what is the value of i^13

Answer:

5

Step-by-step explanation:

Since DE is tangent to the circle, that means DE is perpendicular to EF

==> DF = sqrt(4^2+3^2) = 5

The population mean is 37.64

The mean absolute deviation is 3.333

The ratio of mean absolute deviation to mean is 8.77%

Given,

The weights, in grams of a random sample of bananas;

39.8, 41.9, 42.8, 38.2, 35.1, 36.2, 37.1, 43.0, 37.8, 32.6, 30.3, 36.9

We have to find the mean, mean absolute deviation and mean absolute deviation to mean ratio;

Mean, m = sum of the terms ÷ number of terms

Mean, m = (39.8 + 41.9 + 42.8 + 38.2 + 35.1 + 36.2 + 37.1 + 43.0 + 37.8 + 32.6 + 30.3 + 36.9) ÷ 12

Mean, m = 451.7/12 = 37.64 ≈ 38.

Mean absolute deviation = 1/n ∑ | x - m |

Mean absolute deviation = (| 39.8 - 38 | + | 41.9 - 38| + | 42.8 - 38 | + | 38.2 - 38 | + | 35.1 - 38 | + | 36.2 - 38 | + | 37.1 - 38 | + | 43.0 - 38 | + | 37.8 - 38 | + | 32.6 - 38 | + | 30.3 - 38 | + | 36.9 - 38 | ) / 12

Mean absolute deviation = (2 + 4 + 5 + 1 + 3 + 2 + 1 + 5 + 1 + 6 + 8 + 2) / 12

Mean absolute deviation = 40/12 = 3.333

Mean absolute deviation to mean ratio = (3.333/38) × 100 = 8.77%

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Answer: Null hypotheses \(H_{0}\) :μ = 12

Alternative hypotheses \(H_{1} :\) μ \(\neq\) 12

Null hypothesis : The null hypotheses in scientific inquiry is the assertion that there is no association between the two sets of data or variables being analyzed. The term "null" comes from the idea that any empirically observed difference is only the result of chance and that no causal relationship can be inferred. It is denoted by \(H_{0}\)

Alternative hypotheses : An alternative hypotheses states that two variables have a statistically significant link. In contrast, the null hypotheses claims that there is no statistical connection between the two variables. We frequently encounter numerous kinds of hypotheses when studying statistics. A working statement that is assumed to be reasonable with the available data is what a statistical hypotheses is supposed to be. A hypotheses is neither regarded true nor untrue, it should be noted. It is denoted by \(H_{1}\)

Given: Coke mean volume(x)  =  12.19 oz.

Significance level = 0.01,  Number of cans (n) = 36

Standard deviation ( σ) = 0.11 oz.  Can mean volume (μ) = 12 oz.

Solution: the test static  Z = (x-μ)/(σ/√n) = (12.19-12)/(0.11/√36) = \(\frac{12.19-12}{0.0183} = 10.38\)

So, for test -static Z = 10.38, the p-value will be  p = 0.0001 [ from Z-score table at 0.01 significance level].  Since the p-value is less than 0.01 i.e.

0.0001 < 0.01,  so the result is significant at p < 0.01, so we can reject the null hypotheses and conclude that the cans of regular coke do not have volumes with a mean of 12 oz. as stated on the label.

Hence , the null hypothesis is \(H_{0}\): μ=12 and  alternative hypotheses \(H_{1}:\) μ\(\neq 12\)

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Answer:

-5 and a y- intercept of 2

⁂ We know in factorization we have three options :

1. Taking out common.

2. Applying Identity.

3. Middle term breaking method.

⁂ First we will see which method we will apply :

We will use second identity which is :

\((a-b)^2=a^2-2ab-b^2\)

\(\rule{190pt}{2pt}\)

⁂ Solution :

\({\sf{p^{2}-10 p+25}\\\)

\({\sf{p^{2}+2 (p)(5)+5^{2}}\\\)

\({\sf{(p-5)^2\)

\(\rule{190pt}{2pt}\)

⁂ Answer :

\({\sf{\large{(p-5)^2}}}\)

Answer:

No they are not equivalent.

