Why are there two different formulas for circumference?

The domain of the expression is all real numbers except -7 and 5. In interval notation, the domain can be expressed as (-∞, -7) U (-7, 5) U (5, ∞).

The simplified form of the expression is:

(12 - X) / (x² + 2x - 35) * (x² + 7x) / (x² - 12x)

And the domain of the expression is all real numbers except for values of x that make the denominators equal to zero, as division by zero is undefined.

To find the values of x that make the denominators equal to zero, we can set the denominators equal to zero and solve for x:

x² + 2x - 35 = 0

(x + 7)(x - 5) = 0

x + 7 = 0 or x - 5 = 0

x = -7 or x = 5

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For the data set 29, 20, 15, 13, 35, 20. the mean, median, mode and range are 22, 20, 20, and 22, respectively.

The mean (arithmetic mean), denoted by μ, is a single value defined as the sum of the data values divided by the total number of data values.

[tex]\text{Mean} =\dfrac{x_1+x_2+...+x_n}{\text{N}}[/tex]

[tex]\text{Mean} = \dfrac{29+20+15+13+35+20}{6}[/tex]

[tex]\text{Mean} = 22[/tex]

The median, denoted by , is the single value at the middle of an ordered arrangement of data values according to increasing or decreasing magnitude.

[tex]\text{M}_{\text{d}}=x_{\dfrac{\text{N}+1}{2} }[/tex]     if N is odd, and

[tex]\text{M}_{\text{d}}=\dfrac{^x\frac{\text{N}}{2}^{+x} \frac{\text{N}}{2} +1}{y}[/tex]    if N is even

[tex]\text{N = 8}[/tex]

Data : 13, 15, 20, 20, 29, 35

[tex]\text{M}_{\text{d}}=\dfrac{^x\frac{\text{N}}{2}^{+x} \frac{\text{N}}{2} +1}{y}[/tex]

where [tex]x_\frac{\text{N}}{2}[/tex] = [tex]x_\frac{8}{2}[/tex] = [tex]x_4[/tex] = 20 and [tex]x_\frac{\text{N}}{2}_{+1}=x_\frac{8}{2}_{+1}=x_4_{+1}=x^5[/tex] = 20

[tex]\text{M}_{\text{d}}=\dfrac{20+20}{2}[/tex]

[tex]\text{M}_{\text{d}}=20[/tex]

The mode, denoted by , refers to the most frequent value in the data set.

[tex]\text{Mode = 20}[/tex]

The range (R) is defined as the difference between the maximum and minimum values of a data set.

[tex]\text{R} = \text{MAX} - \text{MIN}[/tex]

[tex]\text{R} = 35- 13[/tex]

[tex]\text{R} = 22[/tex]

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Using mathematical operations of division and multiplication, the total weight of the order in pounds is 3 pounds.

The total weight is firstly computed in ounces before being converted into pounds.

The computation follows the mathematical operations of multiplication and division, respectively.

The number of Orange You Fresh soap bars ordered by a customer = 12

The weight of each bar of soap = 4 ounces

The total weight of 12 bars in ounces = 48 ounces (4 x 12)

1 pound = 16 ounces

3 pounds = 48 ounces (48 ÷ 16)

Thus, based on mathematical operations, the number of pounds this order will weigh is 3 pounds.

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Answer:

100ft²

Step-by-step explanation:

to find the area of the figure you must do the area of the small rectangle plus the area of the large rectangle

area = length* width

so the area of the small rectangle equals

7ft * 4ft = 28ft²

then the large rectangle

9ft*8ft=72ft²

28ft²+72ft²=100ft²

To find the 18th term of a pattern that repeats 5 times (which is a pentagon), we need to divide 18 by 5, which gives us a quotient of 3 and a remainder of 3.

This means that the pattern repeats 3 times, and we need to find the 3rd term of the pattern after the third pentagon.

The third term of the pattern after the third pentagon would be the fourth pentagon in the sequence, since each pentagon consists of 5 terms. Therefore, the 18th term would be the third term of the fourth pentagon in the sequence, which is the 13th term overall.

So the 18th term in the sequence would be the 13th term of the pattern, which is another pentagon.

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The number of students in class a is 15, the mean score of class c is 5.5, and the mean score of all three classes is 6.5.

In mathematics, the mean or average is a measure of central tendency that represents the typical value or a central value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the number of values in the set. The mean is commonly used in statistics to summarize a large amount of data into a single value that is more easily understood. It is often used to represent the "average" or "typical" value of a set of data. For example, the mean score of a class on a test can give an idea of how well the class performed overall.

We can use the formula for the mean to set up two equations, one for the mean score of class a and one for the mean score of all three classes:

For class a and b combined:

(6x + 25 × 8)/ (x + 25) = 7.25

Simplifying this equation gives us:

6x + 200 = 7.25(x + 25)

Expanding the brackets and simplifying further gives:

6x + 200 = 7.25x + 181.25

Subtracting 6x and 181.25 from both sides gives:

18.75 = 1.25x

Therefore, x = 15

For all three classes:

(6x + 25 × 8 + 20y) / (x + 25 + 20) = 6.5

Substituting x = 15 into this equation gives:

(6 ×15 + 25 × 8 + 20y) / (15 + 25 + 20) = 6.5

Simplifying and solving for y gives:

(90 + 200 + 20y) / 60 = 6.5

Simplifying further gives:

y = 5.5

Therefore, the number of students in class a is 15, the mean score of class c is 5.5, and the mean score of all three classes is 6.5.

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the earned interest after 3 years is $1,608.75.

What is simple interest?

Before delving further into the concept of simple interest, it is worth noting that it is a straightforward method for calculating interest on money, whereby interest is added at a constant rate for each time period and always to the initial principal amount. When we deposit our money into a bank, we can earn interest on our investment. Simple interest is one type of interest that banks may offer.

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal (initial amount)

r = interest rate per year (as a decimal)

t = time (in years)

Substituting the given values, we have:

P = $9,750

r = 0.055 (since the interest rate is 5.5%)

t = 3

I = $9,750 * 0.055 * 3

I = $1,608.75

Therefore, the earned interest after 3 years is $1,608.75.

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The equation that can be used to represent number of people who can go to the amusement park is 12 + 33.75x = 215.50.

We have,

the total amount to spent on amusement park = $214.50

And the parking fees = $12

The ticket cost per person = $33.75

let the number of person be x.

Then, the equation can become as

12 + 33.75x = 215.50

Simplifying the equation we get

33.75x = 215.5 - 12

33.75x = 203.5

x= 6.02

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As per the concept of simple interest, the interest amount earned after three years is $306.

To calculate the interest amount earned, we can use the formula:

I = P * r * t

Where:

I = interest earned

P = principal amount

r = interest rate per year (as a decimal)

t = time period in years

Plugging in the values from the problem, we get:

I = $1200 * 0.085 * 3

I = $306

This means that after three years, the bond will be worth the principal amount plus the interest earned, which is:

$1200 + $306 = $1506

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From shortest to longest is:  C. Marisol, Juan, Lucia, Jamal.

By comparing the lengths of the students' walks, it is possible to determine the correct order of the students based on their walks.

Marisol walks 0.62 miles, while Juan walks one mile. So Juan's walk isn't the most limited.

Lucia walks one mile, which is shorter than Jamal's walk of 0.78 miles but longer than Marisol's walk of 0.62 miles. Therefore, neither the shortest nor longest walk is Lucia's.

Therefore, Jamal and Marisol remain choices. The correct order, from shortest to longest, is as follows because Jamal's walk is longer than Marisol's:

C. Marisol, Juan, Lucia, Jamal.

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C) 36 yards   18*6=108

108ft to yards is 36

Answer:C

Step-by-step explanation:

Each jump rope is 6 feet long, so 18 jump ropes would require a total of:

18 x 6 = 108 feet of rope

Since there are 3 feet in a yard, we can convert 108 feet to yards by dividing by 3:

108 ÷ 3 = 36 yards

Therefore, the football coach should buy 36 yards of rope. The answer is (C).

Answer: B and D.

