I think I know the steps to Completing the Square (quadratics) but I'm not entirely sure. Please tell me if these steps are correct, and if they aren't, please tell me what is incorrect about them:

1. Separate the constant term from the variables
2. Factor out the coefficient of the x² term
3. Divide the middle term by the leading coefficient, then square the result
4. Simplify by combining like terms
5. Factor the perfect square trinomial formed on the left side
6. Divide both the left and right side of the equation by 2
7. Do inverse operations to remove the squared sign and its effects
8. Solve remaining equation for x

Answer:

Step-by-step explanation:

Given the equation of a line expressed as y = 3x-1, we are to find y = f(x) for the following values of x in the table.

If y = 3x-1, then f(x) = 3

When x = -1

f(-1) = 3(-1)-1

f(-1) = -3-1

f(-1) = -4

Hence when x = -1, f(x) = -4

When x = 0

f(0) = 3(0)-1

f(0) = 0-1

f(0) = -1

Hence when x = 0, f(x) = -1

When x = 2

f(2) = 3(2)-1

f(2) = 6-1

f(2) = 5

Hence when x = 2, f(x) = 5

Answer:

0.5b + 1.5p ≤ 8

Step-by-step explanation:

The inequality function is as follows:

Let us assume the number of bananas acquired be b

And, the number of peaches acquired be p

Cost of each banana be $0.50

ANd, the cost of each peach be $1.50

Also the total would be $8

The possible values of banana is 0.5b

And, for peaches it would be 1.5p

So, the inequality function is

0.5b + 1.5p ≤ 8

Answer:

0.5b + 1.5p ≤ 8

Step-by-step explanation:

Answer: The answer is 226.2 feet.

Step-by-step explanation: The formula to find the total surface area of a cylinder is 2\(\pi\) x radius squared x height. If you use the formula you will get 226.19 feet as your answer and I rounded that to 226.2 feet.

UR MOM

Step-by-step explanation:

You can remember the commutative property by thinking of the numbers "commuting," or changing places. The example shows us that "negative two plus positive four" is the same as "positive four plus negative two.

The probability that the number of 0's in a randomly generated bit string of length 8 is different from the number of 1's is 56/256, or 7/32.

To understand why, let's consider the possible combinations of 0's and 1's in an 8-bit string. There are a total of 2^8 = 256 possible outcomes. Out of these, we need to determine the number of outcomes where the number of 0's and 1's is different.

One way to approach this is by counting the number of strings with 4 zeros and 4 ones, and then subtracting it from the total number of outcomes. The number of ways to arrange 4 zeros and 4 ones is given by the binomial coefficient C(8,4) = 70. Thus, there are 70 outcomes where the number of 0's and 1's is equal.

Subtracting this from the total number of outcomes, we get 256 - 70 = 186 outcomes where the number of 0's and 1's is different. Therefore, the probability of having an unequal number of 0's and 1's is 186/256, which simplifies to 7/32, or approximately 21.9%.

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Answer:

8 inches from beginning to end

Step-by-step explanation:

8 inches because 1 times 8 is 8

Answer:

First one is A. \(2x^{3} + 1\)

Second one is D. \(8x^{3} + 24x^{2} +24x + 8\)

Step-by-step explanation:

Edge 2020

Answer:

d on edge

Step-by-step explanation:

The ordered pairs representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

Given, the ordered pairs representing the vertices of the polygon.

as, the given ordered pairs are

(-11, 13) , (1, -1) , (1/4 , 2(2/1)) , (1,-3).

Now, from the given ordered pairs

the pairs which are representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

So, the ordered pairs representing the vertices of a polygon are (-11, 13) ,

(1, -1) and (1,-3).

Hence, the ordered pairs representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

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Answer:

d. 18

Step-by-step explanation:

Lengths AG and CF of the parallelogram are equal.

i.e AG = CF

where AG = 2x + 10

          CF = 5x -2

→ 2x + 10 = 5x-2

(collecting like terms): 5x - 2x = 10 + 2

→ 3x = 12

x=12÷3 = 4

∴ CF = 5x -2 = 5(4) -2 = 20 - 2 = 18

∴ CF = 18 (answer)

The P-value for the hypothesis test is approx. 0.7064.

