Subsets

What is the symbol for subset?

4.1.1 and 4.1.3 are discrete variables and 4.1.2 is a continuous variable.

What are discrete and continuous variables?

Discrete variables are those that have distinct, countable values. A continuous variable can be assigned to any value that falls inside a range, which has an infinite number of possible values.

4.1.1 "I am fifty years old"

It is a discrete variable because age is represented in whole numbers.

4.1.2 "I can drink 400.5 ml of juice in a minute"

It is a continuous variable because the amount of juice is consumed every minute so, we can obtain values even in fraction.

4.1.3 "I have 2 brothers and 1 sister"

It is a discrete variable because the given value is countable.

Hence, 4.1.1 and 4.1.3 are discrete variables and 4.1.2 is a continuous variable.

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The correct statement regarding the probability in this problem is given as follows:

D.) A home run by definition is a successful hit, so the probability that he gets a successful hit must be greater than, or at least equal to, the probability that he hits a home run.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For each at bat, there are two possible outcomes:

There are four types of hits, which are given as follows:

Hence only statement D is correct, as the player can either be eliminated or get one of the four types of hits.

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Answer:

A(L) = - L²  + 215L

Domain
0 < L < 215

or

(0, 215) in interval notation

Step-by-step explanation:

Let  L represent the length and W the width

Perimeter of a rectangle = 2(L+W) and is given as 430 meters

Therefore 2(L + W) = 430

L + W = 430/2
L + W = 215

W = 215-L

The area A is given by L x W

Substituting for W in terms of L this becomes

A = L x(215 - L)

A = 215L - L²

which can be expressed as a function of in the form
A(L) = 215L - L² or in standard form(highest degree first)

A(L) = - L²  + 215L

The domain of this function are the values of L which result in a defined , real value for A

Without restrictions, the domain for L is -∞ < L < ∞. However real world facts coming into play

1. Area cannot be zero
So A(L) > 0 (upper bound on area)

-L² + 215L > 0

-L² > - 215L Move 215L to right side

L² < 215L   (dividing by -1 changes signs of variables and also inequality)

L < 215      (divide by L both sides)

2. Length cannot be negative
So lower bound on L is L > 0

Together the domain is
0 < L < 215

or

(0, 215) in interval notation

The quantity of type A coffee will be 37 pounds.

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.

Given that Frank's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Frank $4.20 per pound, and type B coffee costs $5.60 per pound.

The quantity of Type A coffee will be calculated as:-

B = 4A

4.20A + 5.6B = 984.20

4.20A + 4 x 5.6 x A = 984.20

4.20A + 22.4A = 984.22

26.6A = 984.22

A = 37

Therefore, the amount of each type of 37 pounds will equal one coffee.

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A line's point slope form equation is y - y1 = m. (x – x1). Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+b allow us to build an equation for that line.

The slope of the line passing through these points,

[tex]m=\frac{y2-y1}{x2-x1} \\\\m=\frac{7-9}{0} =infinity[/tex]

infinity slope means y axis.

The equation of line will be x=0.

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Answer:

y = -x+5

Step-by-step explanation:

Use point slope formula to find the equation of the line

First find the slope: (-1-4)/(6-1) = -5/5, slope = -1

Then, use the formula: y - y1 = m(x - x1)

y - 4 = -1(x - 1)

y - 4 = -x+1

y = -x + 5

The function has no vertical asymptotes and horizontal asymptotes are at y = 0.

A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels toward as it approaches infinity.

A straight line that serves as the asymptote of the curve y = f(x) or, in its implicit form, f(x,y) = 0, where the distance between the two lends to zero as the points on the curve approach infinity.

Given function,

f(x) = -7/(x² + 4)

in the given function the degree of the denominator is more than the numerator so The horizontal asymptote lies at y = 0 because, as we can see, the degree of the numerator is less than the denominator.

and there will be no vertical asymptote.

The graph of the equation is attached.

Hence horizontal asymptote lies at y = 0 and ni vertical asymptote.

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Answer:

7x-43=5x+43

7x-5x=43+43

2x=86

x=86/2

x=43

Answer: 9

Step-by-step explanation:

12-3=9 or count up from 3 until you get too 12

Answer:

1/2 goes into 3/4 1 1/2 or 1.5 times

Step-by-step explanation:

The expression when evaluated is 46552

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

5,819 x 8.

Using the standard algorithm, we have:

5,819 x 8 = (5800 + 19) * 8

Open the brackets

So, we have the following representation

5,819 x 8 = 5800* 8 + 19 * 8

Evaluate

5,819 x 8 = 46400 + 152

So, we have

5,819 x 8 = 46552

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Answer: E

Step-by-step explanation: Since this is a special right triangle(45,45,90), you know that the ratios of the leg to the hypotenuse is 1:1:sqrt2. 15 sort root two hold true to that rule and is the right answer.

Answer:100 or it just means 10 times

Step-by-step explanation: you need to learn the angles when the number are put on each side and then your answer will come!

Answer: Vegetable consumption per month is 17.33 pounds and fruits consumption per month is 10.47 pounds.

Step-by-step explanation:

Answer: 1. 27/72 = 3/8,  2. 24/40 = 3/5,  3. 6/42 = 1/7

Step-by-step explanation:

1. 27/72 divided by 9/9 equals 3/8.

2. 24/40 divided by 8/8 equals 3/5.

3. 6/42 divided by 6/6 equals 1/7.

The total length of the bolt should be 21/8 inches.

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

Given the thickness of plate 1 = 7/8 inches

the thickness of plate 2 = [tex]1\frac{1}{4}[/tex] inches = 5/8 inches

total thickness of both plates = 7/8 + 5/4

5/4 is equaivalent to (5*2)/(4*2) = 10/8

the total thickness of both plates = 7/8 + 10/8

the total thickness of both plates = 17/8 inches

and the bolt must be at least 1/2 inch longer

total length of bolt = 17/8 + 1/2

convert 1/2 to the same denominator as 17/8

1/2 = (1*4)/(2*4) = 4/8

total length of bolt = 17/8 + 4/8

the total length of the bolt =  21/8 inches

Hence the bolt should be 21/8 inches longer.

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The terms which is not an impact of American consumerism is -

Option C: Cash generators for several nations.

What is consumerism?

The tendency to continuously consume is known as consumerism. It is the need to acquire more possessions and establish one's identity via them. Consumer spending and GDP growth are seen as benefits of consumerism by economists.

The American consumerism includes -

Debts : Due to introduction of credit cards the consumers have ore and more debt on their credit cards whilst they spend on materialistic goods.

Lack of Unemployment : Economists point out that a decline in product demand causes an economic downturn or even depression, which is accompanied by high unemployment.

Stress:  Due to debt, recession and unemployment people are constantly under stress for surviving.

Since, consumerism helps in GDP growth of a country it does not help generate cash for other nations.

Therefore, " Cash generators for several nations" is not an impact.

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The two values of y such that the barn is 50 yards from the well

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-1, 1) and (-1,, y) is calculated to be 50 yards and hence we solve for y

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

50 =√{(-1 - -1)² + (1 - y)²}

50 =√{ (1 - y)²}

2500 = (1 - y) (1 - y)

2500 = 1 - 2y + y²

y² - 2y - 2499 = 0

solving the quadratic equation gives

y = 51 OR -49

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Answer:

[tex]x=42; \ y=14\sqrt{5}.[/tex]

Step-by-step explanation:

1. if the angles of the given triangle are 30-60-90°, then

2. y=0.5*28√5=14√5;

[tex]3. \ x=28\sqrt{5}*sin(60)=28\sqrt{3}*\frac{\sqrt{3} }{2}=42.[/tex]

4. finally, x=42; y=14√5.

Answer:

okay have a nice day haha

Option B: The domain of the function is the set of all real numbers, Option C: the range of the function is the set of all non-negative real numbers, Option D: the graph has an intercept at (0, 0), and option G: the graph is symmetric with respect to the y-axis are correct statements about the graph.

There are only real numbers in the domain, or collection of x-values. This is so because x holds true for all numbers. The set of all non-negative real numbers is known as the range or set of y-values. This is due to the fact that every value we obtain for y is a positive real number. The graph's x-intercept and y-intercept, also known as the intersection point, are located at (0, 0). Instead of the other way around, the graph increases on the interval x>0 and decreases on the interval x<0. Instead of a maximum, the graph shows a minimum at (0, 0). The graph is symmetric with respect to the y-axis because it may be folded in half along that axis.

As per the question, the function described below is an example of a polynomial function since it is a function of a single independent variable that has been raised to an integer power. Adding terms with a numerical coefficient multiplied by a specific power of the independent variables results in polynomial functions.

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Refer image for the complete question.

Answer:

  T〈-7,0〉

Step-by-step explanation:

You want a description of the transformation of triangle ABC to triangle A"B"C".

∆A"B"C" has the same orientation as ∆ABC, so no reflection is involved (eliminates choice B).

Point A" is 7 units to the left of point A, so the translation is 7 units left (and no units up or down).

The transformation is ...

  [tex]\boxed{T_{\langle-7,0\rangle}}[/tex]

The m∠1 and m∠2 which are linear pairs of angles are 72° and 108°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know that the sum of linear pair of angles is equal to 180°.

therefore, From the given information, (x + 36)° + 3x° = 180°.

4x + 36° = 180°.

4x = 144°.

x = 36°.

So, m∠1 = 72° and m∠2 = 108°.

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Answer:

Length = 10cm, Width = 9 cm

Step-by-step explanation:

Let's call the amount that both the length and width are increased by "x". So, the new length is 5 + x and the new width is 4 + x.

The original area of the rectangle was 5 * 4 = 20 cm2.

The new area of the rectangle after the increase is (5 + x) * (4 + x) = 20 + 70 + 2x^2.

Expanding the right-hand side, we have 20 + 70 + 2x^2 = 90 + 2x^2.

Equating the two areas, we get:

20 + 70 + 2x^2 = 90 + 2x^2

Subtracting 2x^2 from both sides:

20 + 70 = 90

Subtracting 20 from both sides:

70 = 70

So x^2 = 50 / 2 = 25.

Taking the square root of both sides, we get:

x = 5

So the length of the longer rectangle is 5 + x = 5 + 5 = 10 cm, and the width is 4 + x = 4 + 5 = 9 cm.

It is given that 2/5 of all patients admitted to ward 17.

Remining fraction is:

So 3/5 of patients admitted to ward 18.

Since 1/6 of all patients moved to another ward, and the reminder assigned as before, the initial fraction becomes:

Now, 3/5 of the new fraction, 5/6 is admitted to ward 18.

That is:

This is half of the patients.

The difference of the number of the patients admitted to ward 17 is the same fraction of the number of infected:

So the difference of patients is 4.

Answer:

102

Step-by-step explanation:

Answer:

150 units (Option C)

Step-by-step explanation:

Perimeter of rectangle = Perimeter of triangle

= {2 × (Length + Width)} = Sum of all three sides

= {2 × [(2x) + (x + 12)]} = [(4x) + (2x) + (x + 3)]

The parenthesis are expanded using the Distributive Law:
= {2 × [2x + x + 12]}  = [4x + 2x + x + 3]

= {2 × [3x + 12]} = [7x + 3]
= 6x + 24 = 7x + 3

Bring all the like terms together and isolate x:

= 24 - 3 = 7x - 6x

= 21 = x

∴x = 21

Substitute this calculated value of x to determine the perimeter of rectangle:

6x + 24

= 6(21) + 24

= 126 + 24

= 150 units

∴Option C

Answer:

- 8.5

Step-by-step explanation:

Answer: The probability that a customer wins a prize 8.3%

Step-by-step explanation:

First off, the dice has twelve sides and only of the sides, 9, will allow a customer to win.

this means that there is a 1/12 chance that the customer will win a prize.

We can rewrite this into a decimal: 0.0833

and then to a percentage rounded to the nearest tenth: 8.3%

The probability that a customer wins a prize is 8.3% to the nearest tenth.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

A clothing store has each customer roll a 12-sided die with faces numbered 1−12 to win a free T-shirt.

Customers who roll a 9 win.

Total possible outcomes = 12

Number of outcomes which results in a win = 1

Probability that a customer wins = 1/12

                                                       = 0.08333

                                                       = 8.3%

Hence the required probability is 8.3%.

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