BD−→− bisects ∠ABC such that m∠ABD = (4x−5)∘ and m∠DBC = (3x+2)∘.

Mathematics

1 answer:

Rzqust [24]3 years ago

3 0

Answer:

$\angle ABC=(46)^{\circ}$

Step-by-step explanation:

Given: BD bisects $\angle ABC$

$\angle ABD=(4x-5)^{\circ}\\\angle DBC=(3x+2)^{\circ}$

To find: $\angle ABC$

Solution:

A bisector of an angle divides it into angles of equal measures.

As BD bisects $\angle ABC$ , $\angle ABD=\angle DBC$

Put $\angle ABD=(4x-5)^{\circ}\,,\,\angle DBC=(3x+2)^{\circ}$

$\angle ABD=\angle DBC\\(4x-5)^{\circ}=(3x+2)^{\circ}\\4x-3x=2+5\\x=7^{\circ}$

So,

$\angle ABD=(4x-5)^{\circ}=(4(7)-5)^{\circ}=(28-5)^{\circ}=(23)^{\circ}\\\angle DBC=(3x+2)^{\circ}=(3(7)+2)^{\circ}=(21+2)^{\circ}=(23)^{\circ}$

$\angle ABC=\angle ABD+\angle DBC\\=(23)^{\circ}+(23)^{\circ}\\=(46)^{\circ}$

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The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 270 day

dusya [7]

Answer:

a) 281 days.

b) 255 days

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 270, \sigma = 8$