A proportion often shows the relationship between:

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:

Step-by-step explanation:

\(\sqrt{x} \sqrt{x} -(-9)^{2} \\=x-81\\x=81\)

Answer:

Answer:

=5^(-4)*5^(-3)

=5^(-7)

=1/5^(7)

Step-by-step explanation:

i took the denominator and multiplied it to the numerator

when powers of the same base are multiplying we add the exponents, so I added the -3 to -4 and got -7 which gives me 5^(-7) which is 1/5^(7)

Answer:

it not

Step-by-step explanation:

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = \(96t - 16t^{2}\)

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

\(\frac{dh(t)}{dt} = 96 - 32t = 0\)

⇒ \(t = 3\)

So, time taken to reach its max height is 3 seconds.

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Answer:

1. 6 + 45 -10 = 41 2. -20 - 20 - 10 = -50 3. 40 4. -18 - 15 + 10 = -23

Step-by-step explanation:

adding/multiplying a negative and a negative = a positive

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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The 98% confidence interval for the true mean statistics anxiety score (μ) is approximately (39.037, 39.763).

To calculate the 98% confidence interval for the true mean statistics anxiety score (μ) for all undergraduate students in the U.S., we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

First, we need to find the critical value associated with a 98% confidence level. Since we are assuming a normal distribution, we can use the Z-table or a statistical software to find this value. For a 98% confidence level, the critical value is approximately 2.33.

Next, we calculate the standard error (SE) using the formula:

SE = standard deviation / √sample size

In this case, the standard deviation is 0.9 and the sample size is 33. Plugging these values into the formula, we get: SE = 0.9 / √33 ≈ 0.156

Now, we can calculate the confidence interval:Confidence interval = 39.4 ± (2.33 * 0.156)

Simplifying the expression:Confidence interval ≈ 39.4 ± 0.363

This gives us the interval (39.037, 39.763). This means we are 98% confident that the true mean statistics anxiety score for all undergraduate students in the U.S. falls within this interval.

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Answer:

3880 ÷ 960 = 4.041

ratio = 4:1

Yaseen's calculation that 20% x 5 = 100% is correct, but the conclusion that the prices will be reduced to $0 after the five reductions is incorrect.

The reason for this is that each week, the price is reduced by 20% of the previous week's price, not the original price. So, after the first week, the price will be 80% of the original price, and after the second week, the price will be 80% of the price from the first week, which is 64% of the original price.

This means that the price after each week's sale is:

Week 1: 80% of the original price

Week 2: 64% of the original price

Week 3: 51.2% of the original price

Week 4: 40.96% of the original price

Week 5: 32.768% of the original price

As we can see, the prices will never be reduced to $0, but they will continue to decrease with each successive week of the sale.

Answer:

area = l×w

Step-by-step explanation:

20 ×5

= 100

so this is the answer for your question

pls mark as brain lest

Answer:

area = l × b

20× 5

100.......

Answer:

291

Step-by-step explanation:

2*2*2=8*2=16

16+(11*5*5)=291

Answer:

291cm^3

Step-by-step explanation:

11×5×5=275cm^3

2×2×2=8cm^3

8cm^3 + 8cm^3= 16cm^3

275+16=291cm^3

Answer:

C

Step-by-step explanation:

Because they both are the same

If y varies inversely as x, we can write the relationship between x and y as:

y = k/x

where k is a constant of proportionality. To find k, we can use the given information that y = 5 when x = 2:

5 = k/2

Solving for k, we get:

k = 10

Now we can write the equation that relates x and y:

y = 10/x

To find y when x = 6, we substitute x = 6 into the equation:

y = 10/6 = 5/3

Therefore, when x = 6, y = 5/3.

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Answer: d

Step-by-step explanation: None needed

Answer:

The y-axis is at 72 with a negative slope

Step-by-step explanation:

Searching will help you by making a graph if you search for " f(x) =72-12x" aka the equation you have :D

Answer:

Width = 8 ft

Length = 53 ft

Height = 9 ft

Step-by-step explanation:

Let width be x

Length will be 8x-11

Height will be x + 1

Volume = width x height x length

=

x * (8x-11) * (x+1) = 3816

(8x^2 - 11x) * (x+1) = 3816

8x^3 + 8x^2 - 11x^2 - 11x = 3816

8x^3 -3x^2 - 11x = 3816

8x^3+64x^2-61x^2-488x +477x-3816= 0

8x^2 (x-8)+61x(x-8)+488(x-8)

(x-8)(8x^2 + 61x + 477) = 0

x-8

8x^2 + 61x + 477 = 0

Solve the equations:

x = 8

Length = 8x -11 = 64-11 = 53

Height = 8+1 = 9

Answer:

8w^3-3w^2-11w=3816

Step-by-step explanation:

Find the equation, in terms of w, that could be used to find the dimensions of the trailer in feet. Your answer should be in the form of a polynomial equals a constant.

Answer:

Well assuming you mean which will be the better option it would be the 60 ounce and 1.20 option. Since if you find the unit rate for that you’d only get 0.02 dollars for each ounce of soda. And for the 20 ounce one you’d get 0.05 dollars per ounce. The better option is the 60 ounces bottle for 1.20.

Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

Answer:

Step-by-step explanation:

L = length    W = width

Length is 1.2 times width ⇒  L = 1.2 x W = 1.2W

Perimeter = 2 x W + 2 x L

                = 2W + 2L = 25

Substitute L = 1.2W into the equation for the perimeter and solve for W

2W + 2L = 25

2W + 2(1.2W) = 25

4.4W = 25

W = 25 ÷ 4.4 = 125/22

Now substitute found value of W into L = 1.2W to find L:

L = 75/11

The Probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

To find the probability that the randomly chosen coin is gold, given that it is small, we need to determine the number of small gold coins and the total number of small coins.

From the given information, Marco has 12 small gold coins and 3 small silver coins, making a total of 12 + 3 = 15 small coins.

The probability that the coin is gold, given that it is small, can be calculated as the ratio of the number of small gold coins to the total number of small coins:

P(Gold|Small) = Number of Small Gold Coins / Total Number of Small Coins

P(Gold|Small) = 12 / 15

Simplifying the fraction, we have:

P(Gold|Small) = 4 / 5

Therefore, the probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

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Answer:

96 cm^2

Step-by-step explanation:

All faces of a cube are equal in area.

Therefore the Formula for SA of a cube is 6*s^2

SA = 6*4*4 = 96

Step-by-step explanation:

in such a case, where we have all the sides and need angles, the best tool is the extended Pythagoras (for general triangles and not just for right-angled ones) :

c² = a² + b² - 2ab×cos(C)

c is the side opposite of angle C.

the side opposite of B is CA.

so, we have

220² = 100² + 160² - 2×100×160×cos(B)

48,400 = 10,000 + 25,600 - 32,000×cos(B)

12,800 = -32,000×cos(B)

cos(B) = -12,800/32,000 = -0.4

B = 113.5781785...° ≈ 114°

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:7/5

Step-by-step explanation:

The ratio of the number of baskets scored by team A to the number of baskets by team B is 2: 5. Then the correct option is B.

In a basketball game, team B scored 5 baskets for every 2 that team A scored.

The utilization of two or more additional numbers that compares is known as the ratio.

Assume that Team A scored two baskets while Team B netted five.

The problem statement states that for every two baskets Team A scored, Team B scored five. This may be expressed as the ratio shown below:

Ratio = 2x : 5x

Ratio = 2: 5

Thus, the correct option is B.

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Answer:

The answer is 10√2.

Step-by-step explanation:

Answer: 1133.5

Step-by-step explanation:

Answer:

1133.5

Step-by-step explanation:

area = 3.14 (19)square

3.14 (361)

1133.54 ( round nearest ten)

1133.5