how to solve equations containing two radicals step by step

Answer:

For me, it always helps to break down equations like this. Divide it up into two separate parts.

4^2*4^2=x

4^2=16

Replace both 4^2 with 16

16*16=256

Answer:

A.

Step-by-step explanation:

This is a geometric sequence with common ratio -12/-3 = 4  ( -48/-12  = 4 and  -192 / -48 = 4).

nth term = a1 r^(n - 1) so the 8th term

= -3 * (4)^(8 - 1)

= -49,152.

The 8th term of the geometric sequence is -768

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Formula for the n th term of a geometric sequence in the form

aₙ=a₁ rⁿ

Given sequence is   -3, -12, -48, -192, . . .

It is a geometric sequence with the ratio between consecutive terms is 4

i.e. r = 4

a₁ = -3

a₈ = -3 ×4⁸

   =-768

Thus the 8th term of this sequence is -768

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The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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For a random sample of 280 adult Internet users, with a population proportion of 35% who have purchased products or services online, the mean, variance, and standard deviation for the number of users who have made online purchases can be calculated.

Given that 35% of adult Internet users have made online purchases, we can use this proportion to estimate the mean, variance, and standard deviation for the sample of 280 users.

The mean can be calculated by multiplying the sample size (280) by the population proportion (0.35). The variance can be found by multiplying the population proportion (0.35) by the complement of the proportion (1 - 0.35) and dividing by the sample size. Finally, the standard deviation can be obtained by taking the square root of the variance.

It's important to note that these calculations assume that the sample is randomly selected and represents a simple random sample from the population of adult Internet users. Additionally, rounding the intermediate calculations to at least three decimal places ensures accuracy in the final results.

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Answer:

11,340

Step-by-step explanation:

5% = 420 420 x 7 = 2940

2940 + 8400 = 11,340

Min needs to gain 80 marks to raise her average to 75.

Average number is got from sum of all numbers divided by the number of values.

Average value is used to compare among different quantities of same terms.

given, Min receives an average score 70 from 5 math test.

let she needs to gain X in her 6th test to obtain an average of 75 from the total six test.

she gained average 70 from 5 test

if average is 75 then

75 = (X+ 70)/2

X=80

hence, in the 6th test she needs to gain 80 marks.

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Step-by-step explanation:

Dealing with a toxic friend can be difficult, and it's important to prioritize your own well-being in such situations. Here are some steps you can take to cut off a toxic friend:

Set boundaries: Communicate your boundaries clearly to your friend. Let her know that you will not tolerate arguments and that you need space.

Limit your interactions: Avoid spending time with your friend as much as possible. You can start by limiting your communication to only when necessary.

Be honest: If you decide to cut off the friendship, be honest about why. Explain how her behavior has impacted you and why you no longer want to be friends.

Seek support: It's important to have a support system when going through a difficult time. Talk to someone you trust about your decision and the reasons behind it.

Move on: Once you've made the decision to cut off the friendship, focus on moving on. Surround yourself with positive people and activities that bring you joy.

Remember, cutting off a toxic friend is not easy, but it is necessary for your own well-being. You deserve to be surrounded by people who uplift and support you.

Answer:

Step-by-step explanation:

yeah so basically

Dealing with a toxic friend can be difficult, and it's important to prioritize your own well-being in such situations. Here are some steps you can take to cut off a toxic friend:

Set boundaries: Communicate your boundaries clearly to your friend. Let her know that you will not tolerate arguments and that you need space.

Limit your interactions: Avoid spending time with your friend as much as possible. You can start by limiting your communication to only when necessary.

Be honest: If you decide to cut off the friendship, be honest about why. Explain how her behavior has impacted you and why you no longer want to be friends.

Seek support: It's important to have a support system when going through a difficult time. Talk to someone you trust about your decision and the reasons behind it.

Move on: Once you've made the decision to cut off the friendship, focus on moving on. Surround yourself with positive people and activities that bring you joy.

Remember, cutting off a toxic friend is not easy, but it is necessary for your own well-being. You deserve to be surrounded by people who uplift and support you.

In the following question, among the conditions given, the option- a,b and c stand the same ie- The level of measurement is a ratio. The statistic used for the central tendency is the mean or median, whereas d. birth, "is ordinal."

1. Body weight in pounds: The level of measurement is a ratio. The statistic used for the central tendency is mean or median, while for variability, standard deviation or variance can be used.

2. Number of cigarettes smoked in a day: The level of measurement is a ratio. The statistic used for the central tendency is mean or median, while for variability, standard deviation or variance can be used.

3. Ethnicity: The level of measurement is nominal. The statistic used for the central tendency is the mode, while for variability, there is no appropriate statistic.

4. Birth order: The level of measurement is ordinal. The statistic used for the central tendency is median or mode, while for variability, range or interquartile range can be used.

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9514 1404 393

Explanation:

RS ≅ RU . . . given

RT ≅ RT . . . reflexive property

TS ≅ TU . . . definition of midpoint

ΔRTS ≅ ΔRTU . . . SSS postulate

Answer:

3.14 cm squared

Step-by-step explanation:

First divide 2 by 2 which equals 1

Then you do pi which equals 3.14 and multiply it by 1^(2) (1 squared)

But you don't do 1 x 2 you do 1 x 1

then you get 3.14

So basically..... divide 2 by 2 then do 3.14 x 1^(2)

The company's expected net gain from this 1-year term-life insurance policy is $30.

Determine the total cost of the insurance policy:

In this case, the cost of the policy is $450.
Calculate the payout if the man dies:  

If the man dies, the insurance company will have to pay out the policy value, which is $21,000.
Determine the probability of each outcome:

The probability that the man will live for another year is given as 0.98.

Since there are only two possible outcomes (the man either lives or dies), the probability that he will die within the year is 1 - 0.98 = 0.02.

Calculate the company's expected gain/loss for each outcome:
  - If the man lives, the company's gain will be the cost of the policy ($450) since no payout is made.
  - If the man dies, the company's loss will be the policy value ($21,000) minus the cost of the policy ($450), which equals $20,550.

Find the company's expected net gain by multiplying each outcome's gain/loss by its respective probability and adding the results:
  - Expected gain if the man lives = 0.98 * $450 = $441
  - Expected loss if the man dies = 0.02 * (-$20,550) = -$411
Add the expected gain and expected loss to find the company's expected net gain: $441 + (-$411) = $30.

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Area = s × s

676 cm² = s²

s = √676

s = 26 cm

V. Cube = s × s × s

= 26 × 26 × 26

= 17,576 cm³

Thus, the answer is option (c) 97 mph.

An outlier is a value that lies significantly away from the rest of the values in the dataset. For a given dataset, we can determine outliers using z-scores.According to the problem statement, the mean speed of the fastballs thrown by major league baseball pitchers is 87 mph, and the standard deviation is 3 mph. To determine which speed is an outlier, we need to find its corresponding z-score.z = (x - μ) / σHere, x is the speed we want to test, μ is the mean speed, and σ is the standard deviation of speeds.Using the formula above, we can calculate the z-scores for each speed given in the options:a. z = (84 - 87) / 3 = -1b. z = (92 - 87) / 3 = 1.67c. z = (97 - 87) / 3 = 3.33d. z = (81 - 87) / 3 = -2Since a z-score of ±2 or higher is generally considered an outlier, the speeds of 97 mph and 81 mph are classified as outliers. Thus, the answer is option (c) 97 mph.

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Rate is the same thing as gradient so to work out the gradient you need to use the formula

change in y / change in x

Change in y = y2 - y1

Pick any two points on the graph

Change in y = 30 - 15

Change in y = 15

Change in x = x2 - x1

Change in x = 2 - 1

Change in x = 1

15/1

= 15 dollars per day.

We can double check this by seeing the increase of money per day, for example, here from day two to day three, the money needed increases by 15, so our answer is correct.

4,610 divided by 16 is 288.125

Work:

After 2 years, the population of trout in the lake will be 2000 trout.

Given:

Initial population = 100

Growth rate = 70%

Time= 2 years

After the first year:

Population after 1 year = Initial population + (70% of the initial population)

                                      = 100 + (0.7 * 100)

                                      = 100 + 70

                                      = 170 trout

After the second year:

Population after 2 years = Population after 1 year + (70% of the population after 1 year)

                                       = 170 + (0.7 * 170)

                                       = 170 + 119

                                       = 289 trout

Since the calculated population exceeds this limit, the population will be limited to the maximum capacity of 2000 trout.

Therefore, the population of trout in the lake will be 2000 trout.

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Answer:

Is it health club c for the second one?

Step-by-step explanation:

Answer:

health club c

Step-by-step explanation:

x=months

so erica: 200+75x

darrell: 350+50x

make them equal:

200+75x=350+50x

get x on one side.

125x=550

500/125=x

x=4.4

The probability that Marcus, Adam, Brittany, and Luisa are chosen in any order can be calculated using the concept of combinations, resulting in a probability of 1/495.

To determine the probability of Marcus, Adam, Brittany, and Luisa being chosen in any order, we need to consider the total number of possible outcomes and the number of favorable outcomes. The total number of ways to choose 4 students out of 12 can be calculated using the combination formula: 12C4 = 12! / (4!(12-4)!).

To find the number of favorable outcomes, we need to consider that Marcus, Adam, Brittany, and Luisa can be chosen in any order. Since there are 4 students, there are 4! = 4 * 3 * 2 * 1 = 24 possible permutations of their selection.

Thus, the probability of choosing Marcus, Adam, Brittany, and Luisa in any order is given by: 24 / (12! / (4!(12-4)!)) = 1 / 495.

Therefore, the probability that Marcus, Adam, Brittany, and Luisa are chosen in any order is 1/495. This means that out of all the possible combinations of 4 students, only one combination will include Marcus, Adam, Brittany, and Luisa in any order.

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Answer:

100

A line segment is 180 and if one side of the line is 80 then the other half has to be 100

Step-by-step explanation:

The mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

The mean of a geometric distribution is given by:

Mean = 1/p

Here, p is the probability of success on a single trial.

In this case, p = 0.80

So, the mean of the geometric distribution = 1/0.80 = 1.25

The variance of a geometric distribution is given by:

Variance =\((1-p) / p^2\)

By substituting the value of p = 0.80, we get:

Variance = \((1-0.80) / 0.80^2 = 0.20 / 0.64 = 0.3125\)

So the variance of the geometric distribution = 0.3125

Therefore, the mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

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We are asked to estimate the arc length of the curve y = x sin(x) using Simpson's Rule with n = 10. Additionally, we need to compare our estimate with the value of the integral produced by a calculator.

To estimate the arc length using Simpson's Rule, we divide the interval [0, 27] into subintervals and approximate the integral using a weighted sum of function values. With n = 10, we have 10 subintervals of equal width.

First, we calculate the width of each subinterval: h = (27 - 0) / 10 = 2.7.

Next, we evaluate the function y = x sin(x) at the endpoints and interior points of the subintervals to obtain the function values.

Using Simpson's Rule formula, the arc length is approximated as:

Arc length ≈ (h/3) * [y0 + 4y1 + 2y2 + 4y3 + 2y4 + ... + 4y9 + y10],

where y0, y1, y2, ..., y10 represent the function values at the respective points.

By performing the calculations according to the formula, we obtain the estimated value of the arc length using Simpson's Rule with n = 10.

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Answer:

6 adult tickets, 4 children tickets

Step-by-step explanation:

Let a = number of adult tickets.

Let c = number of children tickets.

Equation of numbers of tickets:

a + c = 10

Equation of cost of tickets.

8a + 2.5c = 58

Multiply both sides of the first equation by -8 and add it to the second equation.

        -8a -    8c = -80

(+)      8a + 2.5c = 58

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

                 -5.5c = -22

c = 4

a + c = 10

a + 4 = 10

a = 6

Answer: 6 adult tickets, 4 children tickets

Answer:

∠ BDC = 37°

Step-by-step explanation:

the central angle BAC is twice the angle on the circumference subtended on the same arc.

∠ BDC = \(\frac{1}{2}\) ∠ BAC = \(\frac{1}{2}\) × 74° = 37°

Answer:

A

8.5 is the answer

If you test is going on so

all the best!

"1. The end behavior of the function f(x) = -x³ + 2x³ -x+4 can be determined by looking at the highest degree term, which is 2x³. Since this term is positive and has an even degree, the end behavior of the function will be the same on both ends. As x approaches negative infinity, the function will approach negative infinity, and as x approaches positive infinity, the function will approach positive infinity. Therefore, the graph of the function will have two arms pointing upwards.

2. The function f(x) = x² -x² -x -1 can also be analyzed by looking at the highest degree term, which is x². However, since the first two terms cancel each other out, we can simplify the function to f(x) = -x -1. As x approaches negative infinity, the function will approach negative infinity, and as x approaches positive infinity, the function will approach negative infinity as well. Therefore, the graph of the function will have a single arm pointing downwards." (ChatGPT, 2023)

Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:

We had 21 dollars and we spent 5x on the notebooks, this can be express as:

Finally we know that this is equal to the six dollars we had at the end, then we have the equations:

Solving for x we have:

Therefore each notebook cost $3