Will mark brainliest, 60 points

Answer:

a

[tex]0.716 < p < 0.744[/tex]

b

[tex]0.3498 < p < 0.4089[/tex]

c

 With the result obtained from a and b the manager can be 95 % confidence that the proportion of the population that complained about dirty or ill-equipped bathrooms are within the interval obtained at  a

and that

the proportion of the population that complained about loud or distracting diners at other tables are within the interval obtained at  b

Step-by-step explanation:

From the question we are told that

The sample size is  [tex]n = 1003[/tex]

The number that complained about dirty or ill-equipped bathrooms is [tex]e = 732[/tex]

 The number that complained about loud or distracting diners at other tables is  [tex]q = 381[/tex]

Given that the the confidence level is  95% then the level of significance is mathematically represented as  

         [tex]\alpha = (100- 95)\%[/tex]

         [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is  

         [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Considering question a

The sample proportion is mathematically represented as

           [tex]\r p = \frac{e}{n}[/tex]

=>        [tex]\r p = \frac{732}{1003}[/tex]

=>        [tex]\r p = 0.73[/tex]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]

          [tex]E = 1.96* \sqrt{ \frac{ 0.73 (1- 0.73)}{1003} }[/tex]

          [tex]E = 0.01402[/tex]

The 95% confidence interval is  

        [tex]\r p - E < p < \r p +E[/tex]

        [tex]0.73 - 0.01402 < p < 0.73 + 0.01402[/tex]

        [tex]0.716 < p < 0.744[/tex]

Considering question b

The sample proportion is mathematically represented as

           [tex]\r p = \frac{q}{n}[/tex]

=>        [tex]\r p = \frac{381}{1003}[/tex]

=>        [tex]\r p = 0.3799[/tex]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]

          [tex]E = 1.96* \sqrt{ \frac{ 0.3799 (1- 0.3799)}{1003} }[/tex]

          [tex]E = 0.0300[/tex]

The 95% confidence interval is  

        [tex]\r p - E < p < \r p +E[/tex]

        [tex]0.3798 - 0.0300 < p < 0.3798 + 0.0300[/tex]

        [tex]0.3498 < p < 0.4089[/tex]

Answer:

Step-by-step explanation:

1. Subtract 9:

  -10 < n < 8

__

2. Add 12, then divide by 8:

  10 < 8x ≤ 48

  10/8 < x ≤ 6

  5/4 < x ≤ 6 . . . . . with the fraction reduced

_____

The rules of equality allow us the do these operations, provided that we do them to all parts of the compound inequality. That is, when we say "subtract 9", we mean ...

  -1 -9 < 9 +n -9 < 17 -9

This simplifies to the inequality we show above:

  -10 < n < 8

Answer:

700 Minutes

Step-by-step explanation:

For this problem, we need to write an expression that represents the cost per the amount of time used for each phone plan, and set the two expressions equal to each other to find how many minutes would be needed for the costs to be equal.

For the first phone plan, we have a base $28 and additional $0.09 per minute of call.  This can be expressed as:

28 + 0.09x                  Where x is the number of minutes used

For the second phone plan, we have a flat $0.13 per minute of call.  This can be expressed as:

0.13x                           Where x is the number of minutes used

To find how many minutes would be used to make the cost equal, we simply set these expressions as equivalent, and solve for x.

28 + 0.09x = 0.13x

28 + 0.09x + -0.09x = 0.13x + -0.09x

28 = 0.04x

28 = (1/25)x

28 * 25 = (1/25)x * 25

28 * 25 = x

700 = x

Thus, for the cost of these phone plans to be equal, you would have to use 700 minutes per month.

Cheers.

Answer:

Step-by-step explanation:

y= 0

x + 2(0) = 10

x = 10

(10, 0)

x = 0

0 + 2y = 10

2y = 10

y = 5

(0,5)

Answer:

Merlyn realizo 17,6 trucos de magia

Step-by-step explanatio:

Hizo 17,6 trucos de magia porque 22 dividido 5 es igual a 4,4 entonces despues haces 22 menos 4,4 da 17,6

Answer:

-13/30

Step-by-step explanation:

take 1/6 to other side,

x=-3/5 -1/6

taking LCM of denominators,

-8-5/30

=-13/30

Answer:

X=23/30

Step-by-step explanation:

X + 1/6 = -3/5

X + 5/30 = -18/30

-5/30 -5/30

X = -23/30

I feel like i did something wrong... but im pretty sure its right. Let me know if it's right! Hope it helps.

Answer: yes

Step-by-step explanation: 8^2+15^2=17^2 =289 and 17^2=289 ... 17 is the largest number so therefore its the largest side(c) .

equation- a+b=c

Answer:

A

Step-by-step explanation:

Add the number of decimal places of the two numbers being multiplied to know the number of decimal places of the product.

A: 3.48 x 42.37 = 147.4476

2 decimal places + 2 decimal places = 4 decimal places

Only choice A is correct.

Answer:

x = -7

Step-by-step explanation:

4x — 3 = —31

Add 3 to each side

4x — 3+3 = —31+3

4x = -28

Divide by 4

4x/4 = -28/4

x = -7

Your answer would be x=-7 or -7!

Answer:

Purchase Price = $150 and Total Price = $162

Step-by-step explanation:

Purchase price = Tax Amount / Tax Percentage (as decimal)

Purchase Price = $12 / .08

Purchase Price = $150

Total Price = Purchase Price + Tax

Total Price = 150 + 12 = $162

I hope this helps!

-The Business Man

Because if you substitute x = 4 and y = 1 in the equation of y = 3x + 1, you'll see that both sides are different.

So if we substitute x = 4 and y = 1 in the equation, we get:

1 = 3(4)+1

1 = 12+1

1 = 13

The equation isn't true though. Also we can explain why (4,1) isn't the solution to the equation by graph (you can go draw the graph of y = 3x + 1 and notice that the line doesn't pass through (4,1) )

Also how about another example? But this time, we use (0,1) which is the solution of y = 3x + 1.

Substitute x = 0 and y = 1 in the equation as we get:

1 = 3(0)+1

1 = 0 + 1

1 = 1

Since the equation is true, that means the (0,1) is one of the solution of y = 3x + 1.

Maybe, you want another example again? How about (1,4) which is also one of the solution of y = 3x + 1.

Again, substitute x = 1 and y = 4.

4 = 3(1)+1

4 = 3+1

4 = 4

Since the equation is true. Therefore (1,4) is also one of the solution of y = 3x + 1.

Also here's why (4,1) is not the solution of y = 3x + 1

Basically, from (x,y), 4 is the x and 1 is the y. If we substitute "x" in any equations, we get the "y". Meaning that the x value can be meant as "input" and we get the output "y" like Function which is it.

If we substitute x = 4 in the equation...

y = 3(4)+1

y = 12+1

y = 13

Meaning that the actual y value is 13, not 1. This explains why (4,1) isn't the right solution.

Maybe, what if we substitute y instead? Well that works. Now let's try substitute both y = 1 and y = 13 to see which is the right value.

(1) For y = 1,

1 = 3x+1

1-1=3x

0=3x

x=0 (Therefore, x = 0 and y = 1)

So the actual order is (0,1).

(2) For y = 13

13 = 3x+1

13-1 = 3x

3x = 12

x = 4 (Therefore, x = 4 and y = 13)

so the actual order for (2) is (4,13).

Basically, (4,1) is false for y = 3x + 1.

Answer:

See below

Step-by-step explanation:

Given the point (4,1) means

(x,y) = (4,1)

So, x = 4 , y = 1

Given the equation y = 3x+1

Put x = 4 and y = 1

=> 1 = 3(4)+1

=> 1 = 12 + 1

=> 1 ≠ 13

Since Left hand side doesn't equal right hand side, (4,1) is not the solution to y = 3x+1

Answer:

Option B. √x + 3

Step-by-step explanation:

f(x) = (x - 3)²

We can obtain the inverse f¯¹(x) of the above expression as follow:

f(x) = (x - 3)²

Replace f(x) with

f(x) = (x - 3)²

y = (x - 3)²

Next, interchange x and y

y = (x - 3)²

x = (y - 3)²

Make y the subject

x = (y - 3)²

Take the square root of both side

√x = y - 3

Add 3 to both side

√x + 3 = y - 3 +3

√x + 3 = y

y = √x + 3

Finally, replace y with f¯¹(x)

y = √x + 3

f¯¹(x) = √x + 3

Answer:

The answer is

Step-by-step explanation:

[tex] \frac{9x + 3}{12x + 4} [/tex]

To solve the rational expression factorize both the numerator and the denominator.

For the numerator

9x + 3

Factorize 3 out

We have

3( 3x + 1)

For the denominator

12x + 4

Factorize 4 out

That's

4( 3x + 1)

So we now have

Reduce the expression with (3x + 1)

We have the final answer as

Hope this helps you

Answer:

z=-75/17

Step-by-step explanation:

Expand this equation:

-4z+8+4=-21z-63

-4z+21z=-63-8-4

17z=-75

z=-75/17

Answer:

Step-by-step explanation:

Hello,

What other numbers are of this form have exactly four factors?

[tex]8=2^3\text{ has 4 factors } 1, 2, 2^2, 2^3\\\\\text{For any prime p, }p^3\text{ has 4 factors } 1, p, p^2, p^3\\\\[/tex]

Do all the perfect cubes have exactly four factors?

[tex]\text{If p is not prime, then it is not true anymore} \\ \\\text{For instance, }8^3\text{ has more than 4 factors } 1, 2^2, 2^3, 2^4, etc..[/tex]

Is it true that all numbers that have exactly four factors are perfect cubes?

6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.

Thank you.

We know that any number can be decomposed as a product of prime numbers.

For example:

[tex]8 = 1\cdot 2\cdot 2\cdot 2[/tex]

8 has four factors if we count the 1.

Now we need to answer some questions regarding this:

What other numbers are of this form have exactly four factors?

8 is a cube number.

Remember that all cube numbers X can be written as:

[tex]X = n\cdot n\cdot n \cdot 1[/tex]

Now, if n is prime, then we can say that X is of the form of 8 and also has 4 factors.

But let's see the case:

[tex]8\cdot 8\cdot8= 512[/tex]

512 is a perfect cube, and if we decompose it we get:

[tex]512 = 8\cdot 8\cdot 8 = (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot 1[/tex]

So we found a perfect cube that has 10 factors.

This means that not all perfect cubes have exactly 4 factors.

Now, all numbers that have exactly four factors are perfect cubes?

This is also false, just let's create a counterexample.

[tex]1\cdot 2\cdot 3\cdot 5 = 30[/tex]

the number 30 is not a perfect cube, and we can see that it has exactly 4 factors.

If you want to learn more, you can read:

https://brainly.com/question/832797

Answer:

She's 12 years old! i hope this helps you!

Step-by-step explanation:

Answer:

2,100.000

Step-by-step explanation:

Answer:

2000+100.000=2100

Its simple just calculate it in a calculator...

Step-by-step explanation:

Let's look at our expression:

[tex]1.7+8.23-3.4+4.7j[/tex]

The numbers without a variable at the end are like terms here. Let's add them up.

[tex]1.7+8.23=9.93\\9.93-3.4=6.53[/tex]

Then, let's add our answer, 6.53, to the term with a variable, 4.7j.

Our final answer: 6.53 + 4.7j

I hope this helps you!

Answer:

2x

Step-by-step explanation:

Since the tigers hit 2 times the number of x you would get that the tigers hit 2 times x or 2x balls

Answer:

2x.

hope it helps u...

plz mark as brainliest...

Answer:

yes it is

Step-by-step explanation:

Hope this helps✨

Answer: 50 students

Step-by-step explanation: Room D has 22 students, so room A has 28 (22+6). If room D has 22 students, then room C has 24 students (46-22). Room B has 22 students (26-2). In total, rooms A and B will have 50 students (28+22)

Answer:

Kindly check explanation and attached picture

Step-by-step explanation:

Given the time-series data:

Time (x) : 1 - - 2 - - 3 - - - 4 - - - 5

Data (yt) :6 - - 11 - - 9 - - 14 - - 15

The pattern which exists within the data is a linear pattern which could be inferred through the observable decrement and Incremental change in the y values at a steady or constant rate with time. The second attachment shows the linear trend line of the data.

Answer:

4%

Step-by-step explanation:

Since she first goes down 20% you would do 3000 times 20 which is 60000 and divided by 100 which is 600 and you would subtract 600 from 3000 which is 2400 and then you would multiply that by 30 which is 72000 and then you would divide by 100 which is 720 and add that to 2400 which is 3120 and to find the percent change from 3000 to 3120 you would subtract 3120 by 3000 which is 120 and you would divide that by 3000 which is 0.04 and multiply that by 100 which is 4 so the percent change would be 4%

Answer:

36

Step-by-step explanation:

Starting with 4, 9.

9 - 4 = 5 then + 2

So forward.

Answer:

1, 4, 9, 16, 25, 36

Step-by-step explanation:

This is because as you see 1 + 3 = 4, then 4 + 5 = 9, then 9 + 7 = 16. So we see that it goes like 3 + 5 + 7 + 9 + 11 + 13  . . .  That is the pattern. Hope this helps!

Answer:

7.5 seconds

Step-by-step explanation:

[tex]h = - 16 {t}^{2} + 120t \\ \because \: we \: have \: to \: find \: the \: time \: required \: \\ for \: the \: object \: to \: return to \: its \: \\ point \: of departure. \\ \therefore \: plug \: h = 0 \: in \: the \: given \: euation. \\ \therefore \: 0 = - 16 {t}^{2} + 120t \\ \therefore \:16 {t}^{2} - 120t = 0 \\ \therefore \:8t(2t - 15) = 0 \\ \therefore \:8t = 0 \: \: or \: \: (2t - 15) = 0 \\ \therefore \:t = \frac{0}{8} \: or \: t = \frac{15}{2} \\ \therefore \:t = 0 \: or \: t = 7.5 \\ \because \: t = 0 \: is \: not \: possible \\ \huge \purple{ \boxed{ \therefore \: t = 7.5 \: seconds}}[/tex]

Thus, the time required for the object to return to its point of departure is 7.5 seconds.

Answer:

It will take 5.4 hour to paint 720 square feet

Step-by-step explanation:

The question should be like this"Andy painted 400 square  feet in 3 hours. How long  would it take him to paint  720 square feet?"

In 3 hours = 400 square  feet is painted

1 square feet is painted in [tex]\dfrac{3}{400}\ h[/tex]

To find time to paint 720 square feet multiply the above term by 720 as follows :

[tex]720\ ft^2=\dfrac{3}{400}\times 720\ h\\\\=5.4\ h[/tex]

So, it will take 5.4 hour to paint 720 square feet.

Answer:

x-5

Step-by-step explanation:

x=5

cause of the negt 6x and posstive 3 =21 so yeah that it for now so go for it head froce