PLEASE HELP ME
- The value of y varies directly with x. If x= 4,
then y= 32. What is the value of x when y= 176?

Answer:

\(\sf a) y^{\frac{5}{3}}\\\\b) x^{\frac{-1}{5}}\\\\c)w^{\frac{7}{8}}\)

Step-by-step explanation:

Radical to exponent form:

   \(\sf \boxed{\sqrt[n]{x}=x^{\frac{1}{n}} }\)

\(\sf a) \sqrt[3]{y^5}=y^{5*\frac{1}{3}} =y^\frac{5}{3}\)

\(\sf b) \dfrac{1}{\sqrt[5]{x} }=\dfrac{1}{x^{\frac{1}{5}}}=x^{\frac{-1}{5}}\)

\(\sf c) \sqrt[8]{w^7}=w^{7* \frac{1}{8}}=w^{\frac{7}{8}}\)

There is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

Given, the Pearson correlation coefficient of +0.91,

There appears to be a strong +ve correlation between the number of cats she owns and the number of times an old widow was married.

It suggests that the more times a widow was married,the more cats she tends to own.

Approximately 82% of the variance in the number of cats owned can be explained by the number of times a widow was married is indicated by the coefficient of determination (r²).

Hence, we can say that there is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

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The population grows by approximately 0.43% each month. To calculate the monthly growth rate, we could also use the formula for compound interest, which is often used in finance and economics.

To find out how much the population grows each month, we need to first divide the annual growth rate by 12 (the number of months in a year).
So, we can calculate the monthly growth rate as follows:
5.2% / 12 = 0.4333...
We need to round this to two decimal places, so the final answer is that the population grows by approximately 0.43% each month.

The formula is:
A = P (1 + r/n)^(nt)
In our case, we have:
Plugging these values into the formula, we get:
A = 1 (1 + 0.052/12)^(12*1)
Simplifying this expression, we get:
A = 1.052
So, the population grows by 5.2% in one year.
To find out how much it grows each month, we need to take the 12th root of 1.052 (since there are 12 months in a year).
Using a calculator, we get:
(1.052)^(1/12) = 1.00434...

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Answer:

D

Step-by-step explanation:

I plugged each equation into a graphing calculator and compared them to see which one matched the one in the picture.

The value of the trigonometric equation after transformation is given by the value y = 3 [ sin ( x + 3 ) ] - 2

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented as f ( x )

Now , the value of the trigonometric function f ( x ) is

f ( x ) = 3sin ( x )

when the function is translated 3 units to the left and 2 units down , we get

y = 3 [ sin ( x + 3 ) ] - 2

Therefore , the transformed function is y = 3 [ sin ( x + 3 ) ] - 2 and the graph is plotted

Hence , the transformed function is y = 3 [ sin ( x + 3 ) ] - 2

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Answer:

He Has to save $13 every week for six weeks which equals 78,and 78+9 is 87

To compare the 3-month and 12-month moving average forecasts using the mean absolute deviation (MAD) criterion, we need to calculate the MAD for each model and then compare them. The MAD is a measure of the average magnitude of the forecast errors, and a lower MAD indicates a better forecast.

To calculate the MAD for the 3-month moving average model, we need to first calculate the forecasted values for each month by taking the average of the unemployment rates for the previous 3 months. For example, the forecasted value for April 2018 would be the average of the unemployment rates for January, February, and March 2018. We then calculate the absolute deviation between the forecasted value and the actual value for each month, and take the average of those deviations to get the MAD for the 3-month moving average model.

We can repeat this process for the 12-month moving average model, but instead of taking the average of the previous 3 months, we take the average of the previous 12 months.

Once we have calculated the MAD for both models, we can compare them to determine which model yields better results. Generally, a lower MAD indicates a better forecast. However, it is important to note that the MAD criterion only considers the magnitude of the forecast errors and does not take into account the direction of the errors (i.e., overestimation versus underestimation).

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Full Question ;

The accompanying dataset provides data on monthly unemployment rates for a certain region over four years. Compare 3- and 12-month moving average forecasts using the MAD criterion. Which of the two models yields better results? Explain. Click the icon to view the unemployment rate data. Find the MAD for the 3-month moving average forecast. MAD = (Type an integer or decimal rounded to three decimal places as needed.) A1 fx Year D E F G H I 1 2 3 1 с Rate(%) 7.8 8.3 8.5 8.9 9.4 9.6 9.4 9.5 9.7 9.9 9.8 10.1 9.9 9.7 9.8 9.91 9.7 9.4 9.6 9.4 9.3 9.5 9.9 9.5 9.2 9.1 8.9 A B Year Month 2013 Jan 2013 Feb 2013 Mar 2013 Apr 2013 May 2013 Jun 2013 Jul 2013 Aug 2013 Sep 2013 Oct 2013 Nov 2013 Dec 2014 Jan 2014 Feb 2014 Mar 2014 Apr 2014 May 2014 Jun 2014 Jul 2014 Aug 2014 Sep 2014 Oct 2014 Nov 2014 Dec 2015 Jan 2015 Feb 2015 Mar 2015 Apr 2015 May 2015 Jun 2015 Jul 2015 Aug 2015 Sep 2015 Oct 5 7 3 ) 1 2 3 1 5 7 9.1 ) 9. 1 2 3 1 5 7 ) 9.1 8.9 8.9 8.9 8.9 8.7 8.4 8.3 8.3 8.4 8.1 8.1 8.4 8.2 8.3 7.7 7.9 7.9 7.8 1 2 2015 Dec 2016 Jan 2016 Feb 2016 Mar 2016 Apr 2016 May 2016 Jun 2016 Jul 2016 Aug 2016 Sep 2016 Oct 2016 Nov 2016 Dec 3 1 5 3 2 2

Answer:

1.   x< 3

2.   x>12

have a great day :)

Step-by-step explanation:

The Taylor series for f(x) = sin(x) centered at a = π is given by \(\(f(x) = (x - \pi) - \frac{{(x - \pi)^3}}{{3!}} + \frac{{(x - \pi)^5}}{{5!}} - \frac{{(x - \pi)^7}}{{7!}} + \ldots\)\)

The Taylor series expansion of a function f(x) centered at a point a can be obtained by taking the derivatives of f(x) at a and evaluating them at a.

For the sine function, we can start by evaluating the derivatives of sin(x) at x = π. The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x). Evaluating these derivatives at x = π, we find that sin(π) = 0, cos(π) = -1, and sin(π) = 0 again.

Using these values, we can construct the Taylor series for sin(x) centered at a = π. The general term of the series is given by \(\((-1)^{\frac{n}{2}} \cdot (x - \pi)^n / n!\)\), where n is an even number. This series includes only the even powers of (x - π) since the odd powers evaluate to zero at x = π.

By summing up these terms, we obtain the Taylor series for sin(x) centered at π.

Therefore, the Taylor series for f(x) = sin(x) centered at a = π is given by \(\(f(x) = (x - \pi) - \frac{{(x - \pi)^3}}{{3!}} + \frac{{(x - \pi)^5}}{{5!}} - \frac{{(x - \pi)^7}}{{7!}} + \ldots\)\), where the ellipsis indicates that the series continues indefinitely.

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Answer: See explanation

Step-by-step explanation:

To solve this, firstly, we need to calculate the volume of the cylinder which will be:

= πr²h

where r = diameter/2 = 14/2 = 7

h = 18

Volume = πr²h

= 3.14 × 7² × 18

= 3.14 × 49 × 18

= 2769.48meters³

Since the tank is 50% full, the amount if oil it contains will be:

= 50% × 2769.48

= 0.5 × 2769.48

= 1384.74m³

= 1.38km³

The number of arrangements of 6 balls with 2 red balls and 2 blue balls, we need to consider the number of ways to choose 2 red balls from the 4 available red balls and the number of ways to choose 2 blue balls from the 4 available blue balls.

These are both combinations, and we can use the formula for combinations to calculate them:

C(n, k) = n! / (k! (n-k)!).

For the red balls, C(4, 2) = 4! / (2! (4-2)!) = 6.

For the blue balls, C(4, 2) = 4! / (2! (4-2)!) = 6.

The total number of arrangements of 6 balls with 2 red balls and 2 blue balls is the product of the number of arrangements for each type of ball:

C(4, 2) * C(4, 2) = 6 * 6 = 36

So, there are 36 arrangements of 6 balls with 2 red balls and 2 blue balls.

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Answer:

A circle is a bounded object with points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius = diameter / 2 = 20m / 2 = 10m

3.14 x 10² = 314m²

Number of boxes needed to cover the garden = area of the garden / coverage of one box

314m² / 58m² = 5.14

5 boxes to one significant figure

The angle between the rope and the ground is given as follows:

x = 53º.

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle x, we have that:

Hence we apply the sine ratio to obtain the angle x as follows:

sin(x) = 4/5

x = arcsin(0.8)

x = 53º.

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Real-world problem on additive inverse of a rational number and solution:

Peter borrowed one fourth of his salary to Jack. The money way returned to peter at the end of the month without interest because they are friends. how much is Jack owing peter in the transaction?

Jack is owing Peter nothing

Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.

To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.

