A box with a square base and open top must have a volume of 62500 cm3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A'(x). A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x² .] A'(x) = 0 when x =

Answer:

Step-by-step explanation:

[tex]f(x)=\frac{27}{4} x[/tex]

[tex]p(x)=\sqrt{3x}[/tex]

[tex][p(x)]^6=(3^\frac{1}{2}x^\frac{1}{2})^6= 27x^3[/tex]

[tex][p(x)]^6g(x)=27x^3(\frac{x}{4} )=\frac{27x^4}{4}[/tex]

[tex][p(x)]^6g(x)[t(x)]^3=\frac{27x^4}{4} (\frac{1}{x} )^3=\frac{27x^4}{4x^3} =\frac{27}{4} x[/tex]    

Solution:     [tex][p(x)]^6g(x)[t(x)]^3=f(x)[/tex]

I think there might be nicer solutions but this works!

Using the unitary method we calculate that the friend would be 20 miles closer in an hour.

If you are running towards a faraway friend at a speed of 5 miles per hour and she is biking towards you at 15 miles per hour, According to relative motion's concept, the total speed at which you are approaching each other is:

5 miles / hour - (- 15 miles / hour) = 20 miles / hour

Also, we know that

speed= distance/time according to which, after 1 hour, you and your friend would have closed the distance by,

20 miles/hour × 1 hour = 20 miles

Therefore, you would be 20 miles closer to each other after 1 hour.

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Answer: B --3/2

Step-by-step explanation:

-4,8 TO -2,5

You would go down -3 steps first

Then you would go 2 steps.

Not sure if this is right but hopefully it works :D

The variance for the number of defective parts is 0.7125.

(a) What is the probability that exactly 3 parts will be defective? (Round your answer to four decimal places.)In the given question, the probability of a part being defective is 5%, which is represented as p=0.05. The probability of a part being non-defective is (1 - 0.05) = 0.95.The given question represents a binomial experiment, which includes the following conditions:The experiment consists of n identical trials.Each trial has only two possible outcomes, a success, and a failure.Success has probability p and failure has probability 1-p.The trials are independent.To calculate the probability of exactly 3 parts being defective when 15 parts are selected randomly, we use the following formula:P (X = k) = nCk x pk x (1-p) n-kWhere P(X=k) is the probability of getting k defective parts, nCk is the number of ways of getting k defects from n parts, pk is the probability of getting k defective parts, and (1-p) n-k is the probability of getting n-k non-defective parts.p = 0.05q = (1 - 0.05) = 0.95n = 15a. P (X = 3) = 15C3 x 0.05³ x 0.95¹² = 0.2508The probability of getting exactly 3 defective parts is 0.2508. Hence, the required probability is 0.2508.(b) What is the probability that the number of defective parts will be more than 2 but fewer than 6? (Round your answer to four decimal places.)b. We need to calculate the probability of getting defective parts more than 2 but less than 6.P (3 < X < 6) = P (X = 3) + P (X = 4) + P (X = 5)P (X = 3) = 15C3 x 0.05³ x 0.95¹² = 0.2508P (X = 4) = 15C4 x 0.05⁴ x 0.95¹¹ = 0.0925P (X = 5) = 15C5 x 0.05⁵ x 0.95¹⁰ = 0.0204P (3 < X < 6) = 0.2508 + 0.0925 + 0.0204 = 0.3637The probability of getting defective parts between 2 and 6 is 0.3637. Hence, the required probability is 0.3637.(c) What is the probability that fewer than 3 parts will be defective? (Round your answer to four decimal places.)c. We need to calculate the probability of getting fewer than 3 parts defective. The probability of getting zero defective parts or getting one defective part is given by:P (X = 0) = 15C0 x 0.05⁰ x 0.95¹⁵ = 0.4630P (X = 1) = 15C1 x 0.05¹ x 0.95¹⁴ = 0.3456P (X < 3) = P (X = 0) + P (X = 1) = 0.4630 + 0.3456 = 0.8086The probability of getting fewer than 3 defective parts is 0.8086. Hence, the required probability is 0.8086.(d) What is the expected number of defective parts?The expected number of defective parts is given by:μ = npμ = 15 × 0.05μ = 0.75The expected number of defective parts is 0.75.(e) What is the variance for the number of defective parts?The variance for the number of defective parts is given by:σ² = npqσ² = 15 × 0.05 × 0.95σ² = 0.7125The variance for the number of defective parts is 0.7125.

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From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).

To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:

Rewrite the inequality in terms of tangent:

Divide both sides by cos(x) to get:

tan(x) > 1

Find the solutions of the equation tan(x) = 1:

tan(x) = 1 when x = π/4 or x = 5π/4.

