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3 years ago

Find the length of x in simplest radical form with a rational denominator

Mathematics

2 answers:

Alisiya [41]3 years ago

8 0

Answer:

Step-by-step explanation:

$\cos(30^o)=\dfrac{\sqrt3}2$

From triangle: $\cos(30^o)=\dfrac x2$

Therefore:

$\dfrac x2=\dfrac{\sqrt3}{2}\\\\x=\sqrt3$

aleksandrvk [35]3 years ago

7 0

It is equals to 3 I think

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magan wants to ride his bicycle 30.4 miles this week. he has already ridden 4 miles if he rides for 4 more days what is the aver

Kaylis [27]

The average number of miles he will ride each day to meet his goal is 6.6 miles

<h3>How to find the average number of miles she will ride?</h3>

He wants to ride his bicycle 30.4 miles this week.

He has already ridden 4 miles.

He rides 4 more days.

Therefore, the average number of miles he would have to ride each day to meet his goal can be calculated as follows:

let

x = number of miles driven

Hence, the equation can be represented as follows;

4x + 4 = 30.4

Therefore,

4x + 4 = 30.4

4x + 4 - 4 = 30.4 - 4

4x = 26.4

x = 26.4 / 4

x = 6.6

Therefore, the average number of miles he will ride each day to meet his goal is 6.6 miles

learn more on equation here: brainly.com/question/20794747

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4 0

2 years ago

A jewelry store is selling a set of 4 pairs of gemstone earrings for $58, including tax. Neva and three of her friends want to b

Marat540 [252]

Each member should pay $14.5, including tax.

4 0

3 years ago

Read 2 more answers

If you explain and answer i will give brainly

CaHeK987 [17]

6x - 5y = 3 x1

3x - 8y = -15 x2

===============

6x - 5y = 3

6x - 16y = -30

============= -

11y = 33

y = 3

6x - 5(3) = 3

6x -15 = 3

6x = 18

x = 3

(3,3)

7 0

2 years ago

Solve 3x + 5 ⩾ x + 17

Ugo [173]

Answer:

Step-by-step explanation:

Simplifying

3x + 5 = x + 17

Reorder the terms:

5 + 3x = x + 17

Reorder the terms:

5 + 3x = 17 + x

Solving

5 + 3x = 17 + x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

5 + 3x + -1x = 17 + x + -1x

Combine like terms: 3x + -1x = 2x

5 + 2x = 17 + x + -1x

Combine like terms: x + -1x = 0

5 + 2x = 17 + 0

5 + 2x = 17

Add '-5' to each side of the equation.

5 + -5 + 2x = 17 + -5

Combine like terms: 5 + -5 = 0

0 + 2x = 17 + -5

2x = 17 + -5

Combine like terms: 17 + -5 = 12

2x = 12

Divide each side by '2'.

x = 6

Simplifying

x = 6

5 0

3 years ago

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 35, de

Amiraneli [1.4K]

Answer:

a) P=0.1721

b) P=0.3528

c) P=0.3981

Step-by-step explanation:

This sampling can be modeled by a binominal distribution where p is the probability of a project to belong to the first section and q the probability of belonging to the second section.

a) In this case we have a sample size of n=15.

The value of p is p=25/(25+35)=0.4167 and q=1-0.4167=0.5833.

The probability of having exactly 10 projects for the second section is equal to having exactly 5 projects of the first section.

This probability can be calculated as:

$P=\frac{n!}{(n-k)!k!}p^kq^{n-k}= \frac{15!}{(10)!5!}\cdot 0.4167^5\cdot0.5833^{10}=0.1721$

b) To have at least 10 projects from the 2nd section, means we have at most 5 projects for the first section. In this case, we have to calculate the probability for k=0 (every project belongs to the 2nd section), k=1, k=2, k=3, k=4 and k=5.

We apply the same formula but as a sum:

$P(k\leq5)=\sum_{k=0}^{5}\frac{n!}{(n-k)!k!}p^kq^{n-k}$

Then we have:

$P(k=0)=0.0003\\P(k=1)=0.0033\\P(k=2)=0.0165\\P(k=3)=0.0511\\P(k=4)=0.1095\\P(k=5)=0.1721\\\\P(k\leq5)=0.0003+0.0033+0.0165+0.0511+0.1095+0.1721=0.3528$

c) In this case, we have the sum of the probability that k is equal or less than 5, and the probability tha k is 10 or more (10 or more projects belonging to the 1st section).

The first (k less or equal to 5) is already calculated.

We have to calculate for k equal to 10 or more.

$P(k\geq10)=\sum_{k=10}^{15}\frac{n!}{(n-k)!k!}p^kq^{n-k}$

Then we have

$P(k=10)=0.0320\\P(k=11)=0.0104\\P(k=12)=0.0025\\P(k=13)=0.0004\\P(k=14)=0.0000\\P(k=15)=0.0000\\\\P(k\geq10)=0.032+0.0104+0.0025+0.0004+0+0=0.0453$

The sum of the probabilities is

$P(k\leq5)+P(k\geq10)=0.3528+0.0453=0.3981$

8 0

3 years ago