Simplify 6^-7 × 6³ help

Answer:

25

Step-by-step explanation:

8x-20=180

8x=200

x=25

The most important component when reporting a numerical scientific result is the unit.

This is further explained below.

Generally, Our work in numerical and scientific computing includes the creation, analysis, and implementation of computer algorithms with the purpose of finding mathematical solutions to issues originating in engineering and the sciences.

In conclusion, When presenting a numerical result from scientific research, the unit is the single most crucial component.

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The correct Python line to return subset data for the variables "survived" and "age" from a dataframe called "titanic" is subset = titanic[['survived', 'age']].

To extract a subset of data containing only the variables "survived" and "age" from the dataframe "titanic" in Python, you can use double brackets to specify the columns of interest. The line subset = titanic[['survived', 'age']] achieves this.

Here's a breakdown of the line:  

titanic[['survived', 'age']] is used to select the columns 'survived' and 'age' from the dataframe 'titanic'. The double brackets create a new dataframe with only the specified columns.

The resulting subset dataframe is then assigned to the variable 'subset' using the assignment operator '='.

You can use 'subset' to perform further operations or analyze the data containing only the 'survived' and 'age' variables.

By executing this line of code, you will obtain a new dataframe named 'subset' that contains only the columns 'survived' and 'age' from the original 'titanic' dataframe.

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Scoring in the 60th percentile on her math exam means that the student performed better than 60% of other test takers.

Percentile is a measure that indicates the percentage of data points that are below a particular value in a given dataset. In this case, the student's score is in the 60th percentile, which means she scored better than 60% of the other test takers.

Imagine arranging all the scores of the test takers in ascending order. The 60th percentile represents the score that is greater than 60% of the scores below it and less than 40% of the scores above it. It is a way of understanding how a particular score compares to the rest of the scores in the group.

However, it also means that 40% of the test takers scored higher than her.  If the student scored in the 60th percentile, it indicates that she performed relatively well compared to the majority of the test takers.

Percentiles provide a useful way to interpret individual scores in relation to the entire distribution of scores in a dataset.

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The purpose of random sampling is to select a set of items from a population such that the sample description accurately represents the population.

Random sampling is a type of sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected. Data is then collected from as high a percentage of this random subset as possible. Simple random sampling selects a smaller group (sample) from a larger group of the total number of participants (population).

Samples are at the heart of survey research. It is often called the population microcosm, and the process of drawing a sample should maximize the similarity of the sample to the population under study. Sampling is therefore the selection of a set of elements from a population whose description accurately describes the parameters of the total population from which the sample is selected.

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The equation of the tangent line to the curve y = −3x²/2x³ at the point (1, 2) is y = −x + 3.

The first step is to find the derivative of the curve. The derivative of y = −3x²/2x³ is y' = −3(1 + x²)/2x⁴.

The next step is to evaluate the derivative at the point (1, 2). The value of y' at (1, 2) is −3(1 + 1)/2(1)⁴ = −3/2.

The final step is to use the point-slope form of linear equations to find the equation of the tangent line. The point-slope form of linear equations is y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope of the tangent line.

In this case, (x1, y1) = (1, 2) and m = −3/2. Substituting these values into the point-slope form of linear equations, we get y - 2 = −3/2(x - 1). Simplifying this equation, we get y = −x + 3.

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To find the probability that strictly more than 5 customers arrive in a given hour, we can use the Poisson distribution with a mean rate of 11 customers per hour.

The probability mass function of the Poisson distribution is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

Where X is the random variable representing the number of arrivals, λ is the mean rate, and k is the desired number of arrivals.

In this case, λ = 11 (mean rate of 11 customers per hour). We want to find the probability that strictly more than 5 customers arrive, which is equivalent to finding the probability that 6, 7, 8, 9, 10, 11, and so on, customers arrive.

Let's calculate the probability using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

P(X > 5) = 1 - P(X ≤ 5)

To find P(X ≤ 5), we sum the probabilities for k = 0, 1, 2, 3, 4, and 5:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

Using the Poisson distribution formula, we can calculate each term:

P(X = k) = (e^(-λ) * λ^k) / k!

P(X = 0) = (e^(-11) * 11^0) / 0! = e^(-11)

P(X = 1) = (e^(-11) * 11^1) / 1! = 11e^(-11)

P(X = 2) = (e^(-11) * 11^2) / 2!

P(X = 3) = (e^(-11) * 11^3) / 3!

P(X = 4) = (e^(-11) * 11^4) / 4!

P(X = 5) = (e^(-11) * 11^5) / 5!

Now we can calculate P(X ≤ 5):

P(X ≤ 5) = e^(-11) + 11e^(-11) + (11^2 * e^(-11)) / 2! + (11^3 * e^(-11)) / 3! + (11^4 * e^(-11)) / 4! + (11^5 * e^(-11)) / 5!

Finally, we can find P(X > 5) by subtracting P(X ≤ 5) from 1:

P(X > 5) = 1 - P(X ≤ 5)

You can calculate this value using a calculator or software that supports mathematical functions.

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The first statement is true, as the Tolivers are not eligible for a child credit regardless of the number of their children. However, the second statement is false, as the earned income credit is available to low-income taxpayers with dependent children.

The earned income credit helps to offset the burden of the federal payroll tax on low-income families and encourages individuals to seek employment rather than depend on welfare. Finally, the information about Mrs. Starling's employment does not provide enough information to determine any tax-related implications.
The statement regarding Mr. and Mrs. Toliver not being eligible for a child credit is true. Their Adjusted Gross Income (AGI) is $339,000, which is above the income threshold for eligibility for the child tax credit. The credit phases out for joint filers with AGI over $400,000, and they are not eligible due to their high income.
Regarding the Caseys, the earned income credit (EIC) is only available to low-income taxpayers with dependent children. The EIC helps offset the burden of federal payroll taxes on low-income families and encourages individuals to seek employment instead of relying on welfare. In the case of the Caseys, since Mrs. Casey is employed full-time as an attorney and Mr. Casey is an unpublished novelist with no income, they might not qualify for the EIC as they might not be considered low-income, depending on Mrs. Casey's salary.
Mrs. Starling worked for Abbot Inc. and earned $122,000 during her time there. She later worked for JJT Inc., and her salary from both companies should be combined to determine her total income for the year. Based on the given information, Mrs. Starling's total income can be used to determine her tax liabilities and eligibility for tax credits or deductions.

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Answer:

Hi there user! I'll help you!

96 should be the correct answer!

Step-by-step explanation:

4 x 3 = 12

4 x 7 = 28

5 x 7 = 35

3 x 7 = 21

12 + 28 + 35 + 21 = 96

Answer: 10 and 25

Step-by-step explanation:

The approximate values of the non-integral roots of the polynomial equation are -5.57, -1.95, 0.21, 1.27, and 4.73. These values represent the values at which the polynomial equation evaluates to zero, indicating the roots of the equation.

To find the roots of a polynomial equation, we set the equation equal to zero and solve for the unknown variable. In this case, we have a polynomial equation with non-integral roots.

To obtain the approximate values of these roots, numerical methods such as iterative methods or numerical approximation techniques can be used. These methods involve making educated guesses and refining the guesses until the equation evaluates to zero.

The resulting approximate values for the non-integral roots of the polynomial equation are -5.57, -1.95, 0.21, 1.27, and 4.73. These values are not exact, but they are close approximations to the actual roots of the equation.

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Answer:

Step-by-step explanations

simplify: 14-10/5

14-2

=12

The  true statement about the quasi-experiment is , the researcher assigns participants to conditions based on the participant's preexisting level of the independent variable.

In a quasi-experiment, the researcher assigns participants to conditions based on the participant's preexisting level of the independent variable. However, unlike a true experiment, a quasi-experiment cannot control for all possible confounding variables and may not allow for the balancing of participant variables between groups. Therefore, while a quasi-experiment can provide some evidence of causality, it may not be as accurate as a true experiment in this regard.

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In a quasi-experiment, the researcher assigns participants to conditions based on the participant’s preexisting level of the independent variable.

