The sum of two numbers is -12.6 identify the two negative addends that make the statement true

The answer is (b) The margin of error will be about 2 times larger.

The margin of error in a confidence interval is affected by the sample size, so decreasing the sample size will generally increase the margin of error. Specifically, the margin of error is inversely proportional to the square root of the sample size.

That is, if we reduce the sample size by a factor of k, then the margin of error will increase by a factor of sqrt(k).

In this case, the original sample size was 1000, and the proposed sample size is 250, which is 1/4 of the original size. Therefore, the margin of error for the smaller sample will be:

sqrt(1000/250) times the original margin of error.

Simplifying this expression, we get:

sqrt(4) times the original margin of error.

So the margin of error for the smaller sample will be about 2 times the original margin of error.

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Answer:

\(9\frac{3}{5}\)

Step-by-step explanation:

3 3/4 = 15/4

\(\frac{36}{1}\) ÷ \(\frac{15}{4}=\)

\(\frac{36}{1} *\frac{4}{15}=\)

\(\frac{12}{1} *\frac{4}{5}=\)

\(=\frac{48}{5}\)

\(=9\frac{3}{5}\)

Hope this helps

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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The mean exam score of student 2 for all four exams is 87.5.  Based on the information provided, you have a spreadsheet containing the scores of 50 students on 4 different exams. To calculate the mean exam score for Student 2 across all four exams, you need to follow these steps:

1. Locate the scores for Student 2 on all four exams. They should be on the first sheet of the spreadsheet and likely in a row or column corresponding to Student 2.

2. Add the scores of Student 2 for all four exams together. For example, if their scores were 80, 85, 90, and 95, the total would be 80 + 85 + 90 + 95 = 350.

3. To calculate the mean, divide the total score (from step 2) by the number of exams (which is 4 in this case). Using the example scores above, the mean would be 350 / 4 = 87.5.

So, the mean exam score for Student 2 for all four exams is 87.5. Keep in mind that this example assumes hypothetical exam scores; you will need to replace them with the actual scores found in the spreadsheet to obtain the correct mean score for Student 2.

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Answer:

i was born 2008

Step-by-step explanation:

The function which represents the relation between the perimeter and the length of the square is; y = 4x.

For the given question;

Let x be the side of the square.

Let y be the perimeter of the square.

Perimeter is 4 times the side of the square.

Then,

Perimeter = 4×side

y = 4x.

Thus, the function which describes the relation between the perimeter and the side of square is y = 4x.

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Answer:

\(the answer suppose to be \sqrt{4} \)

Ignatius of Loyola, the Spanish priest and theologian who founded the Society of Jesus (Jesuits) in the 16th century, focused on several key issues during the period of the Counter-Reformation.

These issues can be broadly categorized into spiritual, educational, and institutional reforms.

Spiritual Reforms: Ignatius emphasized the importance of personal piety and spiritual discipline. He promoted the practice of spiritual exercises, including meditation, prayer, and self-examination, to cultivate a deep and intimate relationship with God. Ignatius encouraged individuals to reflect on their sins and seek forgiveness through confession and penance.

Educational Reforms: Ignatius recognized the power of education in shaping individuals and society. He established schools and universities to provide a comprehensive education that combined intellectual rigor with spiritual formation. The Jesuits placed great emphasis on academic excellence, encouraging critical thinking, the pursuit of knowledge, and the integration of faith and reason.

Pastoral Reforms: Ignatius focused on improving the quality of pastoral care and religious instruction. He trained his followers to be skilled preachers and spiritual directors, equipping them to guide and support individuals in their spiritual journey. Ignatius also emphasized the importance of catechesis, ensuring that people received proper religious education and understood the teachings of the Catholic Church.

Missionary Work: Ignatius and the Jesuits had a strong missionary zeal. They undertook extensive missionary endeavors, particularly in newly discovered territories during the Age of Exploration. They sought to bring Christianity to non-Christian lands and convert indigenous populations to Catholicism. The Jesuits established missions, schools, and hospitals in various parts of the world, playing a significant role in spreading Catholicism.

Overall, Ignatius of Loyola's reforms aimed to strengthen and revitalize the Catholic Church in response to the challenges posed by the Protestant Reformation. His focus on personal spirituality, education, pastoral care, and missionary work contributed to the renewal and expansion of the Catholic Church during the Counter-Reformation.

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Using the formula of the area of the circle, we know that the base area of the barrel is 3.14 ft² respectively.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

In the center of a circle, equal chords subtend equal angles.

The chord is divided in half by the radius drawn perpendicular to it.

Different-sized circles are comparable.

Rectangles, trapezoids, triangles, squares, and kites can all be encircled by circles.

So, the area of the base of the barrel would be taken out by the formula of the circle:

Radius = 2/2

Radius = 1ft

Now, area:
= πr²

= π1²

= π1

= 3.14*1

= 3.14 ft²

Therefore, using the formula of the area of the circle, we know that the base area of the barrel is 3.14 ft² respectively.

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Answer:

the answer is 56.

