Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take Levi's dad to wash the car by himself

Answer:

the area left to 51 on normal distribution curve

Step-by-step explanation:

we have to find the probability that at most 51 it means the probability of less than 51 . The probability of at most 51 or less than 51 on the normal distribution curve will be the area lest side of 51 for example if we have to find the are of at least 51 then the area on the normal distribution curve will be right of 51

so the answer will be the area left side of 51

When the probability of a binomial random variable is approximated using the normal distribution, the area under the normal curve represents the probability of a certain range of values. To find the probability that at most 51 households have a gas stove, we convert the binomial random variable to a standard normal random variable and find the area to the left of 51 on the normal curve, which is extremely close to 0.

When the probability of a binomial random variable is approximated using the normal distribution, the area under the normal curve represents the probability of a certain range of values. In this case, we want to find the probability that at most 51 households have a gas stove. To do this, we need to find the area to the left of 51 on the normal curve.

To find this probability, we use the standard normal distribution table or a calculator. We convert the binomial random variable to a standard normal random variable using the formula z = (x - np) / √(npq), where x is the number of households, n is the number of trials, p is the probability of success, and q is the probability of failure. In this case, np = 500 * 0.2 = 100 and npq = 500 * 0.2 * 0.8 = 80. So, z = (51 - 100) / √80 ≈ -6.325.

Looking up this value in the standard normal distribution table, we find that the area to the left of -6.325 is extremely close to 0. Therefore, the probability that at most 51 households have a gas stove is approximately 0.

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Answer:

A. The CV is a relative measure of risk/return.

Step-by-step explanation:

The coefficient of variation of any investment, is used to measure and calculate the total risk of that investment with respect to its per unit expected return rate.

We can also define the coefficient of variation as a ratio of standard deviation to the expected value of an investment.

The answer is - A. The CV is a relative measure of risk/return.

The coefficient of variation (CV) is a relative measure of risk/return; thus, statement A is correct, and statement D is correct as it relates to the preferences of risk-averse investors. This measure is useful for assessing the consistency of investment returns, especially when comparing different investment options.

The coefficient of variation (CV) is a statistical measure that is used to assess the relative variability of data. It is calculated by dividing the standard deviation by the mean and multiplying by 100. This ratio provides a standardized measure of the dispersion of data points in a data set around the mean, which is particularly useful when comparing the variability between datasets with different units or scales.

Now let's examine the given statements:

A. The CV is a relative measure of risk/return.

B. The CV is an absolute measure of risk/return.

C. The higher the CV value the more acceptable the risk/return profile for a risk-averse investor.

D. The lower the CV value the more acceptable the risk/return profile for a risk-averse investor.

Statement A is correct: the CV is indeed a relative measure because it expresses the standard deviation as a percentage of the mean, making it unitless and thus comparable across different data sets and scales.

Statement D is also correct: a lower CV indicates that the returns are less volatile relative to the mean return, which is generally preferred by risk-averse investors. Risk-averse investors prefer investments with more predictable and stable returns, as such investments are associated with lower levels of relative risk.

Answer:

15/2 x^2y - 5xy

Step-by-step explanation:

First find the area of the rectangle

A = l*w

   = 5xy * 2x

    10x^2y

The find the area of the triangle

A = 1/2 bh

   = 1/2 (5xy) (x+2)

   = 1/2((5x^2y + 10xy)

   = 5/2 x^2y +5xy

The shaded region is the area of the rectangle minus the area of the triangle

10x^2y -  (5/2 x^2y +5xy)

Distribute the minus sign

10x^2y -5/2 x^2y -5xy

Combining like terms by getting a common denominator

20/2x^2y -5/2 x^2y -5xy

15/2 x^2y - 5xy

Answer:

  18°

Step-by-step explanation:

The law of cosines tells you ...

  a² = b² + c² -2bc·cos(A)

Solve for cos(A) and fill in the numbers. Note that the value of cos(A) is very close to 1, so the angle will be fairly small. This by itself can steer you to the correct answer.

  cos(A) = (b² +c² -a²)/(2bc) = (49 +100 -16)/(2·7·10) = 133/140

  A = arccos(133/140) ≈ 18.2° ≈ 18°

Answer:

a. 8.4 km  b. 20 km/hr or 20,000 m/hr

Step-by-step explanation:

This is your polynomial:

[tex]d(v)=.004v^2+.2v+6[/tex]

The important thing to realize is that d(v) is the distance it takes for the boat to stop.  That will come later, in part b. Besides that, we also need to remember that v is velocity, which is speed, in km/hr.

