Which expression is equivalent to 15 Q exponent two

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \:x = 2i \)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad\displaystyle \tt \rightarrow \: 3 {x}^{2} + 12 = 0\)

\(\qquad\displaystyle \tt \rightarrow \: 3{x}^{2} = - 12\)

\(\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - \frac{12}{3} \)

\(\qquad\displaystyle \tt \rightarrow \: x {}^{2} = - 4 \)

\(\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 4} \)

\(\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ (- 1)(4)} \)

\(\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 1} \sdot \sqrt{4} \)

\(\qquad\displaystyle \tt \rightarrow \: x = i \sdot2\)

\(\qquad\displaystyle \tt \rightarrow \: x = 2i\)

[ i represents iota, i² = -1, (complex number) ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

\(x=2i\)

Step-by-step explanation:

Given equation:

\(3x^2+12=0\)

Factor 3 from the left side of the equation:

\(\implies 3(x^2+4)=0\)

Divide both sides of the equation by 3:

\(\implies\dfrac{3(x^2+4)}{3}=\dfrac{0}{3}\)

\(\implies x^2+4=0\)

Subtract 4 from both sides:

\(\implies x^2+4-4=0-4\)

\(\implies x^2=-4\)

Square root both sides:

\(\implies \sqrt{x^2}=\sqrt{-4}\)

\(\implies x^2=\sqrt{-4}\)

Rewrite -4 as 2² · -1:

\(\implies x=\sqrt{2^2 \cdot-1}\)

\(\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:\)

\(\implies x=\sqrt{2^2}\sqrt{-1}\)

\(\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:\)

\(\implies x=2\sqrt{-1}\)

\(\textsf{Since $\sqrt{-1}=i$}\)

\(\implies x=2i\)

Imaginary numbers

Since there is no real number that squares to produce -1, the number \(\sqrt{-1}\) is called an imaginary number, and is represented using the letter i.

An imaginary number is written in the form \(bi\), where \(b \in \mathbb{R}\).

Answer:

I'm pretty sure the answer to the 1st question is 2.46 and the answer to the 2nd question is just 15. (I'm sorry if I'm wrong!)

Answer: v = 6.4

Step-by-step explanation:

-22.3 + 6v = 16.1

+22.3 to each side

6v = 38.4

divide each side by 4

v = 6.4

Answer:

\(\huge\boxed{\sf v = 6.4}\)

Step-by-step explanation:

\(\sf -22.3 +6v = 16.1\\\\Adding\ 22.3\ to\ both\ sides\\\\6v = 16.1+22.3\\\\6v = 38.4\\\\Dividing \ both \ sides \ by \ 6\\\\v = 38.4 / 6\\\\v = 6.4\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

B: 9 outcomes

Step-by-step explanation:

you have 3 possibilites in the left pocket, and 3 in the right. Multiply the number of possibilites in each pocket to find how many total possibilites there are.

Answer:

$1.00

hopefuly this helped if not let me know!

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

Explanation:

The team won 16 games and lost 11 so far. At this point in the season, they played 16+11 = 27 games total. Their win rate is 16/27.

Set this equal to x/162 which is the win rate for winning x games out of 162 played over the entire season.

Solve for x.

x/162 = 16/27

27x = 162*16 ... cross multiplication

27x = 2592

x = 2592/27

x = 96

The team would win 96 games if it kept the same winning rate going.

Notice that 16/27 = 0.5926 = 59.26% and how 96/162 = 0.5926 = 59.26% as well (both are approximate). This helps confirm we have the correct answer.

-------------------------

Here's another slightly longer way to solve. If you prefer the first method above, then ignore this section.

w = number of games won over the entire 162 game season

162-w = number of games lost over the entire season

w/(162-w) = win to loss ratio

16/11 = win to loss ratio after winning 16 games and losing 11

Setting those last two expressions equal to each other and solving for w gets us...

w/(162-w) = 16/11

11w = 16(162-w)

11w = 2592-16w

11w+16w = 2592

27w = 2592 ... this hopefully looks a bit familiar from before

w = 2592/27

w = 96 games won

The value of (-1678 / 345) + 64 will be -60.86.

In this situation, it's important to use PEDMAS. This implies that the parentheses will be solved first.

The value of (-1678 / 345) +64 is illustrated thus:

= (-1678 / 345) + 64

= -4.86 + 64

= -60.86

In this case, the concept was to solve the numbers in the parentheses before addition

Learn more about numbers on:

brainly.com/question/24644930

#SPJ2

Answer:

C- Every term in pattern B is 5 times the corresponding term in pattern A.

Step-by-step explanation:

First, to see the pattern you should divide the terms of A with the corresponding term in B:

In the options, there is a choice that has the number 1/5, but... Read carefully, it says that EVERY TERM OF B IS 1/5 TIMES THE IT'S THE CORRESPONDING TERM IN A.

The one that we found as 1/5 is the opposite, every term of A is 1/5 times the corresponding term in B.

To find what is the true statement, there are different ways to follow, but the simplest could be dividing the B terms into their corresponding A term:

The correct answer will be that every term in pattern B is 5 times the corresponding term in pattern A.

Hope it helps!!

Answer:

$1.25

Step-by-step explanation:

10-2.50=7.5

7.5/6=1.25

hope this helps :3

Answer: $1.25

Step-by-step explanation:

10-total

(1 notebook)-2.50, 6 pens

10-2.50=7.50

7.50/6(pens)=1.25

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

To know more about Maclaurin series:

https://brainly.com/question/31745715

#SPJ4

If twice the sum of the number of marbles in a bag and 2 is 14 more than the number of marbles in the bag then there are 10  marbles.

we can use algebraic equations to solve problems like these by assigning a variable to represent the unknown quantity and setting up an equation based on the given information. We then simplify the equation and isolate the variable to find the solution.

To solve this problem, we can use algebraic equations. Let's start by assigning a variable to represent the number of marbles in the bag, say "x".

According to the problem, twice the sum of the number of marbles in the bag and 2 is 14 more than the number of marbles in the bag. This can be written as:

2(x + 2) = x + 14

We can simplify this equation by distributing the 2 on the left side, which gives us:

2x + 4 = x + 14

Next, we can isolate the variable on one side by subtracting x and 4 from both sides, which gives us:

x = 10

Therefore, there are 10 marbles in the bag.

Let x represent the number of marbles in the bag. According to the problem, twice the sum of the number of marbles and 2 is equal to the number of marbles plus 14. We can write this as an equation: 2(x + 2) = x + 14. To solve for x, first distribute the 2: 2x + 4 = x + 14. Then, subtract x from both sides: x + 4 = 14. Finally, subtract 4 from both sides: x = 10. Therefore, there are 10 marbles in the bag.

Visit here to learn more about  equation : https://brainly.com/question/29657983
#SPJ11

Step-by-step explanation:

(-3,5) =(x1,y1)

then

slope (M) =

\((y2 - y1 ) \div x2 - x1)\)

={(-8)-5 }÷{(-3)-(-3)}

= -13÷ 0

=0

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

Answer: C) 13

Step-by-step explanation:

The applicable law here is the “Pythagorean Theorem”, which is simply given as: c^2= a^2+b^2

In this case “c” represents the hypotenuse, while “a” and “b” represents the two legs respectively.

This then translates to:

16^2= 9^2+b^2

256= 81+b^2

256-81=b^2

175= b^2

b = √175

b = 13.22

To the nearest whole number:

b = 13

a. Yes, the distribution of the number of cases of type II diabetes in the United States can be approximated by a Poisson distribution since it is a rare event and the number of cases is independent of each other.
b. The probability is calculated as P(X ≤ 10) = e^(-12) * 12^10 / 10!, which is approximately 0.112.
c. we can subtract the probability of X ≤ 10 from the probability of X ≤ 15. The probability is calculated as P(10 < X < 15) = P(X ≤ 15) - P(X ≤ 10) = e^(-12) * (12^11 / 11! + 12^12 / 12! + 12^13 / 13! + 12^14 / 14!) ≈ 0.215.
d. The probability of observing 19 or more cases can be calculated using the Poisson distribution formula, P(X ≥ 19) = 1 - P(X ≤ 18) = 1 - e^(-12) * (12^0 / 0! + 12^1 / 1! + ... + 12^18 / 18!) ≈ 0.0002, which is a very small probability.

a. The distribution of the number of cases of type II diabetes in the United States can be approximated by a Poisson distribution if the cases are rare, random, and independent events. Given the incidence rate of 12 per 100,000, it can be considered a rare event, and if we assume the cases are independent and random, we can approximate the distribution using a Poisson distribution. The mean (λ) is equal to the incidence rate, which is 12 cases per 100,000.

b. To find the probability that the number of cases of type II diabetes is less than or equal to 10 per 100,000, we need to calculate the cumulative probability for the Poisson distribution with λ = 12 and k = 10. This can be found using the formula:

P(X ≤ 10) = Σ [e^(-λ) * (λ^k) / k!] for k = 0 to 10

c. To find the probability that the number of cases of type II diabetes is greater than 10 but less than 15 per 100,000, we need to calculate the probability for the Poisson distribution with λ = 12 and k = 11, 12, 13, and 14. This can be found using the formula:

P(10 < X < 15) = Σ [e^(-λ) * (λ^k) / k!] for k = 11 to 14

d. To determine if we would expect to observe 19 or more cases of type II diabetes per 100,000 in the United States, we can find the probability of observing 19 or more cases using the Poisson distribution with λ = 12. This can be found using the formula:

P(X ≥ 19) = 1 - P(X ≤ 18) = 1 - Σ [e^(-λ) * (λ^k) / k!] for k = 0 to 18

If the probability is low (typically less than 0.05), then it would be unlikely to observe 19 or more cases of type II diabetes per 100,000 in the United States.

Learn more about Poisson distribution:

brainly.com/question/17280826

SPJ11

The headline C is the most acceptable since Lack of Health Insurance Increases Death Risk Lack of Health Insurance May Contribute to 45,000 U.S. Deaths Each Year (WebMD), It effectively conveys both the societal norm and the probability-based scientific method of reporting findings.

As per the details provided in the question are as bellow,

The report helped us realize that two factors—a lack of insurance and a greater rate of mortality among the population—are associated in this situation.

It went on to state the likelihood that there might be a correlation between these two.

The headline will alert the researcher to a study error, as well as allay public fears and encourage people to read the paper so they can learn more about the research.

For such more question on probability

https://brainly.com/question/24756209

#SPJ4

Note: The correct question would be as bellow,

A recent National Health and Nutrition Examination Survey (NHANES) study compared death rates for people with health insurance and people without health insurance. This study included anyone who completed the survey between 1986 and 1994. The study tracked these people through 2000. The study attempted to control for factors such as education, income, smoking, drinking, and obesity. The American Journal of Public Health published an article about this NHANES study. The following headlines appeared in the news based on this article. Which headline is an appropriate summary of this study? a. Lack of insurance to blame for almost 45,000 deaths (ABC News)

b. 45,000 American deaths associated with lack of insurance (CNN)

c. No Health Insurance, Higher Death Risk: 45,000 U.S. Deaths Per Year May Be Linked to Lack of Health Insurance (WebMD)

Answer:

3

Step-by-step explanation:

2r=d

d/2=r

sin (60° - 20)°

sin (40°)

Note that:

sin(A - B) = sinAcosB - cosAsinB

The given trigonometric expression is:

sin 60° cos 20° - cos 60° sin 20°

Applying the addition rule of trigonometry written above:

sin 60° cos 20° - cos 60° sin 20° = sin(60° - 20°)

This can also be written as sin (40°)

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

To learn more about Probability visit :

brainly.com/question/13490624

#SPJ4

Answer:

The answer is 7.96×10⁷ .

Step-by-step explanation:

As the decimal moves to the left , you have to add one more power to the base 10 :

e.g

7 960 000.0 = 7 960 000×10¹

796 000.00 = 796 000×10²

79 600.000 = 79 600×10³

7 960.0000 = 7 960×10⁴

796.00000 = 796×10⁵

79.600000 = 79.6×10⁶

7.9600000 = 7.96×10⁷

* Take note :

\(a \times {10}^{n} \)

0 < a < 10 ('a' must be greater than 0 but smaller than 10)

Answer:

Step-by-step explanation:

Scalene (no equal side): 4th triangle

Isosceles (two equal sides): 1st, 2nd, and 4th triangle

Equilateral (all equal sides): 3rd triangle

Hope this helps!

Answer: $29.10

Step-by-step explanation:

1. Make a table, like the one shown in the image. You will need the item, its price, and how many are being bought.

2. Multiply the price and quantity of each item that is being bought.

3. Add all of the products together. This should get you the final price.

My steps are in the image. Hope this helps!

Answer:

c= 6 1/3

Step-by-step explanation:

Answer:

Hello! :) I hope I’m correct!!

Step-by-step explanation:

I think the answer should be -19/3

The steps for this problem:

~You have to add/subtract the numbers (-13+7=-6)

~now, divide both sides by -9

~simplify...

~C + 7 = 2/3

~Subtract 7 from both sides.

~c + 7 - 7 = 2/3 - 7

~Simplify...

~Answer; -19/3

This is a SIMPLE way to do this^^

Hope this helps! Have a great day!! If you have any questions about these steps, feel free to ask! ٩(^ᴗ^)۶

****~by, BrainlyAnime~ ****

The population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

All these elements are taken into account when formulating the population growth formula.

r = [(b + i) - (d + e)]/1000

Put the values in the formula.

r =  [(2,000 + 100) - (500 + 200)]/1000

r = 2100 - 700/ 1000

r = 1.4

Thus, the population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

To know more about the population growth rate, here

https://brainly.com/question/14174002

#SPJ4

If the true means of the k populations are equal, then MSTR/MSE should be close to 1.00. This can be answered by the concept from ANOVA.

The ratio MSTR/MSE is used in analysis of variance (ANOVA) to determine the variation between means of different populations (MSTR) compared to the variation within each population (MSE).

If the true means of the k populations are equal, then MSTR, which represents the variation between means, should be small or close to zero, because there is little difference between the means. On the other hand, MSE, which represents the variation within each population, would still capture the random variation within each population.

Therefore, the ratio MSTR/MSE would be close to 1.00, indicating that the variation between means is similar to the variation within each population

To learn more about ANOVA here:

brainly.com/question/31239155#

#SPJ11

Answer:

a

Step-by-step explanation:

Answer:

A

I know this is a year later lol

Answer:

y

\( y2 - 2y - 3\)

\((y - 1)(y + 3) \)

\((3y - 1)(3y + 3)\)

Step-by-step explanation:

you multiple the 3 with the 1

then factor

then divide by 3 again but the denominator goes in front of the y.

Answer:

Do you have a graph so that I can answer ?