Please Please help me.

the answer is d ( square root 3 )

tan = oposite / adjacent

tan 60° = √3 / 1

= √3

9514 1404 393

Answer:

  57

Step-by-step explanation:

Apparently, you want to simplify ...

  [tex]\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}[/tex]

so the denominator is rational. It looks like the form you want is ...

  [tex]\dfrac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F}[/tex]

And you want to know the sum A+B+C+D+E+F.

__

We can start by multiplying numerator and denominator by a conjugate of the denominator. Then we can multiply numerator and denominator by a conjugate of the resulting denominator.

  [tex]\displaystyle =\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}\cdot\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{\sqrt{2} + \sqrt{3} - \sqrt{7}}=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\\\\=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\cdot\frac{\sqrt{6}+1}{\sqrt{6}+1}=\frac{(1+\sqrt{6})(\sqrt{2}+\sqrt{3}-\sqrt{7})}{10}\\\\=\frac{\sqrt{2}+\sqrt{3}-\sqrt{7}+2\sqrt{3}+3\sqrt{2}-\sqrt{42}}{10}=\frac{4\sqrt{2}+3\sqrt{3}-\sqrt{7}-\sqrt{42}}{10}[/tex]

Comparing this to the desired form we have ...

  A = 4, B = 3, C = -1, D = -1, E = 42, F = 10

Then the sum is ...

  A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57

The sum of interest is 57.

9514 1404 393

Answer:

  g(x)

Step-by-step explanation:

f(x) is cubic, so can have at most 3 x-intercepts.

g(x) has 4 x-intercepts listed.

h(x) has 2 x-intercepts listed.

__

g(x) has the most x-intercepts.

Answer:

x=7

Step-by-step explanation:

-2(x-4)+8=2(remove brackets by multiplying with -2)

-2x+8+8=2(group like terms and simply)

-2x=2-16(change side change sign)

-2x = -14(divide both sides by -2)

x=7

Answer:

175.

Step-by-step explanation:

40 = 2*2*2*5

1400 = 2*2*2*5*5*5*7

So by inspection we have x = 5*5*7 = 175

Option A

Answered by GauthMath if you like please click thanks and comment thanks

The linear regression model which models the data is :

y = -6.41053X + 103.83509

Obtaining the regression equation could be performed using either the formula method or using technology (excel, calculator, online regression calculators )

Using technology :

• Enter the data into the columns provided ;

The regression equation obtained for the data is : y = -6.41053X + 103.83509

Where ;

Slope = -6.41053

Intercept = 103.83509

X = Rank

y = probability percentage

Hence, from the linear regression equation obtained, we could see that a negative linear relationship exists between rank and probability as implied from it's negative slope value.

Learn more on linear regression : https://brainly.com/question/12164389

Answer:

a  He would take an explanatory tone with readers to reveal the different categories of advertisements

Step-by-step explanation:

a is formal and is the  best tone for the paper

Answer:

3x-z+9

Step-by-step explanation:

last option 3x+z+9 .........

Answer:

x+3

Step-by-step explanation:

that's the line which passes through

[tex]1\pm\sqrt{2}i[/tex]

Step-by-step explanation:

We already know that one of the roots is x = -4 so we can factor this out to get

[tex]x^3+2x^2-5x+12=(x+4)(x^2-2x+3)[/tex]

Using the quadratic equation on the 2nd factor, we find the roots are

[tex]x= \dfrac{2\pm\sqrt{(2)^2 - 4(1)(3)}}{2}=1\pm\sqrt{2}i[/tex]

Answer:

Step-by-step explanation:

Given function is,

h(x) = 1 - 2x

Domain of the function = {-3, -2, 1, 5}

For range of the function,

Substitute the values of 'x' in the function,

h(-3) = 1 - 2(-3)

       = 7

h(-2) = 1 - 2(-2)

       = 5

h(1) = 1 - 2(1)

     = -1

h(5) = 1 - 2(5)

      = -9

Therefore, set of range for the function will be {7, 5, -1, -9}

Now plot the ordered pairs,

(-3, 7), (-2, 5), (1, -1), (5, -9)

Answer:

Being that there are 195 countries, there would have to be 390 students

Step-by-step explanation:

Answer:

Step-by-step explanation:

770

Answer:

• 1 container contains =55ml

• So 18 container contains

• 18ml multiply to 55 =

• 990 Answer.

9514 1404 393

Answer:

  B. $1044.28

Step-by-step explanation:

Putting the given numbers into the given formula, we have ...

  A(8) = $700•e^(0.05•8) ≈ $1044.28

Answer:

Between 38 and 86 months.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Mean of 62, standard deviation of 12.

Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least approximately 75% of the computers?

Within 2 standard deviations of the mean, so:

62 - 2*12 = 38

62 + 2*12 = 86

Between 38 and 86 months.

