A group of researchers wants to estimate the difference in time it takes to heal enough to return to work after knee replacement surgery using two different physical therapy plans. They plan to use the data in the following table to construct a two-sample t interval.

Therapy plan A B
Mean healing time (weeks) 8.2 6.8
Standard deviation (weeks) 1.5 0.9
Number of participants 45 60

Which of the following are conditions for this type of interval?

Choose all answers that apply:


A. The times for each participant are independent of each other.


B. The distributions of times in the population are approximately normal.


C. Each sample includes equal numbers of men and women.

Splitting the rectangle in half creates two right triangles

The value of tan(x) is 4/3

To calculate tan(x), we make use of the following tangent ratio

tan(x) = Opposite/Adjacent

From the figure, we have:

Opposite = AD = 4

Adjacent = CD = 3

So, we have:

tan(x) = 4/3

Hence, the value of tan(x) is 4/3

Read more about tangent ratio at:

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Answer:

4/3

Step-by-step explanation:

Answer:

96 in³

Step-by-step explanation:

Volume = 2(BHD) / 2

The 2s cancel out

Volume = 3(8)4

Volume = 96

Answer:

40

Step-by-step explanation:

Angle KPJ is going to have the same measure as Angle DPE. This problem is a bit tricky, but I'll try my best to explain it. A straight angle is basically just a straight line, and it equals 180 degrees. Angle FPG is a straight angle.

To find the measure of Angle KPJ, we first have to find the measure of angle DPE, and the way we're gonna do that is add together the other angles in the straight angle (which would be Angle FPD and Angle EPG) and then subtract that from 180 (measure of a straight angle).

That might have sounded a bit confusing, but that's the best way I could explain it. Now, let's add Angle FPD and Angle EPG.

105 + 35 = 140

Now, let's subtract that from 180.

180 - 140 = 40

We now know that the measure of Angle DPE is 40, and since it's equivalent to Angle KPJ, our answer is 40!

I know that was confusing, but I hope it helped a little bit! Have a lovely day!! :)

Answer:

C

Step-by-step explanation:

the answer is C

( -6 , 1 )

y = -1/2x - 2

if x = -6

y = -1/2(-6) - 2

y = 3 - 2

y = 1

Answer:

3.38

Step-by-step explanation:

primero tienes que restar 2.23 por 0.58 que es igual a 1.65 luego sumas 1.65 por 4.46 porque 2.23 multiplicado por 2 es igual a 4.46 y eso es igual a 6.11 luego tienes que restar 10 por 6.11 que es igual a 3.89

Answer:

The answer to this question is 0.6

Step-by-step explanation:

Answer:

770 x 9/100 = 69.3

the discound amount = 69.3$

the sale price = 770 - 69.3 = 700.7$

Answer:

66.0°

Step-by-step explanation:

The sum of the measures of the interior angles in a triangle is 180°.

Let "x" represent the measure of the third interior angle. We can use this to set up an equation:

84.0° + 30.0° + x = 180°

Add like terms:

114.0° + x = 180°

Subtract 114.0° from both sides:

x = 66°

The question asks for the answer to be in degrees to one decimal place, therefore:

x=66.0°

35%= 56

100%= 56÷35×100

100%= 160

25%= 40

100%= 40÷25×100

100%= 160

60%= 160÷100×60

60%= 96

Answer:

  A.  {60°, 120°, 420°}

  B.  θ = 15π/4; sec(θ) = √2

Step-by-step explanation:

The sine function is periodic with period 360°, and it is symmetrical about the line θ = 90°. The reference angle for the given value of sin(θ) is ...

  θ = arcsin(√3/2) = 60°

The next larger angle with the same sine is (2×90°) -60° = 120°. Any multiple of 360° added to either one of these angles will give an angle with the same sine. A possible set of 3 angles is ...

  {60°, 120°, 420°}

__

One degree is π/180 radians, so the given angle in radians is ...

  θ = 675° = 675(π/180) radians = 15π/4 radians

This angle has the same trig function values as 7π4, a 4th-quadrant angle with a reference angle of π/4, or 45° The secant of that angle is

  sec(45°) = √2

The 4th-quadrant angle has the same sign, so ...

  sec(675°) = sec(15π/4) = √2

Answer:

A common factor is a whole number which is a factor of two or more numbers.

[tex]factors \: of \: 9 = 1 \times 3 \times 3[/tex]

[tex]factors \: of \: 15 = 1 \times 3 \times 5[/tex]

since both of the numbers have only 1 and 3 in common.

therefore ,

Option A is correct.

______________________________________

______________________________________

Additional information

★ The highest common factor (HCF) is the greatest factor that will divide into two or more numbers.

★ The lowest common multiple (LCM) is the smallest multiple that is common to two or more numbers.

hope helpful :D

Answer:

g< 0.0153

Step-by-step explanation:

0.08g +0.2 < 5

0.08g < 5 + 0.2

0.08g < 5.2

g< 0.0153

Answer:

4x+4y

Step-by-step explanation:

Answer:

4x + 4y

Step-by-step explanation:

To do this you need to know that the number (or variable) on the outside of the parenthesis must be multiplied to all of the numbers/variables on the inside of the parenthesis.

So here, you want to multiply x by 4:

4x

Then multiply y by 4:

4y

And because the expression is adding the x and y, it comes out as:

4x + 4y

Answer:

Straight

Step-by-step explanation:

∠RQT is a straight angle.

Answer:

Straight

Step-by-step explanation:

∠RQT is a straight angle with a measure of 180°.

hope this helps!! p.s. i really need brainliest :)

Answer:

In two years erin grew 7 inches

Step-by-step explanation:

42 - 35 = 7

Answer:

atleast 7 inches

Step-by-step explanation:

35 inches - 42 inches = 7 inches

Two years ago, Erin was 35 inches tall.

To ride the roller coaster at a theme park, she must be at least 42 inches tall. So that means she grew atleast 7 inches

Answer:

70

Step-by-step explanation:

Circumference = pi × diameter

219.8 = pi × diameter

219.8/pi = diameter

Diameter = 69.96....

= 70yd

Jack's problems illustrates algebraic expressions

The given parameters are:

The number of questions solved per day is calculated as:

Daily = Days/Problems

So, we have:

Daily = m/5

We have:

Daily = m/5

He solved 15 daily.

So, the equation becomes

m/5 = 15

Multiply both sides by 15

m = 75

Hence, 75 questions were assigned in total

Read more about expressions at:

https://brainly.com/question/723406

Answer:

83.3%

Step-by-step explanation:

Answer:=8/17

Step-by-step explanation:

Answer:

[tex](4x+7)(4x-7)[/tex]

Step by step explanation:

[tex]16x^2 -49\\\\=(4x)^2-7^2\\\\=(4x+7)(4x-7)~~~~~~~~~~;[a^2-b^2 =(a+b)(a-b)][/tex]

Answer:

You are looking for 1/2 OF 2/3

In word problems such as this OF

means to multiply.

(1/2)(2/3) = 2/6 = 1/3

Step-by-step explanation:

Answer:

x = 10^34

Step-by-step explanation:

length × width = area

area/length = width

width = (1.12 × 10^45 ft²)/(7 × 10^11 ft)

width = 1.12/7 × (10^45)/(10^11)   ft

width = 0.16 × 10^34  ft

width = 1.6 × 10^34  ft

width = 1.6 × x  ft

x = 10^34

The value of x is [tex]10^3^2[/tex]  or [tex]\rm x =10^3^2[/tex]

It is given that the area of a rectangular field is  [tex]\rm 1.12\times10^4^5 \ feet^2[/tex]

It is required to find the value of x

It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.

The formula for finding the area of a rectangle is given by:

Area of rectangle = length × width

We have:

Area of rectangle = [tex]\rm 1.12\times10^4^5 \ feet^2[/tex]

The length of the rectangle = [tex]7\times 10^1^1[/tex] feet

The width of the rectangle = [tex]\rm 1.6\times 10x[/tex] feet

After putting the values in the formula, we get:

[tex]\rm 1.12\times10^4^5 =7\times 10^1^1\times\rm 1.6\times 10x[/tex]

[tex]\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\[/tex]

[tex]\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\\\\rm x = 0.1\times 10^3^3[/tex]

[tex]\rm x =10^3^2[/tex]

Thus, the value of x is [tex]10^3^2[/tex]

Learn more about the area here:

https://brainly.com/question/14383947

Answer:

n=12

m=5

Step-by-step explanation:

n= 12 since they are parallel and equal

m+1=6 since they are parallel and equal

Opposite sides are equal in a paralleogram

And

Done!

Answer:

5y(x^2 - 3)

Step-by-step explanation:

Hope this helps :)

Answer:

9 doller

Step-by-step explanation:

we will find 20 percent of 46.69

is=pxw divided by 100

=9.338

or 9 doller

Answer:

length= 1115 inches

width= 545 inches

Step-by-step explanation:

The perimeter of the rectangular rug is the sum of the lengths of all its sides.

Start by defining the variables that we are going to use throughout our working.

Let the length and the width of the rug be L and W inches respectively.

Perimeter= 2(L +W)

Given that the length is 25 inches more than twice the width,

L= 2W +25 -----(1)

3320= 2(2W +25 +W)

Divide both sides by 2:

1660= 2W +W +25

1660= 3W +25

3W= 1660 -25

3W= 1635

Divide both sides by 3:

W= 1635 ÷3

W= 545

Substitute W= 545 into (1):

L= 2(545) +25

L= 1115

Thus, the length and width of the rug is 1115 and 545 inches respectively.

Answer:

28 cars

Explanation:

Let "n" be the cars added in the collection

solve:

[tex]\rightarrow \sf \dfrac{8+n}{20+n} =75\%[/tex]

[tex]\rightarrow \sf {8+n} =(20+n)75\%[/tex]

[tex]\rightarrow \sf {8+n} =15+0.75n[/tex]

[tex]\rightarrow \sf {8-15} =0.75n-n[/tex]

[tex]\rightarrow \sf -7 =0.25n[/tex]

[tex]\rightarrow \sf n = 28[/tex]

Thus, he needs to add 28 cars in the collection to make the collection 75% cars.

Answer:

28 cars

Step-by-step explanation:

Total number of cars and trucks = 20

Cars make up 40% of the collection

⇒ Number of cars = 40% of 20

                              = 0.4 x 20

                              = 8 cars

⇒ Number of trucks = total collection - number of cars

                                  = 20 - 8

                                  = 12 trucks

To calculate how many cars must be added to make the collection 75% cars, set up a ratio equation with x being the number of cars to be added:

(Added cars + existing cars) to total collection = 75%

⇒ x + 8 : x + 8 + 12 = 75 : 100

⇒ x + 8 : x + 20 = 75 : 100

[tex]\sf \implies \dfrac{x+8}{x+20}=\dfrac{75}{100}[/tex]

⇒ 100(x + 8) = 75(x + 20)

⇒ 100x + 800 = 75x + 1500

⇒ 100x -75x = 1500 - 800

⇒ 25x = 700

⇒ x = 28

Therefore he would need to add 28 cars to his collection to make his collection 75% cars.

Check

Number of cars = 8 + 28 = 36

Number of trucks = 12

Total collection = 36 + 12 = 48

Number of cars / total collection = 36/48 = 0.75 = 75%