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4 years ago

I don't quite understand

Mathematics

1 answer:

Kamila [148]4 years ago

5 0

This is essentially the game mastermind if you want to look up more about it

the first 2 guesses have a number with the correct value and in the right position "bulls", all three guesses start with a 1, so if 1 were correct in the first position the 3rd guess would have a "bull" too

this means either the 6 or 2 from the first guess and the 7 or 5 from the second are correct in the 2nd or 3rd position

in the 3rd guess the 3rd number is a 5 without a "bull" so the 5 in the 2nd guess can't also be the "bull". Because 1 and 5 can't possibly be bulls the only number left is 7 so the code is _7_

Because of this we also know that in the first guess the 2 must be the "bull", as in the second spot only a 7 would be correct and the 1 is incorrect anyways -> the code is _72

"Cows"=right number at wrong position only appeared in the guesses 2 and 3 and we know it's neither the numbers 1 (because of guess 1), 7 (becuse it is a bull in 2) and 6 (because it is only in 3 and not both 2 and 3) -> the only number in guess 2 and 3 left is 5

-> the code is 572

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jonny [76]

Answer:

$2\frac{1}{6}\ frames$

Step-by-step explanation:

we know that

To find out how many frames she can make with the exiting material, divide 1 5/8 by 3/4

$1\frac{5}{8}:\frac{3}{4}$

Convert mixed number to an improper fraction

$1\frac{5}{8}=\frac{1*8+5}{8}=\frac{13}{8}$

substitute

$\frac{13}{8}:\frac{3}{4}=\frac{52}{24}\ frames$

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$\frac{13}{6}\ frames$

Convert to mixed number

$\frac{13}{6}\ frames=\frac{12}{6}+\frac{1}{6}=2\frac{1}{6}\ frames$

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3 years ago

A rectangle has the length of 22 inches less than 7 times the width. If the area of the rectangle is 3197 square inches, find th

Nikolay [14]

The length of rectangle is 139 inches

Solution:

Given that, area of the rectangle is 3197 square inches

Let "L" be the length of rectangle and "W" be the width of rectangle

Also given that rectangle has the length of 22 inches less than 7 times the width

Length = 7 times width - 22

L = 7W - 22

<em><u>The area of rectangle is given as:</u></em>

$\text {Area of rectangle }=\text { length } \times \text { width }$

Substituting the values we get,

$\begin{array}{l}{3197=(7 W-22)(W)} \\\\ {3197=7 W^{2}-22 W} \\\\ {7 W^{2}-22 W-3197=0}\end{array}$

On solving the above quadratic equation using quadratic formula,

$\text {For the quadratic equation } a x^{2}+b x+c=0 \text { where } a \neq 0$

$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$

$\begin{array}{l}{\text {Here in } 7 \mathrm{W}^{2}-22 \mathrm{W}-3197=0} \\\\ {a=7 ; b=-22 ; c=-3197}\end{array}$

Substituting in above quadratic formula,

$\begin{array}{l}{W=\frac{-(-22) \pm \sqrt{\left((-22)^{2}-4(7)(-3197)\right)}}{2 \times 7}} \\\\ {W=\frac{22 \pm \sqrt{90000}}{14}=\frac{22 \pm 300}{14}} \\\\ {W=\frac{22+300}{14} \text { or } W=\frac{22-300}{14}} \\\\ {W=23 \text { or } W=-19.85}\end{array}$

Since width of rectangle cannot be negative, ignore negative value of "W"

So width W = 23 inches

Length L = 7W - 22 = 7(23) - 22 = 139 inches

Thus length of rectangle is 139 inches

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