5 students and a teacher stand in aline. If the space between the teacherand the first student is 1.5 meters andthe space between the teacher andthe last students is 6.7 m. If theteacher spaces out the studentsevenly, how much space should therebe between each student? Ignore thespace taken up by the teacher andthe students. Round your answer tothe nearest tenth of a meter.

The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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Answer:

The formula of the nth term is a₇=48(1/2)⁷⁻¹=48×1/64=3/4

Step-by-step explanation:

The correct statement about trend lines is option A. A trend line should be as close as possible to the points.

When drawing a trend line, the goal is to find a line that best represents the general trend or pattern of the data points. While it is not always possible for the trend line to pass through every single point, it should be as close as possible to the points to accurately capture the overall trend.

Option B, "A trend line connects the points," is not necessarily true. The trend line is an approximation of the trend and may not pass through every data point.

Option C, "A trend line goes through the first and last points," is also not always true. While it can be the case in some scenarios, it is not a requirement for a trend line to pass through the first and last points.

Option D, "A trend line is always horizontal," is incorrect. The slope of a trend line can vary depending on the nature of the data and the trend being analyzed.

Therefore, the true statement about trend lines is that they should be as close as possible to the points, as mentioned in option A.

The complete question is :

Select the true statement about trend lines.

A. A trend line should be as close as possible to the points.

B. A trend line connects the points.

C. A trend line goes through the first and last points.

D. A trend line is always horizontal.

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Answer:

The answer is 0.0026

Step-by-step explanation:

0.00032 x 5200000 = 1664

1664 divided by 640000 is 0.0026

The worth of the share after a 15% fall will be $47.21.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the value of a share of stock on the stock market decreased by 15%. If it used to be worth $55.55.

The value of the share after 15% fall will be calculated as:-

Decreased amount = 55.55 - ( 55.55 x ( 15 / 100)

Decreased amount = $47.21

Therefore, the worth of the share after a 15% fall will be $47.21.

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Answer:

37.5 is the answer

Step-by-step explanation:

all you do is just multiply the 2 numbers

The exponential function f can be written as \(f(x) = 5 \times (8/5)^x\) .

The exponential function f can be written as:

\(f(x) = a \times b^x\)

To find the values of a and b, we can use the given values of f(x) for x = 0 and x = 1:

\(f(0) = a \times b^0 = a = 5\\f(1) = a \times b^1 = 8\)

Substituting the value of a in the second equation, we get:

5 × b = 8

Solving for b, we get:

b = 8/5

Therefore, the exponential function f can be written as:

\(f(x) = 5 \times (8/5)^x\)

These forms are all equivalent and represent the same exponential function.

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By answering the presented question, we may conclude that Sales Rep: expression This entity maintains information about sales reps such as SalesRepID and SalesRepName.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

The ER diagram above depicts the database entities and their connections. Here's a quick rundown of each entity and its characteristics:

Employee: This object contains information on employees such as EmployeeID, Name, DateOfBirth, and Dependents.

ProductID, ProductName, ManufacturingDate, ExpiryDate, and SupplierID are all stored in this object.

Supplier: This entity holds supplier-specific information such as SupplierID, SupplierName, ContactPerson, and ContactNumber.

CustomerID, CustomerName, ContactPerson, and ContactNumber are all stored in the Customer entity.

Sales Rep: This entity maintains information about sales reps such as SalesRepID and SalesRepName.

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Answer:

The new, 2 person ATV can travel 91 more miles than the new, 6 person ATV

Step-by-step explanation:

26% more than 350 = 441
441 miles - 350 miles = 91 more miles

\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)

we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.

if the level of significance is 0.01, we would expect to commit a Type I error 15 times out of 1,500 tests. if the level of significance is 0.05, we would expect to commit a Type I error 75 times out of 1,500 tests.

Assuming that the null hypothesis is true in all 1,500 tests, the probability of committing a Type I error (rejecting the null hypothesis when it is actually true) is equal to the level of significance (alpha) of the test.

(a) If the level of significance is 0.01, then the probability of committing a Type I error in one test is 0.01. Therefore, the expected number of Type I errors in 1,500 tests is:

Expected number of Type I errors = (number of tests) x (probability of Type I error per test)

= 1,500 x 0.01

= 15

So, if the level of significance is 0.01, we would expect to commit a Type I error 15 times out of 1,500 tests.

(b) If the level of significance is 0.05, then the probability of committing a Type I error in one test is 0.05. Therefore, the expected number of Type I errors in 1,500 tests is:

Expected number of Type I errors = (number of tests) x (probability of Type I error per test)

= 1,500 x 0.05

= 75

So, if the level of significance is 0.05, we would expect to commit a Type I error 75 times out of 1,500 tests.

(c) If the level of significance is 0.001, then the probability of committing a Type I error in one test is 0.001. Therefore, the expected number of Type I errors in 1,500 tests is:

Expected number of Type I errors = (number of tests) x (probability of Type I error per test)

= 1,500 x 0.001

= 1.5

So, if the level of significance is 0.001, we would expect to commit a Type I error 1.5 times out of 1,500 tests, which we round to 1 decimal place as 1.5 rounds to 2.

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Collect like terms

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

2/10, 0.2, 20%

Step-by-step explanation:

hope this helps

Answer:

it would bee 51 2a second power

Answer: ok?

Step-by-step explanation:

Answer:

(7, 3)

Step-by-step explanation:

Given segment AB, where:

Mid point

As per mid point formula:

So, the point B is:

Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

The error is related to spelling.

The word affects will be effects.

Answer:

Option c: 0.0022; reject the null hypothesis

Step-by-step explanation:

Using a p value calculator, with a z score of 3.06 at 0.05 level of significance for a two tailed test, the p-value is 0.002213. This value is lower than 0.05 thus the result is significant we will reject the null hypothesis.

To calculate the p value by hand, we do this

The test statistic is 3.06. Since the test possesses a not equal to alternative, we look up the test statistic on the z table find the corresponding probability. Thus we have 3.06 - on the z table - 0.99889

Then we subtract from 1 and double it

1-0.99889 = 0.00111 x 2 = 0.0022.

Answer:

Option 4

Step-by-step explanation:

The parabola has a y-intercept of -3.

The parabola opens upward, so the leading coefficient is positive.

Answer:

20

Step-by-step explanation:

50 = 2x+3x or 5x

x=10

2(10) =20

Answer:

X=3 and Y=2

Step-by-step explanation:

Answer:

48000

Step-by-step explanation:

After rounding each number to the criteria stated, we get the question 800 * 60. Multiply the 8 and the 6 and add the same number of zeros that are there right now. this is 48 + "000" so 48000.

Answer:

(a)p(3,3)=0.0416

(b)p(4,11)=0.0002

Step-by-step explanation:

Number of Customers, X

\(\left\begin{array}{|c|ccccc|}X&0&1&2&3&4\\P(X)&0.1&0.2&0.3&0.25&0.15.\end{array}\right\)

Y = the total number of packages to be wrapped for the customers waiting in line

\(\left\begin{array}{|c|ccccc|}Y&1&2&3\\P(Y)&0.55&0.35&0.1\end{array}\right|\)

a. P(X = 3, Y = 3)

p(3,3) means that there are 3 customers with one gift each

The probability of this event happening:

\(0.25 \times 0.55^3=0.0416\)

p(3,3)=0.0416

b. p(4,11)

For 4 people to have a total package of 11, there must be 3 customers with 3 packages each and 1 customer with 2 packages,

The probability of this happening is:

\(p(4,11)=0.15\times^4C_1\times0.1^3\times0.35\\p(4,11)=0.0002\)

Cara's first error was not 7 - 13, leading to an incorrect result of -32.

Cara's first error was that she did not evaluate (Negative 4) squared.

The expression in question is not provided, so let's assume it is "6 - 2 × (-4)² + 7 - 13".

According to the order of operations (PEMDAS/BODMAS), we evaluate operations inside parentheses first, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

To evaluate the expression correctly, we follow the order of operations:

Evaluate the exponent (-4)².

Since (-4) squared is positive, (-4)² = 16.

Multiply 2 and 16.

2 × 16 = 32.

Evaluate the addition and subtraction from left to right.

6 - 32 + 7 - 13.

At this point, we see that Cara did not evaluate 7 - 13.

Therefore, her first error was not evaluating the subtraction correctly.

Continuing the evaluation:

6 - 32 + 7 - 13 = -32.

So, Cara's first error was not evaluating 7 - 13, leading to an incorrect result of -32.

It's important to carefully follow the order of operations to ensure accurate evaluations of mathematical expressions.

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The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.

The formula for finding the nth term in an arithmetic sequence given as:

= a + (n - 1)d

Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:

= (-1)n + 1

= (-1)5 + 1

= (-1)6

= -6

Here is the complete question:

Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.

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