Find the equation of the line. Write the answer in standard form.
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If Ojemba is sitting on a sled on the side of a hill inclined at 60° and  weight of Ojemba and sled is 160 pounds , then magnitude of force needed for Mandisa to keep sled from sliding down the hill is 355.59 N   .

the inclination angle of the the side of the hill is = 60° ;

the compound mass of Ojemba and Sled is = 160 pounds ,

On conversion we get the mass in Kg is = 72.57 Kg .

the acceleration due to gravity is , [tex]g = 9.8 m/s^{2}[/tex] ;

The force required for Mandisa to keep sled from sliding down the hill can be calculated by the formula ;

[tex]F = mgSin\theta[/tex] , Substituting the values ,

we get ;

[tex]F = 72.57\times 9.8\times Sin(30\textdegree)[/tex]

[tex]F = 72.57\times 9.8\times \frac{1}{2}[/tex] ;

So , [tex]F = 355.59 N[/tex] .

The required magnitude of the force is 355.59 N .

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On solving the provided question, we can say that - the value of the cube root is 19683 =  27

In mathematics, y3 = x since the cube root of a number x equals a number y. Each non-zero real integer has precisely one real cube root, one set of complex conjugate cube roots, and three different complex cube roots. When a number is multiplied three times, the result is the cube root of that number. Three cube roots, the final cube root, is the symbol for the cube root. The opposite of cubing an integer is finding the cube root of that number. Prime factorization is a fairly straightforward technique that may be used to get a number's cube root. The sign stands for a cube root.

here,

we have f(27)

cube will be [tex]( 27 )^3[/tex] = 19683

and f(-343) = -7

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If you want to have $70,000 in 15 years, you need start saving money now in a savings account that earns 6.0% annually compounded weekly.

When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.Compounding is effective for both promised and unguaranteed products. All or part of your money could be lost.

Use the compound interest formula and enter the figures you are familiar with. Then find a solution for the unknown number.

A = P(1 +r/n)^(nt)

where A represents the balance of the account, P represents the amount invested, r represents the yearly rate, n represents the number of times per year interest is compounded, and t is the number of years.

Filling in the given values, we have ...

70000 = P( 1 + 0.06/52)^(52*15) = P(2.4583)

P = 70000/2.4583 = 28474.96

You would need to deposit 28474.96 in order to have 70000 in 15 years.

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The approximate length, in feet, of lights that she needs to create one triangle is 64

This is an approximate estimate as the exact length would depend on the specific measurements of the roof line. However, if the roof line is a typical house roof and the string lights are hung horizontally across to connect the ends of the roof line, creating a triangle, the approximate length of lights needed would be the hypotenuse of the triangle (the longest side) which is equal to the square root of (leg 1^2 + leg 2^2).

A typical house roof is approximately 40 feet wide and 20 feet tall, which creates a right triangle with legs of 40 and 20. The hypotenuse of this triangle (the length of lights needed) would be approximately 64 feet (the square root of (40^2 + 20^2) = 64).

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Answer:

Step-by-step explanation:

1 ft= 12 inches

So 5ft = 60 Inches

4= 0.3

Thus, Its 60.3

Answer:

24

Step-by-step explanation:

24 it's could be ok. I think 24 is good.

Answer: I think it's nonsense??? Not quite sure...

Step-by-step explanation:

Answer:

168 - 147 = 21

21/168 = 12.5

Answer:

42

Step-by-step explanation:

2 + 3(5) + 5(5)

2 + 15 + 25

Which equals..

42

Answer:

42

Step-by-step explanation:

IF b=5

Now,

2+3b+5b

=. 2 + 3*5 + 5*5

=. 2 + 15 + 25

=. 42

The reasonable solutions for this situation is (1, 3.5) and (2, 2)

A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.

Audrey has x pounds of red grapes and y pounds of green grapes.

She has less than 5 pounds of grapes in all, hence:

x + y < 5

Also, x ≥ 0, y ≥ 0

a) The option (–1, 2) is wrong because x = -1 < 0

b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5

c) The option (2, 2) is correct because 2 + 2 = 4 < 5

d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.

e) The option (5, 0) is wrong because 5 + 0 is not less than 5

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Answer:

128cm²

Step-by-step explanation:

Formula to find area of rectangle is l×b

In order to find the area of the rectangle we need to apply that formula

[tex]A =lb[/tex]

[tex]A = 16[/tex]×[tex]8[/tex]

[tex]A = 128[/tex][tex]cm[/tex]²

Hence ,  the area of the given rectangle is 128cm²

The three main parts to a chemical word equations are the reactants , the products  and the arrow .

What is a Chemical Equation ?

A chemical equation is defined as a representation of a chemical reaction expressing it in in terms of symbols of the substances.

The three main parts of the Chemical Equation are :

(i) The Reactants :  During a chemical reaction, these elements combine and undergo some chemical changes. They are present on left side of  reaction equation.

For Example : [tex]CH_{4} + 2O_{2}[/tex] ;

(ii) The Arrow :  It indicates formation of products from reactant . It is represented as " → " ;

(iii) The Products : Products are the result of chemical reactions between their reactants. It is present on right side of the chemical equation.

For example, : [tex]CO_{2} +2H_{2} O[/tex]

So , overall Chemical  Equation can be written as : [tex]CH_{4} + 2O_{2}[/tex] → [tex]CO_{2} +2H_{2} O[/tex] .

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The blend contains 16% of type A and 8% of type B.

When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.

Let p be the percentage of type b used for the mix

2p be the percentage of type a used for the mix

2p × 300 + p × 500 = 0.11 × 800

simplifying the above equation, we get

p = 0.08 or 8%

Substitute the values in the above equation

2p = 2 × 0.08 = 0.16 or 16%

16 % of type a and 8 % of type b exists utilized for the mix.

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The required percentage of raisins are each type of raisin bran are 16% and 8%.

When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.

Let p be the percentage of type b used for the mix

2p be the percentage of type a used for the mix

2p × 300 + p × 500 = 0.11 × 800

simplifying the above equation, we get

p = 0.08 or 8%

Substitute the values in the above equation

2p = 2 × 0.08 = 0.16 or 16%

16 % of type a and 8 % of type b exists utilized for the mix.

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Answer:The cost for each person is not always the same. It is not a linear relationship between number in group and cost in dollars. Since we have only 4 rows it's difficult to make an accurate prediction for cost of $50, In addition, we don't have any formula or equation that can represent this data set.

The best way to find out how many people will go to movie with $50 is by looking at the table.

So the answer is, We don't have any information that can give us a prediction of number in group for a cost of $50,

Step-by-step explanation:

No, 4, 8 and 10 cannot be the sides of a right triangle. So 4, 8 and 10 does not make a right triangle.

In a right triangle, the side opposite the right angle (the hypotenuse) is the longest side. The side opposite the 90-degree angle is the hypotenuse and it follows the Pythagorean theorem which states that the square of the hypotenuse is equal to the sum of the squares of the legs, so:

c² = a² + b²

In this case, c = 10, a = 8 and b = 4,

so 8² + 4² = 64 + 16 = 80 ≠ 10²

That is it does not follows the theorem. Therefore, 4, 8 and 10 cannot be the sides of a right triangle.

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So Amy needs to use 2 pounds of Colombia beans and 32 pounds of Kenya beans to create her blend.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

We are aware that an inverse variation or indirect variation occurs when two values are coupled in a way that a rise in one generates a corresponding reduction in the other, and vice versa.

Let x be the number of pounds of Kenya beans and y be the number of pounds of Colombia beans. We know that:

x + y = 30 (since the blend is 30 pounds)

We also know that the blend sells for $8.50 per pound, so the total cost of the blend is:

8.50(x + y) = 8.50(30) = $255

We know that the cost of the Kenya beans is $9.00 per pound and the cost of the Colombia beans is $7.50 per pound, so the total cost of the Kenya beans is:

9.00x and the total cost of the Colombia beans is 7.50y

We can set up the following equation:

9x + 7.5y = 255

We have 2 equations and 2 variables, we can solve this system of equation by different methods, one of them is substitution:

x + y = 30

9x + 7.5y = 255

We can substitute the first equation into the second equation

9(x + y) + 7.5y = 255

9(30) + 7.5y = 255

270 + 7.5y = 255

7.5y = -15

y = -2

So Amy needs to use 2 pounds of Colombia beans. We can substitute that value into the first equation to find the amount of Kenya beans:

x + (-2) = 30

x = 32

So Amy needs to use 32 pounds of Kenya beans.

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Answer:

x=-12/5

Step-by-step explanation:

2x-7=7x+5

2x-7x=5-(-7)

-5x=5+7

x=12/-5

x=-12/5

One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.

A mole is a unit of measurement in chemistry that expresses the amount of a substance. It is defined as the number of entities (such as atoms, ions, or molecules) in a sample of the substance. The number of entities in one mole of a substance is known as Avogadro's number.

Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.

One mole of a substance is equal to Avogadro's number, which is approximately 6.022 x 10^23.

The mole of H2 (hydrogen gas) is the number of H2 molecules in a sample of hydrogen gas. One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.

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Answer:

A

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

140° is an exterior angle of the triangle , then

∠ B + 90° = 140° ( subtract 90° from both sides )

∠ B = 50°

∠ ACB and ∠ DCB are a linear pair and sum to 180° , that is

∠ ACB + 140° = 180° ( subtract 140° from both sides )

∠ ACB = 40°

Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.

A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.

5 : This is the number of baseball players who are in 8th-grade

73: This is the total of players. You get this number if you add all the numbers given.

Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".

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A polynomial with a degree of two is referred to as a quadratic polynomial.

When the highest power of a variable term in a polynomial expression equals 2, the term is considered a quadratic polynomial. The exponent of a polynomial is all that is considered when determining its degree. It does not account for the power of a coefficient or constant term.

When a quadratic polynomial is equated to 0, it generates a quadratic equation or a quadratic function. The solutions to a quadratic equation are known as its roots or zeros.

A quadratic polynomial is a second-degree polynomial with the highest degree term having the value 2 as its coefficient. A quadratic equation is written in its general form as ax² + bx + c = 0.

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When you log an e, you are essentially taking the natural logarithm of the number. This means that you are taking the logarithm of a number to the base e, which is about 2.718. The result of this calculation is the number of times the number must be multiplied by itself to get the original number.

For example, if you were to log an e, it would be equal to 1, since e x e = e. If you log a number bigger than e, such as 8, the result would be equal to 2.079, which means that 8 must be multiplied by itself twice (2.079 times) to get the original 8.

In general, when you log a number, you can think of it as a way of seeing how many times that number needs to be multiplied by itself to get the original number. This can be useful in many fields, from mathematics to engineering to physics, to find the mathematical relationship between two numbers.

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[tex]\dfrac{15}{4} \div\dfrac{5}{8}[/tex]

In order to divide two fractions, you will need to use the KCF method.

Keep

Change

Flip

This means that we will keep the first fraction, change the division to multiplication, and flip the second fraction(reciprocal).

[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]

Multiply:

[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]

[tex]\dfrac{15\times8}{4\times5}[/tex]

[tex]=\dfrac{120}{20}[/tex]

Simplify:

[tex]120\div20[/tex]

[tex]=\fbox{6}[/tex]

Answer: 6

Step-by-step explanation:

1. 15/4 divided by 5/8 = 120/20

15/4 / 5/8 = 15/4 times 8/5 = 15 time 8 over 4 time 5 = 120/20

2. 120/6 = 6

Elimination is a very easy method when it comes to solving simultaneous equations.

First, the best thing to do is bring the equations down to their lowest form. Try to remove the fractions in the co-efficient and have the equation in the standard form where every variable is expressed as individually as possible.

The next thing to do is to select a variable and manipulate the equations in such a way that the coefficients of that variable across all of the equations are the same. Here select any 2 equations to work on first if more than 2 are given

Now take one of the equations and multiply it by -1.

Add the equations up to eliminate the variable and derive the other variable(s)

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Answer:

You multiply one side and then the other. Basically doing hxw

Nolan would expect to earn $157 in a day when he waits in 12 tables.

Now, According to the question:

We have the following information:

Each day Nolan works, Nolan will make a guaranteed wage of $25, however the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on.

Now, for waiting on 12 tables, he will get the fixed amount of 25 dollars and the amount for 12 tables.

So, the total amount will be:

25+11 × 12

$157

Hence, Nolan would expect to earn $157 in a day when he waits in 12 tables.

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Answer:

1.Solve one of the equations for either variable.

2.Substitute the expression from Step 1 into the other equation.

3.Solve the resulting equation.

4.Substitute the solution in Step 3 into one of the original equations to find the other variable.

5.Write the solution as an ordered pair.

6.Check that the ordered pair is a solution to both original equations.

Step-by-step explanation:

The peak is located at R=1 according to a power curve analysis. To put it another way, the load and source resistance must match.

The ski area's name needs to be changed first. Squaw is not a kind way to refer to a woman. It is an expression that refers to female genitalia. (a decent slang equivalent in English begins with "c" and rhymes with "runt") During my time as a teacher in an Indian school, I learned this in a very embarrassing manner.

If we suppose that each person weighs roughly 70 kilograms (154 lbs) on Earth, then the power required to simply raise the people is P = W/t, and since W = mgh in this situation, P = W/t = mgh/t = (47,000 people)(70 kg/person).

(2 MW) = (1791222.222 W)(9.8 N/kg)(200 m)/(3600 s).

The complete question is:

Squaw Valley ski area in California claims that its lifts can move 47,000 people per hour.  If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.

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The measure of ∠S is 59.4° for trignometric identities

What are trigonometric identities?

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

ΔSTU:

s = 50 inches

t = 58 inches

u = 630 inches

Applying the cosines rule on ΔSTU.

s² = t² + u² - 2 x t x u x cos S

cos S = (t² + u² - s²) / 2tu

cos S = (58² + 27² - 50²) / (2 x 58  x 27)

cos S = (3364 + 729 - 2500) / 3132

cos S = 0.5086.

∠S = (0.5086)

∠S = 59.4°

Thus,

∠s angle value is  59.4°.

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Area of circle and  formula and radius of circle is 9 pi ( x y ^3 )^3.

A circle's area is equal to pi times the radius squared (A = r2).

Pi times the radius r squared equals the area of a circle.

π ⋅ ( r a d i u s)2

In the formula for the area of a circle, substitute the value of the radius r =3. 3.14 is about how big a number pi is.

pi * 3^2

Raise 3 to the power of 2 to arrive at 9.

pi * 9

9 must be moved to the left of. 9 pi ( x y ^3 )^3.

Area of circle and  formula and radius of circle is 9 pi ( x y ^3 )^3.

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