In the problem let peter's salary be x

amount peter borrowed out = x/4

amount paid back = x/4

Addition of the expenses

borrowed + paid back

-x/4 + x/4 = 0

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The foil method is an effective method because you are able to successfully remember the other at which you multiply the brackets to open them using F.O.I.L, so its not only easy to remember but very good to use for quadratic, cubic and to an extent, polynomials.

The FOIL Method stands for First Outer Inner Last. This is a standard method for multiplying two binomials together. It is also a valid method for solving quadratic equations and simplifying expressions.

The FOIL method is a valid method because it helps to simplify complicated expressions, and it is easy to use. It is used to multiply two binomials together.

By following the steps, the user can easily find the product of two binomials. The steps are as follows:

The FOIL method is valid because it helps to simplify expressions by breaking them down into smaller parts. This makes it easier to see how the parts relate to each other and how they combine to create the final expression. It is a straightforward method, and it is easy to use.

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Answer:

The first answer is $1050000

The second answer is $1500000

The third one is $450000

Hope this helps:)

Histograms are used to represent the distribution of continuous or interval data, while bar charts are used to compare different categories or groups of categorical or discrete data.

The difference between a histogram and a bar chart lies in the type of data they represent and the way they are used. Data Representation: Histogram: A histogram is used to display the distribution of continuous or interval data. It represents the frequency or count of data within specific intervals or bins. The x-axis of a histogram represents the range of values or intervals, while the y-axis represents the frequency or count of data points within each interval.

Bar Chart: A bar chart is used to compare different categories or groups of categorical or discrete data. It represents the magnitude or value of each category as separate bars. The x-axis of a bar chart represents the categories, and the y-axis represents the magnitude or value being measured. Data Type: Histogram: Histograms are suitable for displaying continuous or interval data, such as measurements on a scale (e.g., height, weight, time). The data points are grouped into intervals or bins, and the frequency or count of data within each bin is represented.

Bar Chart: Bar charts are suitable for representing categorical or discrete data, where the data points belong to distinct categories or groups. Each category is represented by a separate bar, and the height or length of the bar indicates the magnitude or value associated with that category.

Usage: Histogram: Histograms are commonly used in statistics and data analysis to visualize the distribution of data and identify patterns, central tendencies, and outliers within a continuous dataset.

Bar Chart: Bar charts are widely used in various fields to compare and present categorical data, such as comparing sales figures by product categories, analyzing survey responses by different groups, or displaying the frequency of different outcomes in a dataset.

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Answer:

6.84

Step-by-step explanation:

Hope this helps!!!

Answer:

1.2

Step-by-step explanation:

divide 6 by 5

Answer:

8/1 or 8 minutes per lap

Step-by-step explanation:

The first car has a higher miles per gallon rating with 27.03

The miles per gallon (mpg) rating for a car, we can use the formula

mpg = 100 / (gallons per 100 miles)

For the first car with a rating of 3.7 gallons per 100 miles

mpg = 100 / 3.7 ≈ 27.03 mpg

For the second car with a rating of 4.3 gallons per 100 miles

mpg = 100 / 4.3 ≈ 23.26 mpg

Comparing the two mpg ratings, we find that the first car has a greater mpg rating of 27.03 mpg compared to the second car with a rating of 23.26 mpg. Therefore, the first car has a higher mpg rating.

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Answer:

Step-by-step explanation:

a² - b² = (a +b)(a - b)

a = 525  & b  = 475

525² - 475² = (525 + 475) (525 - 475)

                   =1000 * 50

                   = 50,000

The value of (525)² - (475)² using the identity (a²- b²) = (a+b) (a-b) is 50000.

The expression given is:

(525)² - (475)²

The above expression looks similar to the expression (a²- b²).

The simplified form of the expression (a²- b²) is (a+b) (a-b).

So, (525)² - (475)² can be written as:

(525)² - (475)² = (525+475) (525-475)

(525)² - (475)² = 1000 * 50

(525)² - (475)² = 50000

Therefore, the value of (525)² - (475)² using the identity (a²- b²) = (a+b) (a-b) is 50000.

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To determine the closest Big-Oh notation for the given operation numbers, we need to analyze the dominant term in each expression and identify its growth rate.

The Big O notation represents the upper bound or worst-case scenario for the growth rate of a function.

A. The dominant term is n^3, so the closest Big O notation is O(n^3).

B. The dominant term is n^2 * log(n), so the closest Big O notation is O(n^2 * log(n)).

C. The dominant term is 3^n, which grows exponentially, so the closest Big O notation is O(3^n).

D. The dominant term is log(n), so the closest Big O notation is O(log(n)).

E. The expression is a constant, so the closest Big O notation is O(1).

F. The expression contains multiple terms with varying constants, so we cannot determine a specific Big O notation without more information about the constants.

In Big O notation, we focus on the term with the highest growth rate and ignore constant factors or lower-order terms. This notation provides an asymptotic upper bound on the growth rate of a function as the input size increases.

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The symbol that represents an expression in statistics are That is option A , B and C.

Statistics is defined as the area of study that is concerned with the collection, organization, analysis, interpretation, and presentation of data.

The importance of statistics is that it helps in conducting research, evaluating results, developing critical thinking and making informed decisions.

The various symbols use in statistics include the following:

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False. Randomization distributions are centered at the value where the null is false. This distinction is important in hypothesis testing as it helps determine the statistical significance of observed differences or effects.

Randomization distributions are generated through permutation tests, which involve random shuffling of data points between groups. In hypothesis testing, the null hypothesis assumes that there is no difference between groups or no effect of a treatment. The alternative hypothesis suggests otherwise.

The randomization distribution is created by repeatedly shuffling the data and calculating a test statistic based on the null hypothesis. This distribution represents the expected outcomes if the null hypothesis is true. Therefore, the randomization distributions are centered at the value where the null is false, as they capture the potential differences or effects between groups.

In summary, randomization distributions are not centered at the value where the null is true; rather, they are centered at the value where the null is false. This distinction is important in hypothesis testing as it helps determine the statistical significance of observed differences or effects.

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Answer:

x ≤ 2

Step-by-step explanation:

Expand

3x - 6 + x ≤ 2

Rearrange

4x ≤ 8

x ≤ 2

Answer:

x ≤ 2

Step-by-step explanation:

Step 1: Write inequality

3(x - 2) + x ≤ 2

Step 2: Solve for x

Here we see that any number less than or equal to 2 will work.

Answer:

four x plus three divided by two

Step-by-step explanation:

Answer:

Peter's number is 36.

Step-by-step explanation:

If you subtratct 13 from 36, you get 23.

If you multiply that times -3, you get -69.

(The way I got 23 was by dividing -69 and -3)

I hope this helped you even though it's late.

Answer:

the complementary angles and the supplementary angles

Step-by-step explanation:

m<1=60

m<2=120

m<3=60

m<4=120

m<5=30

m<6=30

We determine the cumulative weight retained at each sieve and then calculate the cumulative percentage passing by dividing the cumulative weight passing by the total weight of the sample and multiplying by 100.

To calculate the percentage passing for each sieve size in a sieve analysis, we need to determine the cumulative percentage passing at each sieve size.

The sieve analysis provides information about the particle size distribution of an aggregate sample. It involves passing the sample through a series of sieves with different mesh sizes, and measuring the amount of material retained on each sieve.

To calculate the percentage passing, we first need to determine the cumulative weight retained at each sieve size. This is done by subtracting the weight retained on a particular sieve from the weight retained on the previous sieve.

Once we have the cumulative weight retained, we can calculate the cumulative percentage passing by dividing the cumulative weight passing by the total weight of the sample and multiplying by 100.

Here is an example:

Sieve Size (mm) | Weight Retained (g)

4.75 | 50

2.36 | 30

1.18 | 20

0.6 | 15

0.3 | 10

0.15 | 5

To calculate the cumulative percentage passing:

Calculate the cumulative weight retained:

Cumulative weight retained at sieve 4.75 mm = 50 g

Cumulative weight retained at sieve 2.36 mm = 50 g + 30 g = 80 g

Cumulative weight retained at sieve 1.18 mm = 80 g + 20 g = 100 g

Cumulative weight retained at sieve 0.6 mm = 100 g + 15 g = 115 g

Cumulative weight retained at sieve 0.3 mm = 115 g + 10 g = 125 g

Cumulative weight retained at sieve 0.15 mm = 125 g + 5 g = 130 g

Calculate the cumulative percentage passing:

Cumulative percentage passing at sieve 4.75 mm = (Total weight - Cumulative weight retained) / Total weight * 100 = (130 g - 50 g) / 130 g * 100 = 61.54%

Cumulative percentage passing at sieve 2.36 mm = (130 g - 80 g) / 130 g * 100 = 38.46%

Cumulative percentage passing at sieve 1.18 mm = (130 g - 100 g) / 130 g * 100 = 23.08%

Cumulative percentage passing at sieve 0.6 mm = (130 g - 115 g) / 130 g * 100 = 11.54%

Cumulative percentage passing at sieve 0.3 mm = (130 g - 125 g) / 130 g * 100 = 3.85%

Cumulative percentage passing at sieve 0.15 mm = (130 g - 130 g) / 130 g * 100 = 0%

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The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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