Gigi’s parents pay $1,400 for a mortgage and $250 for a car loan each month. They pay $175 monthly for health insurance and spend about $300 a month on food. Utilities cost about $150 a month. They pay about $100 for the monthly Internet and cell phone plan and set aside $200 per month for retirement.



This month, Gigi’s parents spend $285 on food, $175 on utilities, and $112 on the Internet and cell phone plan. What are her parents’ total fixed and variable expenses this week?





fixed expenses total: $

variable expenses total: $

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.

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.

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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Answer:

Step-by-step explanation:

Alright, lets get started.

The given expression is :

[tex]2x^3+10x^2+4x+20[/tex]

taking 2 common factor

[tex]2(x^3+5x^2+2x+10)[/tex]

[tex]2(x^3+2x+5x^2+10)[/tex]

[tex]2[(x+5)(x^2+2)][/tex]

So, the correct answer is option B :    answer

Hope it will help :)

The correct option is B. 81 mm, 7 mm, 72 mm could be the lengths of the sides of a triangle.

To determine if a set of numbers could be the lengths of the sides of a triangle, the Triangle Inequality Theorem must be satisfied. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's apply this theorem to each set of numbers:

A. 81 mm, 7 mm, 6 mm

- The sum of the two smallest sides is 81 + 6 = 87 mm, which is greater than the third side, 7 mm. However, the sum of the two smallest sides, 7 + 6 = 13 mm, is not greater than the largest side, 81 mm. Therefore, these lengths cannot form a triangle.

B. 81 mm, 7 mm, 72 mm

- The sum of the two smallest sides is 7 + 72 = 79 mm, which is greater than the third side, 81 mm. This set satisfies the Triangle Inequality Theorem.

C. 81 mm, 7 mm, 88 mm

- The sum of the two smallest sides is 81 + 7 = 88 mm, which is equal to the third side, 88 mm. According to the Triangle Inequality Theorem, the sum must be strictly greater than the third side, so these lengths cannot form a triangle.

D. 81 mm, 7 mm, 77 mm

- The sum of the two smallest sides is 7 + 77 = 84 mm, which is greater than the third side, 81 mm. However, the sum of the two smallest sides, 81 + 7 = 88 mm, is not greater than the third side, 77 mm. Therefore, these lengths cannot form a triangle.

Based on the Triangle Inequality Theorem, the only set of lengths that can form a triangle is option B: 81 mm, 7 mm, 72 mm.

To honor 50 years of business, All Strikes Bowling is having an anniversary special. The game he can bowl is 25.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

To honor 50 years of business, All Strikes Bowling is having an anniversary special.

Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs shoes.

Charlie can bowl 25 games.

= 20 - 1.25

= 18.75

So, he can bowl game

= 18.75/ 0.75

= 25 games

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In this detailed answer, the probabilities of drawing two coins from Kevin's pocket - with 6 nickels and 4 dimes - are explained. The probabilities of both coins being nickels and dimes are 0 due to the lack of replacement, while the probability of one nickel and one dime is 4/15.

To calculate the probabilities of drawing coins from Kevin's pocket, where he has 6 nickels and 4 dimes:

Probability both coins are nickels: Since each draw affects the remaining number of nickels and dimes, the probability is 0.

Probability both coins are dimes: Similarly, as the draws are not independent, the probability here is also 0.

Probability of one nickel and one dime: Since Kevin has 6 nickels and 4 dimes, the probability of drawing a nickel first is 6/10 (6 nickels out of 10 coins) and drawing a dime second is 4/9 (4 dimes remaining out of 9 coins), which equals 24/90 or 4/15.

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:

P(red or blue) = 5/18 + 6/18 = 11/18

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

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.

Therefore, an organic cleaner is not as effective as a non-organic cleaner in killing germs that cause colds and the flu.

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.