So far this semester, Mabel is averaging a score of 72.4 points on math tests, which is 18.6% lower than her average last semester. What was the average of her scores last semester?

Answer:

True ☑

Step-by-step explanation:

\( - 3 \times - 7 \\ = {}^{ + } 21\)

For y-fx)=xex-5, when x= 5 and dx=0.1 : dy Hence the linear approximation using dy is f(5.1)-f(5)+dy)= 0%:  the linear approximation using dy is f(5.1)-f(5)+dy)= 0% (rounded to the nearest percent).

The problem is asking for the linear approximation of the function f(x) = xex-5 at x=5 using dy, when dx=0.1.

To begin, we need to find dy. We can do this by taking the derivative of f(x) with respect to x and then plugging in x=5 and dx=0.1:

f'(x) = ex + xex-5
f'(5) = e^5 + 5e^0 = e^5 + 5

dy = f'(5) dx = (e^5 + 5)(0.1) = e^5/10 + 0.5

Now we can use the linear approximation formula:

f(x+dx) ≈ f(x) + f'(x) dx

Plugging in x=5, dx=0.1, and dy=e^5/10 + 0.5:

f(5.1) ≈ f(5) + f'(5) (0.1) + dy
f(5.1) ≈ (5e^0) + ((e^5 + 5)(0.1)) + (e^5/10 + 0.5)
f(5.1) ≈ 5.7e^0 + 1.05e^5 + 1

Finally, we can check the accuracy of this linear approximation by calculating the percentage error:

(f(5.1) - f(5) - dy) / f(5.1) x 100%

= [(5.7e^0 + 1.05e^5 + 1) - (5e^0 + e^5 - 5) - (e^5/10 + 0.5)] / (5.7e^0 + 1.05e^5 + 1) x 100%

= -0.0005%

Therefore, the linear approximation using dy is f(5.1)-f(5)+dy)= 0% (rounded to the nearest percent).

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Answer: x=8

Step-by-step explanation:

This would be your equation:

x+4=12

Solve.

x=12-4

x=8

You can suggest that managers should avoid the quick-fix mentality that makes management by best-seller so tempting by implementing the following strategies:

1. Understand the Unique Nature of Your Business: Managers should take the time to understand the unique nature of their business. They should realize that what worked for another company may not work for their own company.

2. Avoid Short-Term Solutions: Managers should avoid short-term solutions that provide quick results. They should focus on long-term solutions that will benefit the organization in the long run.

3. Develop a Comprehensive Strategy: Managers should develop a comprehensive strategy that includes long-term goals and objectives. They should also have a plan in place to achieve those goals.

4. Invest in Employee Development: Managers should invest in employee development by providing training and development opportunities. This will help to build a strong workforce that is capable of handling complex challenges.

5. Encourage Collaboration: Managers should encourage collaboration among team members. This will help to create a culture of teamwork and cooperation.

6. Monitor Progress: Managers should monitor progress and adjust strategies as necessary. This will help to ensure that the organization is on track to achieving its goals.

By following these strategies, managers can avoid the quick-fix mentality that makes management by best-seller so tempting. They can focus on long-term solutions that will benefit the organization in the long run.

Hope this helped you...

Answer:

Step-by-step explanation:

Of total variation in "dependent-variable", the proportion which is explained by variation in "independent-variable" is called (b) coefficient of determination.

The "Coefficient-Of-Determination", denoted as R², is a statistical measure which represents the proportion of total-variation in the dependent variable which can be explained by  variation in "independent-variable".

It quantifies the percentage of dependent variable's variability which can be attributed to the independent variable. A higher coefficient of determination indicates a stronger relationship between the variables, which means that more of variation in "dependent-variable" can be accounted for by changes in the independent-variable.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Of the total variation in the dependent variable, the proportion that is explained by the variation in the independent variable is called

(a) the coefficient of correlation

(b) the coefficient of determination

(c) the coefficient of skewness

(d) none of the above

The functions and their transformations are

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

f(x) = 2(x + 1)² - 3

A translation down by 5 units is represented as

f(x) - 5

So, we have

f(x) - 5 = 2(x + 1)² - 3 - 5

f(x) - 5 = 2(x + 1)² - 8

Rewrite as

h(x) = 2(x + 1)² - 8

A translation left by 5 units is represented as

f(x + 5)

So, we have

f(x + 5) = 2(x + 1 + 5)² - 3

f(x + 5) = 2(x + 6)² - 3

Rewrite as

k(x) = 2(x + 6)² - 3

A translation right by 5 units is represented as

f(x - 5)

So, we have

f(x - 5) = 2(x + 1 - 5)² - 3

f(x - 5) = 2(x - 4)² - 3

Rewrite as

g(x) = 2(x - 4)² - 3

A translation up by 5 units is represented as

f(x) + 5

So, we have

f(x) + 5 = 2(x + 1)² - 3 + 5

f(x) + 5 = 2(x + 1)² + 2

Rewrite as

j(x) = 2(x + 1)² + 2

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The total amount by which Todd's biceps will increase in 8 weeks is approximately 29.152 millimeters.

a. To find the rule for the nth term in the sequence representing the amount of muscle increase each week, we can use the given information. The first week's increase is 4 millimeters, and each subsequent week's increase is 90% of the previous week's increase. Therefore, we can establish the rule as follows:

\(a_n = 4 * 0.9^{(n-1)}\)

Where aₙ represents the muscle increase in the nth week.

b. The summation notation using Σ (sigma) for the first 8 terms would be:

= Σ(aₙ) from n = 1 to 8

c. To expand the series and evaluate the amount by which Todd's biceps will increase in 8 weeks, we substitute the values of aₙ from n = 1 to 8 into the summation notation:

= Σ(aₙ) from n = 1 to 8

= a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + a₇ + a₈

Expanding the series using the rule from part a, we have:

\(= 4 * 0.9^{(1-1)} + 4 * 0.9^{(2-1)} + 4 * 0.9^{(3-1)} + 4 * 0.9^{(4-1)} + 4 * 0.9^{(5-1)} + 4 * 0.9^{(6-1)} + 4 * 0.9^{(7-1)} + 4 * 0.9^{(8-1)}\)

\(= 4 + 4 * 0.9 + 4 * 0.9^2 + 4 * 0.9^3 + 4 * 0.9^4 + 4 * 0.9^5 + 4 * 0.9^6 + 4 * 0.9^7\)

Evaluating this expression will give us the total amount by which Todd's biceps will increase in 8 weeks.

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The ending inventory amount is p68,000: (200 x 65) + (300 x 68) + (150 x 70) - (500 x 68) = 68,000.

1. Calculate the total cost of the beginning inventory: 200 units x p65 = p13,000

2. Calculate the total cost of the first purchase: 300 units x p68 = p20,400

3. Calculate the total cost of the second purchase: 150 units x p70 = p10,500

4. Calculate the total cost of the units sold: 500 units x p68 = p34,000

5. Calculate the total cost of the ending inventory amount : (13,000 + 20,400 + 10,500) - 34,000 = p68,000

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Based on the empirical rule, we would expect approximately 0.3% or 30 observations to lie beyond three standard deviations of the mean.

To explain further, the empirical rule, also known as the 68-95-99.7 rule, is a guideline that applies to data that follows a normal distribution. According to this rule, approximately 68% of the observations fall within one standard deviation of the mean, about 95% fall within two standard deviations, and roughly 99.7% fall within three standard deviations.

Since the normal distribution is symmetric, we can estimate that about half of the 0.3% of observations beyond three standard deviations would fall on each side of the mean. Therefore, we would expect around 0.3% / 2 = 0.15% of observations to lie beyond three standard deviations on each side.

To calculate the actual number of observations, we can multiply the percentage by the total sample size of 10,000. So, 0.15% of 10,000 is equal to 0.15 / 100 * 10,000 = 15.

Hence, we would expect approximately 15 observations to lie beyond three standard deviations of the mean in a sample of 10,000 from a normal population.

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Answer: SSS

Step-by-step explanation:

Given:

the 2 left sides are =

and the 2 right sides are =

the line in between are =

So they've given a side, side and side

SSS

Answer:

3e-1.5f-0.375

Step-by-step explanation:

0.5x6 = 3

0.5x3 = 1.5

0.5x.75 = 0.375

Answer:

A

Step-by-step explanation:

3x – 7 > – 1

3x > 6

x < 2

The z-score of a point can be calculated by using the formula :

z = (x - μ) / σ

To calculate the z-score of a data point, you would use the formula:

z = (x - μ) / σ

where x is the data point,

μ is the mean of the data set,

σ is the standard deviation of the data set.

To calculate the z-score using a calculator, follow these steps:

1) Enter the value of the data point (x) into the calculator.

2) Subtract the mean (μ) from the value of the data point (x - μ).

3) Divide the result from step 2 by the standard deviation (σ).

4) The final answer is the z-score.

Different calculator models may have different buttons or functions for calculating the mean and standard deviation, so refer to the manual of your calculator for instructions on how to input these values.

Therefore, we can calculate z-score on calculator

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Answer:

The equation of the line is;

3y = 2x-8

Step-by-step explanation:

Firstly, we need the to get the slope of the given line

To do this, we will write the equation of the line in the standard form

the standard form

is;

y = mx + b

where m is the slope and b is the y-intercept

y -4 = 2/3(x-3)

y -4 = 2x/3 - 2

y = 2x/3 -2 + 4

y = 2x/3 + 2

with respect to the given equation, the slope of the line is 2/3

Mathematically, when two lines are parallel, the slopes of the line are equal

So now, we want to find the equation of the line that has a slope of 2/3 and passes through the point (1,-2)

so;

y = 2x/3 + b

So substitute the values of (1,-2)

1 for x and -2 for y

-2 = 2/3(1) + b

-2 = 2/3 + b

b = -2 - 2/3

b = (-6-2)/3 = -8/3

So the equation of that line is;

y = 2/3x - 8/3

Multiply through by 3

3y = 2x - 8

Answer:

f(1) = 5, f(2) = 8, f(3) = 11

Step-by-step explanation:

Common difference refers to how you get from one value in the sequence to the next.

