Carl knows that the area of a given circle is 400 cm2. He wants to defend an informal argument that the area of a circle can be approximated by dividing the circle into congruent segments, rearranging the segments to resemble a parallelogram, and replacing the dimensions of the parallelogram with appropriate values from the circle. Carl divides the circle into 6 congruent segments and makes his calculations, but the area he calculates for the circle is only 350 cm2. How could Carl defend his informal argument?

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Three red balls, 4 white balls, and 1 green ball are in a bag. A ball is drawn without replacement.

total balls = 3 red + 4 white + 1 green = 8 balls

the number of balls that are not green is 7

pick 3 balls from 7 balls that are not green

[tex]nCr= \frac{n!}{r!(n-r)!}[/tex]

[tex]P(not \ green)=\frac{7C3}{8C3}[/tex]

[tex]7C3= \frac{7!}{3!(7-3)!}=35[/tex]

[tex]8C3= \frac{8!}{3!(8-3)!} =56[/tex]

[tex]P(3 \ balls \ drawn)=\frac{35}{56} =\frac{5}{8}[/tex]

Answer:

[tex]r=f\times m-5b[/tex]

Step-by-step explanation:

Given:

Number of boxes of burger meat = [tex]f[/tex]

Number of slices of meat in each box = [tex]m[/tex]

Number of burgers the family eats each week = [tex]b[/tex]

Number of burger meat remaining = [tex]r[/tex]

To write: An equation in terms of [tex]f, m,\ and\ b[/tex] that represents the number of remaining burger meat, [tex]r[/tex], after 5 weeks.

Now, since each box contain 'm' slices.

Therefore, by unitary method, number of slices of meat in 'f' boxes is given as:

[tex]Total\ number\ of\ slices=f\times m[/tex]

Now, each week burger consumption = 'b'

So, 'b' slices of meat are eaten each week. Again by unitary method, the number of slices eaten in 5 weeks is given as:

[tex]\textrm{Number of slices eaten in 5 weeks}=5b[/tex]

Now, Slices remaining = Total number of slices - Number of slices eaten in 5 weeks.

Therefore, [tex]r=f\times m-5b[/tex]

Hence, the equation that represents the number of slices of burger meat remaining in terms of 'f', 'm', and 'b' is given as:

[tex]r=f\times m-5b[/tex]

Answer:

You will have to pay $ 3.99 for the package of batteries with 20% discount

Step-by-step explanation:

Standard price of the batteries packages = $ 4.99

Discount = 20% = 0.2

Discounted price = Standard price - Discount

Discounted price = 4.99 - (0.2 * 4.99)

Discounted price = 4.99 - 1.00 (Rounding to the next tenth)

Discounted price = 3.99

You will have to pay $ 3.99 for the package of batteries with 20% discount

Final answer:

A package of batteries with a 20% discount off the original price of $4.99 would be approximately $3.99 after subtracting the discount amount, which is $0.998.

Explanation:

To calculate how much the student would have to pay for packages of batteries that normally sell for $4.99 with a 20% discount, we first need to determine the amount of the discount. To find the discount amount, multiply the original price by the discount percentage:

$4.99 × 0.20 = $0.998

Now, subtract the discount amount from the original price to get the sale price:

$4.99 - $0.998 = $3.992

The discounted price will be approximately $3.99, as the final amount is traditionally rounded to the nearest cent.

Answer:

7.5

Step-by-step explanation:

1.25/ (.5) = 2.5

2.5 x 3 = 7.5

Answer:

Option C. is correct.

Step-by-step explanation:

Given:

Adrienne's annual take-home pay = $57,000

To find:

The maximum amount that she can spend per month on paying off credit cards and loans and not be in danger of credit overload.

Solution:

Number of months in a year = 12

So, amount she can spend per month =

Annual pay of Adrienne / Number of months in a year = [tex]\frac{57000}{12} =\frac{28500}{6}=\frac{14250}{3}=4750[/tex]

So, option C. is correct.

Answer:

A. $950.00

Step-by-step explanation:

A p e x

Answer:

x = $3,521

Step-by-step explanation:

let the amount of money that she put towards a house be represented by the variable x

Hence,

total savings = amount put towards house + amount left

$40,000 = x + $36,479   (rearrange)

x + $36,479  = $40,000   (subtract $36,479 from both sides)

x   = $40,000 -  $36,479

x = $3,521

Answer:

Step-by-step explanation:

Answer:

C Less than today

Step-by-step explanation:

If i save $100 at 1% per annum after 1 year I will get $101, but with inflation rate of 2%per annum a commodity that is worth $100 now will be worth $102 after 1 year so u can't buy same commodity I can buy today after 1 year even when my money has increase.

The purchasing power of money in a savings account would decrease after 1 year due to inflation.

To calculate how much you would be able to buy after 1 year, we need to consider the effect of both the interest rate and inflation. With an interest rate of 1% per year, your savings account would increase by 1% over 1 year. However, with an inflation rate of 2% per year, the price of goods and services would also increase by 2% over the same period.

This means that the purchasing power of your money would decrease. To calculate the actual increase or decrease in purchasing power, you can subtract the inflation rate from the interest rate. In this case, 1% - 2% = -1%.

Therefore, the correct answer is c. Less than today. After 1 year, you would be able to buy less with the money in your savings account.

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The horizontal distance covered by pilot is 17,972.2 feet.

Step-by-step explanation:

Given,

Distance covered descending = 1000 feet

Diagonal distance = 18,000 feet

The horizontal distance will form a right triangle, therefore, we can find the horizontal distance by using pythagoras theorem.

Here,

a = 1000

b = horizontal distance

c = 18000

[tex]a^2+b^2=c^2\\(1000)^2+b^2=(18000)^2\\1000000+b^2=324000000\\b^2 = 324000000-1000000\\b^2=323000000[/tex]

Taking square root on both sides

[tex]\sqrt{b^2}=\sqrt{323000000}\\b=17972.2[/tex]

The horizontal distance covered by pilot is 17,972.2 feet.

Keywords: pyathoras theorem, square root

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Answer:

(-7)∧-1

Step-by-step explanation:

(-7)^3 / (-7)^4  

taking each and simplifing it

-7³ = -7 x -7 x -7

(-7)∧4 = -7 x -7 x -7 x -7

(-7)^3 / (-7)^4  = (-7 x -7 x -7 ) / ( -7 x -7 x -7 x -7) = 1/-7

1/-7 ( 1/ means raise to power -1)

1/-7 = (-7)∧-1

Answer:

Step-by-step explanation:

Let x represent the discount in percentage offered for the price of the shirts.

The regular price of the shirts was $20

The price for which the shirt was offered for sale is $17 which also represents the discounted price.

The discount would be

20 - 17 = $3

The percentage discount would be

The discount/ the regular price × 100%.

Therefore,

% discount = 3/20 × 100 = 0.15 × 100

= 15%

Answer:

The answer to your question is letter A

Step-by-step explanation:

From the graph, we conclude that it is a vertical ellipse with center (0, 0).

Also from the graph, we calculate a and b

a = 11, a is the distance from the center to the vertical vertex

b= 9,  b is the distance from the center to the horizontal vertex

Equation

                        [tex]\frac{x^{2}}{9^{2}} + \frac{y^{2}}{11^{2}} = 1[/tex]

Simplification

                      [tex]\frac{x^{2}}{81} + \frac{y^{2}}{111} = 1[/tex]

Answer:

3 hours

Step-by-step explanation:

we know that

The speed is equal to divide the distance by the time

Let

s ----> the speed in mph

d -----> the distance in miles

t ----> the time in hours

x ----> distance traveled by Daisy to the meeting point

60-x ----> distance traveled by Sally to the meeting point

so

[tex]s=\frac{d}{t}[/tex]

Solve for d

[tex]d=st[/tex]

Distance traveled by Daisy to the meeting point

[tex]d=st[/tex]

we have

[tex]d=x\ mi\\s=12\ mph[/tex]

substitute

[tex]x=12t[/tex] ----> equation A

Distance traveled by Sally to the meeting point

[tex]d=st[/tex]

we have

[tex]d=(60-x)\ mi\\s=8\ mph[/tex]

substitute

[tex]60-x=8t[/tex] ----> equation B

substitute equation A in equation B

[tex]60-12t=8t[/tex]

solve for t

[tex]12t+8t=60\\20t=60\\t=3\ hours[/tex]

Answer:

The ratio of mangers to sales people of the stores are not equivalent as the ratios in their simplest form are not equal.

Step-by-step explanation:

Given:

One store has:

3 Managers and 12 sales persons

Another store has:

4 Managers and 15 sales persons.

To find if the ratio of mangers to sales people are equivalent.

Solution:

Store A:

Managers = 3

Sales people = 12

Ratio of mangers to sales people for store A = [tex]\frac{3}{12}[/tex] =[tex]\frac{3\div3}{12\div 3}=\frac{1}{4}[/tex]  (Simplest ratio)

Store B:

Managers = 4

Sales people = 15

Ratio of mangers to sales people for store B = [tex]\frac{4}{15}[/tex]

The ratio is in the simplest form and cannot be reduced further.

