Is the following number rational or irrational? π/2

Answer:

2.5 , 3.5

Step-by-step explanation:

Midpoint = (x1+x2)/2 , (y1+y2)/2

(3+2)/2 , (5+2)/2

5/2 , 7/2

2.5 , 3.5

The given equations: 5(x - 2) = 5x - 7, - 3(x - 4) = - 3x + 12, 4(x + 1) = 3x + 4, 2(x - 3) = 2x - 6, 6(x + 5) = 6x + 11, have no solution, infinitely many solutions, one solution, one solution, and no solution respectively.

"An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign."

Given equations are:

1. 5(x - 2) = 5x - 7

⇒ 5x - 10 = 5x - 7

Therefore, this equation has no solution.

2. - 3(x - 4) = - 3x + 12

⇒ - 3x + 12 = - 3x + 12

Therefore, this equation has infinitely many solutions.

3. 4(x + 1) = 3x + 4

⇒ 4x + 4 = 3x + 4

⇒ x = 0

Therefore, this equation has only one solution.

4. - 2(x - 3) = 2x - 6

⇒ - 2x + 6 = 2x - 6

⇒ 4x = 12

⇒ x = 3

Therefore, this equation has only one solution.

5. 6(x + 5) = 6x + 11

⇒ 6x + 30 = 6x + 11

Therefore, this equation has no solution.

Learn more about an equation here: https://brainly.com/question/12283977

#SPJ3

Answer:

Given equations are:1. 5(x - 2) = 5x - 7⇒ 5x - 10 = 5x - 7Therefore, this equation has no solution.2. - 3(x - 4) = - 3x + 12⇒ - 3x + 12 = - 3x + 12Therefore, this equation has infinitely many solutions.3. 4(x + 1) = 3x + 4⇒ 4x + 4 = 3x + 4⇒ x = 0Therefore, this equation has only one solution.4. - 2(x - 3) = 2x - 6⇒ - 2x + 6 = 2x - 6⇒ 4x = 12⇒ x = 3Therefore, this equation has only one solution.5. 6(x + 5) = 6x + 11⇒ 6x + 30 = 6x + 11Therefore, this equation has no solution.

Step-by-step explanation:

Answer:

please see the attached picture for full solution...

Hope this helps...

Good luck on your assignment..

Step-by-step explanation:

Hi, your question isn't totally complete. Here's the likely full question:

Random walk. A Java programmer begins walking aimlessly. At each time step, she takes one step in a random direction (either north, east, south, or west), each with probability 25%. She stops once she is at Manhattan distance r from the starting point. How many steps will the random walker take? This process is known as a two-dimensional random walk.

Write a program RandomWalker.java that takes an integer command-line argument r and simulates the motion of a random walk until the random walker is at Manhattan distance r from the starting point. Print the coordinates at each step of the walk (including the starting and ending points), treating the starting point as (0, 0). Also, print the total number of steps taken.

Answer:

8s^3

Step-by-step explanation:

In the question it says, triple the product which typically means triple using exponents. It is asking for you to do 8s x 8s x 8s or 8s to the power of 3

Answer:

[tex]3x + 6y = 1200[/tex] is the correct linear equation.

Step-by-step explanation:

Given:

Time taken to manufacture an office chair = 3 hours

Number of office chairs produced = [tex]x[/tex]

Time taken to manufacture an office desk = 6 hours

Number of office desks produced = [tex]y[/tex]

Let us calculate, Total Time taken to manufacture [tex]x[/tex] chairs.

Suppose we manufacture 2 chairs, time taken = 3 hours + 3 hours i.e. = 6 hours

Suppose we manufacture 3 chairs, time taken = 3 hours + 3 hours + 3 hours i.e. = 9 hours

Now, we are manufacturing [tex]x[/tex] number of chairs so we have to add 3 for [tex]x[/tex] number of times:

OR

simply multiply 3 with [tex]x[/tex].

i.e. Total time taken in producing [tex]x[/tex] chairs = 3[tex]x[/tex] hours

Similarly Total time taken in producing [tex]y[/tex] desks = 6[tex]y[/tex] hours

We have a total of 1200 hours to produce this type of office chairs and desks:

So, 1200 = Total time taken in producing [tex]x[/tex] chairs + Total time taken in producing [tex]y[/tex] desks

Putting the values, we get the following:

[tex]3x+6y=1200[/tex] is the correct linear equation for the situation.

Answer:

Step-by-step explanation:

Hello,

please consider the following

[tex]x^4+18x^2+81=(x^2)^2+2*(3^2)x^2+(3)^4\\\\=(x^2+9)^2[/tex]

hope this helps

Answer: The answer is shown in the picure

Answer:

[tex]sin(u) cot(u) cos(u) = cos^{2}(u)[/tex]

Step-by-step explanation:

[tex]sin(u) cot(u) cos(u)[/tex]

First, let us simplify cot(u) as follows:

cot (u) = [tex]\frac{1}{tan(u)}[/tex]

also, [tex]tan (u) = \frac{sin (u)}{cos(u)}[/tex]

∴ [tex]\frac{1}{tan(u)} = \frac{1}{\frac{sin(u)}{cos(u)} } = \frac{cos(u)}{sin(u)}[/tex]

Hence the original expression becomes:

[tex]sin(u).\frac{cos(u)}{sin(u)} .cos(u)[/tex]

Next, sin(u) will cancel each other out, leaving the expression below:

[tex]cos(u) . cos(u) = cos^{2} (u)[/tex]

hence:

[tex]sin(u) cot(u) cos(u) = cos^{2}(u)[/tex]

I also found a similar expression with a plus (+) sign after the "sin(u)" online, and if this was your question, the solution will be as follows:

sin(u)+ cot(u) cos(u)

[tex]sin(u) + \frac{cos(u)}{sin(u)} . cos (u)[/tex]

[tex]= sin(u) + \frac{cos^{2} (u)}{sin(u)}[/tex]

[tex]sin(u).\frac{sin(u)}{sin(u)} + \frac{cos^{2}(u) }{sin(u)} \\[/tex] (note that [tex]\frac{sin(u)}{sin(u)} = 1[/tex], hence multiplying it with sin(u) does not change anything in the expression.)

[tex]\frac{sin^{2} (u)}{sin(u)} + \frac{cos^{2}(u) }{sin(u)} = \frac{sin^{2}(u) + cos^{2}(u) }{sin(u)}[/tex]

Now the relationship sin²(u) + cos²(u) = 1

Therefore:

[tex]\frac{sin^{2}(u) + cos^{2}(u) }{sin(u)} = \frac{1}{sin(u)}[/tex]

Hence, [tex]sin(u)+ cot(u) cos(u) = \frac{1}{sin(u)}[/tex]

Answer:

Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion that support the candidate has significantly changed.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=800 has a proportion of p1=0.58.

[tex]p_1=X_1/n_1=460/800=0.58[/tex]

The sample 2, of size n2=1000 has a proportion of p2=0.52.

[tex]p_2=X_2/n_2=520/1000=0.52[/tex]

The difference between proportions is (p1-p2)=0.05.

[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]

As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

Answer:

first second third

Step-by-step explanation:

Answer:

A,B,C

Step-by-step explanation:

I took the course

Answer:

1

Step-by-step explanation:

All the numbers on the spinner are either even or odd so there is a 7/7 chance you get even or odd.

Answer:

to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]

The resulting function can be written as

[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]

Step-by-step explanation:

Hello,

f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0

and [tex]f(x)\geq 0[/tex]

so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]

and then we can write

[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]

hope this helps

Answer:

1/81.

Step-by-step explanation:

3^-4 = 1 /3^4

= 1/81.