For part a. we are looking for d(v), the stopping distance, when v = 10.  That means that we will sub in a 10 for each v in the function and solve for d(v):

[tex]d(10)=.004(10)^2+.2(10)+6[/tex] so

d(10) = 8.4 km

Now comes the part I was referring to above.  Part b is asking us the speed of the boat if it takes 11.6 meters to stop.  If d(v) is the stopping distance, we sub 11.6 in for d(v) in the function:

[tex]11.6=.004v^2+.2v+6[/tex]

The only way w can solve this for velocity is to get everything on one side of the equals sign, set the polynomial equal to 0, then plug the values into the quadratic formula.  

[tex]0=.004v^2+.2v-5.6[/tex]

Plugging that into the quadratic formula gives you 2 values of velocity:

v = 20 km/hr and -70 km/hr

We all know that neither time nor distance in math will EVER be negative so we can discount the negative number.  However, I believe that you asked for the distance in meters, so 20 km/hr is the same as 20,000 m/hr.

Hey There!

We'd distribute the negative sign first:

[tex]y + 7 = -x - 6[/tex]

Now, we'd have to isolate the variable y by subtracting seven in both sides:

[tex]y = -x - 13[/tex]

Replace y with f(x):

[tex]f(x) = -x - 13[/tex]

Our answer would be [tex]f(x) = -x - 13[/tex]

Answer:

f(x)-x-13

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) For a depth of x, the two sides of the rain gutter are length x, and the bottom is length (12-2x). The cross sectional area is the product of these dimensions:

  A = x(12 -2x)

This equation describes a parabola that opens downward. It has zeros at ...

  x = 0

  12 -2x = 0 . . . . x = 6

The maximum area is halfway between these zeros, at x=3.

The maximum area is obtained when the depth is 3 inches.

__

(b) For an area of at least 16 square inches, we want ...

  x(12 -2x) ≥ 16

  x(6 -x) ≥ 8 . . . . . divide by 2

  0 ≥ x² -6x +8 . . . . subtract the left side

  (x -4)(x -2) ≤ 0 . . . factor

The expression on the left will be negative for values of x between 2 and 4 (making only the x-4 factor be negative). Hence the the depths of interest are in that range.

At least 16 square inches of water will flow for depths between 2 and 4 inches, inclusive.

The maximum cross-sectional area of the gutter which allows the most water flow is achieved at a depth of 4 inches. For a flow rate of 16 square inches, we need to solve the equation for the cross-sectional area equal to 16 to find the corresponding depth.

Your question pertains to maximizing the cross-sectional area of a rain gutter made from 12-inch wide aluminum sheets. This involves the use of calculus, specifically optimization, and basic geometry.

Let's denote 'x' as half the width of the base. When the sides are turned up 90 degrees, the sides will be of length 'x'. Since the gutter is 12 inches wide, the equation for the width is 2x+x=12. So, x=4.

To maximize the cross-sectional area, you need to set the derivative of the area function equals to zero.

For your second question, to find the depths that will allow at least 16 square inches of water to flow, equate the cross-sectional area equals to 16, and solve for 'x'.

In conclusion,

The depth that would allow maximum cross-sectional area and the most water flow is when x = 4 inches,. To allow 16 square inches of water to flow, solve for 'x' when the cross-sectional area equals to 16.

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Answer:

The next two terms after a1 is

-6 and then 18

Step-by-step explanation:

Geometric sequence means your pattern for the terms is multiplication by the same number.

So a1 is the first term and r is your common ratio.

The common ratio is what you are multiplying by each time to figure out the next term.

So the geometric sequence goes like this:

a1 ,  a1*r , (a1*r)*r or a1*r^2 , a1*r^3 ,....

So anyways you have

first term a1=2

second term a2=2(-3)=-6

third term a3=-6(-3)=18

And so on...

Answer:

69 bpm

Step-by-step explanation:

Here we start out finding the z-score corresponding to the bottom 33% of the area under the standard normal curve.  Using the invNorm( function on a basic TI-83 Plus calculator, I found that the z-score associated with the upper end of the bottom 33% is -0.43073.

