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3 years ago

11

Suppose the scores on a history quiz are normally distributed with a mean of 73 and a standard deviation of 4. Which group descr

ibes 16% of the population of history quiz scores?
A. scores below 65

B. scores below 75

C. scores above 77

D. scores above 81

1 answer:

KiRa [710]3 years ago

8 0

B is the correct answer the score is below 75

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Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.

FromTheMoon [43]

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:

$\rho = \sqrt{x^{2}+y^{2}+z^{2}}$

$\phi = cos^{-1}\frac{z}{\rho}$

For angle θ:

If x > 0 and y > 0: $\theta = tan^{-1}\frac{y}{x}$ ;

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

Calculating:

a) (4,2,-4)

$\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}$ = 6

$\phi = cos^{-1}(\frac{-4}{6})$

$\phi = cos^{-1}(\frac{-2}{3})$

For θ, choose 1st option:

$\theta = tan^{-1}(\frac{2}{4})$

$\theta = tan^{-1}(\frac{1}{2})$

b) (0,8,15)

$\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}$ = 17

$\phi = cos^{-1}(\frac{15}{17})$

$\theta = tan^{-1}\frac{y}{x}$

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

c) (√2,1,1)

$\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}$ = 2

$\phi = cos^{-1}(\frac{1}{2})$

$\phi$ = $\frac{\pi}{3}$

$\theta = tan^{-1}\frac{1}{\sqrt{2} }$

d) (−2√3,−2,3)

$\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}$ = 5

$\phi = cos^{-1}(\frac{3}{5})$

Since x < 0, use 2nd option:

$\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }$

$\theta = \pi + \frac{\pi}{6}$

$\theta = \frac{7\pi}{6}$

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

$r=\sqrt{x^{2}+y^{2}}$

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

$r=\sqrt{4^{2}+2^{2}}$ = $\sqrt{20}$

$\theta = tan^{-1}\frac{1}{2}$

z = -4

b) (0, 8, 15)

$r=\sqrt{0^{2}+8^{2}}$ = 8

$\theta = \frac{\pi}{2}$

z = 15

c) (√2,1,1)

$r=\sqrt{(\sqrt{2} )^{2}+1^{2}}$ = $\sqrt{3}$

$\theta = \frac{\pi}{3}$

z = 1

d) (−2√3,−2,3)

$r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}$ = 4

$\theta = \frac{7\pi}{6}$

z = 3

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3 years ago

Write the ratio in simplest form in both fractions and in decimal form.

ValentinkaMS [17]

Answer:

Step-by-step explanation:

3 : 12

Both have table of 3 in common so

1 : 4 or 1/4

4 : 64

Both have table of 4 in common

1 : 16 or 1/16

3 0

3 years ago

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A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken

kotegsom [21]

Answer: 68

Step-by-step explanation:

Formula for sample size when prior estimate of population proportion (p) is available: $n=p(1-p)(\dfrac{z^*}{E})^2$

, where z*= critical-value.

E= Margin of error.

Let p be the population proportion of trees are infected with the citrus red mite.

As per given , we have

$p=\dfrac{1}{5}=0.2$

E= ± 0.08

The critical z-value corresponding to 90% confidence level = z*=1.645

Substitute all the values in the above formula , we get

Required sample size : $n=(0.2)(1-0.2)(\dfrac{(1.645)}{0.08})^2$

$\Rightarrow\ n=(0.2)(0.8)(20.5625)^2$

$\Rightarrow\ n=0.16(422.81640625)\\\\\Rightarrow\ n=67.650625\approx68$ [Rounded to next integer.]

Thus, the minimum sample size should be taken =68

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3 years ago

4. The area of a rhombus with one diagonal is 8.72 cm long is the same as the area of a square of side 15.6 cm. Find the length

Lubov Fominskaja [6]

Answer:

55.82 cm

Step-by-step explanation:

d1= 8.72 cm

a= 15.6 cm

A rhombus= 1/2*d1*d2 = A square

A square= 15.6²= 243.36 cm²

d2= 2A/d1= 2*243.36/8.72 ≈55.82 cm

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3 years ago

Gerald bought 3 shirts for 8.40 each, 2 shirts for 12.89 each, and one shirt for 18.90. What was the average cost of the shirts?

Vanyuwa [196]

So first, you add all the numbers together

8.40*3=25.20
12.89*2=25.78
18.90*1=18.90
____________
$69.88

Divide the number of shirts: 6 by the total amount

69.88
_____ = $11.64666= $11.65 is your answer!
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8 0

3 years ago

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