Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (a) x4 1 x5 5x3

The equation of the circle graphed below is (x - 1)² + (y - 1)² = 4.

To determine the equation of a circle, we need to know the coordinates of its center and the radius. The general equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

where (x,y) are the coordinates of any point on the circle. The equation shows that the distance between any point (x,y) on the circle and the center (h,k) is always equal to the radius r.

To determine the equation of the circle graphed below, we need to identify the coordinates of its center and the radius. One way to do this is to use the distance formula between two points. We can choose any two points on the circle and use their coordinates to find the distance between them, which is equal to the diameter of the circle. Then, we can divide the diameter by 2 to find the radius.

To find the radius, we can choose any point on the circle and use the distance formula to find the distance between that point and the center. We can use the point (5,1), which is on the right side of the circle. The distance between (5,1) and (1,1) is 4 units, which means that the radius is 2 units.

Substituting the values of (h,k) and r in the general equation of the circle, we get:

(x - 1)² + (y - 1)² = 4

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Answer:

D. 25

Step-by-step explanation:

16 divided by 64% is 25

Answer:

25

Step-by-step explanation:

Hope I helped you.

Answer: the answer to this is true

\( \Large{\boxed{\sf y = - \dfrac{5}{4}x - 9}} \)

\( \\ \)

First, let's recall what is an equation of a line in slope-intercept form:

\( \Large{\left[ \begin{array}{c c c} \underline{\tt Slope-Intercept \ Form \text{:}} \\ ~ \\ \tt y = mx + b \end{array} \right] } \)

Where:

\( \\ \)

Since we are given the value of the slope, we can subtitute it into the equation:

\( \sf y =- \dfrac{5}{4}x + b \)

\( \\ \)

We know that the line passes through (-8 , 1), which means that the coordinates of this point verify the equation of the line. Therefore, we can substitute its coordinates into the equation and solve for b:

\( \sf (\underbrace{\sf -8}_{x} \ , \ \overbrace{\sf 1}^{y} ) \\ \\ \\ \rightarrow \sf 1 = - \dfrac{5}{4} \cdot (-8) + b \\ \\ \\ \rightarrow \sf 1 = -\dfrac{5 \cdot (-8) }{4} + b \\ \\ \\ \rightarrow \sf 1 = -\dfrac{- 40}{4} + b \\ \\ \\ \rightarrow \sf 1 = 10 + b \\ \\ \\ \rightarrow \boxed{\sf b = -9} \)

\( \\ \)

Therefore, the equation of the line in slope-intercept form is:

\( \boxed{\boxed{\sf y = - \dfrac{5}{4}x - 9}} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

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To write the equation of a line in slope-intercept form, we can use the formula:

\(\qquad\Large\begin{aligned}\bigstar\:\boxed{\rm{\:\:y = mx + b\:\:}}\end{aligned}\)

where:

\(\\\)

As per the provided information, we know that the line passes through the point (-8, 1) and has a slope of -5/4, we can substitute these values into the equation to find the y-intercept.

\(\\\)

Let's solve for b:

\(\Large\quad\begin{aligned}\rm\dashrightarrow{y}& = \rm{mx + b} \\\\\rm\dashrightarrow{1}& = \rm{ {\large{-\frac{5}{4}}} \cdot -8 + b} \\\\\rm\dashrightarrow{1}& = \rm{{ \large{\frac{40}{4}}} + b} \\\\\rm\dashrightarrow{1}& = \rm{10 + b} \\\\\rm\dashrightarrow{b}& = \rm{1 - 10} \\\\\rm\dashrightarrow{b}& = \rm{-9}\end{aligned}\)

\(\\\)

Now that we have the slope m = -5/4 and the y-intercept b = -9, we can write the equation of the line:

\(\Large\quad\begin{aligned}\boxed{\boxed{\rm{\:\:y = -\dfrac{5}{4}x - 9\:\:}}}\: \overline{\quad} \: \large{\red{\sf{answer}}}\end{aligned}\)

\(\\\\\\\)

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Answer:

10 times greater, because 10x10=100

Step-by-step explanation:

Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.

Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.

To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).

The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.

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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%

Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.

To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.

We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.

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The amount of interest she will earn in one year will be 5 dollars and 12 cents.

The normal interest levied on the amount borrowed from any bank on a yearly basis is called the simple interest.

Given that:-

The simple interest amount will be:-

SI   =   (  P   x   R   x   T  )  / 100

SI  =    (  160   x   x   3.2   x   1  )  /   100

SI   =    $5.12

Therefore the amount of interest she will earn in one year will be 5 dollars and 12 cents.

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Answer:

c. no real solutions

Step-by-step explanation:

because the x's will not be there

Which of the following best describes the diameter of a circle?

1. A segment whose endpoints are points on the circle.

2. A chord which passes the center of the circle.

3. A segment joining the center and any point on the circle.

4. A line that passes through the circle at exactly two points.

Option 2. A chord which passes the center of the circle.

The values of the trigonometric functions are

7. \(sin\theta = \frac{12}{13}\)

\(cos\theta = \frac{5}{13}\)

\(tan\theta = \frac{12}{5}\)

\(csc\theta =\frac{13}{12}\)

\(sec\theta =\frac{13}{5}\)

\(cot\theta =\frac{5}{12}\)

8. \(sin\theta = \frac{\sqrt{7} }{4}\)

\(cos\theta = \frac{12}{16}\)

\(tan\theta =\frac{\sqrt{7} }{3}\)

\(csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}\)

\(sec\theta =\frac{16}{12}\)

\(cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}\)

From the question, we are to determine the values of the given trigonometric functions

7.

In the given triangle,

Opposite = 12

Adjacent = 5

Hypotenuse = ?

Hyp² = Opp² + Adj² (Pythagorean theorem)

∴ Hyp² = 12² + 5²

Hyp² = 144 + 25

Hyp² = 169

Hyp =√169

Hyp = 13

Using SOH CAH TOA

\(sin\theta = \frac{12}{13}\)

\(cos\theta = \frac{5}{13}\)

\(tan\theta = \frac{12}{5}\)

\(csc\theta =\frac{1}{sin\theta} =\frac{13}{12}\)

\(sec\theta =\frac{1}{cos\theta} =\frac{13}{5}\)

\(cot\theta =\frac{1}{tan\theta} =\frac{5}{12}\)

8.

Hypotenuse = 16

Adjacent = 12

Opposite = ?

Hyp² = Opp² + Adj² (Pythagorean theorem)

Opp² = Hyp² - Adj²

∴ Opp² = 16² - 12²

Opp² = 256 - 144

Opp² = 112

Opp =√112

Opp = 4√7

Using SOH CAH TOA

\(sin\theta = \frac{4\sqrt{7} }{16} = \frac{\sqrt{7} }{4}\)

\(cos\theta = \frac{12}{16}\)

\(tan\theta = \frac{4\sqrt{7} }{12}= \frac{\sqrt{7} }{3}\)

\(csc\theta =\frac{1}{sin\theta} =\frac{16}{4\sqrt{7} } = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}\)

\(sec\theta =\frac{1}{cos\theta} =\frac{16}{12}\)

\(cot\theta =\frac{1}{tan\theta} =\frac{12}{4\sqrt{7}} = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}\)

Hence, the values of the trigonometric functions are

7. \(sin\theta = \frac{12}{13}\)

\(cos\theta = \frac{5}{13}\)

\(tan\theta = \frac{12}{5}\)

\(csc\theta =\frac{13}{12}\)

\(sec\theta =\frac{13}{5}\)

\(cot\theta =\frac{5}{12}\)

8. \(sin\theta = \frac{\sqrt{7} }{4}\)

\(cos\theta = \frac{12}{16}\)

\(tan\theta =\frac{\sqrt{7} }{3}\)

\(csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}\)

\(sec\theta =\frac{16}{12}\)

\(cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}\)

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Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Step-by-step explanation:

As you know

\( a_{n} = a_{1} \times {r}^{n - 1} \)

1.

\(3 \times {3}^{4} = {3}^{5} \\ 3 \times {3}^{6} = {3}^{7} \\ 3 \times {3}^{8} = {3}^{9}\)

2.

\(2 \times {2}^{4} = {2}^{5} \\ 2 \times {2}^{6} = {2}^{7} \\ 2 \times {2}^{8} = {2}^{9}\)

3.

\( - \frac{1}{2} \times {( - 6)}^{4} = { \frac{ - 1}{2} } \times {6}^{4} \\ - \frac{1}{2} \times {( - 6)}^{6} = { \frac{ - 1}{2} } \times {6}^{6} \\ - \frac{ 1}{2} \times {( - 6)}^{8} = { \frac{ - 1}{2} } \times {6}^{8} \)

Answer:

$11.25

Step-by-step explanation:

The most important part of this equation is $1.50 a pound.

To find the pounds that equal to $11.25, I just multiplied. Since it's $1.50 per pound, no whole number will equal to $11.25. So, I tried 7.5

$1.50 x 7.5 = $11.25

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.

In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.

Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.

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Answer:

7/4

Step-by-step explanation:

\( \displaystyle\frac{2 + \sqrt{ - 3} }{2} ( \frac{2 - \sqrt{ - 3} }{2} )~~~~~~ \)

Evaluate.

Solution:

Rewrite it as,

Multiplying them,

Applying Distributive property,

Combining each terms,

Last Choice is accurate.

a. The numbers are 23 and -6.

b. The numbers are 22  /3 and - 20 / 3.