Step-by-step explanation:

2(x - 2) + 3

First distribute the 2. It goes to both the x and also to the - 2

= 2x - 4 + 3

Add - 4 + 3

= 2x - 1

This is not equal to 2x - 7

The quarterly operating profit margin of TMG Ltd over the past six years is provided in Table 4.1, indicating the financial performance of the business during that period.

In order to assess the impact of the intervention strategy introduced by the current CEO three years ago, the board of directors (BOD) of TMG Ltd has contracted a researcher to analyze the data and determine if there have been significant improvements in the business outcomes. The quarterly operating profit margin serves as the unit of analysis for this evaluation.

Table 4.1 allows the researcher to examine the trend and fluctuations in the quarterly operating profit margin over the six-year period. By analyzing the data, the researcher can identify any noticeable changes in the financial performance of TMG Ltd, particularly after the implementation of the intervention strategy. The BOD is interested in understanding whether the strategy has resulted in improved profitability and overall financial health of the company.

The researcher will likely perform statistical analysis, such as calculating averages, trends, and identifying any significant variations, to draw conclusions about the effectiveness of the intervention strategy. By comparing the quarterly operating profit margin before and after the strategy's implementation, the researcher can assess whether the new CEO's efforts have had a positive impact on the company's financial performance.

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Answer:

Step-by-step explanation:

The point-slope form of the equation of a line is:

\(y-y_1=m(x-x_1)\)

So, the equation for this problem, let

\((x_1,y_1)=(2,-1)\)

then,

\(y-(-1)=m(x-2)\\y+1=m(x-2)\)

If line (a) is perpendicular to line (b), then \(m_b\) is equal to \(-\frac{1}{m_a}\).  For this problem, let

\(m_a=-\frac{1}{2}\) and \(m_b=2\)

So,

\(y+1=(2)(x-2)\\y+1=2x-4\\(y+1)-1=(2x-4)-1\\y=2x-5\)

Answer:

?

Step-by-step explanation:

Answer:

$4.80/2sodas

4.80/2=2.40

C. 2.40 per soda

The probability that both Dexter and Darwin win a bagel is (1/8) x (1/7) = 1/56.

The probability that both Dexter and Darwin win a bagel is 1 in 56. This means that, out of the 8 people who have entered the lottery, only one combination of 4 people will result in both Dexter and Darwin winning. To calculate this probability, you need to take the probability of Dexter winning (1/8) and multiply it by the probability of Darwin winning (1/7). This is because the probability of both events happening together is equal to the product of the probabilities of the two events. Since there are 8 people in the lottery, the probability of Dexter winning is 1/8 and the probability of Darwin winning is 1/7. Therefore, the probability that both Dexter and Darwin win a bagel is (1/8) x (1/7) = 1/56.

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The exact value of the expression 4cos²(60)24csc²(45) is 12.

To find the exact value of the expression 4cos²(60)24csc²(45), we need to evaluate each trigonometric function separately and then substitute the values into the expression.

Let's start with cos²(60). The cosine of 60 degrees is equal to 1/2, so we have:

cos²(60) = (1/2)² = 1/4

Next, let's consider csc²(45). The cosecant of 45 degrees is equal to the square root of 2 divided by 2, so we have:

csc²(45) = (√2/2)² = 2/4 = 1/2

Now, we can substitute these values into the original expression:

4cos²(60)24csc²(45) = 4(1/4)24(1/2) = 1(24)(1/2) = 12

Therefore, the exact value of the expression 4cos²(60)24csc²(45) is 12.

It's important to note that we used the specific values of the trigonometric functions at the given angles (60 degrees and 45 degrees) to evaluate the expression. The final result is a numerical value without any variables.

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Answer:

c, d.

Step-by-step explanation:

c; A vertical stretch by 4 will put the coefficient (in this case 4) in front of your original equation.

d; the negative in front of the whole equation (-4x) will flip the graph across the x-axis.

The equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection is: y = -3x - 6.

To find the equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection, we need to determine the derivative of the function and evaluate it at the point of inflection. First, let's find the derivative of y with respect to x: dy/dx = 3x^2 + 6x. The point of inflection occurs where the second derivative of the function changes sign. Taking the derivative of dy/dx, we have: d^2y/dx^2 = 6x + 6. Setting d^2y/dx^2 equal to zero and solving for x, we find: 6x + 6 = 0; x = -1.  At x = -1, the point of inflection is (-1, y) on the original function. To find the slope of the tangent line at this point, we substitute x = -1 into the derivative: dy/dx = 3(-1)^2 + 6(-1) = -3. So, the equation of the line tangent to the function at its point of inflection is: y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values, we have: y = -3x + b

To find b, we substitute the coordinates of the point of inflection (-1, y):y = -3(-1) + b; y = 3 + b. Since the point of inflection lies on the line, we can substitute the y-value and solve for b: 3 + b = x^3 + 3x^2 + 2; b = -6. Therefore, the equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection is: y = -3x - 6.

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Answer:

12

Step-by-step explanation:

No. of red flyers = 6

No. of blue flyers = 4

We need to find the minimum number of flyers of each color if she gave out the same number of red and blue flyers. For this we must find the LCM of 6 and 4.

Prime factorization of 6 = 2×3

Prime factorization of 4 = 2×2

Lowest common multiple of 6 and 4 = 12

Hence, there are 12 minimum number of flyers of each color

You have to double 1 and 50 to get 2 and 100

1:50 = 2:100

1x2=2

50x2=100

So the statement, if she studied for 2 hours, she would have gotten 100%,  makes sense

Hope this helps!

The n-point DFT of the signal x[n] = ax1[n] + bx2[n] is given by the linear combination of the individual DFTs: X[k] = a * X1[k] + b * X2[k], where X[k] is the n-point DFT of x[n], X1[k] is the n-point DFT of x1[n], X2[k] is the n-point DFT of x2[n], and a and b are constants.

The Discrete Fourier Transform (DFT) is a mathematical transformation that converts a discrete-time signal from the time domain to the frequency domain. When we have two signals x1[n] and x2[n] with their respective n-point DFTs X1[k] and X2[k], we can combine them in a linear manner to obtain the DFT of their sum or scaled versions.

In the case of x[n] = ax1[n] + bx2[n], where a and b are constants, we can apply the DFT to both sides of the equation. By linearity property of the DFT, the DFT of the left-hand side (x[n]) can be expressed as the sum of the DFTs of the individual terms on the right-hand side (ax1[n] and bx2[n]).

Thus, the n-point DFT of x[n], denoted as X[k], is given by the linear combination of the individual DFTs:

X[k] = a * X1[k] + b * X2[k],

This equation states that each frequency bin of the DFT of x[n] is obtained by multiplying the corresponding frequency bin of the DFTs of x1[n] and x2[n] by their respective constants (a and b), and then summing these contributions.

In summary, the DFT of a linear combination of signals can be computed by taking the corresponding linear combination of their individual DFTs.

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Answer:

7.171428571

Step-by-step explanation:

<3

Answer:

-2x+19

Step-by-step explanation:

We open the parentheses, so

-12x+15+10x+4

Simplify

-2x+19

If the dot indicates the center of the circle, the equation that must be true is

The diameter of the semicircle is shown by line segment bearing the dot at the center.

By drawing a line from each end of the diameter to any location on the semicircle, the inscribed angle is created anywhere you perform this is a 90-degree angle will result.

This mean that angle B = angle A = 90 degrees

hence there addition is 180 degrees

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Answer:

The answer is 3(3m-2)^2

Step-by-step explanation:

We have the following expression:

\( {27m}^{2} - 36m + 12\)

We can take common factor 3 and we got.

\(3( {9m}^{2} - 12m + 4)\)

We can factorize and we got:

\(3(3m - 2)(3m - 2)\)

Then the final answer is:

\(3(3m { - 2})^{2} \)

Given:

The function is:

\(f(x)=x^3-4x^2-37x+40\)

\(f(8)=0\)

To find:

The all of the zeros of f(x) algebraically.

Solution:

We have, \(f(8)=0\) is means 8 is a zero of given function and (x-8) is a factor of given function.

The function is:

\(f(x)=x^3-4x^2-37x+40\)

Spittle the middle terms in such a way so that we get (x-8) as a common factor.

\(f(x)=x^3-8x^2+4x^2-32x-5x+40\)

\(f(x)=x^2(x-8)+4x(x-8)-5(x-8)\)

\(f(x)=(x^2+4x-5)(x-8)\)

Spittle the middle term of the quadratic expression, we get

\(f(x)=(x^2+5x-x-5)(x-8)\)

\(f(x)=(x(x+5)-1(x+5))(x-8)\)

\(f(x)=(x+5)(x-1)(x-8)\)

For zeros, \(f(x)=0\).

\((x+5)(x-1)(x-8)=0\)

\((x+5)=0\text{ and }(x-1)=0\text{ and }(x-8)=0\)

\(x=-5\text{ and }x=1\text{ and }x=8\)

Therefore, the all zeros of the given function are -5, 1 and 8.

Answer: Im not very good at this but from what i do know, a shuold be inverses and b isnt. im probaly wrong so dont take my word for it

Step-by-step explanation:

The annual percent birth rate is 0.576% of the population.

The total number of population in the city in that particular month is given by = 2,500,000

And given the number of babies born in that month in that city is given by = 1200.

If we consider the rate of new born is same then the number of new born babies in that city in that year is = 1200*12 = 14400

Fraction of number of new born babies to the total population of that city in that year is = 14400/2500000 = 18/3125

Thus the percentage of the number of new born babies to the total population of that city in that year is = (18/3125) * 100% = 0.576%.

Hence the annual percent birth rate is 0.576% of the population.

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Answer:

a, b, e

Step-by-step explanation:

They all have angles that are less than 90°.

Answer:

? =30

Step-by-step explanation:

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

sin theta = opp / hyp

sin ? = 25/50

Taking the inverse sin of each side

sin ^-1( sin ?) = sin^-1 ( 1/2)

? =30

Answer:

4

Step-by-step explanation:

4 + 4 + 4 + 4 = 16

16 + 3.50 = 19.50

the 50¢ left is for taxes

The maximum number of pints of raspberries she can buy without spending more than $20 is 4 .

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

According to the question

Mandalee went to a fruit stand to spend on berries = $20

She bought 1 pint of blueberries = $3.50

she bought 1 pint of raspberries =  $4.00

Now,

the number of pints of raspberries = x

inequality represents the maximum number of pints of raspberries she can buy without spending more than $20

i.e

3.50 + 4x < 20

4x < 16.5

x < 4.125

therefore

she can buy 4 raspberries pints .

Hence, the maximum number of pints of raspberries she can buy without spending more than $20 is 4 .

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Answer:

THE CORRECT ANSWER IS THE SECOND CHOICE "BURGER IS 4 DOLLARS AND FRENCH FRIES ARE 3 DOLLARS"

The point be (9, -4) and slope = -2/3 the slope of the equation of line be y = -2x/3 +2

What is meant by slope of the line?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. While there has been no net change in the x coordinate, there has been no net change in the y coordinate.

The slope is m and the y-intercept is b in the slope-intercept version of the equation (y=mx+b). We can also change some equations to be written in slope-intercept form.

Let the equation be y - (-4) = (-2/3)(x - 9)

y + 4 = -2 x/3 + 6

simplifying the equation, we get

y = -2x/3 + 6 - 4

Therefore, the slope of the equation be y = -2x/3 +2

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What is the point of . (9, -4); slope = -2/3

Check the picture below.