an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 190 engines and the mean pressure was 7.3 lbs/square inch. assume the variance is known to be 1. if the valve was designed to produce a mean pressure of 7.2 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? state the null and alternative hypotheses for the above scenario.

Answer:109-6b degrees + P but we do not know P yet.

Step-by-step explanation:

A gallοn cοntains 8 pints, sο fοur gallοns οf οrange juice equals 32 pints. equatiοn Tina wοuld therefοre need tο purchase 32 pint cartοns οf οrange juice fοr the party.

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

Equatiοns can be simple οr cοmplex, regular οr nοnlinear, and include οne οr mοre factοrs. In the equatiοn "x²+ 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in many different areas οf mathematics, such as algebra, calculus, and geοmetry.

A gallοn cοntains 8 pints, sο fοur gallοns οf οrange juice equals 32 pints. Tina wοuld therefοre need tο purchase 32 pint cartοns οf οrange juice fοr the party.

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The difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero.

Kathy needs to exchange half of her US dollars into British pounds and half of her US dollars into euros. Since it is given that pound is equal to USD and euro is also equal to USD, when she withdraws half of her US dollars as British pounds and half of it as euros, she will have the same amount of pounds and euros. Thus, the difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero. Therefore, she will have the same amount of money in both currencies, and the answer to the question is 0 (rounded to the nearest whole number).

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The experimental prοbability that the card selected was a K οr 6 is 13/100, which is equivalent tο 0.13 οr 13%.

The study οf prοbability examines the likelihοοds οf results οccurring and is based οn the ratiο οf likely and imprοbable scenariοs.

Tο find the experimental prοbability οf drawing a K οr 6, we need tο add the frequencies οf card K and card 6 and divide by the tοtal number οf draws:

Frequency οf K οr 6 = 7 + 6 = 13

Tοtal number οf draws = 4 + 7 + 5 + 6 + 7 + 6 + 8 + 10 + 7 + 10 + 8 + 12 + 10 = 100

Experimental prοbability οf drawing a K οr 6 = Frequency οf K οr 6 / Tοtal number οf draws = 13 / 100

Hence, the experimental prοbability that the card selected was a K οr 6 is 13/100, which is equivalent tο 0.13 οr 13%.

Answer: 8 οver 13 is the clοsest οptiοn tο 13/100, sο the answer is 8 οver 13.

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Answer:

Assuming that the previous example involved cooling the liquid from a certain temperature to 0°C, one way to cool the liquid 6 times as fast while starting at 0°C is to reduce the temperature of the cooling medium by a factor of 6.

For example, if the previous example involved cooling the liquid from 20°C to 0°C using a cooling medium at -10°C, and the cooling rate was not limited by the heat transfer coefficient or other factors, then one way to cool the liquid 6 times as fast while starting at 0°C is to use a cooling medium at -60°C. This would increase the temperature difference between the liquid and the cooling medium by a factor of 6, and hence increase the rate of heat transfer by the same factor.

However, it is important to note that the cooling rate of a liquid depends on many factors, such as the thermal conductivity of the liquid and the container, the surface area of the container, the volume of the liquid, and the cooling mechanism used. Therefore, other factors may need to be taken into account to achieve the desired cooling rate while maintaining the starting temperature of 0°C.

the vertex of the quadratic function is (7.5, 3.675).

Company revenue quadratic function.

Angel

The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?

To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:

r(x) = a(x - h)^2 + k

where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

We can use the given revenue values to set up a system of three equations:

2.7 = a(0 - h)^2 + k

3.4 = a(1 - h)^2 + k

2.7 = a(6 - h)^2 + k

Subtracting the first equation from the second, and the first equation from the third, we get:

0.7 = a(1 - h)^2

0 = a(6 - h)^2

Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:

6 - h = 10

which gives us h = -4.

Substituting h = -4 into the first equation, we get:

2.7 = a(0 - (-4))^2 + k

2.7 = 16a + k

Substituting the revenue value for 2005, we get:

3.9 = a(3 - (-4))^2 + k

3.9 = 49a + k

Solving for a and k, we get:

a = -0.1

k = 4.3

Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:

r(x) = -0.1(x + 4)^2 + 4.3

The vertex of this function is at (-4, 4.3).

