What is the greatest common factor
of 48 and 120?

Step-by-step explanation:

Science book weighs = 2 1/2 = 2.5 pounds

Library books weigh = 3/8 = 0.375 pounds

Math book weighs = 2.5 ÷ 2 = 1.25 pounds

Total weight of the books = 2.5 + 0.375 + 1.25 = 4.125 pounds

Answer:

1 and 5

Step-by-step explanation:

The squares have a side length of 10 and 1 square side is the radius of the half-circles. Since there are two half-circles, find the circumference for one full circle:

[tex]C=2\pi r[/tex]

Insert the radius:

[tex]r=10\\C=2\pi *10[/tex]

Simplify pi:

[tex]C=2*3.14*10[/tex]

Simplify multiplication:

[tex]C=6.28*10\\C=62.8[/tex]

The circumference of the circles is 62.8. Now find the perimeter of the exposed squares with side length 10. There are 4 exposed sides, which equals one square. Find the perimeter:

[tex]P=10+10+10+10\\P=10+10+20\\P=10+30\\P=40[/tex]

Add the perimeter of the circle and the square together:

[tex]P=62.8+40=102.8[/tex]

Now see which of the options gives you the perimeter:

1. [tex]40+20\pi =102.8[/tex]  ****

2. [tex]unavailable[/tex]

3. [tex]120+20\pi =182.8[/tex]

4. [tex]300+100\pi =614.2[/tex]

5. [tex]10+10+10\pi +10+10+10\pi =102.8[/tex] ****

Finito.

The expression . 40 + 20π and 10 + 10 + 10π + 10 + 10 + 10π gives the correct value of the perimeter is 102.8 .

We have to determine, the perimeter of the given shape in the question.

According to the question,

The squares have a side length of 10 and 1 square side is the radius of the half-circles.

There are two half-circles,

To find the circumference for one full circle:

[tex]C = 2\pi r[/tex]

Where radius = 10

[tex]C = 2\times 3.14 \times 10\\\\C = 62.8[/tex]

The circumference of the circles is 62.8.

To find the perimeter of the exposed squares with side length 10.

There are 4 exposed sides, which equals one square.

Therefore, perimeter p is given as,

[tex]P = 10+10+10+10\\\\P = 40[/tex]

On adding  the perimeter of the circle and the square together:

[tex]P = 62.8+ 40 = 102.8[/tex]

Check all the statement which give perimeter of the shape,

[tex]40+20\pi = 40+ 20\times3.14 = 102.8\\\\20\pi = 20 \times 3.14 = 62.8\\\\120+20\times \pi = 120+20\times3.14= 182.8\\\\300 + 100\times\pi = 300+100\times3.14 = 614\\ \\10+10+10\times\pi +10+10+10\times\pi = 40+ 20\times3.14 = 102.8[/tex]

Hence, The expression . 40 + 20π and 10 + 10 + 10π + 10 + 10 + 10π gives the correct value of the perimeter is 102.8 .

To know more about Perimeter click the link given below.

https://brainly.com/question/2589784

Answer:

the answer is A

Step-by-step explanation:

if you are really stuck just go through each possible answer to see if its right

here is some help for solving:

area is equal to length times width or   A = L x W

perimeter is equal to length plus width plus length plus width or L+W+L+W

perimeter is just adding up all the sides of the square or rectangle

so if you try with answer a you get:

2 x 6 = 12   and   2 + 6 + 2 + 6 = 16

the answer is A

Answer:

A = [tex]8\sqrt{110}[/tex] [tex]inches^{2}[/tex]

Step-by-step explanation:

In this question, we are tasked with calculating the area of a triangle given the length of its three sides

Mathematically, we can calculate this using the Heron's formula

For Heron's formula, A = [tex]\sqrt{S(S-A)(S-B)(S-C)}[/tex]

WHERE S = [tex]\frac{A+B+C}{2}[/tex]

we take the lengths of the triangle as A,B and C respectively as given

S = (12 + 14 + 18)/2 = 22

Plugging the values into the equation, we have;

