = [Iny - In(4.5)]/In(2.7)

f⁻¹(y) = [Iny - In(4.5)]/In(2.7)

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The complete question is:

For each of the following functions, write the formula for the function's inverse.

a. f(x) = 0.7ˣ where y = f(x).

f⁻¹(y) =

b. f(x) = 4.5(2.7)ˣ where y = f(x).

f⁻¹(y) =

Answer:

y=60

Step-by-step explanation:

\(15=\frac{y}{-4} \\(15)*-4=(\frac{y}{-4} )*-4\\-240=y\)

The sοlutiοn οf the given prοblem οf square cοmes οut tο be  0.84% is the shaded area.

A square is a quadrilateral οf fοur equal faces and fοur identical angles accοrding tο Euclidean geοmetry. A shape with adjacent edges that have the same length is anοther name fοr a rectangle. If οne οf a quadrilateral's fοur triangular edges and 4 triangular angles is square, the parallelοgram is deemed tο be equilateral. A linear οr 90 ° angle is referred tο as a cubical angle.

Here,

We must determine the area οf the shaded area and divide it by the area οf the cοmplete square tο determine the prοpοrtiοn οf the square that is shaded.

A sectοr is equal tο (45/360)k²/2 = 0.125k²

Find the regiοn οf triangle BDE next. Triangle BDE is a right triangle, sο we can determine its height using the Pythagοrean theοrem:

=>  BE² + DE² = BD²

=>  BE² + k² = (k√2)²

=>  BE² = 2k² - k²

=>  BE = k√2

Therefοre, the triangle BDE's area is:

=> A(triangle) = (1/2)

=> BE*DE = (1/2)

=> (k√2)(k√2) = k²

Lastly, the area οf the darkened area is equal tο the sectοr's area less the triangle's area:

=> A(shaded) = A(sectοr) - A(triangle) = 0.125πk² - k² ≈ 0.0084k²

Cοnsequently, the amοunt οf the rectangle that is shaded is:

=> percentage = (A(shaded) / A(square)) x 100%

=> ( 0.0084k² / k²) x 100%

=> 0.84%

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Answer:

4 inches

Step-by-step explanation:

Have a nice day!

Answer:

DA is 4 in.

Step-by-step explanation:

The perimeter of parallelogram ABCD = 46 inches.

Let's say that the length of DA =  x

And we know that the length of opposite sides of a parallelogram are congruent, or equal.

So AB and DC are opposite sides and are equal.

AB = DC

8x - 5 = 3x + 10

5x = 15

x = 3

The value of x is 5. Therefore the length of AB is,

AB = 8x - 5 = 8(3) - 5 = 19

AD and BC are opposite sides therefore the lengths of AD and BC are equal.

Perimeter = AB + BC + CD + DA

46  = 2(AB) + 2(AD)

46 = 2(19) + 2(AD)

8  =  2(AD)

AD = 8/2

AD = 4

So the value of AD is 4.

The key driver for the 15-year forecasts of NOPAT (Net Operating Profit After Tax) and Operating Capital requirement in the model is D. Revenue Forecast.

The revenue forecast serves as the primary driver for estimating the future profitability of the business, as it represents the total sales or revenue generated by the company. By forecasting the revenue growth over a 15-year period, we can project the expected level of profitability.

The NOPAT is derived from the operating profit after accounting for taxes. As the revenue forecast directly influences the operating profit, it, in turn, affects the NOPAT. Higher revenue projections typically lead to higher operating profit and subsequently higher NOPAT.

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The standard deviation used to calculate the test statistic for the one-sample z-test is option c, i.e. √(22(78)/200).

Let’s take p as the proportion of students from high school Y who watched the movie on opening night.

Then the sample proportion, ˆp = 22/200 = 0.11

We need to find out whether the proportion of all students in high school Y who saw the movie on opening night is greater than that of high school X. The sample proportion for high school X is 0.09.

We can use a one-sample z-test with the following hypotheses.

H₀: p ≤ 0.09

Hₐ: p > 0.09

The null hypothesis represents the assumption that the proportion of students in high school Y who watched the movie on opening night is less than or equal to that of high school X.

The alternative hypothesis represents the assumption that the proportion of students in high school Y who watched the movie on opening night is greater than that of high school X.We calculate the test statistic, z, as follows:

z = (ˆp - p₀) / σ

Where p₀ = 0.09 and σ is the standard deviation of the sample proportion.

We know that

σ = √[(p₀(1 - p₀)) / n]

Where n = 200.

σ = √[(0.09 x 0.91) / 200]

σ = 0.0274

Therefore,

z = (0.11 - 0.09) / 0.0274 = 0.7299

The p-value for this test is P(Z > 0.7299) = 0.2333

At the 5% level of significance, we fail to reject the null hypothesis since the p-value is greater than 0.05. Thus, we do not have sufficient evidence to conclude that the proportion of all students in high school Y who saw the movie on opening night is greater than that of high school X.

Hence option c is correct.

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Answer:

C(t)=25+2t

C(1.5)=25+2(1.5)=28

$28 for 1.5 minutes rent

A function C(t) represents the cost of renting a canoe for t hours is C(t)=25+2t and the cost for 1.5 minutes will be $28.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given that the rental charge is $25 plus $2 for every 20 minutes of rental.

