Is -1/2 rational or irrational

Answers

Answer 1

-1/2 is rational, have a good day

Answer 2

-1/2 is rational because it can be expressed as a ratio of 2 integers.

-1 and 2 are both integers because they are either whole numbers or of the opposite value (negative).

Related Questions

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials? a. 0.0554

Answers

Final answer:

For two successes in seven binomial trials with a success probability of 0.06, use the binomial probability formula. Calculate (7 choose 2) * (0.06^2) * (0.94^5) to get the probability of 0.0554.

Explanation:

To calculate the probability of two successes in seven trials with a success probability of 0.06, you can use the binomial probability formula, which is P(X = k) = (n choose k) * p^k * q^(n-k), where 'n' is the number of trials (7), 'k' is the number of successes (2), 'p' is the probability of success (0.06), and 'q' is the probability of failure (q = 1 - p = 0.94).

First, calculate the binomial coefficient using 'n choose k', which is (7 choose 2). Then, raise the probability of success to the power of the number of successes (0.06^2) and the probability of failure to the power of the number of failures (0.94^5). Lastly, multiply these values together to get the probability.

The calculation is as follows:

(7 choose 2) * (0.06^2) * (0.94^5) = 21 * 0.0036 * 0.7339 = 0.0554

What is the vertex of the graph of y + 2x + 3 = –(x + 2)2 + 1?

Answers

There are a lot of steps involved in this, so pay attention. First step is to expand the squared quantity and FOIL it out, like this:
[tex]y+2x+3=-(x+2)(x+2)+1[/tex] and
[tex]y+2x+3=- x^{2} -4x-4+1[/tex]
We are going to combine all the like terms now and get them all on one side of the equation:
[tex]- x^{2} -6x-6=y[/tex]
Now we are going to complete the square on the polynomial in order to find the vertex. Do this by first setting the equation equal to 0 and then moving the constant over to the other side of the equals sign, like this:
[tex]- x^{2} -6x=6[/tex] and now factor out the negative sign (cuz negative signs are a pain):
[tex]-( x^{2} +6x)=6[/tex]. To complete the square, you take half the linear term, square it, and add it in to both sides. Our linear term is 6x. Half of 6 is 3, and 3 squared is 9. That's easy to add in on the left side, but we cannot forget that fact that we factored out a negative 1, and that the negative 1 is still there and has to be taken into consideration when we "add" in a 9 to the other side. We actually multiply the negative 1 times the 9 and that's what's added in to the right:
[tex]-( x^{2} +6x+9)=6-9[/tex]
What you do when you complete the square is create a perfect square binomial on the left, which we have and which looks like this:
[tex]-(x+3) ^{2} = -3[/tex]
When we move the 3 back over to be with its mates (the 3 is the y coordinate for the vertex), we have the actual sign of the y coordinate. The number inside the parenthesis with the x is the x coordiante of the vertex in the form [tex](x-h) ^{2} [/tex]. So the vertex of your problem is (-3, 3). The negative outside the parenthesis just indicates to us that the parabola is an upside down one, like a mountain instead of a valley.

What is the area for this problem?

Answers

It's 324pi since the circumference is 2 pi r, you can divide 36 by 2 to find the radius, after finding the radius plug it into the area equation which is pi r^2

C = 2* pi *r = 36 pi

r = 36pi/2pi = 18

We know that A= r^2 * pi

A = 18^2 * pi = 324 pi

the area would be 324PI square units

A chi-square test involves a comparison between what is observed and what would be expected by _______.

Answers

I believe the correct word to fill in the blank would be "chance". A chi-square test involves a comparison between what is observed and what would be expected by chance. It tests the the observed values and the values that are expected theoretically. The chi-square test is a statistical tool where the distribution of sampling is considered as a chi squared distribution when the null hypothesis is found to be true. There are two types of this test namely the chi-square goodness of fit test and chi-square test for independence. The former type tests a data whether it matches the population while the latter assess two variables using a contingency table testing if a relation is present.

Where does the normal line to the parabola, given below, at the given point, intersect the parabola a second time? illustrate with a sketch. (round the answers to three decimal places.) y = 4 x - 2 x^ 2 p = (2, 0)?

Answers

The graph of the parabola when sketched is shown in the picture illustrated as the blue curve. If you want to find the normal line to the parabola at point (2,0), you want to find the line perpendicular to the curve at that certain point. Note that two equations are perpendicular to each other when the product of their slopes is equal to -1. With that, let's find the slope of the parabola at point (2,0). The slope can be determined by finding the first derivative of the equation and substituting the x-coordinate of the point.

y' = 4 - 4x = 4-4(2) = -4
Thus, the slope of the normal line is 1/4 (negative reciprocal of -4). Its equation would be y = 1/4 x + b. To find b (y-intercept), substitute the coordinates of point (2,0):

0 = 1/4 (2) + b
b = -0.5

Therefore, the equation of the normal line is y = 1/4 x - 0.5. This is illustrated as the orange line in the picture.

I am confused about this question in trigonometry:

Answers

use AE and CE to find the angle

AE = 20, CE = 6

so the angle FOR CAE = tan^-1(6/20) = 16.7 degrees

to Find DF

a^2 = b^2 +c^2-2abcos(A)

a^2 = 10^2 + 14^2 -2(14)(10)cos(16.7)

a^2 = 30

sqrt((30)=5.47 rounded to 5.5

EF =

a^2 = b^2 +c^2-2abcos(A)

a^2 = 20^2 + 14^2 -2(14)(20)cos(16.7)

a^2 = 64

sqrt(64)=8

write the square root of 23 in exponential form

Answers

[tex]\sqrt[n]{x^m}=x^\frac{m}{n}[/tex]
so
[tex]\sqrt{23}=\sqrt[2]{23^1}=23^\frac{1}{2}[/tex]

The answer is 23 to the power of 1/2.

The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?

Answers

multiply 4 by the cos(45)

4 x cos(45) = 2sqrt(2) approximately 2.828cm

so depending how you are supposed to answer, either 2 sqrt(2) or approximately 2.83 cm

parallel lines r and s are cut by two transversals, parallel lines t and u

Answers

its not c or d for sure

i believe it is b

its a <5 and <13 that is the right answer

Karen is trying to determine how long her 4-year-old daughter should sit in time-out for deliberately pouring her juice on the floor. if she uses the suggested estimate, her daughter will be in time-out for:

Answers

A good rule of thumb is one minute per year of your child's age. So Karen’s child is 4 years old, she would get four minutes of time-out. If you find that the shorter time-outs aren't having the wanted result, increase the length by half the time (so your 4-year-old would get an extra two minutes, for a total of six minutes).

Please help me to do this one

Answers

Answer is 4

1. Multiple 29 by both side to get N by itself

2. solve 29/7.25 on a calculator, because it's easier

3. answer is 4.

4. Check your answer. Plug in 4 to see if you get the same answer on both sides. You should get .138 aprox. on both side.

Answer is 4 cross multiply and divide

Has 320 yards of fencing to enclose a rectangular area. find the dimensions of the rectangle that maximize the enclosed area. what is the maximum area

Answers

The dimensions of the rectangle that maximize the enclosed area are L = 80 yards and W = 80 yards. The maximum area is A = 80 * 80 = 6400 square yards.

To find the dimensions of the rectangle that maximize the enclosed area using 320 yards of fencing, we'll use the concept of optimization. Let's solve it step by step:

Let's assume the length of the rectangle is L and the width is W.

Perimeter constraint:

The perimeter of the rectangle is given as 2L + 2W, which must equal 320 yards:

2L + 2W = 320

Simplify the perimeter equation:

Divide both sides by 2 to get:

L + W = 160

Express one variable in terms of the other:

Solve the equation for L:

L = 160 - W

Area equation:

The area of the rectangle is given by A = L * W.

Substitute the value of L from the previous step into the area equation:

A = (160 - W) * W

A = 160W - W^2

Maximize the area:

To find the maximum area, we need to maximize the function A = 160W - W^2. This is achieved when the derivative is zero.

Take the derivative of A with respect to W:

dA/dW = 160 - 2W

Set dA/dW = 0 and solve for W:

160 - 2W = 0

2W = 160

W = 80

Substitute the value of W back into the perimeter equation to find the corresponding value of L:

L = 160 - W = 160 - 80 = 80

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Final answer:

The optimization problem involves finding the dimensions of a rectangle to maximize its area using a fixed amount of fencing. The dimensions that maximize the area are both 80 yards, making the maximum area 6400 square yards.

Explanation:

The subject of this question is Mathematics, specifically a problem about optimization in the field of Calculus. In the given problem, we wish to find a rectangular area that can be enclosed by 320 yards of fencing that maximizes the area.

Let's designate the rectangular area's width and length as x and y respectively. The problem can now be rephrased. With the total length of fencing equal to 320 yards, you can express this as 2x + 2y = 320. Simplifying this equation, we get x + y = 160, or y = 160 - x.

The area of a rectangle is computed as width times length, or in this case, x(160 - x). This is a quadratic function, and its maximum value happens at the vertex of the parabola defined by this function. For a quadratic in standard form like y = ax^2 + bx + c, the x-coordinate of the vertex is at -b/2a. In this case, the maximum area happens when x = 160/2 = 80.

Substituting this value back into the equation for the rectangle's dimensions gives y = 160 - 80 = 80. So, the dimensions that maximize the area for a rectangle with a parameter of 320 yards are both 80 yards. Therefore, the maximum area possible is 80*80 = 6400 square yards.

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A country population in 1991 was 231 million in 1999 it was 233 million . Estimate the population in 2003 using the exponential growth formula. Round you answer to the nearest million

Answers

p(y)=ir^t

233=231r^(1999-1991)

(233/231)^(1/8)=r

p(y)=231(233/231)^((y-1991)/8) so in 2003

p(2003)=231(233/231)^((2003-1991)/8)

p(2003)=231(233/231)^(1.5)

p(2003)=234

So 234 million (to the nearest million people)

Answer:

population in 2003 is 234 million.

Step-by-step explanation:

A country's population in 1991 was 231 million

In 1999 it was 233 million.

We have to calculate the population in 2003.

Since population growth is always represented by exponential function.

It is represented by [tex]P(t)=P_{0}e^{kt}[/tex]

Here t is time in years, k is the growth constant, and is initial population.

For year 1991 ⇒

233 = [tex]P_{0}e^{8k}[/tex] = 231 [tex]e^{8k}[/tex]

[tex]\frac{231}{233}= e^{8k}[/tex]

Taking ln on both the sides ⇒

[tex]ln(\frac{233}{231})=lne^{8k}[/tex]

ln 233 - ln 231 = 8k [since ln e = 1 ]

5.451 - 5.4424 = 8k

k = [tex]\frac{0.0086}{8}=0.001075[/tex]

For year 2003 ⇒

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

P (t) = 231 × [tex]e^{(0.001075)(12)}[/tex]

= 231 × [tex]e^{0.0129}[/tex]

= 231 × 1.0129

= 233.9 ≈ 234 million

Therefore, population in 2003 is 234 million.

In triangle DEF, DG = 10 cm. What is CG?

Answers

The answer is CG=5 CM

Answer:

5 cm is the correct answer it would be half of DG

Step-by-step explanation:

Can you check my work please!! And don't joke about it! Thanks

Answers

1. 86
2. 44
3. 50
4. 86
5. 44
6. 50
7. 130
8. 50
9. 130
10. 50
11. 86
12. 94
13. 86
14. 94

Remember that the triangle's inner angles should equal 180 for angle 8 and that angles that form a straight line add to 180 as well.
If you would like an explanation for any of these, please comment down below.

Simplify the expression: -3(4a-5b)

Answers

−3(4a−5b)=(−3)(4a+−5b)=(−3)(4a)+(−3)(−5b)=−12a+15b

Solve △ABC if B=120°, a=10, c=18

Answers

[tex]b= \sqrt{a^2+c^2-2ac*cosB} = \sqrt{10^2+18^2-2*10*18*(-0.5)} = \\ = \sqrt{100+324+180}= \sqrt{604} \approx 24.58 \ units \\ \\ \\ \frac{b}{sinB} =\frac{a}{sinA} \ \ \to sinA= \frac{a*sinB}{b}= \frac{10*0.866}{24.58} \approx 0.3523 \ \to \ \angle{A} \approx 20.63^o \\ \\ \\ \angle{C}=180-120-20.63=39.37^o \\ \\ \\ Area= \frac{1}{2}ch \\ \\ h=a*sinB=10*sin120^o=10* 0.866=8.66 \ units \\ \\ Area= \frac{1}{2}*18*8.66=77.94 \ units^2[/tex]

Joe gave the following argument: Since lim x→0 0 = 0,
(A) and since 0 = −1 x + 1 x ,
(B) we know that lim x→0 ( −1 x + 1 x ) = 0.
(C) But then, since lim x→0 ( −1 x + 1 x ) = lim x→0 ( −1 x ) + lim x→0 ( 1 x ),
(D) we can say that lim x→0 ( −1 x ) + lim x→0 ( 1 x ) = 0, which means that lim x→0 ( −1 x ) = − lim x→0 ( 1 x ).
(E) no error
In which line, if any, has joe made an error?

Answers

No error - A and B are completely right, and using the subtraction law D is right

A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function? graph of function t of x is a curve which joins the ordered pair 0, 1 and 1, 3 and 3, 27. Graph of function p of x is a curve which joins the ordered pair 0, 2 and 1, 3 and 3, 11 and 5, 27 and 6, 38

Answers

Using the given points, I was able to graph the functions t(x) and p(x) as shown in the picture. The difference between a quadratic function and an exponential is the degree of the equation. The quadratic equation has a degree of 2 while that of an exponential function is a degree raised to a variable. For better illustration, I would provide examples:

Quadratic equation: y = 2x²+5
Exponential equation: y = 2³ˣ

If you would test it quantitatively the rate of change, or the slope, between points is greater for exponential than quadratic equations. Because a slight increase in x, will cause an exponential rise, To you observe visually if the slope is greater if the curve is closer to a vertical line. From the picture, we can see that the blue curve has a greater slope. Therefore, the exponential function is t(x).

Final answer:

The function t(x) with ordered pairs (0, 1), (1, 3), and (3, 27) most likely represents the exponential function because it shows rapidly increasing growth rates, which is a defining feature of exponential behavior.

Explanation:

The function that most likely represents the exponential function is the one whose growth rate increases significantly for larger values of x. Examining the ordered pairs, the function t(x), which passes through the points (0, 1), (1, 3), and (3, 27), clearly demonstrates this behavior as the increase between the y-values gets dramatically larger as x increases.

This is a classic characteristic of exponential growth. In contrast, the function p(x) that passes through (0, 2), (1, 3), (3, 11), (5, 27), and (6, 38) shows a more consistent increase in y-values as x increases, indicative of a quadratic function.

The volumes of two similar figures 27mm^3 and 1331mm^3. If the surface area of the smaller figure is 18mm^2, what is the surface area of the larger figure

Answers

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{small}{large}\qquad \cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\qquad thus\qquad \cfrac{\sqrt[3]{27}}{\sqrt[3]{1331}}=\cfrac{\sqrt{18}}{\sqrt{a}} \\\\\\ \cfrac{3}{11}=\sqrt{\cfrac{18}{a}}\implies \left( \cfrac{3}{11} \right)^2=\cfrac{18}{a}\implies \cfrac{3^2}{11^2}=\cfrac{18}{a}\implies a=\cfrac{11^2\cdot 18}{3^2}[/tex]

and surely, you know how much that is.

Find the difference- (ab+3a+7)- (-5ab-2)

Answers

(ab+3a+7)- (-5ab-2)
=ab+ 3a+ 7+ 5ab + 2
=3a + 6ab + 9

what is 15 square root to the nearest tenth

Answers

mathematically the answer would be a never ending decimal (3.87298...) but in this case it would be 3.9

What is the equation of the line perpendicular to 5x − 2y = −18 that contains the point (10, 4)?

y=-2/5x
y=-2/5x+8
y=-5/2x+29
y=5/2x-29

Answers

To find the slope of the line perpendicular to 5x-2y=-18. I would suggest changing the equation to point slope form or y=(5x/2)+9. The slope of the line perpendicular is the negative reciprocal. To find the reciprocal flip the slope of 5/2 to 2/5 and add a negative sign to -2/5. Now to find the constant of the equation solve the point slope form of y-4=-2/5(x-10) this simlifies to y=-2/5x+8. Your answer is the y=-2/5x+8.

Write the total population of india and china.estimate the total population by rounding off each population to nearest 100000

Answers

As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of China is 1,388,979,446.

China’s population is equivalent to 18.47% of the total world population.

18.47% of the total world population is composed by China’s population.

China is ranked number 1 in the list of countries by population.

Rounding that number off to the nearest 100,000, it would be 1,388,980,000.

As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of India is 1,344,431,890.

17.86% of the total world population is composed by India’s population.

India is ranked number 2 in the list of countries by population.

Rounding that number off to the nearest 100,000, it would be 1,344,400,000.

I'm having trouble finding the answer to this question

Answers

I believe ABC is 125 degrees.

Those two angles are supplementary, so they add up to 180 degrees
180-55=125

17. Evaluate. Show your work.
a. 6!

b. 6P5

c. 12C3

Answers

[tex]6!=1\cdot2\cdot3\cdot4\cdot5\cdot6=720\\\\ 6P5=\dfrac{6!}{1!}=6!=720\\\\ 12C3=\dfrac{12!}{3!9!}=\dfrac{10\cdot11\cdot12}{2\cdot3}=220[/tex]

Rita made $221 for 17 hours of work.At the same rate, how much would she make for 12
hours of work?

Answers

$221 / 17 = $13

$13 per hour

so if 12 hours then 12 x $13 = $156

answer

$156

Using the concept of proportion, Rita would make $156 for 12 hours of work at the same rate.

We have,

We can use proportions to solve this problem.

Let x be the amount of money Rita would make for 12 hours of work.

We know that Rita made $221 for 17 hours of work,

which can be written as:

221/17 = x/12

To solve for x, we can cross-multiply and simplify:

221(12) = 17x

2652 = 17x

x = 156

Therefore,

Rita would make $156 for 12 hours of work at the same rate.

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Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2

***PLEASE HELP**

Answers

Given that
[tex]a_{n+1}=-4a_{n+2}[/tex] and [tex]a_1=2[/tex]

For n = 0,
[tex]a_1=-4a_2 \\ \\ 2=-4a_2 \\ \\ \Rightarrow a_2=-\frac{1}{2}[/tex]

common ratio = [tex]\frac{a_2}{a_1}=\frac{-\frac{1}{2}}{2}=-\frac{1}{4}[/tex]

4th term = [tex]a_4=a_1r^{4-1}=2(-\frac{1}{4})^3=2(-\frac{1}{64})=-\frac{1}{32}[/tex]

Can someone please help me with math for college readiness

Answers

6.79,7.729,31/4,7+5/6

it is best to start by converting all to decimals. so 7 5/6= 7.8333 and 31/4=7.75
o in order of least to greatest it is 6.79, 7.729, 31/4, 7 5/6.

Suppose you are thinking about buying one of two cars. Car A will cost $17,655. You can expect to pay an average of $1230 per year for fuel, maintenance and repairs. Car B will cost about $15,900. Fuel maintenance and repairs for it will average about $1425 per year. After how many years are the total costs for the cars the same? a. 5 years c. 9 years b. 7 years d. 11 years

Answers

A=17655+1230y, B=15900+1425y

We wish to know when A=B so:

15900+1425y=17655+1230y subtract 15900 from both sides

1425y=1230y+1755 subtract 1230y from both sides

195y=1755 divide both sides by 195

y=9

So in 9 years both cars would cost the same.

After 9 years many years are the total costs for the cars the same.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

Given that:-

Car A will cost $17,655. You can expect to pay an average of $1230 per year for fuel, maintenance and repairs. Car B will cost about $15,900. Fuel maintenance and repairs for it will average about $1425 per year. After how many years are the total costs for the cars the same?

We can form two-equation for the total cost of the two cars:-

A = 17655 + 1230y,

B = 15900 + 1425y

We wish to know when the cost will become the same for both the cars.

A = B

15900 + 1425y = 17655 + 1230y

Now subtract 15900 from both sides

1425y = 1230y + 1755

Now subtract 1230y from both sides

195y = 1755

Now divide both sides by 195

y = 9 years

Therefore After 9 years, many years are the total costs for the cars the same.

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