Name all sets of numbers to which each real number belongs

Answers

Answer 1

Real Number
Whole Numbers:0,1,2,3,4,5,6,7,8,9,10,etc.
Counting Numbers:1,2,3,4,5,6,7,8,etc.
Natural Numbers:which is whole or counting numbers depends on the topic
Integers:-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,etc.

Related Questions

Determine the value of a so that the line whose equation is ax+y-4=0 is perpendicular to the line containing the points (2,-5) and (-3,2)

Answers

First, write the equation of the line containing the points (2,-5) and (-3,2).

We can use 2 point form, or point-slope form.

Let's use point-slope form.

the slope m is [tex] \frac{-5-2}{2-(-3)}= \frac{-7}{5} [/tex], then use any of the points to write the equation. (ex, pick (2, -5))

y-(-5)=(-7/5)(x-2)

y+5=(-7/5)x+14/5

y= (-7/5)x+14/5 - 5 =(-7/5)x+14/5 - 25/5 =(-7/5)x-11/5

Thus, the lines are

i) y=-ax+4 and ii) y=(-7/5)x-11/5

the slopes are the coefficients of x: -a and (-7/5),

the product of the slopes of 2 perpendicular lines is -1,

so

(-a)(-7/5)=-1

7/5a=-1

a=-1/(7/5)=-5/7

Answer: -5/7

find the area of triangle QRS.

Answers

Answer: 140 square units.

Step-by-step explanation:

The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\ and\ (x_3,y_3)[/tex] is given by

[tex]\text{Area}=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2][/tex]

Then area of triangle QRS with vertices (6,10), (2,-10) and (-9,5) is given by :-

[tex]\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-10-5)+2(5-10)-9(10-(-10))]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-15)+2(-5)+-9(20)]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[280]|\\\\\Rightarrow\text{Area}=140\text{ square units}[/tex]

Answer:

the answer is 140. I did the assignment

The three sides of a triangle are consecutive odd integers. If the perimeter of the triangle is 39 inches find the lengths of the sides of the triangle

Answers

It should be 11 13 15, the sum is 39 and those are consecutive odd integers

a tower casts a 450 ft shadow at the same time that a 4 ft child casts a 6 ft shadow. Write and solve a proportion to find the height of a tower

Answers

check the picture below.

Answer:

[tex]x=300[/tex]

Step-by-step explanation:

Set up the proportion;

[tex]\frac{x}{450} =\frac{4}{6}[/tex]

then cross multiply;

[tex]6x=450[/tex] · [tex]4[/tex]

[tex]6x=1800[/tex]

[tex]x=\frac{1800}{6} =300[/tex]

[tex]x=300[/tex]

Solve the inequality.

Answers

To solve an inequality, get the variable you're solving for on one side of the inequality and everything else on the opposite side.

[tex]\frac{2}{5} \geq x - \frac{4}{5}[/tex]

You get the x variable on it's own by undoing the operations done to it.

For example, if x is being multiplied by 5, you undo the multiplication operation by using the inverse of multiplication. Which is division.

We need to add [tex]\frac{4}{5}[/tex] to both sides of the inequality to undo the subtraction operation done to x.

[tex]\frac{2}{5} + \frac{4}{5} \geq x - \frac{4}{5} + \frac{4}{5} \\ \\ \frac{6}{5} \geq x[/tex]

Convert the improper fraction into a mixed number.

[tex]\frac{6}{5} = 1 \frac{1}{5}[/tex]

So, D 1 1/5 ≥ x is the answer.

Approximately 7% of people are left-handed. if two people are selected at random, what is the probability of p(one is right-handed and the other is left-handed)

Answers

217/1650. This is the answer because you can do 7/100*93/99 which can be ordered twice so you multiply that by 2 and you get 217/1650.

The required probability that one is right-handed and the other is left-handed is 217/1650.

Given that,
Approximately 7% of people are left-handed. if two people are selected at random, what is the probability of p(one is right-handed and the other is left-handed) is to be determined.

What is probability?

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

Here,
Total number of left-handed people out of 100 = 7

Total number of right-handed people out of 100 = 100 - 7 = 93

Now,
Probability of picking 2 person(one is right-handed and the other is left-handed) = 7 / 100 (93/99) = 217/1650.

Thus, the required probability that one is right-handed and the other is left-handed is 217/1650.

