Derive the Utility Function to find the equation for the
indifference curve.
U(x, y) = (.6T.5 +
.4B.5)1/.5

Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

You can calculate the food cost and then calculate the tax and gratuity and add them to the cost of food to get the final cost to the customer.

The total amount that the customer will pay is given by

Option B: $65.10

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

Cost for food = $7.39 + twice of $16.99 + $5.29 + twice of $2.30

Cost for food = $51.26

Calculating tax on it (7%)

Tax = \(\dfrac{51.26}{100} \times 7 \approx \$3.59\)
Calculating gratuity (20%)

Gratuity = \(\dfrac{51.26}{100} \times 20 \approx \$10.25\)

Total final amount = $51.26 + $3.59 + $10.25 = $65.1

Thus,

The total amount that the customer will pay is given by

Option B: $65.10

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The probability that the engine over heats and leaks is 0.0096

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.

Engine leaks oil AND overheats,

hence P(Engine overheats) = P(Engine overheats) X P(Engine leaks oil) = 0.12 X 0.08 = 0.0096

Hence the probability of leaking of engine due to over heating is 0.0096

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Answer:

48 , 132

Step-by-step explanation:

Let smaller angle = x

Larger angle = 3x - 12

x & (3x - 12) are supplementary

So, x + 3x - 12 = 180°

          4x - 12 = 180

                  4x = 180 +12

                   4x = 192

                     x = 192/4

x = 48°

Larger angle = 3*48 - 12 = 144 - 12 = 132

Answer: The measure of the smaller angle is 48,and the larger angle is 132.

Step-by-step explanation:

The value of integral ∫(0,8)  [4f(x) + 6g(x)] dx on the interval of (0,8) is 264

when ∫(0,8) f(x) dx = 39 and  ∫(0,8)g(x) dx =18.

Integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

Given that,

∫(0,8) f(x) dx = 39 and  ∫(0,8)g(x) dx =18

∫(0,8)  [4f(x) + 6g(x)] dx

Apply linearity rule of integration,

= ∫(0,8) 4f(x) dx + ∫(0,8) 6g(x) dx

=4 ∫(0,8) f(x) dx + 6∫(0,8) g(x) dx

= 4(39) + 6(18)

= 156 + 108

= 264

therefore, the value of integral ∫(0,8)  [4f(x) + 6g(x)] dx on the interval of (0,8) is 264

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Answer:

2 < x < 26

Step-by-step explanation:

The length of the side of a triangle must be less than the sum of the lengths of the other two sides of a triangle.
Therefore:

12+14>x

x<26

However, the following must also be true:

x+12>14 (The sum of x and 14 will always be greater than 12 because 14>12, so we don’t need to include that in the inequality)

So, x>2.
This means that the answer is 2<x<26

Total number of outcomes having sum greater than 7 & with atleast one even number is 7.

In the given question,

Spinner divided into four equal sections.

These are numbered 2, 4, 5, and 7.

The spinner is spun twice.

We have to find how many outcomes have a sum less than 7 and contain at least one even number.

Since the spinner is spun twice.

So total outcomes are:

(2,2),(2,3),(2,5),(2,8),(3,2),(3,3),(3,5),(3,8),(5,2),(5,3),(5,5),(5,8),(8,2),(8,3),(8,5),(8,8)

Outcomes where sum is greater than 7 are (2,8),(3,5),(3,8),(5,3),(5,5),(5,8),(8,2),(8,3),(8,5),(8,8).

Thus outcomes where sum is greater than 7 and atleast one even number are (2,8),(3,8),(5,8),(8,2),(8,3),(8,5),(8,8).

Thus total number of outcomes having sum greater than 7 & with atleast one even number is 7.

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The right answer is:

A spinner is divided into four equal sections that are numbered 2, 4, 5, and 7. The spinner is spun twice. How many outcomes have a sum greater than 7 and contain at least one even number?

A right-angled triangle has one of its angle to be \(90^o\).

The points are given as:

\(A = (3,5)\)

\(B =(5,-4)\)

To have a right-angled triangle, then the third point must be at a right angle.

This means that:

From the given parameters, we have:

\(A_x = 3\)

\(B_y = -4\)

So, the coordinate of the third point is:

\(C =(A_x,B_y)\)

\(C = (3,-4)\)

See attachment for the right-angled triangle.

The distance between the two points is then calculated using the following distance formula

\(d = \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2}\)

So, we have:

\(d = \sqrt{(3-5)^2+ (5--4)^2}\)

\(d = \sqrt{85}\)

\(d = 9.2\)

Hence, the distance between the two points is 9.2 units

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Answer:

q = -14

Step-by-step explanation:

4(q + 17) − 12 = 0

4q + 68 - 12 = 0

4q + 56 = 0

4(q + 14) = 0

4 = 0, q + 14 = 0

          q = -14

I hope this helps!

The positive solution of the quadratic equation \(\rm 0=-x^2+2x+1\)  is x=2.41

It is given that the quadratic equation:

\(\rm 0=-x^2+2x+1\)

It is required to find the solution to the above quadratic equation.