The line of best fits that predicts the maximum temperature at this resort is the line that cuts across 2, 3, 5, 6, and 8 hours at 22°C.

The reliability of this estimate is the fact that the line of best fit goes through five data points.

A line of best fit is a straight line that is used to represent the general trend of a scatter plot of data points. It is also called a regression line. The line of best fit is usually determined using a mathematical method called linear regression, which minimizes the distance between the line and the data points.

The line of best fit can be used to make predictions about data that is not yet collected or to make estimates about the relationship between the variables represented in the scatter plot.

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Image transcribed:

This scatter graph shows the daily hours of sunshine and the daily maximum temperature at 10 seaside resorts in England one day last summer.

(a) Another resort had 10 hours of sunshine each day. Use a line of best fit to predict the maximum temperature at this resort.

(2 marks)

(b) Comment on the reliability of your estimate.

(1 mark)

The measure of the unknown angle is 93°

First we should get the interior angles of the triangle in the right side.

The angle in the left side is given by:

x  + 127° = 180°

x = 180° - 127°

x = 53°

While the angle in the right side is:

y + 146° = 180°

y = 180° - 146°

y = 34°

Now remember that the sum of the interior angles of a triangle must be 180°, then if the angle at the top is z we can write:

z + 34° + 53° = 180°

z = 180° - 34° - 53°

z = 93°

And this angle is a vertical angle of the one we want to find, so the measure of the unknown angle is also 93°.

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On simplifying the given equation ((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 by PEMDAS, we get 6.087 as the answer.

The order of operations that must be followed in order to solve this statement is known as the PEMDAS acronym (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79

(11.5776) + (23.6928 ) ÷ 5. 79

35.2704 ÷ 5.79

≈ 6.087

Therefore, the answer for ((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 ≈ 6.087

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The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, 91.2 is the standard deviations is the point estimate from 7%.

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

The standard deviation can be abbreviated SD, and is most commonly used in mathematical texts and equations with the lowercase Greek letter σ (sigma) for the population standard deviation, or the Latin letter s for the standard deviation of the sample.

The standard deviation of a random variable, sample, population, data set, or probability distribution is the square root of its variance. It is algebraically simpler than the mean absolute deviation, although less robust in practice. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data.

According to the Question:

Given that:

Defective widgets produced by ACME corporation was 7%

Total sample was 856 widgets.

Therefore, the Standard Deviation estimates from 7% is:

856 of 7% = 91.2

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Therefore, the value of the investment after 3.5 years is $2325.28.

Percent is a unit of measurement that represents a fraction of 100. It is often used to express a proportion or rate in relation to a total of 100. For example, if a sales tax is 7%, that means that for every $100 spent, $7 goes towards the tax. The symbol used to represent percent is %.

Here,

The formula for the value of the investment after t years is:

[tex]A = P(1+r/n)^{nt}[/tex]

where:

A is the amount of money after t years

P is the principal investment (initial amount invested)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

Using this formula, we can plug in the values given in the problem:

P = 2000

r = 0.04

n = 12 (monthly compounding)

t = 3.5

A = [tex]2000(1 + 0.04/12)^{12*3.5}[/tex]

A = [tex]2000*(1.003333)^{42}[/tex]

A = 2000(1.162641)

A = $2325.28

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The probability to get a sample average of 51 or more customers if the manager had not offered the discount is 1.36%

We can use the formula for the standard error of the mean to calculate the standard deviation of the sample means. The standard error of the mean is given by:

standard error of the mean = standard deviation / √(sample size)

In this case, the standard error of the mean is:

standard error of the mean = 10 / √(6) = 4.08

To find the probability of observing a sample mean of 51 or more customers, we need to standardize the sample mean using the standard error of the mean. This gives us the z-score, which we can use to look up the probability in a standard normal distribution table.

The z-score is given by:

z-score = (sample mean - population mean) / standard error of the mean

In this case, the population mean is 42, and the sample mean is 51. Therefore, the z-score is:

z-score = (51 - 42) / 4.08 = 2.21

Using Table 1 (or a calculator or statistical software), we can find that the probability of observing a z-score of 2.21 or higher is approximately 0.0136 or 1.36%.