Answer:internal

Step-by-step explanation:

Answer:

internal

Step-by-step explanation:

took  the test

Answer:

Hello, your answer is:

B. 3²×5

Step-by-step explanation:

Prime factorization of 45 is:

45 = 9 x 5

= 3²×5

Hope this helps you.. Good Luck

Answer:

B. 3² × 5

Step-by-step explanation:

45 can be written as a product of its prime factors.

45 = 3 × 3 × 5

45 = 3² × 5

Step-by-step explanation:

here,

C={ a,b,x,y}

D ={ m,n,o,p}

now,

C union D ={a,b,x,y} union {m,n,o,p}

= {a,b,x,y,m,n,o,p}

therefore C union D ={ a,b,x,y,m,n,o,p}

hope u get it...

Answer:

7

Step-by-step explanation:

1/7+1/3= 3/21+7/21= 10/21= 0.476190

the 6 digits after the decimal point get repeated

6*3= 18- three full cycles and the second digit after 3 cycles = 7 so the 20th digit is 7

This person was correct.

Answer:

7

Step-by-step explanation:

1/7+1/3= 3/21+7/21= 10/21= 0.476190

the 6 digits after the decimal point get repeated

6*3= 18- three full cycles and the second digit after 3 cycles = 7 so the 20th digit is 7

Answer: (a) The chart is in the first attachment named table frequency.

(b) The histogram is in the second attachment named frequency vs. enrollment

(c) Mode

(d) x = 9071.4

(e) s = 6677.64

(f) It is -0.16 standard deviation away

Step-by-step explanation:

(c) Mode is the number in the data set which appears more often. When thinking about builiding a new community college, if you choose mode will have which college enrollment will appear more often, i.e., which courses have more students wanting to enroll.

(d) To calculate sample mean of a frequency data:

1) Find the midpoint for each interval;

2) Multiply each midpoint for its correspondent frequency;

3) Sum up each multiplication obtained in the previous step;

4) Sum up all the frequencies;

5) Divide the sum in step 3 by the sum in step 4;

For this chart:

x = [tex]\frac{3000.10+7500.16+12500.3+17500.3+22500.1+27500.2}{35}[/tex]

x = 9071.4

(e) To find the standard deviation:

1) With each midpoint, calculate its square;

2) Multiply the midppoint square by its correspondent frequency;

3) Use the following formula to determine the sample standard:

s = √∑f.M²  - n(μ)² / n-1

For this chart:

s = [tex]\sqrt{\frac{4396250000 - 35*(9071.4)^{2}}{34} }[/tex]

s = 6677.64

(f) To find how many standard deviations away is the enrollment:

z = [tex]\frac{8000-9071.4}{6677.64}[/tex]

z = - 0.16

8000 enrollments are -0.16 standard deviations away from the mean.

Answer: 125 boys and 125 girls = 1:1

Step-by-step explanation:

An equivalent ratio means there will be an equal number of boys and girls.

Since there are 250 students,

Boys = 250/2 = 125

Girls = 250/2 = 125

The ratio of boys to girls = 125 : 125

                                              1   :   1     when simplified

Answer:

873116133

Step-by-step explanation:

18576939 × 47

Multiply the numbers.

= 873116133

Answer: 873116133

Step-by-step explanation:

‘Hope this helps:)

Answer:

Volume = 160 cm³   (Unit = cm³)

Step-by-step explanation:

Length = 4 cm

Width = 4 cm  (Because it's a square based cuboid!)

Height = 10 cm

Now, Volume:

Volume = [tex]Length * Width*Height[/tex]

Volume = 4 * 4 * 10

Volume = 160 cm³

Answer:

160 cm³

Step-by-step explanation:

The base is a square. The side length of the base is 4 cm.

The volume of a square-based cuboid is the area of square × height or length.

4² × 10

16 × 10

= 160

The volume of the square-based cuboid is 160 cm³.

Answer:

-21

Step-by-step explanation:

3×(-7) = - 21

Three times minus seven equals minus twenty one.

Answer:

Step-by-step explanation:

y = -7

3y = 3 * -7

   = (-21)

Answer:

x^2 +5x+6

----------------------

2x+5

Step-by-step explanation:

1

-----------------

1/(x+2) + 1/(x+3)

Multiply by ( x+2) * (x+3) in the numerator and denominator

1 * ( x+2) * (x+3)

-----------------

(1/(x+2) + 1/(x+3)) *( x+2) * (x+3)

Distribute

( x+2) * (x+3)

-----------------

((x+3) + (x+2))

Combine like terms

( x+2) * (x+3)

-----------------

2x+5

Foil the numerator

x^2 +2x+3x+6

---------------------

2x+5

Combine like terms

x^2 +5x+6

----------------------

2x+5

Answer:

B. [tex]\frac{x^2+5x+6}{2x+5}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{\frac{1}{x+2}+\frac{1}{x+3}}[/tex]

Add the fractions in the denominator.

[tex]\frac{1(x+3)}{\left(x+2\right)\left(x+3\right)}+\frac{1(x+2)}{\left(x+2\right)\left(x+3\right)}[/tex]

Denominators are equal, so combine.

[tex]\frac{x+3+x+2}{\left(x+2\right)\left(x+3\right)}[/tex]

Combine like terms.

[tex]\frac{2x+5}{\left(x+2\right)\left(x+3\right)}[/tex]

Back to the problem.

[tex]\displaystyle\frac{1}{\frac{2x+5}{\left(x+2\right)\left(x+3\right)}}[/tex]

Apply fraction rule 1/b/c = c/b

[tex]\frac{\left(x+2\right)\left(x+3\right)}{2x+5}[/tex]

Expand the brackets in the numerator.

[tex]\frac{x^2+5x+6}{2x+5}[/tex]

Answer:

116370.197$

Step-by-step explanation:

Jimmie invested $13,000 at 5.23% compounded monthly.

Jimmie's account balance (B) after 42 years:

B = principal x (1 + rate)^time

  = 13000 x (1 + (5.23/100)/12)^(42 x 12)

  = 116370.197$

Answer:

1/32

Step-by-step explanation:

Multiply the fractions together

1/8 * 1/4 = 1/32

1/32 are left handed glass wearers

Answer:

Experiment

Time..

Step-by-step explanation:

It is an experimental study. An experimental study is a type of study in which all conditions are under the control of the researcher.

The control factor in this case may includes the time...before measurements.

Here we must answer different things about the experiment that the farmer performed. We will see that this is an experiment and the controlled factors are:

What he did is divide his land in two equal parts, and then use different types of seeds in each one of the two parts.

After 3 months, he measures the height of the crops.

The questions are:

Is the study observational or experimental?

It is experimental, because the farmer assigned two areas and he decided what type of seed went into each area.

If it is an experiment, what are the controlled factor?

The controlled factors are the things that are the same for both of the groups of sections and that are relevant for the growth of the seeds. These things are:

If you want to learn more about experiments, you can read:

https://brainly.com/question/11256472

Hi! So, the one that doesn't belong is a) y = 4x.

I think that this doesn't belong because every other option has a number after the variable (I forget the exact term for it but it's like +7, +4, and -1 for the rest of the options)

Please let me know how I can further help you :)

(

Answer:

I think the answer is y = -2x + 4 because that is the only one that has a negative slope. The other choices all have positive slopes.

Answer:

This is correct! Great Job!

Answer:

width = 8 inches; length = 13 inches

Step-by-step explanation:

(x + 5)x = 104

x^2 + 5x - 104 = 0

(x - 8)(x + 13) = 0

x - 8 = 0 or x + 13 = 0

x = 8 or x = -13

Since the width of a rectangle cannot be a negative number, we discard the answer x = -13.

x = 8

The width is 8 inches.

The length is 8 + 5 = 13.

The length is 13 inches.

Answer:

0

Step-by-step explanation:

3 cards

P( odd) = 1 odd/ 3 cards = 1/3

No replacement

2 cards 6,8

No odds

P( odd) = 0/2

P( odd, no replacement, odd) = 1/2 * 0 = 0