Select all expressions that are NOT written correctly in Scientific Notation.

Answer: B. horizontal line; yes

Use the slope-intercept form to find the slope and y-intercept.

Slope:  

0

y-intercept:  

(0,0)

Yes it is a function. It is a horizontal line.  

Every point on this line is of the form (x,4) where x can be any number you want. The y coordinate is fixed at 4 and cannot change. Two points on this line are (0,4) and (1,4). The horizontal line goes through 4 on the vertical y axis.  

Why is it a function? Because it is impossible to draw a vertical line through more than one point on the graph of y = 4. The graph passes the vertical line test. Put another way, for any x input, there is exactly one y output.  

Side Note: y = 4 is the same as y = 0x+4. Note how its in the form y = mx+b

m = 0 is the slope

b = 4 is the y intercept

Step-by-step explanation: A. vertical line; yes

horizontal line; yes

Yes! Horizontal line represents a function y = f(x)

(1):Firstly, lets understand a function. For a function to be defined, we have a set of independent variables(inputs) (Domain), a set of dependent variables (outputs) (Codomain). And a relation between the variables.

(2): Each input in X must be related to exactly one output in Y. Or else it won't represent a function.. like in the following image.. y is a function of x.Because each element ofX has one& only one image in Y

C. vertical line; no

The solution to the above-asked question is mathematically given as

This is further explained below.

The problem is that Andre, while rotating the points by 45 degrees, alters the point that serves as the center of rotation. As a consequence of this, his rotation is inaccurate.

In order to rotate a figure, which can be thought of as a collection of points that are separated from one another by predetermined distances, the center of rotation must stay the same for each point that is rotated inside the figure.

in order to rotate an angle figure by an angle of, we need to have knowledge of the following three things:

1)

Rotation angle.

2)

The point around which the figure is to be rotated, also known as the center of rotation

3)

In conclusion, The direction in which the object is being rotated, either clockwise or counterclockwise.

To rotate the figure, you need just to choose one point to use as the center of rotation

Now, with the help of a protractor, rotate point A by 45 degrees anticlockwise.

Repeat step one for point B, then step one again for point C, but keep the center of rotation the same. This is the mistake that Andre made.

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The value of the line integral along the path c is 132.

To evaluate the line integral along the path c given by x = 2t, y = 4t, where 0 ≤ t ≤ 1, we first need to parameterize the integral in terms of t.

The path c can be written as r(t) = <2t, 4t>, where 0 ≤ t ≤ 1.

Then, we can rewrite the line integral as:

∫c (y − x) dx + 10x^2y^2 dy = ∫0^1 (4t − 2t)(2)dt + 10(2t)^2(4t)^2(4)dt

= ∫0^1 12t^2 + 640t^4 dt

= 4t^3 + 128t^5 | from 0 to 1

= 4 + 128

= 132

Therefore, the value of the line integral along the path c is 132.

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Answer:

So Y, which represents height, goes down depending on how far you are in time, which is X.

The slope of the graph represents the elevator's descent speed, calculated as 12 feet per second based on the points (1, 838) and (2, 826).

The Slope of the line in the graph represents the rate of change of height with respect to time, or the speed of the elevator's descent.

In this case, the slope can be calculated using the formula: slope = (change in height) / (change in time). We know that the elevator's height changes from 838 feet at 1 second to 826 feet at 2 seconds,

So, the change in height is : 838 - 826 = 12 feet, and the change in time is 2 - 1 = 1 second.

Therefore, the slope is 12 feet/second, this indicates that the elevator is descending at a speed of 12 feet per second.

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The rate of change of the angle between the ground and the ladder is given by dθ/dt = [rcos(θ)]/[-rsin(θ) + h], θ is the angle between the ladder and the ground, r is the rate at which the top of the ladder is sliding down the wall, and h is the distance from the top of the ladder to the ground.

Let's consider a right triangle formed by the ladder, the wall, and the ground, where the ladder is the hypotenuse of the triangle.

Let's call the angle between the ladder and the ground θ.

To find dθ/dt, the rate of change of θ with respect to time.

The Pythagorean theorem to relate the length of the ladder, the distance the top of the ladder is sliding down the wall, and the distance from the bottom of the ladder to the ground.

We have:

(ladder)² = (wall)² + (ground + sliding distance)²

Differentiating with respect to time, we get:

2ladder(dladder/dt) = 2wall(dwall/dt) + 2 × (ground + sliding distance) × (d(ground+sliding distance)/dt)

Simplifying, we get:

ladder × (dladder/dt) = wall × (dwall/dt) + (ground + sliding distance) × (d(ground+sliding distance)/dt)

Now, we can use similar triangles to relate the angle θ to the lengths of the ladder, the wall, and the ground. Specifically, we have:

tan(θ) = wall/ground

Differentiating with respect to time, we get:

(sec)²(θ) × (dθ/dt) = (dwall/dt) ×ground/ (ground)²

Substituting wall = laddercos(θ) and ground

= laddersin(θ), we get:

(sec)²(θ) ×(dθ/dt) = (dladder/dt)cos(θ) - (laddersin(θ) × (dθ/dt))/(ground)

Simplifying and solving for dθ/dt, we get:

dθ/dt = [rcos(θ)]/[-rsin(θ) + h]

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The product of rational numbers can always be expressed as the ratio of two integers, where the denominator is not zero.

The product of rational numbers can always be written as a rational number. A rational number is defined as the quotient of two integers, where the denominator is not zero. When we multiply two rational numbers, we are essentially multiplying the numerators and denominators separately.

Let's consider two rational numbers, a/b and c/d, where a, b, c, and d are integers and b, d are not equal to zero. The product of these rational numbers is (a/b) * (c/d), which can be simplified as (a * c) / (b * d). Since multiplication of integers results in another integer, both the numerator and denominator are integers.

Furthermore, as long as the denominators b and d are not zero, the product remains a valid rational number.

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Answer: 370 feet below sea level

Step-by-step explanation: The submarine was 620 feet below and ascend means go up so you add 250 to -620 which would be 370.

Answer:

100 feet

Step-by-step explanation:

620 - 250

We will recommend option C which is Salaried pay. Salaried employees make more per week than hourly employees.

Given that, Salary per year = $78,000.

Hourly employees get paid $26 per hour, but get $39 per hour for each hour over 40 hours.

The total number of working hours from Sunday to Saturday is 47.

The payment for 47 hours of work per week will be given below.

Salary per week = \(40 \times 26 + 7 \times 39\)

Salary per week = $1313

We know that there are 52 weeks in one year. So the salary for one year is given below.

Salary per year = \(1313\times 52\)

Salary per year = $68276

We can see that we calculate the yearly salary with per hour rate, the amount will be lower than the salary per year $78000.

Hence we will recommend option C which is Salaried pay. Salaried employees make more per week than hourly employees.

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The work of  5/6 more than 360 is equal to 660.

To calculate what 5/6 is out of 360, you can use the following steps:

Divide 360 by 6 (the denominator of the fraction) to determine the value of 1/6.

360 / 6 = 60 Multiply the value of 1/6 by the numerator (5) to find the value of 5/6.

60 * 5 = 300

Step 1: Calculate 5/6 of 360.

To find 5/6 of a number, you multiply that number by the fraction 5/6. In this case, we want to find 5/6 of 360. To do that, we multiply 360 by 5/6:

(5/6) * 360 = (5 * 360) / 6 = 1800 / 6 = 300

So, 5/6 of 360 is equal to 300.

Step 2: Add the result to 360.

To find 5/6 more than 360, we take the result from Step 1, which is 300, and add it to 360:

300 + 360 = 660

Therefore, 5/6 more than 360 is equal to 660.

In summary, by calculating 5/6 of 360, we found that it is 300. Adding 300 to 360 gives us the final result of 660, which represents 5/6 more than 360.

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Answer:

See below

Step-by-step explanation:

A) B intersection C = {6,12}     <===== the elements common to both

B)  B union C   = { 2 3 4 6 8 9 10 12 )   <== all the elements from both

C )    { }    { 6}   { 12 }   { 6,12}     <===== Four

The converse of the following conditional True which is If a polygon is a triangle, then it has exactly three sides."

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

A polygon has precisely three sides if it is a triangle. The opposite is also accurate.

Contrarily, a polygon is a triangle if it has precisely three sides. Both of the statements can be joined to create a biconditional because they are both true.

Thus, the converse of the following conditional True which is If a polygon is a triangle, then it has exactly three sides."

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Answer:

Corresponding parts are congruent

Congruent parts:

Sides

Angles in simple form

Angles in full format

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

Congruent parts:

Sides

Angles in simple form

Angles in full format

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

Congruent parts:

Sides

Angles in simple form

Angles in full format

9514 1404 393

Answer:

Step-by-step explanation:

The key with naming corresponding parts is to use the congruence (or similarity) statement. Corresponding vertices are those that are in the same position in the congruence statement, regardless of what the figure may look like.*

Angles can be named using the letter at its vertex--if there is only one angle with that vertex--or using three letters. The three letters name a point on one ray, the vertex, and a point on the other ray. When naming corresponding angles from a congruence statement, it is nice (but not absolutely essential) to name the corresponding rays in the same order. In any event, the named vertices must be corresponding.

Sides are named using two letters--the points at the end of the side. The points used to name corresponding sides must come from the same positions in the congruence statement. Technically, side named AB is the same as side BA, but it is nice to use corresponding points in the same order when naming corresponding sides. Example: in the first figure, CB≅JK, but it is also true that BC≅JK because CB can be named either as CB or BC. In both cases, the points named are the 1st and 2nd in the congruence statements.

In the answer section above, we have used 3-letter angles where a vertex is shared by two or more angles. We have used single-letter names for angles where there is no ambiguity. When asked to name all the names, as here, it is best to make use of a pattern you understand. For angles, we worked left-to-right down the congruence statement; for sides we used the pattern 12, 13, 23 for the positions of the letters in the congruence statement.

_____

* Sometimes, poorly-edited curriculum materials will misstate the congruence statement. It is best to report the problem to your teacher in those cases. Sometimes, the figure is intentionally misleading (as in the second problem here). For those, you must pay careful attention to the congruence statement.

The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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Answer:

13 1/3 pounds.

Step-by-step explanation:

3 feet = 36 inches

3 feet 4 inches = 36 + 4 = 40 inches

By proportion the weight of the larger  bar = 12 * 40/36

= 12 * 10/9

= 120/9

= 13 1/3 pounds.

Answer:

60

Step-by-step explanation:

Answer:

that would be 70%

Step-by-step explanation:

The resulting expression represents the area of the rectangle in terms of 'n'.
Area = (n^3 + 4n^2 + 3nn + 4n + 2)^3 * (n^3 + 7n^2n + 5n + 3)^3

The height of the rectangle is given as (n^3 + 4n^2 + 3nn + 3 + 4n + 2 + 3nn) cubed, plus 4n squared, plus 3n. The width of the rectangle is given as (n^3 + 5n^2n + 3 + 5n + 2n) cubed, plus 5n squared.

To find the area of the rectangle, we need to multiply the height by the width.

Let's simplify the expressions for the height and width separately:

Height:
(n^3 + 4n^2 + 3nn + 3 + 4n + 2 + 3nn) cubed = (n^3 + 4n^2 + 3nn + 4n + 2)^3

Width:
(n^3 + 5n^2n + 3 + 5n + 2n) cubed = (n^3 + 7n^2n + 5n + 3)^3

Now, let's multiply the simplified expressions for the height and width to find the area of the rectangle:

Area = (n^3 + 4n^2 + 3nn + 4n + 2)^3 * (n^3 + 7n^2n + 5n + 3)^3

Since the expressions for the height and width contain variables and exponents, the area of the rectangle cannot be simplified further unless you have a specific value for 'n'. The resulting expression represents the area of the rectangle in terms of 'n'.

Remember to substitute a specific value for 'n' to calculate the actual area of the rectangle.

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To prove that lines l and m are parallel, we need the information that the corresponding angles formed by the intersecting lines satisfy certain relationships. In this case, if the given conditions are true: <1 + <m = 180°, <5 = <m, <8m = <6 + <m, and <3 = 180° - <m, then we can conclude that lines l and m are parallel.

To determine if lines l and m are parallel, we need to examine the angles formed by the intersecting lines. The given conditions state that <1 + <m = 180°, <5 = <m, <8m = <6 + <m, and <3 = 180° - <m.

If we consider the angles formed by the intersection of lines l and m, we can see that <1 + <m = 180° implies that <1 and <m are supplementary angles. Similarly, <5 = <m indicates that <5 and <m are equal.

Furthermore, <8m = <6 + <m implies that <8m and <6 have a relationship with <m. Finally, <3 = 180° - <m indicates that <3 and <m are also supplementary angles.

Based on these relationships, if the given conditions are true, we can conclude that lines l and m are parallel. This is because the corresponding angles formed by the intersecting lines satisfy the necessary conditions for parallel lines.

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Answer:

Step-by-step explanation:

Reduce 88/80 to lowest terms

The simplest form of  

88

80

is  

11

10

.

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 88 and 80 is 8

Divide both the numerator and denominator by the GCD

88 ÷ 8

80 ÷ 8

Reduced fraction:  

11

10

Therefore, 88/80 simplified to lowest terms is 11/10.

MathStep (Works offline)

Download our mobile app and learn to work with fractions in your own time:

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Equivalent fractions: 176/160 44/40 264/240 440/400 616/560

More fractions: 176/80 88/160 264/80 88/240 89/80 88/8187/80 88/79

Fractions Simplifier

your answer is

9/36

Answer:

Hi, not sure of what you're asking here?

Step-by-step explanation:

Try rephrasing it??

Answer:

\(( \sec \theta - \tan \theta)( \sec \theta + \tan \theta)\)

from difference of two squares:

\({ \boxed{ \tt{( {a}^{2} - {b}^{2}) = (a - b)(a + b) }}}\)

\( = { \sec }^{2} \theta - { \tan}^{2} \theta \\ = (1 + { \tan}^{2} \theta) - { \tan}^{2} \theta \\ = 1\)

hence proved

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

We can use the formula for the area of a triangle, which is A = (1/2)bh, where b is the length of the base and h is the height. In this case, we know that the base has length 2a, so we need to find the height.

Let's call the third side of the triangle, which is not given, b. We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, so we have:

a + 2a > b

3a > b

We can rearrange this to solve for b:

b < 3a

Now, let's use the formula for the area of a triangle:

A = (1/2)bh

We want to maximize A, so we want to maximize h. We know that h is the height of the triangle, which is perpendicular to the base, so it forms a right angle. We can use the Pythagorean theorem to find h in terms of a and b:

\(h^2 = b^2 - a^2\)

We can substitute our inequality for b:

\(h^2 < (3a)^2 - a^2\)

\(h^2 < 8a^2\)

h < √(8\(a^2\))

h < 2 √(2)a

Now we can use the formula for the area of the triangle again:

A = (1/2)bh

A < (1/2)(2 √(2)a)(a)

A < \(a^2\) √(2)

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

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The test would be done at 0.10/2 = 0.05 significance level.

To determine if the mean weights differ between baby boys and girls, we need to state the appropriate null and alternative hypotheses.

Null hypothesis (H0): The mean weight of baby boys (μ1) is equal to the mean weight of baby girls (μ2)).

Alternative hypothesis (H1): The mean weight of baby boys (μ1) is not equal to the mean weight of baby girls (μ2)

Since we are comparing the means of two independent samples, this is a two-sample t-test. The null hypothesis assumes that there is no difference in the mean weights between baby boys and girls. The alternative hypothesis suggests that there is a difference.

In this case, we will use the P-value method with a significance level of α = 0.10 to determine if there is enough evidence to reject the null hypothesis. The P-value is the probability of obtaining a test statistic as extreme as the observed one, assuming that the null hypothesis is true.

To perform the two-sample t-test and calculate the P-value, we can use statistical software like Excel or a statistical calculator. We will need the sample weights for boys and girls.

The given data are as follows:

Boys: 7.6, 6.4, 8.1, 7.9, 8.3, 7.3, 6.4, 8.4, 8.5, 6.9, 6.3, 7.4, 7.8, 7.5, 6.9, 7.8, 8.6, 7.7, 7.4

Girls: 7.0, 8.2, 7.4, 6.0, 6.7, 8.2, 7.5, 5.7, 6.6, 6.8, 7.5, 7.2, 6.9, 8.2, 6.5, 6.7, 7.2, 6.3, 5.9

By performing the two-sample t-test and calculating the P-value, we can determine if there is enough evidence to conclude that the mean weights differ between baby boys and girls.

Here are the null and alternate hypotheses that would be suitable for this case:

Null Hypothesis, H0: µ1 = µ2

Alternate Hypothesis, H1: µ1 ≠ µ2

Since it's a two-tailed test, the test would be done at 0.10/2 = 0.05 significance level.

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The test would be done at 0.10/2 = 0.05 significance level. it's a two-tailed test, the test would be done at  0.05 significance level. we need to state the appropriate null and alternative hypotheses.

If the mean weights differ between baby boys and girls, we need to state the appropriate null and alternative hypotheses.

Null hypothesis (H0): The mean weight of baby boys (μ1) is equal to the mean weight of baby girls (μ2)).

Alternative hypothesis (H1): The mean weight of baby boys (μ1) is not equal to the mean weight of baby girls (μ2)

Since we are comparing the means of two independent samples, this is a two-sample t-test. The null hypothesis assumes that there is no difference in the mean weights between baby boys and girls. The alternative hypothesis suggests that there is a difference.

In this case, we will use the P-value method with a significance level of α = 0.10 to determine if there is enough evidence to reject the null hypothesis. The P-value is the probability of obtaining a test statistic as extreme as the observed one, assuming that the null hypothesis is true.

To perform the two-sample t-test and calculate the P-value, we can use statistical software like Excel or a statistical calculator. We will need the sample weights for boys and girls.

The given data are as follows:

Boys: 7.6, 6.4, 8.1, 7.9, 8.3, 7.3, 6.4, 8.4, 8.5, 6.9, 6.3, 7.4, 7.8, 7.5, 6.9, 7.8, 8.6, 7.7, 7.4

Girls: 7.0, 8.2, 7.4, 6.0, 6.7, 8.2, 7.5, 5.7, 6.6, 6.8, 7.5, 7.2, 6.9, 8.2, 6.5, 6.7, 7.2, 6.3, 5.9

By performing the two-sample t-test and calculating the P-value, we can determine if there is enough evidence to conclude that the mean weights differ between baby boys and girls.

Here are the null and alternate hypotheses that would be suitable for this case:

Null Hypothesis, H0: µ1 = µ2

Alternate Hypothesis, H1: µ1 ≠ µ2

Since  0.10/2 = 0.05 significance level.

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Answer:

step 2

and then also in step 3 compensating the error in step 2

Step-by-step explanation:

I think I just answered this for another post.

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

so, step 1 is correct :

sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2)

but step 2 suddenly and incorrectly switched that central "-" to a "+".

yes, sin(3pi/2) = -1, but that is still an explicit factor in step 2. so it was not used to flip the central operation from subtraction to addition, and therefore this change was a mistake.

then, in step 3, another error was made by just ignoring the "-" sign of "-1" and still keeping the central "+" operation. this error compensated for the error in step 2 bringing us back by pure chance to the right result.

The dimensions of the poster be so that the least amount of poster is used are 10 and 20 inches.

Print area of the rectangular poster =128 in²

Let  "x"  and  "y" be the  dimensions for the print area of the poster .

