In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x?1 ? x?2 is normal if the
A. populations are normal.
B. population sizes are both greater than 30.
C. populations are nonnormal and the sample sizes are large.
D. sizes are both greater than 30.

Answer: b) 6.10%

Step-by-step explanation:

to find the probability for the other bag to contain exactly 4 balls at that time;  

is only possible if you have chosen a particular bag 10 times and other bag 6 times.

After that, once again at the 17th attempt

so the required probability =     ¹⁶c₁₀ × (1/2¹⁰ × (1/2)⁶ × (1/2)

= 0.610

CONVERT TO PERCENT

0.610 × 100

= 6.10%

Answer:

Approximately 2 days.

Step-by-step explanation:

The frog can only jump 3 lily pads each day.

24 hours = 1 day

[tex]\frac{24}{3}[/tex] = 8 hours

Thus, it would take the frog 8 hours to cover a lily pad.

To get to the edge of the pond, the frog would jump through 6.5 lily pads (since he is at the middle of a lily pad at the center of the pond).

So that;

Total time required to get to the edge of the pond can be determined by;

6.5 × 8 hours = 52 hours

Number of days to get to the edge of the pond = [tex]\frac{52}{24}[/tex]

                                                                    = 2.2

It would take him approximately 2 days to get to the edge of the pond.

Answer:

x = 78

Step-by-step explanation:

57° + x° = 135° (alternate angles, // lines)

x = 135 - 57

= 78

I hope this helps :)

Answer: ( -0.731,  0.682)

Step-by-step explanation:

The unit vector is defined as a vector that points in the same direction as our vector (137 degrees from the x-axis) and has a magnitude of 1.

Knowing the angle, is really simple to do it.

First, we know that for a radius R and an angle A, the rectangular coordinates can be written as:

x = R*cos(A)

y = R*sin(A)

And if we want that the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 137°

x = 1*cos(137°) = -0.731

y = 1*sin(137°) = 0.682

Then the unit vector is: ( -0.731,  0.682)

The unit vector is ( -0.731,  0.682)

[tex]x = R\times cos(A)\\\\y = R\times sin(A)[/tex]

And the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 137°

so,  

[tex]x = 1\times cos(137) = -0.731y = 1\times sin(137) = 0.682[/tex]

Then the unit vector is: ( -0.731,  0.682)

learn more: https://brainly.com/question/20492533?referrer=searchResults

Hi there! Hopefully this helps!

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[tex]17 = r + 10[/tex]

Swap sides so that all variable terms are on the left hand side.

[tex]r + 10 = 17[/tex]

Subtract 10 from both sides.

[tex]r = 17 - 10[/tex]

Answer:

a. [tex] \boxed{ \bold{ \boxed{ \sf{width \: of \: rectangular \: field \: = 71 \: meter}}}}[/tex]

b. [tex] \boxed{ \bold{ \boxed{ \sf{length \: of \: rectangular \: painting \: = 85 \: cm}}}}[/tex]

Step-by-step explanation:

a. Given,

Perimeter of rectangular field ( P ) = 310 m

Length of the field ( L ) = 84 m

Width of the field ( W ) = ?

Finding the width of the rectangular field

[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}[/tex]

plug the values

⇒[tex] \sf{310 = 2(84 + w)}[/tex]

Distribute 2 through the parentheses

⇒[tex] \sf{310 = 168 + 2w}[/tex]

Swap the sides of the equation

⇒[tex] \sf{168 + 2w = 310}[/tex]

Move 168 to right hand side and change it's sign

⇒[tex] \sf{2w = 310 - 168}[/tex]

Subtract 168 from 310

⇒[tex] \sf{2w = 142}[/tex]

Divide both sides of the equation by 2

⇒[tex] \sf{ \frac{2w}{2} = \frac{142}{2} }[/tex]

Calculate

⇒[tex] \sf{w = 71 \: m}[/tex]

Width = 71 meters

------------------------------------------------------------

2. Given,

Area of rectangular painting ( A ) = 5185 cm²

Width of the painting ( w ) = 61 cm

Length of the painting ( l ) = ?

Finding length of the painting

[tex] \boxed{ \sf{area \: of \: rectangle = l \times w}}[/tex]

plug the values

⇒[tex] \sf{5185 = 61l}[/tex]

Swap the sides of the equation

⇒[tex] \sf{61 \: l \: = 5185}[/tex]

Divide both sides of the equation by 61

⇒[tex] \sf{ \frac{61 \: l}{61} = \frac{5185}{61} }[/tex]

Calculate

⇒[tex] \sf{l = 85}[/tex] cm

Length = 85 cm

Hope I helped!

Best regards !!!

Answer:

Step-by-step explanation:

x+118 degrees =180 degrees

x +118 degrees-118degrees =180 degrees - 118 degrees

                                         x =62 degrees

Answer:

Step-by-step explanation:

Follow PEDMAS

[tex]-2 - (-4)[/tex]

Follow rule : -(-a)= + a

[tex] - 2 + 4 \\ = 2[/tex]

Answer:2

Step-by-step explanation:

Answer: .18

Step-by-step explanation:

Answer:

The number of times Ivan and Adeline have the same number written on the board is 6.

Step-by-step explanation:

Consider the procedure as follows:

Consider the numbers on each half of the board:

          Ivan                            Adeline

             2                                     2

      2 × -2 = -4                        2 × 2 = 4

     -4 × -2 = 8                         4 × 2 = 8

      8 × -2 = -16                      8 × 2 = 16

   -16 × -2 = 32                      16 × 2 = 32

   32 × -2 = -64                    32 × 2 = 64

  -64 × -2 = 128                   64 × 2 = 128

  128 × -2 = -256               128 × 2 = 256

-256 × -2 = 512                256 × 2 = 512

  512 × -2 = -1024              512 × 2 = 1024

-1024 × -2 = 2048           1024 × 2 = 2048

Thus, the number of times Ivan and Adeline have the same number written on the board is 6.

1. 3 times a number less than the sum of twice a number and 2.

Let x be the number

The sum of twice of x and 2 is 2x + 2.

3 times a number less than this is 2x + 2 - 3x = -x + 2.

2. 6 multiplied by the sum of a number and 8.

Let x be the number

The sum of a number and 8 is x + 8.

6 multiplied by this is 6(x+8) = 6x + 48

3. Jane saves $10 per week, so after w weeks, she saves 10w.

She already has $50, so she then has 50 + 10w.

Answer:

Step-by-step explanation:

Before we can calculate the standard deviation of the dataset, we need to get the mean value first.

mean = sum of the values/total number given

mean = -8+2+2+4+15/5

mean = 15/5

mean (xbar) = 3

For ungrouped data:

Variance S²=  ∑(xi-xbar)²/N-1

xi are the individual values

xbar is the mean value = 3

N is the total number in the dataset = 5

Variance = (-8-3)²+(2-3)²+(2-3)²+(4-3)²+(15-3)²/5-1

S² = (-11)²+(-1)²+(-1)²+(1)²+(12)²/4

S² = (121+1+1+1+144)/4

S² = 67

Hence the variance of data sample is 67.00

Standard deviation is the square root of the variance.

√S² = Standard deviation

√67 = Standard deviation

Standard deviation = 8.185

Standard deviation ≈ 8.19 (to 2 decimal place)

Answer:

Hello! Answer below! :)

Step-by-step explanation:

**Least to greatest** => [tex]1/10 < 3/10 < 0.9[/tex]

Look at the picture below!

By: RobloxYt

Answer:

1). Angle c is congruent to angle E

2) BC=FD

Answer:17

Step-by-step explanation:

Plug in 4 in the place of x and then add 1

[tex] &#128075 [/tex] Hello ! ☺️

Step-by-step explanation:

F(x)= x² +1

[tex] f(4) = 4 {}^{2} + 1 [/tex]

[tex] f(4)= 16+1 [/tex]

[tex]\boxed{\color{gold}{f(4) = 17}} [/tex]

[tex]<marquee direction="left" scrollamount="2" height="100" width="150">&#x1F498;Mynea04</marquee>[/tex]

Answer:

forty nine eight hundred in a decimal

= 49800.0

one ten thousands in a decimal​

= 10000.00

Step-by-step explanation:

forty nine eight hundred and one ten thousands in a decimal​

First of all.

Let's take forty nine eight hundred

Converting it to decimal

= 49800.0

forty nine eight hundred= 49800.0

For the second one

one ten thousands in a decimal​

Converting it to decimal

= 10000.00

one ten thousands in a decimal​

= 10000.00 in decimal

Answer:

(0,-4) (5,0)

Step-by-step explanation:

4x-5y=20

First, we must put the equation into slope intercept form: y= mx+b

5y=4x-20=y=4/5x-4

The y intercept, by definition, is b. In this scenario, b is -4.

One ordered pair that works is (0,-4).

Also, we can find the ordered pair for the x intercept. By definition, the x intercept is the value of x when y equals zero. hence, we substitute 0 for y and then we can find an ordered pair that works and solve for x!:

Therefore, (5,0) works as well!

