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2 years ago

Using the technique in the model above, find the missing segments in this 30°-60°-90° right triangle. AB = 8 BC = 4 CD =

Mathematics

2 answers:

sattari [20]2 years ago

7 0

simpler version of answer above / below me

2 square root(3)

zimovet [89]2 years ago

6 0

For a 30-60-90 triangle the sides always have the same relationship
Short leg = a
Long leg = a√3
Hypotenuse = 2a

BC is the short leg of ∆ABC

Given BC = 2
BC = a
Therefor
a = 2
AB = 2a = 4
AC = a√3 = 2√3

For ∆ACD
As above AC = 2√3
Since AC is the hypotenuse of ∆ACD
2a = 2√3
a = √3

CD = a = √3
AD = a√3 = 3

For ∆BCD
As above
BC = 2
CD = √3
Since BC is the hypotenuse of ∆BCD
2a = 2
a = 1

DB = a = 1

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Emma's square patio below has been area=31 sq ft. She decides to decrease one dimension by 1 foot and decreases the other dimens

Andreas93 [3]

Answer:

4.57ft by 1.57 ft

Step-by-step explanation:

We are given that

Emma's square patio has been area=31 sq.ft

One dimension decrease by 1 foot and other dimension decrease by 4 feet.

We have to find the new dimensions of Emma's patio.

Let x be the side of Emma's square patio

We know that

Area of square= $x^2$

$x^2=31$

$x=\sqrt{31}=5.57$ ft

One dimension= $5.57-1=4.57$ ft

other dimension= $5.57-4=1.57 ft$

Hence, the new dimension of Emma's patio is given by

4.57ft by 1.57 ft

5 0

2 years ago

Problem 5 (4+4+4=12) We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely. 1) Fin

tekilochka [14]

Answer:

$p(b) = \frac{1}{6}$

$p(k) = \frac{1}{3}$

$P(a) = \frac{1}{3}$

Step-by-step explanation:

Generally when two fair 6-sided dice is rolled the doubles are

(1 1) , ( 2 2) , (3 3) , (4 4) , ( 5 5 ), (6 6)

The total outcome of doubles is N = 6

The total outcome of the rolling the two fair 6-sided dice is

n = 36

Generally the probability that doubles (i.e., having an equal number on the two dice) were rolled is mathematically evaluated as

$p(b) = \frac{N}{n}$

$p(b) = \frac{6}{36}$

$p(b) = \frac{1}{6}$

Generally when two fair 6-sided dice is rolled the outcome whose sum is 4 or less is

(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)

Looking at this outcome we see that there are two doubles present

The conditional probability that doubles were rolled is mathematically represented as

$p(k) = \frac{2}{6}$

$p(k) = \frac{1}{3}$

Generally when two fair 6-sided dice is rolled the number of outcomes that would land on different numbers is L = 30

And the number of outcomes that at least one die is a 1 is W = 10

The conditional probability that at least one die is a 1 is mathematically represented as

$P(a) = \frac{W}{L}$

=> $P(a) = \frac{10}{30}$

=> $P(a) = \frac{1}{3}$

3 0

1 year ago

Santos flipped a coin 500 times. The coin landed heads up 225 times. Find the ratio of heads to total number of coin flips. Expr

Whitepunk [10]

Here is how you do it....
You will subtract 500 minus 225 to get the number of tails. The number of tails is 275.
Now, you know your ratio is 225:500. All you need to do is simplify it.
225 divided by 25 is 9 and 500 divided by 25 is 20.
Now, the ratio that you have is 9:20.

6 0

2 years ago

Read 2 more answers

Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is highe

Sauron [17]

Answer:

Translate K to N and rotate about K until HK lies on the line containing LN.

Step-by-step explanation:

Hope this helps bb's!!

Lots of love and peace your way!! <3

7 0

1 year ago

Read 2 more answers

A normal distribution curve, where x = 70 and σ = 15, was created by a teacher using her students’ grades. What information abou

mash [69]

Answer:

The median and mode of the students grade is 70.

Most of the students scored between 40 and 100.

Step-by-step explanation:

From the provided information it can be seen that the mean of the distribution is, <em>μ</em> = 70 and the standard deviation is, <em>σ</em> = 15.

For a Normal distributed data the mean, median and mode are the same.

So, the median and mode of the students grade is 70.

The standard deviation of the data represents the spread of the observation, i.e. how dispersed the values are along the curve.

In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is a shortcut used to recall that 68.27%, 95.45% and 99.73% of the values of a Normally distributed data lie within one, two and three standard deviations of the mean, respectively.

$P(\mu-\sigma$

$P(\mu-2\sigma$

$P(\mu-3\sigma$

Assuming that maximum marks of the exam is 100, it can be said that most of the students scored between 40 and 100.

3 0

2 years ago

Read 2 more answers