what is the quotient of 1 over (1 plus the square root of 3)?

Answers

Answer 1

You can rationalize the denominator by multiplying by 1 in the form of the conjugate of the denominator divided by itself.

[tex]\dfrac{1}{1+\sqrt{3}}=\dfrac{1}{1+\sqrt{3}}\cdot \dfrac{1-\sqrt{3}}{1-\sqrt{3}}\\\\=\dfrac{1-\sqrt{3}}{1^{2}-(\sqrt{3})^{2}}=\dfrac{1-\sqrt{3}}{1-3}\\\\=\dfrac{\sqrt{3}-1}{2}[/tex]

This eqvaluates to approximately 0.3660254037844386.

Related Questions

The scores of individual students on the american college testing (act) program composite college entrance examination have a normal distribution with a mean of 18.6 and a standard deviation of 6.0. at northside high, 36 seniors take the test. assume the scores at this school have the same distribution as national scores. what is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?

Answers

The mean of the distribution of the sampling mean is the same as the mean of the population, 18.6.

What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 6.5?

Perimeter = 54 cm, area = 181.25 cm2
Perimeter = 54 cm, area = 2,028 cm2
Perimeter = 182 cm, area = 2,028 cm2
Perimeter = 182 cm, area = 181.25 cm2

Answers

The perimeter of the given rectangle is
2(6 cm + 8 cm) = 28 cm
The area of the given rectangle is
(6 cm)*(8 cm) = 48 cm^2

The larger rectangle will have a perimeter of
6.5*28 cm = 182 cm
The larger rectangle will have an area of
6.5^2*48 cm^2 = 2028 cm^2 . . . . . note the scale factor is squared for area

The appropriate choice is the 3rd one, ...
Perimeter = 182 cm, area = 2,028 cm^2

Answer:

Perimeter = 182 cm, area = 2,028 cm^2

Step-by-step explanation:

Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows that the bank pays a 3 percent interest rate. He sits down with a pen, paper, and calculator to find out the simple interest

Answers

Nice story.

We suppose the question is, "what is the amount of interest Matt will be paid?"

The formula that applies is
I = Prt
I = $550*0.03*1 = $16.50

Matt will be paid $16.50 in interest for the year.

What does same amount means?

Answers

This means two numbers that equal the same amount

How does an earthquake of magnitude 7.9 compare in intensity with an earthquake of magnitude of 3.7 on the Richter scale? The larger earthquake's intensity was nothing times as great as the smaller earthquake's intensity. (Round to the nearest whole number as needed.)

Answers

Answer:

15,849

Step-by-step explanation:

Final answer:

A magnitude 7.9 earthquake releases approximately 2.7 million times more energy than a 3.7 magnitude earthquake, as the Richter scale is logarithmic and represents a 32-fold increase in energy release for each unit increase in magnitude.

Explanation:

The Richter scale is logarithmic, which means that each whole number increase represents a tenfold increase in amplitude and roughly a 32-fold increase in the energy released by an earthquake.

Therefore, when comparing a magnitude 7.9 earthquake to a magnitude 3.7 earthquake, there is a difference of 4.2 on the Richter scale.

This corresponds to a tenfold increase in amplitude 4.2 times, which would be 10 to the power of 4.2 in terms of amplitude.

However, if we consider the energy, which increases by a factor of 32 for each whole number increase, we're looking at 32 to the power of 4.2, which is approximately 2,704,156 times greater in terms of energy release.

To determine the intensity difference in a more simplified manner, taking the base-10 logarithm of the energy ratio is effective.

The simplified comparison tells us that the larger quake's intensity is about 2.7 million times greater than the smaller quake's intensity.

After rounding to the nearest whole number, we find that the intensity is 2,704,156 times as great.

Let μ = 160 and σ = 16. find the z-score for the score, x = 150.

Answers

Put the given values in the formula
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
and evaluate.
z = (150 -160)/16 = -10/16
z = -5/8

The z-score for the score x=150 is -5/8 = -0.625.

How many terms are there in a geometric series if the first terms is 2, the common ratio is 4, and the sum of the series is 2,730 ?

Answers

The sum of n terms of a geometric series is given by
[tex]S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}[/tex]

Substituting the given numbers, you have
[tex]2730=2\dfrac{4^{n}-1}{4-1}\\\\2730\dfrac{3}{2}=4^{n}-1\\\\4096=4^{n}\\\\\dfrac{\log(4096)}{\log(4)}=n=6[/tex]

There are 6 terms in the series.

Rhombus A has base of 7 inches and an area of 35 square inches. Rhombus B has a Base and Height that are three times the base and height of Rhombus A. Find the area of Rhombus b and compare it to the area of rhombus A Explain

Answers

Final answer:

Rhombus B, which has dimensions three times larger than Rhombus A, has an area that is nine times larger than the area of Rhombus A.

