(2a-b-c)³+(2b-c-a)³+(2c-a-b)³ factorise​

Answer:

It will take 22 hours

Step-by-step explanation:

10925 ÷ 500 = 21.9 = 22 hours

Answer:

110 milligrams of potassium

Step-by-step explanation:

The number of milligrams of potassium in the serving of 2 cups of fruit cocktail is 220 milligrams.

Given that:

A \(\frac{1}{2}\) cup serving of fruit cocktail with 55 milligrams of potassium.

It is required to find the milligrams of potassium in 2 cups of fruit cocktail

Here, the proportional concept can be used.

Amount of potassium in \(\frac{1}{2}\) a cup serving of fruit cocktail = 55 milligrams

Amount of potassium in 1 cup serving of fruit cocktail \(=55\div\frac{1}{2}\)

                                                                                         \(=55\times\frac{2}{1}\)

                                                                                         \(=110\)

Now, find the amount of potassium in 2 cups of cocktail.

In 2 cups of fruit cocktail, the amount of potassium = 110 × 2

                                                                                     = 220 milligrams

Hence, the amount of potassium in 2 cups is 220 milligrams.

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The value of sin(u+v) given tan u = 15/8 is -9/221

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the their angles.

A right-angled triangle has 3 sides, hypotenuse, opposite and adjacent. The following should be noted:

Sin = Opposite / Hypothenuse

Tan = Opposite / Adjacent

Cos = Adjacent / Hypothenuse

When tan u = 15/8

Opposite = 15

Adjacent = 8

Hypothenuse will be:

= ✓(15² + 8²)

= ✓(225 + 64)

= ✓289

= 17

Therefore sin u = 15/17

When cos v = -5/13, it should be noted that sin v will be -12/13.

Therefore, sin(u + v) will be:

= 15/17 + (-12/13)

= 15/17 - 12/13

= 195/221 - 204/221

= -9/221

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Answer:

$23

Step-by-step explanation:

First, we find what is 15% of $20.

0.15 times 20 is 3. Therefore, we know there was a markup of $3.

Then, we add the mark-up to the cost to store, and get $23.

So, the selling price is $23.

To find the missing sides and angles of a right triangle with side b = 32 and side c = 51, we can use the Pythagorean theorem and trigonometric ratios.

Let's denote the missing side as a and the angles as A and B, with B being the right angle.

Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c):

a^2 + b^2 = c^2

Plugging in the given values, we have:

a^2 + 32^2 = 51^2

a^2 + 1024 = 2601

a^2 = 1577

a ≈ 39.73

Therefore, the length of the missing side a is approximately 39.73.

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Answer:

4:3

Step-by-step explanation:

16:12=8:6=4:3

Answer:

4:3

Step-by-step explanation:

16 and 12 can both be divided by 4

16/4 = 4 12/4 = 3

so your simplified ratio is 4:3

Answer: Ok, so the tree would start with the ten marbles going to 1 of the reds, 1 of the black , and get till you used up all the black, then do 2/10 and 8/10 to 12 and repeat the 1 part step, and then do 4/12 and 8/12 and add it all up and place the probability out of 22.

Step-by-step explanation:

A water balloon is dropped out of a fifth floor window and hits an unsuspecting person below 4.0 seconds later. the window is approximately 78.4 meters high.

To determine the height of the window from which the water balloon was dropped, we can use the formula for free fall:

\(h = 0.5 × g × t^2\)

where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time in seconds (4.0 seconds in this case).

Step 1: Plug in the given values.

\(h = 0.5 × 9.8 × (4.0)^2\)

Step 2: Calculate the square of the time.

\((4.0)^2 = 16\)

Step 3: Multiply 0.5 by the acceleration due to gravity.

0.5 × 9.8 = 4.9

Step 4: Multiply the result from step 3 by the result from step 2.

4.9 × 16 = 78.4

So, the window is approximately 78.4 meters high.

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PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction. The solution to the Expression (3^0 * 8^2)^-2 is 1/4096.

The expression (3^0 * 8^2)^-2, the order of operations, which is typically referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Simplify the exponent expressions within the parentheses:

(3^0 * 8^2) = (1 * 64) = 64

Step 2: Rewrite the expression with the simplified value:

(64)^-2

Step 3: Apply the exponent rule for a negative exponent:

(64)^-2 = 1 / (64)^2

Step 4: Evaluate the expression within the parentheses:

(64)^2 = 64 * 64 = 4096

Step 5: Rewrite the expression with the simplified value:

1 / 4096

Therefore, the solution to the expression (3^0 * 8^2)^-2 is 1/4096.

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The 16th term of the arithmetic sequence is -60.

To find the 16th term of an arithmetic sequence with a first term of 0 and a common difference of -4

we can use the formula for the nth term of an arithmetic sequence:

nth term = a + (n - 1)d

where:

a = first term

d = common difference

n = term number

Substituting the given values, we have:

16th term = 0 + (16 - 1) × (-4)

= 0 + 15(-4)

= 0 - 60

= -60

Therefore, the 16th term of the arithmetic sequence is -60.

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Step-by-step explanation:

-3x+7y = -18 ...1

4x-4y = 8 ...2

...1 × 4

-12x + 28y = -72 ...3

...2 × 3

12x - 12y = 24 ...4

...3 + ...4

28y - 12y = -72 + 24

16y = -48

y = -3

Replace y = -3 in ...2

4x - 4(-3) = 8

4x + 12 = 8

4x = 8 - 12

4x = -4

x = -1

Answer:

\(\huge\boxed{\boxed{(x,y)=(-1,-3)}}\)

Step-by-step explanation:

multiply first equation by 4 and second by 3 respectively:

\( \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}\)

combine the equations:

\( \underline{ \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}} \\ \displaystyle16y = - 48\)

divide both sides by -48:

\( \displaystyle \: \frac{16y}{16} = \frac{ - 48}{16} \\ y = - 3\)

substitute the value of y to the second equation

\( \displaystyle \: 4x - 4. - 3 = 8\)

simplify multiplication:

\( \displaystyle \: 4x + 12 = 8\)

cancel 12 from both sides:

\( \displaystyle \: 4x = - 4\)

divide both sides by 4

\( \displaystyle \: \frac{4x}{4} = \frac{ - 4}{4} \\ x = - 1\)

therefore our solution is

\(\displaystyle (x,y)=(-1,-3)\)

Answer:

yes

Step-by-step explanation:

Answer:192

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

the slope is -3 because it goes down 3 y for every 1 forward on x

Answer:

\(m=-3\)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (1, -3)

Point (-1, 3)

Step 2: Find slope m

Answer:

-x-15

Step-by-step explanation:

Expand using the FOIL Method.

add me on Discord for step by step pls

\(\implies {\blue {\boxed {\boxed {\purple {\sf {-(x+15)}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

➺\(\:( {x}^{2} - 5)(x + 3) + (x + 4)(x - {x}^{2} )\)

➺\( \: {x}^{2} (x + 3) - 5(x + 3) + x(x - {x}^{2} ) + 4(x - {x}^{2} )\)

➺\( \: {x}^{3} + 3 {x}^{2} - 5x - 15 + {x}^{2} - {x}^{3} + 4x - 4 {x}^{2} \)

Combining like terms, we have

➺\( \: {x}^{3} - {x}^{3} + 3 {x}^{2} + {x}^{2} - 4 {x}^{2} - 5x + 4x - 15\)

➺\( \: - x - 15\)

➺\(\: - (x + 15)\)

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}\)

Answer: 756: 1764

756 girls and 1,764 boys

Step-by-step explanation:

Girls to boys- 3:7

Total Students: 2,520

Using the information given, you will create an equation.

3x + 7x = 2,520

10x = 2,520

X = 252

Now you plug-in 252 for x in your ratio

X is the the number of people

3(252) : 7(252)

756: 1764

Now when you add these numbers, you get 2,520 which is the total number of students in all. This proves your answer to be correct.

Hope this helps!

The number of girls were in the class is 756 and the number of boys were in the class is 1764.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of the number of girls to the number of boys was 3 to 7.

2,520 students were present

Now, 3+7 =10

Number of girls =3/10 ×2,520

= 756

So, the number of boys =2520-756

= 1764

Therefore, the number of girls were in the class is 756 and the number of boys were in the class is 1764.

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The total expenditure for raising the poultry farm is GHC 5458.60.

To calculate the total expenditure for raising the poultry farm, you need to sum up all the expenses:

1. Cost of 3 large coops at GHC650 each:

  Total cost of coops = 3 coops * GHC650/coop

                                   = GHC1950

2. Cost of 1500 day-old chicks at GHC75 for 100 chicks:

  Total cost of chicks = (1500 chicks / 100 chicks) * GHC75

                                   = GHC1125

3. Cost of 1000 bags of feed at GHC1.75 per bag:

  Total cost of feed = 1000 bags * GHC1.75/bag

                                 = GHC1750

4. Transport cost for conveying the 1000 bags of feed at 50gp (GHC 0.50) per bag:

  Total transport cost = 1000 bags * GHC0.50/bag

                                    = GHC500

5. Cost of drugs and vaccines at GHC120:

6. Other expenses amounted to GHC13.60.

Now, add up all these expenses to find the total expenditure:

= Cost of coops + Cost of chicks + Cost of feed + Transport cost + Cost of drugs and vaccines + Other expenses

= GHC1950 + GHC1125 + GHC1750 + GHC500 + GHC120 + GHC13.60

= GHC5458.60

So, the total expenditure is GHC5458.60.

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Answer:

I think the answer is c

Step-by-step explanation:

Answer:

its 1 and 2

Step-by-step explanation:

Because i said so

Brad might have measured the depth of water in a swimming pool.

To determine which items Brad might have measured, we need to convert 2.1 x 10⁴ cm into more familiar units and compare it to the dimensions of each item.

2.1 x 10⁴ cm = 21000 cm

Length of a city block: City blocks can vary in length, but they are typically much longer than 21000 cm. Unlikely.

Length of a city park: City parks can also vary in size, but they are generally much larger than 21000 cm. Unlikely.

Height of a person: The average height of a person is around 170 cm, which is much shorter than 21000 cm. Unlikely.

Distance across a city: Cities can vary in size, but the distance across a city is typically much greater than 21000 cm. Unlikely.

Height of an apple tree: Apple trees can vary in height, but 21000 cm is much taller than any apple tree. Unlikely.

Width of a screen in a theater: Theater screens can vary in size, but 21000 cm is much longer than any theater screen. Unlikely.

Depth of water in a swimming pool: Swimming pools can vary in depth, but 21000 cm is a reasonable depth for a large swimming pool. Possible.

Therefore, Brad might have measured the depth of water in a swimming pool.

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Answer:

4.32

Step-by-step explanation:

if your question was 1.8x2.4 then it is 4.32.

1.8

x2.4

_____

4.32

first you take the 0.8 and multiply it by 0.4 then by 2, then take the 1 and multiply it by 0.4 and 2 after that you should get 4.32 after adding them.

Answer:

45x

Step-by-step explanation:

Just expand and coolect to get 9x5=45 and add x

Answer:

\(9(5x) \\ \\ = 45x\)

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So Is This (80+15) or something

The total number of people going for the field trip is 240 people

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data,

The number of students in the school bus = 36 students

The number of adults in the school bus = 4 adults

So,

Total number of people on 1 school bus = number of students + number of adults

Total number of people on 1 school bus \(= 36 + 4\)

                                                                  \(= 40 \ \text{people}\)

Now,

Total number of people on 6 school buses = Total number of people on 1 school bus x 6

Total number of people on 6 school buses \(= 40 \times 6\)

                                                                       \(= 240 \ \text{people}\)

Hence, the total number of people going for the field trip is 240 people

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By consolidating the two balances onto the credit card with the lower interest rate, Marcia would save a total of $1,526.40 in interest after 5 years.

To calculate the amount saved in interest, we need to determine the interest paid on each credit card over the 5-year period.

For Card A, the initial balance is $1,879.58, and the APR (Annual Percentage Rate) is 14%. To find the monthly interest rate, we divide the APR by 12 (months in a year), which gives us 1.17%. Over 5 years, there will be 60 monthly payments. Using an amortization formula, we can calculate the total interest paid on Card A as follows:

Total interest on Card A = (Monthly payment x Number of payments) - Initial balance

= ($43.73 x 60) - $1,879.58

= $2,623.80 - $1,879.58

= $744.22

For Card B, the initial balance is $861.00, and the APR is 10%. Following the same calculation method, the total interest paid on Card B over 5 years is:

Total interest on Card B = (Monthly payment x Number of payments) - Initial balance

= ($18.29 x 60) - $861.00

= $1,097.40 - $861.00

= $236.40

Therefore, by consolidating the balances onto the card with the lower interest rate, Marcia would save $744.22 on Card A and $236.40 on Card B, resulting in a total interest savings of $980.62 ($744.22 + $236.40). However, the question asks for the amount saved, not the total interest paid. Thus, to calculate the actual savings, we subtract the total interest savings from the sum of the initial balances:

Savings in interest = (Initial balance of Card A + Initial balance of Card B) - Total interest savings

= ($1,879.58 + $861.00) - $980.62

= $2,740.58 - $980.62

= $1,759.96

Therefore, the correct answer is option (a) $1,526.40, which represents the amount saved by consolidating the two balances onto the card with the lower interest rate.

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The probability model for Eitan randomly selecting one volcano in the world on which to conduct an extensive study is approximately 36.1% for cinder cone volcanoes, 50.0% for shield volcanoes, and 13.9% for stratovolcanoes based on the observed frequencies.

To create a probability model based on the observed frequencies, we need to calculate the probabilities of selecting each type of volcano. This can be done by dividing the frequency of each type of volcano by the total number of volcanoes observed.

Let's calculate the probabilities for each type of volcano:

Cinder cone volcanoes:

Probability = Frequency of cinder cone volcanoes / Total number of volcanoes observed

          = 13 / (13 + 18 + 6)

          ≈ 0.361 or 36.1%

Shield volcanoes:

Probability = Frequency of shield volcanoes / Total number of volcanoes observed

          = 18 / (13 + 18 + 6)

          ≈ 0.500 or 50.0%

Stratovolcanoes:

Probability = Frequency of stratovolcanoes / Total number of volcanoes observed

          = 6 / (13 + 18 + 6)

          ≈ 0.139 or 13.9%

Therefore, the probability model for Eitan randomly selecting one volcano in the world on which to conduct an extensive study is approximately:

- Cinder cone volcanoes: 36.1%

- Shield volcanoes: 50.0%

- Stratovolcanoes: 13.9%

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If Jack is given an ice cream and it is equally likely that he is given a chocolate, vanilla, or strawberry flavor, it means that each flavor has the same probability of being given to him.

Let's denote the probability of being given chocolate as P(chocolate), the probability of being given vanilla as P(vanilla), and the probability of being given strawberry as P(strawberry).

Since the probabilities are equal for each flavor, we can say: P(chocolate) = P(vanilla) = P(strawberry) = 1/3 This means that the probability of Jack receiving chocolate, vanilla, or strawberry flavor ice cream is 1/3 for each flavor.

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Answer:

x is given as -1.5. Substitute to confirm

Answer:

GRAPH OF 3x + y = 3 (written on attachment)

GRAPH OF 2y = 10 - 6x (written on attachment)

Answer:

34-13.95 = 20.05

Step-by-step explanation:

Answer:

20.05

Step-by-step explanation:

34 - 13.95 = 20.05

The general solution of the given homogeneous differential equation is:y = ±x√(Cx² + 2)

The given differential equation is: 2xyy' + (x² - y²) = 0

We have to find the general solution of the given homogeneous differential equation. To solve the above differential equation, we will use the substitution method.

Put y = vx and y' = v + xv'

Differentiating both sides w.r.t x: y' = v + xv' ⇒ v' = (y' - v)/x

Differentiating again w.r.t x: y'' = v' + xv'' + v' ⇒ y'' = (y'' - 2y'v + v² + xv')/x

Substituting these values in the given differential equation:

2x(v)(v + xv') + (x² - v²x²) = 0

2v + 2x²v' + x - v² = 0

2x²v' + 2v/x - v³/x = -1/x

We can write the above differential equation as:

2x²dv/dx + 2v/x = v³/x - 1/x

Separating the variables and integrating both sides:

∫dx/x = ∫[v/(v² - 2)]dv/x

⇒ ln |x| + ln |v² - 2| + C

⇒ ln |x(v² - 2)| = ln |Cx|

⇒ v² - 2 = Cx² (where C is a constant)

⇒ v = ±√(Cx² + 2)

Putting the value of v in y = vx, we get:

y = x√(Cx² + 2) and y = -x√(Cx² + 2)

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