A study is testing the effectiveness of a new allergy medication. Sixty people who reported they have allergies volunteered to be part of the study and were randomly assigned to one of two groups, as shown in the design web.

Which of the following accurately describes the benefit of comparison in the experiment shown in the design web?

A. The level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect.
B. The overall level of allergic symptoms can be used to determine if the new allergy medication had a significant effect.
C. The level of allergic symptoms in the group who received the medication can be used to determine if the medication had a significant effect.
D. The level of allergic symptoms in both groups cannot be compared to determine if the medication had a significant effect because one group only received a placebo.

Answer:

1,2, and 4

Step-by-step explanation:

vertical angles theorem, which says that the vertical angles that are formed when two lines intersect are congruent.

All the three locations has been checked below.

Using Pythagoras theorem,

12² = 8² + x²

144 - 64 = x²

x= √80

x=8.9

Now, using Trigonometry

tan F = P/B

tan F= 8/8.9

and, sin F = P/H

      sin F= 8/12 = 2/3

and, cos F = B/H

        cos F= 12/8.9

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The cost of the utility pole with a radius of 17.8 cm and a height of 700 cm is; $3774.4

From the information given, we have the following parameters;

Density = 5.4 g/cm³

Mass = Ikg = 0.71 kg

Cost per mass = $0. 51

Let's determine the volume of this cylinder:

Volume = mass / density

Substitute the values

Volume = 0.71 /5.4

Volume = 0.131 cm³

Thus, 0.131  cm³ costs $0.71

For the utility pole;

Volume = 2 πr²h

Where:

r is 17.8cm

height is 700cm

Volume = 3. 142 × 17.8 × 17.8 × 700

Volume = 696414.32 cm³

If  0.131  cm³ costs $0.71

Then  696414.32  cm³ will cost:

= 696414.32   × 0.71/ 0.131  

= 3774.4

Thus, the cost of a utility pole is  $3774.4

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Answer:

D

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

Yes because the angles are both 120 degree's

(I'm not sure if this is right but btw I love your pfp :))

Answer:

Step-by-step explanation:

Let P(t) be the fox population t years after 2000. We know that the population has a continuous growth rate of 4% per year, which means that the population increases by a factor of 1.04 each year. Therefore, we can model the population as:

P(t) = 21400 * 1.04^t

Here, we start with the population in the year 2000 (21400) and multiply it by 1.04 raised to the power of the number of years after 2000 (t).

For example, if we want to find the population in the year 2015 (15 years after 2000), we can plug t = 15 into the equation:

P(15) = 21400 * 1.04^15

= 21400 * 1.618

= 34694.8

Therefore, we can expect the fox population to be approximately 34,695 in the year 2015.

The number of children ticket sold is 90 while the number of adult ticket sold is 200.

Math land theatre charges $5.00 for children's tickets and $9.00 for adult tickets. One night the theatre sold 290 tickets and took in $2250.

Therefore, let's find the number of each type of ticket sold as follows:

Hence,

Let

Therefore, using equation,

c + a = 290

5c + 9a = 2250

Multiply equation(i) by 5

5c + 5a = 1450

5c + 9a = 2250

subtract the equation

4a = 800

divide both sides by 4

a = 800 / 4

a = 200

Therefore, let's find c

c = 290 - 200

c = 90

Hence,

number of children's ticket = 90

number of adult tickets = 200

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The number of each type of ad that the department can run each month are:

TV Ads = 32

Radio Ads = 12

News Ads =  20

x = number of tv ads

y = number of radio ads

z = number of news ads

Two formulas are indicated.

x + y + z = 64

1000x + 200y + 600z = 46400

they want as many tv ads as radio and news ads combined.

equation for that is x = y + z

since x = y + z, replace x with y + z in both equations to get;

y + z + y + z = 64

1000 * (y + z) + 200 * y + 600 * z = 46400

combine like terms and simplify to get:

2y + 2z = 64

1000y + 1000z + 200y + 600z = 46400

combine like terms again to get:

2y + 2z = 64

1200y + 1600z = 46400

Solving simultaneously gives:

y = 12

z = 20

Thus:

x = 12 + 20

x = 32

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Answer: THE PRODUCT

Step-by-step explanation:

The associative property of multiplication says that the product of three or more numbers remains the same no mater how the numbers are grouped.

example (3x5x2) is the same as ( 5x2x3) both = 30

The hypothesis is

Scientific investigations employ a crucial concept known as the null hypothesis, which asserts that there is no apparent correlation between analyzed data or variables.

The null tells us that the standard deviation is equal to 2.6

Concurrently, an alternate theory sets forth that an effect does indeed exist within the population being investigated. This differentiation allows researchers to draw meaningful conclusions from carefully collected empirical evidence.

H1: SD < 2.6

There is insufficient data to solve for the test stat

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The missing number in the ratios of numbers are 16:10     8:20 and 0:30

Ratios are quantitative relationships between two numbers that describe how many times one value can contain another

the given parameters are

Forks         16          8              ----

Spoons       10         ---            30

The numbers are written in ascending order of magnitude

Using AP,

for forks: a = 16, 2nd term = 8

common difference = 8-16 - -8

For spoons a = 10, 3rd term = a + 2d = 30

30 = 10 + 2d

30 -10 = 2d

d= 20/2 = 10

Therefore the 2nd term = 10+10=20

The table reappears as follows

Forks         16          8             0

Spoons       10        20          30

Therefore the equivalent ratios are 16:10     8:20 and 0:30

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The composition of f. g derived from the equations in the attached image is:  [tex]\frac{1}{10}(2x + 1)[/tex] and f+g as  √(4x-1))/(5x²+3)

Composition is a mathematical operation that combines two functions to form a new function. From our question, we are given two functions f(x) and g(x).

One of their composition can be represented by f(g(x)).f(g(x)) means function out of g(x) will serve as input x for function f(x). In a more simpler words, f(g(x)) is the function obtained by taking the output of g(x) and using it as the input for f(x).

Using the question given as an example,

For f.g:

Firstly, we have to compute the composition of f and g.

This can be expressed as:

f(g(x))f(g(x)) = f(√(4x-1))= 1/[5(√(4x-1))² + 3]= 1/[5(4x-1) + 3]

= 1/(20x + 10)

= [tex]\frac{1}{10}(2x + 1)[/tex]

For f+g:

To find f+g, we will just add the two functions together as below:

f+g = 1/(5x²+3) + √(4x-1)= (√(4x-1) + (5x²+3)

= √(4x-1))/(5x²+3)

So the answers are;

f.g: = [tex]\frac{1}{10}(2x + 1)[/tex]

f+g =  √(4x-1))/(5x²+3)

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The possible outfits that Casey can make is 30 and  this is shown in the image that is attached.

The tree diagram is known to be one that shows the hierarchical organization of tasks and subtasks that must be done to achieve a goal. The branching diagram start with a single element that divides into two or more, each of which further divides into two or more, and so forth.

Based on the question, Casey has:

5 shirts

3 skirts

2 blazers

Therefore, to make a tree diagram of any possible outfits that Casey can make.​, there are a total of:

5 x 3 x 2

= 30

So, the possible outfits that Casey can make is 30.

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The value of the expression is 0.017455065

Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations.

The given expression is (Tan π/18 + Tan π/9) ÷ (1 - Tan π/1 Tanπ/9)

This gives [Tan (π/18 * π/9) ÷ 1/(Tan(π/18 * π/9)

Simplify further to have

Tanπ²/162 * 162/π²)

This gives Tan1 =  0.017455065

This implies that  (Tan π/18 + Tan π/9) ÷ (1 - Tan π/1 Tanπ/9) = 0.017455065

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The probability that the sum exceeds 5 is P ( A ) = 0.6111

Given data ,

To find the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice, we need to count the number of outcomes where the sum of the two numbers is greater than 5, and then divide that by the total number of equally-likely outcomes.

The outcomes where the sum exceeds 5 are:

(2, 4), (2, 5), (2, 6)

(3, 3), (3, 4), (3, 5), (3, 6)

(4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

There are 22 outcomes where the sum exceeds 5 out of a total of 36 equally-likely outcomes.