A = [tex]\sqrt{22(22-12)(22-14)(22-18)}\\ \\\sqrt{22(10)(8)(4)} \\\\\sqrt{7040}[/tex]

A = [tex]8\sqrt{110}[/tex] [tex]inches^{2}[/tex]

Answer:

8*sqrt(110)

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

Compounded Semiannually: $17,574.89

Compounded Quarterly: $17,588.68

Compounded Monthly: $17,597.98

Compounded Continuously: $17,602.66

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 4% into a decimal:

4% -> [tex]\frac{4}{100}[/tex] -> 0.04

Now, plug in the values to the equation:

Compounded Semiannually:

[tex]A=15,000(1+\frac{0.04}{2})^{2(4)}[/tex]

[tex]A=17,574.89[/tex]

Compounded Quarterly:

[tex]A=15,000(1+\frac{0.04}{4})^{4(4)}[/tex]

[tex]A=17,588.68[/tex]

Compounded Monthly:

[tex]A=15,000(1+\frac{0.04}{12})^{12(4)}[/tex]

[tex]A=17,597.98[/tex]

To find the value if compounded continuously, use the following formula:

[tex]A = Pe^{rt}[/tex]

[tex]A=15,000e^{0.04(4)}[/tex]

[tex]A=17,602.66[/tex]

The accumulated value of an investment is calculated differently depending on the compounding period - semiannually, quarterly, monthly or continuously. This involves the compound interest formula and understanding of how interest rates work.

The subject of this question is about calculating the accumulated value of an investment at a given interest rate with various compounding periods i.e., semiannually, quarterly, monthly, and continuously. We first need to understand that compound interest is calculated on the principal plus the accumulated interest.

To calculate the future value of the investment, we use the compound interest formula: P*(1+r/n)^(nt), where P is the principal (or initial investment), r is the annual interest rate (in decimal form), n is the number of compounding periods per year, and t is the time in years.

https://brainly.com/question/34614903

#SPJ3

Answer:

4

Step-by-step explanation:

When M varies inversely P squared rhen this is represented as

[tex]M=\frac {k}{P^{2}}[/tex]

Here, k is a constant of proportionality

Now when M is 9 and P is 2, P squared will be 4. Now substituting the value of P squared and M into the equation we can find the xonstant of proportionality as

K=9*4=36

Now that we have k, when P is 3 then we substitute the value of P as 3 and k as 36 into the first equation hence

[tex]M=\frac {36}{3^{2}}=4[/tex]

Therefore, M=4

Answer:

money they will have saved for his 16th birthday = $18,926

Step-by-step explanation:

This is a geometric series problem.

The sum of a geometric series is given by the formula;

Sn = a1•(rⁿ - 1)/(r - 1)

Where;

a1 is the first term

n is the number of terms

r is the constant ratio

Now, in this question, they started saving since he was born till his 16th birthday. That's 16 years. Thus number of terms; n = 16

Also, the first money saved was $800, thus the first term; a1 = 800

They save 5% more each year than the previous year. That's an increase of 1.05 each year. Thus, the common ratio; r = 1.05

The amount of money they will have by his 16th birthday will be;

S_16 = 800•(1.05^(16) - 1)/(1.05 - 1)

S_16 = 800(1.18287458838/0.05)

S_16 = $18,926

S16 = $800·(1.05^16 -1)/(1.05 -1)

Answer:

15 feet

Step-by-step explanation:

1 yard = 3 feet

2 yards = 6 feet

3 yards = 9 feet

4 yards = 12 feet

5 yards = 15 feet

Answer:

15 feet.

Step-by-step explanation:

Hello there!

First calculate how many feet are in a yard, then multiply it by 5.

[tex]1*3=3\\3*5=15 ft[/tex]

;)

The simplified expression for the number of moons of Neptune, based on the variable for Mars' moons m, is 6m + 2, meaning Neptune has twice as many moons as Mars plus two more.

