What is the difference between a line and a plane?

Since we are given the total utility for each level of consumption, we can find the marginal utility for each level by taking the difference between the total utility of the current level and the previous level.

For example, the marginal utility of the fourth taco is the difference between the total utility of consuming four tacos and the total utility of consuming three tacos:

Marginal Utility of 4th taco = Total Utility of 4 tacos - Total Utility of 3 tacos

= (10 + 8) - (6 + 3)

= 10

Therefore, the marginal utility experienced from consuming the fourth taco is 10 utils.

Answer: C. 10 utils.

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Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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The value of n in the equation (125)^n/2 = 1 is 0

The equation is given as:

(125)^n/2 = 1

Express 125 as 5^3 and 1 as 5^0

So, we have:'

(5^2)^n/2 = 5^0

Evaluate the product of exponent

5^n = 5^0

By comparison, we have:

n = 0

Hence, the value of n in the equation (125)^n/2 = 1 is 0

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Answer:

6 ft

Step-by-step explanation:

slope = \(\frac{rise}{run}\) ( rise is vertical height and run is horizontal distance )

here vertical height = 3 and slope = \(\frac{1}{2}\) , then

\(\frac{1}{2}\) = \(\frac{3}{run}\) ( cross- multiply )

run = 2 × 3 = 6 ft

Answer:

The amount of goo remaining after 32 minutes is approximately 54.7 grams.

Step-by-step explanation:

The half-life of a substance is the amount of time it takes for half of the substance to decay. To find the half-life of the goo in the experiment, we need to solve the equation G ( t ) = G ( 0 ) / 2 for t , where G ( 0 ) is the initial amount of goo and G ( t ) is the amount of goo remaining after time t .In this case, G ( 0 ) = 176 grams and G ( 135 minutes ) = 11 grams, so we can write the equation as follows:11 grams = 176 grams / 2Solving for t , we get:t = 135 minutes * ( 1 / 2 ) = 67.5 minutesThis is the half-life of the goo in the experiment.To find the amount of goo remaining after time t , we can use the equation G ( t ) = G ( 0 ) * ( 1 / 2 ) ^ ( t / t1/2 ) , where G ( 0 ) is the initial amount of goo, t is the time at which we want to find the amount of goo remaining, and t1/2 is the half-life of the goo.In this case, G ( 0 ) = 176 grams, t = 32 minutes, and t1/2 = 67.5 minutes, so we can plug these values into the equation to find the amount of goo remaining after 32 minutes:G ( 32 minutes ) = 176 grams * ( 1 / 2 ) ^ ( 32 minutes / 67.5 minutes )This equation tells us that the amount of goo remaining after 32 minutes is approximately 54.7 grams.

If Naya is filling up the gas tank in her motorcycle she puts 4.145 gallons of gas in the tank if the gas cost $2.57 per gallon then she spend $10.65

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

The cost of one gallon of gas =$2.57

The quantity of gas she puts in the tank = 4.145 gallons

Apply unitary method

Then, the cost of 4.145 gallons of gas = Cost of one gallon of the gas × Quantity of gas

The cost of 4.145 gallons of gas= 2.57×4.145= $10.65

Hence, If Naya is filling up the gas tank in her motorcycle she puts 4.145 gallons of gas in the tank if the gas cost $2.57 per gallon then she spend  $10.65

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Answer:

918

Step-by-step explanation:

891 = -27p

891 + 27 =p

p = 918

Answer:

slope = 3 , y- intercept = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

- 5 - y = - 3x ( add 5 to both sides )

- y = - 3x + 5 ( multiply through by - 1 )

y = 3x - 5 ← in slope- intercept form

with slope m = 3 and y- intercept c = - 5

The approximate probability of exactly two people in a group of seven having a birthday on April 15 is (C) \(7.4 x 10^-^6\)

To calculate the probability of exactly two people in a group of seven having a birthday on April 15, we can use the binomial distribution formula:

\(P(X = k) = C(n, k) * p^k * (1 - p)^(^n^-^k^)\)

Where:

So, plugging in the values, we get:

\(P(X = 2) = C(7, 2) * (1/365)^2 * (1 - 1/365)^(7 - 2)\)

\(= 21 * (1/365)^2 * (364/365)^5\)

\(= 2.38 x 10^-5\)

The probability of exactly two people in a group of seven having a birthday on April 15 can be calculated using the binomial distribution formula.

The formula takes into account the number of trials, the probability of success in a single trial, and the number of successes desired.

In this case, we want to find the probability that exactly two people in a group of seven have a birthday on April 15, assuming that all days of the year are equally likely for a birthday.

Plugging in the values into the formula gives us an approximate probability of \(7.4 x 10^-^6\), which is the answer (C).

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Answer:

1.\(40000000000\)
2.\(500000000000000\)
(In case you were asking me to multiply, 20 × 10^24)

Step-by-step explanation:

Given the following questions:
\(4\times10^{10}\)
\(5\times10^{14}\)

In order to find the answers, we take note on how the exponents are positive. We also need to remember how integers always have invisible decimal points.

