g From a distribution with mean 38 and variance 52, a sample of size 16 is taken. Let X be the mean of the sample. Show that the probability is at least 0.87 that X is in (33, 43)

Answers

Answer 1

Answer:

[tex]P=8.869[/tex]

Step-by-step explanation:

From the question we are told that:

Mean [tex]\=x =38[/tex]

Variance [tex]\sigma=52[/tex]

Sample size [tex]n=16[/tex]

[tex]X=(33, 43)[/tex]

Generally the equation for Chebyshev's Rule  is mathematically given by

[tex]A=(1-\frac{1}{k^2})*100\%[/tex]

Where

[tex]k=\frac{\=x-\mu}{\frac{\sigma}{\sqrt n}}}}[/tex]

[tex]k=\frac{43-38}{\frac{52}{\sqrt 16}}}}[/tex]

[tex]k=2.77[/tex]

Therefore

Probability

[tex]P=(1-\frac{1}{2.77^2})[/tex]

[tex]P=8.869[/tex]


Related Questions

[tex]\lim_{x \to \4} x^{2} -3x[/tex]

Answers

(4)^2-3(4)=4Answer:

Step-by-step explanation:

Multiply (8 + 3i)(3 + 5i).
39 + 491
9+ 491
24 + 152
24 + 491 + 15/2

Answers

24+491+15/2 is
=522.5

(8+3)(3+5)=88

88+(39+491)= 618.

88+(9+491)= 588

88+(24+152)= 264.

sorry could not find the last ansswer..

how many terms are there in the series. 201.208.215......319​

Answers

Answer:

222

Step-by-step explanation:

add 7 no. to each of like 201+7 = 208, 208+7=215 ,215+7=222

Does the point (9, 0) satisfy the equation y = 9x2 + x + 9?

Answers

Answer:

no

Step-by-step explanation:

y = 9x^2 + x + 9
0 = 9(9)^2 + 9 + 9
0 = 9(81) + 9 + 9
0 = 729 + 18
0 = 747

The answer was automatically wrong to begin with because the numbers were already greater than 0

many ® Black pencils cost N75 each and coloured pencils cost N105 each. If 24 mixed pencils cost #2010, how of them were black? (Hint: Let there be x black pencils. Thus there are 24 - x) coloured pencils.)​

Answers

Answer:

85

Step-by-step explanation:

I hope my answer help you

Simplify: 4- (3 1)2 - 6 2 4 2. Combine like terms: 7x3 2x - 5x2 6 x 9 3x3 12x2 3. Simplify: (2x5- ... Multiply: 3x2(4x3 - 2x2 7x - 4) 5. Evaluate: 6x2 ...

Answers

Answer:

The complete question is defined in the attached file please find it.

Step-by-step explanation:

For question 1:

[tex]\to 4-(3+1)^2 - 6\div 2 +4 \\\\\to 4-(4)^2 - 6\div 2 +4\\\\\to 4-16 - 3 +4\\\\\to 4-19 +4\\\\\to 4-15\\\\\to -11[/tex]

For question 2:

[tex]\to 7x^3 +2x -5x^2+6+ x+ 9+ 3x^3 +12x^2 \\\\\to 7x^3 +3x^3+12x^2 -5x^2+2x+x+9+6 \\\\\to 10x^3 +7x^2+3x+15 \\\\[/tex]

For question 3:

[tex]\to (2x^5- 3x^2+4)-(x^5+2x^2+7)\\\\\to 2x^5- 3x^2+4-x^5-2x^2-7\\\\\to x^5- 5x^2-3\\\\[/tex]

For question 4:

[tex]\to 3x^2(4x^3- 2x^2+7x -4) \\\\\to 12x^5- 6x^4+21x^3 -12x^2 \\\\[/tex]

For question 5:

[tex]\to 6x^2+9x-7 \ \ \text{when} \ \ x=2\\\\\to 6(2)^2+9(2)-7 \\\\\to 6(4)+9(2)-7 \\\\\to 24+18-7 \\\\\to 24+11 \\\\\to 35[/tex]

Type your answer into the box. X 30° Calculate the size of angle x. angle x =​

Answers

Answer:

x = 60°

Step-by-step explanation:

We know:

All triangles have internal angles that add up to 180°.

And

All right triangles have acute angles that up to 90°.

Therefore

x + 30° + 90° = 180°

x + 120° = 180°     |subtract 120° from both sides

x + 120° - 120° = 180° - 120°

x = 60°or

x + 30° = 90°     |subtract 30° from both sides

x + 30° - 30° = 90° - 30°

x = 60°

The size of angle x will be 60°

Triangle

It is a plane figure with three straight sides and three angles.

What are steps to solve this  problem?

The steps are as follow:

As per rule of triangle, the sum of all three internal angle must be equal to 180°The given triangle is right angle triangle having one angle 30° and other we have to findGiven:

z = 90°

y = 30°

x = ?

∴ x + y + z = 180°

∴ x + 30 + 90 = 180

∴ x + 120 = 180

∴ x = 60°

So the size of angle x will be 60°

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Find the missing length Indicated

Answers

Answer:

60

Step-by-step explanation:

x² = 144×25

= 3600

x =√3600 =60

Y^2-Y/Y answer please

Answers

Answer:

y - 1

Step-by-step explanation:

y^2 - y / y

Cancel out the numerator with the denominator, so cancel out the y's to get:

y - 1

Remember that there is a "hidden" 1 in front of the y. Meaning that it is "-1."

The height (in meters) of a shot cannonball follows a trajectory given by h(t) = -4.9t^2 + 14t - 0.4 at time t (in seconds). As an improper fraction, for how long is the cannonball above a height of 6 meters? Please show steps. Thank you!

Answers

Solve for 6 = -4.9t^2 + 14t - 0.4 and you will have 2 positive numbers. First one is when cannonball reach 6 meters and second is when after it starts to fall down to 6 meters. I estimate first number to be 0.5 and the second to be 2.5 so the duration is 2 seconds.

Find the area of the shaded regions: the green is the shaded area

PLS HELP ME!!!! I NEED THE ANSWER BY THIS EVENING CUZ I HAVE RSM TOMORROW. PLS HELP!!!!!

Answers

Answer:

the green area stands for the safe operation space

Step-by-step explanation:

u say b×h meaning say 80degrees ×9cm which is 720..

Solve the following equation for
a
a. Be sure to take into account whether a letter is capitalized or not.

Answers

Answer:

6/5 n = a

Step-by-step explanation:

n = 5/6a

Multiply each side by 6/5

6/5 n = 6/5 * 5/6a

6/5 n = a

Talerie has a bathtub that she needs to fill with wa-
ter to fill the tub, she first needs to fill a bucket
with water and then dump this into the bathtub. If
the bucket is a cylinder with a radius of 6 in, and a
height of 12 in, how many buckets will it take to
fill the 5 ft. x3 ft. x3 ft. tub?
a 50 buckets
B. 48 buckets
C. 57 buckets
D. 62 buckets

Answers

Answer:

áedw

Step-by-step explanation:

đá

(2 + i)-(4 - 6/)(-3 +3/)

Answers

Answer:

C

Step-by-step explanation:

(2+i)-(4-6i)(-3+3i)

=(2+i)-(-12+12i+18i-18i^2)

=(2+i)-[-12+30i-18(-1)]

=(2+i)-(-12+30i+18)

=(2+i)-(30i+6)

=2+i-30i-6

=-4-29i

I need help pls help me in geometry homework

Answers

You can use photo math but the first one is b

You are dealt one card from a standard​ 52-card deck. Find the probability of being dealt a diamond

Answers

The probability would be 1/52, since there are only 1 two of diamonds in all 52 cards.

Final answer. 1/52  or 1.92%

Answer:

13/52

Step-by-step explanation:

a standard 52-card deck has 13 diamond cards (1,2,3,4,5,6,7,8,9,10,J,Q,K)

P(diamond) = number of diamonds/number of cards in a deck = 13/52

If the two angles are complementary, find the measure of each of angle.

Answers

Answer:

D 40 and 50

Step-by-step explanation:

Complimentary angles are equal to 90

Answer: D, 40 and 50

Steps:

1. Since complementary angles equal 90 degrees, 4r + 5r = 90

2. 4r + 5r is 9r

3. This makes the equation, 9r=90

4. Divide both sides by 9, and then you get r=10

5. Substitute r=10 into 4r and 5r

6. This should make 4(10) and 5(10)

7. Multiply and then get 40 and 50

Evaluate f(x) when x= 6.
f(x)= {6x^2 +2 if 6 < x <9
12 if 9
6
12
74
218

Answers

Answer:

If i am not wrong the answer is 12

d = 3.2(t+1)(2t - 3)

An air pump increases the oxygen levels in
an aquarium and reduces the build-up of
waste materials. The equation shown above
gives the depth, d, in inches of an air
bubble beneath the surface of the water t
seconds after it emerges from the air pump.
After how many seconds does the air
bubble reach the surface?

Answers

Answer:

3/2=1.5 sec

Step-by-step explanation:

Equate d=0 and solve the expression, t=-1 and 3/2 but t can't be negative.

The air bubble will reach the surface in 1.5 seconds.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression is d = 3.2(t+1)(2t - 3) where d is the height of the aquarium and t is the time taken by the bubbles to come to the surface.

When the bubble will come to the surface height D becomes zero.

d = 3.2(t+1)(2t - 3)

3.2(t+1)(2t - 3) = 0

t + 1 = 0  and  2t - 3 = 0

t = -1  and t = 3 / 2 = 1.5

Therefore, the air bubble will reach the surface in 1.5 seconds.

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Find the tangent line equations for the given functions at the given point(s): f(x) = tan x + 9 sin x at (π, 0)

Answers

Answer:

[tex]{ \bf{f(x) = \tan x + 9 \sin x }}[/tex]

For gradient, differentiate f(x):

[tex]{ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}[/tex]

Substitute for x as π:

[tex]{ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}[/tex]

Gradient of tangent = -8

[tex]{ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi[/tex]

Equation of tangent:

[tex]{ \boxed{ \bf{y = - 8x + 8\pi}}}[/tex]

Aliza is drawing a model of the community swimming pool on grid paper. Each square on the grid is 20 feet by 20
feet.

Answers

Answer:

640 feet

Step-by-step explanation:

Count the length of each side. Add the lengths. Multiply by 20.

Start at the top left corner.

6 across

2 down

3 across

3 down

3 across

2 down

6 across

7 up

total = 32

32 X 20 = 640

surface areas of two similar figures are given. the volume of the larger figure is given. find the volume of the smaller figure​

Answers

9514 1404 393

Answer:

  216 in³

Step-by-step explanation:

The ratio of volumes is the 3/2 power of the ratio of areas.

  small volume = ((small area)/(large area))^(3/2) × (large volume)

  = (212/1325)^(3/2) × 3375 in³ = (4/25)^(3/2) × 3375 in³ = (8/125)×3375 in³

  small volume = 216 in³

Rachel and Hugo sorted 236 crayons into boxes for a local arts project. Each box had 10 crayons. How many crayons were left over?

Help please lol

Answers

Answer:

6

Step-by-step explanation:

236/10 = 23 remainder 6, so 6 crayons is the answer

Solve - 2x - 7 > X+ 8.
O A. x<-3
O B. x<-5
O C. x>-5
O D. x>-3

Answers

Answer:

x < -5

Step-by-step explanation:

- 2x - 7 > x+ 8

Add 2x to each side

- 2x+2x - 7 > x+2x+ 8

-7 > 3x+8

Subtract 8 from each side

-7-8 > 3x+8-8

-15 > 3x

Divide by 3

-15/3 > 3x/3

-5 >x

x < -5

Jarvis invested some money at 6% interest. Jarvis also invested $58 more than 3 times that amount at 9%. How much is invested at each rate if Jarvis receives $1097.19 in interest after one year? (Round to two decimal places if necessary.)

Use the variables x and y to set up a system of equations to solve the given problem.

Answers

9514 1404 393

Answer:

$3309 at 6%$9985 at 9%

Step-by-step explanation:

Let x and y represent amounts invested at 6% and 9%, respectively.

  y = 3x +58 . . . . . . . the amount invested at 9%

  0.06x +0.09y = 1097.19 . . . . . . total interest earned

__

Substituting for y, we have ...

  0.06x +0.09(3x +58) = 1097.19

  0.33x + 5.22 = 1097.19 . . . . . . . . . simplify

  0.33x = 1091.97 . . . . . . . . . . . . subtract 5.22

  x = 3309 . . . . . . . . . . . . . . . . divide by 0.33

  y = 3(3309) +58 = 9985

$3309 is invested at 6%; $9985 is invested at 9%.

52 POINTS I need help!
Question 1

The vertex form of the equation of a vertical parabola is given by
, where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra.

Part A

Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part B

Construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the parabola. What are the coordinates of the point of intersection, A, of the axis of symmetry and the directrix of the parabola?
Part C

Explain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.
Part D

Which way will the parabola open? Explain.
Part E

How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.
Part F

What is the value of p for your parabola?
Part G

Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
Part H

Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
Part I

Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.
Part J

To practice writing the equations of vertical parabolas, write the equations of these parabolas in vertex form:

focus at (-5, -3), and directrix y = -6
focus at (10, -4), and directrix y = 6.

Answers

Answer:

Step-by-step explanation:

A. Directrix: y = 4-6 = -2

:::::

B. Axis of symmetry: x = 6

Axis of symmetry intersects directrix at (6,-2)

:::::

C . Vertex is halfway between focus and directrix, at (6,1)

:::::

D. The focus lies above the directrix, so the parabola opens upwards.

:::::

E. Focal length p = 1/(4×0.5)

:::::

F. p = 0.5

::::

G. y = 0.5(x-6)² + 1

Answer:

the one above is correct

Step-by-step explanation:

h.We start with a circle and a line that goes through the center of the circle (C) and one vertex of the triangle (E).

Using the point on the line opposite the vertex as a center (D), we draw an arc with the same radius the circle has.

The two points of intersection with the circle are the other two vertices of the inscribed triangle (F, G).

line I is parallel to line m. if the measure of line 6 is 75 what is the measure of line <4

Answers

Answer:

75

Step-by-step explanation:

2. What polygon is formed if you divide this figure into three equal parts? A squares B. triangles C. rhombuses D. kites​

Answers

Answer: C

Step-by-step explanation:

Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?

A: Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.


B: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.


C: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.


D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

Answers

Answer:

D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

The radius of a sphere is 6 units.
Which expression represents the volume of the sphere,
in cubic units?
이 (6)
○ (6)
이 (12)
ㅇ (12)

Answers

Answer:

B. ⁴/3π(6)³

Step-by-step explanation:

Formula for volume of a sphere = ⁴/3πr³

Where,

radius (r) = 6 units

Plug in the given value into the volume formula

Volume of the sphere = ⁴/3 × π × (6)³

Volume of the sphere = ⁴/3π(6)³

The expression that represents the volume of the given sphere is therefore ⁴/3π(6)³ cubic units.

The expression for the volume of the sphere is:

V = (4/3)*3.14*(6)^3

Which expression represents the volume?

For a sphere of radius R. the volume is given by:

V = (4/3)*pi*R^3

Where pi = 3.14

Here we know that the radius is 6 units, so we can write the volume as:

V = (4/3)*3.14*(6)^3

As you can see, the second option (counting from the top) is the correct one.

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