The sum of two numbers is 17 and there difference is 29. Therefore, let's find the two numbers as follows:

let the two numbers be x and y

Therefore,

x + y = 17

x - y = 29

add the equations

2x = 46

x = 46 / 2

x = 23

Therefore, let's find y

y = 17 - 23

y = -6

Therefore, the numbers are 23 and -6

b.

The sum of a number and twice a greater number is 8. The sum of the greater number and twice the lesser number is -6.

Therefore, let's find the numbers as follows:

x + 2y = 8

y + 2x = -6

Hence,

x + 2y = 8

2x + y = -6

multiply equation(ii) by 2

2x + 4y = 16

2x + y = -6

subtract the equations

3y = 22

y = 22 / 3

Let's find x

x = 8 - 2(22 / 3)

x = 8 - 44 / 3

x =  24 - 44/ 3

x = - 20 / 3

Therefore, the numbers are 22 / 3 and - 20 / 3

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Minimum sample size (n) = 15

To determine the minimum sample size required, we can use the formula:

n = (Zα/2 * σ / E)^2

Where:
- n is the minimum sample size
- Zα/2 is the z-score at the 95% confidence level, which is 1.96
- σ is the population standard deviation, which is given as 3.8
- E is the maximum error we can tolerate, which is 2 units in this case

Substituting the values, we get:

n = (1.96 * 3.8 / 2)^2
n = 27.44

Rounding up to the nearest whole number, we get a minimum sample size of 28.

Therefore, we need to sample at least 28 individuals from the normally distributed population to be 95% confident that the sample mean is within two units of the population mean, assuming a population standard deviation of 3.8.

To determine the minimum sample size required for a 95% confidence level, we'll need to use the following formula:

n = (Z * σ / E)^2

where:
- n is the minimum sample size
- Z is the Z-score corresponding to the desired confidence level (1.96 for a 95% confidence level)
- σ is the population standard deviation (3.8 in this case)
- E is the margin of error (2 units in this case)

Step 1: Identify the values
Z = 1.96 (from the 95% confidence level)
σ = 3.8
E = 2

Step 2: Plug the values into the formula
n = (1.96 * 3.8 / 2)^2

Step 3: Calculate the result
n = (7.528 / 2)^2
n = (3.764)^2
n ≈ 14.15

Since the sample size must be a whole number, round up to the nearest whole number to ensure the desired level of confidence is achieved.

Minimum sample size (n) = 15

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Answer:

1. tan20=y/600  

y=218.38ft

2.   8.08 ft

The expected value of a ticket in the given lottery game is -$0.60, indicating that, on average, a person can expect to lose $0.60 per ticket.

To calculate the expected value of a ticket, we need to multiply the value of each prize by its respective probability and sum them up.

For the grand prize of $4 million, the probability of winning is 1 divided by the total number of tickets sold, which is 1/3.5 million. Therefore, the contribution to the expected value from the grand prize is (1/3.5 million) * $4 million.

For the second prize of $30, there are 10,000 winners out of 3.5 million tickets sold, giving a probability of 10,000/3.5 million. The contribution from the second prize is (10,000/3.5 million) * $30.

Similarly, for the third prize of $5, there are 50,000 winners out of 3.5 million tickets sold, giving a probability of 50,000/3.5 million. The contribution from the third prize is (50,000/3.5 million) * $5.

To calculate the expected value, we sum up the contributions from each prize and subtract the cost of the ticket, which is $2.

The result is the expected value of -$0.60, indicating an average loss of $0.60 per ticket.

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There is a 0.32 probability that a resident will be too tall to enter the tent without bowing their head.

Based on the empirical rule, approximately 68% of the residents will have heights within one standard deviation (4.2 inches) of the mean (67.8 inches).

Therefore, the probability of a resident being too tall to enter the tent without bowing their head is approximately 32% (100% - 68%).

To express this probability as a decimal to the hundredths place, the answer is 0.32.

In conclusion, there is a 0.32 probability that a resident will be too tall to enter the tent without bowing their head.

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\(\textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{14}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{7} \end{cases} \\\\\\ x=\sqrt{ 14^2 - 7^2}\implies x=\sqrt{ 196 - 49 } \implies x=\sqrt{ 147 }\implies x\approx 12.12\)

To find the missing side in a right triangle, use the Pythagorean theorem.

In this question, we are given two sides of a right triangle, 14 and 7, and we need to find the missing side, which we'll call x. To solve for x, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Using the Pythagorean theorem, we can set up the following equation:

14^2 + 7^2 = x^2

Simplifying this equation, we get:

196 + 49 = x^2

x^2 = 245

Finally, taking the square root of both sides, we find that:

x = √245

Rounding to the nearest tenth, we get:

x ≈ 15.6

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Answer:  B.

200,237.36

Step-by-step explanation: just got it right on the quiz

The complete table of trigonometric functions:

Row 1: θ = π / 3, sin θ = √3 / 2, cos θ = 1 / 2, tan θ = √3

Row 2: θ = 5π / 4, sin θ = - √2 / 2, cos θ = - √2 / 2, tan θ = - 1

Row 3: θ = 7π / 6, sin θ = - 1 / 2, cos θ = √3 / 2, tan θ = - √3 / 3

In this problem we must complete a table with three angles, measured in radians, and three kinds of trigonometric functions (two fundamental function and a derivate function). The procedure to complete the table is shown below:

Now we proceed to complete the table of trigonometric functions:

θ = π / 3, sin θ = √3 / 2, cos θ = 1 / 2, tan θ = √3

θ = 5π / 4, sin θ = - √2 / 2, cos θ = - √2 / 2, tan θ = - 1

θ = 7π / 6, sin θ = - 1 / 2, cos θ = √3 / 2, tan θ = - √3 / 3

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Their sum plus their product has a maximum potential value of 420.

Given that the product of the two positive numbers and their sum is 39.

The highest feasible value of the total of their products must be determined.

Let's tackle this issue step-by-step:

Assume x and y are the two positive integers.

The product's sum is xy, while the two integers' sum is x + y.

The answer to the issue is 39, which is the product of the two integer sums and their sum.

\(\mathrm{xy + (x + y) = 39}\)

We need to maximize the value of to discover the biggest feasible value of the product of their sum and their product \(\mathrm {(x + y) \times xy}\).

Now, we can proceed to solve the equation:

\(\mathrm {xy + x + y = 39}\)

To make it easier to solve, we can use a technique called "completing the square":

Add 1 to both sides of the equation (1 is added to "complete the square" on the left side):

\(\mathrm {xy + x + y + 1 = 39 + 1}\)

Rearrange the terms on the left side to form a perfect square trinomial:

\(\mathrm{(x + 1)(y + 1) = 40}}\)

\(\mathrm{(x + 1)(y + 1) = 2 \times 2 \times 2 \times 5 }}\)

Now, we want to maximize the value of \(\mathrm {(x + y) \times xy}\), which is equal to \(\mathrm{(x + 1)(y + 1) + 1}\)

Finding the two positive numbers (x and y) whose sum is as close as feasible to the square root of 40, or around 6.3246, is necessary to maximize this value.

The two positive integers whose sum is closest to 6.3246 are 5 and 7, as 5 + 7 = 12, and their product is 5 × 7 = 35.

Finally, \(\mathrm {(x + y) \times xy}\)

= \((5 + 7) \times 5 \times 7\)

= 12 × 35

= 420

So, the largest possible value is 420.

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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The error message "x and y must have same first dimension but have shaped" typically occurs in programming languages such as Python or MATLAB when trying to operate on arrays or matrices with incompatible dimensions. In this case, the first dimension of the arrays or matrices must be the same, but they are not.

For example, if we have two arrays, x with shape (3, 4) and y with shape (2, 4), we cannot perform certain operations such as addition or multiplication between them because the first dimension, which represents the number of rows, is different.

To resolve this error, we can either reshape one of the arrays to have the same number of rows as the other, or we can transpose one of the arrays so that their dimensions match up. Another option is to adjust the code to ensure that the arrays being used have the same first dimension.

In summary, the "x and y must have the same first dimension but have shaped" error occurs when we attempt to operate on arrays or matrices with incompatible dimensions, and it can be resolved by reshaping, transposing, or adjusting the code.

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Answer:

True

Step-by-step explanation:

Statistics can add credibility to speech clims when used sparingly.

name me brainiest please.

True, statistics can add credibility to speech claims when used sparingly. By incorporating accurate and relevant statistics in a speech, you can support your arguments and demonstrate your knowledge on the subject. However, it is essential to use them sparingly to avoid overwhelming the audience and maintain their interest in your message.

Statistics, when used appropriately and sparingly, can add credibility to speech claims. By incorporating relevant and reliable statistical data, speakers can support their claims with objective evidence. Statistics have the potential to provide context, demonstrate trends, or highlight the magnitude of a particular issue, thereby strengthening the credibility and persuasiveness of the speaker's arguments.

However, it is important to use statistics accurately, ensuring they are from reliable sources, properly interpreted, and presented in a clear and understandable manner. Overusing statistics or relying solely on statistical evidence without considering other forms of supporting evidence may weaken the overall impact of the speech.

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First is to express all values the same way. For example, convert the fraction and percentage into decimal numbers:

60% → divide it by 100 and you get 0.6

7/11=0.63

Now you can order them

0.6<0.63<0.7

Using the original expressions you get that:

60%<7/11<0.7