Question one:

\(4\times10^{10}\)
\(4\times10^{10} =4.0.0.0.0.0.0.0.0.0.0.\)
\(4.0.0.0.0.0.0.0.0.0.0.=40000000000\)
\(40000000000\)

Question two:

\(5\times10^{14}\)
\(5\times10^{14}=5.0.0.0.0.0.0.0.0.0.0.0.0.0.0.\)
\(5.0.0.0.0.0.0.0.0.0.0.0.0.0.0.=500000000000000\)
\(500000000000000\)

In case you were asking me to multiply:

\(40000000000\times500000000000000=20000000000000000000000000\)
\(20000000000000000000000000=20\times10^{24}\)
\(20\times10^{24}\)

Hope this helps.

The measure of arc BC in circle E, inscribed in triangle BCD with angle DBC measuring 51 degrees, is 102°.

In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Since BD is a diameter, angle DBC is a right angle, and the intercepted arc BC is a semicircle. Therefore, the measure of arc BC is 180°.

However, we are given that angle DBC measures 51 degrees. In an inscribed triangle, the measure of an angle is equal to half the measure of its intercepted arc. So, angle DBC is half the measure of arc BC, which means arc BC measures 2 times angle DBC, or 2 * 51° = 102°.

Hence, the measure of arc BC is 102°.

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Inscribed circle E is formed by triangle BCD, with BD as the diameter. DC and CB are secants, and angle DBC is 51 degrees. We need to find the measure of arc BC.

When a triangle is inscribed in a circle, the measure of an angle formed by two secants that intersect on the circle is half the measure of the intercepted arc.

In this case, angle DBC is 51 degrees, which means the intercepted arc BC has twice that measure. Therefore, the measure of arc BC is 2×51=102 degrees.

To understand why this relationship holds, we can use the Inscribed Angle Theorem. According to this theorem, an angle formed by two chords or secants that intersect on a circle is equal in measure to half the measure of the intercepted arc.

In our scenario, angle DBC is formed by secants DC and CB, and it intersects the circle at arc BC. According to the Inscribed Angle Theorem, angle DBC is equal to half the measure of arc BC.

Hence, if angle DBC is 51 degrees, the measure of arc BC is twice that, which gives us 102 degrees.

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The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

A financing model is a planned, institutionalized strategy for creating a steady income stream to sustain an organization's core services and operations. Nonprofits need funding because it enables them to make investments in their operations and increase their overall effect. Securing funding is crucial to keeping your organization operational because nonprofits frequently rely on grants to assist with operational costs. Grants of all kinds are available to nonprofit organizations.

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Answer:

see below

Step-by-step explanation:

They are 150% of the recommended daily allowance.  There is a certain amount of a vitamin or mineral that a person is supposed to get to meet nutritional needs.  The  amount in the food exceeds that amount

150% is 150:100

   or 3:2

Answer:

A = 63.59

C = 28.26

Step-by-step explanation:

r = 4.5

Area of a circle:

A = πr²

A = 3.14(4.5²)

A = 3.14(20.25)

A = 63.59

Circumference:

C = 2πr

C = 2(3.14)(4.5)

C = 28.26

look on google

Step-by-step explanation:

go on google

search the answer

then BOOM!

Answer:

The answer is the first option x(x-4)(x-1)/2(x+4).

Step-by-step explanation:

because when you simplify after multiplying the denominator is 2x+8 when you simplify that its 2(x+4) and for the numerator after multiplying you get x^3−5x^2+4x when you simply that you get x(x-4)(x-1). Answer would be x(x-4)(x-1)/2(x+4).

The perimeter of the red rectangular tile is approximately 28.66 inches.

Since the blue and red rectangular tiles are similar, their corresponding sides are proportional. Let's find the scale factor between them.

The blue tile has a perimeter of 30 inches and a length of 10 inches. We know that the perimeter of a rectangle is the sum of all its sides, so we can write:

30 = 2L + 2W

where L is the length and W is the width. Since we have a rectangular tile, we know that L = 10 and we can solve for W:

30 = 2(10) + 2W
30 = 20 + 2W
10 = 2W
W = 5

So the blue tile has a width of 5 inches. Now we can find the scale factor between the blue and red tiles:

scale factor = length of blue tile / length of red tile
scale factor = 10 / 6
scale factor = 5/3

This means that the corresponding sides of the red tile are 5/3 times smaller than the corresponding sides of the blue tile. So if the blue tile has a width of 5 inches, the red tile has a width of:

width of red tile = (5/3) * (width of blue tile)
width of red tile = (5/3) * 5
width of red tile = 8.33 inches (rounded to two decimal places)

Now we can find the perimeter of the red tile:

perimeter of red tile = 2L + 2W
perimeter of red tile = 2(6) + 2(8.33)
perimeter of red tile = 12 + 16.66
perimeter of red tile = 28.66 inches (rounded to two decimal places)

So the perimeter of the red rectangular tile is approximately 28.66 inches.

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The probability that the student is a junior is 0.5.