Learn more about probability here:

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determine which of the following logarithms is condensed correctly

Answers

The laws of logarithm has specific theories to be applied depending on the form of the given expression. Some of it are the following:

alogb = log b^a
log a + log b = log (ab)
log a - log b = log (a/b)

for letter A,
xlogb r + logb s - logb t = logb [(rs)^x]/t
is wrong because the s part from logb s has no x before the logb

for letter B,
xlogb r + xlogb s - logb t = logb (rs/t)^x
is wrong because the t part from logb t has no x before logb

for letter C,
logbr - xlogb s + xlogb t = logb (r)/(st)^x
is correct because after the minus sign, condensing it would form a fraction, the plus sign will form a multiplication and both s and t are raised to the power of x.
So the answer is letter C.

Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
What is the length of segment QM'?

Answers

Answer: 6 units

Step-by-step explanation:

Given: Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.

Since in dilation , to calculate the distance of a point on image from center point we need to multiply scale factor to the distance of corresponding point on pre-image from center point .

Thus we have,

[tex]QM'=2\times QM\\\\\Rightarrow QM'=2\times3\\\\\Rightarrow QM'=6[/tex]

Hence, the length of segment QM' = 6 units.

Answer:

6 units

Step-by-step explanation:

rationalize the denominator. write it in simplest terms

3
------
√12x

Answers

the idea being, you multiply top and bottom by a value that will raise the radicand in the denominator, to the same as the root, thus coming out of the root, so, let's do so

[tex]\bf \cfrac{3}{\sqrt{12x}}\cdot \cfrac{\sqrt{12x}}{\sqrt{12x}}\implies \cfrac{3\sqrt{12x}}{\sqrt{(12x)^2}}\implies \cfrac{3\sqrt{12x}}{12x}\implies \cfrac{\sqrt{12x}}{4x}[/tex]

Find all solutions in the interval [0, 2π).

sin^2 x + sin x = 0

Answers

Factoring:-

sin x( sin x + 1) = 0

sin x = 0 , or sinx + 1 = 0 giving sin x = -1

when sin x = 0 x = 0 , pi

when sin x = -1, x = pi + pi/2 = 3pi/2

solutions in given interval are 0,pi and 3pi/2

x - 2(x + 10) = 12 what's x

Answers

Hello there! How are you today?

First, let's rewrite our problem.

x - 2(x + 10) = 12, solve for x.

To start us off, we need to apply the distributive property to the left side of the equation "-2(x + 10)", as since there is no sign between the number and the parenthesis, it is implied that we must multiply.

To distribute, we multiply the number outside of the parenthesis by all numbers inside the parenthesis.

For example;

2(1 + 3)
2(1) + 2(3)
2 + 6
8.

Now that we (hopefully) understand our concept, let's proceed to our equation to solve for x.

x - 2(x + 10) = 12

Apply the Distributive Property.

-2(x) - 2(!0)
-2x - 20.

We now have:

x - 2x - 20 = 12
Combine like-terms

-x - 20 = 12
Add 20 to both sides to isolate -x.

-20 + 20 = 0
12 + 20 = 32

Now we are left with:
-x = 32

However, we are not done as we still have x being multiplied by -1 (-x just means -1x). To get rid of the -1, we need to divide both sides by -1 to cancel them out.

-x / -1 = x
32 / -1 = -32

x = -32 is your solution.

I hope this helps!

Here are some things you should know when solving algebraic equations.
If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.
You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.
To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.
The distributive property is another important rule you will need to understand. The distributive property is used mostly for simplifying parentheses in expressions/equations.
For example, how would you get rid of the parentheses here?
6(x + 1)
If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.
6(x + 1) = 6x + 6

To sum up how to solve algebraic equations:

Use the distributive property if needed

Combine like terms on both sides of the equation if needed

If you do one operation on one side of the equation, do the same on the opposite side
x - 2(x + 10) = 12
x - 2x - 20 = 12 <-- Using the distributive property
-x - 20 = 12 <-- Combing like terms
-x = 32 <-- Add 20 to both sides
x = -32 <-- Divide both sides by -1

So, x is equal to -32.

Rectangle R has varying length l and width w but a constant perimeter of 4 ft. A. Express the area A as a function of l. What do you know about this function? B. For what values of l and w will the area of R be greatest? Give an algebraic argument. Give a geometric arguement.