So, the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice is:

P(sum > 5) = 22 / 36 ≈ 0.6111 or approximately 61.11 %

Hence , the probability is P ( A ) = 0.6111

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The complete question is attached below :

A single die is rolled twice. The 36​ equally-likely outcomes are shown to the right.Find the probability of getting two numbers whose sum exceeds 5

The domain and the range of the function are given as follows:

The function in this problem is given as follows:

y = 600 - 75x.

The input variable x represents the number of months, which cannot be negative, hence the lower bound of the domain is given as follows:

x = 0.

Meaning that the upper bound of the range is of y = 600.

The balance remaining cannot be negative, hence:

The problem asks for the domain and the range of the function.

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The height of the can in inches is 44.68 inches

From the question, we have the following parameters that can be used in our computation:

Volume = 8 cubic inches

Radius = 3/4 inches

The volume of a cylinder is calculated as

V = πr²h

substitute the known values in the above equation, so, we have the following representation

π * (3/4)²h = 8

So, we have

h = 8π/[(3/4)²]

Evaluate

h = 44.68

Hence, the height of the can in inches is 44.68 inches

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Answer:

$124 per week

Step-by-step explanation:

To fins how much she needs to save each week, divide the total cost by the amount of time. In this problem, divide $2,976 by 24 weeks to find the amount she needs to save.

$2976/24=$124 per week

The difference between the median test score in the morning and the afternoon is 12.5

From the question, we are to determine the difference between the median test score in the morning and the afternoon.

From the given diagram, we have box plots.

From the given box plots, we will determine the median test score in the morning and the median test score in the afternoon.

The median test score in the morning = 87.5

The median test score in the afternoon = 75

Thus,

The difference between the median test score in the morning and the afternoon =

Median test score in the morning - Median test score in the afternoon

The difference between the median test score in the morning and the afternoon = 87.5 - 75

The difference between the median test score in the morning and the afternoon = 12.5

Hence,

The difference is 12.5

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The measures of center or variability are greater than 5 degrees

This Week's Mean: (4 + 13 + 6 + 9 + 8) / 5 = 40 / 5 = 8

Last Week's Mean: (10 + 9 + 5 + 6 + 5) / 5 = 35 / 5 = 7

Then the ranges

This Week's Range: (13 - 4) = 9

Last Week's Range: (10 - 5) = 5

The MAD for both weeks

|(4 - 8)| + |(13 - 8)| + |(6 - 8)| + |(9 - 8)| + |(8 - 8)|

= 4 + 5 + 2 + 1 + 0 = 12

This Week's MAD: 12 / 5 = 2.4

|(10 - 7)| + |(9 - 7)| + |(5 - 7)| + |(6 - 7)| + |(5 - 7)| = 3 + 2 + 2 + 1 + 2 = 10

Last Week's MAD: 10 / 5 = 2

Hence the measures of center or variability are greater than 5 degrees are:

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The perimeter of the square with side of 5 cm is 20 cm.

The perimeter of the square with side length of 15 cm is 60 cm.

The area of each square is calculated as follows;

Let the dimension of first square = x

Let the dimension of second square = y

x² + y² = 250 ---- (1)

4(x + y) = 80 ----- (2)

x + y = 80/4

x + y = 20

x = 20 - y

Substitute x in equation (1)

(20 - y)² + y² = 250

400 - 40y + y² + y² = 250

2y² - 40y + 150 = 0

y² - 20y + 75 = 0

solve for y, using formula method;

y = 15 or 5

Solve for x;

x = 20 -15 = 5 or

x = 20 - 5 = 15

The perimeter of first = 4x = 4 x 5 = 20 cm

The perimeter of the second = 4y = 4 x 15 = 60 cm

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Answer:

22

Step-by-step explanation:

length is given by (3--1=4)

width is given by (2--5=7)

perimeter is given by:

P=2l + 2w

P=2(4)+2(7)

P=8+14

P=22

The amount of flour that will be needed for 38 cakes is 912 grams therefore Johan does not have enough amount of flour

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

360 grams is needed for 15 small cakes

therefore for 1 small cake, 369/15 = 24grams will be needed

therefore for 38 small cakes = 38× 24 = 912 grams of flour will be needed.

Johan has 0.85 kg of flours which is equivalent to 0.85 × 1000grams = 850 grams of flour.

