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Sonja [21]
3 years ago
7

i have a bag of trail mix. One half of the bag is peanuts, one quarter of the bag is chocolate candies and one quarter of the ba

g is dried fruit. what is the likelihood of drawing a chocolate candy
Mathematics
1 answer:
Sonja [21]3 years ago
8 0
It’s easier to see with actual numbers therefore, since you are not given a total, say there are 20
Which means, 10 are peanuts, 5 are chocolate candies and 5 are dried fruit.
Out of the 20 options, there are 5 that are the chocolate candies.
This means there is a 5 in 20 chance you will pick the chocolate candies.
5/20 = ¼ (i.e. the likelihood to pick one is the same as the fraction of chocolate candies the bag contains)
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Car Value: In one year a new car decreased in value by 20%. If it sold for $19,400 when it was new, what was it worth after 1 ye
Phantasy [73]
20% of $19,400 is $3,880
($19,400 / 5 = $3,880)
subtract 20% from the original value
($19,400 - $3,880 = $15,520)
it's now worth $15,520
5 0
3 years ago
At 1 P.M., ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast i
Evgen [1.6K]
<span>The distance between the ships is changing at a rate of 21.393 km/h

</span><span>Step 1: First, you must draw an image to help better understand the problem 
</span>

The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.

We know that the rate of Ship A is expressed as <span><span><span>dA</span><span>dt</span></span>=−35</span> and the rate of Ship B is expressed as <span><span><span>dB</span><span>dt</span></span>=25</span>

Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours

<span>ShipA:−35<span><span>km</span>h</span>⋅4hr=−140km</span>

Now if we take this <span>−140km</span> and add it to the <span>150km</span> we can see that Ship A is now only <span>10km</span> away from where Ship B began

<span>ShipB:25<span><span>km</span>h</span>⋅4hr=100km</span>

This means that Ship B is now <span>100km</span> from where it originally started

We can now redraw our information

Step 3: We must use the Pythagorean Theorem to find the third side of the triangle

<span><span>x2</span>+<span>y2</span>=<span>z2</span>→<span>102</span>+<span>1002</span>=<span>z2</span></span>

<span>z=<span>√<span><span>102</span>+<span>1002</span></span></span></span>

Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing

<span><span>x2</span>+<span>y2</span>=<span>z2</span>→2x<span><span>dx</span><span>dt</span></span>+2y<span><span>dy</span><span>dt</span></span>=2z<span><span>dz</span><span>dt</span></span></span>

We can simplify by canceling out the 2's

<span>x<span><span>dx</span><span>dt</span></span>+y<span><span>dy</span><span>dt</span></span>=z<span><span>dz</span><span>dt</span></span></span>

Step 5: Write down all the information and then plug into equation

<span>x=10and<span><span>dx</span><span>dt</span></span>=−35</span>
<span>y=100and<span><span>dy</span><span>dt</span></span>=25</span>
<span>z=<span>√<span><span>102</span>+<span>1002</span></span></span>and<span><span>dz</span><span>dt</span></span>=?</span>

Now plug in the information

<span>x<span><span>dx</span><span>dt</span></span>+y<span><span>dy</span><span>dt</span></span>=z<span><span>dz</span><span>dt</span></span></span>

<span>10<span>(−35)</span>+100<span>(25)</span>=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>−350+2500=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>2150=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>21.393=<span><span>dz</span><span>dt</span></span></span>

The distance between the ships are increasing at a rate of 21.393 km/h

8 0
3 years ago
Scenario: The Cannon Instructions: View the video found on page 1 of this Journal activity. Using the information provided in th
Artyom0805 [142]

Answer:

Part A

Yes

Part B

He will land at a point 30 meters from Cannon

Step-by-step explanation:

Part A

The given function that represent the path of the Cannon, which is the path of a parabolic arc, is presented as follows;

f(x) = -0.05·(x² - 26·x - 120)

We note that the height, 'h', of the path of a parabola at a horizontal distance, 'x' from the origin is equal to f(x)

Therefore, given that at the ground level, at the start and end of the flight, the f(x) = 0, we can write;

-0.05·(x² - 26·x - 120) = 0

∴ x² - 26·x - 120 = 0

x = (26 ± √((-26)² - 4 × 1 × (-120)))/(2 × 1)

Which gives;

x = 30 or x = -4

Therefore, he lands at a point 30 meters from the starting point

Therefore, the function gives enough information to tell where he will land

Part B

He lands at the point, x = 30 from the point the cannon was fired.

3 0
2 years ago
Need hep wit this thx
PSYCHO15rus [73]

Answer:

answer is 3

Step-by-step explanation:

n+1=3+2/2=3

The number is 3 and it is a odd number.

I hope it's helpful!

4 0
3 years ago
Ava and Maria went shopping together. Eva spent $20 more than Maria. Together they spent $209.84. Write and solve an equation to
ad-work [718]

Answer:209.84 - 20.00 = 189.84 / 2 = 94.92

94.92 + 20.00 = 114.92 Eva spent and Martha spent $94.92

Step-by-step explanation:

5 0
3 years ago
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