Next we use the formula for z score to determine the x value representing this woman's heart rate:

       x - mean                              x - 75 bpm

z = ----------------- = -0.43073 = --------------------

       std. dev.                                    15

Thus,  x - 75 = -0.43073(15) = -6.461, so x = 75 - 6.6461, or approx. 68.54, or (to the nearest integer), approx 69 bpm

The quadratic equation 4x^2 - 4x - 7 = 0 is solved using the Quadratic Formula with coefficients a = 4, b = -4, c = -7. The correct solutions obtained are x = 1/2 + √2 and x = 1/2 - √2, corresponding to option (c).

To solve the quadratic equation 4x^2 - 4x - 7 = 0 using the Quadratic Formula, we first identify the coefficients: a = 4, b = -4, and c = -7.

The Quadratic Formula is given by:

x = √((-b ± √(b^2 - 4ac)) / (2a)).

Substitute the identified coefficients into the formula:

x = √(((-(-4) ± √((-4)^2 - 4(4)(-7))) / (2(4))).

Simplify the expression:

x = √(((4 ± √(16 + 112)) / 8),

x = √(((4 ± √(128)) / 8),

x = √((4 ± 8√2) / 8).

Simplify further:

x = 1/2 ± √2.

Therefore, the correct answers are:

x = 1/2 + √2 and x = 1/2 - √2,

which corresponds to option (c).

The solution of the inequality is:

                       [tex]x\leq 3[/tex]

We are given a inequality in terms of variable x as:

[tex]2(4+2x)\geq 5x+5[/tex]

Now we are asked to find the solution of the inequality i.e. we are asked to find the possible values of x such that the inequality holds true.

We may simplify this inequality as follows:

On using the distributive property of multiplication in the left hand side of the inequality we have:

[tex]2\times 4+2\times 2x\geq 5x+5\\\\i.e.\\\\8+4x\geq 5x+5\\\\i.e.\\\\8-5\geq 5x-4x\\\\i.e.\\\\x\leq 3[/tex]

The solution is:      [tex]x\leq 3[/tex]

Answer:

Option C.

Step-by-step explanation:

The given inequality is given as

2(4 + 2x) ≥ 5x + 5

8 + 4x ≥ 5x + 5 [Simplify the parenthesis by distributive law]

Subtract 5 from each side of the inequality

(8 + 4x) - 5 ≥ (5x + 5) - 5

3 + 4x ≥ 5x

subtract 4x from each side of the inequality

(4x + 3) - 4x ≥ 5x - 4x

3 ≥ x

Or x ≤ 3

Option C. x ≤ 3 is the correct option.

Answer:

60060 different ways that teams can be chosen

Step-by-step explanation:

Given data

employees n  = 14

team = 3

each project employees

n(1) =  8

n(2) = 3

n(3) = 3

to find out

how many different ways can the teams be chosen

solution

we know according to question all employees work on a team so

select ways are = n! / n(1) ! × n(2) ! × n(3)     ....................1

here  n! = 14! = 14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1

and n(1)! = 8! =  8 ×7 ×6 ×5 ×4 × 3× 2× 1

n(2)! = 3! =  3× 2× 1

n(3)! = 3! =  3× 2× 1

so now put all these in equation 1 and we get

select ways are = (14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) / (8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) × ( 3× 2× 1) ×  ( 3× 2× 1)

select ways are =  (14 × 13 ×12 ×11 ×10 ×9 ) / ( 3× 2× 1) ×  ( 3× 2× 1)

select ways are =  2162160 / 36

select ways are = 60060

60060 different ways that teams can be chosen

Answer:

60060

Step-by-step explanation:

#copyright

Answer:4

Step-by-step explanation:16/4 = 4

if 75% of equipment is iron then do the math

So it would be 4(2) + 4 = 75% of 16
So if 75% of 16 is 12 you need that extra 4 to get you to 16

The number of woods in the golf club is equal [tex]4[/tex].

" Number is defined as the count of any given quantity."

According to the question,

[tex]'x'[/tex] represents the number of irons

[tex]'y'[/tex] represents the number of woods

As per given condition we have,

[tex]x= 2y +4[/tex]                                  [tex](1)[/tex]

[tex]x = 75\%(x+ y)\\\\\implies x = \frac{75}{100}(x + y)\\ \\\implies x = \frac{3}{4} (x+y)\\\\\implies 4x= 3x + 3y\\\\\implies x = 3y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]

Substitute the value of [tex](2)[/tex] in [tex](1)[/tex] to get the number of woods,

[tex]3y = 2y +4\\\\\implies y =4[/tex]

Therefore,

[tex]x= 3\times 4\\\\\implies x=12[/tex]

Hence, the  number of woods in the golf club is equal [tex]4[/tex].