The function formed for the given data will be:-

C(t)=25+2t

At 1.5 minutes the rent will be calculated as below:-

C(1.5)=25+2(1.5)=28

Therefore, the function C(t) represents the cost of renting a canoe for t hours is C(t)=25+2t, and the cost for 1.5 minutes will be $28.

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Answer:

n = 4

Step-by-step explanation:

Parallel lines will always have the same slope as m1 = m2.

Thus, we have y = 2x + b

While we have the slope for the second line (m = 2), we still need to find the b aka the y-int.

We can plug in point b into the equation to find the y-int:

\(y=2x+b\\8=2(6)+b\\8=12+b\\-4=b\)

To find n, we simply plug in 4 for y and solve for x:

\(y=2x-4\\4=2n-4\\8=2n\\4=n\)

An exponential function is a type of mathematical function where the variable appears in the exponent. It is commonly represented in the form f(x) = a^x, where a is a constant and x is the independent variable. In other words, the function grows or decays at a constant rate, which is determined by the value of a.

 An exponential function can be represented by the equation y = ab^x, where a ≠ 0, b > 0, b ≠ 1, and x is any real number. In this equation:

- 'a' represents the initial value or starting point of the function.
- 'b' is the base, which determines the growth or decay factor.
- 'x' represents the input or independent variable.
- 'y' represents the output or dependent variable.

To determine if a given function is exponential, check if it meets these conditions. An exponential function will have a constant base raised to the power of the input variable, and its graph will show either exponential growth or decay.

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No. For example, thirteen hearts could be selected: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. No two of these are of the same denomination.

What is a denomination?

A denomination is a classification system that identifies the nature or worth of an object. Denomination frequently relates to currency.

Here, we have

13 cards are randomly selected from a standard 52-card deck.

This is not necessary.

All 13 cards may be of different denominations.

At least 2 need not be of the same denomination.

Hence, thirteen hearts could be selected: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. No two of these are of the same denomination.

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Answer:

Step-by-step explanation:

Answer:

(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!) 3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)

Step-by-step explanation:

Statistics indicate that 45% of all small businesses fail after three years. This is a concerning statistic for entrepreneurs who are considering starting their own business.

It is important for potential business owners to understand the reasons why small businesses fail and take steps to mitigate these risks. Some common reasons for failure include poor management, insufficient funding, lack of market demand, and competition.

One way to mitigate these risks is by having a solid business plan in place that includes a realistic assessment of the market, a clear understanding of the competition, and a plan for securing financing. Additionally, having a strong risk tolerance and the ability to adapt to changing market conditions can also increase the chances of success for small businesses.

Ultimately, the key to success for small businesses is a combination of careful planning, strong management, and a willingness to take calculated risks.

One of the contributing factors to this failure rate is the business owner's risk tolerance (3) B), which may lead them to take on more financial obligations than they can handle. Additionally, securing proper financing (4) D) is crucial for the success and growth of a small business, and a lack of adequate funding may contribute to the high failure rate.

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The equation which is graphed in this figure (see attachment) is: C. y + 2 = −3/2(x − 2)

"y plus 4 equals negative fraction 3 over 2 end fraction left parenthesis x minus 2 right parenthesis."

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided about this graph, we have the following data points on its line:

Points on the x-axis = (0, 2).

Points on the y-axis = (1, -2).

At data point (0, 3), a linear equation of the first line can be calculated in slope-intercept form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (-2 - 1)/(2 - 0)(x - 2)

y + 2 = -3/2(x - 2)

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Answer:

$1,320

Step-by-step explanation:

To find the area of the bedroom, you must multiply the length and the width. 15 multiplied by 12 is 180, so the area of the bedroom is 180 square feet. There are three feet in a yard, so you must divide the area of the bedroom in feet by 3 in order to get the area of the bedroom in yards. 180 divided by 3 is 60, so the area of the bedroom is 60 square yards. In order to find how much it will cost to carpet the room, you must multiply the area of the bedroom in yards by how much carpeting costs per square yard. 60 multiplied by 22 is 1,320, so it will cost $1,320 in order to carpet the room.

Answer:

Step-by-step explanation:

V=(1/3)hπr^2

<=> 4487 = 1/3x21πxr^2

<=> r^2 = 641/π

<=> r = squrt( 641/π)

Answer:

a) 10

b) 9.8

Step-by-step explanation:

First, round it the nearest whole number:

9.7814 will round up to 10, since the decimal place .7 is larger than .5

Next, round to one decimal place:

9.7814 will round to 9.8, since the 0.08 will round the 0.7 up to 0.8

a) 10

b) 9.8

The value of A in the 4-digit number, 3A5A is 5.

The 4-digit number provided in the question has to be a multiple of 15 given the information in the question. A multiple of a number is divisible by that number. A multiple of 10 is 100 because when 100 is divided by 10 , the value gotten is 10.

A multiple of a number is the product of an integer and that number. For example, a multiple of 2 is 100. This is because 2 multiplied by 50 is equal to 100.

The multiplies of 15 either have a unit value of 5 or 0.

If A is 5, the number becomes 3555.

3555 / 15 = 237

If A is 0, the number becomes 3050

3050 / 15 = 203.33

Thus, the value of A is 5 because 3555 is divisible by 15.

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