if an open rectangular box is to have a fixed volume v, what relative dimensions will make the surface area a maximum

The points (-10, 0) and (0, 5), on the path of the first boat that can be modeled by a quadratic function and the point (10, 4) on the path of the linear function modelling the second boat, indicates that besides the common starting location, the solution for the point at which the paths of the  boats cross again at (6, 3.2)

The solution to a system of equation is the value of the input variable at which the output of the equations in the system of equations are the same.

Location of the port = (-10, 0)

The vertex of the path of the first boat that can be modeled by a quadratic function = (0, 5)

Point through which the boat that follows a path that can be modeled as a linear function passes = (10, 4)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where;'

(h, k) = The coordinates of the vertex

(h, k) = (0, 5)

Therefore;

y = a·(x - 0)² + 5 = a·x² + 5

When x = -10, y = 0, therefore;

y = 0 = a·(-10)² + 5 = 100·a + 5

0 = 100·a + 5

a = -5/100 = -1/20

a = -0.05

The equation is therefore; y = -0.05·x² + 5

The slope of the straight line path of the other boat is; m = (4 - 0)/(10 - (-10)) = 1/5 = 0.2

The equation is therefore; y - 0 = 0.2·(x - (-10)) = 0.2·x + 2

y = 0.2·x + 2

The point where the two paths cross is therefore;

-0.05·x² + 5 = 0.2·x + 2

-0.05·x² - 0.2·x + 5 - 2

-0.05·x² - 0.2·x + 3 = 0

x = (0.2 ± √((-0.2)² - 4 × (-0.05) × 3))/(2×(-0.05))

Therefore;

x = -10 and x = 6

The x-coordinate of the point the two paths cross, besides the starting location is x = 6

Therefore;

y = 0.2 × 6 + 2 = 3.2

The point besides the common starting location, the paths of the boats cross is; (6, 3.2)

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Answer:

(–6, 3.2)

Step-by-step explanation:

The answer above is correct.

On solving the provided question, we got -  0.001 is a stronger significance level,

any of a product's characteristics taken into account in respect to a certain characteristic. especially: a term's constant component as opposed to its variable. a value that represents a quality or attribute by a number (as of a substance, device, or process)

Whenever a variable is multiplied, a coefficient is used. In this case, "z" is a variable, making 6 a coefficient. 6z stands for 6 times z. Coefficient 1 applies to variables without a value.

0.001 is a stronger significance level, It means that the probability of error for the statistic is greater than 5 in 100, therefore the researchers concluded that the research is not statistically significant.

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The probability the game lasts less than 4.5 hours is 0.2877.

μ = mean population = 5

σ = standard deviation = 0.9

The probability for the game lasts less than 4.5 hours can be calculated using z test formula.

P(x < 4.5) = P(z < [tex]\frac{x-\mu}{\sigma}[/tex] )

= P(z < [tex]\frac{4.5-5}{0.9}[/tex])

= P(z < -0.56)

Using z table for P(z < -0.56). So,

= 0.2877

Thus, the probability is 0.2877 for the game lasts less than 4.5 hours.

Your question is incomplete, but most probably your full question was

on average, an american professional football game lasts about five hours, even though the ball is actually in play only 11 minutes. assume that game times are normally distributed with a standard deviation of 0.9 hour. 1. Find the probability that a game lasts less than 4.5 hours.

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Answer: 144a^14 b^8

Step-by-step explanation:

(-4a^(5)b^(3))^(2)* (-3a^(2)b)^(2) = 144a^14 b^8

Answer:

Step-by-step explanation:

ANSWER: 40x^2+10xy-15y^2

Lenth * Width * Height:

(4x+3y)*(2x-y)*5

Distribute 5 through the parentheses :

(20x+15y)*(2x-y)

Simplify:

40x^2-20xy+30xy-15y^2

Collect like terms:

40x^2+10xy-15y^2

As per the dimensions, the volume of rectangular-shaped glass is equal to 40x² + 10xy - 15y².

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.

As per the given information in the question,

Use the formula of volume:

Length × Width × Height:

(4x+3y) × (2x-y) × 5

5 should be distributed through parenthesis:

(20x+15y) × (2x-y)

Now, simplify the above equation,

40x² - 20xy + 30xy - 15y²

Now, keep all like terms together,

40x² + 10xy - 15y²

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Answer:

Step-by-step explanation:

hi

Answer:

Step-by-step explanation:

You want to know the x- and y-intercepts of a function described by a data table.

The x-intercept is the x-value where y = 0. There is no y=0 entry in the table, and the entries there are not regular enough to support any speculation as to how the function might be extrapolated.

There is no x-intercept.

The y-intercept is shown in the table where x=0.

The y-intercept is (0, 7).

The GPA of the student who scored 63 in the performance test is 2.394.

Given, a researcher analyzed data using linear regression correlating a performance test and GPA and calculated a slope of 0.028 and y-intercept of 0.63.

we have find the GPA of a student who scored 63 in the performance test.

Let the score of the student in performance test be, x

and the GPA of the student be, y

So, y = mx + c

as, m = 0.028 and c = 0.63

y = 0.028x + 0.63

at x = 63

y = 0.028×63 + 0.63

y = 2.394

So, the GPA of the student who scored 63 in the performance test is 2.394.

Hence, the GPA of the student who scored 63 in the performance test is 2.394.

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The quadratic equation 15[tex]x^{2}[/tex]-22x -7 = 0 has solution x = 1.7355 or -0.26886

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as

a[tex]x^{2}[/tex] + bx + c =0

where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation

given that

5(x-1)3x = 7(x+1)

15[tex]x^{2}[/tex]-15x = 7x +7

15[tex]x^{2}[/tex]-22x -7 = 0

x = -b ± [tex]\sqrt{b^{2}-4ac }[/tex]/2a

x = -(-22) ± [tex]\sqrt{(-22)-4(15)(-7)}[/tex] /2(15)

x = 1.7355 or -0.26886

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Answer: x = 12

Step-by-step explanation:  

Distribute the parenthesis on both sides of the equation

5x - 5 + 3x = 7x + 7

8x - 5 = 7x + 7 ( subtract 7x from both sides )

x - 5 = 7 ( add 5 to both sides )

x = 12

Therefore, your answer is: x = 12

The type of sample that the sample taken by Marlene represents is a Convenience sample.

Researchers who use convenience sampling obtain market research data from a pool of respondents who are conveniently accessible. Because it is so rapid, easy, and economical, it is the sampling procedure that is used the most frequently. If members choose to be part of the sample, they are frequently simple to get in touch with.

Therefore, Marlene employed a convenience sampling technique by going to the park, which was close by, and taking a sample of the people present.

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Answer:

Step-by-step explanation:

(attached)

Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

The fundamental presumptions of the binomial distribution are that each trial has only one possible outcome, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.

The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.

Hence, Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

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Answer:

He rolled a 6, 16 times

He rolled not a 6, 4 times

Brian did not roll 6 in the dice 14 times.

Subtraction is mathematic operation. Which is used to remove terms or objects in expression.

Given, Brian is playing a game of dice. He gets 10 points for each 6 he rolls. He loses 4 points every time he does not roll a 6.

After 20 tries his score is 144 points.

If he rolled 6 each time,

his score would be 200.

Subtracting the number 144 to 200.

200 - 144

= 56

And 56/4

= 14

That means he did not roll 6, 14 times.

Therefore, 14 times he did not roll 6.

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The simplification that explains the statement is [tex](9^{\frac{1}{2} })^{2} = (9^{\frac{1}{2} } )(9^{\frac{1}{2} } ) = 9^{\frac{1}{2} + \frac{1}{2} } = 9^{\frac{2}{2} } = 9^{1} = 9[/tex]

The law of indices(exponent) can be used to explain the following statement:

[tex]\sqrt{9} = 9^{\frac{1}{2} }[/tex]

Therefore, using the law of indices.

[tex](a^{x}) (a^{y} ) = a^{x+y}[/tex]

Hence, applying this law of exponents.

Exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent:

[tex](9^{\frac{1}{2} })^{2}[/tex]

[tex](9^{\frac{1}{2} } )(9^{\frac{1}{2} } )[/tex]

[tex]9^{\frac{1}{2} + \frac{1}{2} }[/tex]

[tex]9^{1}[/tex]

9

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The required relation between independent and dependent variables is y = x/4.

A simple method for considering  independent and dependent variables is, the point at which you're leading an examination, the free factor is what you change, and the reliant variable changes hence. You can likewise consider the autonomous variable the reason and the reliant variable as the impact

The independent variable x is the total number of students in the class.

And the dependent variable y is number of students in each group.

Therefore,

y = x / 4

Here, when we change the value of x then value of y automatically changed.

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Answer:

33.45 is the price of 11 dog food cans

The test hypothesis using 0.05 significance level has the following results:The treatment means differ, The block means do not differ.

A poll or study's findings can be tested using the statistical procedure known as hypothesis testing to see if the findings are significant. By calculating the likelihood that the findings happened by chance, you are basically evaluating if the findings are genuine. If it's possible that your results were a coincidence, the experiment won't be reproducible and won't be of much help.

Hypothesis testing may be one of the most perplexing components for students, mostly because you must first determine what your null is so that you can conduct a test. These challenging word problems that you encounter might sometimes be challenging to understand.

Make a plan for your null hypothesis.

Write down your null hypothesis

Determine the type of test you must do,

How to solve?

Describe the null and alternate treatment hypotheses:

Null hypothesis: No difference in treatment means

Alternative interpretation: The means differ

Indicate the treatment decision-making process:

F(1,2)=18.51 as seen in the table

Reject the null hypothesis if the estimated F exceeds 18.51.

Treatments Calculated F=43.75 > 18.51; hence, the null hypothesis is rejected.

As a result, we find that the treatment means differ.

Write out the null and alternative hypotheses for blocks.

Block means are not different under the null hypothesis.

A different theory There exists at least one pair of distinct meanings.

State the block decision rule as well:

Table F(2,2)=19.0 value

If the estimated F is greater than 19, reject the null hypothesis.

Blocks determined that F=8.14 19.0, thus we did not reject the null hypothesis.

Our conclusion is that the block means are equivalent.

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The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.

Given that,

A marksman has a 0.89 percent chance of hitting the target each time he fires.

We have to find what is the probability that he will only hit the target 13 times out of 15 shots.

We know that,

The probability of getting exactly k successes in n trials is given by the probability mass function that is,

P(X=k)=[tex](\frac{n}{k} )p^{k}(1-p)^{n-k}[/tex]

Where [tex](\frac{n}{k})= n!/k!(n-k)![/tex]

The probability that he hits the target at most 13 times is,

1-[P(he hits 14 times)+P(he hits 15 times)]

So, calculate the probability that he hits a target 14 times as follows:

P(X=14)=[tex](\frac{15}{14} )0.89^{14}(1-0.89)^{1}[/tex]

P(X=14)=15×(0.89)¹⁴×(0.11)

P(X=14)=0.3228

And the probability that he hits a target 15 times is

P(X=15)=[tex](\frac{15}{15} )0.89^{15}(1-0.89)^{0}[/tex]

P(X=15)=1×(0.89)¹⁵×(1)

P(X=15)=0.1741

And the required probability is

=1-[P(he hits 14 times)+P(he hits 15 times)]

=1-[0.3228+0.1741]

=0.5031

Therefore, The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.

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The equation of the path to find the dimensions of the patio is x² + (x + 5)² = 841.

Here we have to find the equation of the dimensions of the patio.

Data provided:

the path = 29 meters

length of the path is 5 meters more than the width of the path.

So let us assume that the length of the path is x

with this, the width of the path is x + 5

The formula for the diagonal:

Diagonal²  = length² + width²

Putting the data we have:

29² = x² + (x +5)²

841 = x² + (x+5)²

Therefore we get the equation as x² +(x + 5)² = 841.

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The slope and y-intercept of the given linear equation are [tex]-\frac{5}{4}[/tex] and [tex]5[/tex] respectively. The equation of the given graph is [tex]y=-\frac{5}{4} x+5[/tex]

What is the Slope of a graph?

What is a y-intercept?

Here, from the graph, we can find a line passing through the two points, [tex](4,0)[/tex] and [tex](0,5)[/tex].