The student has asked to write and interpret a simplified expression that represents the number of moons of Neptune, based on the information that Mars has m moons, Pluto has one more than twice the number of moons of Mars, and Neptune has one less than three times the number of moons of Pluto.

Let's denote the number of moons of Mars as m. According to the information, Pluto has 2m + 1 moons. Therefore, Neptune would have 3(2m + 1) - 1 moons. Simplifying this expression:

Neptune's moons = 3(2m + 1) - 1

= 6m + 3 - 1

= 6m + 2

The simplified expression 6m + 2 represents the number of moons of Neptune, which means that Neptune has twice as many moons as Mars plus an additional two moons.

https://brainly.com/question/31374667

#SPJ2

Answer:

r=2.5%

Step-by-step explanation:

An exponential growth distribution is generally expressed as:

[tex]P_t=P_oe^{rt}[/tex]

where:

#Substitute the given values to solve for r:

[tex]P_{2010}=P_{1999}e^{(2010-1999)r}\\\\56780=43129e^{11r}\\\\1.31652=e^{11r}\\\\\\r=\frac{In \ 1.31652}{11}\\\\=0.024999\approx 2.5\%[/tex]

Hence, the rate of growth is approximately 2.5%

The population of Cirque City was growing exponentially at a rate of approximately 2.5% per year from 1999 to 2010.

To determine the exponential growth rate of the population in Cirque City, we will use the formula for exponential growth:

P(t) = P0 × [tex]e^{rt}[/tex]

Here, P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the time period. Given data: P0 = 43,129 (population in 1999), P(t) = 56,780 (population in 2010), and t = 11 years. Our goal is to find r.

Start with the formula and substitute the known values:

P(t) = 43,129 × [tex]e^{11r}[/tex] = 56,780

Isolate the exponential term:

[tex]e^{11r}[/tex] = 56,780 / 43,129

[tex]e^{11r}[/tex] ≈ 1.315

Take the natural logarithm (ln) of both sides to solve for r:

ln( [tex]e^{11r}[/tex]) = ln(1.315)

11r = ln(1.315)

r ≈ ln(1.315) / 11

Calculate the value:

r ≈ 0.025

Convert to a percentage:

r ≈ 2.5%

Therefore, the population of Cirque City was growing at an exponential rate of approximately 2.5% per year.

Answer:

the second one

Step-by-step explanation:

Option (b) represents the graph of r = 4 sin θ.

"A polar curve is a shape constructed using the polar coordinate system."

We have been given a function r = 4 sin θ .

We need to determine the graph for given function.

We know, r = a sin θ is a circle where “a” is the diameter of the circle that has its bottom-most edge at the pole (origin).

This means, r = 4 sin θ is a circle that has bottom-most edge at the origin (0, 0).

In the graph (b), a circle has bottom-most edge at the pole.

Therefore, the correct graph is option (b)

Learn more about polar graphs here:

https://brainly.com/question/19392344

#SPJ2

Answer:

Quentin made a total of 4 shots

Step-by-step explanation:

The complete question is as follows;

Quentin was challenged to a half-court shooting completion. For every half-court shot he makes, he will earn 20 points. For each half-court shot he misses, he will lose five points. After 20 half-court shots, Quentin has zero points. How many half-court shots did he make?

Now let's answer;

Let the number of shot he makes be x and the number of shot he misses be y

For every shot made, we have +20, for every shot missed, we have -5

Firstly we know that adding both numbers would give 20.

Mathematically;

x + y = 20        (i)

Now, we add the number of points he made to the number of points he missed to give a total of 0

Mathematically, that would be;

+20x -5y = 0  (ii)

from i, y = 20-x

Substitute this in ii

20x -5(20-x) = 0

20x - 100 + 5x = 0

25x = 100

x = 100/25

x = 4

This means that he made 4 shots

Answer:

2(e^2+6e+11) is the GCF

Answer:

Yes, it does

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

12*12=144

Answer:

C≈157.08ft

Solution

C=2πr=2·π·25≈157.07963ft

Answer:

157.0796327 is my answer

Answer:

65 quarts of water and 39 quarts of juice are required to make 104 quarts of banana berry smoothies

Step-by-step explanation:

Given:

Ratio of water and juice in banana berry smoothies = [tex]5:3[/tex]

To find:

Amount of water and juice required to make 104 quarts of banana berry smoothies

Solution:

Amount of water required to make 104 quarts of banana berry smoothies = [tex]\frac{5}{8}[/tex]×104 = 5×13 = 65 quarts

Amount of juice required to make 104 quarts of banana berry smoothies = [tex]\frac{3}{8}[/tex]×104 = 3×13 = 39 quarts

So,

65 quarts of water and 39 quarts of juice are required to make 104 quarts of banana berry smoothies.

To make 104 quarts of banana berry smoothies with a water to juice ratio of 5:3, Just Juice should mix 65 quarts of water with 39 quarts of juice.

To make banana berry smoothies with a mix of water and juice in a ratio of 5 to 3, and to create a total of 104 quarts, we need to find the amount of water and juice separately. Since the total parts of the ratio is 5 parts water plus 3 parts juice, which equals 8 parts, we can calculate the amount of each as follows:

Therefore, Just Juice should mix 65 quarts of water with 39 quarts of juice to make 104 quarts of banana berry smoothies.

Answer: its a ^

Step-by-step explanation:

y = 0.433x2 is the quadratic equation that best models the data in the graph. Therefore, the correct option is option A.

A second-order equation with the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real-number coefficients and a 0. Applications in the real world involve quadratic equations. For instance, if school administration decides to build a prayer hall with a floor size of 400 square metres.

A length that is two metres longer than its width, we will need the aid of a quadratic formula to determine the length and breadth. y = 0.433x2 is the quadratic equation that best models the data in the graph.

Therefore, the correct option is option A.

To know more about quadratic equation, here:

https://brainly.com/question/2279619

#SPJ3

Your question is incomplete but most probably your full question was,  

Which quadratic equation best models the data in the graph? y = 0.433x2 y = 2.31x2 y = (0.433x)2 y = (2.31x)2

Answer:

11.43 gallons used exactly per week asuming not changes in schedule or any other reasons to drive and that a one way trip is 24 miles.

Step-by-step explanation:

48 as total for two trips

five of these need to be done, so 240 miles a week assuming no other reason to drive

240 / 21 = 10 with remainder 30

so 11 and remainder 9

9/21 = nearly .43 gallons, which means as a minimum she shouldn't go below 11.5 and better yet 12 gallons.

Candace drives 240 miles each week (48 miles per day * 5 days). Given her car's fuel efficiency is 21 miles per gallon, she would therefore need approximately 11.43 gallons of gas (240 miles / 21 miles per gallon) for her weekly commute.

To answer the question of how many gallons of gas Candace needs to get to work and back home each week, you need to first know how many miles she is driving in total for that week.

First, let's find the total miles she drives weekly. We know she drives 48 miles each day to work and back home and she works 5 days a week. So, miles per week = 48 miles per day * 5 days per week = 240 miles per week.

Next, we know her car gets 21 miles per gallon of gas. To find the gallons required, we divide the weekly miles by the miles per gallon. So, Gallons used per week = 240 miles per week / 21 miles per gallon ≈ 11.43 gallons per week.

So, she needs approximately 11.43 gallons of gas to drive to work and back home each week.

https://brainly.com/question/16541056

#SPJ2

Answer:

The answer is x=10

Step-by-step explanation:

Answer:

the answer to the equation is x=10

Answer:

4quarters and 14dimes

Step-by-step explanation:

Answer:

Find the five number summary of the data:

Minimum = x

Quartile 1 = x

Quartile 2 (median) = x

Quartile 3 = x

Maximum = x

Then, make the plot based on that information. If you are provided with a list of data, you should be able to use a calculator to find out that information.

Final answer:

A box-and-whisker plot is graphed by organizing data, finding the five key data points (minimum, Q1, median, Q3, maximum), plotting a box from Q1 to Q3 with a median line, drawing whiskers to the minimum and maximum values, and indicating outliers if any.

Explanation:

To graph a box-and-whisker plot, start with organizing the data in ascending order and then identify the five key data points: the minimum value, the first quartile (Q1), the median (the second quartile or Q2), the third quartile (Q3), and the maximum value. Follow these steps:

Answer:

[tex]\sigma=547.1125[/tex]

Step-by-step explanation:

-The margin of error is calculated using the formula:

[tex]ME=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\\\[/tex]

-We substitute the values, n=900 and ME=30 in the formula to solve for standard deviation:

[tex]ME=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\\\\\30=1.645\times\frac{\sigma}{\sqrt{900}}\\\\\sigma=\frac{30^2}{1.645}\\\\=547.1125[/tex]

Hence, the population standard deviation is 547.1125

Answer: The difference between the mean cost to treat dogs at A New Leash on Life

Animal Clinic and the mean cost to treat cats at A New Leash on Life Animal

Clinic is about 10 times the MAD This is a large difference.

Step-by-step explanation:

I GOT THIS RIGHT! THIS IS THE ANSWER

The differences in mean costs to treat dogs and cats compared to the MAD at A New Leash on Life Animal Clinic suggest different levels of variability in the data. A 19 times difference labeled as 'moderate' implies high variability, while if labeled as 'large', the implication is that the variability is lower.

The question relates to the comparison of the mean costs to treat dogs and cats at A New Leash on Life Animal Clinic, using the Mean Absolute Deviation (MAD) as a measure of variability. When we say that the difference between the mean cost to treat dogs and cats is about 19 times the MAD, and that this is a moderate difference, it suggests that the variability within each of the distributions is quite high, making a 19-fold difference in means seem less extreme. Conversely, the same difference being described as a large difference implies that the variability (MAD) is comparatively lower, hence a difference of the same scale appears more substantial relative to the spread of the data. This provides insight into the differences in treatment costs and the consistency of those costs within each group of animals.

Answer:

They predict 1350 renters will buy liability insurance.

The answer is 1350 renters.

Step-by-step explanation:

Given:

A car rental company at the local airport estimates they sell liability insurance to 45% of their customers.

If they rent 3,000 cars next month.

Now, to find the renters they predict will buy liability insurance.

So, the rate of the car rental company which estimates of selling liability insurance to their customers is 45%.

And, the cars they rent next month = 3,000.

Now, to get the renters they predict of buying liability insurance by getting the rate of the cars they rent next month:

[tex]45\%\ of\ 3,000\\\\=\frac{45}{100}\times 3,000\\\\=0.45\times 3,000\\\\=1350.[/tex]

Hence, they predict 1350 renters will buy liability insurance.

Therefore, the answer is 1350 renters.

Answer:

3 fold or 3 times

Step-by-step explanation:

The rate of increase of the house is 200%.

To calculate the rate of increase of the house, we can use the formula:

Rate = ((Final Value - Initial Value) / Initial Value) * 100

Using the given values, the rate of increase of the house is: ((150000 - 50000) / 50000) * 100 = 200%

https://brainly.com/question/11450403

#SPJ3

Answer:

c

Step-by-step explanation:

Answer:

C.                                                  

Step-by-step explanation:

Answer:

9 yd

Step-by-step explanation:

15 yd - 6 yd = 9 yd

Please mark my answer as brainiest

Answer:

9 yd

Step-by-step explanation:

The top has a length of 15 yd

The bottom has a length of 6 +x

15 = 6+x

Subtract 6 from each side

15-6 = 6-6+x

9 = x

9 yds in the missing length

Answer:

g(x) = 1

Step-by-step explanation: