The median of a quanitive data set is always one of the infiviual data values. True or false

The amount accumulated after investing a principal P for t years at an interest rate compounded annually is  $46,057.58.

Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Therefore, let's find the amount accumulated after investing a principal P for t years at an interest rate compounded annually.

\(A = p(1 + \frac{r}{n} )^{nt}\)

where

p = 15,500

r = 9.5%

t = 12

n = 1

\(A = 15500(1 + \frac{0.095}{1} )^{1(12)}\)

A = 15,500.00(1 + 0.095)¹²

A = $46,057.58

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$46,057.58, answer for acellus

Answer:

8) 10 15/16 ft³

9) 20 5/6 ft³

Step-by-step explanation:

Volume of a rectangular prism is

l * b * h,

Question 8

We're given the area

Area = l * b

So we substitute the area for length and breadth.

Volume = Area * height

Volume = 4 3/8 * 2 1/2

Volume = 35/8 * 5/2

Volume = 175/16

Volume = 10 15/16 ft³

Question 9

Volume = 5 * 1 2/3 * 2 1/2

Volume = 5 * 5/3 * 5/2

Volume = 5 * 25/6

Volume = 125/6

Volume = 20 5/6 ft³

Tell Me if I'm Wrong But I Believe It's 198m3

According to the question, the critical value for finding a 90% confidence interval estimate for a mean from a sample of 15 observations is 1.761.

To find the critical value for a 90% confidence interval estimate for a mean when the standard deviation is unknown and the sample size is 15, we need to use the t-distribution.

The critical value is determined by the confidence level and the degrees of freedom. For a 90% confidence level, the corresponding area in the tails of the t-distribution is \(\(\frac{{1 - 0.90}}{2} = 0.05\)\).

Since the sample size is 15, the degrees of freedom for the t-distribution is \((n - 1) = 15 - 1 = 14\).

We can use statistical software or a t-table to find the critical value associated with a 0.05 area in the tails of the t-distribution with 14 degrees of freedom. The critical value is approximately 1.761.

Therefore, the critical value for finding a 90% confidence interval estimate for a mean from a sample of 15 observations is 1.761.

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Answer: $15.90/hr

Step-by-step explanation:

We need to add 6% to her $15/hr current pay.  This can be calculated with:

$15/hr *(1+0.06) = $15.90/hr

The "(1+0.06)" represents a) 1  the current salary, and b) the 6% raise.

Efficiency refers to the extent to which resources, such as time, money, or energy, are utilized effectively and productively to achieve a desired outcome.

The fuel efficiency, in miles per gallon, of an American-made car: Continuous. Fuel efficiency can be measured in decimals and have a range of values.

(b) The temperature of a burrito served to a customer in a local Mexican restaurant: Continuous. Temperature can be measured in decimals and have a range of values.

(c) The actual length of a roll of plastic wrap is advertised to be 30 feet long: Continuous. Length can be measured in decimals and have a range of values.

(d) The number of children in a household: Discrete. The number of children can only be whole numbers (e.g., 0, 1, 2, 3).

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Statistical process control (SPC) is a technique used in quality control to monitor and control a process over time

What is used to periodically check that a process is in statistical control?

a. sampling

b. scrap parts

c. the process is only measured in the beginning 100 percent inspection.

a. Sampling is used to periodically check that a process is in statistical control.

Statistical process control (SPC) is a technique used in quality control to monitor and control a process over time. SPC involves collecting and analyzing data on the process, and using statistical methods to determine whether the process is in statistical control (i.e., producing consistent and predictable results) or is out of control (i.e., producing inconsistent or unpredictable results).

One way to monitor a process using SPC is to use sampling. This involves taking a sample of parts or products from the process at regular intervals, and measuring certain characteristics of the sample (such as dimensions, weight, or color). The data collected from the samples can then be analyzed using statistical methods to determine whether the process is in control or out of control.

If the data collected from the samples indicates that the process is out of control (i.e., producing inconsistent or unpredictable results), corrective action can be taken to bring the process back into control. By regularly monitoring and adjusting the process using SPC techniques like sampling, organizations can ensure that their processes are producing consistent and high-quality results.

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Answer:

n= -11/5+ 3/5m

Step-by-step explanation:

Answer:

g(n) = \(\frac{5n+11}{3}\)

Step-by-step explanation:

Given

3m - 5n = 11

Rearrange making m the subject

Add 5n to both sides

3m = 5n + 11 ( divide both sides by 3 )

m = g(n) = \(\frac{5n+11}{3}\)

Answer:

Just 19 is a factor of both.

GCF of 38 m and 57 n is :19.

Hope this helps!

√36×25×49×15×3

2×3×5×3×7√5

630√5

Answer:

x = 5.87 cm

Step-by-step explanation:

The triangle shown is a right triangle with congruent legs.

That makes it a 45-45-90 triangle.

The ratio of the lengths of the sides of a 45-45-90 triangle is

1 : 1 : √2

The length of either leg is hypotenuse/√2.

8.3 cm / √2 = 5.87 cm

Answer: x = 5.87 cm

Answer:

Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values. Tap for more steps.

Step-by-step explanation:

The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.

We have,

To find the three consecutive prime numbers with a sum that is a multiple of 5 and each less than 100, start by listing the prime numbers less than 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Check each combination:

(2, 3, 5): Sum = 2 + 3 + 5 = 10 (which is a multiple of 5)

(3, 5, 7): Sum = 3 + 5 + 7 = 15 (which is a multiple of 5)

(5, 7, 11): Sum = 5 + 7 + 11 = 23 (not a multiple of 5)

(7, 11, 13): Sum = 7 + 11 + 13 = 31 (not a multiple of 5)

(11, 13, 17): Sum = 11 + 13 + 17 = 41 (not a multiple of 5)

(13, 17, 19): Sum = 13 + 17 + 19 = 49 (which is not a multiple of 5)

(17, 19, 23): Sum = 17 + 19 + 23 = 59 (not a multiple of 5)

(19, 23, 29): Sum = 19 + 23 + 29 = 71 (not a multiple of 5)

(23, 29, 31): Sum = 23 + 29 + 31 = 83 (not a multiple of 5)

(29, 31, 37): Sum = 29 + 31 + 37 = 97 (not a multiple of 5)

(31, 37, 41): Sum = 31 + 37 + 41 = 109 (which is not a multiple of 5)

(37, 41, 43): Sum = 37 + 41 + 43 = 121 (which is not a multiple of 5)

(41, 43, 47): Sum = 41 + 43 + 47 = 131 (not a multiple of 5)

(43, 47, 53): Sum = 43 + 47 + 53 = 143 (which is not a multiple of 5)

(47, 53, 59): Sum = 47 + 53 + 59 = 159 (which is not a multiple of 5)

(53, 59, 61): Sum = 53 + 59 + 61 = 173 (not a multiple of 5)

(59, 61, 67): Sum = 59 + 61 + 67 = 187 (not a multiple of 5)

(61, 67, 71): Sum = 61 + 67 + 71 = 199 (not a multiple of 5)

(67, 71, 73): Sum = 67 + 71 + 73 = 211 (not a multiple of 5)

(71, 73, 79): Sum = 71 + 73 + 79 = 223 (not a multiple of 5)

(73, 79, 83): Sum = 73 + 79 + 83 = 235 (which is a multiple of 5)

(79, 83, 89): Sum = 79 + 83 + 89 = 251 (not a multiple of 5)

(83, 89, 97): Sum = 83 + 89 + 97 = 269 (not a multiple of 5)

Thus,

The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.

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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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The maximum speed the cube reaches when the spring is initially compressed by 5 cm is the same as the maximum speed when it is initially stretched by 5 cm.