If f(0) = 2, f(1) = 2 + 3 = 5 etc

Answer:x>7

Step-by-step explanation:

Its saying a nuber greater than 7 and 3 plus 8 would be 11

Answer:

\(y^{5}\times y^{3}=y^8\)

Step-by-step explanation:

exponent property :

\(\left( a\right)^{n} \times \left( a\right)^{m} =\left( a\right)^{n+m}\)

………………………………………

\(\Longrightarrow y^{5}\times y^{3}=y^{5+3}=y^8\)

Answer:

Step-by-step explanation:

2.

u would use probability for that which gives them the answer

4.

looking at the chart it may be a 14% chance

5.

i would use 3 coins so that the number of coins is equivalent to the amount of pets they have. so that they can see what pets they may have (cats or dogs)

Answer:

Option A

Step-by-step explanation:

To find all missing sides of a right triangle we use the sine, cosine or tangent ratio as below,

sinθ = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

cosθ = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

tanθ = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

Now we take an angle measuring 60°

sin(60°) = \(\frac{6}{y}\)

\(\frac{\sqrt{3} }{2}=\frac{6}{y}\)

y = 4√3

tan(60°) = \(\frac{6}{x}\)

√3 = \(\frac{6}{x}\)

x = 2√3

Therefore, Option A will be the correct option.

\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_2(x)=-5\implies 2^{-5}=x\)

Answer:

y=mx+b

Step-by-step explanation:

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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The friend has to save for 5 and 2/3 of a month to in order to make up the remaining 85 to get the 125 headphone.

An inequality that consists of two or more parts is called a compound inequality. Either "or" or "and" may be used in these components. A number between 5 and 10 could be used as x in an inequality, for instance, if it states that "x is larger than 5 and less than 10". Any time one of the two inequalities is true when the two inequalities are united by the word or, the compound inequality is solved. The two separate solutions have been combined to form the final answer. Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and."

Cost of the headphone 125.

What the friend have: 40.

What need to save: 125-40 = 85

Let x = amount to be saved per month

Months to save up the 85 is 15

The equation would be 15 x = 85

Therefore x = 85/15

Which is 5 2/3 months.

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The main answer to your question is "interchanging". To find the inverse of a function, we interchange the numbers in each ordered pair of the function. This means that we switch the x and y values of each point in the function.

For example, if we have a function f(x) = 2x + 3, the ordered pairs would be (1,5), (2,7), (3,9), etc. To find the inverse function, we would switch the x and y values of each point to get ordered pairs such as (5,1), (7,2), (9,3), etc.

The explanation for why we interchange the numbers is that the inverse function "undoes" the original function. If we apply the original function to a number, the inverse function will take us back to the original number. By switching the x and y values, we make sure that the inverse function will undo the original function.

In conclusion, to find the inverse of a function, we interchange the numbers in each ordered pair of the function. This ensures that the inverse function will undo the original function.
Hi! I'm happy to help you with your question.

Main answer: The inverse of a function can be found by interchanging the numbers in each ordered pair of the function.

Explanation: When finding the inverse of a function, you are essentially swapping the input and output values in each ordered pair (x, y) to create a new ordered pair (y, x). This process is called interchanging the numbers in the ordered pair.

Conclusion: To find the inverse of a function, you need to interchange the numbers in each ordered pair of the function, which essentially swaps the input and output values.

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It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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The sentences describing the ratio of small balls (S) to total balls (T) should be completed as follows:

There are 9 small balls for every 15 total balls.

There are 3 small balls for every 5 total balls.

What is ratio?

Ratio can be defined as a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

What is a proportion?

A proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By critically observing the image (see attachment) and counting the number of balls, we have the following information:

Number of small balls, S = 9 small balls.

Total balls, T = 15 balls.

In this context, the ratio of small balls (S) to total balls (T) is given by:

S:T = 9:15 = 3:5.

In conclusion, we can infer and logically deduce that the sentences describing the ratio of small balls (S) to total balls (T) should be completed as follows:

There are 9 small balls for every 15 total balls.

There are 3 small balls for every 5 total balls.

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Answer:

B.) \(6^{\frac{1}{2}}\)

Step-by-step explanation:

Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\).  For this problem, let

a=6

m=2

So,

\(\sqrt6=6^{\frac{1}{2}}\)

The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

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