How to Factor out the coefficient of the variable 3n-24

The radius of the penny is 9.54 millimeters.

The circumference means the length of the literal line that surrounds and forms a circle.

The formula for the circumference of the circle is given by

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

Where,

r is the radius

and π = 3.14

A radius is a straight line from the center of a circle to the circumference of a circle.

According to the given question.

We have a penny whose circumference is 59.69 millimeters.

Let r be the radius of the penny and 2πr be the circumference of the penny.

Since we know that, the shape of the penny is circular.

Therefore,

The radius, r of the penny is given by

[tex]2\pi r= 59.69[/tex]

[tex]\implies r = \frac{59.69}{2\pi }[/tex]

[tex]\implies r = \frac{59.69}{2(3.14)}[/tex]

[tex]\implies r = \frac{59.69}{6.28}[/tex]

[tex]\implies r = 9.54\ millimeters[/tex]

Hence, the radius of the penny is 9.54 millimeters.

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The equation that represents each mixed number as a sum of whole numbers and unit fractions of [tex]4\frac{1}{4}[/tex] is  [tex]4\frac{1}{4}[/tex] = 4 + 1/4.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

We have the mixed fraction,

[tex]4\frac{1}{4}[/tex].

Converting the mixed fraction to an improper fraction,

[tex]4\frac{1}{4}[/tex] = 17/4

We need to write it as a sum of whole numbers and unit fractions:

So, it becomes,

[tex]4\frac{1}{4}[/tex] = 4 + 1/4

[tex]4\frac{1}{4}[/tex] = (16 + 1)/4

[tex]4\frac{1}{4}[/tex] = 17/4

Therefore, [tex]4\frac{1}{4}[/tex] = 4 + 1/4 is the required equation.

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Answer:

3(x+6)

Step-by-step explanation:

A line plot has been created based on the number of pages Consuela read each night over a week, showing the data without any outliers. Values range from 7 to 11 pages, with no significant deviations that would classify as outliers.

To create a line plot of the number of pages Consuela read each night, you would place a horizontal axis labeled with numbers representing the number of pages read, e.g., 7, 8, 10, and 11. Above each number, you would put a dot for each night that she read that number of pages. For example, she read 8 pages 3 times across the week, so above the number 8 on the line plot, you would place three dots.

Line Plot Creation and Outliers

The line plot for Consuela's reading log:

7 pages: 1 dot (Thursday)

8 pages: 3 dots (Monday, Friday, Saturday)

10 pages: 2 dots (Wednesday, Sunday)

11 pages: 1 dot (Tuesday)

To determine if there are any outliers in the data, we have to look for any dots that are not close to the other dots. An outlier is typically a data point that is significantly higher or lower than the rest of the data. In the case of Consuela’s reading log, the values are all quite close to each other, with the range being from 7 to 11 pages. There doesn't appear to be a value significantly different from the others; therefore, there are no outliers.

To find the length of the model car, set up a proportion and cross multiply.

To find the length of the model car, we need to use the scale factor given. The scale factor is 1.5 inches:3 feet. This means that for every 1.5 inches in the model, there are 3 feet in the actual car.

Given that the actual car is 13.75 feet long, we can set up a proportion:

1.5 inches / 3 feet = X inches / 13.75 feet

Cross multiplying, we get:

1.5 inches * 13.75 feet = 3 feet * X inches

Simplifying, we find that the length of the model car is approximately 6.88 inches.

Final answer:

To cover a cylindrical candle with a height of 10 inches and diameter of 1.5 inches, Khalil would need at least 50.635 square inches of wrapping paper, calculated by adding the lateral surface area and the areas of the top and bottom circles.

Explanation:

Khalil needs to calculate the amount of wrapping paper to cover a cylindrical candle. To find the surface area needed to wrap around the sides of the candle, we'll use the formula for the lateral surface area of a cylinder, which is Area (A) = 2πrL, where 'r' is the radius and 'L' is the height of the cylinder. Given that the candle is 10 inches tall and has a diameter of 1.5 inches, we calculate as follows:

To calculate the area needed to cover the top and bottom of the candle, we use the formula for the area of a circle, which is Area (A) = πr². The candle has two circular ends.

Adding the side area and the areas of the ends, the total wrapping paper needed is 47.1 square inches + 3.535 square inches = 50.635 square inches. Khalil should therefore use at least 50.635 square inches of wrapping paper to fully cover the cylindrical candle.

the ship would travel approximately 9685.82 miles from Iceland to Antarctica.

To convert the angle from degrees to radians, we use the conversion factor[tex]\( \pi \)[/tex]radians = 180 degrees.

[tex]\[ \text{Angle in radians} = \frac{\text{Angle in degrees} \times \pi}{180} \][/tex]

In this case, the angle in degrees is 140 degrees:

[tex]\[ \text{Angle in radians} = \frac{140 \times \pi}{180} \]\[ \text{Angle in radians} = \frac{140}{180} \times \pi \]\[ \text{Angle in radians} = \frac{7}{9} \pi \][/tex]

Next, we'll find how far the ship would travel using Earth's radius. The distance traveled on a circle is given by the formula:

[tex]\[ \text{Distance} = \text{radius} \times \text{angle in radians} \][/tex]

Given Earth's radius as 3960 miles and the angle in radians as [tex]\( \frac{7}{9} \pi \)[/tex], we can calculate the distance:

[tex]\[ \text{Distance} = 3960 \times \frac{7}{9} \pi \]\[ \text{Distance} = 3080 \pi \]\[ \text{Distance} \approx 9685.82 \text{ miles} \][/tex]

So, the ship would travel approximately 9685.82 miles from Iceland to Antarctica.

Answer:

30 bags

Step-by-step explanation:

Nc + Nd = 50

5Nc + 3Nd = 190

Multiply by -5 becomes:

-5Nc - 5Nd = -250

5Nc + 3Nd = 190

Equals:

-2Nd= -60

simplify:

-2Nd/-2 and -60/-2 = Nd= 30 bags

The probability that a randomly chosen student is a girl is 56%, calculated by subtracting the probability of a boy (44%) from 100%.

The question asks us to find the probability that a student selected at random is a girl, given that the probability of selecting a boy is 44%. Since the question does not provide information about any other genders, we can imply that all remaining students are girls.

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1, or 0% and 100%. So, if the probability of selecting a boy is 44% or 0.44, then the probability of selecting a girl would be the remaining percentage or fraction to reach 100% or 1.

This is calculated by subtracting the probability of selecting a boy from 1 or 100%, so 1 - 0.44 = 0.56 or 100% - 44% = 56%.

Therefore, the probability that a student selected at random is a girl is 56% or 0.56.

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The above me is clearly wrong. However, the reason I'm not going to post an actual answer is because this post is over 2 years old and there is a good chance the they aren't even in school anymore.

To factor 1/5 out of the algebraic expression 1/5x + 29/5, we remove the common term 1/5. This leaves us with 1/5 * (x + 29), not altering the value of the original expression.

To factor 1/5 out of 1/5x+29/5, we first need to understand what factoring entails. Factoring is basically expressing an algebraic equation as a product of its factors.

Step 1: Look at the expression '1/5x + 29/5'. We can see that '1/5' is common in both terms.

Step 2: Factor out the common term, which in this case is '1/5'.

So the expression '1/5x + 29/5' factored out would be '1/5 * (x + 29)'. Throughout this process, we have not changed the value of the original expression, only rewritten it in a different form.

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Answer:

The correct answer is C. Borrowing $10,000 more in students loans.

Option C - Borrowing $10,000 more in student loans is the correct Alternative.

We have list of assets and liabilities.

We have to determine which of given modification would  result in negative net worth.

Assets are the items your company owns that can provide future economic benefit. Liabilities are what you owe other parties.

According to the question -

Assets = House + Car + Stocks + Savings.

Total Assets = $90,000 + $11,000 + $2,500 +  $3,000 = $106500

Liabilities = Mortgage + Car loan + Student loan.

Total Liabilities = $78,000 +  $5,000 + $13,700 = $96700

Now if you borrow $10000 more in student loan then -

Total Liabilities = $78,000 +  $5,000 + $13,700 + $10000 = $96700 + $10000 = 1,06,700 > Assets.

Hence, Option C is the correct Alternative.

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The least number of rows she can make is when she puts N marbles in each row, such that N is the greatest common factor between 150 and 360.

To find the greatest common factor between 150 and 360 we can write them as the product of prime numbers.

150 = 15*10 = (3*5)*(2*5)

360 = 36*10 = (6*6)*(2*5) = (2*3*2*3)*(2*5)

greatest common factor between 150 and 360 is the product of these 3 factors:

GCF = 2*3*5 = 30

this means that we need to make rows with 30 marbles each.

150/30 = 5 rows of red marbles

360/30 = 12 rows of pink marbles.

A total of 5 + 12 = 17 rows.

The required Kristin bought 2 fancy shirts and 5 plain shirts.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Let's assume that Kristin bought x fancy shirts and y plain shirts. We know that the total number of shirts is 7, so:

x + y = 7

We also know that the total cost of the shirts is $131, that fancy shirts cost $28 and plain shirts cost $15. So we can write another equation:

28x + 15y = 131

Now we have two equations with two variables. We can use substitution or elimination to solve for x and y. Let's use substitution:

x + y = 7 -> x = 7 - y (subtract y from both sides)

28x + 15y = 131 -> 28(7-y) + 15y = 131 (substitute x with 7-y)

Expanding the brackets, we get:

196 - 28y + 15y = 131

-13y = -65

y = 5

So Kristin bought 5 plain shirts. We can substitute this value into either equation to find x:

x + y = 7 -> x + 5 = 7 -> x = 2

So Kristin bought 2 fancy shirts and 5 plain shirts.

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it would cost an employee $140 to purchase the coat at the sale.

Let's break down the problem step by step:

1. The store charges $280 for the coat, which is 40% more than the amount it cost the store to buy. This means that the store's cost (let's call it ( C )) can be found by first determining what 100% of the cost is (since $280 is 140% of the cost, as 100% + 40% = 140%). We can set up the equation:

[tex]\[ 140\% \text{ of } C = $280 \]\[ 1.4C = $280 \]\[ C = \frac{$280}{1.4} \]\[ C = $200 \][/tex]

So, the store's cost for the coat is $200.

2. At the end-of-season sale, store employees can purchase any remaining coats at 30% off the store’s cost. This means they pay 70% of the store's cost. We can calculate this as:

[tex]\[ 70\% \text{ of } $200 = 0.7 \times $200 = $140 \][/tex]

Therefore, it would cost an employee $140 to purchase the coat at the sale.

The possible combinations of reviews and new written pieces can be represented by the inequality 60r + 120n ≥ 600.

To represent the possible combinations of reviews and new written pieces, we can use the variables r for reviews and n for new pieces.

The total earnings can be calculated by multiplying the number of reviews by $60 and the number of new pieces by $120, and this must be greater than or equal to $600.

Therefore, the inequality that represents the possible combinations is 60r + 120n ≥ 600.

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