A researcher wants to compare the performance of three types of pain relievers in volunteers suffering from arthritis. Because people of different ages may suffer arthritis of varying degrees of​ severity, the subjects are split into two​ groups: under 60 and over 60. Subjects in each group are randomly assigned to take one of the medications. Twenty minutes later they rate their levels of pain. Which of the following is true about this​ study?
a.
.
It has two​ factors, medication and age.
B.
It has one factor​ (age) blocked by type of medication.
C.
It uses matched pairs.
D.
It is completely randomized.
E.
It has one factor​ (medication) blocked by age.

Answer:

\(\huge\boxed{\sf x = 85}\)

Step-by-step explanation:

0.2x - 6 = 11

0.2x = 11 + 6

0.2x = 17

x = 17/0.2

\(\rule[225]{225}{2}\)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

hope it helps!

The radian measure of the angle at the center of the circle is approximately 1.6623 radians.

We are given that the radius of the circle is 77.0 cm and the length of the intercepted arc is 128 cm. We need to find the radian measure of the angle at the center of the circle.

To solve this problem, we use the formula relating the angle at the center of a circle, the radius of the circle, and the arc length intercepted by the angle.

The formula is given byθ = s/rwhereθ = angle at the center of the circle in radians s = arc length intercepted by the angle r = radius of the circle Substituting the given values, we getθ = 128/77.0 = 1.6623 radians (rounded to four decimal places)

Therefore, the radian measure of the angle at the center of the circle is approximately 1.6623 radians.

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Answer:

one side is 16, the other is 8\(\sqrt{3}\)

Step-by-step explanation:

30-60-90 angle triangle always give the following sides

1-\(\sqrt{3}\)-2 , which is a-b-c

to label your triangle as such

8= a

other leg =b

hypotenuse = c

so. if a =8, then

c = 8*2 =16

b=8\(\sqrt{3}\)

The length of the rectangular field is 164 yards and the width is 41 yards

From the question,

We are to determine the fields dimensions

From the given information

A rectangular field is four times as long as it is wide

That is

l = 4w -------- (1)

The perimeter of a rectangle is given by

P = 2(l + w)

Where

P is the perimeter

l is the length

and w is the width

From the given information

The perimeter of the field is 410 yards

∴ 2(l + w) = 410 ------ (2)

Substitute equation (1) into equation (2)

2(4w + w) = 410

2(5w) = 410

10w = 410

∴  w = 410 ÷ 10

w = 41 yards

Substitute the value of w into equation (1)

l = 4(41)

l = 164 yards

Hence, the length of the rectangular field is 164 yards and the width is 41 yards.

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Given that the total sales of a company in millions of dollars t months from now is given by S(t) = 41.04785t. We need to find the values of S(6), S(12), and S(42) and interpret the values of S(11) and S(11) - S(0).

a) To find S(6), we substitute t = 6 in the given formula, S(t) = 41.04785t.

Therefore, we have S(6) = 41.04785(6) = 246.2871 million dollars.

Hence, S(6) = 246.2871 million dollars.

b) To find S(12), we substitute t = 12 in the given formula, S(t) = 41.04785t.

Therefore, we have S(12) = 41.04785(12) = 492.5742 million dollars.

Hence, S(12) = 492.5742 million dollars.

c) To find S(42), we substitute t = 42 in the given formula, S(t) = 41.04785t.

Therefore, we have S(42) = 41.04785(42) = 1724.0807 million dollars. Rounded off to two decimal places, S(42) = 1724.08 million dollars.

d) S(11) represents the total sales of the company in 11 months from now and S(11) - S(0) represents the total increase in sales of the company between now and 11 months from now.

Substituting t = 11 in the given formula, S(t) = 41.04785t, we have S(11) = 41.04785(11) = 451.52635 million dollars.

Hence, S(11) = 451.52635 million dollars.

Substituting t = 11 and t = 0 in the given formula, S(t) = 41.04785t, we haveS(11) - S(0) = 41.04785(11) - 41.04785(0) = 451.52635 - 0 = 451.52635 million dollars.

Hence, S(11) - S(0) = 451.52635 million dollars.

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The slope of the graph of the total cost function represents the rate of change of the total cost with respect to the number of golf balls produced each month, the total cost function is given by C(x) = 3390 + 0.48x.

The coefficient of x in the equation represents the slope of the graph. Therefore, the slope of the total cost function is 0.48.

In this case, the marginal cost is equal to the derivative of the cost function with respect to x. Taking the derivative of C(x) = 3390 + 0.48x with respect to x, we get:

C'(x) = 0.48

Therefore, the marginal cost for the product is 0.48.

The cost of each additional ball that is produced in a month is equal to the marginal cost. From the previous calculation, we determined that the marginal cost is 0.48. Therefore, the cost of each additional ball produced in a month is $0.48.

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Answer:

I think it's A if i am wrong pls say so

Step-by-step explanation:

When a trapezoid is rotated 180° on the coordinate plane, the angles of the trapezoid remain the same, but their orientation is reversed. The correct answer is A. 20.

When a shape is rotated 180° on the coordinate plane, the angles of the shape remain the same, but their orientation is reversed.

In this case, angle B is 20° in the original trapezoid. After a 180° rotation, angle B' will be the same as angle B, but in the opposite direction. Therefore, angle B' will also be 20°.

Hence, the correct answer is A. 20°.

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Answer: C 70%

Step-by-step explanation:

First you need to add up how many students are participating in the study. 4+6+12+8+4=34. There are 24 people who own more than 5 video games. This means that it is 24/34. This equals about 70%

The solution involves calculating the mass of aggregates after extraction, filter after extraction, and filter after extraction, and calculating the weight percent of the aggregates in the solvent. The volume of the solvent is 24 ml.

Given information: Mass of dish 1631.5 g, mass of dish and mix 1822 g, mass of dish and agg. after extraction 1791g, mass of clean filter 25 g, mass of filter after extraction 30 g, mass of agg. in 150 ml solvent 1.2g, and Ac% 5%.We have to find the volume of the solvent. Here is the step by step solution for the given question:

Step 1: Calculate the mass of the aggregates after extraction:M1 = mass of dish + mass of mix - mass of dish and agg. after extractionM1 = 1631.5 g + 1822 g - 1791 gM1 = 1662.5 g

Therefore, the mass of the aggregates after extraction is 1662.5 g.

Step 2: Calculate the mass of the aggregates:M2 = mass of filter after extraction - mass of clean filterM2 = 30 g - 25 gM2 = 5 g

Therefore, the mass of the aggregates is 5 g.

Step 3: Calculate the weight percent of the aggregates in the solvent: Ac% = (mass of agg. in 150 ml solvent / volume of solvent) x 1005% = (1.2 g / V) x 100V = (1.2 g / 5%)V = 24 ml

Therefore, the volume of the solvent is 24 ml.

Hence, the volume of the solvent is 24 ml.

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Answer:

Step-by-step explanation:

3x^2 - 4x - 2 = 0

4/6 + (sqrt(16 - 4(3)(-2)))/6

2/3 + (sqrt(16+24))/6

2/3 + (sqrt(40))/6

2/3 + 2(sqrt(10)/6

2/3 + (sqrt(10))/3

Answer:

Step-by-step explanation:

3x² - 4x - 2 = 0

Using the quadratic formula

That's

From the question

a = 3 , b = - 4 , c = - 2

So we have

We have the final answer as

Hope this helps you

Answer:

105 sq cm

Step-by-step explanation:

The bottom rectangle is 6 x 15 = 90 sq cm

The triangle at the top has a length of 15 - 9 = 6 cm and a height of 11 - 6 = 5 cm.

A triangle is 1/2bh so 1/2 x 6 x 5 = 15 sq cm

Add the areas together

From the information given in the statement you know that:

*a is the amount of money Thomas needs to save

*Thomas needs to save more than $ 50.45.

Then, the inequality that models the amount Thomas needs to save is

Answer:

60 dollars

Step-by-step explanation:

well it's simple

Answer:

($75)(0.20)=     then add that answer to 75

Step-by-step explanation:

The interesting 5-digit number is 60000. there is an interesting 5 digit number n with the property that with a 1 after it, is 3 times as large as it is with a 1 before it.

Let's call the 5-digit number n. We know that if we add a 1 to the end of n, we get a 6-digit number that is three times as large as n with a 1 before it. In other words, we have:

10n + 1 = 3(100n + 1)

Expanding the right side of the equation, we get:

10n + 1 = 300n + 3

Subtracting 10n from both sides, we get:

1 = 290n + 3

Subtracting 3 from both sides, we get:

-2 = 290n

Dividing both sides by 290, we get:

n = -1/145

However, we are looking for a 5-digit number, so this solution doesn't make sense. We made a mistake by assuming that the number with a 1 before it is a 4-digit number, which is not necessarily true. Let's try again, but this time we'll call the number with a 1 before it "m" and assume that it has the same number of digits as n. Then we have:

10m + n = 3(10n + 1)

Expanding the right side of the equation, we get:

10m + n = 30n + 3

Subtracting n from both sides, we get:

10m = 29n + 3

We know that n is a 5-digit number, so it must be between 10000 and 99999. We can use this to narrow down the possibilities for m. If n is less than 34482 (the largest integer less than 100000/29), then the left side of the equation is less than 344820, which means that m must be less than 34482. On the other hand, if n is greater than or equal to 34482, then the left side of the equation is greater than or equal to 344820, which means that m must be greater than or equal to 34482. Therefore, we have:

34482 ≤ m < n

Let's try some values of n within this range. If n = 40000, then we have:

10m + 40000 = 120001

Subtracting 40000 from both sides, we get:

10m = 80001

This doesn't work, since m is not an integer. Let's try n = 50000:

10m + 50000 = 150001

Subtracting 50000 from both sides, we get:

10m = 100001

This also doesn't work, since m is not an integer. Let's try n = 60000:

10m + 60000 = 180001

Subtracting 60000 from both sides, we get:

10m = 120001

This works! We have found that n = 60000 and m = 12000. Therefore, the interesting 5-digit number is 60000.

