Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
a. (4,2,−4)
b. (0,8,15)
c. (√2,1,1)
d. (−2√3,−2,3)

Answers

Answer 1

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]

[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]

For angle θ:

If x > 0 and y > 0: [tex]\theta = tan^{-1}\frac{y}{x}[/tex];If x < 0: [tex]\theta = \pi + tan^{-1}\frac{y}{x}[/tex];If x > 0 and y < 0: [tex]\theta = 2\pi + tan^{-1}\frac{y}{x}[/tex];

Calculating:

a) (4,2,-4)

[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6

[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]

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

For θ, choose 1st option:

[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]

[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]

b) (0,8,15)

[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17

[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]

[tex]\theta = tan^{-1}\frac{y}{x}[/tex]

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]

c) (√2,1,1)

[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2

[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]

[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]

[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]

d) (−2√3,−2,3)

[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5

[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]

Since x < 0, use 2nd option:

[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]

[tex]\theta = \pi + \frac{\pi}{6}[/tex]

[tex]\theta = \frac{7\pi}{6}[/tex]

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

[tex]r=\sqrt{x^{2}+y^{2}}[/tex]

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]

[tex]\theta = tan^{-1}\frac{1}{2}[/tex]

z = -4

b) (0, 8, 15)

[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8

[tex]\theta = \frac{\pi}{2}[/tex]

z = 15

c) (√2,1,1)

[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]

[tex]\theta = \frac{\pi}{3}[/tex]

z = 1

d) (−2√3,−2,3)

[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4

[tex]\theta = \frac{7\pi}{6}[/tex]

z = 3


Related Questions

7. Suppose that y varies inversely with x. Write an equation for the inverse variation,
y = 4 when x = 6
A
у
x =
2
B
х
y =
24
с
24
y =
OD y = 2x

Answers

Answer:

The answer is

[tex]y = \frac{24}{x} [/tex]

Step-by-step explanation:

The statement

y varies inversely with x is written as

[tex]y = \frac{k}{x} [/tex]

where k is the constant of proportionality

To find k substitute the values of x and y into the equation

From the question

y = 4

x = 6

We have

[tex]4 = \frac{k}{6} [/tex]

Cross multiply

k = 4 × 6

k = 24

So the formula for the variation is

[tex]y = \frac{24}{x} [/tex]

Hope this helps you

Answer: 5

Step-by-step explanation:

Which of the following graphs accurately displays a parabola with its directrix and focus?

Answers

Answer:

Hey there!

The first graph is the correct answer. A point on the parabola is equally far from the focus as it is to the directrix.

Let me know if this helps :)

The graph that  accurately displays a parabola with its directrix and focus is the first graph.

How do we make graph of a function?

Suppose the considered function whose graph is to be made is  f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values  f(x) are plotted on the vertical axis.

They are together plotted on the point  (x,y) = (x, f(x))

This is why we usually write the functions as:  y = f(x)

A point shown in the graphs on the parabola is equally far from the focus as it is to the directrix.

Therefore, The first graph is the correct answer.

Learn more about graphing functions here:

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a kicker starts a football game by "kicking off". The quadratic function y = -10x^2 + 25x models football's height after x seconds. How long, in seconds, is the football in the air?​

Answers

Answer:  2.5 seconds

Step-by-step explanation:

x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)

0 = -10x² + 25x

0 = -5x(2x - 5)

0 = -5x     0 = 2x - 5

[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]

x = 0 seconds is when the ball was kicked

x = 5/2 --> 2.5 seconds is when the ball landed on the ground

Complete each equation with a number that makes it true. 5⋅______=15 4⋅______=32 6⋅______=9 12⋅______=3

Answers

Answer: blank 1:  3   Blank 2:  8   blank 3:  1.5    blank 4:   0.25

Step-by-step explanation:

5 times 8=15

4 times 8=32

6 times 1.5=9

12 times 0.25=3

The complete equation is

5⋅____3__=15

4⋅___8___=32

6⋅___1.5___=9

12⋅__0.25____=3

What is Multiplication?

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.

