A used electronics store pays $40 for each cell phone, spends $25 refurbishing the phone, and sells the refurbished phone to a customer for $100.

The ratio of kittens to puppies is [tex]\dfrac{16}{3}[/tex].

Given:

The number of puppies is 9.

The number of kittens is 48.

To find:

The ratio of kittens to puppies.

Explanation:

The ratio of kittens to puppies is the fraction of the number of kittens and the number of puppies. So,

[tex]\text{Ratio}=\dfrac{\text{Number of kittens}}{\text{Number of puppies}}[/tex]

[tex]\text{Ratio}=\dfrac{48}{9}[/tex]

[tex]\text{Ratio}=\dfrac{16}{3}[/tex]

Therefore, the ratio of kittens to puppies is [tex]\dfrac{16}{3}[/tex].

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Answer: Option D is the right answer. The practical domain of the function=all integers from 1 to 10, inclusive.

Step-by-step explanation:

Given function  f(r)=40r+26, where r is the number of rolls of nickels she gets.

as it is already mentioned that she can get up to 10 rolls of nickels.

Therefore domain of function contains r ≤10,such that r is a natural number.

i.e.Domain of f(r)=all integers from 1 to 10, inclusive.

Domain of a f(x) is a set of values of x which make function f(x) well defined.

// Solve equation [1] for the variable  x  
 

// Plug this in for variable  x  in equation [2]

// Plug this in for variable  x  in equation [3]

// Solve equation [2] for the variable  y  

// Plug this in for variable  y  in equation [3]

// Solve equation [3] for the variable  z  

// By now we know this much :

// Use the  y  and  z  values to solve for  x  
  x = -6(-2)-3(-1)-18 = -3 

Answer:

The ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]

Explanation:

The circumference of a circle is given by the formula \(C = \pi \times d\), where [tex]\(d\)[/tex] is the diameter.

For Circle P with a diameter of 20 feet, the circumference is:

[tex]\[ C_P = \pi \times 20 \][/tex]

For Circle Q with a diameter of 30 feet, the circumference is:

[tex]\[ C_Q = \pi \times 30 \][/tex]

To find the ratio of the circumferences of Circle P to Circle Q, we divide the circumference of Circle P by the circumference of Circle Q:

[tex]\[ \text{Ratio} = \frac{C_P}{C_Q} = \frac{\pi \times 20}{\pi \times 30} \][/tex]

[tex]\[ \text{Ratio} = \frac{20}{30} = \frac{2}{3} \][/tex]

So, the ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]

Answer:

56°F

Step-by-step explanation:

Given : The formula[tex]F = \frac{n}{4} + 37[/tex]estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute.

To Find: Use the formula to estimate the  temperature when n = 75 chirps/min.

Solution:

Formula : [tex]F = \frac{n}{4} + 37[/tex]

Where  F in degrees Fahrenheit when crickets chirp n times per minute.

Now we are supposed to substitute n = 75

So,  [tex]F = \frac{75}{4} + 37[/tex]

[tex]F = 55.75[/tex]

Hence  the  temperature is 56°F when n = 75 chirps/min.

We know that numbers with periodic decimals (there are decimals that repeat infinitely) can be written as a fraction of two integer numbers.

Here we have the number:

0.212121...

Where the decimals "21" are repeating decimals, and we want to write this as a fraction.

And we will find that the fraction form of this number is: 21/99

To find it, first let's define:

x = 0.212121...

Now we need to multiply this by 10^n, where n is the number of repeating decimals, here we have two (2 and 1) then n = 2.

Now we need to multiply:

x×10^2 = x×100 = (0.2121...)×100 = 21.212121...

Now we can subtract the original number so we get:

x×100 - x = x×99 = 21.212121... - 0.212121... = 21

Then we just found that:

x×99 = 21

Solving for x, we get:

x = 21/99 = 0.212121...

Then the fraction that we want to find is 21/99

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Final answer:

Leslie can find out which yogurt gives her more by converting pounds to ounces. A 2-pound container is equivalent to 32 ounces, which is more than the total of 30 ounces from five 6-ounce containers.

