The surface area of a cube may be found using the formula A=6s^2. What is the edge length of a cube with a surface area of 81 cm^2? Round your answer to the nearest tenth.

To break even for her initial expenses, Cara must give at least 50 massages as per the quadratic equation of profit and losses modeled by her.

It is given to us that Cara has modeled her initial profit and losses by the formula

f(x) = -0.1944x² + 29.16x - 972

where,

x = number of 30-minute massages

We have to find out the number of massages she must give to break even for her initial expenses.

The given equation f(x) = -0.1944x² + 29.16x - 972 is in the form of a quadratic equation ax² + bx + c.

The roots of this quadratic equation is given by

\(x_{1} =\frac{-b+\sqrt{b^{2} -4ac} }{2a}\) ----- (1)

and, \(x_{2} =\frac{-b-\sqrt{b^{2} -4ac} }{2a}\) ----- (2)

From the given quadratic equation f(x) = -0.1944x² + 29.16x - 972, we can find out the values of a, b, and c such that -

a = -0.1944

b = 29.16

c = - 972

Substituting these values of a, b, and c in equations (1) and (2), we have

\(x_{1} =\frac{-b+\sqrt{b^{2} -4ac} }{2a}\\= > x_{1} =\frac{-29.16+\sqrt{29.16^{2} -4*(-0.1944)*(- 972)} }{2(-0.1944)}\\= > x_{1} =\frac{-29.16+\sqrt{850.30-755.82} }{-0.3888}\\ = > x_{1} =\frac{-29.16+9.72}{-0.3888} \\= > x_{1} =\frac{-19.44}{-0.3888} \\= > x_{1} =50\)

and,

\(x_{2} =\frac{-b-\sqrt{b^{2} -4ac} }{2a}\\= > x_{2} =\frac{-29.16-\sqrt{29.16^{2} -4*(-0.1944)*(- 972)} }{2(-0.1944)}\\= > x_{2} =\frac{-29.16-\sqrt{850.30-755.82} }{-0.3888}\\ = > x_{2} =\frac{-29.16-9.72}{-0.3888} \\= > x_{2} =\frac{-38.88}{-0.3888} \\= > x_{2} =100\)

Thus, Cara may give 50 or 100 massages. To break even for her initial expenses, Cara must give at least 50 massages as per the quadratic equation of profit and losses modeled by her.

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Answer:

I hope this helps you, now you have to do part c

Step-by-step explanation:

Please refer to the attachment

The multiplicative rate of change for the function  is approximately.

To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.

The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.

Using the chain rule, the derivative of is:

Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is

The value of ln(2/5) is approximately -0.916.

It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.

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A function modeling the volume of the box can be found, and the values of x for which the volume is greater than 230 in2 are x = [-2.636, 2.636]. The largest volume is 480 in2, which is achieved when x = 5.

A function that models the volume V of the box can be found by subtracting four \(x2\)from both the length and the width, and then multiplying the result to get the volume:

V = \((12 - 4x2)(20 - 4x2)\)

To find the values of x for which the volume is greater than 230 in2, we can solve the equation

V = \((12 - 4x2)(20 - 4x2) = 230\) for x.

This gives x values of ±2.636

Thus, the values of x for which the volume is greater than 230 in2 are x = [\(-2.636, 2.636\)].

The largest volume that such a box can have is 480 in2, which is obtained when x is equal to the length or width divided by two. This occurs when x = 10/2 = 5. Thus, the largest volume that such a box can have is 480 in2.

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Answer: 161.28

Step-by-step explanation:

1. 230/48 = 4.79 or 4.8 calories per gram.

2. 33.6 x 4.8 = 161.28 or 161.3

Answer:

$2,482.94

Step-by-step explanation:

\(p {e}^{.09 \times 13} = 8000\)

\(p = \frac{8000}{ {e}^{.09 \times 13} } = 2482.94\)

The measurement is the same for Charles and Jermod are lower quartile and upper quartile. Therefore, options C and D are the correct answer.

From the given dot plot.

The number of minutes Charles spent on homework.

15, 15, 20, 20, 25, 30, 30, 30, 30, 30, 45, 50, 55, 60, 60.

Here, lower quartile = 20

Upper quartile = 50

Median = 30

Range = 60-15

= 45

The number of minutes Jermod spent on homework.

15, 15, 15, 20, 20, 30, 35, 45, 45, 45, 50, 50, 55, 55.

Here, lower quartile = 20

Upper quartile = 50

Median = 45

Range = 55-15

= 40

Therefore, options C and D are the correct answer.

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Answer: 9

Step-by-step explanation:

72÷9=8

9÷9=1

72/9 = 8/1

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

Answer:

it is C

Step-by-step explanation:

Answer:

It is C. An undercover police officer joins a gang in order to observe its members and activities

Step-by-step explanation:

I just recently took the quiz, I hope this helps you. Have an awesome day/night/afternoon!

Answer:

The 95%  confidence interval is

           \( 5.92  <   \mu  <  7.284 \)

Step-by-step explanation:

From the question we are told that

  The data is  6.5   6.7    7.2    6.4    7.3

Generally the sample  mean is mathematically represented as

         \(\= x = \frac{\sum x }{n}\)

=>      \(\= x = \frac{ 5.5 + 6.5 + \cdot 7.3 }{ 6}\)

=>      \(\= x = 6.6\)

Generally the standard deviation is mathematically represented as

         \(\sigma = \sqrt{ \frac{ \sum (x_i - \= x )^2 }{ n-1} }\)

=>      \(\sigma = \sqrt{ \frac{ (5.5 - 6.6 )^2 +(6.5 - 6.6 )^2 + \cdot + (7.3 - 6.6 )^2 }{ 6-1} }\)

=>      \(\sigma = 0.6512\)

Gnerally the degree of freedom is mathematically represented as

         \(df = n- 1\)

=>       \(df = 6 -1\)

=>       \(df = 5\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the t distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(t_{\frac{\alpha }{2} , 5 } = 2.571 \)

Generally the margin of error is mathematically represented as  

      \(E = t_{\frac{\alpha }{2}, 5  } *  \frac{\sigma }{\sqrt{n} }\)

=>    \(E =  2.571  *  \frac{0.6512}{\sqrt{6} }\)

=>    \(E = 0.6835 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x  -E <   \mu  <  \= x  +E\)

=>     \(6.6  - 0.6835 <   \mu  <  6.6  +  0.6835\)

=>     \( 5.92  <   \mu  <  7.284 \)

Answer:9/41

SOH = opposite over hypotenuse

Step-by-step explanation:

Answer:

D) A search warrant

Step-by-step explanation:

A search warrant is required before the search and collection of evidence to ensure legal authorization and protection of individuals' rights against unreasonable searches and seizures.

Option B, "A crime", is incorrect because the presence of a crime is not a prerequisite for conducting a search and collection of evidence. There are various situations where searches and evidence collection may occur without a crime being involved, such as regulatory inspections, consented searches, or investigations into potential threats or risks.

By your logic when you say law enforcement can conduct a search without a search warrant if there is consent by the owner, that would mean option A would be right, but of course, it's not.

Answer:

6÷9 this is the right answer

Answer:

2/3

Step-by-step explanation:

\(\frac{5}{9} + \frac{1}{9} = \frac{6}{9}\\)

\(\frac{6/3}{9/3} = \frac{2}{3}\)

The stock price rose by 14%

Percentage is the fraction of a sum expressed as a number out of hundred.

Percentage price increase = (change in price / initial price) x 100

In order to determine the answer, the following information is needed :

New price - Initial price

$57 - $50 = $7

Percentage increase in stock price : ($7 / $50) x 100 = 14%

In order to determine the percentage increase in the stock price, express the increase in price as a fraction of the initial price and multiply by 100

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Answer:

3

Step-by-step explanation:

The answer is three because u need to simply the fractions

Answer:

The answer is : x > 2

Based on the information given, it should be noted that the length of other leg 12.

Based on the information, the owner of the course asks you to provide a scale drawing of the green section he requested that you use the length of the legs of the right triangle.

Based on the information, 1/2ab = 54

1/2 × 4/3b² = 54

b² = 81

b = ✓81

b = 9

a will be

= 4/3 × 9

= 12 feet.

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Answer:

H= -35/4

Decimal form: -8.75

Explanation:

Answer:

z>-4

Step-by-step explanation:

-2z-3<5

-2z<5+3

-2z<8

z<8/-2

z<-4

z>-4

Answer:

1. . Group all constants on the right side of the inequality

Step-by-step explanation:

2. Isolate the f

Answer:b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: −200y−125

Step-by-step explanation:

Answer:

800 grams flour ÷ 5 grams flour/biscuit = 160 biscuits

160 biscuits × 3 grams butter/biscuit = 480 grams butter

160 biscuits × 2 grams sugar/biscuit = 320 grams sugar

Katie needs 320 grams sugar.

Kate needs 270g of sugar to make the maximum number of biscuits possible.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Now, Based on the ratio of flour, butter, and sugar of 5:3:2, we can determine that Kate needs;

⇒ 800g + 550g

= 1350g of the mixture.

Hence, For find out the amount of sugar needed, we need to determine the proportion of sugar in the mixture.

We can do this by adding up the ratio numbers;

(5+3+2) = 10.

Then we can divide each ratio number by the total (10) to get the proportion of each ingredient.

So the proportion of sugar in the mixture is 2/10. To find out how much sugar Kate needs, we can set up a proportion:

2/10 = x/1350

We can solve for x by cross-multiplying:

2 × 1350 = 10x

2700 = 10x
x = 270

Therefore, Kate needs 270g of sugar to make the maximum number of biscuits possible.

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Answer:

n ≤ 1 or n ≥ 7

Step-by-step explanation:

solve each part separately

86n + 13 ≤ 99 ( subtract 13 from both sides )

86n ≤ 86 ( divide both sides by 86 )

n ≤ 1

n + 90 ≥ 97 ( subtract 90 from both sides )

n ≥ 7

solution is n ≤ 1 or n ≥ 7

Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!

area equation is pi*r^2. divide by pi then square root. so the answer is the square root of 40

Answer:

√40 centimeters

Step-by-step explanation:

Given :

Area of circle = 40π cm²

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

Formula for area of a circle :

Area = πr²

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

Equating the given term and formula to find r :

⇒ 40π = πr²

⇒ r² = 40

⇒ r = √40 centimeters

Answer:

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