The weight of an energy bar is approximately normally distributed with a mean of 42.05 grams and a standard deviation of 0.025 grams. (a) What is the probability that an individual energy bar contains less than 42.035 grams? (b) If a sample of four energy bars is selected, what is the probability that the sample mean weight is less than 42.035 grams? (c) If a sample of 25 energy bars is selected what is the probability that the sample mean weight is less than 42.035 grams? (d) Explain the difference in the results in (a) and (c) (e) Explain the difference in the results in (b) and (c)

Fill the 3-gallon jug all the way.

Pour those 3 gallons of water into the 5-gallon jug.

Fill the 3-gallon jug all the way again, and pour as much as it takes to fill the 5-gallon jug (which is 2 gallons).

Now you have 5 gallons in the 5-gallon jug and 1 gallon in the 3-gallon jug.

Empty the 5-gallon jug.

Pour the 1 gallon in the 3-gallon jug into the 5-gallon jug.

Now fill the 3-gallon jug all the way, and pour all 3 gallons into the 5-gallon jug, which, added to the 1 gallon already in there, and leaves you with exactly 4 gallons.

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Fill the 3-gallon jug all the way.

Pour those 3 gallons of water into the 5-gallon jug.

Fill the 3-gallon jug all the way again, and pour as much as it takes to fill the 5-gallon jug (which is 2 gallons).

Now you have 5 gallons in the 5-gallon jug and 1 gallon in the 3-gallon jug.

Empty the 5-gallon jug.

Pour the 1 gallon in the 3-gallon jug into the 5-gallon jug.

Now fill the 3-gallon jug all the way, and pour all 3 gallons into the 5-gallon jug, which, added to the 1-gallon already in there, leaves you with exactly 4 gallons.

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The correct answer is "98i; n = 77".

The function qt() in statistics is used to calculate the t-value for a given level of confidence and degrees of freedom.

In this case, qt(.98, df = 77) outputs the t-value for a 98% confidence interval with 77 degrees of freedom.

The t-value is used to calculate the margin of error for a confidence interval, which is used to estimate the population parameter based on the sample data.

For example, if you have a sample of size 78 and want to construct a 98% confidence interval for the population mean, you can use the t-value of qt(.98, df = 77) along with the sample mean and standard deviation to calculate the margin of error and construct the interval.

Therefore, the correct answer is "98i; n = 77".

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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Answer:

I can't see the questions i don't know if it's a bug or something but yeah i don't see anything

Step-by-step explanation:

Chelsea made a mistake in simplifying the equation 3(x-3). To find the solution to 4x-5=2(3(x-3)), we first simplify the expression inside the parentheses.

Now, to isolate the variable x, we need to move the terms with x to one side of the equation. Let's subtract 4x from both sides, which gives us -5-4x=6x-18-4x. Simplifying this, we get -5-4x=2x-18.

Next, let's move the constant terms to the other side. Adding 18 to both sides, we get -5-4x+18=2x-18+18. Simplifying this, we get -4x+13=2x.

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Chelsea made a mistake when subtracting the variable term from both sides. By identifying this error and correctly following the steps, we find that the solution to the equation 4x - 5 = 2 3(x - 3) is x = -7.

Chelsea made a mistake in her work when finding the solution to the equation 4x - 5 = 2 3(x - 3). To determine where she went wrong, let's analyze her steps.

Step 1: Distribute 3 to (x - 3): 4x - 5 = 2 3x - 6.
Step 2: Combine like terms: 4x - 5 = 6x - 12.
Step 3: Move the variables to one side and the constants to the other side. Chelsea may have mistakenly subtracted 4x from both sides instead of 6x. This would result in: -5 = 2x - 12.
Step 4: Solve for x. Chelsea may have then incorrectly added 12 to both sides instead of adding 5, leading to: 7 = 2x.
Step 5: Divide both sides by 2: x = 7/2.

Upon reviewing her work, Chelsea should have subtracted 6x from both sides in Step 3, not 4x. This would have resulted in the equation 2x - 5 = -12. Correctly following the steps would lead to the correct solution: x = -7.

Therefore, Chelsea made a mistake when subtracting the variable term from both sides. By identifying this error and correctly following the steps, we find that the solution to the equation 4x - 5 = 2 3(x - 3) is x = -7.

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Answer:

3.4

Step-by-step explanation:

Answer:

e=\frac{4.1\sin 50}{\sin 111} \approx 3.364 \approx 3.4  e=  4.1sin50/sin 111 ≈3.364≈3.4

Step-by-step explanation:

deltamath

Answer:

0

Step-by-step explanation:

A six-sided die has the numbers 1, 2, 3, 4, 5, and 6, not 7. And even is 7 was on there the probability would be 1/6 whihc is approximently 0.167 which is about 0.2 so the probability is 0.

The probability of rolling a seven is 0.

The probability of an event occurring is defined by probability.

The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given:

A single six-sided die is rolled.

So, the Sample space is= (1, 2, 3, 4, 5, 6}

As, there is no possibility of getting number 7 on the dice.

Hence, the probability of rolling a seven is 0.

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Answer:

domain: all real numbers

range : y ≥ 7

Step-by-step explanation:

The domain is the values that x can take

X can take any value so the domain is all real numbers

The range is the values that y can take

The smallest value  for the absolute value is 0

0+7 =7 so the smallest value for y is 7

range is y ≥ 7

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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This relationship is not transitive, symmetrical, or reflexive.

It is not reflexive because, for any x ∈ R, xd x = xx ≥ 0 is not always true.

It is not symmetric because, for any x,y ∈ R, if xd y = xy ≥ 0, then the reverse is not necessarily true (i.e. yd x = yx ≥ 0).

It is not transitive because, for any x,y,z ∈ R, if xd y = xy ≥ 0 and yd z = yz ≥ 0, then the reverse is not necessarily true (i.e. xd z = xz ≥ 0).

The relation d is defined as xd y ⇔ xy ≥ 0 for all x,y ∈ R. This relation is not reflexive because for any x ∈ R, xd x = xx ≥ 0 is not always true. It is not symmetric because for any x,y ∈ R, if xd y = xy ≥ 0, then the reverse is not necessarily true (i.e. yd x = yx ≥ 0). Lastly, it is not transitive because for any x,y,z ∈ R, if xd y = xy ≥ 0 and yd z = yz ≥ 0, then the reverse is not necessarily true (i.e. xd z = xz ≥ 0). Therefore, the relation d is none of these.

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Answer:

x ≈ 5.9

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 2.7² = 6.5²

x² + 7.29 = 42.25 ( subtract 7.29 from both sides )

x² = 34.96 ( take the square root of both sides )

x = \(\sqrt{34.96}\) ≈ 5.9 ( to 1 dec. place )

Answer:

1/7

Step-by-step explanation:

y = -7x - 1 so slope is -7

The slopes of two perpendicular lines are negative reciprocals of each other

so negative reciprocal of -7 is 1/7

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

\(y = \stackrel{\stackrel{m}{\downarrow }}{-7}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

thus a line perpendicular to that slope will have a slope of

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-7}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-7}\implies {\LARGE \begin{array}{llll} \cfrac{1}{7} \end{array}}}}\)

Answer:

x = 3

Step-by-step explanation:

-24 < x - 3 - 8x

-24 < -7x - 3

-24 + 3 = -21

-7x - 3 + 3 = -7x

-21 = -7x

-21 / -7 = 3

-7x / -7 = x

3 = x

See attachment for math work and answer.

The length of the required fence to make a square field that encloses = 5.66 km

For given question,

A farmer wants to make a square field that encloses exactly 2km² of area.

Let 'm' be the side length of the square field.

so, the area of the square field would be,

⇒ A = m²

⇒ 2 = m²

⇒ m = √2 km

We need to compute the length of the required fence.

The length of the required fence would be,

= perimeter of the square field

= 4 × m

= 4 × √2

= 5.66 km

Therefore, the length of the required fence to make a square field that encloses = 5.66 km

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18 mm is the height of the cone.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.

We can use the formula for the volume of a cone to solve for the height:

V = (1/3)πr²h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we have:

1884 = (1/3)π(10²)h

Simplifying, we get:

h = 1884 / [(1/3)π(10²)]

h ≈ 18

Therefore, the height of the cone is approximately 18 mm.

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Complete question:

the volume of this cone is 1,884 cubic millimeters. What is the height of this cone when the radius is 10 mm? Use 3.14 and round your answer to the nearest hundredth

Raj started practicing the saxophone at 7:06 p.m.

To determine when Raj started practicing the saxophone, we can subtract 1 hour and 57 minutes from 8:23 p.m.

First, we convert 1 hour and 57 minutes to minutes:

1 hour = 60 minutes

1 hour and 57 minutes = 60 + 57 = 117 minutes

Next, we subtract 117 minutes from 8:23 p.m.:

8:23 p.m. - 117 minutes = 7:06 p.m.

Therefore, Raj started practicing the saxophone at 7:06 p.m.

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The present value of the loan, rounded to the nearest cent, is $37,196.88.

To calculate the present value of a loan, we can use the formula for the present value of an ordinary annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r),

where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is $3,400, the interest rate is 5.19% compounded semi-annually, and the loan term is 7 years, which is equivalent to 14 semi-annual periods.

First, let's convert the interest rate to its semi-annual equivalent by dividing it by 2. So, the interest rate per semi-annual period is 5.19% / 2 = 2.595%.

Now, we can plug these values into the formula:

PV = $3,400 * ((1 - (1 + 0.02595)^(-14)) / 0.02595).

Calculating this equation, we find that the present value of the loan is approximately $37,196.88 when rounded to the nearest cent.

Therefore, the present value of the loan, rounded to the nearest cent, is $37,196.88.

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Answer:

59.322% or 59%

Step-by-step explanation:

devide 59,000 from 35,000 to get the answer.

After that, you will get 59% (rounded).

the answer is D (59.3%)

i jus got done takin the math quiz on knowledgematters

The gravitational potential energy of the vacationers will decrease as they approach the end of the pier.

As the vacationers approach the end of the pier, their gravitational potential energy will decrease.

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It depends on the height of the object and the acceleration due to gravity.

In this scenario, as the vacationers walk out on the horizontal pier, their height above the ground remains constant. Since the height does not change, the gravitational potential energy also remains constant.

However, as they approach the end of the pier, their distance from the center of the Earth decreases. As a result, the gravitational potential energy decreases because it is directly proportional to the distance from the center of the Earth.

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The probability that a person will wait for more than 9 minutes is approximately 0.0912 or 9.12%. This means that out of 100 people, about 9 of them will wait for more than 9 minutes in the line.

To solve this problem, we need to use the normal distribution and standardize the variable of interest. We know that the mean waiting time is 5 minutes and the standard deviation is 3 minutes, so we can write: Z = (X - μ) / σ

where X is the waiting time, μ is the mean waiting time (5 minutes), σ is the standard deviation (3 minutes), and Z is the standardized variable.

To find the probability that a person will wait for more than 9 minutes, we need to find the area under the normal curve to the right of 9. We can do this by standardizing 9 using the formula above: Z = (9 - 5) / 3 = 1.33 .

We can use a standard normal table or a calculator to find the probability that Z is greater than 1.33. Using a calculator, we find that this probability is approximately 0.0912.

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Answer: multiply both sides by 2

Answer:

16.25, 20, 13.75, 12.5, 7.5

Step-by-step explanation:

1cm= 2.5m

6.5x2.5= 16.25

8x2.5= 20

5.5x2.5= 13.75

5x2.5= 12.5

3x2.5= 7.5

The substances in order of increasing oxidizing ability are: x < z < y.

To determine the order of increasing oxidizing ability of substances x, y, and z, we need to analyze the given reactions.

In reaction 1, y oxidizes x by removing an electron from x, forming y- and x+. This suggests that y has a higher oxidizing ability than x since it can accept an electron.

In reaction 2, y oxidizes z by removing an electron from z, forming y- and z+. Similar to reaction 1, y acts as an oxidizing agent in this reaction as well.

In reaction 3, z oxidizes x by removing an electron from x, forming z- and x+. Here, z exhibits oxidizing behavior by accepting an electron.

Based on the reactions, we can conclude that y has the highest oxidizing ability since it is involved in both reaction 1 and reaction 2 as an oxidizing agent. Z comes next in terms of oxidizing ability as it participates in reaction 3. Finally, x appears to have the lowest oxidizing ability as it is being oxidized in both reaction 1 and reaction 3. Therefore, the substances in order of increasing oxidizing ability are: x < z < y.

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Answer:

the answer is B

\(3( \frac{7}{5} x + 4) - 2( \frac{ 3}{2} - \frac{5}{4} x)\)

\((3 \times \frac{7}{5} x) + (3 \times 4) - 2( \frac{3}{2} - \frac{5}{4} x)\)

\( \frac{21}{5} x + 12 - 2( \frac{3}{2} - \frac{5}{4} x)\)

\( \frac{21}{5} x + 12 + ( - 2 \times \frac{3}{2} ) + ( - 2 \times ( - \frac{5}{4} x))\)

\( \frac{21}{5} x + 12 - 3 + \frac{5}{2} x\)

\( \frac{21}{5}x + \frac{5}{2} x + 12 - 3\)

\( \frac{67}{10}x - 9 \)

Answer:

B

Step-by-step explanation:

if you drew a line on top of any part of the parabola, you will only touch the line once.

(when drawing a line, they are always vertical, not horizontal)

Answer:

i'd say c.) and e.)

Step-by-step explanation:

......