A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows:




Hours of Training Defects per Countertop


1 5


4 1


7 0


3 3


2 5


2 4


5 1


5 2


1 8


6 2



The estimated regression equation and the standard error are given.



Defects per Countertop = 6. 717822−1. 004950 (Hours of Training)


Se= 1. 2297787



Suppose a new employee has had 9 hours of training. What would be the 99% prediction interval for the number of defects per countertop?

Answer:

t=744

Step-by-step explanation:

t/3+t/2-350=270 add 350 on both sides

t/3+t/2=620 convert both fractions containing t into a fraction with a common base

2t/6+3t/6 = 620 add the fractions containing t

5t/6=620 factor out the 5

5*(t/6)=620 divide both sides by 5

t/6=124 multiply both sides by 6 (note, you could have just divided 620 by 5/6 on both sides, or multiplided both sides by 6/5)

t=744

Similar to when a woman is 1 cm dilated, 2 cm dilation does not indicate that labor will start soon. If a woman is 2 cm dilated, some of them may give birth in a few of hours. For a few days or weeks until labor advances, some women will stay 2 cm dilated.

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The limit of the function is 1 and it does exist .

Given,

\(\lim_{x \to \ -5} 5 - |x| / 5 + x\)

|x| : modulus function, also known as the absolute value function, is a function that takes any real number as input and returns its distance from zero on the number line.

In mathematical notation, the modulus function can be represented as |x|, where x is the input.

For example, if x = -3, then |x| = 3, and if x = 5, then |x| = 5.

Solving the limits further,

\(\lim_{x \to \ -5} 5 - |x| / 5 + x \\ \lim_{x \to \ -5} 5 - (-x) /5 + x\\ \lim_{x \to \ -5} 5 + x/ 5 + x\\\)

\(\lim_{x \to \ -5} 1\) = 1

Thus the limit exist and it is equal t o 1 .

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Answer:

\(9n - 12 \rightarrow \frac{1}{3} (9n - 12) \\ = \frac{3}{3} (3n - 4) \\ l = 3n - 4\)

The perimeter of an equilateral triangle is 9n - 12. Write an expression to represent the length of each side.

\( = \frac{9n-12}{3} \\ = \frac{3(3n - 4)}{3} \\ = 3n - 4\)

The length of each side of the triangle is 3n-4.

Hope it helps!!

The percentage of Rie's body that is Rie's legs is: 60%.

A percentage can be defined as an amount in each hundred or, simply put, a proportion of a quantity in relation of a whole.

To find the percentage of a quantity in a whole, divide the quantity by the whole quantity, then multiply the quotient by 100.

The "whole" in this problem is Rie's height, which is: 165 cm

The "quantity" in the context of this question is the length of Rie's leg, which is: 99 cm.

Therefore, to find the percentage of Rie's legs in Rie's body, we have the following:

99/165 × 100

= 0.6 × 100

= 60%.

Therefore, Rie's leg is 60% of Rie's body.

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The percentage increase of the stereo cable is 14.2%

The cost of the stereo cable yesterday is $14

The cost rose to $16

The first step is to calculate the increase

16-14

= 2

The percentage increase can be calculated as follows

increase/original price × 100

= 2/14 × 100

= 0.142 × 100

= 14.2

Hence the percentage increase is 14.2%

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The products obtained from the reactions of (E)- and (Z)-hex-3-ene with D2 in the presence of a platinum catalyst are related as enantiomers.

Hence, the correct option is E.

Enantiomers are stereoisomers that are non-superimposable mirror images of each other. In this case, the (E)- and (Z)-isomers have different spatial arrangements around the C=C double bond. When they react with D2 in the presence of a platinum catalyst, the deuterium atoms add to the double bond, resulting in two new chiral centers.

Since the two isomers have different spatial arrangements around the double bond, the addition of deuterium atoms will produce enantiomeric products. Therefore, the products obtained from the reactions of (E)- and (Z)-hex-3-ene with D2 are related as enantiomers.

Hence, the correct option is E.

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9514 1404 393

Answer:

  -101 feet

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relevant relation is ...

  Tan = Opposite/Adjacent

  Opposite = Adjacent × Tan

  height = (0.5 × 5280 ft) × tan(47°) ≈ 2831 ft

__

The usual relation between estimates and errors is ...

  error = estimate - actual

Then ...

  actual = estimate - error

For the given angle and error, the actual angle is ...

  actual angle = 47° -(-1°) = 48°

  actual height = (2640 ft)·tan(48°) ≈ 2932 ft

Then the change in the height of the mountain due to the error is ...

  2831 ft -2932 ft = -101 ft

The error of -1° in angle estimate creates an error of -101 ft in the height estimate.

Answer:

<GHC congruent to <EHD

Step-by-step explanation:

<GHC congruent to <EHD

By vertical angles

:]

The line integral, where C is the given curve. ∫C(xy)ds, C:x=t3, y=t4, 1≤t≤2 = 255/2.

To evaluate the line integral ∫C(xy)ds, we need to parameterize the curve C and then substitute into the integral expression. From the given equation of the curve, we can parameterize it as follows:

x = t^3, y = t^4, 1 ≤ t ≤ 2

To find ds, we need to calculate the differential of arc length ds along the curve C:

ds = sqrt(dx^2 + dy^2) = sqrt((3t^2)^2 + (4t^3)^2) dt = 5t^2 dt

Substituting x, y, and ds into the line integral, we get:

∫C(xy)ds = ∫1 to 2 (t^3)(t^4)(5t^2) dt

= 5 ∫1 to 2 t^9 dt

= 5 [t^10/10]_1^2

= 5 [(2^10)/10 - 1/10]

= 5 (512/10 - 1/10)

= 255/2

Therefore, the value of the line integral is 255/2.

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The value of the clock will increase by 69%. Option A is correct.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Mary bought an antique clock in its first year its value increased by 30% in the second year its value increased by 30%.
Let the cost of the clock be $1,
Cost increase by 30%
Cost of the clock = 1 + 1×30% = 1.30

Next year cost increase by again 30%,
Cost of the clock = 1.3 + 1.3×30%
Cost of the clock = 1.3 + 0.39 = 1.69

So the total percentage increase is 69%.

Thus, the value of the clock will increase by 69%. Option A is correct.

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Answer:

2nd option is the correct one

log|x|-f(x)+k

The equation setups are y = x² - 3x + 2 and y = 5x² - 6x - 4

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

A quadratic equation is represented as

y = ax² + bx + c

Using the above as a guide, we have the following equations

The solutions to the are

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Answer:

231.01

Step-by-step explanation:

The Kutta-Joukowski theorem, which is represented by equation (3.140), was originally derived for the case of a lifting cylinder. However, it can also be applied to a two-dimensional body of arbitrary shape, as stated in section 3.16.

A more detailed explanation of the answer.
To make a physical argument for this generalization, we can draw a closed curve around the body.

The key is to draw the curve far enough away from the body such that the body appears as a very small speck in the middle of the domain enclosed by the closed curve.

By doing this, we are essentially treating the body as a point object at the center of the curve. Since the body is now a very small speck in comparison to the large domain, its specific shape becomes insignificant to the overall flow around it.

Therefore, the lifting force calculations derived from the Kutta-Joukowski theorem for the lifting cylinder should also apply to the two-dimensional body of arbitrary shape, as long as the body is small in comparison to the domain enclosed by the closed curve.

This physical argument allows us to accept that equation (3.140) can be applied in general to a two-dimensional body of arbitrary shape without requiring a mathematical proof.

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Answer: 48 in 1 hour

Step-by-step explanation:

32 divided by 40 = 0.8

0.8 times 60 = 48

hope this helped you out :))

Based on the provided information of speed, A) Beth gets to San Francisco first. B) The first to arrive has to wait for 20 minutes for the second to arrive.

A) To find out who gets to San Francisco first, we need to calculate the time it takes for each of them to travel the distance of 400 miles.

For Brian, we use the formula time = distance / speed:

time = 400 miles / 50 mph = 8 hours

So Brian will arrive in San Francisco at 4:00 p.m. (8:00 a.m. + 8 hours).

For Beth, we use the same formula:

time = 400 miles / 60 mph = 6.67 hours

So Beth will arrive in San Francisco at 3:40 p.m. (9:00 a.m. + 6.67 hours).

Therefore, Beth gets to San Francisco first.

B) To find out how long the first to arrive has to wait for the second, we subtract the arrival time of the first from the arrival time of the second:

wait time = 4:00 p.m. - 3:40 p.m. = 0.33 hours = 20 minutes

So the first to arrive has to wait for 20 minutes for the second to arrive.

Note: The question is incomplete. The complete question probably is: Brian leaves Los Angeles at 8:00 a.m. to drive to San Francisco, 400 miles away. He travels at a steady speed of 50 mph. Beth leaves Los Angeles at 9:00 a.m. and drives at a steady speed of 60 mph. A) Who gets to San Francisco first? B) How long does the first to arrive have to wait for the second?

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The graph that shows the number of bottles that need to be sold to earn back the money spent on water is Graph C.

The number of bottles that need to be sold to earn back the amount spent on water is :

= Total spent / profit per bottle

= 50 / 2

= 25 bottles

Graph C starts from - $ 50 to show that the amount you have is - $ 50 to show the amount spent on the bottles.

Graph C then ends at 25 bottles to show that this is where you would need to stop to have made back what you spent.

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Answer:

0.44444444444

Step-by-step explanation:

Answer:

so x = 20 , y = -21 , which is in quad IV

r^2= 400+441 = 841

r = √841 = 29

then cos Ø = 20/29

sec Ø = 29/20 = 1.45

Step-by-step explanation:

please give brainliest

To convert the decimal number (-14.3) into 2's complement representation with an absolute error of less than 5%, we need to determine the binary representation of the number and apply the 2's complement operation.

To convert a negative decimal number into 2's complement representation, we follow these steps:
1. Convert the absolute value of the number into binary representation. In this case, the absolute value of (-14.3) is 14.3.
2. Convert the integer part of the absolute value into binary using 8 bits. The integer part of 14.3 is 14, which is represented as 00001110 in 8-bit binary.
3. Convert the fractional part of the absolute value into binary. The fractional part of 14.3 is 0.3.
  To convert the fractional part into binary, we can use the method of multiplying by 2 and extracting the integer part of the result. Multiply 0.3 by 2:
  0.3 * 2 = 0.6
  Integer part = 0
  Multiply 0.6 by 2:
  0.6 * 2 = 1.2
  Integer part = 1
  Multiply 0.2 by 2:
  0.2 * 2 = 0.4
  Integer part = 0
  Multiply 0.4 by 2:
  0.4 * 2 = 0.8
  Integer part = 0
  Repeat the process until we achieve the desired precision or the fractional part becomes zero. The binary representation of 0.3 with 5 bits of precision is 01001.
4. Combine the binary representations of the integer and fractional parts. The combined binary representation of 14.3 is 00001110.01001.
5. Apply the 2's complement operation to obtain the negative representation. To do this, invert all the bits in the binary representation and add 1 to the least significant bit. The resulting 2's complement representation of (-14.3) with an 8-bit integer part and 5-bit fractional part is 11110001.10111.
Note: The absolute error being less than 5% means that the difference between the original decimal number (-14.3) and its 2's complement representation should be within 5% of the range spanned by the number.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{3} x + 3\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{3\implies\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}\)

so we're really looking for the equation of a line whose slope is -1/3 and that is passes through (3 , 2)

\((\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-2=- \cfrac{1}{3}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{3}x+3 \end{array}}\)

Answer:

emma is 20 because 49-9/2=40/2 which is 20

Step-by-step explanation:

Answer:20 years old

Step-by-step explanation:

49 = 20 + 29

40/2 = 20

9 years older than 20 is 29

Answer:

15?

Step-by-step explanation:

The value of y in the given figure is 108°.

The angles formed by a transversal line on the same side and position of the line, if lines are parallel then the corresponding angle are congruent.

Given is a figure, where two line AB and CD are being intersected by a transversal FE,

Let FE intersects AB and CD at P and O, respectively, (refer to the figure attached)

Since, AB ║ CD

Therefore, ∠ FPB  ≅ ∠ POD by the definition of corresponding angles,

2x+16 = 3x-12

x = 28

∠ POD = 28×3-12 = 72°

∠ POD and ∠ EOD are forming linear pair and therefore are supplementary,

∠ POD + y = 180°

72° + y =180°

y = 180°-72°

y = 108°

Hence, y = 108°

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The correct inequality is: six x is greater than or equal to five.

To determine the minimum number of hours Julian needs to practice on each of the two days, we can set up an inequality.

Let x represent the number of hours Julian needs to practice on each of the two days.

We know that Julian has already practiced 5 and one third hours, which can be written as 16/3 hours.

So, the total practice time for the remaining two days would be 7 hours (the minimum number of hours he needs to practice each week) minus 16/3 hours.

Thus, the inequality would be:
2x ≥ 7 - 16/3

Simplifying the right side:
2x ≥ 21/3 - 16/3
2x ≥ 5/3

To get rid of the fraction, we can multiply both sides by 3:
3 * 2x ≥ 3 * 5/3
6x ≥ 5

Therefore, the correct inequality is:
six x is greater than or equal to five.

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Answer:

10 $20 bills and 20 $5 bills

Step-by-step explanation:

To dilate a point at a point, you start by selecting a center of dilation and a scale factor.

Then, for each point that you want to dilate, you do the following:

For example, if you wanted to dilate point P by a scale factor of 2, with the center of dilation at O, you would draw a line segment from O to P, double its length, and then draw a new line segment from O to the new point, using the new length that you calculated. The new point would be the point that you arrive at when you complete this line segment.

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None of the given answers are correct, The value of  128{1/7} will be a fraction number.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given a number 128{1/7}

Simplification of this number

=> 128(1/7)

=> 18.28

therefore, the Given number is a fraction number or a real number.

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Answer:

\(f(x)=4^{2x}\)

Step-by-step explanation:

So we are given:

\(f(x)=(8^{\frac{2}{3}x})(16^{\frac{1}{2}x})\)

and we have to find a function that will produce a similar graph. To do this, lets first simplify the given function.

Here are some properties of exponents that I will be using:

\(c^{\frac{n}{x}}=\sqrt[x]{c^{n}}=(\sqrt[x]{c})^{n}\)

\((c^{x})^{n}=(c^{n})^{x}=c^{xn}\)

\(c^{x}*c^{n}=c^{x+n}\)

Now lets begin simplifying the function.

\(f(x)=(8^{\frac{2}{3}x})(16^{\frac{1}{2}x})\)

\(=((\sqrt[3]{8^{2}})^{x})((\sqrt{16})^{x})\)

\(=(4^{x})(4^{x})\)

\(=4^{2x}\)

So the correct answer would be \(f(x)=4^{2x}\).

I hope you find my answer and explanation to be helpful. Happy studying.