Simplify the expression. (-3 + 6i)(-3 + 5i)

Answer:

Step-by-step explanation:

The exact value of tan 4π/3 is √3.

Trigonometry is a discipline of mathematics dealing with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).

We have to find the exact value of tan4pi/3.

tan 4π/3

= tan (π + π/3)

= tan (π/3)

= √3.

So, the value is √3.

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Answer:

Induction

Step-by-step explanation:

Induction reasoning refers to conjectures which is what you will need for this

The Inductive reasoning allows to use observation to find the next three

values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

For given example,

We have been given the number pattern 1, 4, 7, 10, . . .

Here, 4 - 1 = 3                             ..................(i)

7 - 4 = 3                                       ..................(ii)

10 - 7 = 3                                      ..................(iii)

From (i), (ii) and (iii),

the common difference between consecutive terms is 3.

The next three values would be,

10 + 3 = 13

13 + 3 = 16

16 + 3 = 19

So, the number pattern would be 1, 4, 7, 10, 13, 16, 19, . . .

Therefore, an Inductive reasoning allows to use observation to find the next three values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

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Answer:

Option C is correct.

The 437 county residents were a random sample of all county residents.

a) If p is the proportion of Hispanics in the county,

The null hypothesis is represented as

H₀: p = 0.16

The alternative hypothesis is represented as

Hₐ: p ≠ 0.35

b) The model of the test is two-tailled, one-proportion test. And it satisfies all of the required conditions for an hypothesis test.

c) The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).

Test statistic = -4.09

p-value = 0.000043

d) We can conclude that the proportion of the county that are Hispanics is different from the proportion of the country that are Hispanics.

Step-by-step explanation:

According to the question, it was clearly stated that the 437 county residents are a random sample of the residents in the county, hence, it is evident that option C is the right statement.

a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the county supervisor wants to check if proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. (0.16).

Hence, the null hypothesis is that there isn't enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. That is, there is no significant difference between the proportion of the county that are Hispanics and the proportion of the whole nation that are Hispanics. (0.16).

The alternative hypothesis will now be that enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics (0.16).

Mathematically,

The null hypothesis is represented as

H₀: p = 0.16

The alternative hypothesis is represented as

Hₐ: p ≠ 0.16

b) To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough.

Hence, the model of this test is two-tailled, one-proportion test.

And the major conditions for an hypothesis test is that

- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another. This is already clearly given in the question.

- The sample must be a normal distribution sample or approximate a normal distribution.

The conditions to check this is that

np ≥ 10

and

np(1-p) ≥ 10

p = sample proportion = (44/437) = 0.101

np = 437×0.101 = 44 ≥ 10

np(1-p) = 437×0.101×(1-0.101) = 39.7 ≥ 10

The two conditions are satisfied, hence, we can conclude that this distribution at least approximates a normal distribution.

c) So, we compute the t-test statistic

z = (x - μ)/σₓ

x = sample proportion = 0.101

μ = p₀ = The proportion we are comparing against = 0.16

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 437

σₓ = √[0.101×0.899/437] = 0.0144145066 = 0.0144

z = (0.101 - 0.16) ÷ 0.0144

z = -4.093 = -4.09

checking the tables for the p-value of this z-statistic

Degree of freedom = df = n - 1 = 437 - 1 = 436

Significance level = 0.05 (when the significance level isn't stated, 0.05 is used)

The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).

p-value (for z = -4.09, at 0.05 significance level, df = 436, with a two tailed condition) = 0.000043

The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).

d) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.000043

0.000043 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics.

Hope this Helps!!!

Answer:

(-3,18) and (-1,6)

Step-by-step explanation:

[tex]x^2-2x+3=-6x\\<=> x^2+4x+3 = 0\\<=> (x+2)^2 -4+3=0\\<=> (x+2)^2-1^2 = 0\\<=> (x+2+1)(x+2-1) = 0\\<=> (x+1)(x+3) = 0\\<=> x+1 = 0 \ or \ x+3 = 0\\<=> x = -1 \ or \ x=-3[/tex]

so the solutions are

(-3,-6*-3=18) that we can write (-3,18)

and

(-1,-6*-1=6) that we can write (-1,6)

Answer:

-10

Step-by-step explanation:

[tex]-\dfrac{3}{5}x=6 \\\\\\x=\dfrac{6}{-\dfrac{3}{5}} \\\\\\x=6\times -\dfrac{5}{3} \\\\\\x=-10[/tex]

Hope this helps!