A quadratic equation is a second-degree algebraic equation represented by the:

\(\rm ax^2+bx+c=0\)........(1)

Where a, b, and c are the constants and \(\rm a\neq 0\)

We know that:

\(\rm x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

We have:

\(\rm 0=-x^2+2x+1\\\rm or \\\rm -x^2+2x+1=0\) ..........(2)

After comparing (1) and (2) we get:

\(\rm a=-1, b=2, and \ c=1\)

Put these values in the above formula we get:

\(\rm x=\frac{-2\pm \sqrt{2^2-(4)(-1)(1)}}{(2)(-1)}\\\rm x=\frac{-2\pm \sqrt{8}}{-2}\\\rm x=\frac{-2\pm 2\sqrt{2 }}{-2}\\\rm x={1\pm \sqrt{2}}\)

\(\rm x=1+\sqrt{2} \ or \ x=1-\sqrt{2} \\\\\sqrt{2} = 1.41\\\rm so \ x= 1+1.41 \ or \ x= 1-1.41\\\rm x=2.41 or \ x=-0.41\)

Thus, the positive solution of the quadratic equation is x=2.41

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Answer:

x= 2.41

Step-by-step explanation:

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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Answer:

X>5273

Step-by-step explanation:

I did the math cuz I needed the answer and got it right so hope I could help.

If 8089 pizzas are taken away from a total of 10000 pizza rolls, then Tom is left with 1911 pizzas

Therefore, the correct answer is: Burger Quick, because it has a smaller IQR.

A box plot, also known as a box-and-whisker plot, is a graphical representation of a dataset that displays the distribution of the data and its range. Box plots are useful for comparing the distribution of data between different groups or for identifying outliers within a dataset. A box plot consists of five main components:

Minimum: the smallest value in the dataset, excluding any outliers.

Maximum: the largest value in the dataset, excluding any outliers.

Median: the middle value in the dataset, which divides the data into two equal halves.

Quartiles: the 25th percentile (Q1) and the 75th percentile (Q3) of the data, which divide the data into four equal quarters. The interquartile range (IQR) is the difference between Q3 and Q1.

Outliers: individual data points that fall outside the range of the whiskers. Outliers are plotted as individual points or asterisks.

In a box plot, the box represents the IQR, with the median line inside the box. The whiskers extend from the box to the minimum and maximum values, excluding any outliers, and are usually represented by vertical lines. Outliers are plotted as individual points or asterisks. Box plots are often used to compare the distribution of data between different groups, such as different treatment groups in a medical study or different categories of a survey response. They can also be used to identify any outliers or extreme values within a dataset.

Here,

Burger Quick is able to estimate their wait time more consistently than Super Fast Food because it has a smaller IQR (Interquartile Range). The IQR is a measure of the spread or variability of the data and is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data. A smaller IQR indicates that the data is less spread out and there is less variability in the wait times reported by the customers.

In this case, the IQR for Burger Quick is (24 - 9.5) = 14.5, while the IQR for Super Fast Food is (15.5 - 12) = 3.5. This shows that Burger Quick has a much smaller IQR, indicating that their wait time estimates are more consistent and less variable than those of Super Fast Food.

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Answer:

The solution is:

Step-by-step explanation:

First, we'll calculate the function's average rate of change over [-1,1] as following:

Now, we make f'(x) = 3 and solve for x, as following:

Therefore, we can conlcude that the solution is:

Riya earns $45 in commission for selling 15 newspaper ads at $50 each.

A commission is a charge or payment given to a person or group in exchange for a good or service. When selling goods or services on behalf of a corporation, sales representatives or agents are frequently compensated with commissions in the business world. For instance, a stockbroker may receive a fee for carrying out a trade on behalf of a customer, while a real estate agent may receive a commission depending on the sale price of a property they assist in selling.

Riya receives a 6% commission for selling newspaper ads, and if she sells 15 ads for $50 each, her total earnings can be calculated as follows:

Total earnings = Total sales x Commission rate

The total sales from selling 15 ads at $50 each are:

Total sales = 15 x $50 = $750

The commission rate is 6%, which can be written as 0.06 as a decimal.

Plugging these values into the formula, we get:

Total earnings = $750 x 0.06 = $45

Therefore, Riya earns $45 in commission for selling 15 newspaper ads at $50 each.

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Step-by-step explanation:

3x + 8y + 5

The true statements

5 is a constant

3x + 8y + 5 is written as a sum of three terms

3x and 5 are like terms

Answer:

2 3/4 divided by 5/6 = 3 3/10

1 1/3 divided by 1/4 = 5 1/3

2/5 divided by 1 2/5 = 2/7

5/7 divided by 3 1/5 = 25/112

2 2/7 divided by 2 2/7 = 1

An equation which has an extraneous solution is: C. √x = -5.

In Mathematics, an extraneous solution can be defined as a type of solution (root) to a squared equation or transformed equation that isn't a direct solution (root) of the original equation.

This ultimately implies that, extraneous solutions are numerical values that are obtained when we solve equations that aren't solutions to the original equation as shown below:

Taking the fifth root of both sides of the equation, we have:

\(\sqrt[5]{x} = -2\\\\(\sqrt[5]{x})^5 = -2^5\\\\\)

x = -32.

Taking the cubic root of both sides of the equation, we have:

∛(x + 1) = 10

[∛(x + 1)]³ = 10³

x + 1 = 1000

x = 1000 - 1

x = 999.

Taking the fourth root of both sides of the equation, we have:

\(\sqrt[4]{x-5} =3\\\\(\sqrt[4]{x-5})^4 =3^4\)

x - 5 = 81

x = 81 + 5

x = 86.

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Answer:

32 sqrt(35)

16 sqrt(33)

Step-by-step explanation:

Multiply the numbers outside the square root and then multiply the numbers inside the square root.  Check to see if you can simplify inside the square root.

8 sqrt(7) * 4 sqrt(5) = 32 sqrt(35)

2 sqrt(11) * 8 sqrt(3) = 16 sqrt(33)

If a and b two values then

\(\\ \sf\Rrightarrow 3√6(5√7)\)

\(\\ \sf\Rrightarrow 15√6(7)\)

\(\\ \sf\Rrightarrow 15√42\)

#2

\(\\ \sf\Rrightarrow 8√7(4√5)\)

\(\\ \sf\Rrightarrow 32√7(5)\)

\(\\ \sf\Rrightarrow 32√35\)

#3

\(\\ \sf\Rrightarrow 2√11(8√3)\)

\(\\ \sf\Rrightarrow 16√11(3)\)

\(\\ \sf\Rrightarrow 16√33\)

The critical value(s) for the given hypothesis test, where the sample mean is 21.6, the population mean is hypothesized to be greater than 20.6, the sample size is 109, the mean is 20.6.

The standard deviation is 7, we need to determine the appropriate critical value from the t-distribution. The critical value(s) will help determine the rejection region for the hypothesis test.

To find the critical value(s), we can use the t-distribution since the population standard deviation is unknown. The critical value(s) will correspond to the desired significance level or level of confidence for the hypothesis test.

Given that the sample size is large (n = 109) and assuming the sampling distribution of the sample mean is approximately normal due to the Central Limit Theorem, we can use the standard normal distribution to find the critical value(s).

To find the critical value(s) for a one-tailed test where the alternative hypothesis is u > 20.6, we need to find the z-score corresponding to the desired significance level or level of confidence. This can be done using a standard normal distribution table or a statistical calculator.

Once the z-score is obtained, it can be converted back to the original scale using the formula: z = (x - mean) / (standard deviation / sqrt(n)).

By plugging in the values (x = 21.6, mean = 20.6, standard deviation = 7, n = 109), we can calculate the critical value(s) rounded to 3 decimals.

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All of the statements that are true include the following:

B. Position is a function of time.

C. The position is highest at 9.8 seconds.

F. There is a 2 seconds period where the position does not change.

In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled by an object from its starting position with respect to the time when it is started moving.

Generally speaking, the position or distance traveled by a physical object in a position vs time graph is always plotted on the y-coordinate while time is always plotted on the x-coordinate (x-axis).

In this scenario, we can logically deduce that the position of this physical object is a function of time because it increases and decreases with respect to time. However, between 4 and 6 seconds the position is constant and does not change.

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Step-by-step explanation:

The cosine double angle formula tells us that cos(²θ) is always equal to cos²θ- sin²θ. For example cos(60) = cos²(30) - sin² (30). We can use this identity to rewrite expressions or solve problems

The required identity for cos^2θ = (cos2θ+1)/2.

Identity for  cos^2θ to be determine using cos(2θ) = 2cos^2θ-1.

Equation that enables trigonometric operators such as sin, cos.. etc.

Here, cos(2θ) = 2cos^2θ-1
         cos(2θ) + 1 = 2cos^2θ
    (cos(2θ) + 1)/2 = cos^2θ

Thus, the required identity for cos^2θ = (cos2θ+1)/2.

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Answer:

2.45

Step-by-step explanati

Answer: B

Step-by-step explanation:

B) Copernicus rediscovered Aristarchus's heliocentric model. The event which took place during the Copernican revolution.

Answer: HELP

Step-by-step explanation:

HELP MEEEE

Answer:

6c² + 15c + 12

Step-by-step explanation:

Given

(3c² + 6c + 7) + (3c² + 9c + 5) ← remove the parenthesis

= 3c² + 6c + 7 + 3c² + 9c + 5 ← collect like terms

= 6c² + 15c + 12

Answer:

option B is the correct answer

Step-by-step explanation:

please make me as a brainlist answer

Answer:

40

Step-by-step explanation:

Total is 150

Germany=1/3 *150 = 50

Italian= 2/5 * 150 = 60

Total - Germany- Italian= French

150 - 50 -60= 40