And A[p] = print area of poster

⇒A(p)  = Print area of the poster = xy

⇒128 = xy    

⇒ y  = 128/x

Total area of the poster is:

A( t ) = ( y + 4 )( x + 2 )

A( t ) = yx +2y +4x + 8    And as  y = 128/x

Poster 's area as function of x is -

A(x)  =( 128 /x)x + 2 (128/x) + 4x + 8

⇒ A(x)  = 128 x² + 256/x + 4x + 8    ⇒  A(x)  = 128 + 256 /x + 4*x

On taking the derivatives on both sides of the equation :

A´(x)  =  - 256/x² + 4

A´(x)  = 0        

⇒ - 256 /x²  = -4    

⇒  4x² = 256

⇒ x² = 256/4     ⇒  x²  = 64

x = 8inches

And   y  =  128/x    

⇒y = 128/8   ⇒ y = 16 inches

After finding out the values of x and y the dimensions of the poster are:

w = x + 2    ⇒  w  = 8+ 2    w  = 10 in

Y  = y + 4   ⇒  Y  = 16+ 4   Y  =  20 in

Hence, the dimensions of the poster be so that the least amount of poster is used are 10 and 20 inches.

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Answer:

\(1996.5\)

Step-by-step explanation:

\(16.5 X 4 X 30.25\)

Hope this helped, please give brainliest

Thank you!

Answer:

To calculate the volume of a object, all you need to do is multiply the length, width and height.  In this equation, that would be 1996.5cm or 786.02362204 inches

Step-by-step explanation:

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Thank you

The probability that the telephone company will have more than 12 monthly failures on a particular 150 miles of line is approximately 0.029.

To find the probability that a telephone company will have more than 12 monthly line failures on a particular 150 miles of line, we can use the Poisson distribution. Given that the company experiences an average of 3 monthly line failures per 50 miles of line, we need to calculate the probability of having more than 12 failures in 150 miles. By applying the properties of the Poisson distribution, we can compute the answer.

Let's denote the number of monthly line failures per 100 miles of line as x. We know that x follows a Poisson distribution. The average number of failures per 50 miles of line is given as 3, so the average number of failures per 100 miles would be 2 * 3 = 6.

To find the probability of having more than 12 failures in 150 miles, we need to calculate the cumulative probability of the Poisson distribution up to 12 failures and subtract it from 1.

Using the Poisson distribution formula, the probability mass function is given by P(x; λ) = (e^(-λ) * λ^x) / x!, where λ is the average number of occurrences.

Let's calculate the cumulative probability up to 12 failures in 150 miles. We can use the formula:

P(X ≤ 12; λ) = Σ[(e^(-λ) * λ^x) / x!] from x = 0 to 12.

Substituting the values, we have:

P(X ≤ 12; 6) = Σ[(e^(-6) * 6^x) / x!] from x = 0 to 12.

Next, we need to calculate the individual terms of the summation and add them up.

P(X ≤ 12; 6) = [(e^(-6) * 6^0) / 0!] + [(e^(-6) * 6^1) / 1!] + [(e^(-6) * 6^2) / 2!] + ... + [(e^(-6) * 6^12) / 12!].

By calculating this summation, we find that P(X ≤ 12; 6) ≈ 0.971.

Finally, to find the probability of having more than 12 failures in 150 miles, we subtract this cumulative probability from 1:

P(X > 12; 6) = 1 - P(X ≤ 12; 6) ≈ 1 - 0.971 = 0.029 (rounded to 4 decimal places).

Therefore, the probability that the telephone company will have more than 12 monthly failures on a particular 150 miles of line is approximately 0.029.



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The equation that represents the line closest to the curve of best fit would be the equation of the line with the smallest sum of squared residuals.

In order to determine the equation that represents the line closest to the curve of best fit, we first need to find the equation of the curve of best fit. This can be done using regression analysis, such as linear regression or polynomial regression, depending on the shape of the data.
Once we have the equation of the curve of best fit, we can then find the equation of the line that is closest to this curve. This can be done by finding the line that has the smallest sum of squared residuals, which measures the distance between each data point and the line.
Therefore, the equation that represents the line closest to the curve of best fit would be the equation of the line with the smallest sum of squared residuals.

To determine the equation that represents the line closest to the curve of the best fit, you'll need to analyze the given data points and compare the residual errors for each candidate equation. The equation with the smallest sum of squared residuals is generally considered the best fit.

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