Explanation:

This question is based on geometry and compares the areas of two rhombuses. Firstly, remember that the area of a rhombus is obtained by the formula A = base x height. For Rhombus A, with a base of 7 inches and area 35 square inches, this implies that its height is 5 inches (since 7 x 5 = 35). Therefore, the height of Rhombus B which is three times larger than that of Rhombus A would be 15 inches, and its base would be 21 inches (three times that of Rhombus A).

Now applying these values into the formula for the area of a rhombus, for rhombus B we get A = 21 x 15, which equals 315 square inches - this is the area of Rhombus B. Comparing this with the area of Rhombus A (35 square inches), we find that Rhombus B is 9 times larger than Rhombus A (because 315 divided by 35 equals 9).

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Final answer:

By increasing the base and height of Rhombus A by three times, the resulting area of Rhombus B is nine times the area of Rhombus A. The area of Rhombus A is 35 square inches and the area of Rhombus B is 315 square inches.

Explanation:

The subject of this question is area of rhombuses. A key concept to remember is that the area of a rhombus is calculated by the formula: Area = base x height.

Rhombus A has base of 7 inches and an area of 35 square inches. This means the height h of Rhombus A is A/base = [tex]35/7 = 5[/tex] inches.

The base and height of Rhombus B are three times the base and height of rhombus A. So, Rhombus B has a base of [tex]7 * 3 = 21[/tex] inches and height of [tex]5 * 3 = 15[/tex] inches.

To find the area of Rhombus B, you apply the same formula, Substituting the values we get, B = base x height = [tex]21 * 15 = 315[/tex] square inches. Therefore, the area of Rhombus B is nine times the area of Rhombus A since 315/35 = 9.

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Suppose x is a normal random variable with μ = 35 and σ = 10. find p(55.5 < x < 69.7).

Answers

Answer:

[tex]\boxed{\boxed{P(55.5 < X< 69.7)=0.01992}}[/tex]

Step-by-step explanation:

We know that,

[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]

where,

Z = z-score,

X = raw score,

μ = mean,

σ = standard deviation.

So,

[tex]=P(55.5 < X< 69.7)[/tex]

[tex]=P(55.5-35 < X-35< 69.7-35)[/tex]

[tex]=P(\dfrac{55.5-35}{10}< \dfrac{X-35}{10}< \dfrac{69.7-35}{10})[/tex]

[tex]=P(\dfrac{55.5-35}{10}< Z< \dfrac{69.7-35}{10})[/tex]

[tex]=P(2.05< Z<3.47)[/tex]

[tex]=P(Z<3.47)-P(Z<2.05)[/tex]

[tex]=0.99974-0.97982\\\\=0.01992[/tex]

Lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. a bank conducts interviews of job applicants with the use of the lie detector. there are 15 applicants who are interviewed.
a.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that all 15 are telling the truth?
b.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that at least one is lying?
c.what are the mean and standard deviation of the 15 applicants the lie detector concludes are lying?
d.what is the probability that the number of truthful applicants classified as liars is greater than the mean?

Answers

Part A:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector correctly determined that a selected person is saying the truth has a probability of 0.85
Thus p = 0.85

Thus, the probability that the lie detector will conclude that all 15 are telling the truth if all 15 applicants tell the truth is given by:

[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(15)={ ^{15}C_{15}(0.85)^{15}(0.15)^0} \\ \\ =1\times0.0874\times1=0.0874[/tex]

Part B:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.25
Thus p = 0.15

Thus, the probability that the lie detector will conclude that at least 1 is lying if all 15 applicants tell the truth is given by:

[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(X\geq1)=1-P(0) \\ \\ =1-{ ^{15}C_0(0.15)^0(0.85)^{15}} \\ \\ =1-1\times1\times0.0874=1-0.0874 \\ \\ =0.9126[/tex]

Part C:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The mean is given by:

[tex]\mu=npq \\ \\ =15\times0.15\times0.85 \\ \\ =1.9125[/tex]

Part D:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The probability that the number of truthful applicants classified as liars is greater than the mean is given by:

[tex]P(X\ \textgreater \ \mu)=P(X\ \textgreater \ 1.9125) \\ \\ 1-[P(0)+P(1)][/tex]

[tex]P(1)={ ^{15}C_1(0.15)^1(0.85)^{14}} \\ \\ =15\times0.15\times0.1028=0.2312[/tex]

I need help on this one please

Answers

Try this solution (see the attachment).

19 hundred thousandths in scientific
notation

Answers

19 hundred thousandths is the same thing as 0.00019. With scientific notation the number must be greater than or equal to one and less than two, so the answer would be 1.9*10⁻⁴ since it is in the decimals

Final answer:

The scientific notation of 19 hundred thousandths which is 0.000019 is 1.9 x 10^-5.

Explanation:

The number 19 hundred thousandths would mean 19 divided by 1,000,000 which equals 0.000019. When we convert this decimal to scientific notation, it becomes 1.9 x 10^-5. In scientific notation, we want to express a number as a value between 1 and 10 multiplied by a power of 10. So, to convert 0.000019 to scientific notation, we need to move the decimal point five places to the right, which gives us 1.9. The '10^-5' shows that the decimal point has moved five places to the right from the original number.

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400,000 + 80,000 + 4,000 + 50 + 9 Write the standard form of the number shown above.

Answers

Add:

400,000
80,000
4,000
59
--------------
484,059 (answer)

Hello there, and thank you for posting your question here on brainly.

Short answer: 484,059

Why?

This equation shown is an expanded form of a number. 400k is the largest number, so that'd go first. 80k is the second largest, so that would go next to the largest number, 4. (400k) 4k is the third largest, so that'd go next to the first and second largest numbers, 48. (480k) Now, we have 484,000. Since there is no hundred, we put a zero there. Now, add a 59 at the end of the zero. Which gives us the number 484,059.

Hope this helped you! ♥

The graph represents the feasible region for the system: y<2x x + y 45 x > 30 Minimize the objective function P = 20x + 16y.

Answers

minimum value= 780
and occurs when x= 15
and y=30

Which number has a repeating decimal form?
a) square root of 15
b)11/25
c)3/20
d)2/6

Answers

Which number has a repeating decimal form?
a) square root of 15
b)11/25
c)3/20
d)2/6

The correct answer is d)2/6
Since, once solved, the value would give, 0.33333333333333333333333333333333

the answer to this question is 2/6

The continuous function f is defined on the interval -4 ≤ x ≤ 3. there is no point c, -4 ≤ c ≤ 3, for which

Answers

We can say that there is no point c, which is not defined on this function's domain. Indeed, the intervals of this function and the interval of c coincide.

In what form is the following linear equation written?

A. standard

B. Point Slope

C. Slope intercept

D. Rise Run

Answers

This is point slope form which in general is

y - y1 = m(x-x1)

The slope is m, which in this case is m = 2/3
The point this line goes through is (x1,y1) = (1,3)

As the name "point slope form" suggests, this form quickly lets us know the slope and one point that is on the line.

NEED HELP WILL GIVE OUT BRAINLIEST AND POINTS

11. Find the area. The figure is not drawn to scale.

12. Find the area of the kite. The figure is not drawn to scale.

Answers

part 1) Find the area

we know that
the area of the triangle is
A=b*h/2
in this problem
b=9
h=12
so
A=9*12/2-----> A=54 units²

the answer part 1) is
Area=54 units²

Part 2) Find the area of the kite

see the picture attached with letters to better understand the problem

we know that
The area of a Kite is half the product of the diagonals

step 1
find CB
applying Pythagoras Theorem
AB²=AC²+BC²------> BC²=AB²-AC²-----> BC²=5²-3²----> BC²=16
BC=4
so
the diagonals are
(10+4) and (3+3)---------> 14 and 6
Area=(1/2)*[14*6]----> Area=42 units²

the answer Part 2) is
the area of a kite is 42 units²

Stocks are units of ownership in a company. The stock market is a place where stocks are bought and sold. When you buy a stock, you own a part of the company. If the company’s profits go up, the stock value goes up. If the profits fall, so does the value of the stock. Stock prices rise and fall every day. Last week, Isabelle bought stock in a toy company. Since then, the price of the stock had a change of -3 dollars. What is the absolute value of -3?

Answers

The absolute value is three.
Think of it like this. Whenever the absolute value is there, the number or expression inside, whether negative or positive takes a shower. When they are done showering, they are clean. The clean equals positive, all numbers after absolute value are positive so the answer is three.

Answer:

The absolute value is three!

Step-by-step explanation:

have a nice day/night!

what problem does the model show?

Answers

4/8 which is the same as 1/2 (one half)

1/2 is the fraction represents the diagram.

What is Fraction?

A fraction represents a part of a whole.

Fractions are of three types.

Proper fraction, improper fraction and mixed fraction.

A proper fraction is a fraction which has its numerator value less than the denominator.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

A fraction represented with its quotient and remainder is a mixed fraction

In the diagram there are 8 boxes in whole, the number of boxes shaded are 4 out of 8.

4/8 is the fraction represents the diagram, 1/2 is another way of representing 4/8.

Hence, 1/2 is the fraction represents the diagram.

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Solve, if 1.32 : 3 1/7 = (14y) : 5/6

Answers

we have that
1.32 : 3 1/7 = (14*y) : 5/6

we know that
3 1/7------> (3*7+1)/7------> 22/7

substitute
1.32 : 22/7 = (14*y) : 5/6
1.32*(5/6)=14*y*(22/7)
1.1=44*y
y=1.1/44--------> y=0.025

the answer is
y=0.025

Of the 5th grade boys, 2/3 play sports. Of the boys who play sports, 1/4 play baseball. what fraction of the 5th grade boys play baseball?

Answers

So, to find this rate, we simply multiply the two fractions together:
2/3 * 1/4
2/12
Simplify:
1/6 of the 5th grade boys play baseball

the function of (x) varies directly with x^2, and f(x)=96 when x=4 what is the value of f(2)

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \textit{f(x) varies directly with }x^2\qquad f(x)=kx^2 \\\\\\ \textit{we also know that } \begin{cases} f(x)=96\\ x=4 \end{cases}\implies 96=k(4)^2\implies 96=16k \\\\\\ \cfrac{96}{16}=k\implies 6=k\qquad therefore\qquad \boxed{f(x)=6x^2} \\\\\\ \textit{now, when }\stackrel{f(2)}{x=2}\textit{ what is \underline{f(x)}?}\qquad f(2)=6(2)^2[/tex]

help with this question?

Answers

The rational expression [tex]\dfrac{(x-4)(x+9)}{(x-1)(x+9)}[/tex] has a removable discontinuity at x=-9. The definition of f(x) removes the discontinuity at x=-9. However, the function remains undefined at x=1.

The appropriate choice is ...
c. continuous at every real number except x = 1.

The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of (u-v)(x)?

Answers

For domain to work, we would need to find intersection of two domain sets. Because if one input causes one function to be undefined, then combined function would be undefined too.

So then domain of (u-v)(x) would be the set of all real values except 0 and 2.

Hope this helps.

Answer: x = 2 and x cannot be any value for which v(x) = 0

Step-by-step explanation:

expand (x^2-3/2)^9 using binomial process

Answers

Use the Binomial expansion theorem to find and simplify each term.

[tex] x^{18} - \frac{ 27x^{6} }{2}+ 81x^{14}- \frac{ 567x^{12} }{2}+ \frac{ 5103x^{10} }{16}- \frac{ 15309x^{8} }{16}+ \frac{ 15309x^{6} }{16} - \frac{ 59049x^{2} }{256}- [/tex][tex] \frac{19683}{512} [/tex]

Man that was a lot to type out, hopefully i helped, and Gosh I hope I get a brainly for all that freaking typing. hehe~ ^.^

Ramone tossed 1 quarter, 2 dimes, and 13 pennies in the wishing well at the party. What is the total amount of money as a fraction and as a decimal?

Answers

For this case we have:
1 quarter:
(1) * (0.25) = 0.25 $
2 dimes:
(2) * (0.1) = 0.2 $
13 pennies:
(13) * (0.01) = 0.13 $
Adding we have:
0.25 + 0.2 + 0.13 = 0.58 $
As a fraction:
58/10 = 29/5 $
Answer:
The total amount of money as a fraction and as a decimal are:
$ 29/5
$ 0.58

hey can some one look at this?

Answers

I'm just going to give you a very quick answer, but I can answer the question
1 foot = 12 inches.
x feet = 60 inches.

1 foot * 60 inches = 12 * x divide by 12

60 / 12 = 5

So the person is at least 5 feet tall. The height you want is 5 feet 4 inches.

So add 4 inches to 5 feet.
or
Add 4 inches to 60 inches.
you get 64 inches.

There are 20 entries all together. 2 people are 64 inches tall.

P(64) = 2/20 = 1/10 = 0.1

Answer P(64) = 0.1

I would check all of this if I were you. I'm not sure I counted either one correctly.

If the typos are randomly distributed over the 10 pages, find the probability of having a single typo on each page

Answers

1/10 assuming there is are 10 typos in total

does anyone know the answer???

Answers

The slope of line AB is
slope = (change in y)/(change in x)
slope = (14 -(-3))/(7 -(-10)) = 17/17 = 1

The slope of line CD is the negative reciprocal of that, -1/1 = -1.
The point-slope form of the equation for line CD can be written as
y = -1(x -5) +12
y = -x +17

The x-intercept is the value of x when y = 0.
0 = -x +17
x = 17
The x-intercept is ...
(17, 0)

Another way to write the equation for line CD is "standard form." For this, we add x to the slope-intercept form to get ...
x + y = 17

For the second part of your question, we can find the answer by adding the x- and y-coordinates to see which sum is 17.
-5 +24 = 19
-2 +19 = 17 . . . . . . . . . the point (-2, 19) is the correct choice
7 +(-10) = -3
8 +11 = 19

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