Let P be a point outside the circle such that triangle LMP has legs coincident with chords MW and LK (i.e. M, W, and P are colinear, and L, K, and P are colinear). By the intersecting secants theorem,

$m\angle LPM=\dfrac{m\widehat{LM}-m\widehat{WK}}2\impliesm\angle LPM=48^\circ$

The angles in any triangle add to 180 degrees in measure, and $\angle MLK\congruent\angle MLP$ and $m\angle LMW=m\angle LMP$ , so that

$m\angle MLK+m\angle LPM+m\angle LMP=180^\circ$

$\implies\boxed{m\angle LMW=67^\circ}$

6 0

3 years ago

Suppose 15 quarts of a solution that is 35% antifreeze is mixed with 5 quarts of a solution that is 72% antifreeze. 1.how many q

Finger [1]

Answer:

1. 8.85 quarts

2. 44.25%

Step-by-step explanation:

In 15 quarts of a solution with percentage of antifreeze = 35%

Amount of antifreeze = 35% × 15

= 0.35 × 15

= 5.25 quarts

that solution is mixed with 5 quarts of a solution with percentage of antifreeze = 72%

Amount of antifreeze = 72% × 5

= 0.72 × 5

= 3.6 quarts

Total amount of mixture = 15 quarts + 5 quarts = 20 quarts

1. Now we will calculate the total amount of antifreeze in the resulting mixture.

= 5.25 + 3.6 = 8.85 quarts

2. The percentage of the resulting mixture is antifreeze

= $\frac{8.85}{20}\times 100$

= 44.25%

1. total amount of antifreeze is 8.85 quarts

2. the percentage of antifreeze is 44.25%

3 0

3 years ago

A set of city temperatures in April are normally distributed with a mean of 19.7 degrees Celsius and a standard deviation of 2 d

Sati [7]

Answer:

19.77% of average city temperatures are higher than that of Cairo

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 question, we have that:

$\mu = 19.7, \sigma = 2$