To find the P-value for the hypothesis test, we need to perform a two-sample proportion test. The formula to calculate the test statistic for this test is given by:

\(\[ z = \frac{{(\hat{p}_1 - \hat{p}_2) - 0}}{{\sqrt{\hat{p}(1 - \hat{p})\left(\frac{1}{{n_1}} + \frac{1}{{n_2}}\right)}}} \]\)

where \(\hat{p}_1\) and \(\hat{p}_2\) are the sample proportions, \(\hat{p}\) is the combined sample proportion, \(n_1\) and \(n_2\) are the sample sizes, and 0 is the hypothesized difference in proportions.

In this case, we have \(n_1 = 50\), \(x_1 = 8\) (number of successes in sample 1), \(n_2 = 50\), and \(x_2 = 7\) (number of successes in sample 2).

First, we calculate the sample proportions:

\(\[ \hat{p}_1 = \frac{x_1}{n_1} = \frac{8}{50} = 0.16 \]\)

\(\[ \hat{p}_2 = \frac{x_2}{n_2} = \frac{7}{50} = 0.14 \]\)

Next, we calculate the combined sample proportion:

\(\[ \hat{p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{8 + 7}{50 + 50} = 0.15 \]\)

Then, we calculate the standard error:

\(\[ SE = \sqrt{\hat{p}(1 - \hat{p})\left(\frac{1}{{n_1}} + \frac{1}{{n_2}}\right)} = \sqrt{0.15(1 - 0.15)\left(\frac{1}{50} + \frac{1}{50}\right)} \approx 0.0529 \]\)

Finally, we calculate the test statistic:

\(\[ z = \frac{(\hat{p}_1 - \hat{p}_2) - 0}{SE} = \frac{(0.16 - 0.14) - 0}{0.0529} \approx 0.3772 \]\)

To find the P-value, we look up the test statistic in the standard normal distribution table. In this case, the P-value is the probability of observing a test statistic greater than 0.3772 or less than -0.3772.

Consulting the table, we find that the P-value is approximately 0.7064. Therefore, the P-value for the hypothesis test is approximately 0.7064.

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Answer:

17

Step-by-step explanation:u will make the second fraction postive it will be 12+4 which is 16 and a half plus a half is a whole

Answer: 17

Step-by-step explanation:

Square root of one hundred and seventy is greater than square root of one hundred and sixty eight.

A perfect square number is a number which when taken square root comes out as an integer.Every number which is not a perfect square when taken square root of it is irrational number.We can obtain square root of a perfect square number by prime factorisation method.

Given we have to compare \(\sqrt{170}\) and \(\sqrt{168}\).

We know that if the square roots are not given then we have easily concluded that 170 > 168.Same in the case of square root:

\(\sqrt{170} > \sqrt{168}\).

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\(y > 2x + 1 \\ 3 > 2(1) + 1 \\ 3 > 3 \\ false\)

\(y < - 3x \\ 3 < - 3(1) \\3 < - 3 \\ also \: false\)

Answer: \(x=13, y=132\)

Step-by-step explanation:

Using the same-side interior angles theorem, \(y=132\).

Using the alternate interior angles theorem, \(5x-17=48 \implies x=13\)

The experimental probability that the next customer to come into Kurt's boutique wears a size medium is 0.25, or 25%.

To calculate the experimental probability that the next customer to come into Kurt's boutique wears a size medium, follow these steps:

1. Find the total number of customers: Add the number of medium-sized customers (15) to the number of customers wearing different sizes (45).

Total customers = 15 (medium) + 45 (different sizes) = 60

2. Calculate the experimental probability: Divide the number of medium-sized customers (15) by the total number of customers (60).

Probability (medium) = 15 (medium) / 60 (total customers) = 0.25

So, the experimental probability that the next customer to come into Kurt's boutique wears a size medium is 0.25, or 25%.

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The 98% confidence interval for the number of chocolate chips per cookie in Big Chip cookies is approximately 13.5529 to 15.0471 chips.

To find the 98% confidence interval for the number of chocolate chips per cookie in Big Chip cookies, we'll use the t-distribution since the sample size is relatively small (n = 61) and we don't know the population standard deviation.