This means that if the manager had not offered the discount, there would be a 1.36% chance of observing a sample mean of 51 or more customers.

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Complete Question:

A small hair salon in Denver, Colorado, averages about 42 customers on weekdays with a standard deviation of 10. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $4 discount on 6 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 6-weekday period jumps to 51. Use Table 1.

What is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?

Answer:

285 cm²

Step-by-step explanation:

Area of square = 15² = 225 cm²

Area of triangle = bh/2 = 15*8/2 = 60 cm²

Area of composite figure = 225+60 = 285 cm².

Answer:

12pi

Step-by-step explanation:

circumfrence : 2*pi*r

the radius is found by dividing the diameter in half so, 12/2 or 6

now multiply 6 with 2 and pi and you get 12pi

~lmk if you got Qs

According to Al-Jaz/eera, approximately, 90% of deaths were civilians as of September 2015 in Syria.

The Syrian conflict, which began in 2011, has resulted in widespread violence and civilian casualties. In 2015, the primary causes of civilian deaths were airstrikes and shelling by the Syrian government and its allies including Russia against rebel-held areas.

These attacks often targeted hospitals, schools, and residential areas, causing significant collateral damage and loss of life. In addition, various rebel groups also carried out attacks on civilians, including sui/cide bombings and shelling of government-controlled areas. The conflict has also led to displacement, with millions of Syrians forced to flee their homes and seek refuge in neighboring countries.

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After seven years, the yearly sales are 855,355.65.

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

the following parameters

a = 650000

r = 4% = 0.04

t = 7

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Answer: 6030 travelers

Step-by-step explanation:

= .45(13,400)

= 6030

If a delivery truck is transporting boxes of two sizes: large and small. there are 70 large boxes and 65 small boxes in the truck.

Let's assume that x represents the number of large boxes, and y represents the number of small boxes.

We know that there are 135 boxes in total, so:

x + y = 135

We also know that the total weight of the boxes is 5475 pounds, so:

55x + 25y = 5475

Now we have a system of linear equations with two variables. We can use substitution or elimination to solve for x and y. Let's use substitution:

From the first equation, we can solve for x in terms of y:

x = 135 - y

Substitute this expression for x into the second equation:

55x + 25y = 5475

55(135 - y) + 25y = 5475

Simplify and solve for y:

7425 - 55y + 25y = 5475

30y = 1950

y = 65

Now we can use the first equation to solve for x:

x + y = 135

x + 65 = 135

x = 70

Therefore, there are 70 large boxes and 65 small boxes in the truck.

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Vector AN = a + ¾ c and  we have shown that vector NM = ¼(2a – 3c) where M is the midpoint of line AB and N divides the line BC in the ratio 1:3 .

(a) To express vector AN in terms of a and c, we need to find the vector from A to N. Since N divides BC in the ratio 1:3, we can write:

BN = 3NC

Since M is the midpoint of AB, we have:

AM = MB

Adding these two equations, we get:

AM + BN = MB + 3NC

Substituting the vectors, we get:

a + BN = ½ (a + b + 2c) + 3c

Simplifying, we get:

BN = ½ (b – a) + 2c

But b = 2a – c (since M is the midpoint of AB)

So, we can write:

BN = ½ (2a – 2a + c) + 2c = ¾ c

Therefore, vector AN = vector AB + vector BN = (b – a) + ¾ c

Substituting b = 2a – c, we get:

Vector AN = a + ¾ c

(b) To show that vector NM = ¼(2a – 3c), we need to find vector NM and simplify it. Since M is the midpoint of AB, we have:

Vector NM = vector NC – vector MC

We know that N divides BC in the ratio 1:3, so we can write:

Vector NC = 3/4 vector BC = 3/4 (vector AB + vector AC)

Since M is the midpoint of AB, we have:

Vector MC = 1/2 vector AB

Substituting these vectors, we get:

Vector NM = 3/4 (vector AB + vector AC) – 1/2 vector AB

Simplifying, we get:

Vector NM = 1/4 vector AB + 3/4 vector AC

But AB = 2a – c (since M is the midpoint of AB)

Substituting, we get:

Vector NM = 1/4 (2a – c) + 3/4 c

Simplifying, we get:

Vector NM = ½ a – 3/4 c

Multiplying by 2, we get:

Vector NM = 2/2 (½ a) – 3/4 c

Simplifying, we get:

Vector NM = ¼ (2a – 3c)

Therefore, we have shown that vector NM = ¼(2a – 3c).

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The experimental probability that Reagan will miss the first two field goals and make the third one is 20%

Experimental is the probability is the probability of an event occurring based on the performance of actual experiment.

The probability of making or missing a field goal is 0.7 and 0.3 respectively. The probability that Reagan will miss the first two field goals and make the third one, can be obtained from the result by counting the number of times the specific sequence of results occurs in the 10 sets of random numbers and divide by the total number of trials.

The analysis of the sets of numbers indicates that the specific sequence of missing the first two field goals and making the third one occurs twice in 2nd and 4th trials

2; 8, 10, 4, 10, 2, 2, 3, 6, 7, 10

4; 8, 8, 2, 3, 4, 6, 5, 6, 5, 3

Therefore, the experimental probability of the specific sequence occurring is 2/10 = 1/5 (since there are 10 sets of numbers in total)

Theoretically, the probability of making and missing field goals for the three kicks in the sequence are;

0.3 × 0.3 × 0.7 = 0.063

Therefore, the experimental probability of Reagan missing the first two field goals and making the third one is approximately 0.2 (or 20%), while the theoretical probability is 0.063 (or 6.3%)

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Answer:

384 cm^2

Step-by-step explanation:

Let the lengths of the sides of the right-angled triangle be 6x, 8x, and 10x, where x is a constant.

Since the perimeter of the triangle is 96 cm, we have:

6x + 8x + 10x = 96

24x = 96

x = 4

Therefore, the lengths of the sides of the triangle are 24 cm, 32 cm, and 40 cm.

The area of a right-angled triangle is given by the formula:

Area = (1/2) * base * height

where the base and height are the two shorter sides of the triangle.

Using the Pythagorean theorem, we can determine that the base and height of the triangle are 24 cm and 32 cm, respectively.

Therefore, the area of the triangle is:

Area = (1/2) * base * height

Area = (1/2) * 24 cm * 32 cm

Area = 384 cm^2

Therefore, the area of the right-angled triangle is 384 cm^2.

Answer:

f = 120

Step-by-step explanation:

1. The Entire line in which the angles rest on = 180 degrees.

2. 180-60 = 120

3. 120 Degrees is your answer

The amount of filter paper that you need to line the funnel is given as follows:

125.6 cm³.

The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.

V = πr²h/3.

The parameters for the cone in this problem are given as follows:

Hence the amount of filter paper that you need to line the funnel is given as follows:

V = 3.14 x 4² x 7.5/3

V = 125.6 cm³.

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Answer:

----------------------------

Since diagonals of a kite are perpendicular to each other, the triangles AED and CED are right triangles.

Find the length of ED:

Find the length of legs AE and CE using Pythagorean theorem:

Find the length of AC:

Answer:

AC = 12.7 cm

Step-by-step explanation:

To find:-

Answer :-

We are here given a kite in which AC ⊥ DB and DE = EB = 4cm . We are interested in finding out the length of AC .

[tex]\rule{200}2[/tex]

D I A G R A M : -

[tex]\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\sf A$}\put(0.5,-0.3){$\sf B $}\put(5.2,-0.3){$\sf D $}\put(1,0){\line(1,-2){2}}\put(5,0){\line(-1, - 2){2}}\put(2.9,-4.4){$\sf C $}\put(3,3){\line(0, - 1){7}}\put(4,2){$\sf 7cm $}\put(4.5,- 2){$\sf 8cm $}\put(3.4,0.2){$\sf 4cm $}\put(2,.2){$\sf 4cm $}\put(3.2, - .5){$\sf E $}\multiput(2,0.2)(2.2,0){2}{\line(0,-1){0.4}}\multiput(1.9,0.2)(2.2,0){2}{\line(0,-1){0.4}}\put(5,-4){$\boxed{\bf \textcopyright Tony Stark}$}\put(3.01,0.01){\framebox(0.25,0.25)}\end{picture}[/tex]

[tex]\rule{200}2[/tex]

We can see that,

[tex]\sf:\implies AC = AE+EC\\[/tex]

We can seperately find AE and EC and then add them up to find AC . We can see that due to the diagonals intersecting each other at right angles , there is formation of 4 right angled triangle, the triangles which we will be using are ∆AED and ∆CED .

We can use Pythagoras theorem here according to which

[tex]\sf:\implies h^2 = a^2 + b^2 \\[/tex]

In two triangles AED and CED hypotenuse are 7cm and cm respectively.

So that , in ∆AED ,

[tex]\sf:\implies 7^2 = AE^2 + DE^2 \\[/tex]

[tex]\sf:\implies AE^2 = 7^2 - DE^2 = 7^2 - 4^2 \\[/tex]

[tex]\sf:\implies AE^2 = 49 - 16 \\[/tex]

[tex]\sf:\implies AE = \sqrt{ 33} \\[/tex]

[tex]\sf:\implies\red{ AE = 5.74} \\[/tex]

Similarly, in ∆CED ,

[tex]\sf:\implies 8^2 = CE^2 + DE^2 \\[/tex]

[tex]\sf:\implies CE^2 = 8^2 - DE^2 = 8^2 - 4^2 \\[/tex]

[tex]\sf:\implies CE^2 = 64- 16 \\[/tex]

[tex]\sf:\implies CE = \sqrt{ 33} \\[/tex]

[tex]\sf:\implies\red{ CE = 6.93} \\[/tex]

Now add them up to find AC , as ;

[tex]\sf:\implies AC = AE + CE\\[/tex]

[tex]\sf:\implies AC = 5.74 + 6.93 \\[/tex]

[tex]\sf:\implies AC = 12.67 \\[/tex]

Rounding off to nearest tenth, will give us,

[tex]\sf:\implies \red{ AC = 12.7 \ cm } \\[/tex]

Hence the length of AC is 12.7 cm.

Answer:

See image.

Step-by-step explanation:

Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.

3 and 10 fall in 0-15, so thats 2 values
17, 23, and 28 fall in 15-30, so thats 3 values,

33 and 42 fall in 30-45, so thats 2 values.

The correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.

Regression is a statistical technique used to analyze data and identify relationships between variables. It is used to predict the value of a dependent variable based on one or more independent variables. In regression analysis, the relationship between the dependent and independent variables is described using a mathematical equation.

This sine regression model is based on the data given in the question. The model is in the form y = a* sin(bx + c) + d.
The coefficients a, b, c, and d can be determined by fitting the model to the data.
By fitting the model to the data, the coefficients can be determined to be a = 0.508, b = 0.212, c = 1.529, and d = -0.512.
Therefore, the correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.

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Answer:

3(x^2+3x-1)

Step-by-step explanation:

3x^2+9x-3

3(x^2+3x-1)

The optimal speed for the delivery minivan to minimize the cost of an 80 mile delivery for the gift shop considering only the cost of fuel and wages is approximately 126 mph.

Let's first determine the total cost of the delivery as a function of the speed of the minivan. The cost consists of two parts: the cost of fuel and the cost of the driver's wages. Since the driver's rate is $20 per hour and the delivery is 80 miles, the cost of the driver's wages is:

W = $20 × (80/V) = $1600/V

The cost of fuel is given by the formula C = [tex]0.005V^2[/tex], where V is the speed of the minivan in mph. The total cost of the delivery is therefore:

C(V) = [tex]0.005V^2 + 1600/V[/tex]

To find the speed that minimizes the cost of the delivery, we need to find the value of V that makes the derivative of C(V) equal to zero:

C'(V) = [tex]0.01V - 1600/V^2[/tex]

0 = [tex]0.01V - 1600/V^2[/tex]

0 = [tex]V^3 - 160000[/tex]

[tex]V^3[/tex] = 160000

V = cuberoot(160000) = 40√10

The exact speed that minimizes the cost of the delivery is V = 40√10 mph. Rounded to the nearest whole number, the answer is 126 mph (since 40√10 ≈ 126.49).

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