A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females​ 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ (a) through​ (c) below.

Answer:

Length of Carla's living room is 20 feet

Step-by-step explanation:

The perimeter of a rectangle is 2(L + W)
In the case of both dining and living rooms, we are given the widths as dining room width = 18, living room width = 12 and asked to calculate living room length from the information given

Let x be the length of the dining room and y the length of the living room

Perimeter of dining room = 2(18 + x)

Perimeter of living room = 2(12 + y)

Since these are equal
2(18 + x) = 2(12 + y)

=> 18 + x = 12 + y

Subtract x from both sides:
18 = 12 + y - x

Subtract 12 from both sides:
18 - 12 = y - x

Simplifying and rearranging terms we get

- x + y = 6  [1]

We are also given that:
The length of her dining room is 1 foot less than 3/4 the length of her living room.

This mathematically translates to:
[tex]x = \dfrac{3}{4}y - 1[/tex]

which can be re-written as

[tex]x - \dfrac{3}{4} = -1 \; \cdots[2][/tex]

So the two equations are

[tex]- x + y = 6 \;\cdots [1][/tex]

[tex]x - \dfrac{3}{4}y = - 1 \; \cdots [2][/tex]

Notice that the coefficients of x are the same(1) but with opposite signs

Add [1] and [2]

[tex](-x + y) +(x - \dfrac{3}{4}y) = 6 - 1\\\\-x + x + y - \dfrac{3}{4}y = 5\\\\\dfrac{1}{4}y = 5\\\\y = 20\\\\[/tex]

So the length of the living room is 20 feet

(If you wanted to find the length of the dining room, substitute 20 into equation 1 to get -x + 20 = 6 which will give x = 14 and is the length of the dining room)

Answer:sqrt 38

Step-by-step explanation:32+8-2 is 38

Answer:

A reflection is a congruence transformation because it maintains the original shape and size of the pre-image. A reflection is a figure flipped over a line of reflection. A common example is a mirror but a reflection can also be shown in water, like with a picture of a lake, the line of reflection would be the divide between the water and the shore.

The graph of an absolute value is always equal to or greater than zero and can never be negative.

We define the absolute value function f: R→R as:

f(x) = |x|

The absolute value function is also named the modulus function.

An alternative form to express the function is

|x| = -x if x ≤ 0 and x if x ≥ 0

The absolute value function is defined for all real numbers.

For x≥0, f(x) returns the same value, that is, x.

For x<0, f(x) returns the negative of the value of x.

So, we arrive at the conclusion that the domain and range of absolute value function are R and [0, ∞).

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If the interior angle of a regular polygon is 108°.The polygon has five (5) sides.

Method 1: Each exterior angle of a regular polygon is equal to 180-108°, or 72°, if each internal angle is 108°.Regardless of the number of sides, any figure's outer angles add up to 360 degrees.

The figure has 360/72 or 5 sides since each outer angle is 72 degrees. Therefore, the polygon is a standard pentagon. Answer.

Method 2: Using n isosceles triangles, a regular polygon with n sides is created. 54° is the basis angle, or 108/2. Each vertical angle is equal to 2*36°, or 72°, which is the semi-vertical angle of 90-54°. 360/72 equals 5, the number of isosceles triangles. Therefore, the polygon is a standard pentagon.

Method 3: [n-2]*180 or 108n, which is the sum of the internal angles of a regular polygon.

[n-2]*5=3n, or

5n-10 = 3n, or

5n-3n = 2n = 10, or

n = 5.

The polygon is a regular pentagon as a result.

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Answer:

{-1, 2, 47}

Choice B

Step-by-step explanation:

Function is g(x) = x² - 2

Domain is the possible set of x values and range is the set of function values for that domain

Here Domain = {- 2, - 1, 7}. This means these are values for which the function value g(x) exists

(Note this is not the entire domain, only a subset of the domain)

At x = - 2, g(x) = (-2)² - 2 = 4 - 2 = 2

At x = - 1, g(x) = (-1)² -2 = 1 -2 = -1

At x = 7, g(x) = (7)² -2 = 49 - 2 = 47

These are the corresponding range values for the given domain

Both domain and range sets are expressed from lowest to highest so we get range of g(x) as

{-1, 2, 47}

Choice B

Answer:

8/10 = 4/5

6/12 = 1/2

10/20 = 1/2

4/5= 4/5

3/12= 1/4

13/21= 2/3

9/24 = 3/8

7/14 = 1/2

15/30 = 1/2

12/16 = 3/4

Step-by-step explanation

Hope this helps

Three-fifths is equivalent to 6/10.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let the number of fifth be = x

So,

(1/5)x = 6/10

Now,

Solve for x.

(1/5)x = 6/10

x = (6 x 5) / 10

x = 30/10

x = 3

Thus,

There are three-fifths to make 6/10.

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The likelihood that the first question will be true is equally likely and unlikely.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,

The teacher gave a true and false quiz where P(true) = 0.5 for each question.
From the above-given probability, it can be interpreted that the likelihood of giving a true answer is 50% and this is the same for the given wrong answer. So the likelihood that the first question will be true is equally likely and unlikely.

Thus, the likelihood that the first question will be true is equally likely and unlikely

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Answer:

The likelihood that the first question will be true is equally likely and unlikely.

Step-by-step explanation:

Answer:

The time t, in seconds, it takes a runner to finish a race depends on the distance in miles m of the race.

Step-by-step explanation:

Hope this helps !

Answer:

x = 2

y = 5

Step-by-step explanation:

A system of equations is a set of two or more equations that contain multiple variables. To solve a system of equations, you can use different methods such as substitution, elimination or graphing.

The given system of equations is:

y = 2x + 1

y = x + 3

We are trying to find the x and y values that make both equations true at the same time.

One way to solve this system is to use the substitution method, by replacing one of the variables in one equation with the other equation.

Let's replace y from the second equation with the first equation:

x + 3 = 2x + 1

Subtract x from both sides:

3 = x + 1

Subtract 1 from both sides:

2 = x

Now that we have the value of x, we can substitute it back into either one of the original equations to find the value of y.

Let's substitute it back into the first equation:

y = 2(2) + 1

y = 5

So the solution to this system of equations is x = 2 and y = 5. It means that both equations are true when x = 2 and y = 5

You can also check your solution by substituting x and y back into the equations and see if both of them are true.

They combine their money to buy as much ice cream as they can afford. If . each pair of socks costs $4.50, what is the maximum number of pairs of socks .

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It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.

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if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

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30 1/2 cups soup divided by 3: 10 1/6 cups or 10 1/2 cups per container.

What is interpretation ?

Interpretation is the process of understanding and explaining the meaning of something, such as a text, a piece of artwork, or a scientific data. In the context of mathematics and problem solving, interpretation refers to understanding the meaning of a mathematical expression or equation in the context of the problem or situation being described.

In this context, "30 and 1 half cups of oup" refers to the amount of soup that Avery has in the large pot, and "divided by 3" refers to the number of smaller containers Avery plans to divide the soup into. There are two different ways to interpret 30 and 1 half divided by 3 in this context ,

Avery will divide the 30 and 1 half cups of soup equally among 3 smaller containers. This means that each container will hold (30 + 1/2) / 3 = 10 and 1/6 cups of soup.

Avery will pour out 10 and 1/2 cups of soup from the large pot into each of the 3 smaller containers. This means that after Avery has poured out all the soup, the large pot will be empty and the 3 smaller containers will each contain 10 and 1/2 cups of soup.

30 1/2 cups soup divided by 3: 10 1/6 cups or 10 1/2 cups per container.

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Avery will divide the 30 and 1 half cups of soup equally among 3 smaller containers. This means that each container will hold (30 + 1/2) / 3 = 10 and 1/6 cups of soup.

Avery will pour out 10 and 1/2 cups of soup from the large pot into each of the 3 smaller containers. This means that after Avery has poured out all the soup, the large pot will be empty and the 3 smaller containers will each contain 10 and 1/2 cups of soup.

Answer:

2 is multiplied by -4 and then a4 is gone to the bottom

Answer:

4

Step-by-step explanation:

To make the exponent -4 put it over 1.

[tex]\frac{1}{(2a)^{4} }[/tex]

[tex]\frac{1}{2^{4}a^{4} }[/tex]

[tex]\frac{1}{2x2x2x2xaxaxaxa}[/tex]

[tex]\frac{1}{16a^{4} }[/tex]

Como la cuerda está formando un ángulo de 30 grados con la horizontal, la componente de la fuerza en la dirección de la cuerda se calcula utilizando el coseno del ángulo: 86.6 N.

