Scientific Notation-Tutorial
The average diameter of an atom's nucleus is
about 1x 10- meter. The diameter of a proton is
about 1x 10-15 meter.
The diameter of a proton times 10 raised to what power is equivalent to
the diameter of a nucleus?
Proton
10-15 x 10
?
DONE
10-14
Nucleus

The values on the interval [0, 2π) where the two fishes will be at the same height above the water is

To find the values on the interval [0, 2π) where the two fish will be at the same height above the water, we need to find the values of x that satisfy the equation f(x) = g(x).

Given:

f(x) = 2sin(2x - 1)

g(x) = cos(x)

We can solve this by plotting the two equations and the point of intersections denotes the points of equal height

Therefore, the values from the graph, on the interval [0, 2π) where the two fish will be at the same height above the water are:

x = 0.581, 1.194, and π.

The correct answer choice is d. {π}.

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Answer:

Well if it is rounding to the nearest 10 it is 10

but if you meant round to the nearest 10th then it is 10.7

Step-by-step explanation:

For 10 you look at the ones place if it is 0-4 round down if it is 5-9 round up so for this number round down which is 10

FOr 10.7 look at the hundredths place if it is 0-4 round down if it is 5-9 round up so for this number round down which is 10.7

Hope this helps!

The evaluation of the equation to find the value of n in the rational function \(\frac{1}{n^2} + \frac{1}{n} = \frac{1}{2\cdot n^2}\) is; n = -1/2

A rational function is a function that contains rational fractions, such that the dividend and the divisor are polynomial expressions.

2) The specified rational equation or function can be presented as follows;

The above equation consists of rational expressions. The expressions can be resolved by collecting like terms as follows;

The like terms are terms that can be resolved by simple addition or subtraction.

1/n = 1/(2·n²) - 1/(n²) = (1 - 2)/(2·n²) = -1/(2·n²)

1/n = -1/(2·n²)

Multiplying both sides by n, we get;

(1/n) × n = (-1/(2·n²)) × n

(1/n) × n = 1 = (-1/(2·n))

1 = (-1/(2·n))

Multiplying both sides by n, we get;

1 × n = (-1/(2·n)) × n

n = -1/2

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Answer:

VT = 50√3 , PT = 50

Step-by-step explanation:

Given

PV = 100

With reference angle 60°

hypotenuse (h) = 100

perpendicular (p) = ?

Now

Sin 60° = p/h

√3 / 2 = p / 100

p = √3 * 100 / 2

p = 50√3

Also

With reference angle 30°

hypotenuse (h) = 100

perpendicular (p) = ?

sin 30° = p/h

1/2 = p / 100

p = 100 / 2

p = 50

Hope it will help :)

Answer:

The answer is "\(f(x) = 3(1.05)x + 2\)".

Step-by-step explanation:

She starts off with 3 hours with pop music.

Next month, she will have 3 hours she has had and + 3*0.05.

3hrs + 3*0.05hrs = 3*1.05 hrs

We add 2 hours of classical music to the 3 * 1.05 hours to achieve 3 * (1.05) hours + 2 hours of classical music.

Answer: f(x):2(0.05)^x+3

Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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Answer:

5.4 ++ 18 that is so far fo ,e fhd

Step-by-step explanation:

Answer: a=-4

Step-by-step explanation:

The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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Answer:

x = 30

2x =60

Step-by-step explanation:

the angle is a right angle- so that means it’s a 90 degree angle

so let’s set up an equation..

We get 90 degrees when we add 2x Plus x

So 2x + x = 90

then, 3x = 90

x= 30

you Can check your Answer by:

Do 2 times 30 = 60

and then 60+ 30

you will Get 90

The expected amount of money in the end for reward rule 1 is F, and the expected amount of money in the end for reward rule 2 is 2F * (1 - \(0.8^{20\)).

Reward rule 1

The expected amount of money in the end is:

E = 2F * Pr(T) + 0 * Pr(H) = 2F * 0.5 = F

This is because the probability of the opponent flipping tails is 0.5, and if they flip tails, you double your money. The probability of the opponent flipping heads is also 0.5, and if they flip heads, they take all your money. So, the expected amount of money in the end is just the amount of money you start with, multiplied by the probability that the opponent flips tails.

Reward rule 2

The expected amount of money in the end is:

E = 2F * 0.2 + 2 * F * 0.8 * 0.2 + 4 * F * \(0.8^2\) * 0.2 + ... + \(2^{20\) F * \(0.8^{20}\) * 0.2

This is because the probability of the opponent flipping tails for the first time in their first attempt is 0.2. The probability of the opponent flipping tails for the first time in their second attempt is 0.8 * 0.2, and so on. So, the expected amount of money in the end is the sum of the amount of money you get for each possible outcome, weighted by the probability of that outcome.