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Based on the balance sheet of Company MSK, we can find the unknown amount of Net Income (loss) to be $18,843.

The Assets as at 2021 should be equal to the sum of liabilities and equity.

The Equity is:

= Issued stocks + Net income - Dividends

The missing figure is therefore:

35,564 = 15,721 + 1,400 + Net Income - 400

Net Income = 35,564 + 400 - 15,721 - 1,400

= $18,843

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Answer:

Step-by-step explanation:

(⅚ pound)/(3 people) = (⅚÷3 pound)/person = 5/18 pound per person.

Answer:

the last answer

no solution

i just did this in my math class today

Step-by-step explanation:

Answer: (A) Associative property.  (B) Identity Property

(C) Distributive Property.  (D) Commutative Property.

Hope it Helps (:

Alex has five cups of strawberries and wants to use 1 3/4 cups of strawberries for a fruit salad and 3 1/2 cups for jam. Alex has enough strawberries to make both recipes.

To check if Alex has enough strawberries, we add the amount of strawberries needed for the fruit salad (1 3/4 cups) and the amount needed for the jam (3 1/2 cups)

1 3/4 cups + 3 1/5 cups

= 1 + 3/4 + 3 + 1/5

Multiplying 3/4 with 5/5 and 1/5 with 4/4 to make denominator equal

= 1 + 15/20 + 3 + 4/20

= 4 + 19/20

= 4 19/20 cups

4 19/20 is less than 5 cups. So Alex has enough strawberries for both recipes.

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Answer:

AB || CE, so we have triangle DEO, two of whose angles are 100° and 26° (from point D, draw DE such that CD + DE = CE intersects BO). The third angle of this triangle measures 54°, so

x = 180° - 54° = 126°.

Answer:

17 chairs in 30 minutes

Step-by-step explanation:

272/8 = 34

34/2 = 17

17 there ya go

Answer:

Step-by-step explanation:Method 2 of 2: Solving for Slope Get a line of which you want to know the slope. Make sure that the line is straight. ... Pick any two coordinates that the line goes through. Coordinates are the x and y points written as ( x, y ). Pick which point's coordinates are dominant in your equation. ... Set up the equation using the y-coordinates on top and the x-coordinates on bottom. More items.

Answer:

The slope is 1/3

Answer: the answer is 55 degrees

Step-by-step explanation:

Answer:

$16.50

Step-by-step explanation:

$27.50/5=5.5

5.5*3=16.5

Answer:

What we can do is calculating what one bag cost. If we know that 5 cost 27.50 dollars, to know how much does one cost we only divide:

27.50/5 = 5.50 dollars

Now, we know how much does one bag cost, so we multiply it by three:

5.50 * 3 = 16.50

Now, we know 3 bags cost 16.5 dollars

Answer:

4 and a half i think

To orthogonally diagonalize the matrix A, we will follow these steps:
1. Find the eigenvalues of matrix A.
2. Find the eigenvectors corresponding to each eigenvalue.
3. Normalize the eigenvectors to form an orthogonal basis.
4. Construct the orthogonal matrix Q and the diagonal matrix D.

To orthogonally diagonalize the matrix A, we need to find the eigenvalues and eigenvectors of A.

A = [[3, -1], [-1, 3]]

The characteristic polynomial of A is:

det(A - λI) = det([[3-λ, -1], [-1, 3-λ]]) = (3-λ)² - 1 = λ² - 6λ + 8 = (λ-2)(λ-4)

So the eigenvalues are λ₁ = 2 and λ₂ = 4.

To find the eigenvectors, we need to solve the system of equations:

(A - λ₁I)x = 0 and (A - λ₂I)x = 0

For λ₁ = 2, we have:

(A - 2I)x = [[1, -1], [-1, 1]]x = 0

This system has two linearly independent solutions:

v₁ = [1, 1] and v₂ = [-1, 1]

For λ₂ = 4, we have:

(A - 4I)x = [[-1, -1], [-1, -1]]x = 0

This system has one linearly independent solution:

v₃ = [1, -1]

To orthogonalize the eigenvectors, we need to normalize them and put them as columns of an orthogonal matrix Q.

Q = [[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]]

The diagonal matrix D has the eigenvalues on the diagonal:

D = [[2, 0], [0, 4]]

Finally, we can check that QTAQ = D:

QTAQ = [[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]]T[[3, -1], [-1, 3]][[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]] = [[2, 0, 0], [0, 4, 0], [0, 0, 4]] = D

Therefore, matrix A is orthogonally diagonalized by Q and D.

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Answer:

she

Step-by-step explanation:

bc c

Answer:

180

Step-by-step explanation:

i did the math hope this helps