Explanation:

Comparing Yogurt Quantities

To determine which yogurt option provides more quantity, Leslie needs to convert the weights into the same units. This means converting pounds to ounces, or ounces to pounds. In this case, converting pounds to ounces is more straightforward because we deal with whole numbers.

There are 16 ounces in 1 pound, so a 2-pound container of yogurt is equivalent to 32 ounces (2 x 16 = 32). On the other hand, five 6-ounce containers of yogurt total 30 ounces (5 x 6 = 30). Therefore, the 2-pound container gives more yogurt since 32 ounces is more than 30 ounces.

Linear equations are algebraic equations which represents the value of variables. These equations have unique solutions or sometimes there may be a number of solutions. Linear equation may contain n number of variables.

Given:  

              [tex]\begin{aligned}\rm\:Total\: time\: taken\: by \:MR. Smith \: &= 6 hours\\\\\rm\:Speed\:while\:going &= 4 \:miles\:per\:hour.\\\\\rm\:Speed \:while\:coming\:back &= 2\: miles\:per \:hour \end[/tex]

Let time taken to walk out be [tex]x[/tex] and time taken to walk back be [tex]2x[/tex]. The total time taken will be the summation of [tex]x[/tex] and [tex]2x[/tex] .

                                  [tex]\begin{aligned}\rm\:Total\:time&= 6\:hours\\\\x+2x&= 6\: hours\\\\3x&=6\:hours\end[/tex]

Continuing further,

                                               [tex]x=\dfrac{6}{3}\:hours \\\\x=2\:hours[/tex]

Therefore it can be said that the time taken by Mr. Smith to reach the end of the trial is 2 hours.

It is also observed that the speed while coming back was half of the speed of walking out. So it can be said that the time taken to walk back was twice the time Mr. Smith took to reach the end of the trail.

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Answer:

The radius of cylinder is 8 inches.

Step-by-step explanation:

We have given,

Volume of cylinder = 320π   cubic inches

Height of cylinder = 5 inches

We know, Formula for volume of cylinder as : V =πr²h

where r is radius of cylinder and h is the height of cylinder.

So, We can plug values for V and h to get radius of cylinder.

i.e  V = πr²h

320π = πr²* 5

Solving for r.

We get,

320 = r² * 5

320/5 = r²

64 = r²

or r = ±8 , Since radius of cylinder can not a negative number so we neglect -8.

Hence the radius of cylinder is 8 inches.

Final answer:

Using the given approximation, the temperature at the Sun's core would be 46,800,000 degrees Celsius. However, scientific data indicates that the accurate temperature is 15 million degrees Celsius, due to nuclear fusion processes occurring at the core.

Explanation:

If the temperature halfway to the Sun from Mercury is approximately 1,800 Celsius and scientists theorize that it may be 26,000 times hotter at the center of the Sun, we can calculate the temperature at the center by multiplying 1,800 Celsius by 26,000. This gives us an estimated temperature of the sun's core at 46,800,000 degrees Celsius. However, according to scientific data, the temperature near the center of the Sun is thought to be around 15 million degrees Celsius (1.5 ×[tex]10^7[/tex] °C) or kelvin, which is much more accurate than the extrapolation from the original question.

Mercury's proximity to the Sun accounts for its high surface temperatures, but without a significant atmosphere, the temperatures fluctuate dramatically between day and night. At the Sun's core, however, the temperatures reach extremes due to nuclear fusion, which releases vast amounts of energy and maintains the central temperature around 15 million degrees Celsius.

Answer: The value of m∠ABC is 102° .

Step-by-step explanation:

Since we have given that

m CD = 128°

m DA = 76°

We need to find the m∠ABC, Angle subtended at the center is half of the sum of the measure of the arc intercepted by it.

[tex]\frac{m\ CD+m\ DA}{2}=\angle ABC\\\\\frac{128^\circ+76^\circ}{2}=\angle ABC\\\\102^\circ=m\angle ABC[/tex]

The value of m∠ABC is 102° .

The required equation is  C.) y−5 = 3/4(x−6)

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (6,5) and, (-2,-1)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y-5)/(x-6)=(-1-5)/(-2-6)

=>4y-20=3x-18

=>y-5=3/4(x-6)

Hence, the required equation is, C.) y−5 = 3/4(x−6)

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Step-by-step explan

I got it right on the test