7. Let A=(8,9,10,11,12,13).
n=
a. How many subsets does A have?
b. How many proper subsets does A have?
subsets.
a. A has
(Type a whole number.)
b. A has
(Type a whole number.)
proper subsets.

The function, [tex]\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }[/tex] has a limit that is undefined (does not exist) as x approaches 0. The correct option therefore option b;

b. As x approaches 0, the limit of p(x) does not exist

The given function is presented as follows;

[tex]\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }[/tex]

Required;

The limit of the function as x approaches (zero) 0

Solution;

The limit of a function at a given point within the domain of the function is the value of the function as the function's argument approaches a.

Therefore, the limit of the given function at the point x = 0 is given by the function's value as the argument of the function, x approaches 0.

cos²(0) = 1

sin(2×0) = sin(0) = 0

Therefore;

[tex]\displaystyle { p(x) = \frac{ {cos}^{2}0 }{sin(2 \times 0)} = \frac{ 1 }{0} = \infty}[/tex]

Therefore, the limit of the function does not exist as x approaches 0

The correct option is therefore, option b

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a.) The expression of the sketch is:

2 - 1 + 2 - 1 - 1 + 1 = 2

So, the value of the expression is 2.

b.) The expression of the sketch is:

4 - 6 = -2

So, the value of the expression is -2.

c.) The expression of the sketch is:

-1 + 2 - 1 + 1 - 2 + 1 = 0

So, the value of the expression is 0.

d.) The expression of the sketch is:

- 4 + 7 = 3

So, the value of the expression is 3.

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The absolute functions when matched to the respective vertex is as follows;

(-1, -3/7) → f(x) = (1/2)|x + 1| - (3/7)

(5, 2/3) → f(x) = (-3/5)|x - 5| + (2/3)

(0, -4/5) → f(x) = (1/2)|x| - (4/5)

(2/5, 5/3) → f(x) = (-3/2)|x - (2/5)| + (5/3)

We can solve all of them by writing the equations in a general form;

f(x) = a|x + b| + c

This is a function transformation of f(x) = |x|

where:

a = Factor of vertical stretch

b = Horizontal shift (- shifts right, + shifts left)

c = Vertical shift (+ shifts right, - shifts left)

The original function has its vertex in (0, 0)  so the horizontal shift will be the new x coordinate in the new vertex and the vertical shift will be the new y in the new vertex like this:

f(x) = (1/2)|x + 1| - (3/7)

b = 1 horizontal shift of -1

c = -3/7 vertical shift of -3/7

Thus, (-1, -3/7)

f(x) = (-3/5)|x - 5| + (2/3)

b = -5 horizontal shift of 5

c = 2/3 vertical shift of 2/3

Thus, (5, 2/3)

f(x) = (1/2)|x| - (4/5)

b = 0 horizontal shift of 0

c = -4/5 vertical shift of -4/5

Thus, (0, -4/5)

f(x) = (-3/2)|x - (2/5)| + (5/3)

b = -2/5 horizontal shift of 2/5

c = 5/3 vertical shift of 5/3

Thus, (2/5, 5/3)

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The expression divide r by 8 when doubled is r/4

An algebraic expression can be seen or described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.

These expressions are also known to be composed of mathematical operations, such as;

From the information given, we have;

divide r by 8

This is expressed as;

r/8

In doubling the expression, we get;

2(r/8)

expand the bracket

2r/8

Simplify further

r/4

Hence, the expression is r/4

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Based on the number of trucks needed and the snowfall per inch, the relationship between snowfall and trucks is proportional.

A relationship is said to be proportional when the two variables increase at a set rate. In other words, proportional relationships will see variables increasing at the same rate.

The rate of snowfall per trucks for 6 inches of snowfall is:

= 15 / 6

= 2.5 trucks per inch of snowfall

The rate of snowfall per trucks for 12 inches of snowfall is:

= 30 / 12

= 2.5 trucks per inch of snowfall

The rate is therefore the same across the table so the relationship between snowfall and the number of trucks is proportional.

