Please help me asap.

Mathematics

1 answer:

Makovka662 [10]3 years ago

6 0

The first one is the answer you're looking for

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Can someone please help me asap!

Ahat [919]

Hopes that somehow helps✍︎︎

8 0

3 years ago

Using sum or difference formulas, find the exact value of sin(165∘)

Nikitich [7]

$\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})\\\\
-------------------------------\\\\$

$\bf sin(165^o)\implies sin(120^o+45^o)
\\\\\\
sin(120^o)cos(45^o)~+~cos(120^o)sin(45^o)\implies \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}~+~\cfrac{-1}{2}\cdot \cfrac{\sqrt{2}}{2}
\\\\\\
\cfrac{\sqrt{6}}{4}~-~\cfrac{\sqrt{2}}{4}\implies \cfrac{\sqrt{6}-\sqrt{2}}{4}$

6 0

3 years ago

The weight of laboratory grasshoppers follows a Normal distribution, with a mean of 90 grams and a standard deviation of 2 grams

JulsSmile [24]

Answer:

95.44% of the grasshoppers weigh between 86 grams and 94 grams.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 90 grams and a standard deviation of 2 grams.

This means that $\mu = 90, \sigma = 2$