A quasi-experiment is a research design that lacks the control of random assignment to groups. Instead, the researcher assigns participants to conditions based on pre-existing levels of the independent variable. This means that the groups may not be equivalent at the outset, and there is a greater risk of confounding variables affecting the results.

Therefore, we cannot balance participant variables between groups in a quasi-experiment, nor can we randomly assign participants to groups. While quasi-experiments can provide valuable information, they do not allow us to infer causality more accurately than other research designs.

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Answer:

\( \cos \beta = \dfrac{8}{17} \)

Step-by-step explanation:

\( \cos A = \dfrac{adj}{hyp} \)

For angle beta, adj = BC = 8, and hyp = AB = 17

\( \cos \beta = \dfrac{adj}{hyp} \)

\( \cos \beta = \dfrac{BC}{AB} \)

\( \cos \beta = \dfrac{8}{17} \)

Answer:

Cos B = 8/17

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos B = adjacent/ hypotenuse

Cos B = 8/17

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Now, ORQ is a straight angle and RS its bisector.

It means:

So, ∠ORS and ∠QRS are supplementary.

We also have ray RP, that divides the angles ORQ and QRS.

It gives us one more pair of supplementary angles:

Since ∠QRS is right angle, its parts are forming a pair of complementary angles:

The equation of the tangent line to the curve f(x) = x csc(x) - (1/2) cot(x) at x = π/2 is y - (π/2) = (3/2)(x - π/2).

First, let's find the derivative of f(x) with respect to x:

f'(x) = d/dx [x csc(x) - (1/2) cot(x)]

To simplify the derivative, we can use the properties of trigonometric functions and logarithmic differentiation:

f'(x) = csc(x) - x csc(x) cot(x) + (1/2) csc²(x)

Now, let's evaluate the derivative at x = π/2:

f'(π/2) = csc(π/2) - (π/2) csc(π/2) cot(π/2) + (1/2) csc²(π/2)

Since csc(π/2) is equal to 1 and cot(π/2) is equal to 0, we have:

f'(π/2) = 1 - (π/2)(0) + (1/2)(1²)

= 1 + 1/2

= 3/2

The slope of the tangent line at x = π/2 is 3/2.

Now, let's use the point-slope form of a line, where (x₁, y₁) is the point on the curve:

y - y₁ = m(x - x₁)

Substituting the values x₁ = π/2 and m = 3/2, we have:

y - f(π/2) = (3/2)(x - π/2)

y - f(π/2) = (3/2)(x - π/2)

This is the equation of the tangent line.

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SOLUTION

To find the percentage increase, we need to know the percentage change

Recall that

Where

Substitute into the formula above, we have

After simplification, we have

Therefore

The percentage increase is 10%

The straight line distance from the airplane to the observer is 476. 70 feet

Note that there are six different trigonometric identities in mathematics, they are;

From the diagram shown, we have that;

Opposite side = 400 feet

Angle of elevation, θ = 40 degrees

Adjacent side = distance

Using the tangent identity, we have;

tan 40 = 400/x

x = 400/0.8391

x = 476. 7 feet

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Step-by-step explanation:

In a rectangle

Area (A) = 248 m²

length (L) = 4 m

breadth (b) = ?

We know

A = L * b

248 = 4 * b

b = 62 m

Now

Perimeter of the rectangle

= 2 ( L + b)

= 2 ( 4 + 62)

= 2 * 66

= 132 m

Hope it will help :)

Answer:

first we have to get the width.

A=L*w

so, A =L *W

L L

W=A

L

248m²=4m*W

248m²=4m*w

4m 4m

w=248m²

4m

w=32m

now we can find the perimeter.

p=2(L+w)

p=2(4m+32m)

p=2(36m)

p=72m

there for the answer is 72m

The expression is equivalent to "\(z^4 * (z + 6)^2 + (z + 6)\)".

To clarify, I understand the expression as: "z * (z + 6) * z * (z + 6) * z + (z + 6)". Let's break down the expression and simplify it step by step:

Distribute the multiplication:

z * (z + 6) * z * (z + 6) * z + (z + 6)

becomes

z * z * z * (z + 6) * (z + 6) * z + (z + 6)

Combine like terms:

z * z * z simplifies to \(z^3\)

(z + 6) * (z + 6) simplifies to (z + 6)^2

The expression now becomes:

\(z^3 * (z + 6)^2 * z + (z + 6)\)

Multiply \(z^3\) and z:

 \(z^3 * z\) simplifies to \(z^4\)

The expression becomes:

  \(z^4 * (z + 6)^2 + (z + 6)\)

So, an equivalent expression to "z (z + 6)z (z + 6)z + (z + 6)" is "\(z^4 * (z + 6)^2 + (z + 6)\)".

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

The distribution for town A is positively skewed, but the distribution for town B is symmetric.

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

Explanation:

The length of the whiskers tell us if we're dealing with a symmetric distribution, or a skewed distribution. For town A, the right whisker is longer than the left whisker. So this distribution is positively skewed. We can say it is skewed to the right, or right skewed.

Town B has whiskers of equal length. In addition, the two distances inside the box are equal to one another. We have a perfectly symmetric distribution. One half is a mirror copy of the other half.

Answer:

Hey there!

This is a box and whisker plot, and since the right whisker is longer, this is positively skewed. (For town A)

This is also a box and whisker plot, and since it is even on both sides, it is symmetric.

Hope this helps :)

Using The Weak Duality theorem ,

only change in the dual problem is that the kᵗʰ variable is replaced by μ times that variable if

the kᵗʰ primal constraint is multiplied by a nonzero scalar number (i.e., μ)

Suppose we have a primal problem of

min cᵀ x

subject to Ax=b, x≥0.

All primals have a dual and that dual is allowed. consider λ be an optimal solution of the dual. We need to see what happens when we multiply the primal's kᵗʰ constraint equation by μ≠0 (non-zero scalar)

This is wₖ=λₖ/μ and wᵢ=λᵢ for i≠k.

Multiplying the kᵗʰ constraint of primes by μ does not change the feasible region of primal and therefore the optimal solution to primes. The value z* of the best prime solution does not change.

The only change in the dual problem is that the kᵗʰ variable is replaced by μ times that variable. Since z* is the value of the original dual-optimal solution, wᵢ=λᵢand wk=λₖμ for i≠k gives a new dually feasible solution with value z*. Therefore, due to the weak duality, w must be optimal.

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Answers in bold:

S9 = 2

i = 20

R = -2

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

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

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

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

To write the equation in standard form for the circle passing through (–2, 4) centered at the origin, we need to find the radius and the center of the circle.

Since the circle passes through (–2, 4), we can use the distance formula to find the radius, which is the distance from the origin to (–2, 4).

The distance formula is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, x1 = 0, y1 = 0, x2 = –2, and y2 = 4. So, the radius is:

radius = sqrt((-2 - 0)^2 + (4 - 0)^2) = sqrt(20) = 2sqrt(5)

The center of the circle is the origin, since the circle is centered at the origin. Therefore, the equation of the circle in standard form is:

x^2 + y^2 = (2sqrt(5))^2 = 20

So, the equation of the circle passing through (–2, 4) centered at the origin is x^2 + y^2 = 20.

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Answer:

When you roll a 6-sided cube, numbered 1 to 6, the probability of rolling a 2 is 1:6. This is an example of theorectical probability.

Step-by-step explanation:

The probability of rolling a 2 on a 6-sided dice is  

1

6

The probability of rolling two 2s on two 6-sided die is, by the multiplication principle,  

1

6

×

1

6

=

1

36

Subjective is something that is based on personal opinion, so I think the answer is actually theoretical probability! Theoretical probability is a method to express the likelihood that something will occur. It is calculated by dividing the number of favorable outcomes by the total possible outcomes.

Hope this helps, have a good day :)

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Answer:

h ≈ 66.4 ft

Step-by-step explanation:

The situation can be modelled by a right triangle with h representing the height of the tree.

Using the tangent ratio in the right triangle

tan39° = \(\frac{opposite}{adjacent} \) = \(\frac{h}{82} \) ( multiply both sides by 82 )

82 × tan39° = h , then

h ≈ 66.4 ft ( to the nearest tenth )