Speed can be constant or variable. An object with constant speed moves at the same rate over a given distance and time interval. An object with variable speed changes its rate of motion over the same interval. Average speed is calculated by dividing the total distance traveled by the total time taken, and instantaneous speed is the speed at a particular moment in time.

Assuming that the spring has a spring constant of k and the mass of the cube is m, the potential energy stored in the spring when it is compressed or stretched by 5 cm is given by:

U = (1/2)k(0.05)² = 0.00125k

When the spring is released, this potential energy is converted into kinetic energy of the cube. Therefore, the maximum speed the cube can reach is given by:

(1/2)mv² = 0.00125k

Solving for v, we get:

v = √(0.0025k/m)

Therefore, the maximum speed the cube reaches when the spring is initially compressed by 5 cm is the same as the maximum speed when it is initially stretched by 5 cm. This is because the potential energy stored in the spring is the same in both cases, and this potential energy is converted completely into kinetic energy when the spring is released. The maximum speed depends only on the spring constant and the mass of the cube, and is independent of the initial compression or stretching of the spring.

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14 students had none of the pets mentioned in the problem.

Given Question is related to Sets and Function

By using the principle of inclusion-exclusion,

D = set of students who had a dog

C = set of students who had a cat

F = set of students who had a fish

Let's determine the sizes of the sets and their intersections:

|D| = 50

|C| = 40

|F| = 20

|D ∩ C| = 19

|C ∩ F| = 2

|D ∩ F| = 3

|D ∩ C ∩ F| = 0

|D ∪ C ∪ F| = ?

The size of the union of the sets as follows:

|D ∪ C ∪F| = |D| + |C| + |F| - |D ∩ C| - |C ∩ F| - |D ∩ F| + |D ∩ C ∩ F|

|D ∪ C ∪ F| = 50 + 40 + 20 - 19 - 2 - 3 + 0 = 86

Therefore, there were 86 students who had at least one of these pets.

To find the number of students who had none of these pets, we can subtract this number from the total number of students:

100 - 86 = 14

Therefore, 14 students had none of the pets mentioned in the problem.

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No

A point is on a line if that point satisfies the equation.

Testing Points

To test if the point (2,7) is on the line y = 2x + 7, we need to plug the point into the equation. For the coordinate pair (2,7), the x-value is 2 and the y-value is 7. So, plug 2 in for x and 7 in for y.

Then, simplify.

As you can see, 7 does not equal 11. Thus, point (2,7) cannot be a point on the given line.

Other Points

We can do this same test with other points such as (1,9). The x-value is 1 and the y-value is 9, so now we can plug them in.

Since 9 equals 9 is a true statement, the point (1,9) is a point on the given line.

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

cross multiply so it becomes 8x=18 then divide both sides by 8 and x= 2 2/8

Step-by-step explanation:

Answer:

2.8 ounces

Step-by-step explanation:

4/10= 0.4

0.4*7= 2.8 ounces

Answer:

2.8 ounces per 7 servings.

Step-by-step explanation:

set a proportion

10 servings 7 servings

---------------- = ---------------

4 ounces x ounces

7/10 = 0.7

4 x 0.7 = 2.8

x = 2.8

The bias based on the naive forecast method for the given data is 2.0.

To calculate the bias using the naive forecast method, we first need to calculate the average of the time series values. The formula for the naive forecast is simply taking the last observed value as the forecast for the next period.

The time series values given are 13, 19, 8, and 14. To find the average, we sum up these values and divide by the number of values:

Average = (13 + 19 + 8 + 14) / 4

= 54 / 4

= 13.5

Next, we take the last observed value, which is 14, as the forecast for the next period.

Finally, we calculate the bias by subtracting the average from the forecast:

Bias = Forecast - Average

= 14 - 13.5

= 0.5

Rounding the bias to 1 decimal place, we get a bias of 0.5, which can also be expressed as 2.0 when rounded to the nearest whole number.

Therefore, the bias based on the naive forecast method for the given data is 2.0.

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Answer:

Let length of bc be x cm

Thus, ab=4x

ab+bc=ac

4x+x=75

5x=75

x=75/5

x=15

Therefore, ab=x=15cm

bc=4x=60cm

Step-by-step explanation:

Answer:

(-1, -3)

Step-by-step explanation:

What is the ordered pair that satisfies the system 2x - 7y >5 and 3x-y < 4?

Using the coordinate point (-1, 3)

If x = -1 and y = 3

Substitute into the expressions and check if they are true

2x - 7y >5

= 2(-1)-7(-3)

= -2 + 21

= 19

Since 19 is greater than 5, hence the inequality 19 > 5 is true

Substituting into 3x - y < 4

3(-1)-(-3)

= -3 + 3

= 0

Since 0 < 4, hence this is also true for the inequality.

The coordinate point that satisfies the inequality is therefore (-1, -3)

Given, the sum of the family members age is divided by 2, 3, 4, 5, 6, or 10 there is always a remainder of 1. Let x be the sum of the ages of all family members.

Hence, the LCM of 2, 3, 4, 5, 6, and 10 with the remainder 1 is the sum of the ages of all the family members. LCM of 2, 3, 4, 5, 6 and 10 is 60. We need a number more than 100 which is exactly divisible by 60 and when 1 is subtracted from that number it will leave no remainder. So, the required sum of the ages of all family members = 60 + 1 = 61 years. Therefore, option C (121 years) is the correct answer.

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Answer:

\(6.25\) x \(10^{9}\)

The average rate of change of f(x) from x = 1 to x = 3 is 0.5

The average rate of change of a function over an interval is the change in the function value (y) divided by the change in the input value (x) over that interval.

To find the average rate of change of f(x) = \(x^{3}\) - \(4x^{2}\) + 5 from x = 1 to x = 3, we can use the following formula:

(f(3) - f(1)) / (3 - 1)

substituting the function value, we get

(\(3^{3}\) - 4\((3)^{2}\) + 5 - (\(1^{3}\) - 4\((1)^{2}\) + 5)) / (3 - 1)

= (27 - 36 + 5 - (1 - 4 + 5)) / 2

= (1) / 2

So the average rate of change of f(x) from x = 1 to x = 3 is 0.5

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Step-by-step explanation:

\( {x}^{2} - 12x + 36 = 90 \\ {x}^{2} - 12x - 54 = 0 \\\)

Let a=1, b=-12, c=-54

Use formula

\( \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \)

You will get

\(x = 6 + 3 \sqrt{10} \\ x = 15.48683298 \\ or \\ x = 6 - 3 \sqrt{10} \\ x = - 3.48683298\)

Answer:

x = 6 + 3\(\sqrt{10}\)

Step-by-step explanation:

if you 'un-foil' the equation \(x^{2}\) - 12x + 36 = 90 you will get the following:

(x - 6)^2 = 90

take the square root of each side and you will get the following:

x - 6 = \(\sqrt{90}\)

Add 6 to each side

x = 6 + \(\sqrt{90}\)

simplify \(\sqrt{90}\) to be \(\sqrt{9}\) x \(\sqrt{10}\)  which equals 3 \(\sqrt{10}\)

Final answer:  6 + 3\(\sqrt{10}\)

In the given scenario ladder is 6.52 feet long.

Given that,

The angle between ground and ladder = 62 degree

The distance of ladder from ground and ladder = 3 feet

We have to find the length of  ladder.

Since we know that,

The trigonometric ratio

cosθ = adjacent/ Hypotenuse

Here we have,

Adjacent =  3 feet

Hypotenuse = length of ladder

Thus to find the length of ladder we have to find the value of hypotenuse.

Therefore,

⇒ cos62 = 3/ Hypotenuse

⇒    0.46 = 3/ Hypotenuse

⇒ Hypotenuse =  3/0.46

                          = 6.52

Thus,

length of ladder  = 6.52 feet.

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