How do you factor 18x^4y^2+21x^5y-6x^3y^2

For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.

For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.

Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.

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use Pythagorean Theorem

2.5^2 + 6^2 = x^2

6.25 +36 = 42.25

x= sqrt(42.25) = 6.5 miles

Final answer:

To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.

Explanation:

The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.

Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.

The standard deviation of the miles Henry biked to the nearest tenth is 17.1. The standard deviation is calculated following the steps below.

First calculate the mean of the numbers that where given which is = 25 + 40 + 35 + 25 + 40 + 60+ 75/7

= 300/7

= 42.9

Then for each number, subtract the Mean and square the result.

(25 - 42.9)² = −17.9² = 320.41

(40-42.9)² = -2.9²= 8.42

(35-42.9)² = -7.9² = 62.41

(25-42.9)² = −17.9² = 320.41

(40-42.9)² = -2.9²= 8.42

(60-42.9)² = 17.1²= 292.41

(75-42.9)² = 32.1²= 1030.41

Then work out the mean of those squared differences. That is,

320.41+ 8.42+62.41+320.41+8.42+292.41+1030.41/7

= 2042.89/7

= 291.8

Take the square root of 291.8 which is,

√291.8 = 17.08215443

= 17.1 to the nearest tenth.

Therefore, the standard deviation of the miles Henry biked to the nearest tenth is = 17.1

Learn more about standard deviation here:

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Answer:

17.1

Step-by-step explanation:

got it right

Answer: d on eng

Step-by-step explanation:

Answer:

120 possible arrangements.

It is a permutation

Step-by-step explanation:

Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.

Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:

N= Total number possibilities:

[tex]N=6*5*4=120[/tex]

This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.

The permutation can be learnt by the formula:

[tex]N=\frac{p!}{(p-n)!}[/tex]

where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:

[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]

This is about half life of elements with exponential decay.

Half life = 20 years

We are given;

y = ab^(t)

Where;

t is the half life

y = a/2 is the amount of substance remaining after decay

a is amount of substance initially

b = 100% - 3.411% = 96.589% = 0.96589

a/2 = a(0.96589)^(t)

a will cancel out to give;

0.5 = 0.96589^(t)

ln (0.5) = t(ln 0.96589)

t = ln(0.5)/ln(0.96589)

t = 19.968 days

This is approximately 20 days.

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Answer:

the answer is 4500 i got it right

Step-by-step explanation:

Answer:

The correct answers are 45,41,73

Step-by-step explanation:

Answer: $154.00

Step-by-step explanation:

I am assuming you are looking for how much the person made.

Multiply 40 hours times $3.85

$154.00

For this case we have the following quadratic expression:

[tex] (5y + 6) ^ 2 = 24
[/tex]

From here, we must clear the value of y.

For this, we follow the following steps:

1) We clear the square term:

[tex] (5y + 6) =+/-\sqrt{24} [/tex]

[tex] (5y + 6) =+/-2\sqrt{6} [/tex]

2) Pass the value of 6 by subtracting:

[tex] 5y =-6+/-2\sqrt{6} [/tex]

3) Pass the value of 5 to divide:

[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]

Answer:

The solutions to the quadratic equation are:

[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]

[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]

Answer:

Joint variation.

Step-by-step explanation:

There are four types of variation,

Direct variation : When a variable varies directly as another variable,

Example : y varies directly with x ⇒ y = kx,

Where, k is the constant of variation,

Inverse variation : When a variable varies inversely as another variable,

Example : y varies inversely with x ⇒ [tex]y=k\frac{1}{x}[/tex]

Joint variation : When a variable varies directly with two or more than two variables,

Example : y varies directly with both x and z ⇒ y = kxz

Combined variation : When a variable varies both directly and indirectly as another variables,

Example : y varies directly with x and inversely with z ⇒ [tex]y=k\frac{x}{z}[/tex]

Now, here the given expression,

y = 4mt,

Where, y, m and t are variables and 4 is the constant of variation,

⇒ y varies directly as both m and t,

⇒ y = 4mt is an example of joint variation.