Answers

Given:
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter

Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l (1)

Part A.
The area is
A = w*l
= (2 - l)*l
A = 2l - l²
This is a quadratic function or a parabola.

Part B.
Write the parabola in standard form.
A = -[l² - 2l]
= -[ (l -1)² - 1]
= -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.

The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).

Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.

what is the product? 3x^5 (2x^2+4x+1)

Answers

the answer is C.) 6x^7...

Answer:

The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex] is [tex]6x^7+12x^6+3x^5[/tex]

Step-by-step explanation:

Given: Polynomial [tex]3x^5(2 x^2+4x+1)[/tex]

We have to find the product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]

Consider the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]

Apply distributive rule, [tex]a(b+c)=ab+ac[/tex]

Multiply [tex]3x^5[/tex] with each term in brackets, we have,

[tex]=3x^5\cdot \:2x^2+3x^5\cdot \:4x+3x^5\cdot \:1[/tex]

[tex]=3\cdot \:2x^5x^2+3\cdot \:4x^5x+3\cdot \:1\cdot \:x^5[/tex]

Apply exponent rule, [tex]a^b\cdot \:a^c=a^{b+c}[/tex]

Simplify, we have,

[tex]=6x^7+12x^6+3x^5[/tex]

Thus, The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex] is [tex]6x^7+12x^6+3x^5[/tex]

Find the slope in line perpendicular x-y=16

Answers

Change to y = mx + b format
X - y = 16
-y = -x + 16

So slope = - 1 / 1

The figures in each pair are similar. Find the value of each variable. Show your work.

Answers

When a pair of figure is similar, it means the lengths have a scale factor. So we have to find what times 8 gives 16, which is the length if the bigger rectangle. 8×2=16, so we have to use the scale factor, which is 2, to multiply by the other length of the rectangle. 2×2=4, so x=4.
Next question is basically like the first one, but you have to divide instead. 12÷4=3, and so 8×3=24, so y=24. 18÷3=6, so x=6. Last one, 6÷4= 1.5. 8÷1.5=5.3 and 7÷1.5=4.6, so x=4.6 and y=5.3

We know that the figures in each pair are similar and that x,y>0, so:

The rectangle:
[tex]\frac{16}{8}=\frac{x}{2}[/tex]
[tex]2=\frac{x}{2}\quad |\cdot 2[/tex]
[tex]4=x[/tex]

The triangle I:
[tex]\frac{y}{12}=\frac{8}{4}[/tex]
[tex]\frac{y}{12}=2\quad |\cdot 12[/tex]
[tex]y=24[/tex]

[tex]\frac{12}{4}=\frac{18}{x}[/tex]
[tex]3=\frac{18}{x}\quad |\cdot x[/tex]
[tex]3x=18\quad |:3[/tex]
[tex]x=6[/tex]

The triangle II:
[tex]\frac{8}{6}=\frac{y}{4}[/tex]
[tex]32=6y\quad |:6[/tex]
[tex]y=5\frac{1}{3}[/tex]

[tex]\frac{6}{4}=\frac{7}{x}[/tex]
[tex]\frac{3}{2}=\frac{7}{x}[/tex]
[tex]3x=14[/tex]
[tex]x=4\frac{2}{3}[/tex]

:)

Factor the expression

4b^2+28b+49

Answers

(2b + 7(2b + 7) : the factor to this expression

A rectangular picture frame measures 4.0 inches by 5.5 inches. To cover
the picture inside the frame with glass costs $0.99 per square inch.
What will be the cost of the glass to cover the picture?

Answers

area = 4 x 5.5 = 22 square inches

cost is 0.99 per sq. inch

22 * 0.99 = 21.78

cost is $21.98

To find the cost of the glass for a 4.0 inch by 5.5 inch picture frame, calculate the frame's area and multiply it by the cost per square inch. The glass would cost $21.78.

To calculate the cost of the glass needed to cover the picture, you first need to determine the area of the glass required. The frame measures 4.0 inches by 5.5 inches, so the area can be found using the formula for the area of a rectangle, which is length multiplied by width.

The area is therefore 4.0 inches × 5.5 inches = 22.0 square inches. With the cost of glass being $0.99 per square inch, the total cost can be calculated by multiplying the area of the glass by the cost per square inch:

Total cost = 22.0 square inches × $0.99/square inch = $21.78.

Therefore, the cost of the glass to cover the picture would be $21.78.

06.01 LC)

Four graphs are shown below:
Which graph represents a positive nonlinear association between x and y?
Graph A
Graph B
Graph C
Graph D

Answers

Graph D.

Graph D is the correct answer because it represents a POSITIVE and EXPONENTIAL (non-linear) relationship.

Answer:

Step-by-step explanation:

In a random sample of 75 individuals, 52 people said they prefer coffee to tea. 99.7% of the population mean is between 84/80/74 % and 64/58/54%. (Choose the option closest to your answer.)

Answers

84 and 54 are your answers

Tim bought a soft drink for 2 dollars and 5 candy bars. He spent a total of 22 dollars. How much did the candy bar costs?

Answers

5x+2=22

Subtract 2 from both sides
5x=20

Divide both sides by 5
x=4

Final answer: $4.00

Probability theory predicts that there is a 44% chance of a water polo team winning any particular match. If the water polo team playing 2 matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?

Answers

After playing 2 matches possible outcomes are:
water polo team wins none, wins 1 or wins both games.

chance that they win both matches are:
0.44*0.44 = 0.1936 in relative value

Chance that they lose both matches are:
(1-0.44)*(1-0.44) = 0.3136 in relative value

If we multiply these relative values by number of matches and subtract that from number played double games (10000) we will get number of times they won only once.

10000 - 10000* (0.3136+ 0.1936) = 4928

Simplify
[tex] \frac{ \frac{1}{x+h} + \frac{1}{x} }{x} [/tex]

Answers

[tex]\bf \cfrac{\frac{1}{x+h}+\frac{1}{x}}{x}\implies \cfrac{\frac{(x\cdot 1)+(1\cdot (x+h))}{x(x+h)}}{\frac{x}{1}}\implies \cfrac{\frac{x+x+h}{x(x+h)}}{\frac{x}{1}}\implies \cfrac{x+x+h}{x(x+h)}\cdot \cfrac{1}{x} \\\\\\ \cfrac{2x+h}{x^2(x+h)}[/tex]

Sixty-five percent of men consider themselves knowledgeable football fans. if 12 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.

Answers

Answer:

P(x)= 0.0198

Step-by-step explanation:

Given : 65% men are knowledgeable football fans, 12 are randomly selected ,

To find : Probability that exactly four of them will consider themselves knowledgeable fans.

Solution : Let P is the success rate = 65% = 0.65

Let Q is the failure rate = 100-65= 35%= 0.35

Let n be the total number of fans selected = 12

Let r be the probability of getting exactly four = 4

Formula used : The binomial probability

[tex]P(x)= \frac{n!}{(n-r)!r!}P^rQ^{n-r}[/tex]

putting values in the formula we get ,

[tex]P(x)= \frac{12!}{(12-4)!4!}(0.65)^4(0.35)^{12-4}[/tex]

[tex]P(x)= (495)(0.1785)(o.ooo22 )[/tex]

P(x)= 0.0198

The probability that exactly four out of the twelve randomly selected men will consider themselves knowledgeable football fans is approximately 0.236 or 23.6%.

Step 1: Model Selection (Binomial Distribution)

This scenario can be modeled using the binomial distribution if the following conditions are met:

Fixed number of trials (n): In this case, we have a fixed number of men being selected (n = 12).Binary outcome: Each man can be classified into two categories: either a "knowledgeable fan" (success) or a "not knowledgeable fan" (failure).Independent trials: The knowledge level of one man doesn't affect the selection of another.Constant probability (p): The probability (p) of a man being a knowledgeable fan remains constant throughout the random selection (given as 65%).

Since these conditions seem reasonable, the binomial distribution is a suitable model for this scenario.

Step 2: Formula and Values

The probability (P(x)) of exactly x successes (knowledgeable fans) in n trials (men selected) with probability p of success (knowledgeable fan) can be calculated using the binomial probability formula:

P(x) = nCx * p^x * (1 - p)^(n-x)

where:

n = number of trials (12 men)x = number of successes (4 knowledgeable fans - what we're interested in)p = probability of success (knowledgeable fan - 65% converted to decimal: 0.65)(1 - p) = probability of failure (not knowledgeable fan)

Step 3: Apply the Formula

We are interested in the probability of exactly 4 men being knowledgeable fans (x = 4). Substitute the known values into the formula:P(4) = 12C4 * 0.65 ^ 4 * (1 - 0.65) ^ (12 - 4)

Step 4: Calculate Using Calculator or Software

While it's possible to calculate 12C4 (combinations of 12 choosing 4) by hand, using a calculator or statistical software is often easier.12C4 = 495 (combinations of 12 elements taken 4 at a time)

Step 5: Complete the Calculation

Now you have all the values to complete the calculation:P(4) = 495 * 0.65 ^ 4 * (1 - 0.65) ^ 8Using a calculator or software, evaluate the expression. You'll get an answer around 0.236.

Find the slopes of the asymptotes of the hyperbola with the following equation.
36 = 9x ^{2} - 4y^{2}

Answers

Final answer:

The given equation is a hyperbola, and by converting it to standard form we find a = 2 and b = 3. Therefore, the slopes of the asymptotes are ±3/2.

Explanation:

The equation given is in the form of a hyperbola equation which could be written as [tex]x^2/a^2 - y^2/b^2 = 1.[/tex] This suggests that the transverse axis is horizontal meaning the hyperbola opens to the left and right. The slopes of the asymptotes for hyperbola is given by ±b/a.

First, we need to rewrite our equation in standard form. The equation given is [tex]36 = 9x^{2} - 4y^{2}.[/tex] To convert it into the standard form, we divide whole equation by 36 to isolate 1 on one side. This yields [tex](x^2/4) - (y^2/9) = 1.[/tex] Now, it is in the standard form of hyperbola.

By comparing it with the standard equation, we see that [tex]a^2 = 4 \ and\ b^2 = 9[/tex]which gives a = 2 and b = 3. Based on these, we can now find the slope of the asymptotes which is ±b/a = ±3/2.

Learn more about hyperbola here:

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Write a segment addition problem using three points that asks the student to solve for x but has a solution x = 20

Answers

The segment addition problem was given below which gives the value of x as 20.

Segment addition problem:

Consider three points on a line: A, B, and C. Point B is located between points A and C.

The lengths of the line segments are as follows:

Length of segment AB: 12

Length of segment BC: x

Length of segment AC: 32

Find the value of x.

We have the equation for segment addition: AB + BC = AC

Substitute the given values:

12 + x = 32

Now, solve for x:

x = 32 - 12

x = 20

Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.

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Final answer:

To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.

Explanation:

To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:

AB + BC = AC

x + (20 - x) = 20

By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.

Here is the step-by-step problem phrased as a question:

Let points A, B, and C be collinear with B between A and C.If AB = x and BC = 20 - x, and AC = 20, find the value of x.

What is the value of X that makes the given equation true? 4x-16=6(3+x)

Answers

See the attached picture for how we solved it.

To answer that question

Answers

First, we get ax^2+bx+c. Next, we know that the line of symmetry is -b/2a. Since we know that there is a maximum value, the parabola is facing downwards, so a is negative. For random numbers, we can say that a = -0.5 and b=-10 (b needs to be negative for -b/2a to equal -10), getting -0.5x^2-10x+c. Plugging -10 in for x (since -10 is the middle it is the max), we get -50+100=50. Since the maximum needs to be 5, not 50, we subtract 45 from the answer to get it and therefore make c = -45, getting -0.5x^2-10x-45

9log9(4) =

A. 3
B. 4
C. 9
D. 81

Answers

"9log9(4) = " What do you mean by this?

When simplified, the expression (x ^1/8) (x^3/8) is 12. Which is a possible value of x?

Answers

(x ^1/8) (x^3/8) = x^4/8=x^1/2 = 12, x = 12^2 = 144

x=144

the possible value of x is 144

How many radians are contained in the angle AOT in the figure? Round your answer to three decimal places.

A. 0.459 radian
B. 2.178 radians
C. 1.047 radians
D. 0.955 radian

Answers

1 radian = 57.3 degrees

60 ÷ 57.3 = 1.047

correct answer: C

Answer:

Option C. 1.047 radians

Step-by-step explanation:

We have to find the measure of angle AOT in radians.

To convert measure of an angle from degree to radians we use the formula

[tex]\text{radians}=\frac{\pi(\text{degrees})}{180}[/tex]

= [tex]\frac{\pi(60)}{180}=\frac{\pi }{3}[/tex]

(Since measure of angle AOT is 60°)

= [tex]\frac{3.14}{3}[/tex] (since π = 3.14)

= 1.047 radians

Therefore, option C. 1.047 radians is the correct option.

Other Questions

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