Answer:

C. 1365

Step-by-step explanation:

The expression nCr can be written with the simple equation:

n! / ((n-r)! * r!)

So to evaluate 15C4:

15! / ((15-4)! * 4!)

= 1365

So 15C4 = 1365

Cheers.

Answer:

1365

Step-by-step explanation:

15!/4!(15-4)!

1365

Answer:

f(x) = -5 if -5 <= x <= -3

f(x) = -2 if -3 < x <= 2

f(x) = 5 if 2 < x <= 6

Step-by-step explanation:

This is a simple piece wise function. Notice there are three lines or "solutions" for y-values over a range of x-values. Also notice there are filled in and not filled in circles. If the circle is not filled in, then it is not a solution. If it is, then it is a solution.

So for this, -5 is the solution if the range of x is from -5 through -3 inclusive since it has filled in circles.

-2 is a solution if the range of x is from -3 exclusive through 2 inclusive since at -3 it's open circle and 2 is filled.

5 is a solution if the range of x is from 2 exclusive through 6 inclusive since 2 it's open circle and 6 is filled.

To right that in notation simply

f(x) = -5 if -5 <= x <= -3

f(x) = -2 if -3 < x <= 2

f(x) = 5 if 2 < x <= 6

Cheers.

Answer:

49 or 7^2

Step-by-step explanation:

9 x 5 + 4

=> 45 + 4

=> 49 or 7^2

Answer: 49

Step-by-step explanation: Multiply 9 and 5. Then add 4. Use PEMDAS.

9 × 5 = 45

45 + 4 = 49

Answer:

−(−45)

I hope this helps.

Answer:

−(−45)

Step-by-step explanation:

Answer:

No, Nadia is incorrect. She could multiply both the numerator and denominator of the unit fraction equivalent to 2/10 by 3 and arrive at the equivalent fraction 3/15.

*Credits to another Brainly question. The person who asked the question put this answer in the answer options.*

Answer:

Hey there!

For question 1:

C(11,5) = (11!)/(5!*(11-5)!)

C(11,5) = (11!)/(5!*6!)

C(11,5) = (11*10*9*8*7*6!)/(5!*6!)

C(11,5) = (55440)/(120)

C(11,5) = 462 ways

For question 2:

10!=10*9*8*7*...*2*1= 3628800 ways.

This can be a challenging and confusing topic, so let me know if you want a easier to understand explanation, I'm always here to give one :)

A number of ways to choose the players are 462 and The coach made a batting order is 3,268,800.

A permutation is an act of arranging the objects or elements in order.

1.  Rylan's basketball team has 11 players.

His coach chooses five starting players.

The number of different ways to choose the players.

[tex]\rm ^{11}C_{5} = \dfrac{11!}{5! (11-5)!} = 462[/tex]

2.  Sarah plays softball over the summer. If there are 10 players on the team.

The coach made a batting order that will be

[tex]10! = 10*9*8*7*6*5*4*3*2*1 = 3268800[/tex]

Thus, A number of ways to choose the players are 462 and The coach made a batting order is 3,268,800.

More about the permutation link is given below.

https://brainly.com/question/1216161

Answer:

work is shown and pictured

Answer:

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius of the circle

From the question

Area = 154cm²

To find the radius substitute this value into the above formula and solve for the radius

That's

154 = πr²

Divide both sides by π

We have

[tex] {r}^{2} = \frac{154}{\pi} [/tex]

Find the square root of both sides

Thats

[tex]r = \sqrt{ \frac{154}{\pi} } [/tex]

r = 7.0014086

We have the final answer as

radius = 7.0 cm

Hope this helps you

Answer:

Hey there!

Well first, don't feel bad, since trig is really hard, especially if you are just learning it.

If you've learned about SOH CAH TOA, you will see that TOA is the best identity to use here.

tangent 20=x/10

tangent 20 (10)=x

x=3.64

Let me know if you have any other trig questions, I'm always here to help :)

Answer:

vertical angles

Step-by-step explanation:

Opposite angles that are congruent are known as vertical angles.

Answer:

30

2ab=2*5*3

30

hope it helps

Answer:

30

The equation re-written would be

2 · 5 · 2 = 30

Answer:

Just two

Step-by-step explanation:

Glorias teacher asks her to draw a triangle with 90 degree angle and a 42 degree angle.

The presence of 90 degrees indicates that it's a right angle triangle.

The remaining angle= 180-90-42

The remaining angle= 48 degrees

Due to the presence of 90 degrees, the angle 42 and 48 degrees will interchange two times only to form only two unique triangles.