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Answer:

The actual price is 13.6 % lower than the expected price....

Step-by-step explanation:

Lets suppose the expected price = x

CPI = ( expected price ) : ( price in 1983 ) *100

219  =  ( x  : 12.95 ) *100

Divide both sides by 100.

x : 12.95 = 2.19

x =2.19*12.95

= $28.36  ( expected price )

p = ( 24.50*100 ) / 28.36

p= 2450/28.36

= 86.4 %

100 % - 86.4 % = 13.6 %

The actual price is 13.6 % lower than the expected price....

Answer:

c

Step-by-step explanation:

because i said so brudda

Answer:

GLH is congruent to JLK as the quadrilateral is a parallelogram,

KJ = GH OR HJ = GK

GL = LJ OR. HL = LK

triangle JKG = GHJ

triangle HGK = KJH

Answer:

A parallelogram has two pairs of opposite parallel congruent sides.

Given :

Quadrilateral GKJH is a parallelogram,

To prove :

Δ GLH ≅ Δ JLK

Proof :

          Statement                                     Reason

1.   GH ║ KJ                                      Definition of parallelogram

2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ     Alternate interior angle theorem

3. GH ≅ KJ                                        Definition of parallelogram

4.  Δ GLH ≅ Δ JLK                            ASA postulate of congruence

Hence, proved...

Answer:

Step-by-step explanation:

Part A:

The solution of a system is not just the x coordinates; it is the whole coordinate pair that is the solution, where both x and y are the same.  Normally, when you have a system and are solving them simultaneously, you are looking for the point at which they are equal.  This is a very useful concept in business and finance, both in the home for personal information, and in the office setting where companies are.  Where the 2 equations intersect is a point where they are equal.  

Part B:

The graphs do not intersect right at a perfect integer of x.  Therefore, we will solve these equations simultaneously to solve first for x, then we will plug in x to solve for y.  Since we have the equations set to equal each other, we can solve for x by getting everything on one side of the equation and then setting it equal to 0.  

2 - x = 4x + 3 so

5x + 1 = 0.  Solving for x,

5x = -1 so

[tex]x=-\frac{1}{5}[/tex]

The y coordinate can be found by subbing in this value of x into either equation.  If y = 2 - x, and x = -1/5, then

y = 2 -(-1/5) and y = 2 + 1/5 and y = 10/5 + 1/5 gives us that y = 11/5

Thus, the coordinate pair that is the solution to that system is

[tex](-\frac{1}{5},\frac{11}{5})[/tex]

Part C:

You would solve the system graphically by graphing both lines on the same window.  However, since their intersection is not an integer pair, but are fractions, you would not be able to tell EXACTLY where they intersect.  From the graphing window, you would hit your 2nd button then "trace" which is in the row at the very top of the buttons below the window.  Then hit 5:  intersect.  You'll be back to your graph of the lines, and there will be a cursor blinking along the line you graphed under Y1.  Move the cursor til it is right over the intersection of the lines and hit "enter".  Then you'll be back to the graphs with a blinking cursor over the line you entered in Y2.  Move that cursor along the line til it is dead-center over the other point on the first line and hit "enter" again.  At the bottom, you will see the x and y coordinates that are the intersection of this system.

Answer:

[tex]m(RS)=17[/tex] inches  (answer rounded to nearest tenths)

Step-by-step explanation:

Central angle there is 150 degrees.

The radius is 6.48 inches.

The formula for finding the arc length, RS, is

[tex]m(RS)=\theta \cdot r[/tex]

where [tex]r[/tex] is the radius and [tex]\theta[/tex] ( in radians ) is the central angle.

I had to convert 150 degrees to radians which is [tex]\frac{150\pi}{180}[/tex] since [tex]\pi \text{rad}=180^o[/tex].

[tex]m(RS)=\frac{150\pi}{180} \cdot 6.48[/tex]

[tex]m(RS)=16.96[/tex] inches

Answer: [tex]17\ in[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Arc Lenght:

[tex]Arc\ Length=2(3.14)(r)(\frac{C}{360})[/tex]

Where "r" is the radius and  "C" is the central angle of the arc in degrees.

You can identify in the figure that:

[tex]r=6.48\ in\\C=150\°[/tex]

Then, you can substitute values into the formula:

[tex]Arc\ Length=Arc\ RS=2(3.14)(6.48\ in)(\frac{150\°}{360})\\\\Arc\ RS=16.95\ in[/tex]

Rounded to the nearest tenth, you get:

[tex]Arc\ RS=17\ in[/tex]  

Answer: Price of a discount amision= Full Admission Price - discount Amount

Step-by-step explanation:

We have two variables "X" and "Y", where X= Full Admision Price and  Y= Discount Price of Admision  and we have to get the price of a discount admision or "Z" so the expresion will be Z= X-Y or Price of a discount admision = Full admision Price- discount Amount.