The probability that the selected student takes calculus is given by:

P(C) = probability that the selected student takes calculus= probability of seniors taking calculus + probability of juniors taking calculus= 0.4 x 1/2 + 0.2 x 1/2= 0.2

Now,Let's find the probability that a calculus student selected is a junior.i.e., we need to find P(J|C).We know that,

P(J|C) = probability that the selected student is a junior given that the student takes calculus= P(C|J) × P(J) / P(C)

We already know,P(C) = 0.2

Also,P(C|J) = probability that a junior student takes calculus= 0.2

So,P(J|C) = probability that the selected student is a junior given that the student takes calculus= P(C|J) × P(J) / P(C)= 0.2 × 1/2 / 0.2= 1/2= 0.5

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Answer:

Yes

Step-by-step explanation:

8/10 can be simplified to become 3/4

Answer:

The answer is D =35°

Tan inverse of 19/27

Answer:

21

Step-by-step explanation:

This is extremely hard to do on paper so I used a calculator but this is my explanation. So 12% = .12 so the decimal way is 175 x .12 = 21. Pizza was 21 times.

Answer:

Pizza was served on 21 days.

Step-by-step explanation:

12% of 175 days comes out to 21 days.

Pizza was served on 21 days.

The required probabilities for the events in question are:

Based on the parameters given :

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Total number of slots = 18+18+2 = 38

A.)

Probability of green slots 2 or more times :

(2/38)² × (36/38)²³ = 0.00080

B.)

Probability of ball not entering the green slots

1 - P(green slots)

P(not entering green slot ) = 1 - 0.0008 = 0.9992

C.)

probability that ball falls into black slot 15 or more times :

(18/38)¹⁵ * (20/38)¹⁰ = \(2.21\times10^{-8}\)

D.)

Probability that ball falls into red slot 10 or less times :

(10/38)¹⁰ * (28/38)¹⁵ = \(1.63\times10^{-8}\)

Therefore, the required probabilities are :

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Answer:

5.6

Step-by-step explanation:

y = 53- 47.4=?

Answer:

A) (0,0)

Step-by-step explanation:

1.) graph the equation, 3x+2y = x+y

2.) the line intersects (0,0) on the coordinate plane

The test statistic in this case is 3.

To test the hypothesis H0: μ = 100, where the sample size is n = 100, σ = 10, and the sample mean is 103, we can calculate the test statistic using the z-test.

The formula for the z-test statistic is:

z = (x - μ) / (σ / √n)

x is the sample mean,

μ is the population mean under the null hypothesis (H0),

σ is the population standard deviation, and

n is the sample size.

Plugging in the values from the given information, we have:

x = 103 (sample mean)

μ = 100 (population mean under H0)

σ = 10 (population standard deviation)

n = 100 (sample size)

Substituting these values into the formula, we can calculate the z-test statistic:

z = (103 - 100) / (10 / √100)

z = 3 / (10 / 10)

z = 3

Thus, the appropriate answer is 3.

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Answer:

1. 0.3333333

2. 0.4166666

3. 0.6666666

Step-by-step explanation:

add them all up for a total of 12. then divide 4 into 12 for the probability of number 1. Next, divide 5 into 12 for the probability of green. Finally, add 3 and 5 to get 8 and divide by 12.  

Answer:

\(\implies x = 1 \quad or -6 \\\\\implies f(x) = -3x^2-15x + 18 \)

Step-by-step explanation:

Given :-

And we need to find out the zeroes of the quadratic function and we need to express it in Standard form. T

Function :-

\(\implies f(x)= -3(x-1)(x+6) \)

\(\implies f(x)=0 \\\\\implies -3(x-1)(x+6)=0 \\\\\implies (x - 1 )(x+6) = 0 \\\\\implies x = 1 \quad or \quad -6 \)

Therefore the zeroes are 1 and -6 .

Expressing in Standard form :-

The standard form of a quadratic equation is ,

\(\implies ax^2+bx + c = 0 \)

And that of a quadratic function is ,

\(\implies f(x) = ax^2+bx + c \)

Simplifying the equation :-

\(\implies f(x)= -3(x-1)(x+6)\\\\\implies f(x) = (-3x +3)(x+6) \\\\\implies f(x) = -3x(x+6)+3(x+6)\\\\\implies f(x) = -3x^2 -18x +3x + 18\\\\\implies f(x) = -3x^2-15x + 18 \)

Hence the Standard form of the equation is -3x² - 15x + 18 .

The answer is (B) (31.56, 38.44) which means we are 95% confident that the true population mean lies between 31.56 and 38.44.

The 95% confidence interval for the population mean, µ, is given by:

CI =  ± tα/2 * (s/√n)

where  is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom at the α/2 level of significance.

Here,  = 35, s = 9.38, and n = 22. From the t-distribution table with (n-1) = 21 degrees of freedom and a 95% confidence level, we have tα/2 = 2.08.

Plugging in the values, we get:

CI = 35 ± 2.08 * (9.38/√22)

= (31.56, 38.44)

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Answer:

WebMath is designed to help you solve your math problems. Composed of forms to fill-in and then returns analysis of a problem and, when possible, provides a ...

Step-by-step explanation: