An industrial process produces batches of a chemical whose impurity levels follwo a normal distribution with standard deviation 1.6 grams of chemical. A random sample of 100 batches is selected in order to estimate the population mean impurity level. The probability is 0,0367 that the sample mean impurity level exceeds the population mean by how much?
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Answer:

Percent error = 11.6%

Step-by-step explanation:

Given the following data;

Actual height, A = 14.7 m

Estimated height, E = 13 m

a. To find the absolute error;

Absolute error = A - E

Absolute error = 14.7 - 13

Absolute error = 1.7

b. To find the percent error;

Percent error can be defined as a measure of the extent to which an experimental (estimated) value differs from the actual or theoretical value.

Mathematically, it is given by this expression;

[tex] Percent \; error = \frac {experimental \;value - theoretical \; value}{ theoretical \;value} *100[/tex]

Substituting into the equation, we have;

[tex] Percent \; error = \frac {13 - 14.7}{14.7} *100[/tex]

[tex] Percent \; error = \frac {1.7}{14.7} *100[/tex]

[tex] Percent \; error = 0.1157 *100[/tex]

Percent error = 11.57 ≈ 11.6%

Answer:

Miguel's account

Step-by-step explanation:

Miguel's account savings are doubled every month. Hence, they will eventually surpass the savings of Anita, even though Anita's account has more money atm.

Answer:

Miguel's account

Step-by-step explanation:

Even though Anita had more money at first compared to Miguel, Miguel savings will double each month while Anita will get only $200 each month. As a result, Miguel's account will grow faster compared to Anita's.

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

[tex](x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}[/tex]

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

[tex]a=b=c=0,p=5[/tex]

That is, the equation of the sphere in cartesian coordinates is,

[tex](x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}[/tex]

[tex]\Rightarrow x^{2}+y^{2}+z^{2}=25[/tex]

Now, the cylindrical coordinate system is represented by [tex](r, \theta,z)[/tex]

The relation between cartesian and cylindrical coordinates is given by,

[tex]x=rcos\theta,y=rsin\theta,z=z[/tex]

[tex]r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z[/tex]

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

[tex]r^{2}+z^{2}=25[/tex]

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

[tex](x-a)^{2}+(y-b)^{2}=p^{2}[/tex]

Here, it is given that the center is at origin & radius is 1. That is, here, we have, [tex]a=b=0,p=1[/tex]. Then the equation of the cylinder in cartesian coordinates is,

[tex]x^{2}+y^{2}=1[/tex]

Now, the spherical coordinate system is represented by [tex](\rho,\theta,\phi)[/tex]

The relation between cartesian and spherical coordinates is given by,

[tex]x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi[/tex]

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

[tex](\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi=1[/tex] (As [tex]sin^{2}\theta+cos^{2}\theta=1[/tex])

Note that [tex]\rho[/tex] represents the distance of a point from the origin, which is always positive. [tex]\phi[/tex] represents the angle made by the line segment joining the point with z-axis. The range of [tex]\phi[/tex] is given as [tex]0\leq \phi\leq \pi[/tex]. We know that in this range the sine function is positive. Thus, we can say that [tex]sin\phi[/tex] is always positive.

Thus, we can square root both sides and only consider the positive root as,

[tex]\Rightarrow \rho sin\phi=1[/tex]

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is [tex]r^{2}+z^{2}=25[/tex]

(b) The equation of the given cylinder in spherical coordinates is [tex]\rho sin\phi=1[/tex]

Answer:

c

Step-by-step explanation:

because I have a great day and I will be in the representation

Step-by-step explanation:

7x + 12 = 6

7x=-6

x=-6/7

Don't enter into link, it contains viruses

Answer:

split the other three in half

Step-by-step explanation:

Answer:

The committee of 8 members can be selected in 990,675 different ways.

Step-by-step explanation:

The order in which the teachers and the students are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

4 teachers from a set of 6.

4 students from a set of 37.

Then

[tex]T = C_{6,4}C_{37,4} = \frac{6!}{4!2!} \times \frac{37!}{4!33!} = 990675[/tex]

The committee of 8 members can be selected in 990,675 different ways.

Answer:

y = 4x - 5

Step-by-step explanation:

for slope intercept form

y = mx + c

where m is the slop so

M = 4

point = (1, -1)

a point on the line must satisfy the equation so replacing y and x by -1 and 1 respectively to get to c.

-1 = 4 × 1 + c

-1 - 4 = c

-5 = c

placing these values in y = mx + c

y = 4x - 5

Answer:

y = 4x - 5.

Step-by-step explanation:

First write it in point-slope form:

y - y1 = m(x - x1)

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

y + 1 = 4x - 4

y = 4x - 4 - 1

y = 4x - 5.  <------- Slope-intercept.

Answer: Pretty sure its the value of the expression is 11

Step-by-step explanation:

Step 1. Add and evaluate 4x and 1/3y^2

Step 2. After evaluating, add 4(2) and 1/3 (3)^2

Step 3. 8 + 1/3(9)

Step 4. 8 + 3 = 11

Step 5. Value of Expression = 11

Answer:

13

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area = [tex]Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85[/tex]

Answer:

[tex]area = 28.27 {m}^{2} \\ c = 18.84m[/tex]

Explanation is attached to the picture

Hope this helps you.

Answer and Step-by-step explanation:

Try putting a bracket ( ] ), so it looks like this:

(-infinity, -5]

this is because the -5 is included and that's where it stops.

#teamtrees #PAW (Plant And Water)

Step-by-step explanation:

The range of a parabola that opens up starts at its vertex (1,−5)(1,-5) and extends to infinity.

Interval Notation:

[−5,∞)[-5,∞)

Set-Builder Notation:

{y|y≥−5}{y|y≥-5}

Determine the domain and range.

Domain: (−∞,∞),{x|x∈R}(-∞,∞),{x|x∈ℝ}

Range: [−5,∞),{y|y≥−5}

Answer:

Step-by-step explanation:

Answer:

The product of the slopes of  and the line perpendicular to  through C is -1 in all cases. So, I can conclude that any two perpendicular lines have slopes that are negative reciprocals of each other.

Step-by-step explanation:

its correct

Answer:

no because it is apporxametely 1/4th of the pizza

Step-by-step explanation:

this is not a trick question, anyone adding more than 2 sentances on their explanation is tricking themselves and is thinking too hard

Answer:

No I actually received 1/4 of the pizza

Step-by-step explanation:

Piece B shows 1/4 of the pizza meaning I'm receiving less than half of the pizza

If I receiveed 2/4 of the pizza, it would've maked senes for me to receive 1/2 of the pizza because 2/4 = 1/2

Answer:

[tex]a \frac{x}{n} = \sqrt[n]{a}^x .

\sqrt[3]{x}^4 \sqrt[3]{y} \sqrt[5]{z}^2 [/tex]

Answer: (f)

Step-by-step explanation:

Given

Line that passes through [tex](-\frac{1}{2},3)[/tex] and [tex](0,0)[/tex]

Using two point form, equation of a line is given by

[tex]\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Insert the values

[tex]\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x[/tex]

Thus, option (f) is correct

Answer:

[tex]\tan{\theta} = \frac{\sqrt{11}}{11}[/tex]

Step-by-step explanation:

Cosecant:

The cosecant is one divided by the sine. Thus:

[tex]\csc{\theta} = \frac{1}{\sin{\theta}}[/tex]

Tangent is sine divided by cosine, so we first find the sine, then the cosine, to find the tangent.

Sine and cosine:

[tex]\sin{\theta} = \frac{1}{\csc{\theta}} = \frac{1}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{6}[/tex]

[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]

[tex]\cos^{2}{\theta} = 1 - \sin^{2}{\theta}[/tex]

[tex]\cos^{2}{\theta} = 1 - (\frac{\sqrt{3}}{6})^2[/tex]

[tex]\cos^{2}{\theta} = 1 - \frac{3}{36}[/tex]

[tex]\cos^{2}{\theta} = \frac{33}{36}[/tex]

First quadrant, so the cosine is positive. Then

[tex]\cos^{2}{\theta} = \sqrt{\frac{33}{36}} = \frac{\sqrt{33}}{6}[/tex]

Tangent:

Sine divided by cosine. So

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{\frac{\sqrt{3}}{6}}{\frac{\sqrt{33}}{6}} = \frac{\sqrt{3}}{\sqrt{33}} = \frac{\sqrt{3}}{\sqrt{3}\sqrt{11}} = \frac{1}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{11}}{11}[/tex]

The answer is:

[tex]\tan{\theta} = \frac{\sqrt{11}}{11}[/tex]

Answer:

-2y (x+2)

Step-by-step explanation:

remove greatest common factors.

both terms have a (y) and a (-2)

Answer:

-2y ( x - 2 )

Step-by-step explanation:

- 2yx - 4y

factor out -2y from the equation

-2y ( x - 2 )

Answer:

1.97 years

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(17,500.00/15,000.00) / ( 2 × [ln(1 + 0.08/2)] )

t = ln(17,500.00/15,000.00) / ( 2 × [ln(1 + 0.04)] )

t = 1.965 years

:D

Answer:

false

Step-by-step explanation:

The function given in the table is a linear function:

f(x) = 3x+2

Answer:

5

Step-by-step explanation:

[tex]\frac{15}{3} =5\\3 friends=1 pizza\\15 friends=5 pizzas\\[/tex]

Answer:

b

Step-by-step explanation:

Answer:

if you put that equation into a graphing calculator the answer is 4188.37

Answer:

C. reflection across the x-axis, translation 6 units left

Answer:

79

100

0.79%

76

100

0.76%

Answer:

120 times

Step-by-step explanation:

On a dice, there are 6 sides.

Since one of these sides is a 5, the chance of rolling a five is 1/6.

Find how many times Malachy can expect to roll a five by multiplying 720 by 1/6:

720(1/6)

= 120

So, Malachy can expect to roll a five 120 times

9514 1404 393

Answer:

  J. 2085

Step-by-step explanation:

Fill in the desired value for y and solve for x.

  1500 = 50(1.05^x)

  30 = 1.05^x . . . . . . . divide by 50

  log(30) = x·log(1.05) . . . . . take logarithms

  x = log(30)/log(1.05) ≈ 69.71

Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.

Answer: A

Step-by-step explanation:

(1,3) ez la respuesta

Let the number be x

7/8 of the number is 7/8x and it equals -35:

7/8x = -35

Find x by dividing both sides by 7/8

When you divide by a fraction, flip the fraction over and then multiply:

x = -35 x 8/7 = (-35 x 8) / 7 = -280/7 = -40

The number is -40