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olga nikolaevna [1]
2 years ago
3

Tyler and Katie started a lemonade stand to raise money. They donated \dfrac{2}{10} 10 2 ? start fraction, 2, divided by, 10, en

d fraction of their profits to their school library, \dfrac{1}{10} 10 1 ? start fraction, 1, divided by, 10, end fraction to the animal shelter, and \dfrac{4}{10} 10 4 ? start fraction, 4, divided by, 10, end fraction to the food bank. They saved the rest to buy materials for their next project. What fraction of their profits did Tyler and Katie donate?
Mathematics
2 answers:
Korvikt [17]2 years ago
5 0

Answer:

\frac{7}{10}

Step-by-step explanation:

Fraction of the amount donated to school library = \frac{2}{10}

Fraction of the amount donated to animal shelter = \frac{1}{10}

Fraction of the amount donated to food bank = \frac{4}{10}

The rest of the amount was saved for next project.

Thus, the total fraction of the amount donated will be the sum of fractions of amount donated to school library, animal shelter and food bank.

i.e.

Fraction of the amount donated = \frac{2}{10}+\frac{1}{10}+\frac{4}{10} = \frac{7}{10}

This means, Tyler and Katie donated \frac{7}{10} of their profits.

Sergio039 [100]2 years ago
3 0

Answer:−1.825

Step-by-step explanation:

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G(x)= -\dfrac{x^2}{4} + 7g(x)=− 4 x 2 ​ +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, squared,
RUDIKE [14]

Answer:

<h2>-1/2</h2>

Step-by-step explanation:

Given the function G(x)= -\dfrac{x^2}{4} + 7, the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;

Rate of change of the function is expressed as g(b)-g(a)/b-a

where a - -2 and b = 4

G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\

G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6

average rate of change of g(x) over the interval [-2,4] will be;

g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2

6 0
2 years ago
Arti is mixing some orange paint for the class mural.
vitfil [10]

Answer:

6

Step-by-step explanation:

6 0
2 years ago
A church spire casts a shadow on the level ground. At the tip of the shadow, the tip of the spire lies 25° upward. Walking 100 m
malfutka [58]

Answer:

The height of the spire must be 69.24 m

Step-by-step explanation:

The information given are;

The initial angle of elevation of the tip of the spire from the tip of the shadow = 25°

The  angle of elevation of the tip of the spire from the tip of the shadow after moving 100 m closer = 55°

The change distance moved closer to the church spire = 100 m

Let the base angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow be 25° and ∠x°

We have;

∠x° and the 55° angle of the ray from the tip of the spire to the tip of the shadow are supplementary angles (angle on a straight line)

Therefore;

∠x° = 180° - 55° = 125°

The calculated angle 125° above, the given 25° and the angle in between the two rays from the tip of the spire to the tip of the shadows are the interior angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow

Let the angle in between the two rays from the tip of the spire to the tip of the shadows = y

Therefore;

125° + y° + 25° = 180 (Angle sum theorem)

y° = 180° - (125° + 25°) = 30°

By sin rule, we have;

100/(sin (30°)) = (The length of the initial ray from the tip of the spire to the tip of the shadow before the shift)/(sin(125°))

Let the length of the initial ray from the tip of the spire to the tip of the shadow before the shift = l

100/(sin (30°)) = l/(sin(125°))

l = (sin(125°))×100/(sin (30°)) = 163.83 m

The height of the spire, by trigonometric ratio = sin(25°) × 163.83 m = 69.24 m

The height of the spire = 69.24 m.

4 0
2 years ago
A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, thi
marysya [2.9K]
For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.

So, all we have to do is substitute θ=45° to the function given. 
A = 16 sin 45° ⋅ (cos 45° + 1)

The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.

A = 16(√2/2) ⋅ (√2/2 + 1)
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