The sum can be simplified as follows:

E = 2F * (1 - \(0.8^{20\))

This is because the probability of the opponent never flipping tails is \(0.8^{20\), so the probability of them flipping tails at least once is 1 - \(0.8^{20\). So, the expected amount of money in the end is just the amount of money you start with, multiplied by the probability that the opponent flips tails at least once.

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The most likely culprit is whoever was responsible for filing the paper work. They likely failed to properly organize and file the documents.

The most likely culprit for the paper work not being in order is whoever was responsible for filing it. To determine who this is, it is helpful to look at who had access to the documents. This could include the person who initially created the paperwork, anyone who has handled the paperwork since then, and anyone with access to the file where the paperwork is stored. Once the list of possible suspects has been narrowed down, it is important to check if any of them have a history of filing incorrectly or not following proper procedure. It is also helpful to look at any recent changes to the filing system or personnel which may have caused an inadvertent disruption in the filing process. Taking all of these factors into account can help to identify the most likely culprit.

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Answer:

the statement will be true

The probability that the sample proportion of households spending more than $125 a week on groceries is less than 0.3 is approximately 0.057, or 5.7%.

To solve this problem, we can use the properties of the normal distribution and the Central Limit Theorem. Since the sample size is large (209 households) and the sample is randomly selected, we can assume that the sampling distribution of the sample proportion will be approximately normal.

First, we calculate the standard deviation of the sampling distribution using the formula: standard deviation = sqrt((p * (1 - p)) / n), where p is the population proportion and n is the sample size. In this case, p = 0.29 and n = 209. Plugging in these values, we find that the standard deviation is approximately 0.031.

Next, we need to find the z-score corresponding to a sample proportion of 0.3. The z-score formula is given by: z = (x - μ) / σ, where x is the sample proportion, μ is the population proportion, and σ is the standard deviation of the sampling distribution. Plugging in the values, we have z = (0.3 - 0.29) / 0.031, which results in a z-score of approximately 0.323.

Finally, we can find the probability using the z-table or a statistical calculator. Looking up the z-score of 0.323 in the table, we find that the probability is approximately 0.573. However, since we are interested in the probability that the sample proportion is less than 0.3, we need to subtract this probability from 0.5 (as the normal distribution is symmetric). Therefore, the probability that the sample proportion is less than 0.3 is approximately 0.5 - 0.573 = 0.057, or 5.7%.

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We can fill in the boxes to make each equation complete as follows:

1. x³x⁹ = x¹²

2. x⁷/x³ = x⁴

3. 1/x⁻⁵ = x⁵

4. (7b³c⁵)³ = 343b⁹c¹⁵

To solve the exponents as provided above, the rules have to be factored in. One of the rules is that when multiplying exponents of the same base, we simply add their powers together. So, we have the powers of 3 and 9 for the first expression and they add up to 12.

1. x³x⁹ = x³ ⁺ ⁹ = x¹²

For the second expression, the rule of exponents says that when dividing, we will subtract the powers. This gives us x⁴ for the second expression.

2. x⁷/x³ = x⁷ ⁻ ³ = x⁴

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The ride that has the greatest elevation based on the information is B. Lightning bolt : 327 feet.

The term elevation is typically used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.

Elevations show how your house will appear from various perspectives. Regarding these particular angles, there are many elevation kinds. Some varieties include split elevations, rear elevations, side elevations, and front elevations.

From the information, it was stated that the lightning bolt starts at an elevation of 15ft from the platform and speeds the passengers to an elevation of 327 ft.

It should be noted that the information is to simply find the elevation that is the greatest.

Based on the figures given, the appropriate elevation will be 327 feet.

Therefore, the correct option is B.

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Answer:

In 25 minutes, the monthly phone charges of both companies will be the same.

Step-by-step explanation:

If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:

Phoenix equation:  C = 0.5m + 30

Nuphone equation: C - 0.10m + 40

Now, we can set the two equations equal to each other.  Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:

0.5m + 30 = 0.10m + 40

Step 1:  Subtract 30 from both sides:

(0.5m + 30 = 0.10m + 40) - 30

0.5m = 0.10m + 10

Step 2:  Subtract 0.10m from both sides:

(0.5m = 0.10m + 10) - 0.10m

0.4m = 10

Step 3:  Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)

(0.4m = 10) / 0.4

m = 25

Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.

Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:

Checking m = 25 with Phoenix equation:

C = 0.5(25) + 30

C = 12.5 + 30

C = 42.5

Checking m = 25 with Nuphone equation:

C = 0.10(25) + 40

C = 2.5 + 40

C = 42.5

Thus, m = 25 is the correct answer.

Answer:

50

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(1) = 10(5)^1 = 10(5) = 50

The balance sheet that correctly represents the engineer's income, expenses and balance is illustrated below.

We should know that a balance sheet is a summary of assets and liabilities and income and expenses of a  legal person. We are told that the balance sheet shows a bi-weekly net pay.

This implies that a month has two bi-weeks, therefore every income and expense is multiplied by 2 to get the following figures.

Income                                             Amount

Bi-weekly income                          $2,175.25

Total Monthly Income                   $4,350.50

Expenses                 Percent                              Amount

Housing                        35%                                $1,522.68

Food/Household          10%                               $435.05

Savings                         10%                                $435.05

Transportation              15%                                $652.58

Debt                              5%                                   $217.53

Entertainment               6%                                   $261.03

Medical/Personal Care 5%                                  $217.53

Giving                             5%                                 $217.53

Clothing                         4%                                  $174.02

Miscellaneous               5%                                 $217.53

                                                                          $4,350.50

Balance

Income $4,350.50

Expenses $4,350.50

Balance $0

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To evaluate the given prefix expression, let's break it down step by step:

1. − ↑⏐ 3 2 ↑⏐ 2 3 / 6 − 4 2

2. Evaluate the sub-expression ↑⏐ 3 2. This represents the exponentiation of 3 to the power of 2:

  ↑⏐ 3 2 = 3^2 = 9

3. Evaluate the sub-expression ↑⏐ 2 3. This represents the exponentiation of 2 to the power of 3:

  ↑⏐ 2 3 = 2^3 = 8

4. Evaluate the sub-expression / 6 − 4 2. This represents the division of 6 by the difference of 4 and 2:

  / 6 − 4 2 = 6 / (4 - 2) = 6 / 2 = 3

5. Substitute the evaluated sub-expressions back into the original expression:

  − 9 8 3

6. Finally, evaluate the remaining sub-expression − 9 8. This represents the subtraction of 8 from 9:

  − 9 8 = 9 - 8 = 1

Therefore, the value of the given prefix expression is 1.

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490909/200000 is the answer

Have a great day!

Stay safe and healthy!

Happy holiday seasons!

May I please have brainliest?

Answer:

1.6i + 12 is a complex number. There is no answer since there is no question.

\(\huge \boxed{\sf 8+4\sqrt{5} }\\\\\\\sf Using\ the\ distance\ formula \\\\\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\)

\(\sf A(0,4)\ and\ B(2,0)\\\\d = \sqrt{(2 - 0)^2 + (0-4)^2}=2\sqrt{5} \\\\B(2,0)\ and\ C(2,-2)\\\\d = \sqrt{(2 - 2)^2 + (-2-0)^2}=2 \\\\C(2,-2)\ and\ D(0,-2)\\\\d = \sqrt{(0 - 2)^2 + (-2-(-2))^2}=2 \\\\D(0,-2)\ and\ E(-2,2)\\\\d = \sqrt{(-2 - 0)^2 + (2-(-2))^2}=2\sqrt{5} \\\\E(-2,2)\ and\ F(-2,4)\\\\d = \sqrt{(-2 - (-2))^2 + (4-2)^2}=2\\\\F(-2,4)\ and\ A(0,4)\\\\ d=\sqrt{(0-(-2))^2+(4-4)^2} =2\)

\(\sf Adding\ all\ the\ distances \\\\2\sqrt{5} +2+2+2\sqrt{5}+2+2 =8+4\sqrt{5} =16.94427190...\)

Answer:

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

Four of the segments are horizontal or vertical with the length of 2 units:

Two of the segments have same length (parallel segments) with 4 units vertical and 2 units horizontal difference of coordinates:

The perimeter is:

Answer: need brainliest

Step-by-step explanation:

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-\frac{5}{2}})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{\left( -\frac{5}{2} \right)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{-8+\frac{5}{2}}{3+3}\implies \cfrac{~ \frac{ -16+5}{2 } ~}{6}\implies \cfrac{~ \frac{ -11}{ 2} ~}{6} \\\\\\ \cfrac{~ \frac{ -11}{ 2} ~}{\frac{6}{1}}\implies \cfrac{ -11}{ 2}\cdot \cfrac{1}{6}\implies -\cfrac{11}{12}\)

Answer:

\(P( 2 \ green ) = \frac{4}{121}\)

Step-by-step explanation:

\(Probability \ of \ green \ i n \ the \ first \ try = \frac{2C_1}{11C_1} = \frac{2}{11}\\\\Probability \ of \green \ i n \ the \ Second \ try = \frac{2C_1}{11C_1} = \frac{2}{11}\\\\Probability \ of \ 2 \ green = \frac{2}{11} \times \frac{2}{11 } = \frac{4}{121}\)

Answer:yes

Step-by-step explanation:

Answer:

I hope it helped you☺️☺️☺️

The sequence of transformations performed by Isabella is Rotate 90° clockwise about the origin; translate 10 units down.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, Luther drew on his graph paper. After performing a series of transformations, Isabella drew. we need to find the transformations performed by Isabella,

We see, that, the sequence performed by Isabella is a rotation of 90°, from the origin, also the image is 10 units down to the original figure.

Hence, the sequence of transformations performed by Isabella is Rotate 90° clockwise about the origin; translate 10 units down.

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The complete question :-