a piece of solid aluminum is in the shape of a cube. if the temperature of the cube is increased so that the length of each side increases by a factor of 0.001 (that is, by 0.10%), by what factor does the volume of the cube increase?

the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Now the simplest way to write an equation is to multiply all the factors.

The zeroes of the equation are 1,2,3,4,5,6,7.

The factors can be written as (x-1)* (x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-7).

So the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]

Hence, the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]

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When the population standard deviation is much greater than 5.

What is the standard deviation?

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Here, we have

The circumstance is a score that is 5 points above the mean considered a central value.

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

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Answer:

rhe general pattern in data is........

Step-by-step explanation:

.....

The coefficient of determination is 0.588 and the percentage of the total variation is 58.8%.

The coefficient of determination (r^2) refers to a measurement used to explain how much variability of one variable can be caused by its relationship to another related variable. It is the fit of goodness and measures how well a statistical model fits the observed data and is a number between 0 and 1. When the value of linear correlation coefficient r is known, the coefficient of determination can be computed simply by squaring r.

Hence if r = 0.767, then the coefficient of determination = r^2 = 0.588

As percentage of the total variation is same as the coefficient of determination (given in percentage) and is given by the R² value = 58.8%. Hence, about 58.8% of variation is explained by the linear relationship between the two variables.

Note: The question is incomplete. The complete question probably is: Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.767.

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Option B, The center 95% of players had an average weight of 151 pounds.

Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.

So, let x represent a football player's weight.

X ≅ N(200, (25)²)

The minimal weight of the center 95% of the members is

P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)

P(X > 95) = P(-4.2 < z)

P(X > 95) = - P(z < -4.2)

P(X > 95) = 0.1512

The needed percentage is 0.1512 × 100 = 151.2 percent.

A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

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Answer:

y = x × 3, 12

Step-by-step explanation:

If a recipe for cheesecake requires 3 cups of sugar per batch, we can use this equation:

y = x × 3

Using this, we can determine how many cups are needed when we need to make 4 batches.

y = 4 × 3 = 12

You need 12 cups of sugar for 4 batches.

The summary of the percent of times each and every category appears for the entire sample is called the frequency distribution , the correct option is (d) .

In the question ,

it is asked about what is The summary of the percent of times each and every category appears for the entire sample is called ,

it is called frequency distribution ,

Frequency distribution : it lists all categories of data and number of occurrences for each data category and

it  is also the summary of percent of times each and every category appears for entire sample .

Therefore , the correct option is (d) .

The given question is incomplete , the complete question is

The summary of the percent of times each and every category appears for the entire sample is called the ,

(a) mode

(b) categorical percentage rate

(c) percentage distribution

(d) frequency distribution

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Answer:

Step-by-step explanation:

Answer 3700

It will take 3 years for the value of the computer of initial value $1000 to reach $512.

Given, Timothy purchased a computer for $1,000.

The value of the computer depreciates by 20% every year.

we have to find the number of years value of computer will take to reach $512.

Let, the function representing this situation be,

V(t) = AB^t

where, A is the initial value of the computer and B is the depreciating rate.

So, V(t) = (1000)(1 - 20/100)^t

V(t) = (1000)(0.8)^t

Now, the value will be, 512

512 = 1000(0.8)^t

0.512 = (0.8)^t

t = 3

So, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

Hence, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

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The equation representing the situation is written as

the number of customers Olaf had originally is 80

From the given information the following is deduced

Olaf has 11 more than triple the amount of customers as when he started selling newspapers

let the amount be x

3x + 11 = ?

He now has 71 customers

3x + 11 = 71

solving the equation

3x = 71 - 11

3x = 60

x = 20

Olaf had 80 customers

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Answer:

Commutative Property of Multiplication

Step-by-step explanation:

Hope it helps!