Check the sign of tangent in the intervals between the solutions:

We need to check the sign of tan(x) for x values in the following intervals:

(0, π/4), (π/4, 5π/4), and (5π/4, 2π).

In the interval (0, π/4), tan(x) is positive and less than 1.

In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.

In the interval (5π/4, 2π), tan(x) is negative and less than -1.

Determine the solution set:

Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:

π/4 < x < 5π/4

In interval notation, we can write:

(π/4, 5π/4)

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As per the given coordinates, dimensions of the rectangle are √13 x √13.

One way to do this is to find the distance between two parallel sides of the parallelogram. In this case, we can look at sides AB and CD, which are parallel to each other.

The distance between points A and B is the

=> √((3-1)² + (2-(-1))²) = √13

which simplifies to the square root of 13. Similarly, the distance between points C and D is the

=> √((1-(-1))² + (3-0)²) = √13.

Therefore, the length of the rectangle is the distance between sides AB and CD, which is the square root of 13.

Therefore, the width of the rectangle is 2 units. So the dimensions of the rectangle are 2 units by the square root of 13 units.

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Answer:

4 units by 4 units

Step-by-step explanation:

i got it correct on edg :)

The numbers that are solutions to the inequality w < 1 are: -1.3, -5 and 0

Numbers 5 and 0.9 are not solutions to the inequality because they are greater than or equal to 1. An inequality is a statement that compares two quantities or expressions using a mathematical symbol indicating their relative sizes. Inequalities are used to describe a range of values or solutions, rather than a single solution, and are often represented on a number line. Inequalities are commonly used in algebra, calculus, and other areas of mathematics, as well as in science, economics, and engineering. Solving inequalities involves finding all possible values of the variable that satisfy the inequality. This can be done by applying algebraic operations and graphing techniques to isolate the variable and determine the appropriate range of values.

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Answer:

If the value of Mike's car decreased by 30%, we can calculate the new value of the car as follows:

New value = Original value - (Percentage decrease × Original value)

Percentage decrease = 30%

Original value = 12000

New value = 12000 - (0.30 × 12000)

New value = 12000 - 3600

New value = 8400

Therefore, at the end of the decrease, the value of Mike's car was 8400.

Answer:

[tex]\sqrt{231}[/tex] cm

Step-by-step explanation:

The Pythagorean theorem is a mathematical principle that relates to the three sides of a right triangle. The formula for this is:

[tex]a^2 + b^2 = c^2[/tex]

In this case, the hypotenuse (c) is 16 cm, and one of the legs (a) is 5 cm. We can plug in the values and solve for the missing value.

[tex]5^2+b^2=16^2[/tex]

[tex]25+b^2=256[/tex]

[tex]b^2=256-25[/tex]

[tex]b^2=231[/tex]

[tex]b = \sqrt{231}[/tex] cm

Answer:

-3, 2+3i, and 2-3i.

Step-by-step explanation:

To find the roots of x^3-x^2+x+39=0, we use the Rational Root Theorem and synthetic division to test possible rational roots. We find that -3 is a root, and divide by (x+3) to get the quadratic factor x^2-4x+13=0. Solving this using the quadratic formula gives us the remaining roots of 2+3i and 2-3i. Therefore, the roots of the equation are -3, 2+3i, and 2-3i.

Answer: the answer is c I think

There is an 11/15, or around 0.733, chance that you won't be a hobbit or wear an umbrella.

Since, A total of 3 x 5 = 15 outcomes are possible given the presence of 3 characters and 5 defense mechanisms.

There are three scenarios if the character is a hobbit (hobbit with magic, hobbit with sword, and hobbit with shield), three scenarios where the tool is an umbrella (any character with an umbrella), and one scenario where neither.

As a result, there are the following number of possibilities where neither the character nor the tool is a hobbit:

15 - 3 - 1 = 11

One of these 11 outcomes is likely to occur at a rate of:

= 11/15

As a result, there is an 11/15, or around 0.733, chance that you won't be a hobbit or wear an umbrella.

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Given:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

put the given values in tha equation

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

The volume of water in each bowl is approximately 666.67 ml.

Miko bought five 2-liter bottles of water, which means that she had a total of 10 liters of water. She then poured all the water equally into 15 bowls. To find out the volume of water in each bowl, we need to divide the total volume of water by the number of bowls.

We can start by converting the 10 liters of water into milliliters (ml), which will make it easier to work with. To do this, we multiply 10 by 1000, since there are 1000 ml in one liter. This gives us a total of 10,000 ml of water.

Next, we divide the total volume of water (10,000 ml) by the number of bowls (15) to find the volume of water in each bowl. This can be written as:

Volume of water in each bowl = Total volume of water / Number of bowls

Volume of water in each bowl = 10,000 ml / 15

Volume of water in each bowl = 666.67 ml (rounded to two decimal places)

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Therefore , the solution of the given problem of triangle comes out to be the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.