Multiplication Formula

The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:

Multiplicand: The first number (factor).Multiplier: The second number (factor).Product: The final result after multiplying the multiplicand and multiplier.Multiplication symbol: '×' (which connects the entire expression)

5 * 3=154 * 8=326 * 1.5=912 * 0.25=3

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Let A and B be events. The symmetric difference A?B is defined to be the set of all elements that are in A or B but not both.
In logic and engineering, this event is also called the XOR (exclusive or) of A and B.
Show that P(AUB) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.

Answers

Correction:

P(AΔB) = P(A) + P(B) - 2P(AnB)

is what could be proven using the axioms of probability, and considering the case of symmetric difference given.

Answer:

P(AΔB) = P(A) + P(B) - 2P(AnB)

Has been shown.

Step-by-step explanation:

We are required to show that

P(AUB) = P(A) + P(B) - 2P(AnB)

directly using the axioms of probability.

Note the following:

AUB = (AΔB) U (AnB)

Because (AΔB) U (AnB) is disjoint, we have:

P(AUB) = P(AΔB) + P(AnB)..................(1)

But again,

P(AUB) = P(A) + P(B) - P(AnB)...............(2)

Comparing (1) with (2), we have

P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)

P(AΔB) = P(A) + P(B) - 2P(AnB)

Where AΔB is the symmetric difference of A and B.

For a free lunch giveaway, a restaurant draws 1 card from a bowl of business cards. Val puts in 5 cards. The bowl has 50 cards. What is the probability that Val will win?

Answers

Answer:The probability Val will win is 1/5 or 10/50 or 2/10

Step-by-step explanation:

What is lim x → 0 e^2x - 1/ e^x - 1

Answers

Hello, please consider the following.

[tex]\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }[/tex]

Thank you

PLS HELP:Find all the missing elements:

Answers

Answer:

b = 9.5 , c = 15

Step-by-step explanation:

For b

To find side b we use the sine rule

[tex] \frac{ |a| }{ \sin(A) } = \frac{ |b| }{ \sin(B) } [/tex]

a = 7

A = 23°

B = 32°

b = ?

Substitute the values into the above formula

That's

[tex] \frac{7}{ \sin(23) } = \frac{ |b| }{ \sin(32) } [/tex]

[tex] |b| \sin(23) = 7 \sin(32) [/tex]

Divide both sides by sin 23°

[tex] |b| = \frac{7 \sin(32) }{ \sin(23) } [/tex]

b = 9.493573

b = 9.5 to the nearest tenth

For c

To find side c we use sine rule

[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]

C = 125°

So we have

[tex] \frac{7}{ \sin(23) } = \frac{ |c| }{ \sin(125) } [/tex]

[tex] |c| \sin(23) = 7 \sin(125) [/tex]

Divide both sides by sin 23°

[tex] |c| = \frac{7 \sin(125) }{ \sin(23) } [/tex]

c = 14.67521

c = 15.0 to the nearest tenth

Hope this helps you

Rewrite the expression as an equivalent ratio of logs using the indicated base.log17(52.875) to base 10.

Answers

Answer:

[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Step-by-step explanation:

Given

[tex]log_{17}(52.875)[/tex]

Required

Convert to base 10

To do this, we make use of the following logarithm laws;

[tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]

In the given parameters;

[tex]a = 52.875[/tex]

[tex]b = 17[/tex]

Substitute these values in [tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]

[tex]log_{17}52.875 = \frac{log_{10}52.875}{log_{10}17}[/tex]

Represent as a ratio

[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Hence;

[tex]log_{17}(52.875)[/tex] is represented as [tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Expression  [tex]log_{17} 52.875[/tex] can be written as in form of ratio of log  [tex]\frac{log_{10} 52.875}{log_{10} 17}[/tex] .

Any logarithmic expression [tex]log_{a} b[/tex] can we written as in form of ratio of log on base 10.

                   [tex]log_{a} b=\frac{log_{10} b}{log_{10} a}[/tex]

Here logarithmic expression is,  [tex]log_{17} 52.875[/tex] comparing with above expression.

