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2 years ago

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A school has 60% girls and 40% boys. If 30% of the girls wear glasses and 20% of the boys wear glasses, what percent of all stud

ents wear glasses?
A 36%
B 25%
C 42%
D 26%

1 answer:

Zina [86]2 years ago

7 0

Answer:

25%

Step-by-step explanation:

there is total boys and total girls so 200%

30%girls take

20%boys it is 50% of 200 % so 25% of all

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The probability it will rain tomorrow is 1/2. The probability that our team will win tomorrow's basketball game is 3/5. Which ex

irga5000 [103]

Answer:

4.

Step-by-step explanation:

if the probability it win is 3/5 then 5/5 - 3/5 equals 2/5

which you multiply with 1/2

hope this helps

7 0

2 years ago

answer as a mixed number if possible. A bowl of cereal had 3 3/6 grams of sugar in it. If Victor ate 2 bowl8a week, how many gra

GrogVix [38]

<em>7 grams of sugar</em>

<h2>Explanation:</h2>

________________________________________

I'll assume your answer is as follows:

<em>A bowl of cereal had 3 3/6 grams of sugar in it. If Victor ate 2 bowl a week, how many grams of sugar would he have eaten?</em>

________________________________________

If so, then we know that:

A bowl of cereal had 3 3/6 grams of sugar in it.

Victor ate 2 bowl a week

In other words, the total of sugar he ate can be calculated as:

$3\frac{3}{6}\times2 \\ \\ Converting \ mixed \ fraction \ into \ improper \ fraction: \\ \\ =(3+\frac{3}{6})\times2 \\ \\ =(\frac{3(6)+3}{6})\times 2 \\ \\ =(\frac{21}{6})\times 2 \\ \\ =(\frac{7}{2})\times 2 \\ \\ =7$

So <em>he'd have eaten 7 grams of sugar</em>

<h2>Learn more:</h2>

Mixed numbers: brainly.com/question/383603

#LearnWithBrainly

7 0

3 years ago

EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =

Taya2010 [7]

Answer:

$\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}$

<em>Maximum value of f=2.41</em>

Step-by-step explanation:

<u>Lagrange Multipliers</u>

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

$\bigtriangledown f=\lambda \bigtriangledown g$

for some scalar $\lambda$ called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

$\bigtriangledown f=\lambda \bigtriangledown g+\mu \bigtriangledown h$

The gradient of f is

$\bigtriangledown f=$

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in $x,y,z,\lambda,\mu$ .

We have

$f(x, y, z) = x + 2y + 11z\\g(x, y, z) = x - y + z -1=0\\h(x, y, z) = x^2 + y^2 -1= 0$

Let's compute the partial derivatives

$f_x=1\ ,f_y=2\ ,f_z=11\ \\g_x=1\ ,g_y=-1\ ,g_z=1\\h_x=2x\ ,h_y=2y\ ,h_z=0$

The Lagrange condition leads to

$1=\lambda (1)+\mu (2x)\\2=\lambda (-1)+\mu (2y)\\11=\lambda (1)+\mu (0)$

Operating and simplifying

$1=\lambda+2x\mu\\2=-\lambda +2y\mu \\\lambda=11$

Replacing the value of $\lambda$ in the two first equations, we get

$1=11+2x\mu\\2=-11 +2y\mu$

From the first equation

$\displaystyle 2\mu=\frac{-10}{x}$

Replacing into the second

$\displaystyle 13=y\frac{-10}{x}$

Or, equivalently

$13x=-10y$

Squaring

$169x^2=100y^2$

To solve, we use the restriction h

$x^2 + y^2 = 1$

Multiplying by 100

$100x^2 + 100y^2 = 100$

Replacing the above condition

$100x^2 + 169x^2 = 100$

Solving for x

$\displaystyle x=\pm \frac{10}{\sqrt{269}}$

We compute the values of y by solving

$13x=-10y$

$\displaystyle y=-\frac{13x}{10}$

For

$\displaystyle x= \frac{10}{\sqrt{269}}$

$\displaystyle y= -\frac{13}{\sqrt{269}}$

And for

$\displaystyle x= -\frac{10}{\sqrt{269}}$

$\displaystyle y= \frac{13}{\sqrt{269}}$

Finally, we get z using the other restriction

$x - y + z = 1$

Or:

$z = 1-x+y$

The first solution yields to

$\displaystyle z = 1-\frac{10}{\sqrt{269}}-\frac{13}{\sqrt{269}}$

$\displaystyle z = \frac{-23\sqrt{269}+269}{269}$

And the second solution gives us

$\displaystyle z = 1+\frac{10}{\sqrt{269}}+\frac{13}{\sqrt{269}}$

$\displaystyle z = \frac{23\sqrt{269}+269}{269}$

Complete first solution:

$\displaystyle x= \frac{10}{\sqrt{269}}\\\\\displaystyle y= -\frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{-23\sqrt{269}+269}{269}$

Replacing into f, we get

f(x,y,z)=-0.4

Complete second solution:

$\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}$

Replacing into f, we get

f(x,y,z)=2.4

The second solution maximizes f to 2.4

5 0

2 years ago

5/6 in cubic cm rounded to the nearest tenth

ollegr [7]

Answer:

5/6 cubic inches = 5/6 x 16.38 cubic cms

= 13.65 cubic cms

Step-by-step explanation:

We are asked to convert 5/6 cubic inches in cubic cm rounded to the nearest tenth

1 inch =2.54 cms.

Hence 1 cubic inches = 16.38 cubic cms

Hence 5/6 cubic inches = 5/6 x 16.38 cubic cms

= 13.65 cubic cms

7 0

3 years ago

Please help only correct answers.

Ymorist [56]

True
False
True
Brainliest?

6 0

2 years ago