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bogdanovich [222]
3 years ago
8

Jenny had a snack mix. For every 2 chocolate chips, there are 6 peanuts. If there are 108 peanuts in the mix,how many chocolate

chips are in the mix
Mathematics
1 answer:
JulijaS [17]3 years ago
6 0
Use proportions. 

2 chocolate chips : 6 peanuts =     ?   chocolate chips : 108 peanuts

Find the scale factor of the information that matches. In this case it would be 108 peanuts divided by 6 peanuts. Then use this scale factor to multiply 2 chocolate chips by to get your answer.

SF: 108 <span>÷ 6 = 18

18 x 2 = 36 chocolate chips

2 chocolate chips : 6 peanuts =  36 chocolate chips : 108 peanuts

ANSWER: If there are 108 peanuts in the mix, there will be 36 chocolate chips in the mix.</span>
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The question is show a dilation of a rectangle with a dilation of 8/3
miv72 [106K]

It's always easier to understand a concept by looking at specific examples with pictures, so I suggest looking at the dilation examples below first...before you try to internalize the steps listed below and that explain the general formula for dilating a point with coordinates of (2,4) by a scale factor of <span><span>12</span><span>12</span></span>.

<span><span>1) multiply both coordinates by scale factor<span>(<span><span>2⋅<span>12</span>,4⋅<span>12</span></span><span>2⋅<span>12</span>,4⋅<span>12</span></span></span>)</span></span><span>2)

2. Simplify(1,2)</span><span>3)

3. Graph(if required)<span> </span></span></span>
5 0
3 years ago
Can someone help me
erik [133]

Answer:

   6 < x < 23.206

Step-by-step explanation:

To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.

The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...

  (2x -12)/2 = arcsin(16/22×sin(24°))

  x ≈ 23.206°

Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...

  2x -12 = 0

  x -6 = 0 . . . . . divide by 2

  x = 6 . . . . . . . add 6

Then the range of values of x will be ...

  6 < x < 23.206

_____

* One way to do this is to make use of the law of cosines:

  22² = AB² + AC² -2·AB·AC·cos(48°)

  16² = AD² + AC² -2·AD·AC·cos(2x-12)

The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...

  22² = 2·AB²·(1-cos(48°))

  16² = 2·AB²·(1 -cos(2x-12))

The value of AB drops out of the ratio of these equations, and the result for x is as above.

4 0
2 years ago
Read 2 more answers
Use Structure Tyler explained how he multiplies
aleksandrvk [35]

Answer:

The property that I would use is that however many decimal points are in the equation is the number of decimal places in the answer

Step-by-step explanation:

3 0
3 years ago
g: Consider the following game. A coin is flipped. If it lands tails we stop playing and winnothing. If it lands heads we spin a
galben [10]

Answer:

E[W] = $25 (assuming the currency is in dollars)

Var(W) = 1041.67

Step-by-step explanation:

Probability of winning first starts with the coin toss.

For a win, the coin needs to land on heads.

Probability of that = 1/2 = 0.5

Then probability of winning any amount = 1/100 = 0.01

Total probability of winning any amount = 0.5 × 0.01 = 0.005

But expected value is given by

E(X) = Σ xᵢpᵢ

where xᵢ is each amount that could be won

pᵢ is the probability of each amount to be won and it is the same for all the possible winnings = 0.005

So,

E(W) = Σ 0.005 xᵢ

Summing from 0 to 100 (0 indicating getting a tail from the coin toss). This could be done with dome faster with an integral sign

E(W) = ∫ 0.005 x dx

Integrating from 0 to 100

E(W) = [0.005 x²/2]¹⁰⁰₀

E(W) = [0.0025 x²]¹⁰⁰₀ = 0.0025(100² - 0²) = 0.0025 × 10000 = $25

Variance is given by

Variance = Var(X) = Σxᵢ²pᵢ − μ²

μ = expected value

We calculate the expression, Σxᵢ²pᵢ which is another sum from 0 to 100

Σxᵢ²pᵢ = Σ 0.005xᵢ²

Σ 0.005 xᵢ² = ∫ 0.005 x² dx

Integrating from 0 to 100

∫ 0.005 x² dx = [0.005 x³/3]¹⁰⁰₀ = [0.1667x³]¹⁰⁰₀ = 0.1667(100³ - 0³) = 1666.67

Var(W) = 1666.67 - 25² = 1666.67 - 625 = 1041.67.

5 0
2 years ago
A hockey player hits a puck along the ice, giving it an initial speed of 2.9 meters per second. If there is no friction between
Alborosie
2.9 × 1.7 = 4.93

After 1.7 seconds, the puck's speed would be 4.93 meters per second.
5 0
2 years ago
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