The formula for the confidence interval is:

\(CI = \bar X \pm t_{critical} \times \dfrac{s } {\sqrt{n}}\)

where:

X is the sample mean,

\(t_{critical\) is the critical value for the t-distribution corresponding to the desired confidence level (98% in this case),

s is the sample standard deviation,

n is the sample size.

First, let's find the critical value for the t-distribution at a 98% confidence level with (n-1) degrees of freedom (df = 61 - 1 = 60). You can use a t-table or a calculator to find this value. For a two-tailed 98% confidence level, the critical value is approximately 2.660.

Given data:

X (sample mean) = 14.3

s (sample standard deviation) = 2.2

n (sample size) = 61

\(t_{critical\) = 2.660 (from the t-distribution table)

Now, calculate the confidence interval:

\(CI = 14.3 \pm 2.660 \times \dfrac{2.2} { \sqrt{61}}\\CI = 14.3 \pm 2.660 \times \dfrac{2.2} { 7.8102}\\CI = 14.3 \pm 0.7471\)

Lower bound = 14.3 - 0.7471 ≈ 13.5529

Upper bound = 14.3 + 0.7471 ≈ 15.0471

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Answer:

X=15

Step-by-step explanation:

Answer:

84 inches

Step-by-step explanation:

12 inches are in 1 foot, so you take the number of feet (28) and multiply by the number of inches in a foot (12)

28×12=336 (inches)

then you take 336 and divide by 4 to get your 4 equal pieces.

336 divided by 4 = 84, 84 inches

a) The null hypothesis (H₀) is u1 ≤ u2, and the alternative hypothesis (Ha) is u₁ > u₂. b) Since the alternative hypothesis is u1 > u2, the rejection region is t > t₀, where t0 is the critical value for a one-tailed test with a significance level of 0.025. c) The value of t is approximately 0.814. d) We compare the calculated test statistic (t) with the critical value (t₀) to make a decision. If t > t₀, we reject the null hypothesis; otherwise, we fail to reject it. e) If the null hypothesis is rejected, it means there is enough evidence to support the personnel director's.

a) The claim made by the personnel director is that the mean annual income is greater in County A than in County B. This corresponds to the alternative hypothesis (Ha), which states that u₁ > u₂

b) To find the critical value(s) and rejection region(s), we need to perform a one-tailed t-test with a significance level of 0.025. Since the sample sizes are small (n₁ = 13, n₂ = 11) and the population variances are assumed to be unequal, we use the t-distribution. The critical value can be found using a t-table or calculator.

c) To find the standardized test statistic (t), we use the formula: t = (x₁ - x₂) / √((s₁²/n1) + (s₂²/n₂)), where x₁ and x₂ are the sample means, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.

Plugging in the values:

t = (42200 - 39800) / √((9000²/13) + (5200²/11))

√((9000²/13) + (5200²/11)) = √((81000000/13) + (27040000/11))

= √(6230769.23 + 2458181.82)

= √(8688951.05)

= 2949.15

Now, let's substitute the values into the formula:

t = (42200 - 39800) / 2949.15

= 2400 / 2949.15

≈ 0.814

d) To make a decision, we compare the calculated test statistic (t) with the critical value (t₀). If t > t₀, we reject the null hypothesis; otherwise, we fail to reject it.

e) If the null hypothesis is rejected, it means there is enough evidence to support the personnel director's claim that the mean annual income is greater in County A than in County B. Conversely, if the null hypothesis is not rejected, there is not enough evidence to support the claim.

To complete the calculation, we need to determine the critical value and compare it with the calculated test statistic. The critical value can be obtained from a t-table or calculator based on the degrees of freedom (df) and the significance level (α = 0.025).

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(a) Forecast: Linear regression  the next year is approx 191.6007.

(b) MSE: Mean Squared Error is approximately 249.1585.

(c) MAPE: Mean Absolute Percent Error is approximately 10.42%.

(a) (a) Forecast using linear regression:
To forecast the number of disk drives for the next year, we can use linear regression to fit a line to the given data points. The linear regression equation is of the form y = mx + b, where y represents the number of disk drives and x represents the year.