Carrying out the operations on the polynomials shows that

A + B - polynomial

A - B - polynomial

A * B - polynomial

The given polynomials are  

A = 3x²( x − 1 )

B = -3x³ + 4x² − 2x + 1

A + B

= 3x²( x − 1 ) + (-3x³ + 4x² − 2x + 1)

= 3x³ - 3x² - 3x³ + 4x² − 2x + 1

= x² − 2x + 1

This is a polynomial

A - B

= 3x²( x − 1 ) - (-3x³ + 4x² − 2x + 1)

= 3x³ - 3x² + 3x³ - 4x² + 2x - 1

= 6x³ - 7x² + 2x - 1

This is a polynomial

A * B

= 3x²( x − 1 ) * (-3x³ + 4x² − 2x + 1)

= (3x³ - 3x²) * (-3x³ + 4x² − 2x + 1)

= -9x^6 + 12x^5 - 6x⁴ + 3x³ + 9x^5 - 12x⁴ + 6x³- 3x²

= -9x^6 + 21x^5 - 18x⁴ + 9x³- 3x²

This is a polynomial

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The expected value of distribution A is 1 and distribution B is 3. The standard deviation for both distributions is the same which is 1.225. In conclusion, distribution B is better than distribution A.

Events with countable or finite outcomes are counted in a discrete probability distribution. This includes the probability values for the discrete random variable. The expected value for this type of distribution is calculated by E(X)=μ=ΣxP(x). And the standard deviation is calculated by σ=√(E(X²)-(E(X))²).

a) Expected value for the distributions A and B is calculated as follows,

The expected value for distribution A,

[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.50)+(1\times0.20)+(2\times0.15)+(3\times0.10)+(4\times0.05)\\&=1\end{aligned}[/tex]

The expected value for distribution B,

[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.05)+(1\times0.10)+(2\times0.15)+(3\times0.20)+(4\times0.50)\\&=3\end{aligned}[/tex]

b) The standard deviation for the distributions A and B is calculated as follows,

First, find E(X²) for distribution A and B to substitute in the standard deviation formula.

The  E(X²) for distribution A is,

[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.50)+(1^2\times0.20)+(2^2\times0.15)+(3^2\times0.10)+(4^2\times0.05)\\&=2.5\end{aligned}[/tex]

The  E(X²) for distribution B is,

[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.05)+(1^2\times0.10)+(2^2\times0.15)+(3^2\times0.20)+(4^2\times0.50)\\&=10.5\end{aligned}[/tex]

Then, the standard deviation for distribution A is,

[tex]\begin{aligned}\sigma_A&=\sqrt{2.5-1^2}\\&=1.225\end{aligned}[/tex]

The standard deviation for distribution B is,

[tex]\begin{aligned}\sigma_B&=\sqrt{10.5-3^2}\\&=1.225\end{aligned}[/tex]

Distribution A and B have the same standard deviation.

c) The standard deviation values are the same for both distributions.  But the expected value of distribution A is lesser than the expected value of distribution B. So distribution B looks better than distribution A.

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The hypotheses for [tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)

Given:

Nationwide scores as  n1=1000, [tex]x_{1}[/tex]` = 21.4 ,σ1 = 3

Carolina scores as n2=500,  [tex]x_{2}[/tex]` = 21.2 ,σ2 = 3

So from here we can say

µ represents population mean.

[tex]u_{1}[/tex] represent population mean for nationwide scores.

[tex]u_{2}[/tex] represents population mean for Carolina scores.

[tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)

Given Question is incomplete, Complete Question here,

a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south Carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south Carolina average?

use α=0.01 and [tex]\µ_{1}[/tex] for the nationwide mean act score.

State the hypotheses and identify the claim.

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The change in rate of length of shadow is 2.692 ft/sec.