We get,    [tex]b=52.875,a=17[/tex]

Substitute values of a and b in above expression.

 We get,      [tex]log_{17} 52.875=\frac{log_{10} 52.875}{log_{10} 17}[/tex]

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A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two. What is the probability of no defects in 10 feet of steel

Answers

Answer:

the probability of no defects in 10 feet of steel = 0.1353

Step-by-step explanation:

GIven that:

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.

Let consider β to be the average value for defecting

So;

β = 2

Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.

Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2

i.e

[tex]Y \sim P( \beta = 2)[/tex]

the probability mass function can be represented as follows:

[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]

where;

y =  0,1,2,3 ...

Hence,  the probability of no defects in 10 feet of steel

y = 0

[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]

[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]

P(y =0) = 0.1353

If possible, find AB. & State the dimension of the result.

Answers

Answer:

The answer is "[tex]AB= \left[\begin{array}{cc} -2 &51 \\-8&33\\0&27&\end{array}\right][/tex]"

Step-by-step explanation:

If the value of A and B is:

[tex]A= \left[\begin{array}{cc}-1&6\\-4&5\\0&3\end{array}\right][/tex]

[tex]B=\left[\begin{array}{cc}2&3\\0&9\end{array}\right][/tex]

Find the value of A[tex]\times[/tex]B:

[tex]AB =\left[\begin{array}{cc}-1 \times 2+6 \times 0 &-1 \times 3+6 \times 9\\ -4 \times 2+5 \times 0& -4 \times 3+5 \times 9\\ 0 \times 2+3 \times 0&-1 \times 2+3\times 9\end{array}\right] \\ \\\\AB =\left[\begin{array}{cc}-2+0 &- 3+54\\ -8+0& -12+45\\ 0+ 0&-2 +27\end{array}\right] \\ \\[/tex]

[tex]AB= \left[\begin{array}{cc} -2 &51 \\-8&33\\0&27&\end{array}\right][/tex]

Please answer fast! :)

Answers

Answer:

D

Step-by-step explanation:

The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.

When you plug 3 into equation D the entire right side it will become.

y-1=0

y=1, which is true.

When you plug 6 into that equation.

y-1=5

y=6 which is also true.

im sorry but the thing is i cant translate these words but the answer is D

a westward moving motorcycle slows down from 24.0 m/a to 12.0 m/s in 3.0 seconds. what is the magnitude and direction of the acceleration

Answers

Answer:

0

Step-by-step explanation:

Consider a bag of jelly beans that has 30 red, 30 blue, and 30 green jelly beans. a) How many color combinations of 15 beans have at least 6 green beans

Answers

Answer:

680

Step-by-step explanation:

Number of red beans = 30

Number of Blue beans = 30

Number of green beans = 30

How many color combinations of 15 beans have at least 6 green beans?

Since at least 6 of the beans must be green,

Then (15 - 6) = 9

Then, the remaining 9 could be either red, blue or green.

Therefore, C(9 + (9 - 1), 3)

C(17, 3) = 17C3

nCr = n! ÷ (n-r)! r!

17C3 = 17! ÷ (17 - 3)! 3!

17C3 = 17! ÷ 14!3!

17C3 = (17 * 16 * 15) / (3 * 2)

17C3 = 4080 / 6

17C3 = 680 ways

Using the combination formula, it is found that there are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

The order in which the beans are chosen is not important, hence, the combination formula is used to solve this question.

Combination formula:

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

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

Th total number of combinations of 15 beans from a set of 30 + 30 + 30 = 90 is:

[tex]C_{90,15} = \frac{90!}{15!75!} = 45795674000000000[/tex]

With less than 6 green, we have:

0 green:

[tex]C_{30,0}C_{60,15} = \frac{60!}{15!45!} = 53194089000000[/tex]

1 green:

[tex]C_{30,1}C_{60,14} = \frac{30!}{1!29!} \times \frac{60!}{14!46!} = 520376960000000[/tex]

2 green:

[tex]C_{30,2}C_{60,13} = \frac{30!}{2!28!} \times \frac{60!}{13!47!} = 2247585600000000[/tex]

3 green:

[tex]C_{30,3}C_{60,12} = \frac{30!}{3!27!} \times \frac{60!}{12!48!} = 5681396900000000[/tex]

4 green:

[tex]C_{30,4}C_{60,11} = \frac{30!}{4!26!} \times \frac{60!}{11!49!} = 9391696900000000[/tex]

5 green:

[tex]C_{30,5}C_{60,10} = \frac{30!}{5!25!} \times \frac{60!}{10!50!} = 10744101000000000[/tex]

Hence, the total for the number of combinations with less than 5 green is:

[tex]53194089000000 + 520376960000000 + 2247585600000000 + 5681396900000000 + 9391696900000000 + 10744101000000000 = 28638351000000000[/tex]

Subtracting the total amount of combinations from the number with less than 5 green, the number of combinations with at least 6 green is:

[tex]T = 45795674000000000 - 28638351000000000 = 17157323000000000[/tex]

There are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

A similar problem is given at https://brainly.com/question/24437717

A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?

Answers

Answer:

its multiple choice

A. 26inches (1inch/25.4mm)

B. 26inches (25.4mm/1inch)

C. 25.4inches (1mm/26inch)

D. 26inches (1mm/25.4inch)

and its b

) If the half-life of 238Pu is 87.7 yr, write a function of the form =QtQ0e−kt to model the quantity Qt of 238Pu left after t years. Round the value of k to five decimal places. Do not round intermediate calculations.

Answers

Answer:

0.079

Step-by-step explanation:

According to the given situation, the calculation of the value of k is presented as follows:

[tex]Q(t)= Q_0e^{-kt}\\\\ 0.5Q_0 = Q_0e^{-k(97.7)}\\\\ 0.5 = e^{-k(87.7)}[/tex]

now,

[tex]k = \frac{In0.5}{-87.7}[/tex]

After solving the above equation we will get the value of k.

= 0.079

Therefore for determining the value of k we simply solve the above equation i.e. by considering all the information mentioned in the question

Answer:

3.5e^-0.0079t

Step-by-step explanation:

None, Good luck mate

The first step in a mathematical induction proof is to divide by n. (True or False).

Answers

Answer:

Step-by-step explanation:

Hello, this is false.

The first step of a mathematical induction proof is to prove the statement for the initial value, which is most of the time for n = 0 or n = 1.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

A couple has a total household income of $84,000. The husband earns $18,000 less than twice what the wife earns. How much does the wife earn? Select the correct answer below:

Answers

Answer:

$34000

Step-by-step explanation:

We can set up a systems of equations, assuming [tex]h[/tex] is the husbands income and [tex]w[/tex] is the wife's income.

h + w = 84000

h = 2w - 18000

We can substitute h into the equation as 2w - 18000:

(2w - 18000) + w = 84000

Combine like terms:

3w - 18000 = 84000

Add 18000 to both sides

3w = 102000

And divide both sides by 3

w = 34000

Now that we know how much the wife earns, we can also find out how much the husband earns by substituting into the equation.

h + 34000  = 84000

h = 50000

Hope this helped!

Choose the correct ray whose endpoint is B.

Answers

Answer:

The second option.

Step-by-step explanation:

The first option consists of a line that extends at both opposite sides to infinity, with no precise end.

The third option is a ray that has an endpoint of A, and extends to infinity towards B.

The fourth option is a line segment. It has two endpoints, B and A.

The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.

The answer is the 2nd option.

p(a) = 0.60, p(b) = 0.20, and p(a and b) = 0.15 what is p(a or b) choices: A. 0.12, B. 0.65, C. 0.40, or D. 0.80 (Note- This is on AP3X)

Answers

Answer:

[tex]p(a\ or\ b) = 0.65[/tex]

Step-by-step explanation:

Given

[tex]p(a) = 0.60[/tex]

[tex]p(b) = 0.20[/tex]

[tex]p(a\ and\ b) = 0.15[/tex]

Required

[tex]p(a\ or\ b)[/tex]

The relationship between the given parameters and the required parameters is as follows;

[tex]p(a\ and\ b) = p(a) + p(b) - p(a\ or\ b)[/tex]

Substitute values for the known parameters

[tex]0.15 = 0.60 + 0.20 - p(a\ or\ b)[/tex]

[tex]0.15 = 0.80 - p(a\ or\ b)[/tex]

Collect Like Terms

[tex]p(a\ or\ b) = 0.80 - 0.15[/tex]

[tex]p(a\ or\ b) = 0.65[/tex]

Hence;

[tex]p(a\ or\ b) = 0.65[/tex]

What is the image of point (8,-4) under the rotation R90° about the origin?

A) (8,4)
B) (4,8)
C) (-4,8)
D) (-4,-8)​

Answers

Answer:

D). (-4,-8)​

Step-by-step explanation:

An image at (8,-4) if rotated at an angle of 90° wipl have another location.

First of all, an image at (8,-4) is in the fourth quadrant, and if it's to rotate clockwise at 90° iths supposed to be in the third quadrant.

And in the third quadrant both x and y is negative.

So the new position is at (-4,-8)​

An airline claims that the proportion of no-shows for passengers who booked on its flights is less than 0.06. In a random sample of 380 reservations, 19 were no-shows. A hypothesis test is to be performed to test the airline's claim that the proportion of no-shows on its flights is less than 0.06. Calculate the test statistic associated with this sample. An airline claims that the proportion of no-shows for passengers who booked on its flights is less than 0.06. In a random sample of 380 reservations, 19 were no-shows. A hypothesis test is to be performed to test the airline's claim that the proportion of no-shows on its flights is less than 0.06. Calculate the test statistic associated with this sample.

Answers

Answer:

≈ -0.821

Step-by-step explanation:

Given:

n= 380, samplex= 19, no-shows countp = 0.06, proportion of no-shows

Then, the sample proportion is:

p' = x/n = 19/ 380 = 0.05

Hypothesis test:

H₀: p = 0.06H₁: p< 0.06

Test statistics:

z = (p' - p) /[tex]\sqrt{p(1-p)/n}[/tex] z = (0.05 - 0.06)/[tex]\sqrt{006(1-0.06)/380}[/tex] ≈ -0.821

Assume the triangular prism has a base area of 49cm^2 and a volume of 588cm^3. What side length does the rectangular prism need to have the same volume?

Answers

Answer:

Length = Width = 7 cm

Step-by-step explanation:

Volume of a triangular prism is represented by the formula,

Volume = (Area of the triangular base) × height

588 = 49 × h

h = [tex]\frac{588}{49}[/tex]

h = 12 cm

We have to find the side length of a rectangular prism having same volume.

Volume = Area of the rectangular base × height

588 = (l × b) × h [l = length and b = width ]

588 = (l × b) × 12

l × b = 49 = 7 × 7

Therefore, length = width = 7 cm may be the side lengths of the rectangular prism to have the same volume.              

How many cabinets must he sell to break even?

Answers

Answer:   He must sell 7 cabinets.

Step-by-step explanation:

So it gives us the equations y= 400x + 1400  and the equations  y=600x and to find the break even point we need to set the two equations equal each other to solve for x.

400x + 1400 = 600x

-400x               -400x

1400 = 200x

 x = 7    

On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain. Yes, since the coin is fair. No, each outcome is equally likely regardless of the previous outcome. Yes, tails will always result on the second toss. No, tails will never occur on the second toss.

Answers

Answer:

No, each outcome is equally likely regardless of the previous outcome.

Given the set of data: 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25 a. Find the mode. b. Find the median. c. Find the mean, to the nearest tenth. d. Find the midrange. e. Find the standard deviation, to the nearest hundredth. f. Determine the quartiles.

Answers

Answer: a. 43

b. 27

c.  34.8

d. 45

e. 17.72

f. First quartile = 23

Second quartile = 27

Third quartile =43

Step-by-step explanation:

The given set of data:  24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25

Arrange in Ascending order:

12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25 , 29, 31, 43, 43 , 43 , 53 , 53, 65 , 78

Total data points: n= 18 ( even)

a. Mode= Most repeated data value = 43

i.e. mode =43

b. Median = [tex]\dfrac{(\frac{n}{2})^{th}\text{term}+(\frac{n}{2}+1)^{th}\text{term}}{2}[/tex]

[tex]=\dfrac{(\frac{18}{2})^{th}\text{term}+(\frac{18}{2}+1)^{th}\text{term}}{2}\\\\=\dfrac{9^{th}\text{term}+10^{th}\text{term}}{2}\\\\=\dfrac{25+29}{2}\\\\=27[/tex]

i.e. median = 27

c. Mean = (sum of data points)÷n

Sum =12+18+18 + 20 +23 +24 + 24 +25 + 25 + 29+ 31+ 43+ 43 + 43 + 53 + 53+ 65 + 78=627

Mean = 627 ÷ 18 ≈34.8

i.e. Mean = 34.8

d. Mid range = [tex]\dfrac{\text{Maximum value +Minimum value}}{2}[/tex]

[tex]=\dfrac{78+12}{2}\\\\=\dfrac{90}{2}\\\\=45[/tex]

e. Standard deviation =[tex]\sqrt{\dfrac{\sum (x-mean)^2}{n}}[/tex][tex]\sum (x-\mean)^2=(12-34.8)^2+(18-34.8)^2+(18 -34.8)^2+( 20 -34.8)^2+(23 -34.8)^2+(24 -34.8)^2+( 24 -34.8)^2+(25 -34.8)^2+2( 25 -34.8)^2+( 29-34.8)^2+( 31-34.8)^2+( 43-34.8)^2+( 43 -34.8)^2+( 43 -34.8)^2+( 53 -34.8)^2+( 53-34.8)^2+( 65 -34.8)^2+( 78-34.8)^2\\\\=5654.56[/tex]

[tex]\sqrt{\dfrac{5654.56}{18}}=\sqrt{314.1422}\approx17.72[/tex]

f. First quartile = Median of first half (12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25)

= 23  (middle most value)

Second quartile = Median = 27

Third quartile = Median of second half (29, 31, 43, 43 , 43 , 53 , 53, 65 , 78)

= 43 (middle most value)

Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register. The store is required to reveal (in the fine print) the distribution of discounts available. Determine whether the following probability assignment is legitimate?


10% off 20% off 30% off 50% off
a. 0.2 0.2 0.2 0.2
b. 0.5 0.3 0.2 0.1
c. 0.8 0.1 0.05 0.05
d. 0.75 0.25 0.25 -0.25
e. 1 0 0 0

Answers

Answer:

b

Step-by-step explanation:

it makes the most senses the lower the discount the higher the chance

You know only the given information about
the measures of the angles of a triangle. Find the probability that the triangle is equiangular.
39. Each is a multiple of 12.

Answers

Since they are multiples if 12

The possibilities are

12, 12, 156

12,24,144

12,36,132

12,48,120

12,60,108

12,72,96

12,84,84

24,24,132

24,36,120

24,48,108

24,60,96

24,72,84

36,36,108

36,48,96

36,60,84

36,72,72

48,48,84

48,60,72

60,60,60

Hence the probability is 1/19 or 0.0526

What is the solution to the linear equation?
2/5 + p = 4/5 + 3/5p​

Answers

Answer:

p = 1

Step-by-step explanation:

[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]

Multiply through by the LCM

The LCM for the equation is 5

That's

[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]

We have

2 + 5p = 4 + 3p

Group like terms

5p - 3p = 4 - 2

2p = 2

Divide both sides by 2

We have the final answer as

p = 1

Hope this helps you

In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.

Answers

Answer:

40,000 populations

Step-by-step explanation:

Initial population in 2018 = 25,000

Annual growth rate (in %) = 4%

Yearly Increment in population = 4% of 25000

= 4/100 * 25000

= 250*4

= 1000

This means that the population increases by 1000 on yearly basis.

To determine what the  population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.

Amount of years we have between 2018 and 2033 = 2033-2018

= 15 years

After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.

Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.

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