Answer:

  (2.31079, 6.83083)

Step-by-step explanation:

The transformation due to rotation about the origin in the counterclockwise direction by an angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

Here, that means the new coordinates are ...

  (4·cos(15°) -6·sin(15°), 4·sin(15°) +6·cos(15°)) ≈ (2.31079, 6.83083)

To rotate the point (4,6) counterclockwise about the origin by 15 degrees, we can use the rotation formulas. The new coordinates are approximately (2.833, 6.669).

To rotate a point counterclockwise about the origin, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Using the given point (4,6) and an angle of 15 degrees, we can substitute the values into the formulas to find the new coordinates:

x' = 4 * cos(15) - 6 * sin(15) = 4 * 0.9659258263 - 6 * 0.2588190451 ≈ 2.833166271

y' = 4 * sin(15) + 6 * cos(15) = 4 * 0.2588190451 + 6 * 0.9659258263 ≈ 6.669442572

Therefore, the new coordinates of the point after rotation are approximately (2.833, 6.669).

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Answer:

  -3

Step-by-step explanation:

The average rate of change is the y-difference divided by the x-difference:

  (2 -14)/(6 -2) = -12/4 = -3

The average rate of change for the sequence is -3.

Answer:

-3

Step-by-step explanation:

Answer:

  $240

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

[tex]m=\dfrac{12,000+12,000rt}{12t}=\dfrac{12,000+12,000\cdot 0.04\cdot 5}{12\cdot 5}\\\\m=\dfrac{14,400}{60}=240[/tex]

Keri's monthly loan payment is $240 per month.

Answer: 300 per month

Step-by-step explanation:

1. (3 + xz)(–3 + xz)

2. (y² – xy)(y² + xy)

3. (64y2 + x2)(–x2 + 64y2)

Explanation

The difference of 2 squares is in the form (a+b)(a-c).

(3 + xz)(–3 + xz) = (3 + xz)(xz -3)

                           = (xz + 3)(xz - 3)

                          = x²y²-3xy+3xy-9

                          =x²y² - 3²

(y² – xy)(y² + xy) = y⁴+xy³-xy³-x²y²

                          = y⁴ - x²y²

(64y2 + x2)(–x2 + 64y2)= (64y²+x²)(64y²-x²)

                                      = 4096y⁴-64y²x²+64y²x²-x⁴

                                      = 4096y⁴ - x⁴

Check the picture below.

For this case we have that by definition, the arc length of a circle is given by:

[tex]AL = \frac {x * 2 \pi * r} {360}[/tex]

Where:

x: Represents the angle between JM. According to the figure we have that x = 90 degrees.

[tex]r = \frac {16.4} {2} = 8.2[/tex]

So:

[tex]AL = \frac {90 * 2 \pi * 8.2} {360}\\AL = \frac {90 * 2 * 3.14 * 8.2} {360}\\AL = 12.874[/tex]

Rounding:

[tex]AL = 12.9[/tex] miles

Answer:

12.9 miles

Answer: 12.9

Step-by-step explanation:

Answer:

C: [tex]V=4840 (2 s.f.)[/tex]

Step-by-step explanation:

The formula for the volume of a cone is:

[tex]V= \frac{1}{3} \pi r^2h[/tex]

Therefore,

[tex]V=\frac{1}{3}\times 3.14\times(\frac{34}{2})^2\times 16\\\\V=4840 (2 s.f.)[/tex]

The volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

Volume can be defined as a three-dimensional space enclosed by an object or thing.

It is given that:

A pile of tailings from a gold dredge is in the shape of a cone.

The diameter of the base is 34 feet and the height is 16 feet.

As we know,

The volume of the cone is given by:

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

r = 34/2 = 17 ft

h = 16 feet

Plug the above values in the formula:

[tex]\rm V=\pi (17)^2\dfrac{16}{3}[/tex]

After solving:

V = 1541.33π cubic feet

Take π = 3.14

V = 1541.33(3.14) cubic feet

V = 4839.78 ≈ 4840 cubic ft

Thus, the volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.