Given,

Height of tall person =7 ft

Height of tall lamp post = 20 ft

Rate at which tall person walks = 5 ft/sec

Let,

Distance between tall person and lamp post be x ft

the length of shadow be y ft

From similar triangles,

[tex]\frac{x+y}{20}=\frac{y}{7}\\\\7(x+y)=20y\\\\7x+7y=20y\\\\13y=7x\\\\y=\frac{7x}{13}[/tex]

Differentiating on both sides with respect to time 't'

[tex]\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}[/tex]

here, [tex]\frac{dx}{dt}[/tex] is nothing but the change in distance between tall person and lamppost it means rate at which tall person walks=5 ft/sec

[tex]\frac{dy}{dt}=\frac{7}{13}*5\\\\\frac{dy}{dt}=\frac{35}{13}=2.692\ ft/sec[/tex]

Thus, the change in rate of length of shadow is 2.692 ft/sec.

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The p-value is greater than the significance level, so we do not reject the null hypothesis for the significance level is 0.01 (1%)

What is significance level?

"Significance" in statistics refers to something that is "not by chance" or "likely true." We can infer that when a statistician claims that a finding is "very significant," he or she is implying that it may very well be true. It does not imply that the finding is very significant, but it does imply that it is highly likely. The fixed likelihood of incorrectly eliminating the null hypothesis when it is, in fact, true is what is referred to as the level of significance. The probability of type I error is defined as the degree of significance, and the researcher sets it based on the results of the error. The statistical significance is measured by its level of significance. It specifies whether the null hypothesis is thought to be accepted or rejected.

The p-value for ACT is 0.0286

The significance level is 0.01 (1%)

Hence, the p-value is greater than the significance level, so we do not reject the null hypothesis. We conclude that there is insufficient evidence to conclude that there is any linear relationship at a 1% level of significance between GPA and ACT scores.

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For maximum area the wire should be bent in the form of circle  and for minimum area the wire should bent into equilateral triangle.

What is the area of any geometrical shape?

The area of a shape is the “space enclosed within the perimeter or within the boundary” of the given shape. We calculate the area for different shapes using math formulas.

Given that a piece of wire 10m long is cut into two pieces so now we have two wires with lengths of 5m and 5m.

One wire is bent into an equilateral so the perimeter of that triangle would be 3 m.

Perimeter = 3 m

3*side = 3 m

side = 1 m

Now the area of the equilateral triangle = [tex]A=\frac{\sqrt{3}}{4}\times (side)^2[/tex]

                                                                    A = 0.4330 m² -----(I)

Now the circumference of the circle = 5 m

                      2π×r = 5

                          r = 5/2π

                          r = 0.7957 m.

Now the area of the circle = π×r²

                                            = 3.14 × (0.7957)²

                                            = 1.988 m² --------(II)

From (I) and (II), we can say that

Area of the equilateral triangle < Area of the circle

Hence, for maximum area the wire should be bent in the form of circle  and for minimum area the wire should bent into equilateral triangle.

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There isn't a ton of information regarding exactly what you are looking for to answer this question. However, if you are trying to simply convert the following word phrase to an expression, here you go:

Hence, the final expression would be written as:

[tex](3x+4) < 4(x+1)[/tex]

Hope this helps!

The probability that a randomly chosen mango of this type won't be deemed to be large in size is 26.43%.

For the stated question;

The formula for the z-score is;

z = (x - μ)/σ

x < 425 gram

mean  μ = 400,

standard deviation σ = 40:

Thus,

z = (425 - 400)/40

z = 0.625

P(X < 425) = 1 - P(z = 0.625)

P(X < 425) = 1 - 0.7357

P(X < 425) = 0.2643

Thus, there is a 26.43% chance that a randomly chosen mango of this sort will not be regarded as being huge in size.

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Answer:0.8413

Step-by-step explanation:

0.8413

The mean is μ=400, and the standard deviation is σ=25.

Open Excel.  Click on an empty cell.  Type =NORMDIST(425,400,25,1) and press ENTER.

The probability, rounded to four decimal places, is P(X<425)≈0.8413.

Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.

A Gram-positive bacterium called S. epidermidis is a component of the flora of humans. Anaerobic bacteria are what it is. It promotes the growth of pathogens that are present in medical equipment. These may enter the bloodstream. Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling s. epidermidis.

Molds produce a class of antibiotics known as penicillium. Actinomycetes produce the antibody known as novobiocin, which has antibacterial characteristics. Gentamicin is one of the antibodies that can treat infections and aid in halting bacterial development.

Hence the answer is Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.

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Answer:

H

Step-by-step explanation:

The solution of the system of equation are;

⇒ x = 6

⇒ y = - 7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equations are,

4x + 2y = 10

x = y + 13

Now,

Since, The system of equations are,

⇒ 4x + 2y = 10  ..(i)

⇒ x = y + 13  

⇒ x - y = 13    ..(ii)

Multiply by 2 in equation (ii) and add with (i);

⇒ 2x - 2y + 4x + 2y = 26 + 10

⇒ 6x = 36

⇒ x = 6

And, x - y = 13

⇒ 6 - y = 13

⇒ 6 - 13 = y

⇒ y = - 7

Thus, The solution of the system of equation are;

⇒ x = 6

⇒ y = - 7

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The two positive numbers that satisfy the given requirements are √17 and 34

Given the sum of the first number squared and the second number

is 51.

Let's assume first number is x.

second number is y.

Square of first number is [tex]x^2[/tex].

sum of the first number squared and the second number = [tex]x^2 + y[/tex].

[tex]x^2 + y = 51[/tex]

subtract [tex]x^2[/tex] from both side of equal sign.

[tex]x^2 + y- x^2 = 51 - x^2[/tex]

[tex]y = 51 - x^2[/tex]

Product of both numbers p  = x*y.

[tex]p = x*(51 - x^2)[/tex]

[tex]p = 51*x - x^3.[/tex]

Given the product is a maximum.

so derivative of p with respect to x  will be = 0.

derivative of p with respect to x is  [tex]51-3*x^2[/tex]

[tex]51-3*x^2 = 0[/tex]

[tex]3*x^2=51[/tex]

[tex]x^2 = 17[/tex]

x = √17.

put value of x in [tex]y = 51 - x^2[/tex]

[tex]y = 51 - (\sqrt17)^2[/tex] = 51 - 17 = 34

So the value of x and y is √17 and 34 respectively.

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98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

mean x = 16

standard deviation σ = 2.4

sample size n = 65

z score for 98% = 2.576

Interval = x±z*s/

= 16±2.576*2.4/

= 16±2.576*0.39629

= 16±1.0208

Interval = (21.0208,18.9792)

Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

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To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

The equation of the line is written in the slope-intercept form, which is:

y = mx + b, where m represents the slope and b represents the y-intercept.

Finding the distance from the known endpoint to the midpoint and then applying the same transformation to the midpoint is the quickest way to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, so the new x-coordinate is 2-2 = 0.

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If multiplying 2 negative integers then it's a positive

If multiplying 2 positive integers it's positive

Answer: I hope this is helpful

Step-by-step explanation:

The proceeding pattern is summarized in the following rule for multiplying integers. Rule for Multiplying Two Integers: TO MULTIPLY INTEGERS WITH THE SAME SIGN, multiply the absolute value of the factors. The product is positive.

What is your question dude???????

The numerical side length of length AD is 44 units

From the question, we have the following lengths that can be used in our computation:

AD= 4x + 8

CD = 5x - 1

Also, from the complete question (added at the end of the solution), we understand that

The lengths AD and CD are congruent

These parameters and statements above mean that

AD = CD

Substitute the known values in the above equation, so, we have the following representation

4x + 8 = 5x - 1

Collect the like terms

5x - 4x = 1 + 8

Evaluate the like terms

x = 9

Substitute x = 9 in AD= 4x + 8

AD= 4 x 9 + 8

Evaluate

AD= 44

Hence, the length is 44 units

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Complete question

Given that lengths AD and CD are congruent.

Find AD

CD = 5x-1 and AD = 4x+8

Answer:

x=36

Step-by-step explanation:

The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.

When two rays are linked at their ends, they create an angle in geometry.

The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.

Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

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