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scoray [572]
3 years ago
13

There are 11 sixth grade students and 7 eighth grade students in the art club. The number of seventh grade students in the art c

lub is half the combined number of sixth and eighth grade students in the club. What is the ratio of seventh grade students in the club to the total number of students in the art club, written as a fraction in lowest terms?
Mathematics
2 answers:
ch4aika [34]3 years ago
6 0

Answer:

1:3

Step-by-step explanation:

(11+7)/2=9 9:27 and simplify it. There really isn’t much explaining but hope this helps.

olya-2409 [2.1K]3 years ago
4 0

Answer:

1:3

Step-by-step explanation:

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Select the correct answer.
IRISSAK [1]

Answer:

B is tbe correct option here

3 0
3 years ago
Use the method of lagrange multipliers to find
Yanka [14]

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y,  λ) = x + y +  λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx =  λ*y + 1

dL/dy =  λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate  λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

6 0
3 years ago
Balloon Payment (Math)
fiasKO [112]

Answer:

  96

Step-by-step explanation:

The loan duration is for 8 years, a total of 12·8 = 96 monthly payments. The 96th payment is the balloon payment.

7 0
3 years ago
There once was a student named chandler. In 5 minutes, chandler texted 435 words. At the rate how many words did chandler text p
Sergio [31]

Answer:

87

Step-by-step explanation:

7 0
3 years ago
How do u solve 63=-9d?
Len [333]
-9d = 63
you divide both side by -9

sooo...

d = -7
7 0
3 years ago
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