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3 years ago

∠ABC is formed by two tangents intersecting outside of a circle. If minor arc AC = 110°, what is the measure of ∠ABC?

Mathematics

2 answers:

tatyana61 [14]3 years ago

6 0

The answer to this problem is 70. Hope I helped :)

Mariulka [41]3 years ago

5 0

Answer:

∠ABC = 70°

Step-by-step explanation:

As shown in the figure attached AB and BC are two tangents drawn on a circle touching at A and C.

Measure of minor arc = 110°

And we have to find the measurement of ∠ABC.

Since measure of minor arc AC = 110°

and m(minor arc AC) + m(major arc AC) = 360°

110° + major arc AC = 360°

major arc AC = 360 - 110 = 250°

and angle formed outside the circle by two tangents formed at B = 1/2(difference of intercepted arcs)

= $\frac{1}{2}(major arc - minor arc)=\frac{1}{2}(250-110)=\frac{1}{2}(140)=70$

Therefore answer is ∠ABC = 70°

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In a survey of a community, it was found that 85% of the people like winter season and 65% like summer season. If none of them d

KengaRu [80]

Answer:

50%

Step-by-step explanation:

Let :

Winter = W

Summer = S

P(W) = 0.85

P(S) = 0.65

Recall:

P(W u S) = p(W) + p(S) - p(W n S)

Since, none of them did not like both seasons, P(W u S) = 1

Hence,

1 = 0.85 + 0.65 - p(both)

p(both) = 0.85 + 0.65 - 1

p(both) = 1.50 - 1

p(both) = 0.5

Hence percentage who like both = 0.5 * 100% = 50%

6 0

2 years ago

A rectangular athletic field is three times as long as it is wide. If the perimeter of the athletic field is 128 yards, what are

larisa [96]

Length=3x
Width=x
3x+x+3x+x=128
8x=128
Divide both sides by 8
x=16
3(x)
3(16)=58
Width= 16 yards
Length= 58 yards

4 0

2 years ago

What happens to outlier of mean and median are approximately the same

olya-2409 [2.1K]

Answer: Effect of outliers on mean median and mode

Outlier An extreme value in a set of data which is much higher or lower than the other numbers. Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.

Step-by-step explanation:

3 0

3 years ago

Gwen volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen

n200080 [17]

A linear relation is a relationship between two variables that when the corresponding pair of values of the variables are plotted, a straight line is obtained

The equation for the relationship between hours Gwen worked and number of tickets is t = 15·h

The reason the above equation is correct is as follows:

The given parameters are;

The table of values;

Hours(h): 1, 2, 3, 4

Tickets (t): 15, 30, 45, 60

Required: To write an equation that gives the relation between the number of hours Gwen worked and the number of tickets sold

Solution:

From the given table, we have;

The common difference between successive h-values is 1

The common difference between successive t-values is 30 - 15 = 45 - 30 = 60 - 45 = 15 = Constant

Given that the common difference of the h, and t-values are constant, the relationship is a linear relationship of the form, t = m·h + c

Where;

m = The rate of change of t with h, as follows;

m = (30 - 15)/(2 - 1) = 15

∴ t - 15 = 15 × (h - 1)

t - 15 = 15·h - 15

t = 15·h - 15 + 15 = 15·h

t = 15·h

The equation for the relation between the number of hours Gwen worked and the number of tickets she sold is t = 15·h

Learn more about mathematical relationships here:

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7 0

2 years ago

The figure below shows a shaded rectangular region inside a large rectangle: (pic)

mariarad [96]

Answer:

Step-by-step explanation:

Probability of falling NOT in the shaded region is "area of white region" divided by "area of whole rectangle (big one)".

Area of whole rectangle:

Area of rectangle = length * width = 10 * 5 = 50

Area of White Region:

First, area of shaded region = length * width = 4 * 2 = 8

Now,

Area of white region = area of whole rectangle - area of shaded rectangle

Area of white region = 50 - 8 = 42

Hence, probability is $\frac{42}{50}=0.84$

0.84 = 84%

Answer choice D is right.

8 0

3 years ago