Step by step explanation:

0.5 x 0.4 = 0.20

0.5 x 0.6 = 0.30

84/x = 0.30

84/0.30 = x

280 = x

0.2 x 280 = 56

Answer:

the original numbers are 5 and 2

Step-by-step explanation:

fistly it says inorder to find x one has to add the larger number to the square of the smaller number. So in this case start off with smaller guesses of positive integers as it is simpler that way.

the first guesses that would end up giving you 9 as an answer is 5 and 2

So now that the integers chosen fit in when calculating x we have to check if it also checks out in calculating y.

For y the difference between the 2 integers have to give an answer of 3. after calculations it the numbers comply to the statement for y;

hence the answers are 5 and 2

Answer:

60 degrees

Step-by-step explanation:

hii so basically theres this rule called vertical angles and this is where if one angle is vertical (or opposite) to an angle which you know the degree for, then the angle verticle to it is the same. so <2 is 60 degrees as well. hope you understand

Answer:

The answer is 60 degrees because the circle consists of a vertical angle. So no matter how much you move a line, the other side of the angle will always match.

More explanation:

Vertical angles are a pair of opposite angles formed by intersecting lines. In the figure, ∠1 and ∠3 are vertical angles. Vertical angles are always congruent . So, in this figure, ∠1≅∠3 and ∠2≅∠4 .

Have the best day ever! :D

The standard deviation of quiz scores is 0.

To find the standard deviation:

Therefore, the standard deviation of quiz scores is 0.

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Step-by-step explanation:

14x + 4 = 39

14x= 39-4

14x=35

x= 35/14

Answer:

see explanation

Step-by-step explanation:

in (1) and (2) use the rule of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\) , then

(1)

\(H^{-6}\) = \(\frac{1}{H^{6} }\)

(2)

\(N^{-3}\) = \(\frac{1}{N^{3} }\)

question (3) involves expanding a binomial

(B - 4)²

= (B - 4)(B - 4)

each term in the second factor is multiplied by each term in the first factor, that is

B(B - 4) - 4(B - 4) ← distribute both parenthesis

= B² - 4B - 4B + 16 ← collect like terms

= B² - 8B + 16

Answer:

15cm

Step-by-step explanation:

180/12=15

Answer:

1.00 significant figures

The required, 0.9967 rounded to 2 significant figures is approximately 1.0.

To round 0.9967 to 2 significant figures, we look at the first two non-zero digits: 0.9967

The first two non-zero digits are 99. Since there is no third significant digit, we round according to the following rules:

If the third digit is 5 or greater, round up the second digit.

If the third digit is less than 5, leave the second digit unchanged.

In this case, the third digit is 6, which is greater than 5. So, we round up the second digit:

Thus, 0.9967 rounded to 2 significant figures is approximately 1.0.

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There are 9 possible schedules to play basketball such that dave can play on monday or wednesday or both which is union of two set .

so this question seems like we have to take union of ways of palying on monday or wednesday

let n(m) be number of ways of playing on monday

n(w) be number of ways of playing on wednesday

we have to find n(m∪w)

n(mUw) = n(m) +n (w) - n(m∩ w)

so n(m) = \(4_C__2\) as one day is now fixed which is monday so we have 4 available days and 2 days to play.

n(m) = \(4_C__2\)  = 6

similary n(m) = n(w) = 6

now  n(m∩w) = \(3_C__1\) as now we have  2 fixed day and we have 3 day remaining and only one day to play.

n(m∩w) = \(3_C__1\) =3

now n(mUw) = n(m) +n (w) - n(m∩ w)

=> 6 + 6 -3

=> 12 - 3

so n(mUw) = 9

so we have 9 schedules to paly keeping condition given in the question.

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Answer:

r = \(\sqrt{\frac{3V}{4\pi h} }\)

Step-by-step explanation:

V = \(\frac{4}{3}\) πr²h ( multiply both sides by 3 to clear the fraction )

3V = 4πr²h ( isolate r² by dividing both sides by 4πh )

\(\frac{3V}{4\pi h}\) = r² ( take square root of both sides )

\(\sqrt{\frac{3V}{4\pi h} }\) = r

Answer:

x = 3, x = 4

Step-by-step explanation:

Given

x³ - 2x² - 11x + 12 = x³ - 13x - 12

Subtract x³ - 13x - 12 from both sides

- 2x² + 2x + 24 = 0 ← in standard form ( divide all terms by - 2 )

x² - x - 12 = 0

(x - 4)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 3 = 0 ⇒ x = 3

Answer:

1. 2x+8

2. 3x-6

3. -6x-3

Step-by-step explanation:

I dunno what you're supposed to do for the modeling, but I simplified the expressions

Answer:

C. 56

Step-by-step explanation:

252/4.5=56

Using the formula you can get this answer

Answer:

5

Step-by-step explanation:

Answer:

2916 and 6724 respectively

Step-by-step explanation:

the steps on how to evaluate 54^2 and 82^2 using the formula for squaring a binomial are:

1. Write the binomial as a sum of two terms.

\(54^2 = (50 + 4)^2\)

\(82^2 = (80 + 2)^2\)

2. Square each term in the sum.

\(54^2 = (50)^2 + 2(50)(4) + (4)^2\\82^2 = (80)^2 + 2(80)(2) + (2)^2\)

3. Add the products of the terms.

\(54^2 = 2500 + 400 + 16 = 2916\\82^2 = 6400 + 320 + 4 = 6724\)

Therefore, the values  \(54^2 \:and \:82^2\)are 2916 and 6724, respectively.

Answer:

54² = 2916

82² = 6724

Step-by-step explanation:

A binomial refers to a polynomial expression consisting of two terms connected by an operator such as addition or subtraction. It is often represented in the form (a + b), where "a" and "b" are variables or constants.

The formula for squaring a binomial is:

\(\boxed{(a + b)^2 = a^2 + 2ab + b^2}\)

To evaluate 54² we can rewrite 54 as (50 + 4).

Therefore, a = 50 and b = 4.

Applying the formula:

\(\begin{aligned}(50+4)^2&=50^2+2(50)(4)+4^2\\&=2500+100(4)+16\\&=2500+400+16\\&=2900+16\\&=2916\end{aligned}\)

Therefore, 54² is equal to 2916.

To evaluate 82² we can rewrite 82 as (80 + 2).

Therefore, a = 80 and b = 2.

Applying the formula:

\(\begin{aligned}(80+2)^2&=80^2+2(80)(2)+2^2\\&=6400+160(2)+4\\&=6400+320+4\\&=6720+4\\&=6724\end{aligned}\)

Therefore, 82² is equal to 6724.

To find the probability that a randomly selected worker has a retirement plan or health insurance, we need to add the probabilities of having a retirement plan and having health insurance and then subtract the probability of having both,

Since we don't want to count those workers twice. P(retirement plan or health insurance) = P(retirement plan) + P(health insurance) - P(both), P(retirement plan or health insurance) = 0.56 + 0.68 - 0.49, P(retirement plan or health insurance) = 0.75.

Therefore, the probability that a randomly selected worker has a retirement plan or health insurance is 0.75. we'll use the formula: P(A or B) = P(A) + P(B) - P(A and B), where A represents having a retirement plan, B represents having health insurance, and P(A and B) represents having both.

Given:
P(A) = 56% (retirement plan)
P(B) = 68% (health insurance)
P(A and B) = 49% (both)

Now we can plug these values into the formula: P(A or B) = 0.56 + 0.68 - 0.49 = 0.75, The probability that a randomly selected worker has a retirement plan or health insurance is 75%.

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In conclusion In the given solution for finding the perimeter or area of the polygon, there is an error in calculating the height of the triangle.

Why it is?

The height (h) should be the perpendicular distance from vertex B to line AC. However, the given solution has calculated the distance between points B and A.

To correct this error, we can use the formula for the distance between a point and a line. The line AC has the equation y = 1, so we can find the distance from point B to line AC as follows:

distance = |(1-3)(5-1) - (1-1)(4)| / √((1-3)²2 + (5-1)²2)

distance = 4 / 2√5

distance = 2/√5

Now, we can use this value to find the area and perimeter of the triangle:

Area = 1/2× base × height

Area = 1/2 ×4 × (2/√5)

Area = 4/√5

Perimeter = AB + BC + AC

Perimeter = √((5-4)²2 + (1-3)²2) + √((1-5)²2 + (1-1)²2) + √((4-1)²2 + (3-1)²2)

Perimeter = √5 + 4 + √13

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Step-by-step explanation:

the volume = 3.14×12²×20

= 9043.2 cm³

To calculate Emily's weighted average in the class, we need to multiply each exam grade by its corresponding weight, then sum these products. In this case, her first exam counts for 20% of her grade, the second exam counts for 30%, and the third exam counts for 50%.

The weighted average can be computed using the formula:

Weighted Average = (Exam 1 Grade * Exam 1 Weight) + (Exam 2 Grade * Exam 2 Weight) + (Exam 3 Grade * Exam 3 Weight)

Substituting the given values:

Weighted Average = (67 * 0.2) + (84 * 0.3) + (78 * 0.5)

Weighted Average = 13.4 + 25.2 + 39

Weighted Average = 77.6

Therefore, Emily's weighted average in the class is 77.6.

In this calculation, each exam grade is multiplied by its corresponding weight, which represents the proportion of the final grade that each exam contributes. The weighted average takes into account both the performance on each exam and the weight assigned to it in determining the final grade.

By summing these weighted products, we obtain a value that represents Emily's overall performance in the class, reflecting the different weights assigned to each exam. The resulting weighted average of 77.6 indicates her overall achievement in the course, considering the relative importance of each exam in the final grade calculation.

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Answer:

x = 15

Step-by-step explanation:

Using the Altitude on Hypotenuse theorem

( leg of large Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

Thus

x² = 9 × (9 + 16) = 9 × 25 = 225 ( take the square root of both sides )

x = \(\sqrt{225}\) = 15