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3 years ago

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Sam has $\frac{5}{8}$ of a pound of chocolate. If he eats $\frac{1}{3}$ of the chocolate he has, how many pounds of chocolate do

es he eat?

2 answers:

givi [52]3 years ago

3 0

1/3 of 5/8...." of " means multiply
1/3 * 5/8 = 5/24 lbs

Tju [1.3M]3 years ago

3 0

Answer:

1/3 of 5/8...." of " means multiply

1/3 * 5/8 = 5/24 lbs

Step-by-step explanation:

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Fabio and Gwen are saving money to buy a new gaming station. They need at least $510 to purchase the new gaming station. Gwen we

Phoenix [80]

<u>Answer-</u>

Set of constraints to model the problem are,

$12x+9y\geq 510$

$y \leq 2x$

$y \geq 25$

<u>Solution-</u>

<em>x = the number of lawns weeded by Gwen,</em>

<em>y = the number of dogs walked by Fabio.</em>

1.

As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,

$\text{Earnings of Gwen} = 12x$

$\text{Earnings of Fabio} = 9y$

$\text{Total earning} = 12x+9y$

They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.

The equation for this is,

$12x+9y\geq 510$

2.

The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means

y must be less than or equal to 2x.

The equation for this is,

$y \leq 2x$

3.

Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.

The equation for this is,

$y \geq 25$

8 0

3 years ago

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park ranger spent $208 to buy 12 trees.Redwood trees cost $24 each and spruce trees cost $16 each. How many of each tree did the

katovenus [111]

Answer:

The park ranger bought 2 redwood trees and 10 spruce trees.

Step-by-step explanation:

24 * 2 = 48

208 - 48 = 160

160 / 16 = 10

7 0

3 years ago

The standard diameter of a golf ball is 42.67 mm. A golf ball factory does quality control on the balls it manufactures. Golf ba

sergiy2304 [10]

THE ANSWER IS A:

This is the function:

f(x)=|42.67-x|.

42.670 -.002 =42.668

42.668 mm to 42.670

Explanation:

Production will be stopped if the difference in diameter is greater than 0.002 mm.

This difference can mean that the golf ball has a diameter more than 0.002 larger than 42.67 mm, or a diameter more than 0.002 smaller than 42.67. This is the reason for using an absolute value function.

Absolute value represents the distance a number is from 0. For this function, we would want only the values where the function is less than 0.002.

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3 years ago

What is 7.2 times 10^5 equal to.

FromTheMoon [43]

The answer to this is 720000

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3 years ago

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Determine whether parallelogram JKLM with vertices J(-7, -2), K(0, 4), L(9, 2) and M(2, -4) is a rhombus, square, rectangle or a

White raven [17]

Check the picture below

now, we know is a parallelogram, so the diagonals will bisect

looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason

is it a rhombus? well, a rhombus, is a parallelogram, that's "slanted" per se, but regardless of how slanted it may be, the sides are all equal

now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
J&({{-7 }}\quad ,&{{ -2}})\quad 
% (c,d)
K&({{ 0}}\quad ,&{{ 4}})\\\\
K&({{ 0}}\quad ,&{{ 4}})\quad 
% (c,d)
L&({{ 9}}\quad ,&{{ 2}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
JK=\sqrt{[0-(-7)]^2+[4-(-2)]^2}\implies JK=\sqrt{(0+7)^2+(4+2)^2}
\\\\\\
JK=\sqrt{7^2+6^2}
\\\\\\
KL=\sqrt{(9-0)^2+(2-4)^2}\implies KL=\sqrt{9^2+(-2)^2}$

now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL

and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
K&({{ 0}}\quad ,&{{ 4}})\quad 
% (c,d)
M&({{ 2}}\quad ,&{{ -4}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-4}{2-0}$

$\bf -------------------------------\\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
J&({{ -7}}\quad ,&{{ -2}})\quad 
% (c,d)
L&({{ 9}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-(-2)}{9-(-7)}\implies \cfrac{2+2}{9+7}$

then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.

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3 years ago

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