A survey about phone service has a margin of error of 5%. Out of 150 people surveyed, 103 said that they were pleased with their service. The phone company has 72,000 customers. What is the range of the number of people that are satisfied?

A. 46,968 to 51,912 customers
B. 46,986 to 51,192 customers
C. 46,698 to 51,291 customers
D. 48,696 to 52,191 customers

42.9

"74% of 58" translates to ...

... 74/100 × 58 = 42.92

Rounded to the nearest tenth, this is 42.9.

_____

Comment on translation

In this context, "of" means "times." Of course, % means /100, so ...

... 74% = 74/100 = 0.74

Answer:

A: 1 Minute

Step-by-step explanation:

Buses start running at 7 and run every eight minutes. This means that:

Bus 1: 7:00 AM

Bus 2: 7:08 AM

Bus 3: 7:16 AM

Bus 4: 7:24 AM

Bus 5: 7:32 AM

Bus 6: 7:40 AM

Bus 7: 7:48 AM

Bus 8: 7:56 AM

Bus 9: 8:04 AM

Bus 10: 8:12 AM

Bus 11: 8:20 AM

The waiting time of the bus is 7 minutes,

To calculate the waiting time, we need to break down the time difference between your arrival (8:19 am) and the next bus arrival (scheduled to come every 8 minutes). Let's start by determining the time between 8:19 am and the next scheduled bus at 8:20 am. This is only 1 minute of waiting time.

However, you want to know how long you'll have to wait until the next bus after 8:20 am, which means we need to consider the remaining time until the next 8-minute interval. From 8:20 am to 8:24 am, the bus does not arrive yet, resulting in an additional 4 minutes of waiting time

=> (8:24 am - 8:20 am = 4 minutes).

Now, we have reached the second 8-minute interval from 8:24 am to 8:28 am. As you arrived at 8:19 am, you will have to wait for 5 more minutes

=> (8:28 am - 8:19 am = 7 minutes)

to catch the bus.

So, the Main Answer: c: 7 minutes.

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[tex]a,\ b-the\ length\ of\ sides\\\\(1)\qquad4a+4b=40\qquad\text{divide both sides by 4}\\\\a+b=10\to a=10-b\\\\(2)\qquad a^2+b^2=58\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\(10-b)^2+b^2=58\qquad\text{Use}\ (x-y)^2=x^2-2xy+y^2\\\\10^2-2(10)(b)+b^2+b^2=58\\\\100-20b+2b^2=58\qquad\text{subtract 58 from both sides}\\\\42-20b+2b^2=0\\\\2b^2-20b+42=0\qquad\text{divide both sides by 2}\\\\b^2-10b+21=0\\\\b^2-7b-3b+21=0\\\\b(b-7)-3(b-7)=0\\\\(b-7)(b-3)=0\iff b-7=0\ \vee\ b-3=0\\\\\boxed{b=7\ \vee\ b=3}[/tex]

[tex]\text{Put the values of b to }\ (1):\\\\for\ b=7\to a=10-7=3\\\\for\ b=3\to a=10-3=7\\\\Answer:\ \boxed{7cm\ and\ 3cm.}[/tex]

The sides of the squares will be 3 and 7.

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

Area of square = Side²

The perimeter of the square = 4× side

Length of diagonal of square = √(2) × side

Let's say the side of the first square is a while the second is b

Now,

the sum of the perimeter of two squares is 40cm

4a + 4b = 40

a + b = 10

Now,

The Sum of the area is 58cm²

So,

a² + b² = 58

By substituting,

a² + (10 - a)² = 58

a² - 10a + 21 = 0

a² - 7a - 3a + 21 =0

a(a - 7) - 3(a - 7) = 0

(a-3)(a - 7) = 0

a = 3 ,7

Corresponding to 3 and 7

b = 10 - 3 = 7 and b = 10 - 7 = 3.

Hence "The sides of the squares will be 3 and 7".

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Answer: C

Step-by-step explanation: The equation is y = x/7. For every 7 numbers that x increases, y increases by 1.

The population decreased 96.8%.

Initial value = 100,000

Final value = 3,200

The percentage decrease is

= (Final value - initial value) * 100% /initial value

= [tex]\frac{\left(3200-100000\right)}{100000}\cdot100 \%[/tex]

= −96.8%

Negative sign because of decrease.

