What happens to the rounding digit when the test digit is greater than or equal to 5 and the rounding digit is 9?

Answer:

\(16 (1 +0.09)^{8}\\\)

Future Amount = 38 (rounded)

Step-by-step explanation:

hope this helps.

Answer:

17 I think

Step-by-step explanation:

\(The series [infinity] 1 / n^6 n = 1 represents a p-series with p = 6.\)

Here's how to find the tenth partial sum, s10:

\(First, we can write the sum using sigma notation as follows:∑(n = 1 to 10) 1 / n^6\)

\(The nth term of the series is 1 / n^6.\)

T\(he first ten terms of the series are 1/1^6, 1/2^6, 1/3^6, 1/4^6, 1/5^6, 1/6^6, 1/7^6, 1/8^6, 1/9^6, 1/10^6.\)

To find the tenth partial sum, we need to add the first ten terms of the series.

\(Using a calculator, we get:∑(n = 1 to 10) 1 / n^6 ≈ 1.000000006\)

\(For the tenth partial sum, s10 ≈ 1.000000006 (rounded to six decimal places).\)

\(Therefore, the tenth partial sum of the series [infinity] 1 / n^6 n = 1 is approximately 1.000000.\)

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Compound interest formula:

A = P (1+r/n)^nt

Where:

A = total amount

P = principal investment

r= interest rate in decimal form = 2/100 = 0.02

t= years

n= number of compounding periods in a year= 12

Replacing:

A = 30,000 (1+0.02/12)^4x12

A = 30,000 (1.001666667)^48

A= 32,496.45

The percentage discount on the hammers is about 21%.

The discount is the difference between the original price and the discounted price.

Discount = $12 - $9.50

subtract the numbers

= $2.50

To find the percentage discount, we divide the discount by the original price and multiply by 100

Percentage discount = ( Discount / Original price ) x 100

Substitute the values in the equation and find the percentage discount

Percentage discount = ( $2.50 / $12 ) x 100

Do the arithmetic operation

Percentage discount = 20.83%

Rounding to the nearest whole percentage, the discount is approximately equal to 21%.

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The claim we need to check is that 16 is the 50% of 36.

Recall that if we add 50% and 50%, we should end up with 100%. In our case, we have that our 100% is 36. So, if it was true that 16 is the 50% of 36, then it should happen that if we add 16 with itself, we should get 36.

Note that

Since 16+16 is not 36, it is not true that 16 is the 50% of 36.

Answer:

it's A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Just got it correct

Answer:

3 units.

Step-by-step explanation:

In the equation x = 1/12 (y-1)², the vertex of the parabola is at the point (1,1). The focus of the parabola is located a distance called the "focal length" from the vertex.

The focal length is given by the formula f = 1/(4*p), where p is the coefficient of the x term in the standard form of the equation of the parabola.

In this case, the coefficient of the x term is 1/12, so the focal length is f = 1/(4*(1/12)) = 3. This means that the distance from the focus to the vertex is 3 units.

Answer:

8.) -120

9.) -5

10.) -1

Step-by-step explanation:

8.)  ab - c

     5(-12) - 60

     -60 - 60 = -120

9.)   -10 - (-7) + 2 (3 - 4)

      -3 + 2(-1)

      -3 + (-2) = -5

10.) Add all the numbers up then divide by how many numbers there are.

Given the equation of the line :

It is required to write the equation of the line parallel to the given line and pass through the point ( 12 , 4 )

The general equation of the line in slope - intercept form is :

Where m is the slope and b is y - intercept

As the line are parallel , so, the slope of the required line will be equal to the slope of the given line

So, the slope = m = -1/4

So, the equation of the line will be :

Using the given point ( 12 , 4 ) to find b

so, when x = 12 , y = 4

So, the equation of the required line is :

B1 is also a linear estimator since it takes a linear form, hence it satisfies the third property. Hence, B1 is BLUE.

(a) To show that B = - 1/∑Xi^2 ∑XiYi is an unbiased estimator for β, we need to show that E(B) = β.

Being given that Y1 = β + e1, where e1 is a random error term that has a mean of 0 and a constant variance.

The equation for the mean of B is E(B) = E[-1/∑Xi^2 ∑XiYi], which is equivalent to:

E[B] = -1/∑Xi^2 * E[∑XiYi]Considering that Xi and Yi are independent, we can simplify the above expression to:

E[B] = -1/∑Xi^2 * ∑XiE[Yi]We have that

E[Yi] = E[β + ei] = β, hence:

E[B] = -1/∑Xi^2 * β ∑Xi

Hence, we have that

E[B] = β * -1/∑Xi^2 *

∑Xi = β*(-1/∑Xi^2)*∑Xi

This is equivalent to: E[B] = β(-1/∑Xi^2*∑Xi), which implies that the estimator is unbiased. Hence, the answer to part (a) is YES.

(b) An unbiased estimator for β is given by:

B1 = ∑XiYi/∑Xi^2

A Linear Least Squares Estimator is considered the Best Linear Unbiased Estimator (BLUE) if it satisfies three properties:

1. Unbiasednes

s2. Minimum variance

3. LinearityB1 satisfies the first property of unbiasedness. If the population variances of errors are equal, then B1 is the minimum variance estimator, so it satisfies the second property.

B1 is also a linear estimator since it takes a linear form, hence it satisfies the third property. Hence, B1 is BLUE.

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After considering the given data we conclude that the correct answer which is the correct option is b which is 3/28, regarding the conditional probability.

We are given that an urn contains 3 green balls and 5 red balls. Let Rᵢ be the event that the i-th ball without replacement is red. We need to find \(P(R_3| R_2 \cap R_1).\)
Using the conditional probability formula, we have:
\(P(R_3| R_2\cap R_1) = P(R_3 \cap R_2 \cap R_1) / P(R_2 \cap R_1)\)
Since we are drawing balls without replacement, the probability of drawing a red ball on the first draw is 5/8. The probability of drawing a red ball on the second draw given that the first ball was red is 4/7. Similarly, the probability of drawing a red ball on the third draw given that the first two balls were red is 3/6 = 1/2. Therefore, we have:
\(P(R_3 \cap R_2 \cap R_1) = (5/8) * (4/7) * (1/2) = 5/56\)
To find P(R₂ ∩ R₁), we can use the law of total probability:
\(P(R_2 \cap R_1) = P(R_2 \cap R_1 | R_1) * P(R_1) + P(R_2 \cap R_1 | R_1') * P(R_1')\)
where R₁' is the complement of R₁ (i.e., the event that the first ball drawn is not red). Since we are drawing balls without replacement, the probability of drawing a red ball on the second draw given that the first ball was not red is 5/7. Therefore, we have:
\(P(R_2 \cap R_1) = (5/8) * (5/7) + (3/8) * (3/7) = 29/56\)
Substituting these values into the conditional probability formula, we get:
\(P(R_3| R_2 \cap R_1) = (5/56) / (29/56) = 5/29\)
Therefore, the answer is (b) 3/28.
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The complete question is
An urn contains 3 green balls and 5 red balls. Let R, be the event the i-th ball without replacement is red. Find P(R3| R2 \cap R₁).
a) 1/56
b) 3/28
c) 1/2
d) 5/8

The value of the given and completed expression in this problem is

-1

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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Answer:

180ft

Step-by-step explanation:

Answer:

140

Step-by-step explanation:

so you will have to do 10 x 12 to get 120 and then 5 x 4= 20 and add then equal to 140

plz mark the brainliest

Answer:

X= 13

Step-by-step explanation:

Given that using the letters A and B, the numbers two-letter code words can be formed: AA, AB, BB, BA. We are asked to use the letters A, B, and C to determine the number of different three-letter code words that can be formed.

A code word is a string of characters used to represent a message, where each character is usually represented by a unique symbol.A code word is a set of $3$ distinct elements of since it is three letters long. There are a total of $3$ choices for the first letter, $3$ choices for the second letter, and $3$ choices for the third letter.

We then have $3\times3\times3$ or $27$ possible code words that can be formed using these letters. Thus, the number of different three-letter code words that can be formed using the letters A, B, and C is $27$.

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Hi,

x/2 = 2x - 3

x/2 - 2x = - 3

x = 3 /(3/2)

x = 3 * 2/3 = 2

The number is 2.

Answer:

associative property

Step-by-step explanation:

because it involves grouping

Answer:

20

Step-by-step explanation:

55% of x = 11

\(\frac{55}{100}*x = 11\\\\x = 11 *\frac{100}{55}\\\\x = 20\)

Given:

The two exponential functions are shown in the given table.

To find:

The correct conclusion about the functions f(x) and g(x).