A polygon is a hexagon if it has over one extra segment. It's shape is a simple rectangle. Only the sides A and B can differentiate something like this arrangement from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a portion of the cube. Three edges and three angles make up a triangle.

Here,

The rule of cosines can be applied to the triangle PQR to determine the length of side PQ:

=>  PQ² = PR² + QR² - 2(PR)(QR)cos(∠PQR)

=>  PQ² = 9² + 12² - 2(9)(12)cos(62°)

=>  PQ² ≈ 110.03

=> PQ ≈ 10.49

As a result, side PQ is roughly 10.49 units long.

The rule of sines can then be used to determine the dimensions of angles P and Q:

=> sin(∠P) / PQ = sin(62°) / PR

=>  sin(∠P) / 10.49 = sin(62°) / 9

=>  sin(∠P) ≈ 0.6322

=>  ∠P ≈ 39.39°

=>  sin(∠Q) / PQ = sin(77°) / QR

=>  sin(∠Q) / 10.49 = sin(77°) / 12

=>  sin(∠Q) ≈ 0.8559

=>  ∠Q ≈ 58.10°

As a result, the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.

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Answer:

Step-by-step explanation:

you are going to give more info ?????

As per the coordinate, the equation of the tangent line is  y = (-1/2)x - 3.

In this problem, we are given the equation of a circle, x² + y² = 20, which represents all the points on the plane that are equidistant from the origin (0,0) with a distance of √20 or a radius of

=> √20/2 = 2√5.

Now, let's consider point A. We know that it lies on the circle, so it must satisfy the equation x² + y² = 20. Additionally, we are told that its y-coordinate is -4. Using this information, we can substitute y=-4 into the equation of the circle to get

=> x² + (-4)² = 20,

which simplifies to x² = 4.

Thus, point A has coordinates (±2, -4), and we can determine which one is correct by looking at the circle's equation.

Next, let's consider point B. We are told that its x-coordinate is √10. Since point B lies on the circle, it must also satisfy the equation

=> x² + y² = 20.

Using this equation, we can substitute x=√10 to get

=> (√10)² + y² = 20,

which simplifies to y² = 10. Thus, point B has coordinates (√10, ±√10).

To find the y-intercept, we can use the fact that point A lies on the tangent line. Substituting the coordinates of point A into the equation of the tangent line, we get -4 = (-1/2)(±2) + b, which simplifies to b = -3. Thus, the equation of the tangent line at point A is y = (-1/2)x - 3.

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Complete Question:

A point A lies on the circle with the equation x² + y² = 20 and has y-coordinate -4

A point B lies on the circle and has x-coordinate √10

A tangent line set at A intersects the tangent at B at point C

Find the equation of the tangent line.

In order to decrease the insurance premium, the insurance company should charge an ordinary deductible of $18,400.

The expected insurance payment without a deductible is the full value of the damage, or $46,000.

With a deductible.

The expected insurance payment would be 60% of that, or $27,600.

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The total number of marbles in the bag is[tex]8 + 3 + 8 = 19[/tex]. We can represent the sample space as follows:

[tex]S = {(R, R), (R, B), (R, Y), (B, R), (B, B), (B, Y), (Y, R), (Y, B), (Y, Y)}[/tex]

Note that the sample space contains 9 elements.

The experiment involves selecting two marbles (without replacement) from a bag containing eight red marbles (denoted by R), three blue marbles (denoted by B), and eight yellow marbles (denoted by Y).

The sample space of the experiment is the set of all possible outcomes.

Each outcome is represented by an ordered pair of the colors of the two marbles selected. Since we are selecting two marbles without replacement, the order in which we select the marbles matters. Hence, we use ordered pairs to represent each outcome.

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Draw rectangles for each interval with a height equal to the frequency. The rectangles should be adjacent to each other and have equal width.

What is rectangle?

A rectangle is a two-dimensional shape with four sides, where the opposite sides are equal and parallel, and all angles are right angles (90 degrees).

To create a histogram, you need to first group the data into intervals or bins. You can use the intervals given in the table as a guide, or you can create your own intervals.

For this example, I will use the intervals [0-10), [10-20), [20-30), [30-40), [40-50), [50-60), [60-70), [70-80), [80-90), and [90-100).

Next, count the number of scores that fall into each interval. For example, there are no scores between 0 and 10, one score between 10 and 20, two scores between 20 and 30, and so on.

Therefore, plot the intervals on the x-axis and the frequency (or count) on the y-axis. Draw rectangles for each interval with a height equal to the frequency. The rectangles should be adjacent to each other and have equal width.

below is the histogram -

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The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].

Given:

Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]

Expand the equation

[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]

[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]

[tex]5^2 = 25[/tex]

Then, substitute the expanded expressions into the equation

[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]

Simplify and combine like terms

[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]

Rearrange the equation so that one side is 0

[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.

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Answer:

Step-by-step explanation:

It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.

Answer:

120 minutes / 2 hours

Step-by-step explanation:

time = distance / velocity

[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]

Answer:

first one

Step-by-step explanation:

The equation that models the future cost of gasoline is y=1.19(1.003)^(x), where "y" represents the future cost of gasoline per gallon and "x" represents the number of months since January 1, 1999.

In this equation, the initial cost of gasoline is $1.19 per gallon, and the cost increases by 0.3% per month, which is represented by the factor of (1.003)^(x).

Using this equation, you can calculate the future cost of gasoline for any number of months after January 1, 1999. For example, if you want to calculate the cost of gasoline 24 months after January 1, 1999, you can plug in x=24 and calculate y as follows:

y = 1.19(1.003)^(24)

y = 1.19(1.08357)

y = 1.288 per gallon

Therefore, the predicted cost of gasoline 24 months after January 1, 1999 is $1.288 per gallon.

0.1 for the top left, 0.2 for bottom middle

All the reasonable measurement for each object can be define as given table below.

Measurements refer to the process of determining the magnitude, quantity, or degree of something using standardized units or instruments. It involves observing and recording data about an object, event, or phenomenon, and then comparing it to a reference standard to obtain a numerical value. They allow us to quantify and compare physical properties accurately and provide a universal language for expressing quantities.

                Objects                                           Measurements

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answer is in the image below:

The suggest that the method is effective.

Assuming different groups of couples use a particular method of gender selection and each couple gives birth to one baby, the probability of a girl is 0.5, and the groups consist of 17 couples, then:

a. The mean is μ= 8.5, and the standard deviation is σ= 3.5.

b. The values separating results that are significantly low or significantly high are 8.5 girls or fewer are significantly low, and 11.5 girls or greater are significantly high.

c. The result of 15 girls is significantly high, because 15 girls is greater than 11.5 girls. This would suggest that the method is effective.

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This means that when the bacteria culture is first created (at 9:00 AM), there are already 300 bacteria present.

What is a graph?

A graph is a visual representation of data or mathematical functions. Graphs are used to present data in a clear and concise manner, making it easier for people to understand and interpret the information being presented.

a. To estimate the number of bacteria at 11 AM, we need to plug in t = 2, since 11 AM is two hours after 9:00 AM. Therefore:

P = 300(2.7)^(0.02*2)

P = 300(2.7)^0.04

P ≈ 369.13

So, there are approximately 369.13 bacteria at 11 AM.

b. To graph the function, we can use a graphing calculator or software. The p-intercept is the point where the graph intersects the y-axis, which occurs when t = 0. We can find the p-intercept by setting t = 0 in the equation:

P = 300(2.7)^(0.02t)

P = 300(2.7)^(0.02*0)

P = 300

Therefore, the p-intercept is (0, 300). This means that when the bacteria culture is first created (at 9:00 AM), there are already 300 bacteria present.

The domain of this situation is all non-negative values of t, since time cannot be negative. The range is all positive values of P, since the number of bacteria is always increasing. Therefore, a reasonable domain for this situation would be [0, ∞) and a reasonable range would be (0, ∞).

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Answer:

Step-by-step explanation:

You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.

a) The probability that the player is a non-pitcher not from the Dominican Republic is given as follows: 0.7578 = 75.78%.

b) The probability that a Dominican player is a pitcher is given as follows: 0.8595 = 85.95%.

c) The probability that a non-pitcher is not Dominican is given as follows: 0.4985 = 49.85%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Of the Dominican players, the percentages are given as follows:

The total percentage of Dominican players is of 10.5%, hence the value of x is given as follows:

0.056 x 0.42 + 0.58x = 0.105

x = (0.105 - 0.056 x 0.42)/0.58

x = 0.1405.

Of the 58% of the batter, 14.05% are from the Dominican Republic, hence the probability of chosen a batter not from the Dominican Republic is of:

p = 1 - 0.1405/0.58

p = 0.7578 = 75.78%.

14.05% of the players from the Dominical Republic are batters, hence the probability of choosing a pitcher is given as follows:

1 - 0.1405 = 0.8595 = 85.95%.

Of the 58% of the batters, 14.05% are Dominican, hence the 85.95% are not Dominican, thus the probability of choosing a non-Dominican batter is given as follows:

0.58 x 0.8595 = 0.4985 = 49.85%.

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Answer:

C

m= 7 LO= 14 MO= 14

Step-by-step explanation:

LO and NO are going to be the same length



m + 7 = 2m

to get the variable alone subtract m from both sides

7 = m)

plug 7 into both equations

7 + 7 = 14

2 x 7 = 14