Calculating the slope (m):
m = (Σ(xy) - n(Σx)(Σy)) / (Σ(x^2) - n(Σx)^2)

Σ(xy) = (1)(140) + (2)(160) + (3)(190) + (4)(200) + (5)(210) = 2820
Σ(x) = 1 + 2 + 3 + 4 + 5 = 15
Σ(y) = 140 + 160 + 190 + 200 + 210 = 900
Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) + (5^2) = 55

m = (2820 - 5(15)(900)) / (55 - 5(15)^2)
m = (2820 - 6750) / (55 - 1125)
m = -3930 / -1070
m ≈ 3.6729

Calculating the y-intercept (b):
b = (Σy - m(Σx)) / n
b = (900 - 3.6729(15)) / 5
b = (900 - 55.0935) / 5
b ≈ 168.1813

Using the equation y = 3.6729x + 168.1813, where x represents the year, we can predict the number of disk drives for the next year. To do so, we substitute the value of x as the next year in the equation. Let's assume the next year is represented by x = 6:

y = 3.6729(6) + 168.1813
y ≈ 191.6007

Therefore, according to the linear regression model, the predicted number of disk drives for the next year is approximately 191.6007.

(b) Calculation of Mean Squared Error (MSE):

To calculate the Mean Squared Error (MSE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 = 171.8542
Year 2: y = 3.6729(2) + 168.1813 = 175.5271
Year 3: y = 3.6729(3) + 168.1813 = 179.2000
Year 4: y = 3.6729(4) + 168.1813 = 182.8729
Year 5: y = 3.6729(5) + 168.1813 = 186.5458
Next, we calculate the squared difference between the predicted and actual values, and then take the average:

MSE = (Σ(y - ŷ)^2) / n

MSE = ((140 - 171.8542)^2 + (160 - 175.5271)^2 + (190 - 179.2000)^2 + (200 - 182.8729)^2 + (210 - 186.5458)^2) / 5

MSE ≈ 249.1585

The Mean Squared Error (MSE) for the linear regression model is approximately 249.1585.

This value represents the average squared difference between the predicted values and the actual values, providing a measure of the accuracy of the model.

(c) Calculation of Mean Absolute Percent Error (MAPE):

To calculate the Mean Absolute Percent Error (MAPE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 ≈ 171.8542
Year 2: y = 3.6729(2) + 168.1813 ≈ 175.5271
Year 3: y = 3.6729(3) + 168.1813 ≈ 179.2000
Year 4: y = 3.6729(4) + 168.1813 ≈ 182.8729
Year 5: y = 3.6729(5) + 168.1813 ≈ 186.5458

Next, we calculate the absolute percent error for each year, which is the absolute difference between the predicted and actual values divided by the actual value, multiplied by 100:

Absolute Percent Error (APE):

Year 1: |(140 - 171.8542) / 140| * 100 ≈ 18.467
Year 2: |(160 - 175.5271) / 160| * 100 ≈ 9.704
Year 3: |(190 - 179.2000) / 190| * 100 ≈ 5.684
Year 4: |(200 - 182.8729) / 200| * 100 ≈ 8.563
Year 5: |(210 - 186.5458) / 210| * 100 ≈ 11.682
Finally, we calculate the average of the absolute percent errors:

MAPE = (APE₁ + APE₂ + APE₃ + APE₄ + APE₅) / n

MAPE ≈ (18.467 + 9.704 + 5.684 + 8.563 + 11.682) / 5 ≈ 10.42

The Mean Absolute Percent Error (MAPE) for the linear regression model is approximately 10.42%.

This value represents the average percentage difference between the predicted values and the actual values, providing a measure of the relative accuracy of the model.

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The probability of obtaining a 1 on a fair six-sided die is 1/6 or approximately 0.1667, assuming each outcome is equally likely.

While moving a bite the dust, there are six potential results, each comparing to one of the essences of the block numbered 1 to 6. In the event that the kick the bucket is fair, every result is similarly logical, and the likelihood of acquiring a specific result is given by the quantity of ways that result can happen partitioned by the complete number of potential results. Since there is just a single face numbered 1, the quantity of ways of getting a 1 will be 1, and the all out number of potential results is 6. Hence, the likelihood of getting a 1 while moving a pass on is 1/6 or roughly 0.1667. Overall, we would hope to get a 1 on one out of each and every six rolls of the kick the bucket, it is reasonable to expect it.

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Answer:

Using letter grades (a, b, c, d, and f) to classify student performance is an example of measurement on an ordinal scale of measurement.

Explanation:

The given problem states that using letter grades (a, b, c, d, and f) to classify student performance is an example of measurement on an ordinal scale of measurement.

What is a nominal scale of measurement?

The nominal scale of measurement is the classification of a variable into different categories and does not possess any specific or recognizable order or structure. For example, gender, nationality, race, religion, language, and so on can be the nominal scale of measurement.

What is an ordinal scale of measurement?

The ordinal scale of measurement is a type of categorical scale of measurement in which data can be ranked or arranged in some sort of order, but the distance between each of the data points is undefined or unknown. For example, the order of finishing places in a race (first, second, third, and so on) is a perfect example of an ordinal scale of measurement.

What is an interval scale of measurement?

An interval scale is a numerical measurement scale in which the intervals between the measurements are equivalent in value. For example, if you measure temperature in Celsius or Fahrenheit, the difference between 20 and 30 degrees Celsius or Fahrenheit is the same as the difference between 30 and 40 degrees Celsius or Fahrenheit.

What is a ratio scale of measurement?

A ratio scale is a measurement scale that has an absolute zero point and provides data with an equal interval of value. For example, weight, height, and duration are all measured on a ratio scale, since they all have an absolute zero point, unlike the temperature in Celsius and Fahrenheit scales.

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Answer:

x=12.3

Step-by-step explanation:

Yan po Ang x

pa brainlest po

pa follow po

pa heart and 5 star

pls

Answer:

your answer would be 9753/1000

Step-by-step explanation:

2 1/3-1.5x=12.3

step 1:

to solve for x. You have to add 2 1/3 to 12.3 and get x by itself.

2 1/3+ 12.3= 14.63..

step 2 :

now that you have x by itself you're going to divide both sides by x which is -1.5x.

-1.5x/ -1.5x     14.63/ -1.5  =  9.753  

step 3:

to put 9.753 in a fraction get rid of the decimal and put it over 1000 since there are 3 numbers after the decimal point.

so your final answer is 9753/1000

-

Answer:

V = 50.3 in ^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the radius is 2 and the height is 4

V = (3.14) * (2)^2 * 4

V =50.24

Rounding to the nearest tenth

V = 50.3 in ^2

We will multiply by 26 / 31 in the first number to get second number for fraction in simplest form.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Given that;

In the fraction,

The first number = 62

The second number = 52

Let the number which can be multiply by the fraction = x

Since, The given condition is,

Multiply the first number by to get the second number.

So, We can formulate;

⇒ 62 × x = 52

Solve for x, as;

⇒ 62 × x = 52

⇒ 62x = 52

Divide by 62, we get;

⇒ x = 52 / 62

Multiply and divide by 2;

⇒ x = 26 / 31

Therefore,

We will multiply by the number 26 / 31 in the first number to get second number for fraction in simplest form.

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Answer: Two equivalent ratios form a proportion. Equivalent ratios have the same value.

Answer:

1.) 60

2.) 36

3.) -9

4.) 74

5.) -36

6.) \(\frac{2}{6} =\frac{1}{3}\)

Step-by-step explanation:

1.) 2×3[7+(6÷2)]

2×3[7+3]

2×3×10

2×30

60

2.) 3[-3(2-8)-6]

3[-3(-6)-6]

3[18-6]

3×12

36

3.) 3×3[2-(9÷3)]

3×3[2-3]

3×3[-1]

3×3×-1

9×-1

-9

4.) 2[-5(4-12)-3]

2[-5(-8)-3]

2[40-3]

2×37

74

5.) [(3×3)-(30÷6)]+(-27)-13

[9-5]+(-27)-13

4-27-13

4-40

-36

6.) 2÷[(4÷2)+(32÷8)]

2÷[2+4]

2÷6

\(\frac{2}{6} =\frac{1}{3}\)

Hope this helps!

Answer: 6.25^12

Step-by-step explanation: