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3 years ago

On one side of the balance scale, Henry placed a 6-gram weight. On the other side of the scale, he placed a ballet slipper.

Mathematics

1 answer:

olchik [2.2K]3 years ago

7 0

Answer:

A. 6,000 miligrams

Explanation:

A balance scale is balanced when the weights on both sides are equal. Then, since the image shows that both sides are equal, the weight of the 6-gram weight, placed by Henry on one side of the balance scale is equal to the weight of the ballet slipper placed on the other side.

Weight of the balance slipper = weight of the 6-gram weight

Weight of the balance slipper = 6 grams

Conversion of units:

6 grams × 1,000miligrams/1gram = 6,000 miligrams

Weight of the balance slipper = 6,000 miligrams

That is the option A.

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Delta makes 12-volt car batteries. These batteries are known to be normally

blondinia [14]

Answer:

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

Step-by-step explanation:

Step(i):-

Given that the sample size n =12 -volt car batteries

Let 'X' be a Random variable in a normal distribution

Given that mean of the normal distribution = 45 months

Given that the Standard deviation of the normal distribution = 8months

Step(ii):-

Let X₁ = 3 years = 12 × 3 = 36 months

$Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{36-45}{8} = -1.125$

Let X₂ = 4 years = 12 × 4 = 48 months

$Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{48-45}{8} = 0.375$

Step(iii):-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = P(-1.125≤Z≤0.375)

= P(Z≤0.375) - P(Z≤-1.125)

= 0.5 +A(0.375) - (0.5-A(1.125)

= 0.5 + 0.1480 - (0.5 -0.3708)

= 0.1480 + 0.3708

= 0.5188

Final answer:-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

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3 years ago

By definition, (fog)(x) = f(g(x))So if g(2) = 3 and f(3) = 16, then (fog)(2) =

marusya05 [52]

Answer:

$(f\circ g)(2)=16$

Step-by-step explanation:

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$\begin{gathered} (f\circ g)(x)=f(g(2))=f(3) \\ \text{Hence,} \\ (f\circ g)(2)=16 \end{gathered}$

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Answer:

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Step-by-step explanation:

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76/4=19

multiply by 3

19x3=57

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Answer:

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