Answer:

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

Step-by-step explanation:

Test if the proportion is less than 40%:

At the null hypothesis, we test if the proportion is of at least 0.4, that is:

[tex]H_0: p \geq 0.4[/tex]

At the alternative hypothesis, we test if the proportion is of less than 0.4, that is:

[tex]H_1: p < 0.4[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that [tex]\mu = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]

74 out of the 200 workers sampled said they would return to work

This means that [tex]n = 200, X = \frac{74}{200} = 0.37[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.37 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}[/tex]

[tex]z = -0.87[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.37, which is the p-value of z = -0.87.

Looking at the z-table, z = -0.87 has a p-value of 0.1922.

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

Answer:

24 and 45

Step-by-step explanation:

Okay, now that I can answer this question with the right answers:

The easy way to do this is to first solve the left hand side of the equation.

1/2 of 12 is the same as 12/2 = 6.

So 6 = 1/4 * x

To solve for that unknown x, just multiply both sides by 4 to cancel out the fraction:

6*4 = 4* 1/4*x

24 = x

For the other equation, do the same thing:

1/3 * 90 = 90/3 = 30

30 = 2/3*x

30*3 = 3* 2/3 *x

90 = 2x

90/2 = 2x/2

45 = x

Answer:

1260000 millimeters

Step-by-step explanation:

You multiply 1400mm x 900mm and this is the correct answer.

Hope it helps c:

The area of the rectangular board which is 1400 millimeters long and 900 millimeters wide is 1.26 square meters.

If x and y be the length and width of a rectangular board respectively, then the area of that rectangular board is xy square unit.

Since 1000 millimeters = 1 meter.

i.e. 1 millimeter = 1/1000 meter.

Now, length of the board = 1400 millimeters = 1400/1000 meters = 1.4 meters

Width of the board = 900 millimeters = 900/1000 meters = 0.9 meter

Area of the board = 1.4 * 0.9 = 1.26 square meters.

Therefore, the area of the rectangular board which is 1400 millimeters long and 900 millimeters wide is 1.26 square meters.

Learn more about area here -

https://brainly.com/question/6843862

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Answer:

[tex]x=0,x=-2[/tex]

Step-by-step explanation:

From the question we are told that:

[tex]y=2x^5+5x^4-19[/tex]

Generally the equation if differentiated is mathematically given by

[tex]y'=10x^4+20x^3-0[/tex]

Where

y'=0

[tex]10x^4+20x^3=0[/tex]

Factorizing,We have

[tex]x=0,x=-2[/tex]

Therefore

The critical points are

[tex]x=0,x=-2[/tex]

Excellent question, but let's rephrase it.

Suppose you have a square of surface area of 2851.

What would be a hundredth of such square?

What would be surface area of that hundredth.

Why hundredth? Because percent denotes hundredths cent is a latin word for hundred. You would usually encounter similar word that describes 100 years: century.

Well it is actually very easy. Just divide 2851 into 100 pieces and look at what is the area of one piece.

[tex]2851/100=285.1=y[/tex]

So a single piece has an area of 258.1.

Hope this helps. :)

9514 1404 393

Answer:

  B. 6

Step-by-step explanation:

The products of the lengths of the parts of the chord are the same.

  7×12 = 14x

  7(12)/14 = x = 6 . . . . . divide by 14

Answer:

Option (B)

Step-by-step explanation:

If two chords are intersecting each other at a point insides a circle,

"Product of the measures of the line segments on each chord are equal"

By this property,

MH × HY = TH × HN

By substituting the measures of each segment,

7 × 12 = 14 × ([tex]x[/tex])

[tex]x=\frac{84}{14}[/tex]

[tex]x=6[/tex]

Therefore, Option (B) will be the correct option.

Answer:

The domain is the number of copies made (N)

The range is the is the total cost of the books (C)

The domain we know that they made 200 copies, so the domain would be 0-200.

The range would be:

C=10(200)+700

C=200+700

C=900

Range would be 700-900

(C) You're given a probability mass function,

[tex]P(X=x)=\begin{cases}\frac17&\text{if }x\in\{1,6,16\}\\\frac27&\text{if }x\in\{11,21\}\\0&\text{otherwise}\end{cases}[/tex]

The mean is

[tex]\displaystyle E[X] = \sum_x x\,P(X=x) = \frac{1\times1}7 + \frac{1\times6}7 + \frac{1\times16}7 + \frac{2\times11}7 + \frac{2\times21}7 = \boxed{\frac{87}7} \approx 12.43[/tex]

The variance is

[tex]\displaystyle V[X] = \sum_x x^2\,P(X=x) = \frac{1^2}7 + \frac{6^2}7 + \frac{16^2}7 + \frac{2\times11^2}7 + \frac{2\times21^2}7 = \boxed{\frac{1417}7} \approx 202.43[/tex]

The standard deviation is simply the square root of the variance:

[tex]\sqrt{V[X]} = \boxed{\sqrt{\dfrac{1417}7}} \approx 14.23[/tex]

(D) I'm not entirely sure what is being asked here, so I'm kinda guessing at the meaning. I think the question is saying there is a large set of 5000 test scores that are normally distributed with mean µ = 86 and standard deviation σ = 10.