Since 912 grams will be needed for 38 small cakes , it shows that Johan does not have enough amount of flour for 38 small cakes.

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The composite numbers between 10 and 20 are: 12, 14, 15, 16 and 18 which have more than 2 factors.

To find a composite number, we find the factors of the given number. The best way to determine a composite number is to do a divisibility test. The divisibility test helps us determine if the number is prime or composite. Divisibility means that one number is divided completely (without remainder) by another number.

The solutions to y = –8x for x = 2, 4, and 8 are (2, –16), (4, –32), (8, –64), hence, option D is correct.

We are given the equation y = -8x and asked to find the solutions for x = 2, 4, and 8. To find the solutions, we substitute the given values of x into the given linear equation and solve for y.

For x = 2, we have,

y = -8x

y = -8(2)

y = -16

Therefore, the solution for x = 2 is (2, -16).

For x = 4, we have,

y = -8x

y = -8(4)

y = -32

Therefore, the solution for x = 4 is (4, -32).

For x = 8, we have,

y = -8x

y = -8(8)

y = -64

Therefore, the solution for x = 8 is (8, -64).

Putting these solutions together, we get {(2,-16), (4,-32), (8,-64)}. Hence, the correct answer is option D.

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1. To find the probability that the length of a single trout taken at random from the pond is between 7 and 11 inches long, we need to use the normalcdf command with the given parameters. The formula for normalcdf is normalcdf(lower bound, upper bound, mean, standard deviation).

Thus, normalcdf(7, 11, 10.5, 1.2) = 0.6827.

Therefore, the probability that the length of a single trout taken at random from the pond is between 7 and 11 inches long is 0.6827.

2. To find the probability that the mean length of five trout taken at random is between 7 and 11 inches, we need to use the central limit theorem, which states that the sample mean will also follow a normal distribution with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of the sample size (i.e., sigma/sqrt(n)).

Thus, we first need to find the standard deviation of the sample mean, which is sigma/sqrt(n) = 1.2/sqrt(5) = 0.5367.

Then, we can use the normalcdf command with the given parameters. The formula for normalcdf is normalcdf(lower bound, upper bound, mean, standard deviation).

Thus, normalcdf(7, 11, 10.5, 0.5367) = 0.9468.

Therefore, the probability that the mean length of five trout taken at random is between 7 and 11 inches is 0.9468.

The probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.

The probability that the student does not own a trampoline is equal to the number of students who do not own a trampoline divided by the total number of students in the class.

The number of students who do not own a trampoline is equal to the total number of students in the class minus the number of students who own a trampoline:

24 - 14 = 10

Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is:

P(not owning a trampoline) = 10/24

Simplifying the fraction,

P(not owning a trampoline) = 5/12

Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.

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The angles formed by the chords and secants of the circle are;

28) m[tex]\widehat{AB}[/tex] = 60°

29) m[tex]\widehat{GH}[/tex] = 52°

30) m[tex]\widehat{DH}[/tex] = 90°

31) m∠1 = 90°

32) m∠2 = 58°

33) m∠3 = 32°

34) m∠5 = 49°

35) m∠6 = 90°

36) m∠7 = 99°

37) m∠8 = 96°

38) m∠9 = 116°

A chord is a segment that joins two distinct points on the circumference of a circle.

The angles formed by the arcs in the circle indicates that we get;

28) m[tex]\widehat{AB}[/tex] = 360° - 56° - 18° - 42° - 180° = 60°

29) m[tex]\widehat{GH}[/tex] = 90° - 38° = 52°

30) m[tex]\widehat{DH}[/tex] = 90°

31) m∠1 = 180°/2 = 90°

32) m∠2 = (56° + 18° + 42°)/2 = 58°

33) m∠3 = 90° - 58° = 32°

34) m∠5 = (1/2) × (38° + 18° + 42°) = 49° (Angles of intersecting chords theorem)

35) m∠6 = 90° (Supplementary angle to a right angle is 90 degrees angle is )

36) m∠7 = 180° - 32° - 49° = 99°

37) m∠8 = (1/2) × (52° + 38° + 60° + 42°) = 96°

38) m∠9 = m∠3 + (180° - m∠8) (External angles theorem and linear pair angles)

m∠9 = 32° + (180° - 96°) = 116°

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