Answer:

x = -10

Step-by-step explanation:

So first and easily we have to multiply to --> -3/5x = 6

After that you just do the regular formula -->

Factor divided by the x

6 / (-3/5) = -10

-10

Hope this helps

Answer:

Only the question 2 is a statistical question.

Step-by-step explanation:

Questions

2. How much time do the students in my school spend on the Internet each  night?

3. What is the height of the tallest waterslide at Wild Rides Water Park?

4. What are the cabin rental prices for each of the state parks in Kentucky?

The question 2 is a statistical question.

Is the only question that can be answered with a parameter of a population (mean number of hours spent on the internet by the students).

The other two ask for individual values: the height of the tallest waterslide at Wild Rides Water Park, and the cabin rental prices for each of the state parks in Kentucky. This need specific values that are not statistical, but deterministic.

Answer:

Heun's method is also known by its other name called Modified Euler methods. This method is used in computational or mathematical science.

Step-by-step explanation:

Euler method is the method that is also pronounced in two similar stages such as Runge- Kutta methods. This method has been named after Dr. Heun.

This method is used for the solution of ordinary differential equations with its given values. There is some method to calculate this method. The improved Runge Kutta methods are also called the Butcher tableau method, the other methods are also called the Ralston methods.

Answer:

Step-by-step explanation:

The answer is 54.5 on edg

For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.

[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]

Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.

The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.

Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,

[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]

Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.

For the second part, we need to find the value of x. Thus solve the above equation further as,

[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]

Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

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Answer:

[tex]\pi =\frac{C}{d}[/tex]

Step-by-step explanation:

[tex]C=\pi d[/tex]

[tex]\pi =\frac{C}{d}[/tex]

Answer:

I'm not 100%sure but i'm think that it is c

Step-by-step explanation:

Hope this helps! May have gotten it wrong really sorry if I did

Answer:

4 C, 5 C

Step-by-step explanation:

4) Sum of all candies = 14

Total number of cherry candies = 5

probability of not getting a cherry candy = 14-5 / 14 = 9/14

5) Number of supporters for Lyshon = 14

Total number of supporters = 100

Probability that a student chosen at random will vote vote for lyshon =

14/100 = 7/50

The correct answer is B. 24

Explanation:

If you consider the shaded part of the rectangle is a triangle the best way to calculate the area of this is by calculating the total area or space occupied by this triangle. This can be done if you multiply the base by the height and divide the result in 2 or b x h / 2.

6 squares (base) x 8 squares (height) = 48 / 2 = 24 squares

Also, the shaded area is approximately the half area of all the rectangle, in this case, you can calculate the area of the rectangle by multiplying side x side or length by width. This means 6 squares x 8 squares = 48 squares (total area), which divided by 2 (shaded area) is also equal to 24.

Answer:

B, 24.

Step-by-step explanation:

I solved it with my teacher

Answer:

s+(2s+3)+12

Step-by-step explanation:

Answer:

  4 hours

Step-by-step explanation:

For three visits, the electrician earned $40 × 3 = $120 in "per-visit" charges. For working x hours, he earned 20x in "per-hour" charges. The total of these came to 50x:

  120 +20x = 50x

  120 = 30x . . . . . . . . subtract 20x

  4 = x . . . . . . . . . . . . . divide by 30

The electrician worked 4 hours that day.

Answer:

X

Step-by-step explanation:

X and Y make up a graph

Answer:

[tex](a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)[/tex]

Step-by-step explanation:

[tex]6(1)-2=4[/tex]

[tex]6(2)-2=10[/tex]

[tex]5 \times 3^{(3)-1}=45[/tex]

[tex]5 \times 3^{(4)-1}=135[/tex]

[tex]5(-1^{(5)}+3)=10[/tex]

[tex]5(-1^{(6)}+3)=20[/tex]

a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)

b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹

c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is  an = 10 + 10 * ((n + 1) % 2)

(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.

(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.

(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.

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Answer:

x < 6

Step-by-step explanation:

5x < 21 +9

5x < 30

x < 30/5

x < 6

so the value of x is 5,4,3,2,1, 0, -1, ....

Answer: x<6

Step-by-step explanation:

For this problem, we approach it as if it had an equal sign instead of an inequality.

5x-9<21      [add 9 on both sides]

5x<30         [divide 5 on both sides]

x<6

Step-by-step explanation:

I don't know if the first set of numbers is all in one set, but I'll do my best to give you an answer.

Really all you need to do is use PEMDAS for the first question.

(Parentheses, exponents, multiply, divide, add, subtract. In that order)

[tex]1 2 + 8 \div (9 - 5) \\ 12 + 8 \div 4 \\ 12 + 2 \\ 14[/tex]

Then to simplify that fraction next to it, notice that 0.018 is 3x 0.06.

that's a 3:1 ratio, so it ends up simplifying to this:

[tex] \frac{3}{1} [/tex]

Lastly, to solve the division of that fraction. If you divide by a fraction, you multiply whatever it's dividing by its inverse.

So...

[tex] \frac{5}{7} \div \frac{2}{5} \\ \frac{5}{7} \times \frac{5}{2} \\ \frac{25}{14} [/tex]

Answer: 72.

Step-by-step explanation:

You can solve this by representing the number in an equation that models the problem given. I will use the variable x to represent the number:

[tex]x + \frac{1}{3}x = 96[/tex]

In the equation, I listed the number and added one-third of the same number to it to equal 96.

Now, solve:

[tex]\frac{4}{3}x = 96\\ \\x = 96 / \frac{3}{4} \\\\x = 96 * \frac{3}{4} \\\\x = 72[/tex]

The number is 72.

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1100

A = 1900

n = 4 because it was compounded 3 times in a year and n = 12/3 = 4

t = 10 years

Therefore,.

1900 = 1100(1 + r/4)^4 × 10

1900/1100 = (1+ r/4)^40

1.73 = (1+ r/4)^40

Taking log to base 10 of both sides, it becomes

Log 1.73 = 40log(1 + 0.25r)

0.238 = 40log(1 + 0.25r)

Log(1 + 0.25r) = 0.238/40 = 0.00595

Take exponent of both sides, it becomes

10^log(1 + 0.25r) = 10^0.00595

1 + 0.25r = 1.0138

0.25r = 1.0138 - 1 = 0.0138

r = 0.0138/0.25

r = 0.0552

The The required annual interest rate is

0.0552 × 100 = 5.5%

Corrected Question

A cylinder with a base diameter of x units has a volume of  [tex]\pi x^3[/tex] cubic units

Which statements about the cylinder are true? Check all that apply.

Answer:

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]

Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]

Volume =Base Area X Height

[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]

Therefore:

Answer:

2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 185

Standard deviation = 26

The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.

What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages?

133 = 185 - 2*26

So 133 is two standard deviations below the mean.

By the Empirical Rule, of the 50% of the measures below the mean, 95% are within 2 standard deviations of the mean, that is, above 133 and below 185. The other 5% is below 133

p = 0.05*0.5 = 0.025

2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages

Answer:

Step-by-step explanation:

The monthly interest rate is ...

  [tex]\dfrac{8\%}{12}=0.00708\overline{3}[/tex]

a) The monthly payment is given by the amortization formula:

  A = Pr/(1 -(1+r)^-n)

where r is the monthly interest rate on a loan of amount P for n months.

  A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95

The monthly payment is $1214.95.

__

b) The amount to interest is the product of the remaining principal and the monthly interest rate.

 first month's interest = $140,000·0.0070833 = $991.67

__

c) The balance after the first payment is ...

  new balance = $140,000 +991.67 -1214.95 = $139,776.72

__

d) The amount to interest for the second payment is computed the same way:

  second month's interest = $139,776.72·0.00708333 = $990.09

__

e) The balance after the second payment is computed the same way:

  new balance = $139,776.72 +990.09 -1214.95 = $139,551.86

Answer:

y = (-1/3)x + 2

Step-by-step explanation:

Equation of line in slope-intercept form is given by

y = mx +c

where m is the slope of line

c is y intercept

Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)

_________________________________________________

let the equation of required line be y = mx +c

Since points given are  (3,1) and (-6,4)

Then, its slope is

m = 4-1/-6-3 = 3/-9 = -1/3

Thus, slope of line is m = -1/3

lets use m = -1/3 in place of m in equation y = mx +c

y = (-1/3)x + c

Since points   (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation.

hence lets plug 3 in place of x and 1 in place of y

1 =  (-1/3)3 + c

=> 1 = -1 + c

=> c = 1 +1 = 2

Thus, intercept is 2.

Thus, Equation of line in slope-intercept form is y = (-1/3)x + 2.

Answer:

Step-by-step explanation:

Let P be the population of the community

So the population of a community increase at a rate proportional to the number of people present at a time

That is

[tex]\frac{dp}{dt} \propto p\\\\\frac{dp}{dt} =kp\\\\ [k \texttt {is constant}]\\\\\frac{dp}{dt} -kp =0[/tex]

Solve this equation we get

[tex]p(t)=p_0e^{kt}---(1)[/tex]

where p is the present population

p₀ is the initial population

If the  initial population as doubled in 5 years

that is time t = 5 years

We get

[tex]2p_o=p_oe^{5k}\\\\e^{5k}=2[/tex]

Apply In on both side to get

[tex]Ine^{5k}=In2\\\\5k=In2\\\\k=\frac{In2}{5} \\\\\therefore k=\frac{In2}{5}[/tex]

Substitute [tex]k=\frac{In2}{5}[/tex]  in [tex]p(t)=p_oe^{kt}[/tex] to get

[tex]\large \boxed {p(t)=p_oe^{\frac{In2}{5}t }}[/tex]

Given that population of a community is 9000 at 3 years

substitute t = 3 in [tex]{p(t)=p_oe^{\frac{In2}{5}t }}[/tex]

[tex]p(3)=p_oe^{3 (\frac{In2}{5}) }\\\\9000=p_oe^{3 (\frac{In2}{5}) }\\\\p_o=\frac{9000}{e^{3(\frac{In2}{5} )}} \\\\=5937.8[/tex]

Answer:

  37

Step-by-step explanation:

I find 37 numbers in that range:

  {0, 1/16, 1/8, 1/5, 1/3, 1/2, 3/4, 4/5, 1, 5/4, 4/3, 2, 3, 7/2, 15/4, 4, 17/4, 9/2, 5, 6, 7, 8, 9, 12, 15, 16, 17, 20, 24, 28, 32, 36, 48, 60, 64, 68, 80}

For these numbers we have used only the indicated operations. No minus signs were used.

_____

Additional comment

Of the 320 ways the numbers can be combined, 15 result in division by zero. Many other results are outside the 0-99 range of interest. In total, there are 56 unique rational results.

Answer:

-4 · [tex]4^{7}[/tex]

Step-by-step explanation:

Answer:

8000 cubic centimeters

Step-by-step explanation:

The surface area of a cube is 6 times the square of the side length. If we call the side length of the cube s:

[tex]6s^2=2400 \\\\s^2=400 \\\\s=20[/tex]

Since the volume of a cube is the side length cubed, the volume of this is [tex]20^3=8000\text{ cm}^3[/tex].

Hope this helps!

Answer:

A. Yes. Each subject is randomly assigned to a treatment

Step-by-step explanation:

In an experimental study design, subjects are usually grouped into one or more groups in a random manner or by chance, in order to study and ascertain the effect of a treatment.

In the study cited in the question above, students were grouped by chance it randomly into a treatment group or the other. This is typical of an experimental study where subjects are usually categorised and placed randomly in control and treatment groups.