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maria [59]
3 years ago
12

In a 4 3/5 mile race, there are two water stations. The first water station is 1/3 of the way from the starting point. The secon

d water station is 2/3 of the way from the starting point. How far is the first water station to the second water station?
Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
7 0

The difference between the first water station and the second would be 1/3 of the total mile distance.

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For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perim
Marina86 [1]

Area of the shaded region $=36(\pi -2) square cm

Perimeter of the shaded region =6 (\pi + 2\sqrt 2) cm

Solution:

Radius of the quarter of circle = 12 cm

Area of the shaded region = Area of quarter of circle – Area of the triangle

                                             $=\frac{1}{4} \pi r^2 - \frac{1}{2} bh

                                             $=\frac{1}{4} \pi \times 12^2 - \frac{1}{2} \times  12 \times 12

                                             $=36\pi -72

                                             $=36(\pi -2) square cm.

Area of the shaded region $=36(\pi -2) square cm

Using Pythagoras theorem,

AC^2=AB^2+BC^2

AC^2=12^2+12^2

AC^2=288

Taking square root on both sides of the equation, we get

AC= 12\sqrt 2 cm

Perimeter of the quadrant of a circle = \frac{1}{4} \times 2\pi r

                                                             $=\frac{1}{4} \times 2 \times \pi \times 12

                                                             $=6 \pi cm

Perimeter of the shaded region = 6 \pi + 12\sqrt 2 cm

                                                    =6 (\pi + 2\sqrt 2) cm

Hence area of the shaded region $=36(\pi -2) square cm

Perimeter of the shaded region =6 (\pi + 2\sqrt 2) cm

6 0
3 years ago
Carmen deposited $6,000 into a savings account that earns 2.8% interest compounded annually. How much will she have in her accou
Anna [14]

To help Carmen find the total after 3 years

We'll have to use the annual compound interest formula: A = P(1 + r)ⁿ

A = Final balance (?)

P = Principal balance (6000)

r = Rate (0.028)

n = years (3)

A = 6000(1 + 0.028)³

A = 6000(1.028)³

A = 6000(1.086373952)

A = 6518.243712

Round that to the nearest cent, and we get $<u>6,518.24 </u>as the answer.

6 0
2 years ago
Here is a sketch of y=x^2+bx+c The curve intersects
atroni [7]

Answer:

y = 18  and  x = -2

Step-by-step explanation:

y = x^2+bx+c   To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c. We are given two different solutions of the equation. First, (2, 0).  Second, (0, -14). So we have a value (-14) for c. We can substitute that into our first equation to find b. We can now plug in our values for b and c into the equation to get its standard form. To find the vertex, we can convert this equation to vertex form by completing the square. Thus, the vertex is (4.5, –6.25). We can confirm the solution graphically     Plugging in  (2,0) :

y=x2+bx+c  

0=(2)^2+b(2)+c  

y=4+2b+c  

-2b=4+c  

b=-2+2c  

Plugging in  (0,−14) :

y=x2+bx+c  

−14=(0)2+b(0)+c  

−16=0+b+c  

b=16−c  

Now that we have two equations isolated for  b , we can simply use substitution and solve for  c .   y=x2+bx+c  16 + 2 = y   y = 18  and  x = -2

4 0
2 years ago
How can you use the properties of operations to evaluate this expression?<br> 18 + 4(28). Explain.
maxonik [38]

Answer:

130.

Step-by-step explanation:

18 + 4(28(

= 18 + 4 * 28   Multiplication is done before addition so we have:

18 + 112

= 130.

4 0
3 years ago
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LOTS OF BRAINLY POINTS HELP ASAP PLS TYSM
Sedbober [7]

Answer:

3/10

Step-by-step explanation:

So, you already have the experimental probability. The theoretical probability is 5/10, but that's not what you're lookig for.

5 0
2 years ago
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