The equation for the slope formula is given as, [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Using the slope formula, we get the slope of the given graph as,

[tex]m=\frac{ 5-0 }{0-4 }\\\implies m=-\frac{5}{4}[/tex]

The y-intercept (c) is the value of y when x equals zero.

The line is passing through the point [tex](0,5)[/tex]

Here, the value of x is equal to 0 and the value of y is equal to 5.

So, the y-intercept of the given graph, [tex]c=5[/tex]

We know that the equation of a straight line is expressed as, [tex]y=mx+c[/tex]

Substituting the values of m and c in the straight line equation form, we get the equation of the given line as,

[tex]y=-\frac{5}{4} x+5[/tex]

Therefore, the slope of the given graph, [tex]m=-\frac{5}{4}[/tex] and the y-intercept, [tex]c=5[/tex].

Also, the equation of the given line is [tex]y=-\frac{5}{4} x+5[/tex]

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Answer:

yes y/x = 5/2

Step-by-step explanation:

y/x = 5/2, 10/4=5/2, 15/6=5/2, 20/8=5/2

Answer:

Segment CE is 12 units.

Step-by-step explanation:

CD and DE add together to make CE. See image.

Use this idea to write an equation. Combine like terms and solve for x. Use the x value you find to calculate the length of CE. See image.

Answer:Answer:

D.

{(-9,8), (-5,-8), (-7,8), (-6,-8)}

Step-by-step explanation:

The value of z-stat is -0.6721.

What is z stat?

The relationship between a value and the mean of a group of values is quantified by a Z-stat. The Z-stat is calculated using standard deviations from the mean. When a data point's Z-stat is 0, it means that it has the same score as the mean.

One standard deviation from the mean would be indicated by a Z-stat of 1.0. Z-stats can be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the mean.

Solution Explained:

We use the formula,

[tex]z = \frac{P - \pi }{\sqrt{\frac{\pi (1-\pi )}{200} }}[/tex], where P is the observed proportion, π is the hypothesized proportion

Therefore, P = 42/200 = 0.21 & π = 23/100 = 0.23

Putting the values in

[tex]z = \frac{0.21 - 0.23 }{\sqrt{\frac{0.23 (1-0.23)}{200} }}[/tex]

After calculating, z-stat is therefore equal to -0.6721

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The number line that represents the number 0.7 is number line (B)

From the question, we have the following parameters:

From the dots on each line, we have the following statement

At minus 0.7 on B

This statement means that

B = -0.7

Hence, the number line represented by the statement is the number line B

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Answer:

Length=18 feet

Width=7 feet

Hope this helps! :)

Step-by-step explanation:

perimeter=50

length=18

width=w

Rectangle:2l+2w=50           2(18)+2(7)=50

36+2w=50

50-36=14

14/2=7

(36+14+50)

The formula that represents the volume of water in the tank in terms of the number of minutes since the water began draining is v = 40 - 1.5t.

This can be seen by realizing that the volume of water in the tank decreases by 1.5 gallons per minute, so after t minutes the volume will be 40 - 1.5t. The graph of this formula is a straight line with a slope of -1.5 and an intercept of 40. This means that the graph starts at the point (0,40), which represents a tank that is full of water, and decreases linearly as the number of minutes increases.

The statement "The graph of v in terms of t represents all possible values of v and t" is true. This is because the formula v = 40 - 1.5t is defined for all possible values of t, and the graph of this formula includes all possible pairs of (v, t) values that satisfy the formula.

The statement "The point (7.5,35.75) conveys that when the tank has been draining for 7.5 minutes, it has 35.75 gallons of water remaining" is false. This is because the point (7.5,35.75) does not lie on the graph of the equation v = 40 - 1.5t. The correct point on the graph that represents the volume of water in the tank after 7.5 minutes would be (7.5,26.25), which can be found by substituting t = 7.5 into the equation v = 40 - 1.5t.

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Answer:

60

Step-by-step explanation:

she read 60 pages in just 2 days

Both the given expression are equivalent expression as 5m + 4.

Given that,
to determine whether the two given expressions are equivalent ot each other,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
5(m + 1 ) - 1 = 2(2m + 2) + m
5m + 5 - 1 = 4m + 4 + m
5m + 4 = 5m + 4

Thus, Both the given expression are equivalent expression as 5m + 4.

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