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[tex]|\Omega|=50\cdot49=2450\\|A|=15\cdot14=210\\\\P(A)=\dfrac{210}{2450}=\dfrac{3}{35}\approx8.6\%[/tex]

The probability of randomly selecting two jelly beans in succession without replacement is;

0.0857

The jar contains 50 jellybeans.

Thus; N = 50

The individual berries include;

5 lemon

10 watermelon

15 blueberry

20 grape

Probability of first being a jelly bean = 15/50

Probability of second being jelly bean = 14/49

Thus,probability of selecting 2 jelly beans in succession without replacement is =

15/50 × 14/49 = 0.0857

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Answer:

f(x) is an odd function and g(x) is an even function

Step-by-step explanation:

Even Function :

A function f(x) is said to be an even function if

f(-x) = f(x) for every value of x

Odd Function :

A Function is said to be an odd function if

f(-x)= -f(x)

Part a)

[tex]f(x)=x^3+x[/tex]

let us substitute x with -x

[tex]f(-x) = (-x)^3-x\\=-x \times -x \times -x\\=-x^3-x\\=-(x^3+x)\\=-f(x)[/tex]

Hence

f(-x)=-f(x)

There fore f(x) is an odd function

[tex]g(x)=x^2+1[/tex]

Substituting x with -x  we get

[tex]g(-x)=(-x)^2+1\\=-x \times -x+1\\=x^2+1\\=g(x)[/tex]

Hence g(-x)=g(x)

Therefore g(x) is an even Function.

Part b)

hf(x)=hx^3

Answer:

9 bottles of water

Step-by-step explanation:

Marginal benefit is a microeconomic concept that explains how much the consumer adds satisfaction to each unit consumed of a given product. Usually, the marginal benefit is decreasing, which makes logical sense, the more a customer consumes a particular good, the smaller the benefit of the next unit.

At first, the first bottle of water has a high benefit as mentioned in the exercise:  9

In the second, you are a little less thirsty, so the benefit will be 10 - 1x2 = $8

In the ninth bottle, you will have very little thirst and the benefit will be 10 - 1x9 = $1

In the tenth bottle there is no benefit, the consumer is indifferent. As a rational consumer, you will buy until the bottle is still usable, even if minimal, for 9 bottles when your benefit is $1.

As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, you will buy a total of 10 bottles of water.

As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, the price of water is $1 per bottle.

The marginal benefit equation is given as MB = $10 - $x, where x represents the number of bottles of water you have had. So, for each bottle of water you consume, the marginal benefit decreases by $1.

To determine the number of bottles of water you will buy, you need to compare the marginal benefit to the price of water:

Therefore, you will buy a total of 10 bottles of water.

Answer:

b.

Step-by-step explanation:

First off, let's name these endpoints.  We will call them J(3, -2) and K(8, 0).  The point we are looking for that divides this into a 3:1 ratio let's call L.  We are looking for point L that divides segment JK into a 3:1 ratio.

A 3:1 ratio means that we need to divide JK into 3 + 1 equal parts, or 4.  Point L divides JK into a 3:1 ratio.  We need to find the constant of proportionality, k, that can be used in the formula to find the coordinates of L.  k is found by putting the numerator of the 3/1 ratio over the sum of the numerator and denominator.  Therefore, our k value is 3/4.

Now we need to find the slope of the given segment.

[tex]m=\frac{0-(-2)}{8-3}=\frac{2}{5}[/tex]

The coordinates of L can be found in this formula:

[tex]L(x, y)=(x_{1}+k(run),x_{2}+k(rise))[/tex]

Filling in:

[tex]L(x,y)=(3+\frac{3}{4}(5),-2+\frac{3}4}(2))[/tex]

Simplifying we have:

[tex]L(x,y)=(3+\frac{15}{4},-2+\frac{6}{4})[/tex]

Simplifying further:

[tex]L(x,y)=(\frac{12}{4}+\frac{15}{4},\frac{-8}{4} +\frac{6}{4})[/tex]

And we have the coordinates of L to be

[tex]L(x,y)=(\frac{27}{4},-\frac{1}{2})[/tex]

27/4 does divide to 6.75

Answer:

  x = 5

Step-by-step explanation:

You want to find x such that ...

  x^2 +(x +1)^2 = 61

  2x^2 +2x -60 = 0 . . . . . simplify, subtract 61

  x^2 +x -30 = 0 . . . . . . . divide by 2

  (x +6)(x -5) = 0 . . . . . . . . factor; solutions will make the factors be zero.

The relevant solution is x = 5.