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2 years ago

Which set of angles can form a triangle

Mathematics

1 answer:

Aleksandr [31]2 years ago

7 0

Answer:

2 acute and 1 right

Step-by-step explanation:

The sum of angles of a triangle is always 180°.

Right angles are 90°, and obtuse angles are more than 90°. If each of the angles in the triangle is more than 0°, there obviously cannot be two angles that measure 90° or more. Just the sum of those two would be 180° or more, and that sum doesn't include the third angle.

So, any triangle can have at most one angle that is 90° or more (right or obtuse). The remaining two angles must be acute for the sum of angles to be 180°.

2 acute and 1 right angle can form a triangle

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Jordan used the distributive property to write an expression that is equivalent to 6c – 48. 6c - 48 is equivalent to 6(c - 48) I

Katyanochek1 [597]

It’s incorrect.

The correct answer is 6(c - 8)

8 0

2 years ago

Read 2 more answers

Someone help! you have 44 text messages in your inbox. How many messages can your cell phone hold? (and inbox is 88% full)

marin [14]

We can set up a proportion.

88% = 0.88

44/0.88 = x/1

Cross multiply:

0.88x = 44

Divide 0.88 to both sides:

x = 50

So your cell phone can hold 50 messages.

4 0

2 years ago

Read 2 more answers

Compare the values of the underlined digits. 2,783 and 7,283.

netineya [11]

The value of the 2 in the thousands place is 10 times the value of 2 in the hundreds place.

200 x 10 = 2000

hope this helps

4 0

2 years ago

Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in

Hitman42 [59]

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of Americans who decide to not go to college = 48%

n = sample of American adults = 331

p = population proportion of Americans who decide to not go to

college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\hat p-p$ < $1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

P( $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

90% confidence interval for p = [ $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ , $0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ ]

= [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

$0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }$

$\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}$

$\sqrt{n}$ = 54.79

n = $54.79^{2}$

n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

5 0

2 years ago

Juan walks a circular path with a radius of 280 yards at the local park. How far does she walk? Use 3.14 for pi.

belka [17]

Answer: Juan walks 246,176 yards around the circular path.

To find the distance around the circular path, we are looking for the circumference. The formula for the circumference is: C = pi(r^2).

Simply plug in the radius and evaluate the expression.

C = 3.14(280^2)
C = 3.14(78400)
C = 246,176 yd

4 0

2 years ago