Solution:

The given functions are:

\(f(x)=2^x\)

\(g(x)=\left(\dfrac{1}{2}\right)^x\)

The function g(x) can be written as:

\(g(x)=\dfrac{1}{2^x}\)

\(g(x)=2^{-x}\)

\(g(x)=f(-x)\)

It means the graphs of f(x) and g(x) are reflections over the y-axis. So, option B is correct.

Since \(g(x)\neq -f(x)\), therefore the functions f(x) and g(x) are not the reflections over the x-axis. So, option A is incorrect.

The function f(x) is an increasing function because the base of the exponent is \(2>1\). The function g(x) is a decreasing function because the base of the exponent is \(\dfrac{1}{2}<1\). So, option C is incorrect.

At x=0 the value of f(x) is 1 and the value of g(x) is also 1. It means the functions has same initial values. So, option D is incorrect.

Therefore, the correct option is B.

We can conclude that g(x) is a reflection over the y-axis of f(x).

The two functions are:

You can see the graph of these functions at the end of the answer.

You can also notice that g(x) can be written as:

g(x) = (1/2)^x = 2^(-x) = f(-x)

Then this is a reflection over the y-axis, thing that you can also see in the graph below.

So the correct option is:

"The functions f(x) and g(x) are reflections over the y-axis."

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In a set S whic is said to be infinite if there is a one-to-one correspondence between S and a proper subset of S, then
the set of integers is infinite, the set of real numbers is infinite and if a set S has a subset A which is infinite, then S must be infinite.

Given that a set S is said to be infinite if there is a one-to-one correspondence between S and a proper subset of S, we want to prove the following statements:

(a) The set of integers is infinite.

(b) The set of real numbers is infinite.

(c) If a set S has a subset A which is infinite, then S must be infinite.

(a) Let A be the set of positive integers, i.e., A = {1, 2, 3, 4, 5, ...}. We define a function f: A → Z (the set of integers) by f(n) = n - 1. It can be shown that f is both one-to-one and onto. This means that there is a one-to-one correspondence between A and Z. By repeating the same argument, we can also prove that there is a one-to-one correspondence between the negative integers and A. Hence, Z is infinite.

(b) Suppose, for contradiction, that the set of real numbers, R, is finite. Then there would be a one-to-one correspondence between R and some finite set F. Without loss of generality, let F = {a_1, a_2, ..., a_n} where a_1 < a_2 < ... < a_n. Let ε > 0 be such that ε < min{|a_1|, |a_2| - |a_1|, ..., |a_n| - |a_(n-1)|, |a_n|}. For any x ∈ R, we consider different cases:

- If x < 0, then x < -ε < a_1.

- If 0 ≤ x < a_1, then 0 ≤ x + ε < a_1.

- If a_i < x < a_(i+1) where 1 ≤ i ≤ n - 1, then a_i + ε < x + ε < a_(i+1) - ε < a_(i+1).

- If x > a_n, then x - ε > a_n.

We define a function g: R → F by:

- g(x) = a_1 + ε if x < 0,

- g(x) = x + ε if 0 ≤ x < a_n,

- g(x) = a_(i+1) - ε if a_i < x < a_(i+1) where 1 ≤ i ≤ n - 1,

- g(x) = a_n - ε if x > a_n.

It can be shown that g is both one-to-one and onto. This contradicts the assumption that R is finite. Therefore, R must be infinite.

(c) Let S be a set such that A is a subset of S, and A is infinite. Suppose, for contradiction, that S is finite. Then, there would be a one-to-one correspondence between S and some finite set F. Let F = {a_1, a_2, ..., a_n}. There are finitely many elements in S that are not in A, denoted as {b_1, b_2, ..., b_m}. We choose ε > 0 such that ε < min{|a_1 - b_1|, |a_2 - b_2|, ..., |a_m - b_m|}. We define a function f: A → S as follows: f(a_i) = a_i for 1 ≤ i ≤ n, and f(a_i) = b_i + ε for 1 ≤ i ≤ m. It can be shown that f is both one-to-one and onto. This contradicts the assumption that S is finite. Therefore, S must be infinite.

Hence, we have proved the statements:(a) The set of integers is infinite, (b) The set of real numbers is infinite and (c) If a set S has a subset A which is infinite, then S must be infinite.

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Answer:

y=8x+6

Step-by-step explanation:

To find the derivative of f(x) = (9x^3 - 3) / (10x^2 + 2), we can use the quotient rule. The derivative is given by f'(x) = [(9x^3 + 30x) / (10x^2 + 2)] - [(9x^3 - 3)(20x) / (10x^2 + 2)^2].

To differentiate f(x) = (9x^3 - 3) / (10x^2 + 2), we can apply the quotient rule. The quotient rule states that if we have a function u(x) divided by v(x), the derivative is given by (u'(x)v(x) - u(x)v'(x)) / (v(x))^2.

In this case, u(x) = 9x^3 - 3 and v(x) = 10x^2 + 2. Taking the derivatives, u'(x) = 27x^2 and v'(x) = 20x.

Now we can substitute these values into the quotient rule formula:

f'(x) = [(u'(x)v(x) - u(x)v'(x)) / (v(x))^2]

= [((27x^2)(10x^2 + 2) - (9x^3 - 3)(20x)) / (10x^2 + 2)^2]

= [(270x^4 + 54x^2 - 180x^4 + 60x) / (10x^2 + 2)^2]

= [(90x^4 + 54x^2 + 60x) / (10x^2 + 2)^2].

Thus, the derivative of f(x) = (9x^3 - 3) / (10x^2 + 2) is f'(x) = (90x^4 + 54x^2 + 60x) / (10x^2 + 2)^2.

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The first two numbers in each row of the relative frequency table represent the percentage of cars and trucks of a particular color out of the total number of vehicles in the parking lot.

To create a relative frequency table, we need to divide the frequency of each color by the total number of vehicles (65) and then multiply by 100 to get a percentage.

Relative Frequency Table by Color:

The first two numbers in each row must add up to 100% because we are calculating the relative frequency of each color with respect to the total number of vehicles (65). Therefore, the percentage of cars and trucks of each color must add up to 100% of that color's total frequency. The total row must also add up to 100% because it represents the entire population of vehicles.

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The given question is incomplete, the complete question is:

There are 65 vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%. Frequency Table Type of Vehicle Color Car Truck Total Blue 22 14 36 Red 12 17 29 Total 34 31 65

The length of the vertical pole is 24 feet.

The length between the pole and stake is 8 feet.

We are asked to find the length of the cable needed from the top of the pole and anchored to a stake.

Let us draw a sketch to better understand the problem.

Notice that it is a right-angled triangle, so we apply the Pythagorean theorem given by

Where c is the hypotenuse (length of the cable required)

a and b are the shorter legs (length of pole and the length between pole and stake)

a = 24 feet

b = 8 feet

Let us substitute these values into the above formula and solve for c

Therefore, the required length of the cable is 25 feet. (to the nearest foot)

The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.

To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.

Plugging these values into the formula, we get

P(A | B) = 0.45 / 0.60 = 0.750.

To find P(B | A), we use the formula:

P(B | A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) = 0.45 and P(A) = 0.50.

Substituting the values, we find

P(B | A) = 0.45 / 0.50 = 0.900.

A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.

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Answer and Step-by-step explanation:

So, the negatives cancel and turn into a positive.

The red squared of 5 become green squares.

The corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

To perform u-substitution with indefinite integrals, follow these steps:

Identify a suitable substitution: Look for a part of the integrand that resembles the derivative of a function. Choose a variable u to substitute for that part.

Calculate du: Take the derivative of u with respect to the original variable. This will help us express du in terms of the original variable.

Rewrite the integral: Substitute the chosen variable and du in the original integral, replacing the part to be substituted with u and the corresponding differential element du.

Integrate with respect to u: Treat the integral as a new integral with respect to u. Evaluate the integral using the rules of integration.

Replace u with the original variable: Rewrite the result of the integration in terms of the original variable.

Simplify and solve: If necessary, simplify the expression further or perform additional algebraic manipulations to obtain the final result.

Let's illustrate these steps with an example:

Consider the integral ∫(2x + 3)² dx.

Identify a suitable substitution: Let u = 2x + 3.

Calculate du: Take the derivative of u with respect to x: du/dx = 2. Rearrange the equation to solve for du: du = 2 dx.

Rewrite the integral: In terms of u and du, the integral becomes ∫u² (du/2).

Integrate with respect to u: Treat the integral as a new integral with respect to u: (1/2) ∫u² du = (1/2) * (u³/3) + C, where C is the constant of integration.

Replace u with the original variable: Substitute back u = 2x + 3 in the result: (1/2) * ((2x + 3)³/3) + C.

Simplify and solve: Further simplify the expression if necessary to obtain the final result.

In summary, to perform u-substitution with indefinite integrals, identify a suitable substitution, calculate the corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

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