Step-by-step explanation: We can simplify the expression -3.75+ 2(-4x +6.1) - 3.25x as follows:

-3.75+ 2(-4x +6.1) - 3.25x

= -3.75 - 8x + 12.2 - 3.25x (distributing the 2)

= -11.25x + 8.45 (combining like terms)

Now, let's check each expression to see if it is equivalent to -11.25x + 8.45:

A. 7x-2x +8.2

= 5x + 8.2

Not equivalent to -11.25x + 8.45

B. 8.45-8x-3.25x

= 8.45 - 11.25x

Equivalent to -11.25x + 8.45

C. -1.75-7.25x=6.1

This is not an expression, it is an equation. It is not equivalent to -11.25x + 8.45.

D. -11.25x +12.2 - 3.75

= -11.25x + 8.45

Equivalent to -11.25x + 8.45

Therefore, the expressions that are equivalent to -3.75+ 2(-4x +6.1) - 3.25x are B and D.

We need to round up to the nearest integer, the required sample size is 76 households.

To estimate the required sample size, we can use the formula:

[tex]n = (z^2 * s^2) / E^2[/tex]

Where:

z is the z-score corresponding to the confidence level (90% = 1.645)

s is the standard deviation of the population (square root of the variance, so s = sqrt(3.61) = 1.898)

E is the maximum error allowed (0.15 gallons)

Plugging in the values, we get:

[tex]n = (1.645^2 * 1.898^2) / 0.15^2[/tex]

n = 75.57

Since we need to round up to the nearest integer, the required sample size is 76 households.

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The journal entries fro the transaction for October 31 and November 19 are as follows:

Oct. 31: Cash                                              $3,840,000

             ($12 x 320,000)

                       Common Stock                                      $1,600,000

                       ($5 x 320,000)

                       Paid-In Capital in Excess of Par-com.   $2,240,000  

                       ($3,840,000 - $1,600,000)

Nov. 19: Cash                                            $3,240,000

              ($72 x 45,000)

                       Preferred Stock                                     $2,700,000

                        ($60 x 45,000)

                       Paid-In Capital in Excess of Par-Pre.    $540,000

                        ($3,240,000 - $2,700,000)

Full question "On October 31, Pidgeon Stones Inc. , a marble contractor, issued for cash 320,000 shares of $5 par common stock at $12, and on November 19, it issued for cash 45,000 shares of preferred stock, $60 par at $72. Journalize the entries for October 31 and November 19".

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Answer:

x = 8/3

Step-by-step explanation:

y = mx + b

y = -3x + 16

8 = -3x + 16

Subtract 16 from both sides

-8 = -3x

Divide both sides by -3

8/3 = x

The slant height of the Teepee is 32.76 feet.

The square footage of one of the rooms is 44 square feet.

Check the attached for the sketch of the cone. From the image, the slant height is labelled l. Note that the base diameter is 14 feet, so the base radius will be 7 feet.

(a) Thus, the slant height can be found by considering one of the right triangles in the cone. That is:

l² = 32² + 7²   (Pythagoras Theorem)

l²  = 1024 + 49

l = √1073

l = 32.76 feet

(b) The shape of base is a circle.

Area of circle = πd

where d is the base diameter

Area of circle = 22/7 * 14

Area of circle = 44 square feet

Thus, the square footage of one of the rooms is 44 square feet

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The number that could be expected to have ordered a medium was 64 people.

The number that could be expected to have ordered a small would be 108 people.

The number that could have been expected to have ordered a small, medium, or large was 75 people.

The number that could have been expected to have ordered a medium was :

= 16 / ( 9 + 16 + 5 + 10 ) x 160 people

= 64 people

The number that could have been expected to have ordered a small would be :

= 9 / ( 9 + 16 + 5 + 10 ) x 480 people

= 108 people

The number that could have been expected to have ordered a small, medium, or large was :

= ( 9 + 16 + 5 ) / ( 9 + 16 + 5 + 10 ) x 100

= 75 people

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Step-by-step explanation:

The value of the expression can be calculated using the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

The expression is:

2 + [(15 + 3) × 2]

According to PEMDAS, we should first evaluate the expression within the parentheses:

15 + 3 = 18

So, the expression becomes:

2 + [18 × 2]

Next, we perform the multiplication:

18 × 2 = 36

Now, we substitute the result back into the original expression:

2 + 36

Finally, we perform the addition:

2 + 36 = 38

So, the value of the given expression is 38.

The time since the rock reached its closure temperature is approximately 579.8 years. When the rock was discovered, it had 4.375 grams of europium-151.

To find the time since the rock reached its closure temperature, we can use the following formula

t = t(1/2) * log(N0/Nt)

where t is the time elapsed, t(1/2) is the half-life, N0 is the initial amount of the isotope, and Nt is the amount of the isotope at the time it was discovered.

Substituting the given values, we get

t = 96.6 * log(5/0.625) ≈ 579.8 years

Therefore, the time since the rock reached its closure temperature is approximately 579.8 years.

To find the amount of europium-151 in the rock when it was discovered, we can use the fact that the total amount of samarium-151 and europium-151 in the rock is constant.

Since the rock originally contained 5 grams of samarium-151, it must have contained 5 - 0.625 = 4.375 grams of europium-151 when it was discovered.

Therefore, the rock had 4.375 grams of europium-151 when it was discovered.

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The value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

Expanding the determinant using the first row, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a | b c 7d + 7e b 7f + g h i| - b |a c 7d + 7e c 7f + g h i| + c |a b 7d + 7e 7f + g h i|

= a | b c 7d + 7e b 7f + g h i| + b |a c 7d + 7e c 7f + g h i| - c |a b 7d + 7e 7f + g h i|

Now, we can expand each of the three determinants on the right-hand side using the first row and simplify:

| b c 7d + 7e b 7f + g h i| = b | c 7f h i| - 7e |b 7f h i| + g |b c h i|

= -7e b |7f h i| + g |b c h i| - h |b c 7f i| + i |b c 7f h|

= -7e bi + gh - bhf + chi

|a c 7d + 7e c 7f + g h i| = a |c 7f h i| - 7e |c 7d h i| + g |c 7d 7f i|

= 7e ac - gci + chd - ahf

|a b 7d + 7e 7f + g h i| = a |b 7f h i| - 7e |b 7d h i| + g |b 7d 7f i|

= -7e ab + ghi - bgd + aef

Substituting these expressions back into the expanded determinant and simplifying, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a(-7e bi + gh - bhf + chi) + b(7e ac - gci + chd - ahf) + c(-7e ab + ghi - bgd + aef)

= -7abe - 7bdf - 7cfg + 7aef + bch + cgi + ahk - ceh - afg - bdi

= -7(abe + bdf + cfg - aef) + (bch + cgi + ahk - ceh - afg - bdi)

Since |a b c d e f g h i| = 5, we have:

abe + bdf + cfg - aef = 5

Therefore, we can simplify the expression further:

| a b c 7d + a 7e + b 7f + c g h i|

= -7(5) + (bch + cgi + ahk - ceh - afg - bdi)

= -35 + b(ch - di) + c(gi - eh) + a(hk - fg)

Hence, the value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

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The simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

First, factor out the 7 from the second row:

| a b c 7(d + e + f) g h i| = 7| a b c d + e + f g h i|

Expand the second row using the property of determinants that allows us to break up a row sum:

7(| a b c d g h i| + | a b c e g h i| + | a b c f g h i|)

Now, use the property of determinants that allows us to switch rows and multiply by -1:

7(| a b c d g h i| + | a b c e g h i| - | d e f a b c g h i|)

Recognize that the third determinant is equivalent to the given determinant, but with rows 1 and 3 switched, which

gives us:

7(| a b c d g h i| + | a b c e g h i| - 5)

Finally, multiply 7 by the expression inside the parentheses:

7| a b c d g h i| + 7| a b c e g h i| - 35

So, the simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

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Answer:

The area of the shaded sector is

(π/4)(6^2) = (π/4)(36) = 9π

Answer: There is an approximate 10.7% probability that it will snow on Sunday, making it the day with the lowest likelihood of snow.

Step-by-step explanation: Snow is highly likely on Friday with an 80% probability. The likelihood of no snowfall occurring on Friday is 20%, which can be calculated by subtracting 0.8 (or 80%) from 1.

There is a high probability of snowfall on Saturday with a 7 in 9 likelihood. In simpler terms, the probability can be reduced to 7 out of 9 or around 0.78. The likelihood of snowfall on Saturday is 78%, therefore the chance of no snow on that day is 22% which is equivalent to 1 minus 0.78.

There is a high likelihood of snow on Sunday with a probability of 75 out of 100 or 14 out of 19. It is possible to reduce this to a likelihood of 0.7514, or about 0.107. The likelihood of Sunday not having snow is equivalent to subtracting 0.107 from 1, resulting in a 0.893 or 89.3% probability.

The final expression that gives us the cost of x skirts and y hats in pounds is 24x + 15y.

In this case, our variables are x and y, which represent the number of skirts and hats, respectively. Our constants are 24 and 15, which represent the cost of one skirt and one hat, respectively. And our operations are multiplication and addition.

The cost of x skirts is simply the cost of one skirt (which is 24) multiplied by the number of skirts (which is x). So, the expression for the cost of x skirts would be:

24x

Similarly, the cost of y hats is the cost of one hat (which is 15) multiplied by the number of hats (which is y). So, the expression for the cost of y hats would be:

15y

To find the total cost of x skirts and y hats, we simply add the two expressions together. Thus, the expression for the cost in pounds of x skirts and y hats is:

24x + 15y

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Answer:

4

Step-by-step explanation:

4-0=4

Answer:

4 left

Step-by-step explanation:

then you have 4 apples

The function best models the data in the table is y=-0.6x+132 (option a).

The table shows the minimum target heart rates by age, which implies that as a person ages, their heart rate should be maintained within a certain range during exercise to achieve optimal cardiovascular benefits. In order to determine the target heart rate for a given age, we need a mathematical function that can accurately model the data in the table.

This is a linear function, which means that it assumes a constant rate of change in the target heart rate as age increases.

However, the data in the table shows that the target heart rate decreases gradually with age. Therefore, this function does  accurately model the data and is a suitable option.

Hence (a) is the right one.

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Complete Question:

Age x (year)                           Minimum Target Heart Rates by Age

30                                                                114

35                                                                 111

40                                                                108

45                                                                105

50                                                                102

Which function best models the data in the table?

a) y=-0.6x+132

b) y=(x-30)²+114

c) y= 19/30x

The width of the path is 24 meters.

Let's call the width of the path "x".

The dimensions of the inner rectangle (the lawn without the path) are 46m by 34m. The dimensions of the outer rectangle (the lawn with the path) are (46+2x) by (34+2x).

Area of path = Area of outer rectangle - Area of inner rectangle

425m² = (46+2x)(34+2x) - (46)(34)

Simplifying and solving for x:

425m² = (2x+46)(2x+34)

425m² = 4x² + 80x + 1564

4x² + 80x - 1161 = 0

We only want the positive value for x, so:

x = (-80 + 272) / 8

x = 24m

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Therefore , the solution of the given problem of ratio comes out to be this indicates that there are 4 black pens in the package for every red pen.

A group comprising values both variable "a" and "" that seem to be equal is found using the straightforward formula "a / b," whenever "b" might be a greater number than zero. A ratio is created by combining two ratios. The ratio , fraction could have been 1:1 if there were just one guy and three women. There are 1/4 men and 3/4 women in the group.

Here,

By dividing the numerator and denominator by their greatest common divisor (GCD), the ratio 3/12 can be made simpler.

Due to the fact that both 3 and 12 can be divided by 3, their GCD equals 3.

The result of dividing the numerator and denominator by 3 is:

=> 3 ÷3 = 1.

=> 12 ÷ 3 = 4

Thus, 1/4 is the simple ratio that corresponds to 3/12.

Let's now use a simplified equivalent ratio to represent the ratio of red to black pens in the package:

Black pens 3: 12 Red pens:

=> 3 ÷ 3 = 1

=> 12 ÷ 3 = 4

Consequently, the rounded equivalent ratio of red to black pens is 1 to 4.

This indicates that there are 4 black pens in the package for every red pen.

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We can start by drawing a diagram of the situation: