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"a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years.

The 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].According to the central limit theorem , a sampling distribution of the means is usually distributed in a normal distribution, given a big enough sample size, which means that it has a bell-shaped curve. It has a standard deviation that can be estimated by dividing the population standard deviation by the square root of the sample size. Using the formula below,

we can calculate the 95% confidence interval for the population average.= 13.8 ± (1.96 × 7.3 / √45)

= 13.8 ± (1.96 × 1.088)

= 13.8 ± 2.13The limits are calculated by adding and subtracting the calculated value from the sample mean.13.8 + 2.13

= 15.9313.8 - 2.13

= 11.67Therefore, the 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].

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Answer:

y = -3

Step-by-step explanation:

X-2y=3

Let x=-3

-3 -2y = 3

Add 3 to each side

-3+3 -2y = 3+3

-2y = 6

Divide by -2

-2y/-2 = 6/-2

y = -3

Plotting the points into the rectangular coordinate system :

The next point should be in the same level as the point (9, 2)

The measurement of top and bottom side must be the same.

By counting, the measurement of top is 3, so the bottom must be 3 also.

Counting 3 units to the left of (9, 2), we will get the point (6, 2)

The answer is (6, 2)

Answer:

5.8/8=0.725

Rounded number: 0.7

Step-by-step explanation:

Estimate 6/8=0.75

6 because 5.8 rounded to a whole number=6

Counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics, there are six (6) common types of numbers and these include the following:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length. Also, the negative numerical values are positioned at the left from zero while the positive numerical values are positioned at the right from zero.

Note: Each of the tick represents 1 unit.

Therefore, counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

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Considering a quadratic equation, it is found that:

Considering the height in feet, it is given by:

h(t) = -4.9t² + v(0)t + h(0)

In which:

In this problem, we have that h(0) = 6, v(0) = 16, hence the equation is given by:

h(t) = -4.9t² + 16t + 6

Which is a quadratic equation with coefficients a = -4.9, b = 16, c = 6. Hence the maximum height is found as follows:

\(\Delta = b^2 - 4ac = 16^2 - 4(-4.9)(6) = 373.6\)

\(h_{MAX} = -\frac{\Delta}{4a} = -\frac{373.6}{-4(4.9)} = 19.06\)

The maximum height of the volleyball is of 19.06 feet.

It hits the ground at the roots, hence:

The solutions are:

\(x_1 = \frac{-16 + \sqrt{373.6}}{-9.8} = -0.34\)

\(x_2 = \frac{-16 - \sqrt{373.6}}{-9.8} = 3.6\)

Time is a positive measure, hence:

The volleyball will hit the ground after 3.6 seconds.

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a continuous probability distribution the outcomes can take any value within a given range.

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Answer:

  84 square units

Step-by-step explanation:

Triangles DUM and DAP are similar, so their corresponding dimensions are proportional.

  UM/AP = MD/PD

  UM/4.5 = 10/3.75

  UM = (4.5)(10)/3.75 = 12

The area of triangle DUO is ...

  A = 1/2bh

  A = 1/2(DO)(UM) = 1/2(14)(12) = 84 . . . square units

The area of triangle DUO is 84 square units.

Answer:

22.5 cm

Triangle area is (L x W) / 2

7.5 x 6 = 45

45 / 2 = 22.5

Step-by-step explanation:

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We can expect the longest 20% of these scorpions to be above a length of approximately 2.0272 inches.

To find the value above which we could expect the longest 20% of these scorpions, we need to use the z-score formula. First, we need to find the z-score that corresponds to the 80th percentile, which is the complement of the top 20%. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 80th percentile is 0.84.

Next, we use the formula z = (x - mu) / sigma, where z is the z-score, x is the value we are trying to find, mu is the mean, and sigma is the standard deviation. We plug in the given values and solve for x:

0.84 = (x - 1.96) / 0.08

0.0672 = x - 1.96

x = 2.0272

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Answer:

wait I'll give the answer on the comment box.....

Answer:

x=7/2.

Step-by-step explanation:

5(2x-1)+4(x-1)/20 = 2

10x-5+4x-4/20=2

14x-9/20=2

14x-9=40

14x=49

x =49/14

x=7/2

*/ refers to this sign ______

Answer:

Yes

Step-by-step explanation:

because it is going to keep saying LUNCH

The marginal frequency of students who favor going to the beach in the summer is 26.7%.

The marginal frequency of students who favor going to the beach in the summer is found by adding up the number of students who like going to the beach across all categories.

For boys, the frequency is 10.

For girls, the frequency is 29.

So the total frequency for both boys and girls is 10+29=39.

To find the percentage, we divide the total frequency by the total number of students and multiply by 100:

(39/146) x 100 =  26.7%

Therefore, the marginal frequency of students who favor going to the beach in the summer is approximately 26.7%.

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Answer:  see below

Step-by-step explanation:

Note that an open dot means NOT included and a closed dot means included.

11) 1 < x < 3

   (1, 3)

12) 2 ≤ x ≤ 7

    [2, 7]

13) -3 < x ≤ -1

    (-3, -1]

14) -3 < x ≤ 4

    (-3, 4]

1a)The values of l range from 0 to (n-1), so for n = 3, l can have the values 0, 1, and 2.

b) The values of m can be -2, -1, 0, +1, and +2

c) There are a total of 9 orbitals

The qualities and traits of quantum systems, like the electrons in atoms, are described by a set of numbers known as quantum numbers. They offer knowledge on the system's energy, angular momentum, orientation, and spin, among other characteristics.

Using the formula, number of electrons = \(n^2\)

Number of electrons =\(3^2 = 9\)

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Answer:

1.a

2.c

3b

4.c

5.a or b

Step-by-step explanation:

After adding (-7) to each value in the given data set, the mean is 38.25, the median is 38, the mode does not exist, the range is 24, and the standard deviation is approximately 8.85.

To find the mean of the data set, add all the values together (49, 30, 34, 43, 31, 37, 25, 47) and divide the sum by the total number of values (8). The mean is the average value of the data set.

To determine the median, arrange the values in ascending order (25, 30, 31, 34, 37, 43, 47, 49) and find the middle value. In this case, the median is the average of the two middle values (34 and 37).

The mode refers to the value(s) that appear most frequently in the data set. In this case, there is no mode since no value appears more than once.

The range is calculated by subtracting the smallest value (25) from the largest value (49). Thus, the range is 24.

To calculate the standard deviation, subtract the mean from each value, square the differences, calculate the mean of those squared differences, and finally take the square root of the resulting value. This provides a measure of the dispersion or spread of the data around the mean.

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In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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Answer:

b.b d.d e.e

Step-by-step explanation:

Step-by-step explanation:

full work and answers for all 12 problems

Answer:

x = 5

Step-by-step explanation:

90 - 55 = 35

8x - 5 = 35

    +5    +5

8x = 40

x = 5

A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

It requires only a small fraction of the arch's width to support itself while a lintel requires the full width of the structure that it spans. Thus, a stone arch can span a larger gap than a stone lintel and be twice as wide while using the same material.

For example, the Roman Colosseum uses an arch to span the entrances and exits while the walls supporting the upper levels use a series of stone lintels to support the structure.

Moreover, the arc prevents the need for a central support structure, which would be in the way of any events taking place in the structure. The technology of arches made them fundamental to ancient Roman architecture. For example, the arches were used to construct aqueducts, which provided a steady supply of water to the city of Rome.

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first what us 2, -11 use a calculator, never mind. it is -9 and the first one is  -1

Complementary angles has sum of \(90^{o}\) and supplementary angles have sum of \(180^{o}\) , The answer is \(62^{o}\) and \(48^{o}\) .

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.

When two angles' measurements add up to 90 degrees, they are said to be complementary. When two angles' measures sum up to 180 degrees, they are said to be supplementary. Keeping in mind that the letter s follows the letter c in the alphabet and that 180 is greater than 90 can help you avoid conflating these definitions.

\(28^{o}\)

complement = \(90^{o}-28^{o}\) = \(62^{o}\)

\(132^{o}\)

supplement= \(180^{o}-132^{o}\) = \(48^{o}\)

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Answer:

C

Step-by-step explanation:

perpendicular lines intersect at a 90 degree angle, meaning it is not answer choice A.

B is incorrect because perpendicular lines intersect, so they can not be parallel.

C is correct because parallel lines never intersect, so perpendicular lines can never be parallel to each other.

D is incorrect because perpendicular lines only intersect at one point and create four consistent right angles.

Answer:

\(\sf 12-5x+6x=4\)  (Given)

\(\sf 12+x=4\)  (Combine like terms)

\(\sf x=-8\)  (Subtraction property of equality)

--------------------------------------------------

Hope this is what you're looking for!

Answer:

1. given

2. combine like terms,

3. subtraction property of equality

Step-by-step explanation:

Answer:

b=130°

Step-by-step explanation:

b=180°-50°=130°

Answer:

130⁰

the sum of the two angles is 180⁰ as demonstrated by forming a straight line. 180-50=130

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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Answer:

where is the table to solve the problem??

Answer:

its 17.6

the second question is 82

third is 9

blank d is 12

Step-by-step explanation: