A sheet of metal 10 inches by 8 inches is to be used to make a open box. Squares of equal sides x are cut out of each corner then the sides are folded to make the box. Find the value of x (correct to 2 decimal places) that makes the volume a maximum.

Rewrite [tex]x^4y^2-3x^3y^3[/tex] using a common factor.

A) [tex]3xy(x^3y-x^2y)[/tex]

B) [tex]3xy^2(x2-x^2y)[/tex]

C) [tex]x^2y(xy-3xy^2)[/tex]

D) [tex]x^2y^2(x^2-3xy)[/tex]

option d

From the given graph we get, the coordinates of original P are (-6,-6).

So initial x=-6 and y=-6

Also from the graph we can see that the coordinates of transformed point P' are (-1,3)

So now, (-1,3) = (-6+5,-6+9) = (x+5,y+9)

Hence the first and second box are 5 and 9 respectively.

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Answer:

see explanation

Step-by-step explanation:

4x + 9 = 16

the error being made is that on dividing both sides by 4 all terms must be divided by 4.

to obtain x + 9 = 4 from 4x + 9 = 16

the term 9 has not been divided by 4

correct solution is

4x + 9 = 16 ( divide through by 4 )

x + [tex]\frac{9}{4}[/tex] = 4 ( each term being divided by 4 )

x + [tex]\frac{9}{4}[/tex] = 4 ( subtract [tex]\frac{9}{4}[/tex] from both sides )

x = 4 - [tex]\frac{9}{4}[/tex] = [tex]\frac{16}{4}[/tex] - [tex]\frac{9}{4}[/tex] = [tex]\frac{7}{4}[/tex] = 1.75

or

4x + 9 = 16 ( subtract 9 from both sides )

4x = 7 ( divide both sides by 4 )

x = [tex]\frac{7}{4}[/tex] = 1.75

A farmer has 180 bushels of wheat to sell at her roadside stand. She sells an average of 14 5/8 bushels each day.

The total change in the number of bushels she has for sale after 5 days can be represented as [tex]\frac{117}{8} X 5[/tex].

Define average.

The average is defined as the mean value, which is equal to the ratio of the sum of the number of values in a given set to the total number of values present in the set.

In plain English, an average is a single number taken as representative of a list of numbers, typically the sum of the numbers divided by how many numbers are in the list. For instance, the average of the digits 2, 3, 4, 7, and 9 is 5.

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Answer:

10.6m

Step-by-step explanation:

height of cylinder:

h= V/pie r^2

h= 48/3.14x1.2^2

h=48/3.14x1.44

h=48/4.5216

h=10.61meter

round to the nearest tenth

= 10.6m

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The value for expression 1 that is 3z+8 is 29 and for expression 2 that is 8y-x is 12 by substituting the values.

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation.

Here,

For expression 1,

3z+8 where z=7

3*7+8=29

For expression 2,

8y-x where x=20 and y=4

8*4-20=12

By substituting the values, the value for expression 1 ,(3z+8) is 29, and the value for expression 2, (8y-x) is 12.

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a. The system of inequalities that models the situation is:

The equation for the cost is: C(x,y) = 0.2x + 0.4y.

b. The graph is given by the image at the end of the answer, and the vertices are (4,4), (10,4) and (10,7).

c. The number of clay beads and glass beads in a necklace that costs the least to make is: 4 clay beads and 4 glass beads.

The variables for the system are presented as follows:

Each necklace has no more than 10 clay beads and at least 4 glass beads, hence the constraints are listed as follows:

The numbers of each beads are countable amounts, meaning that they cannot assume negative values.

Four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads, hence the final constraint is of:

4y ≤ 8 + 2x.

Each clay bead costs $0.20 and each glass bead costs $0.40, hence the cost function is given as follows:

C(x,y) = 0.2x + 0.4y.

Using the three constraints, the graph is given by the image at the end of the answer, and the vertices are as follows:

The minimum cost is at the vertex with the smallest numeric value of the cost function, hence the numeric values are listed as follows:

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Answer:

Step-by-step explanation:

Exact Form: 6/5

Decimal Form : 1.2
Mixed Number Form : 1 (whole number) 1/5

The equation of the line that passes through (-1, -1) and is parallel to x + y = 8 is x + y = -2

The equation of the line that passes through (-5, -2) and is parallel to y + 3x = 10 is 3x + y = -17

From the question, we are to determine the equation of the line passing through the given points and parallel to the given line.

NOTE: If two lines are parallel, then their slopes are equal

First, we will determine the slopes of the given line

x + y = 8

Write the equation in the slope-intercept form, y = mx + b

Where m is the slope

and b is the y-intercept

x + y = 8 becomes

y = -x + 8

Therefore, m = -1

Now, we will determine the equation of a line that has a slope of -1 and that passes through (-1, -1)

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

y - (-1) = -1(x - (-1))

y + 1 = -1(x + 1)

y + 1 = -x -1

x + y = -1 -1

x + y = -2

Hence, the equation is x + y = -2

Now, we will determine the slope of y + 3x = 10

Express the equation in slope-intercept form

y + 3x = 10

y = -3x + 10

Therefore, m = -3

Now, we will determine the equation of a line that has a slope of -3 and that passes through (-5, -2)

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

y - (-2) = -3(x - (-5))

y + 2 = -3(x + 5)

y + 2 = -3x - 15

3x + y = -15 -2

3x + y = -17

Hence, the equation is 3x + y = -17

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Step-by-step explanation:

b^3 x b^8 / b^5

b^11/b^5

b^(11-5)

b^6

The equation for the relation is [tex]p=k \frac{qr^2}{s}[/tex].

The value of k when q = 5, r = 4 and s = 6 is 3.

The value of p when q = 8, r= 6 and s= 9 is 96.

The value of s when p= 10, q=5 and r = 2 is 6.

A connection between two different items is called variation. There are two categories of difference. Direct Variation is the name of the first one. When two variables move in the same direction, direct variation occurs. Additionally, as one variable rises, the other variable rises as well. Inverse Variation is the second kind. When the two variables move in the opposite direction, inverse variation occurs. Additionally, this occurs when one variable rises while the other falls.

Since p varies directly as q and the square of r and inversely as s. So the equation will be [tex]p=k \frac{qr^2}{s}[/tex].

Now, finding the value of k, for p = 40 when q = 5, r = 4 and s = 6,

[tex]p=k \frac{qr^2}{s}\\40=k \frac{5\times4^2}{6}\\k = 3[/tex]

Now, finding the value of p when q = 8, r= 6 and s= 9,

[tex]p=3 \frac{8\times 6^2}{9}\\=96[/tex]

Now, finding the value of s when p= 10, q=5 and r = 2,

[tex]10=3 \frac{5\times 2^2}{s}\\\\10=3\times \frac{20}{s}\\s=6[/tex]

Therefore, the equation for the relation is [tex]p=k \frac{qr^2}{s}[/tex] , the value of k when p = 40 when q = 5, r = 4 and s = 6 is 3, the value of p when q = 8, r= 6 and s= 9 is 96 and the value of s when p= 10, q=5 and r = 2 is 6.

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The minimum value of the expression is -9

From the question, we have

the expression is 4cosx–3sinx−4.

minimum value of the expression =[tex]c- \sqrt{a^{2} +b^{2} }[/tex]

[tex]=-4- \sqrt{4^{2} +(-3)^{2} }\\=-4-5\\=-9[/tex]

Subtraction:

The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign. For instance, supposing there are nine oranges stacked together (as indicated in the above image), four oranges are taken out and put in a basket, leaving nine – four oranges, or five oranges, in the stack. Therefore, 9 minus 4 equals 5, or the difference between 9 and 4.

Different kinds of numbers can also use subtraction, which is not just applicable to natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.

The minuend, from which we subtract another number, is the first number in a subtraction process.

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Answer:127.5

Step-by-step explanation:

15% of 150 = 22.5

150-22.5=127.5

Answer:

Step-by-step explanation:

We must find p′, q′ in order to calculate the confidence interval; the sample proportion is p′ = 0.842; This is the population proportion's point estimate. Since CL = 0.95 is the requested confidence level, = 1 – CL = 1 – 0.95 = 0.05 (2) (2) = 0.025.

For P, what is the confidence interval at 95 percent?

Since 95% of the area under the curve falls within this interval, the interval (-1.96, 1.96) serves as a 95% confidence interval for the standard normal distribution.

What is the 95 percent confidence interval for the population's proportion of smokers?

Standard Error for Proportion Calculating a 95% Confidence Interval for each group separately is another way to consider whether smokers and nonsmokers have significantly different proportions with wrinkles. For the smokers, we have a certainty time period ± 2(0.0394) or 0.63 ± 0.0788.

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The weight of the pig now is 54.9562 kg.

Given that the farm veterinarian, checked, a particular pig weighed 59.8 kilograms. Dr. Mason just weighed the pig again and found out that it weighs 8.1% less now.

The reduction will be:

= Percentage × Original weight

= 8.1% × 59.8

= 4.8438 kg

Therefore the weight of the pig will be:

= Original weight - Reduction

= 59.8 - 4.8438

= 54.9562 kg

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when you are interrogating the external validity of a sample, option(b). how was the sample collected? is the most important question to ask.

What is External validity?

The concept of external validity is related to the concept of generalization. It's imperative to keep that in mind. It is important to remember that validity refers to the approximate truth of a proposition, an inference, or a conclusion. In other words, external validity refers to the relative truth of generalizations based on generalizations. The external validity of your study is the degree to which the conclusions are applicable to other people, places, and times.

An external validity threat is an explanation of how a generalization could be flawed. A study you conducted in a particular place, with certain types of people, at a particular time, can be generalized to another context (for instance, another place, with slightly different people, at a slightly different time). External validity can be compromised in three ways: people, places, and times.

Question

When you are interrogating the external validity of a sample, which is the most important question to ask?

a. how many people are in the sample?

b. how was the sample collected?

c. how were the participants measured?

d. how many people are in the population?

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The trigonometric function that can be used when given 2 sides that are not the hypotenuse is tangent.

When two sides are given that is not the hypotenuse, the trigonometric function that can be employed is the tangent.

A right-angle triangle has the following sides:

Hypotenuse

Adjacent side

the opposite side

The following trigonometric ratios can be used to determine the angles in a right-angle triangle:

sin = opposite/hypotenuse

cos = neighboring / hypotenuse

tan = opposite /adjacent

Tangent is the trigonometric function that can be used to determine the angle of a right-angle triangle given two sides other than the hypotenuse.

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Answer:

To make straight commission the better offer, you would have to sell more than $16666.67  per week.

Step-by-step explanation:

Set inequality, assuming the sales amount is x:

Answer:

More than $16,666.67.

Step-by-step explanation:

Define the variables:

Create an equation for each job offer using the defined variables and given information.

Job Offer 1

Straight commission of 5% of sales:

[tex]\implies y=0.05x[/tex]

Job Offer 2

A salary of $500 per week plus 2% of sales:

[tex]\implies y=500+0.02x[/tex]

For Job Offer 1 to be better, set the expression for this offer to be greater than the expression for Job Offer 2 and solve the inequality:

[tex]\implies 0.05x > 500+0.02x[/tex]

[tex]\implies 0.05x-0.02x > 500+0.02x-0.02x[/tex]

[tex]\implies 0.03x > 500[/tex]

[tex]\implies \dfrac{0.03x}{0.03} > \dfrac{500}{0.03}[/tex]

[tex]\implies x > 16666.66666...[/tex]

Therefore, to make straight commission (Job Offer 1) the better offer, you would have to sell more than $16,666.67 (nearest cent) per week.

The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2)  , the correct option is (b)  .

In the question ,

it is given that ,

the equation of the line is parallel to 2x + 2y = -12 ,

2x + 2y = 12

2y = -2x + 12

Dividing both sides by 2  , we get

y = -x + 6

So , the slope of the line is -1 ,

since the required line is parallel , so the slope of the required line is -1 .

So , the equation of the line passing through the points (2,-7) with slope -1 is

(y - y₁) = m(x - x₁)

(y -(-7)) = -1(x - 2)

y + 7 = -1(x - 2)

y + 7 = -(x - 2)

Therefore , The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2)    .

The given question is incomplete , the complete question is

Find the equation of a line parallel to 2x + 2y = -12 that passes through the point (2, -7) ?

(a) y+7=x-2

(b) y+7= -(x - 2)

(c) y-7=x+2

(d) y-7= -(x + 2)

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The height of the tree was 56 inches.

We can calculate the percentage of a certain amount by :

Subtracting  New - Original / New multiplied by 100

this implies it will be

75 - x / 75 × 100 = 25 %

7500 - 100 x = 1875

this implies 7500 - 1875 = 100 x

5625 = 100 x

Thus , On dividing both sides by 100 we get

56.25 = x

Now on rounding off this number we will get

56 = x

Thus the original height of the corn plant was 56 inches

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The probability that the first drawing gives green ball and second drawing a red ball is 2/7

Number of green balls = 4 green balls

Number of red balls = 4 red balls

Total number of balls in the bag = 4 + 4

= 8 balls

The probability = Number of favorable outcomes / Total number of outcomes

The probability of getting green balls in first draw = 4 / 8

= 1/2

First ball drawn was not replaced before drawing the second one

The probability of getting red ball in second draw = 4 / 7

The probability that the first drawing gives green ball and second drawing a red ball = (4/8) × (4/7)

= 2/7

Hence, the  probability that the first drawing gives green ball and second drawing a red ball is 2/7

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The equation for the line that runs between the points (8, 4) and (0, 2) has the following slope-intercept form is : y = 1/4 x + 2

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

Here,

A line's equation can be written as y = mx + b in slope-intercept form.

slope = m and y-intercept = b.

You can rewrite the equation in point-slope form as y = mx + b.

Given,

y - 4 = 1/4 (x - 8)

Change the formula to y = mx + b.

So,

y - 4 = 1/4 x - 2

We have to add 4 on both sides,

y - 4 + 4 = 1/4 x - 2 + 4

y = 1/4 x + 2

As a result, the equation of the line passing through the points (8, 4) and (0, 2) has the slope-intercept form is y = 1/4 x + 2 .

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The lower limit of the 95% confidence interval for the average miles per gallon is 23.32 mpg.

How to calculate the lower limit of the confidence interval?

Given,

n = 30

mean = μ = 24.1

standard deviation = σ = 2.1

confidence interval = 95%

Since the sample is 30, use t-table. If sample is greater than 30 use z-table.

Level of significance, α = 1 - 0.95 = 0.05

degree of freedom, df = n - 1 = 30 - 1 = 29

t value = 2.045

Lower limit = [tex]\mu-t\frac{s}{\sqrt{n}}[/tex]

= [tex]24.1 - 2.045\frac{2.1}{\sqrt{30}}[/tex]

= 24.1 - 0.784

= 23.316

= 23.32 mpg

Thus, the lower limit of the 95% confidence interval for the average miles per gallon is 23.32 mpg.

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Answer:

B 1/4

Step-by-step explanation:

f(x) = y = x⁴ + 5

the inverse function is

y - 5 = x⁴

x = 4th root(y - 5)

now we rename y and x to make it a regular function definition :

g(x) = y = ±4th root(x - 5) = ±(x - 5)^(1/4)

because g(6) = 1 (positive), we have

g(x) = (x - 5)^(1/4)

and since we are using the positive branch, it means also that all the tangent slopes (= g'(x)) are positive.

g'(x) = 1/4 × (x - 5)^(-3/4) × 1 = 1/4 × (x - 5)^(-3/4)

because (x - 5)' = 1

g'(6) = 1/4 × (6 - 5)^(-3/4) = 1/4 × (1/1³)^(1/4) =

= 1/4 × 1^(1/4) = 1/4 × 1 = 1/4

please note, we are using only the positive root result in this case to get a positive result as tangent slope for g(x) as enforced by g(6) = 1.

Answer:

[tex]y = 2x - 5[/tex]

Step-by-step explanation:

The first step in finding the equation of a line from a given set of points is to find its slope. The slope of a line is defined by the formula:

[tex]m = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

In this problem, we are given two points in the form [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].

So, we can define the x's and y's as:

[tex]x_1 = 3[/tex], [tex]y_1 = 1[/tex], [tex]x_2 = 1[/tex], [tex]y_2 = -3[/tex].

Hence, the slope of the line can be solved for.

[tex]m = \dfrac{-3 - 1}{1 - 3}[/tex]

[tex]m=\dfrac{-4}{-2}[/tex]

[tex]m = 2[/tex]

So, the slope of the line is 2.

Now, we can plug this into the point-slope equation for a line where (a, b) is a point on the line and m is its slope.

[tex]y - b = m(x - a)[/tex]

I will use the point (3, 1):

[tex]y - 1 = 2(x - 3)[/tex]

and isolate y to put it into slope-intercept form.

[tex]y - 1 = 2x - 6[/tex]

[tex]y = 2x - 6 + 1[/tex]

[tex]y = 2x - 5[/tex]

So, the equation in slope-intercept form for the line that goes through the points (3, 1) and (1, -3) is [tex]y = 2x - 5[/tex].

Yes, the triangle with the given side lengths exists because the triangle inequality holds true.

At first, students might think that the lengths of the sides of a triangle can be any three lengths, but that is not so. The triangle inequality says that the length of any side must be less than the sum of the lengths of the other two sides.

We are given a set of three side lengths. The side lengths are 3, 4, and 5. We need to check whether a triangle can be formed using the given three side lengths. We will use the triangle inequality.

The first inequality is 3 + 4 > 5. This inequality holds true because 7 is greater than 5. The second inequality is 4 + 5 > 3. This inequality holds true because 9 is greater than 3. The first inequality is 5 + 3 > 4. This inequality holds true because 8 is greater than 4. The triangle inequality holds true, so a triangle with the given side lengths exists.

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The equation of the situation is t = 400 - 25w. The y-intercept and slope of the equation are 400 and - 25 respectively.

You have 400 turkeys on your farm and you decide to shoot 25 each week. The slope and y-intercept for the situation can be represented as follows;

Using slope intercept form equation,

y = mx + b

where

t = 400 - 25w

where

Therefore, the y-intercept is 400 and the slope is - 25.

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The speed of the output shaft is 182 rpm.

Given:

Gear index i = 0.33

Input speed = 60 rpm.

Let output shaft speed is x.

we know that:

gear index = [tex]\frac{n_{in} }{n_{out} }[/tex]

i = 60/x

0.33 = 60/x

x = 60/0.33

= 60/033/100

= 60*100/33

= 6000/33

= 181.818 ≈ 182 rpm.

Therefore The speed of the output shaft is 182 rpm.

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The example demonstrating the commutative property is 12*8 = 8*12, the examples demonstrating associative property are (2+3)+6 = 2+(3+6) and 6*(7*3) = (6*7)*3 and the examples for the distributive property are 5*(2+5) = 10+25 and 4*(3+6) = 12+24.

According to the question,

We have the following information:

1) 5*(2+5) = 10+25

2) (2+3)+6 = 2+(3+6)

3) 4*(3+6) = 12+24

4) 6*(7*3) = (6*7)*3

5) 12*8 = 8*12

We know that commutative property of multiplication states:

a*b = b*a

So, this applies to 5th one.

Associative property of addition:

(a+b)+c = a+(b+c)

Associative property of multiplication:

(a*b)*c = a*(b*c)

Now, this applies to 2nd and 4th one.

Distributive property:

a*(b+c) = a*b+a*c

This applies to 1st and 3rd one.

Hence, the example demonstrating the commutative property is 12*8 = 8*12, the examples demonstrating associative property are (2+3)+6 = 2+(3+6) and 6*(7*3) = (6*7)*3 and the examples for the distributive property are 5*(2+5) = 10+25 and 4*(3+6) = 12+24.

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