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Answer:

37.50%

Step-by-step explanation:

Use the formula: Old Value minus New Value (in absolute value bars) divided by Old Value times 100

New Value = $25 / Old Value = $40

$40 - $25 =  $15

$15 divided by $40 is 0.375

0.375 times 100 (0.375 x 100) is 37.50

Answer:

5x+30-2x+9

Step-by-step explanation:

first you have to do the ''distributive property'' then you will get 5x+30-2x+9

Question

Write an expression equivalent to the one below

5(x + 6)-2x + 9

Answer:

Step-by-step explanation:

5(x + 6)-2x + 9 =

5x + 30 - 2x + 9 =

3x + 39

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

2x + 10 + 29 + x =

3x + 39

Answer:

percent error = 15%

Step-by-step explanation:

The following question is missing: What is the percent error?

percent error = (measure error/ actual weight)*100

where:

measure error = incorrect weight - correct weight  = 11.5 - 10 = 1.5 pounds

percent error = (1.5/10)*100 = 15%

Answer:

6.75

Step-by-step explanation:

1. You want to divide 47.25 by 7 because then you can see how much money you earned in one hour.

Answer: $6.75

Step-by-step explanation: In order to find per hour, you multiply 47.25 and 7 and get a answer of 6.75

Answer:

Step-by-step explanation:

the answer is

t=5c+35

t=10c

i just did this problem and got it right.

To represent the scenario of two training programs with different costs, we can use the equations t = c + 35 and t = 5c.

In this scenario, we have two different training programs at a pet store. The first program charges a $35 membership fee and $5 for each class.

The second program does not have a membership fee, but charges $10 for each class. We want to find out for how many classes the total cost will be the same for both programs.

To create the system of equations, we can use the variable c to represent the number of classes and t to represent the total cost. The equations that represent the scenario are:

t = c + 35

t = 5c

Answer:0.8 or 4/5

Step-by-step explanation:1/5 x 4 = 4/5

And to check your work  

4/5 / 4 = 1/5

Answer: 4/5

Step-by-step explanation: First you have to set up a multiplacation problem.

1/5 x 4 or 1/5 x 4/1 = 4/5

Answer:

Without math, how would we know how to count seconds minutes, etc.?

Math is extremely important for knowing how to do simple things like cooking, you need to know for how much time to put something in the oven or microwave or stove. Those are just the basics. There is a lot more stuff out there that math is used for.

If you want to get a job, you have to know about math. Without math, you will be unable to get a job. Every single job you can get requires math. Even working in a grocery store, you need math. Whether we like it or not, you will have to learn math or you'll end up homeless and without a job.

Leila needs to score 23 points in her next game to have an average of 27 points per game.

To find out how many points Leila needs to score in her next game in order to have an average of 27 points per game, we need to use the formula for finding an average. The sum of all the points scored is 33 + 28 + 24 + x (the points in the next game), and we divide this sum by the number of games, which is 4. So, the equation is (33 + 28 + 24 + x) / 4 = 27. To solve for x, we multiply both sides of the equation by 4 to get 33 + 28 + 24 + x = 27 * 4. Simplifying this gives us 85 + x = 108. To isolate x, we subtract 85 from both sides of the equation, which gives us x = 108 - 85. So, Leila needs to score 23 points in her next game to have an average of 27 points per game.

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Answer:

two tires for $35 -------------------------$70  total

three rims for $75---------------------------   $225

five headlights for $ 4.00  ----------------$20

Emma spends ($225+$70+$20) =$315

Now Emma sells them for 2 tires for $65 =130

3 rims for $136         =   $408

5 headlights for $15  = $75

total money Emma makes = $613.

the profit is $613- $315= $298

the profit is $298

Answer:

50 mi

Step-by-step explanation:

Two hours after leaving port,

The triangle formed by their tracks and the line joining their current positions is a right-angled triangle.

According to Pythagoras,

        a² + b² = c²

   30² + 40² = c²

900 + 1600 = c²

            2500 = c²

     √(2500) = c

                    c = 50 mi

The boats will be separated by 50 mi two hours after leaving port.

Answer: n=42

Step-by-step explanation: Lets suppose n is a number. Since the numbers are consecutive, they would be:

n

n+1

n+2

If the sum is 129, then an equation would be

n+n+1+n+2=129

3n=126

n=42

So, the smallest number would be 42

Answer:

The row with x = 2 and y = 4 is incorrect. The y value should be y = 3 when x = 2.

==============================================================

Explanation:

Fractions can be a bit of a pain, so I'm going to be converting to decimal form to help with the computation; however, I will convert the y value results to mix number form so that it matches what the table shows.

Keep in mind that 3/4 = 0.75 when you use a calculator or long division. So a number like 2.75 means 2 & 3/4 (two and three quarters)

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

Let's check the first row. Plug in x = 0 and it leads to...

y = (3/4)*x^2

y = (3/4)*0^2

y = (3/4)*0

y = 0.75*0

y = 0

This shows us that row 1 is correct. When x = 0, y = 0 leading to (x,y) = (0,0).

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

Repeat the same basic outline of steps, but now use x = 2

y = (3/4)*x^2

y = (3/4)*2^2

y = (3/4)*4

y = 0.75*4

y = 3

So instead of 4, the proper y value is y = 3 when x = 2. This means row 2 is the answer (the row that has the incorrect values).

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

For the sake of completeness, let's see if the third row is correct or not. Plug in x = 3

y = (3/4)*x^2

y = (3/4)*3^2

y = (3/4)*9

y = 0.75*9

y = 6.75

y = 6 & 3/4

We see that x = 3 points to y = 6 & 3/4, so we have the correct values in this row. We can cross this off the list of choices.

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

Finally, let's check x = 5

y = (3/4)*x^2

y = (3/4)*5^2

y = (3/4)*25

y = 0.75*25

y = 18.75

y = 18 & 3/4

We get the proper y value. So we can also cross this off the list.

Answer:

slope is -4 or in a fraction, -4/1

Step-by-step explanation:

When you have 2 points, you can find the slope by subtracting them by each other. You must do 8 - 0 which is 8, then -2 - 0 which is -2. Then you get 8/-2. Once simplified, you get -4, and you know if the number is alone, there is always a 1 under it so you get -4/1.

Hello!

Step-by-step explanation:

[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{8-0}{(-2)-0}=\frac{8}{-2}=-4[/tex]

Slope is -4

Final answer is -4

*The answer must have a negative sign.*

I hope this helps you!

Have a nice day! :)

-Charlie

:D

The water used will be greater than 1600000 thousands of gallons for the fixed amount to be less expensive.

The users can either pay 77 cents per thousand gallons, or pay a fixed amount of $1,232,000 for unlimited water usage for one year.

Therefore,

77 cents = 0.77 dollars

Hence,

The user can pay 0.77 per thousand gallons.

He can pay a fixed amount of $1,232,000 .

Therefore, the amount of water the company will use for the fixed amount to be less expensive is as follows;

let

x = amount of water use in thousand gallons

Using inequalities,

0.77x ≥ 1,232,000

x ≥ 1,232,000 / 0.77

x ≥ 1600000

Therefore, the water used will be greater than 1600000 thousands of gallons for the fixed amount to be less expensive.

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Answer:

5.) Proportionality is 3/1 or 3 simplified

6.) Proportionality is 1/6

Step-by-step explanation:

You would take the first column (or in this case row (pens and packs) and place the 2nd row under it in fraction form.

That would be your proportion

Then you would (in place of numbers) use letters to symbolize in the equation

Then create an equation to figure out how to get the correct numbers.

Answer:

Domain: all real numbers

Step-by-step explanation:

The domain of a function is the set of values that x can be replaced with.

In this function, x can be replaced by any real number, so the domain of the function is all real numbers.

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

The first thing we need to do is to define the domain of a function.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers.

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The problem requires setting up a system of two equations: one representing the total number of tickets sold (c + a = 150) and the other representing the total revenue from ticket sales (7.75c + 10.25a = 1470). Solving this system will yield the number of adult and child tickets sold.

To determine how many adult tickets, a, and child tickets, c, were sold by the Grand Prix Cinema, we need to establish a system of equations based on the given information:

These two equations can be used simultaneously to solve for the variables a (adult tickets) and c (child tickets). This problem is an example of a linear system of equations that can be solved by various methods such as substitution, elimination, or matrix operations.

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[tex]p\%=\dfrac{p}{100}\\\\40\%=\dfrac{40}{100}=\dfrac{4}{10}=0.4;\ 60\%=\dfrac{60}{100}=\dfrac{6}{10}=0.6;\ 55\%=\dfrac{55}{100}=0.55\\\\\left\{\begin{array}{ccc}x+y=5&\to x=5-y\\0.4x+0.6y=0.55\cdot5\end{array}\right\\\\\text{Use substitution method}\\\\0.4(5-y)+0.6y=2.75\qquad\text{use distributive property}\\\\(0.4)(5)+(0.4)(-y)+0.6y=2.75\\\\2-0.4y+0.6y=2.75\qquad\text{subtract 2 from both sides}\\\\0.2y=0.75\qquad\text{multiply both sides by 5}\\\\\boxed{y=3.75}[/tex]

[tex]\text{Put the value of y to the first equation}\\\\x=5-3.75\\\\\boxed{x=1.25}\\\\Answer:\ x=1.25\ and\ y=3.75.[/tex]

Answer:

[tex]6<x<8.[/tex]

Step-by-step explanation:

The sides MN, NP and MP of the triangle MNP should satisfy inequalities:

Then

[tex]\left\{\begin{array}{l}4x+9+x+5>7x-20\\4x+9+7x-20>x+5\\x+5+7x-20>4x+9\end{array}\right..[/tex]

Simplify this system:

[tex]\left\{\begin{array}{l}4x+x-7x>-9-5-20\\4x+7x-x>20-9+5\\x+7x-4x>20-5+9\end{array}\right.\Rightarrow \left\{\begin{array}{l}-2x>-16\\10x>16\\4x>24\end{array}\right.\Rightarrow \left\{\begin{array}{l}x<8\\x>1.6\\x>6\end{array}\right..[/tex]

Thus, the range of possible values for x is [tex]6<x<8.[/tex]

The question, from high school Mathematics related to geometry and algebra, asks to find the possible values for x using the triangle inequality theorem. These inequalities when solved gives the required range for x.

The subject of this question is Mathematics, specifically pertaining to geometry and algebra. This question asks to find the range of possible values for x given that the sides of triangle MNP are MN= 4x+9, NP= x+5, MP= 7x-20.

Firstly, we utilize the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. With this theorem, we can set up three inequalities:

Solving these inequalities will provide the range of possible values for x.

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Answer:

the answer is 10

Step-by-step explanation:

if b is congruent to e

(which it is)

e=50 degrees

50/5=10

x=10

The value of x is 50 degrees.

In the given question, if ABC is congruent to DEC and angle B is 50 degrees, we want to find the value of angle E.

Since ABC and DEC are congruent, their corresponding angles are equal.

Therefore, angle E will also be equal to angle B, which is 50 degrees.

So, x = 50 degrees.

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Answer:

C) y=3x+2

Step-by-step explanation:

Looking at the graph, we can see the y intercept is at 2.

All of the answers are in the form y = mx +b

where b is the y intercept

y = mx+2

The only answer that has the y intercept of 2 is y = 3x+2

Answer:

x = 2.696, x = -0.696

Step-by-step explanation:

We are given the following function of x and we are to find the zeros for the given quadratic function:

[tex]f(x)= 8x^2-16x-15[/tex]

To find its zeros, we will use the quadratic formula:

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

Substituting the values in the formula where [tex]a=8[/tex], [tex]b=-16[/tex] and [tex]c=-15[/tex].

[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4(8)(-15)} }{2(8)}[/tex]

[tex]x=\frac{16+-\sqrt{736} }{16}[/tex]

[tex]x=\frac{16+27.13}{16}[/tex] , [tex]x=\frac{16-27.13}{16}[/tex]

[tex]x = 2.696[/tex] , [tex]x=-0.696[/tex]

Therefore, the solutions are 2.696 and -0.696.

Answer: c on edge

Step-by-step explanation:

x=1-square root 23/8 and x=1+square root 7

For both questions, you essentially use the equation r = d/t

a. 34/7 = about 4.86 dollars per hour

b. 4/10 = 0.40 dollars per pound.