Para calcular el valor de la normal y la fuerza de rozamiento, primero debemos calcular la componente de la fuerza de gravedad que actúa en dirección perpendicular a la superficie de apoyo. La componente de la gravedad en dirección perpendicular se calcula utilizando el seno del ángulo formado por la cuerda con la horizontal (30º):

F_normal = F_grav * sen(30º)

Donde F_grav es la fuerza de gravedad del cuerpo, que se calcula como:

F_grav = m * g

Donde m es la masa del cuerpo (40 kg) y g es la aceleración debida a la gravedad (9.8 m/s²)

Por lo tanto,

F_normal = (40 kg) * (9.8 m/s²) * sen(30º) = 392 N

La fuerza de rozamiento se calcula utilizando la fórmula:

F_fric = μ * F_normal

Donde μ es la coeficiente de rozamiento estático entre el cuerpo y la superficie de apoyo. Como no se especifica el valor del coeficiente de rozamiento, no se puede calcular la fuerza de rozamiento.

La tensión en la cuerda es igual a la fuerza neta en la dirección de la cuerda. Como la cuerda está formando un ángulo de 30 grados con la horizontal, la componente de la fuerza en la dirección de la cuerda se calcula utilizando el coseno del ángulo:

T = F * cos(30º) = 100 N * cos(30º) = 86.6 N

(Los valores de las respuestas están en notación científica)

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The reason that supports the property in statement 8 is substitution. The correct option is C.

Substitution is the process of replacing variables (letters) in an algebraic expression with numerical values. The total value of the expression can then be calculated.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The reason that supports the property in statement 8 is substitution. Because in the expression 6x - 7 the value of the variable x is substituted to get the value of the angle.

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Step-by-step explanation:

UW must be equal to UV. the distance from the same point of origin of 2 tangents to their touching points in the circle must be the same.

so, UV = UW = 3

XV connects the tangential touching point with the center of the circle, and must therefore be perpendicular (90°) to the tangent UV.

we have therefore a right-angled triangle UVX and can use Pythagoras to find the Hypotenuse UX :

UX² = UV² + XV² = 3² + 1.6² = 9 + 2.56 = 11.56

UX = sqrt(11.56) = 3.4

Because they do not support survival and reproduction, undesirable features are chosen against and inherited less frequently over time.

By examining the connection between natural selection and evolution, Darwin's theory of evolution is examined. Controlling natural selection in an interactive population will help you achieve this. Each species displays.

For instance, while some beetles are brown, others are green. Not every member of a population will live long enough to reproduce. Those that do pass on their traits to their progeny.

Evolution and Natural Selection A species' members do not all resemble one another. Each species displays. For instance, while some beetles are brown, others are green. Not every member of a population will live long enough to reproduce. Those that do pass on their traits to their progeny.

Because they do not support survival and reproduction, undesirable features are chosen against and inherited less frequently over time.

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The probability that a pupil would excel in math's or English = 0.691

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages range from 0% to 100% can be used to describe probabilities.

120 students are enrolled in total. Let A represent the scenario in which a student receives a mathematics award, and B represent the scenario in which a student receives an English award. The odds of these events are as follows:

48 won awards for mathematics

78 won awards for English.

14 students  won awards for mathematics and English.

P(A) = 48/120

P(B) = 78/120

P(A ∩ B) = 14/120

Due to the fact that 14 students shared the honors from both events, the following equation should be written for overlapping sets:

P(A or B ) =   P(A) + P(B)  -  P(A ∩ B)

                 = 48/120 + 78/120 - 14/120

                  = 56/ 81

                  = 0.691

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Explanation:

The log equation [tex]\text{x} = \log_b(\text{y})[/tex] is equivalent to its exponential form [tex]\text{y} = b^\text{x}[/tex]

For the exponential equation, we can replace x with any real number. We don't have to worry about things like dividing by zero. Therefore the domain of the exponential equation is "set of all real numbers".

The domain of  [tex]\text{y} = b^\text{x}[/tex] is the range of [tex]\text{x} = \log_b(\text{y})[/tex]. The domain and range swap roles when going from original to inverse.

Therefore, the range of any logarithmic function is "set of all real numbers".

On a graph notice how the log curve stretches forever upward and downward. The base of the log doesn't matter.

$12188.04 is the cost that school to purchase agenda books for all of its students

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that  Last year, the school purchased 350 books at a total cost of $1,137.50.

The school charges the same amount this year, but their population has grown to 375 students.

We have to find the cost the school to purchase agenda books for all of its students

Let us consider it as x.

Form an proportional equation.

350/1137.5=375/x

apply cross multiplication

350x=11375.5×375

350x=4265812.5

Divide both sides by 350

x=$12188.035

Hence, $12188.04 is the cost that school to purchase agenda books for all of its students

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To have a unique solution for the given equations, k should not be equal to 3.

Given equations are:

kx - y = 2

and, 6x - 2y = 3

The second equation can be written as, 3x - y = 3/2

The system of equations kx-y=2 and 3x - y = 3/2 has a unique solution when the coefficients of x and y are not equal, meaning k is not equal to 3.

This is because when the coefficients are not equal, the equations are not dependent on each other and can be solved independently. If the coefficients were equal, then the equations would be parallel and have infinitely many solutions.

Additionally, the specific value of k does not affect the uniqueness of the solution, as long as it is not equal to 3.

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Answer:

Step-by-step explanation:

14+(-8)14+(-8)

-122+14=-108+-8=116

An algebraic expression (or) a variable expression is a combination of terms by operations such as addition, subtraction, multiplication, and division. For example, let's look at the expression 5x + 7.

Algebraic Expression:

Algebraic expressions are mathematical expressions that result when you perform operations such as addition, subtraction, multiplication, and division on variables and constants. For example, let's say James and Natalie were playing with matches and wanted to create a pattern of numbers in matches. James played four games and formed No. 4. Natalie added three more games and two he formed a pattern of four. They realized they could add 3 matches to each round to get an extra '4'. From this, they concluded that, in general, 4 + 3 (n-1) double crochet stitches are required to create n 4 patterns. Here 4+ 3(n-1) is called an algebraic expression. To solve a linear equation with one variable, use the transpose method. Follow this procedure to perform the same operations on both sides of the equal sign. That is, perform operations to isolate variables.

Example:

5x + 7 = 32

Subtract 7 from both sides

⇒ 5x = 25

Divide both sides by 5

⇒ x = 5

⇒ 5x = 25

Divide both sides by 3

⇒ 2y – 12 = 24

Add 12 to both sides

⇒ 2y = 36

Divide both sides by 2

⇒ y = 18.

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First, find out how much each text will cost, which is always $ 0.25. When there are no text messagers, collukate the fee to $2 per hour .

When 50 texts are added, the price goes up for each text when there are two of them (57,5-50=7.5).  [tex](7.5 \div 30=0.25)[/tex] Zach would incur costs if there were no texts. [tex](50-20 \times 0.25=45)$[/tex] , And Laura's price without a text is $65 Thus, (65-45=20) would apply. [First, find out how much each text will cost, which is always $ 0.25. When there are no text messagers, collukate the fee to $2 per hour.]

Laura's monthly cell phone service fee is $65 plus $0.10 for each text message sent. Based on how many texts Zach sends, the following table displays the cost of his cell phone service. When no text messages are sent, Zach's cell phone service is $2 per hour less expensive than Laura's.

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The correct answer is B. The set of output values (y-values) of a function.

The range of a function is the set of all possible output values (y-values) of the function. It is the set of values that the dependent variable (y) can take on, given the domain (set of input values or x-values) of the function.

It can also be represented graphically by plotting the function on a coordinate plane and observing the set of y-values that the function takes on.

We have the following options:

A. The set of input values (x-values) of a function

B. The set of output values (y-values) of a function

C. The set of all possible x-y pairs of a function

D. The set of all possible x-values of a function

Therefore, The correct answer is B. The set of output values (y-values) of a function.

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The experimental probability of landing on a number greater than 4 is 0.25 or 25%.

To find this probability, we need to determine the number of successful outcomes (landing on a number greater than 4) and divide that by the total number of trials (60).

The successful outcomes are 5 and 6, with a frequency of 10 and 8 respectively. To add these two frequencies together, we can use 10 + 8 = 18.

So, the experimental probability is 18/60 = 0.3 or 25%.

It's important to note that experimental probability is based on the outcomes of an experiment or a sample and it may not be the same as a theoretical probability which is based on the ratio of favorable outcomes to the total number of outcomes in a theoretical model.

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the answer in fraction form is 18/60

if thats what you are looking for.