Let X be the random variable representing these test scores. Then

(D.A)

[tex]P(96 < X < 106) = P\left(\dfrac{96-86}{10} < \dfrac{X-86}{10} < \dfrac{106-86}{10}\right) = P(1 < Z < 2)[/tex]

where Z follows the standard normal distribution with mean 0 and variance 1.

To find the remaining probability, you can use the empirical rule (68/95/99.7) which says

• approximately 68% of a normal distribution lies within 1 standard deviation of the mean; in other words, [tex]P(-1<Z<1)\approx0.68[/tex]

• approximately 95% of the distribution lies within 2 standard deviations; [tex]P(-2<Z<2)\approx0.95[/tex]

The normal distribution is also symmetric about its mean. Taking these facts together, we find

[tex]P(1<Z<2) = \dfrac{P((-2<Z<-1)\text{ or }(1<Z<2))}2 = \dfrac{P(-2<Z<2)-P(-1<Z<1)}2 \approx 0.135[/tex]

So roughly 13.5% of all test scores will fall between 96 and 106, and 13.5% of 5000 is 675. (The actual probability is closer 0.135905, and the projected test score count is closer to 679.)

(D.B) Any 50% of the distribution is still 50% of the distribution, so half of all the test scores would fall in this range. There would be 2500 test scores in that group.

(E) No choices given here...

Answer:

3 x 2 = 6 years to get Rs. 1324

Step-by-step explanation:

This is a mathematical relationship that transcends currencies. In other words, it also applies to Dollars, Pounds and Yen.

“Annual compound interest” is a phrase of dubious meaning. The process is a “compound interest problem”, but the item I think you are looking for is simply the amount of interest.

Month 0: interest: 0 balance: 4,000

Month 6: interest; 200 balance: 4,200

Month 12: interest 210 balance: 4,410 12-month total interest: 410

Month 18: interest: 220.5 balance: 4,630.5 12-month total interest: 430.5

Month 24: interest: 231.525 balance: 4,862.025 12-month total interest: 452.025

Month 30: int: 243.10125 bal: 5,105.12625 12-month total int: 474.35125

Keep expanding this progression until the 12-month total interest meets or exceeds 1324, the answer will be the number of months in the last line.

Answer:

f(x) = log x - 1 --> (10, 0)

f(x) = -(log x - 2) --> (100, 0)

f(x) = log(- x - 2) --> (-3, 0)

f(x) = -log-(x-1) --> (0, 0)

Step-by-step explanation:

An x-intercept is the position where the value of y(in this case f(x)) is 0.

Let's start with the first equation:

f(x) = log x - 1

If f(x) is 0, we would get this equation:

0 = log x - 1

Now, we solve for x:

1 = log x

x = 10

This means the x-intercept is (10, 0).

f(x) = -(log x - 2)

Again, we can set f(x) to 0, and solve for x:

0 = -(log x - 2)

0 = log x - 2

2 = log x

x = 100

This means the x-intercept is (100, 0)

Same process applies for the third:

f(x) = log(- x - 2)

0 = log(- x - 2)

1 = -x - 2

3 = -x

x = -3

(-3, 0)

f(x) = -log-(x-1)

0 = -log-(x-1)

0 = log-(x-1)

1 = -(x-1)

1 = -x + 1

0 = -x

x = 0

(0, 0)

Answer:

0.3333 = 33.33% probability that this red ball is from box A.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Red ball

Event B: From box A.

Probability of a red ball:

3/10 = 0.3 of 1/2 = 0.5(box A)

6/10 = 0.6 of 1/2 = 0.5(box B). So

[tex]P(A) = 0.3*0.5 + 0.6*0.5 = 0.45[/tex]

Probability of a red ball from box A:

0.3 of 0.5, so:

[tex]P(A \cap B) = 0.3*0.5 = 0.15[/tex]

What is the probability that this red ball is from box A?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.45} = 0.3333[/tex]

0.3333 = 33.33% probability that this red ball is from box A.

Answer:

0.4 = 40% probability that one die resulted in a 3.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Outcomes for the dice:

For the pair of dice:

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

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

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

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

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

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

So 36 total outcomes.

In this question:

Event A: Sum of 8

Event B: One dice resulting in 3.

Probability of a sum of 8:

These are the following desired outcomes:

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

5 outcomes out of 36, so:

[tex]P(A) = \frac{5}{36}[/tex]

Probability of a sum of 8 and one dice resulting in 3.

(3,5) or (5,3), so 2 outcomes out of 36, and:

[tex]P(A \cap B) = \frac{2}{36}[/tex]

Probability that one die resulted in a 3, given that the sum is 8:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{2}{36}}{\frac{5}{36}} = \frac{2}{5} = 0.4[/tex]

0.4 = 40% probability that one die resulted in a 3.