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The equation that represents this relationship is h*n = 24.

How do we solve linear equations?
First order equations include all linear equations as a subset. In the coordinate system, lines are defined as having linear equations. A linear equation in one variable is made up of one homogeneous variable of degree one (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.

Given, number of hours needed to paint a house = h
Number of painters needed to paint the house = n
Also, the relation between h and n is inverse, thus:
h*n = k, where k is the proportionality constant.
Therefore, initial equation derived is h*n = k --(i)
Putting h = 6 and n =4 in (i), we can get the value of k as
k = h*n = 6*4 = 24 --(ii)
Comparing (i) and (ii), we get,
h*n = 24, which is the required equation.

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We need to find the mean salary for the employees:

There are

15 employees with a salary of $21,900, 10

10 employees with a salary of $24,800

3 employees with a salary of $31,200

4 employees with a salary of $37,700

1 employee with a salary of $149, 600

33 total of employees:

The mean formula is given by:

Replacing :

Therefore:

The result is rounded to the nearest hundred.

If members of a softball team raised $1,186.50 to go to a tournament they rented a bus for $842.50 and budgeted $21.50 per player for Meals. The  number of players the team can bring to the tournament is 16.

Let x represent the number of players

Formulate an equation

$842.50 + $21.50 × x = $1,186.50

Using the formulated equation to determine the number of players

$842.50 + $21.50 × x = $1,186.50

$842.50 + $21.50 x = $1,186.50

Collect like terms

$21.50 x =  $1,186.50 -$842.50

$21.50 x =  $344

Divide both side by $21.50 x

x = $344 / $21.50

x = 16 players

Therefore the team can bring 16 players to the tournament.

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A randomly chosen beagle has a 0.86508  probability of weighing more than 21.8 pounds.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be represented as percentage with values between 0 and 1.

The relationship between a value and the mean of a group of values is quantified by a Z-score.

Adult male beagle weight is normally distributed, with a mean of 25.0 pounds and a standard deviation of 2.9 pounds.

Given values are:

Mean(μ) = 25 pounds

Standard deviation(σ) = 2.9 pounds

Sample mean(x') = 21.8

We need to calculate z-score:

z = (x' - μ)/σ

z = (21.8 - 25)/2.9

z = 1.25

P-value from Z-Table:

P(x>21.8) = 1 - P(x<21.8) = 0.86508

As a result, the probability of a randomly selected beagle weighing more than 21.8 pounds is 0.86508.

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The time at which the population of bacteria will be 25,000 is 2:49 pm.

Given that:-

Population of bacteria at 1:00 PM = 5,400

Population of bacteria at 1:20 PM = 9,000

The rate at which a population of bacteria grows is proportional to the size of the population.

We have to find the time at which the population of bacteria will be 25,000.

The rate at which population of bacteria grows = 3600 bacteria/ 20 min = 180 bacteria/min

Let the population of bacteria takes t minutes to become 25,000.

Hence, we can write,

5400 + 180t = 25000

180t = 25000 - 5400

180t = 19600

t = 19600/180

t = 108.889

t = 109 minutes =  1 hour 49 minutes

Hence, the time will be 2:49 pm.

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Based on the value of the angles in this triangle, the value of x can be found to be 82 degrees

The interior angles of different polygons always add up to a certain number of degrees. For instance, the interior angles of a heptagon add up to 900 degrees.

In triangles, the the interior angles will always add up to 180 degrees. The value of x can then be found by the formula:

180 = 52 + 46 + x

x = 180 - 52 - 46

x = 82 degrees

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The graph is about a tangent function.

We have to find the parameters a and b.

The period formula is

If we find the period, we can find b.

Remember that the period is the distance between two consecutive asymptotes. In this case, the period is 2pi.

Looking at the graph

the value is currently increasing, because the slope of the line is positive

so

I agree with Mr. Alvarez reasoning

Answer: student A

The nearest half of 7.68 is 7.5  

Given,

A number is given by:

7.68

and, to find the rounded to the nearest half

Now, The number 7.68 is  between 7.5 and 8.

Let's find which of these two numbers 7.68 is closer too.

We can do this by subtracting 7.68 from each of those numbers:

8 - 7.68 = 0.32

7.5 - 7.68 = -0.18

So, 7.68 is 0.32 away from 8, but it's only 0.18 away from 7.5

Hence, The nearest half of 7.68 is 7.5  

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You will need to sell 14 baskets to meet/exceed the goal

Small baskets are sold at $12

Large baskets are sold at $20

The goal is to sell $300 worth of baskets at the upcoming craft show

Let x represent the small baskets and let y represent the large baskets

12x + 20y= 300

7 large baskets are sold, the equates to

7 × 20

= 140

The number of small baskets that must be sold to reach the goal can be calculated as follows

300-140

= 160

160/12

13.33

Hence 14 small basket needs to be sold to meet/exceed the goal

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One example of real-world situation that uses logarithms is for amount of substance that are decaying over time.

An amount of a decaying substance after t years is modeled by the following exponential equation:

[tex]P(t) = P(0)e^{-kt}[/tex]

In which:

The simplest example of the use of logarithms is to find the half-life of the substance, that is, the year t for which P(t) = 0.5P(0).

Then:

[tex]0.5P(0) = P(0)e^{-kt}[/tex]

[tex]e^{-kt} = 0.5[/tex]

The natural logarithm is used to find the half life, as it is the inverse of the exponential.

[tex]\ln{e^{-kt}} = \ln{0.5}[/tex]

[tex]-kt = \ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{k}[/tex]

Hence we showed another application of logarithms in a real-word model.

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Answer:

83/8 , decimal form 10.375, mixed number form 10 3/8

Step-by-step explanation:

The probability would be 0.074 that a randomly selected night has exactly 25 vehicles passing through the toll booth.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes

Let X be the number of vehicles passing through the toll booth per night

X~Poisson(27)

The probability that exactly 25 vehicles passing through the toll booth is

⇒ P(X = 25) = (e⁻²⁷ × 27²⁵) / 25!

⇒ P(X = 25) = 0.074

Thus, Excel Command = POISSON.DIST(25,27,FALSE)

Therefore, the probability would be 0.074 that a randomly selected night has exactly 25 vehicles passing through the toll booth.

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We can define the translation of building from location C to location E by the following rule -

(x, y) → (x - 4 , y + 6)

A translation is a movement of the graph either horizontally (parallel to the x -axis) or vertically (parallel to the y -axis) without changing its orientation.

Given is a Building C translated to Building E.

In order to translate the building from location C to location E, we will first shift the building near the x - axis vertically upwards. For this we will shift the y coordinate by -

- 7 + y[s] = - 1

y[s] = -1 + 7

y[s] = 6

So the y - coordinate of the translated graph will be -

(y + 6)

Now, we will shift the x coordinate -

1 + x[s] = -3

x[s] = -3 - 1

x[s] = -4

So the x - coordinate of the translated graph will be -

(x - 4)

Therefore, we can define the translation by the following rule -

(x, y) → (x - 4 , y + 6)

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[tex]\begin{array}{ccll} scarves&\$\\ \cline{1-2} 2 & 22.80\\ 3& x \end{array} \implies \cfrac{2}{3}~~=~~\cfrac{22.80}{x} \\\\\\ 2x=3(22.80)\implies x=\cfrac{3(22.80)}{2}\implies x=34.2[/tex]

Answer: $34.20

Step-by-step explanation:

2 scarves = $22.80

22.80 ÷ 2 = $11.40

11.40 x 3 = $34.20

To check your work you could do:

$22.80 + $11.40 = $34.20

or

$34.20 ÷ 3 = $11.40

Simplifying the given term

What is Like Terms?

In algebra, equal terms are terms that have the same variables and powers. Coefficients do not have to match. Dissimilar terms are two or more terms that are not similar terms. That is, they do not have the same variable or exponentiation. The order of the variables does not matter unless there are exponentiations.

To simplify and combine the like terms of the given question

7) -4x^2 - y^2 - 6x^2 +  2xy - 4x^2 + 7xy - xy +4y^2-9xy - 4x^2 + xy

    Now, arranging them with the like terms

 = -4x^2- 4x^2- 4x^2- 6x^2- y^2 +4y^2+  2xy- xy-9xy + xy

= -10x^2 + 3y^2 - 7xy

8) n+n^2-5n+40n-10+3n^2+1-5n+n^2+18n-2

    Now, arranging them with the like terms

= n^2+n^2+3n^2+n-5n+40n-5n+18n-10+1-2

= 5n^2 + 49n - 11

9) 14y - y^2 + 9y^2 + 12 - 5y^2 + 25y - y +8y^2 - 9y +25y + y

  Now, arranging them with the like terms

= 9y^2- y^2- 5y^2+8y^2+ 25y- y - 9y + y +25y + 14y +12

= 11y^2 + 45y + 12

10) 12b + 2b^2 + 6a^2 + a - 5b + 2a - ab + 4a^2 - b - ab + 10b

  Now, arranging them with the like terms

= 2b^2+ 6a^2+ 4a^2  + a+ 2a + 12b  - 5b - b+ 10b - ab- ab

= 10a^2 + 2b^2 + 3a + 16b - 2ab

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The undefined terms are parallel lines are line and plane.

What is parallel lines?

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. In this essay, let's study more about parallel lines. No matter how far we extend a parallel line, it will never meet another parallel line. See the parallel lines in the following illustration. Lines "a" and "b" are parallel, while lines "p" and "q" are also parallel.

Given that,

Parallel lines are two or more lines in a plane that are the same distance apart and will never intersect.  

This definition uses two undefined terms, line and plane.

Therefore,  undefined terms are parallel lines are line and plane.

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The amount of money Lamonte makes is $22.5 per hour

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let e represent the total earnings in dollars if Lamonte works for h hours. Hence:

e = 22.5h

e/h = $22.5 per hour

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A.

The length of the diagonal is given by the Pythagorean theorem therefore

The length of the diagonal is ) units

B.

The area of the square is given by the next formula

where s is the side

s=4

The area of the square is 16 units^2

C.

For the area of the triangle we will use the next formula

where b is the base and h is the height

b=4 units

h=4units

The area of the triangle formed by a diagonal and two of the sides is 8 units^2

D.

For the area of this triangle, we will use the same formula that we use in C. but in this case

b=sqrt(32)/2

h=sqrt(32)/2

We substitute the values

The area of one of these triangles is 4 units^2

ANSWER

A. sqrt(32) units

B.16 units^2

C. 8 units^2

D. 4 units^2

The population proportion when the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200 must be D. 0.35 or 0.65.

Based on the information, it should be noted that the formula for the standard error for the population will be:

✓p(1 - p)/n

where

p = population proportion

n = sample size

Therefore, this will be illustrated as:

✓p(1 - p)/n = 0.0337

Remove the square root

p( 1 - p)/200 = 0.00113569

Cross multiply

p(1 - p) = 0.227138

p - p² = 0.227138

Equate to 0

p² - p + 0.227138 = 0

Using almighty formula, P1 = 0.6512 and P2 = 0.3488

Therefore, the correct option is D.

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If the standard error of the sampling distribution of the sample proportion is .0337 for samples of size 200, then the population proportion must be:

A) 0.25

B) 0.75

C) 0.20 or 0.80

D) 0.35 or 0.65

The bathroom must be tiled with 49 tiles, each of which has a surface area of 1 square meter and measures 7 meters by 7 meters.

How can I figure out how many tiles I need to tile the bathroom?

The bathroom's area is,

A= 7m x 7m

A= 49m^2

likewise the area of each tile = 1 square meter

The total amount of tiles needed to tile the bathroom is thus,

49/1 = 49

Therefore, the bathroom must be tiled with 49 tiles.

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Answer: True

Step-by-step explanation: