All categories

3 years ago

One angle in a triangle has a measure that is three times as large as

1 answer:

7 0

We know that the sum of all angles in any triangle is always 180 and we know that:

The smallest angle = x
Angle 2 = x + 35
Angle 3 = 3 * x

So:

180 = x + x + 35 + 3 * x
180 = x + x + 35 + 3x
180 = 2x + 35 + 3x
180 = 5x + 35 / - 35 (both sides)
145 = 5x / ÷ 5 (both sides)
x = 29

The smallest angle = 29
Angle 2 = 29 + 35 = 64
Angle 3 = 3 * 29 = 87

Check:

29 + 64 + 87 = 180, so it's correct :)

You might be interested in

I need to understand question 14 and 15 and the last one cut off for tens in one

sp2606 [1]

Question # 14

Given the numbers

10 11 12 13 14 15 16 17 18 19 20

Let 'x' be the number

The condition breakdown:

I am less than 20.

So the number 'x' must be less than 20 i.e. x < 20

I am more than 13.

So the number 'x' must be greater than 13 i.e. x > 13

I am less than 17.

So the number 'x' must be less than 17 i.e. x < 17

Finally:

I am 4 more than 12

i.e. 12+4 = 16

Thus, the number is x = 16

Question # 15

Part a)

Given the numbers

10 11 12 13 14 15 16 17 18 19 20

Let 'x' be the number

The condition breakdown:

I am more than 10.

x > 10

I am less than 20.

x < 20

I am more than 12.

x > 12

I am less than 15.

x < 15

As the numbers left after all the conditions are fulfilled are 13 and 14.

But the last condition is, of the numbers that left, the number is greater than all the remaining numbers.

So, from the remaining number 13 and 14;

14 > 13

Thus, the number x = 14

Part b)

Drawing the number 14 in the place value:

Chart

Tens Ones

1 4

6 0

3 years ago

Combine like terms 9p + 2x -6p ?

Tcecarenko [31]

Answer:

3p +2x

Step-by-step explanation: subtract 6 from 9 and keep the p since it is the like term

8 0

3 years ago

The number of eggs e in the carton and the total costs t of the eggs. what is the dependent variable

just olya [345]

T because you need to know the number of eggs, e, to know how much it costs.

6 0

3 years ago

A study by the National Athletic Trainers Association surveyed random samples of 1679 high school freshmen and 1366 high school

nekit [7.7K]

Answer:

We conclude that there is no significant difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids.

Step-by-step explanation:

We are given that a study by the National Athletic Trainers Association surveyed random samples of 1679 high school freshmen and 1366 high school seniors in Illinois.

Results showed that 34 of the freshmen and 24 of the seniors had used anabolic steroids.

Let $p_1$ = proportion of Illinois high school freshmen who have used anabolic steroids.

$p_2$ = proportion of Illinois high school seniors who have used anabolic steroids.

SO, Null Hypothesis, $H_0$ : $p_1=p_2$ {means that there is no significant difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids}

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$ {means that there is a significant difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids}

The test statistics that would be used here Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of high school freshmen who have used anabolic steroids = $\frac{34}{1679}$ = 0.0203

$\hat p_2$ = sample proportion of high school seniors who have used anabolic steroids = $\frac{24}{1366}$ = 0.0176

$n_1$ = sample of high school freshmen = 1679

$n_2$ = sample of high school seniors = 1366

So, the test statistics = $\frac{(0.0203-0.0176)-(0)}{\sqrt{\frac{0.0203(1-0.0203)}{1679}+\frac{0.0176(1-0.0176)}{1366} } }$

= 0.545

The value of z test statistics is 0.545.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is no significant difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids.

3 0

3 years ago

The theoretical probability of a given event is a fraction of 9 and 13. explain what each number represent

Lostsunrise [7]

9 represents the event, 13 represents all possible events.

I have a bag of 13 marbles. 9 of my marbles are blue, 4 are red. My probability of reaching in and pulling out a blue marble at random is 9/13 (Which is 69%)

5 0

3 years ago