We can see that : [tex]\frac{1}{4}\neq \frac{4}{15}[/tex]

Hence, the ratio of mangers to sales people of the stores are not equivalent.

Answer: 9:11

Step-by-step explanation:

Let x be the total number of students.

If 3/4 of students study a language That mean 3x/4 students study a language.

Number of students that don't study a language becomes

x - 3x/4 = x/4.

and 3/5 of those who study language study French, that means 3x/4 * 3/5 of students study French.

This gives 3x/4 * 3/5 = 9x/20 Studying French.

Number of students that study language but do not study French becomes

3x/4 - 9x/20 = 6x/20

Total number of students that do not study French becomes

[total number of students not studying any language] + [total number of students studying a language but do not study French ]

Which becomes

x/4 + 6x/20 = 11x/20

Hence ratio of those that study French to those that do not study French Becomes

9x/20 : 11x/20

9:11.

Answer:

Jacob ran 40 yards more than Ali.

Step-by-step explanation:

Football field is in the shape of a rectangle having dimensions 120 yards × 50 yards

Since Jacob runs around the perimeter of the field from one corner to other corner, therefore, distance run by Jacob = [tex](\text{Length+width})[/tex]

Distance run by Jacob = 50 + 120 = 170 yards

Ali runs through the middle of the field diagonally on a straight line.

Therefore, distance covered by Ali = [tex]\sqrt{\text{length}^{2}+\text{width}^{2}}[/tex]

= [tex]\sqrt{(50)^{2}+(120)^{2}}[/tex]

= [tex]\sqrt{2500+14400}[/tex]

= [tex]\sqrt{16900}[/tex]

= 130 yards

Now difference between the distance covered by Jacob and Ali

= 170 - 130

= 40 yards

Therefore, Jacob ran 40 yards more than Ali.

Answer:

a). 18

b). 26%

c). 39

Step-by-step explanation:

Given question is incomplete; here is the complete question attached.

a). In this part we have to calculate the number of the people surveyed who make less than 5 calls.

From the given table,

Number of people surveyed who make less than 5 calls Or 1 - 4 calls = 18

b). Total number of people surveyed = 18 + 11 + 5 + 3 + 2 = 39

Number of people surveyed, make at least 9 calls = 5 + 3 + 2 = 10

Percentage of these people = [tex]\frac{\text{People who make calls more than 9 calls per day}}{\text{Total number of people surveyed}}\times 100[/tex]

= [tex]\frac{10}{39}\times 100[/tex]

= 25.64%

≈ 26%

c). Total number of people surveyed = 18 + 11 + 5 + 3 + 2 = 39

Answer:

7/12 of a chance

Step-by-step explanation:

If you have 12 batteries and 5 are dead, 12 - 5 is 7, so there's going to be 7/12 of a chance.

Answer:

a) Domain = [tex](-\infty,400)\cup (400,\infty)[/tex]

b) [tex]x \in [0,100][/tex]

c) 53.03 worker hours

d) 83.33 worker hours

e) 83.33 worker hours

Step-by-step explanation:

We are given the following in the question:

[tex]W(x) = \dfrac{250x}{(400-x)}[/tex]

where W(x) is the number of worker-hours required to distribute new telephone books to x% of the households in a certain rural community.

a) Domain of function.

The domain is the all the possible values of x that the function can take.

Domain = [tex](-\infty,400)\cup (400,\infty)[/tex]

b) Values of x

Since x is a percentage in reference to context, it can only take value upto 100. Also it cannot take any negative value.

So domain n reference to context will be

[tex]x \in [0,100][/tex]

c) worker-hours were required to distribute new telephone books to the first 70% of the households

[tex]W(70) = \dfrac{250(70)}{(400-70)} = 53.03[/tex]

53.03 worker hours were required to distribute new telephone books to the first 70% of the households.

d) Worker hour for entire community

For entire community, x = 100

[tex]W(100) = \dfrac{250(100)}{(400-100)} = 83.33[/tex]

83.33 worker hours were required to distribute new telephone books to the entire households.

e) Percentage of the households in the community for 3 worker hours

[tex]3 = \dfrac{250x}{(400-x)}\\\\1200-3x = 250x\\253x = 1200\\\\x = \dfrac{1200}{253} = 4.74\%[/tex]

Thus, 4.74% of the households in the community had received new telephone books by the time 3 worker-hours had been expended.

Final answer:

The domain of the function W(x) is (-∞, 400) U (400, +∞). The values of x that have a practical interpretation in this context are in the interval [0, 100]. Approximately 53.03 worker-hours were required to distribute new telephone books to the first 70% of households, and approximately 83.33 worker-hours were required to distribute to the entire community. After 3 worker-hours, approximately 4.73% of the households had received new telephone books.

Explanation:

(a) The domain of the function W is the set of all possible values of x that make the function defined and meaningful. In this case, the function W(x) is defined except when the denominator 400-x is equal to zero. So, we need to find the values of x that make the denominator zero.

To do that, we solve the equation 400-x = 0, which gives x = 400.

Therefore, the domain of the function W is the set of all real numbers except x = 400. We can express this in interval notation as (-∞, 400) U (400, +∞).

(b) In this context, the function W(x) represents the number of worker-hours required to distribute new telephone books to x% of the households in the rural community. A practical interpretation is only meaningful when x represents a valid percentage, meaning that it is between 0% and 100%, inclusive. So, the values of x that have a practical interpretation in this context are in the interval [0, 100].
(c) To find the worker-hours required to distribute new telephone books to the first 70% of households, we substitute x = 70 into the function W(x). Evaluating the expression, we get: W(70) = 250(70) / (400 - 70) = 17500 / 330 = 53.03.

Therefore, approximately 53.03 worker-hours were required to distribute new telephone books to the first 70% of households.

(d) To find the worker-hours required to distribute new telephone books to the entire community, we substitute x = 100 into the function W(x). Evaluating the expression, we get: W(100) = 250(100) / (400 - 100) = 25000 / 300 = 83.33.

Therefore, approximately 83.33 worker-hours were required to distribute new telephone books to the entire community.

(e) To find the percentage of households that had received new telephone books after 3 worker-hours, we rearrange the function W(x) to solve for x. We have:

W(x) = 250x / (400 - x)

3 = 250x / (400 - x)

3(400 - x) = 250x

1200 - 3x = 250x

1200 = 253x

x = 1200 / 253 ≈ 4.73

Therefore, approximately 4.73% of the households in the community had received new telephone books after 3 worker-hours.

Answer:

  A: When using polynomial long division, the multiply, subtract, and bring down portion applies just like when dividing integers

  B: Polynomial long division uses powers of variables instead of place values used when dividing integers, and only the first term of the divisor is considered in the divide step

Step-by-step explanation:

The above answers are pretty self-explanatory.

I find polynomial division easier, because the "trial division" step uses only the highest-degree terms, so always gives the exact result you need for the quotient. (There's no "guess and check" as with integer long division.) Powers of the variable take the place of powers of 10 (or whatever number base you're using) in integer long division.

__

For integer long division, the steps are ...

For polynomial long division, the steps are similar.

_____

Examples of each are shown in the attachments.

Answer:The procedure to use the find the value of x calculator is as follows:

Step 1: Enter the values in the divisor and the product field

Step 2: Now click the button “Solve” to get the output

Step 3: The dividend or the x value will be displayed in the output field

Step-by-step explanation: In algebra, it is easy to find the third value when two values are given. Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication, and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Answer:

In order to find the correct answer you must use finances and use algebraic equations . You may also have to use precalculus. There is a group of answer choices, its really difficult to find the answer without more instructions. I don't understand what answer your looking for. You may be able to find the answer using finances and other detailed measures. Try using graph paper and write down finances I'm trying my best to help you.

Step-by-step explanation:

finances                                                                                                                     Algebra                                                                                                                       Precalculus

$56, $57, $56.25 is the 4-day SMA for the following closing prices: $56, $61, $50, $57, $60, $58, and $57

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To calculate the 4-day SMA (Simple Moving Average)

We need to add up the closing prices for the last 4 days and divide the sum by 4.

We then move the window one day forward and repeat the process.

Using the given closing prices, we can calculate the 4-day SMA as follows:

Day 1: (56 + 61 + 50 + 57) / 4 = 56

Day 2: (61 + 50 + 57 + 60) / 4 = 57

Day 3: (50 + 57 + 60 + 58) / 4 = 56.25

Day 4: (57 + 60 + 58 + 57) / 4 = 58

The 4-day SMA for the given closing prices is: $56, $57, $56.25, $58.

Hence,  $56, $57, $56.25 is the 4-day SMA for the following closing prices: $56, $61, $50, $57, $60, $58, and $57.

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Answer:

B. Median

Step-by-step explanation:

We have been given data about time spent on Internet (min/day). We are asked to determine the best measure of central tendency for the given data.

Data: 75, 38, 43, 120, 65, 48, 52,

We can see that our given data has a very large value outlier (120), so it will increase the mean.

There is no mode for the given data set as no value repeats.

We know that median is best measure for data set with large valued outliers because median is not affected by outliers.

Therefore, option B is the correct choice.

The measure of central tendency that best describes the data is B. Median.

Mean:

= (75 + 38 + 43 + 120 + 65 + 48 + 52) / 7

= 69.86

Median:

We arrange data in ascending order: 38, 43, 48, 52, 65, 75, 120. Since there are seven values, the median is the middle value: 52

Mode: There is no value that appears more than once in the data set.

Therefore, the measure of central tendency that best describes the data is B. Median.

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Answer:

40% students play the saxophone.

Step-by-step explanation:

Given:

Total Number of students who play woodwind instrument = 45

Number of students who play saxophone = 18

We need to find the percent of students who play saxophone.

Solution:

Now we can say that;

To find the percent of students who play saxophone we will divide Number of students who play saxophone by Total Number of students who play woodwind instrument and the multiply by 100.

framing in equation form we get;

percent of students who play saxophone = [tex]\frac{18}{45}\times100= 40\%[/tex]

Hence 40% students play the saxophone.

The percent of these students play the saxophone is 40%.

Using this formula

Percentage=Number of student that play saxophone/Number of student that play woodwind instrument×100

Where:

Number of student that play saxophone=18

Number of student that play woodwind instrument=45

Let plug in the formula

Percentage=18/45×100

Percentage=40%

Inconclusion the percent of these students play the saxophone is 40%.

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Answer:

Step-by-step explanation:

The total amount of punch that Jennifer made for her party is 5 Liters. Her brother made another 750 milliliters.

1000 milliliters = 1 liter

750 milliliters = 750/1000 = 0.75Liter

if they combine the two batches, the total amount made would be

5 + 0.75 = 5.75Liter

= 5.75 × 1000 = 5750 milliliters

The number of 180 milliliters servings would be

5750/180 = 31 servings

There would be leftovers of 170 milliliters

See the attached picture:

Answer:

Total interest =$1296

Step-by-step explanation:

Kevin invested $8,000 for one year at a simple annual interest rate of 6 percent

Simple interest = [tex]\frac{Pnr}{100}[/tex]

P=8000, n=1 year  and r=6

interest = [tex]\frac{8000(1)(6)}{100}[/tex]

Interest = 480  dollars

[tex]compound \ interest =P(1+\frac{r}{n} )^{nt}-p[/tex]

P= 10000, t=1, r=8%=0.08, n=2 for semiannually

[tex]compound \ interest =10000(1+\frac{0.08}{2} )^{2(1)}-10000[/tex]

Interest = 10816- 10000=816

Total interest = [tex]480+816=1296[/tex]

Answer: d) negative

Step-by-step explanation:

The term correlation is used to define the relationship between the two variables .

Here, the variables vary in the same direction.

Here, the variables vary in the opposite direction.

∴ A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a: negative correlation.

Hence, the correct answer is  d) negative

93÷1.1= 84.545454545

Answer:approximately 30 times

Step-by-step explanation:

The wheel on Carmen's bike circular in shape and has a diameter of 1.1 meter.

Radius = diameter/2 = 1.1/2 = 0.55 meter.

When the wheel completes one revolution, the distance covered is equal to the circumference of the wheel.

The formula for determining the circumference of the wheel is expressed as

Circumference = 2πr

Where π is a constant whose value is 3.14

Circumference = 2 × 3.14 × 0.55 = 3.454 metres.

Carmen races the bicycle for 93m. Therefore, the number of times that the wheel of the bicycle turns as it travels this distance would be

93 / 3.454 = 26.9 times

Answer:

0.6826

Step-by-step explanation:

Mean(μ) = 37

Standard deviation (σ) = 9

P(28 < x < 46) = ???

Using normal distribution

Z = (x - μ)/σ

For x = 28

Z = (28 - 37)/9

Z = -9/9

Z = -1

For x = 46

Z = (46 - 37)/9

Z = 9/9

Z = 1

We now have

P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

From the table, Z = 1 = 0.3413

φ(Z) = 0.3413

Recall that

When Z is positive, P(x<a) = 0.5 +φ(Z)

P(Z<1)= 0.5 + 0.3413

= 0.8413

When Z is negative, P(x<a) = 0.5 - φ(Z)

P(Z< -1)= 0.5 - 0.3413

= 0.1587

We now have

0.8413 - 0.1587

= 0.6826