6 divided by 1 5/16

Answer:

100.

Step-by-step explanation:

25%*400

=100

¡Espero que esto haya ayudado!

A complementary angle is 90 degrees. The ratio is 2:3 so the equation would be:

2x+3x=90

5x=90

x=18

One of the angles would be 2(18) or 36 degrees and the other angle would be 3(18) or 54 degrees.

36+54 is equal to 90 degrees so it checks out.

Answer:

0.01 goes in the first box

0.10 goes in the second box

Therefore, the first equation is 0.01p + 0.10d = 1.50

===========================================================

Reason:

The last part mentions "A penny is 0.01" which means $0.01 or 1 cent. The 0.01 is the coefficient of the variable p.

1 penny = $0.01

p number of pennies = 0.01p dollars

A similar situation happens with the dimes.

Answer:

-1

Step-by-step explanation:

(9,3) (0,12)

(x1,y1) (x2,y2)

to find the slope, use this equation:

y2-y1/x2-x1

12-3/0-9

the slope is 9/-9 = -1

Answer:

5 7/12

Step-by-step explanation:

Convert 5.5833333333333

The length of the guy wire is approximately 21 feet

From the question, we are to calculate the length of the guy wire.

To calculate the length of the guy wire,

First, we will determine the height of the tower.

Let the height of the tower be h

From the given diagram, we can write that

h/(9 +4) = 5/4

h/13 = 5/4

h = (13×5)/4

h = 65/4

h = 16.25 feet

Let the length of the guy wire be l

Then,

From the Pythagorean's theorem we can write that

l² = 16.25² + (9+4)²

l² = 264.0625 + 13²

l² = 264.0625 + 169

l² = 433.0625

l = √433.0625

l = 20.81015

l ≈ 21 feet

Hence, the length is approximately 21 feet

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we have two points (x, y): (0,1) and (1,3)

We can use the point-slope form

(y - y1) = m (x -x1)

The slope = m= (y2-y1)/ (x2-x1)

or

The slope-intercept form.

y = mx + b

m= (y2-y1)/ (x2-x1)

y-intercept is (0, b)

__________________________

Using The slope-intercept form,

y = mx + b

b = 1

point (0,1)

Replacing

y = mx + 1

finding the slope

point 1 (0, 1), x1= 0; y1= 1

point 2 (1, 3); x2= 1; y2= 3

m= (y2-y1)/ (x2-x1)

Replacing

m= ( 3- 2)/ (1 - 0) = 2/1 = 2

___________________

Replacing the slope

y = 2x + 1

__________________

Answer

y = 2x + 1

Answer:

last option

Step-by-step explanation:

-8,√1,2.12,25/8

The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

a) The probability that in any given hour zero new visitors will arrive at the website is given by;P(X = 0) = (e^-λ λ^0)/0!Where λ = 2.3Thus;P(X = 0) = (e^-2.3 2.3^0)/0!P(X = 0) = (0.1003)/1P(X = 0) = 0.1003b) The probability that in any given hour exactly one new visitor will arrive at the website is given by;P(X = 1) = (e^-λ λ^1)/1!Where λ = 2.3Thus;P(X = 1) = (e^-2.3 2.3^1)/1!P(X = 1) = (0.2303)/1P(X = 1) = 0.2303c) The probability that in any given hour two or more new visitors will arrive at the website is given by;P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)Thus;P(X ≥ 2) = 1 - 0.1003 - 0.2303P(X ≥ 2) = 0.6694d) The probability that in any given hour fewer than three new visitors will arrive at the website is given by;P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)Thus;P(X < 3) = 0.1003 + 0.2303 + 0.2642P(X < 3) = 0.5948Therefore,The probability that in any given hour zero new visitors will arrive at the website is 0.1003.The probability that in any given hour exactly one new visitor will arrive at the website is 0.2303.The probability that in any given hour two or more new visitors will arrive at the website is 0.6694.The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

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The series solution of the given differential equation at x = 0 is y(x) = ∑ limit k=0 to ∞​[ (k+2)(k+1)a(k+2) + ak ] \(x^k\), with the values of a0 and a1 determined by y(0) and y'(0).

The differential equation is not provided, but I can help you with the series solution.

Assuming the differential equation is of the form:

y''(x) + p(x)y'(x) + q(x)y(x) = 0

We can guess a solution of the form:

y(x) = ∑ limit k=0 to ∞​ ak \(x^k\)

Taking the first and second derivatives of y(x), we get:

y'(x) = ∑ limit k=0 to ∞​  akk

y''(x) = ∑ limit k=0 to ∞​  akk(k-1)\(x^{(k-2)\)

Substituting these into the differential equation and simplifying,

We get the following recurrence relation:

[(k+2)(k+1)ak+2​+ak​] = 0

We are also given that the series solution is valid at x = 0.

So we can use this condition to find the values of a0 and a1 as follows:

a0 = y(0)

a1 = y'(0)

The general solution in summation notation with the summation index symbol is:

y(x) = ∑ limit k=0 to ∞​[ (k+2)(k+1)a(k+2) + ak ] \(x^k\)

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Answer:

0<r<4

Step-by-step explanation:

-8<8-4r<8

Subtract 8 from each side

-8-8<8-4r-8<8-8

-16<-4r<0

Divide by -4, remembering to flip the inequality

-16/-4>-4r/-4>0/-4

4>r>0

Rewriting

0<r<4

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).

A) \(log(n^200) log(n^2)\)

Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100

This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.

B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sqrt(n) / log(n)]

As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

C) 3^n 5^n

Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([3^n / 5^n]\)

As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

D) sin(n) + 3 cos(n) + 1

Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]

As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.

Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.

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Answer:

Step-by-step explanation:

show picture

\(12 {x}^{2} + 8x + 1\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((4 {x}^{2} + 6x + 7) - ( - 8 {x}^{2} - 2x + 6) \\ = 4 {x}^{2} + 6x + 7 + 8 {x}^{2} + 2x - 6 \\ = 4 {x}^{2} + 8 {x}^{2} + 6x + 2x + 7 - 6 \\ = 12 {x}^{2} + 8x + 1\)

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

The expression becomes:

Explanation:

We want to solve the expression:

First of all, notice there is a mixed fraction in the expression. This can be converted into an improper fraction. Doing that, the expressioin becomes:

Next, we remove the bracket by multiplying each element in the bracket by 4.

Which becomes:

Now, we make this expression a single fraction as:

The correct answer is  your friend needs to deposit approximately $13,334.45 annually from her 26th birthday to her 65th birthday to be able to make the desired withdrawals at retirement.

To determine the annual deposit your friend needs to make for her retirement fund, we'll calculate the present value of the desired withdrawals during retirement and then solve for the equal annual deposit.

Step 1: Calculate the present value of the withdrawals during retirement

Using the formula for the present value of an annuity, we'll calculate the present value of the $250,000 withdrawals per year for 20 years after retirement.

\(PV = CF * [1 - (1 + r)^(-n)] / r\)

Where:

PV = Present value

CF = Cash flow per period ($250,000)

r = Rate of return after retirement (5%)

n = Number of periods (20)

Plugging in the values, we get:

PV = $250,000 * \([1 - (1 + 0.05)^(-20)] / 0.05\)

PV ≈ $2,791,209.96

Step 2: Calculate the equal annual deposit before retirement

Using the formula for the future value of an ordinary annuity, we'll calculate the equal annual deposit your friend needs to make from her 26th birthday to her 65th birthday.

\(FV = P * [(1 + r)^n - 1] / r\)

Where:

FV = Future value (PV calculated in Step 1)

P = Payment (annual deposit)

r = Rate of return before retirement (8%)

n = Number of periods (40)

Plugging in the values, we get:

$2,791,209.96 = \(P * [(1 + 0.08)^40 - 1] / 0.08\)

Now, we solve for P:P ≈ $13,334.45

Therefore, your friend needs to deposit approximately $13,334.45 annually from her 26th birthday to her 65th birthday to be able to make the desired withdrawals at retirement.

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The formula using the pronumerasl we get

For 'e' the formula stands as 2f = g+1

For 'f' the formula stands as c = 3s + 1

For 'g' the formula stands as a = 4d-3

For 'h' the formula stands as g = 5g-4

For 'i' the formula stands as e = 11f- 20

For 'j' the formula stands as q = 20p + 4

For 'k' the formula stands as t = 4b

For 'l' the formula stands as p = 3u - 1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.

One of the significant forms used to express a straight line algebraically is the two point form. Each point on the line fulfills the equation for the line, which means that the equation for the line represents every single point on the line. When two points on a line, (x 1, y 1) and (x 2, y 2), are known, the two-point form of a line is used to get the equation of the line.

For 'e' the formula stands as 2f = g+1

For 'f' the formula stands as c = 3s + 1

For 'g' the formula stands as a = 4d-3

For 'h' the formula stands as g = 5g-4

For 'i' the formula stands as e = 11f- 20

For 'j' the formula stands as q = 20p + 4

For 'k' the formula stands as t = 4b

For 'l' the formula stands as p = 3u - 1

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Answer:

It's a bit hard to explain, in my opinion. but I'll give it a go. Lets say you have 10 full pizzas, and you want to split it upon 5 people. Now 5 2 slices is 10, like 5x2 so basically, it's kind of like backwards multiplying. if that makes sense. Think of it like this. if you see something like 14 ÷ 2,  think of what number times 2 would be 14. 7, exactly. So Just write the number thats missing. Thats how i like to think of it. What number is missing.

Step-by-step explanation:

Sorry if this doesnt make sense and sorry if you dont understand.

I just started 6th grade so im not sure if i had the right idea in my noggin

The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

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Answer:

Yes.

Step-by-step explanation:

Yes.   Because opposite angles are congruent.

Answer:

yes

Step-by-step explanation:

because opposite angles are congruent

The number of ways for filling 4 positions out 17 applicants is 57120

For the local dry cleaner 17 candidates were interviewed.

There are four positions available cashier, washer, salesperson, and delivery driver.

To calculate number of ways by which they can fill those 4 positions first we need to find the no of ways to select 4 candidates out of 17 candidates.

No of ways to select r candidates out of n

= nCr

=( n!) / (r!)(n-r)!

= 17!/( 4! ) ( 17-4)!

17Cr = 2380.

For assigning the four positions to the four candidates there are

17C4 x 4! ways.

So, The number of ways for filling 4 positions out 17 applicants = 2380 x 4!

The answer to this problem is 57120.

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Answer:

Step-by-step explanation:

The first four nonzero terms in the power series expansion option (D) - \(x^{3/6} + x^{5/120} - x^{7/5040\)

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the co-domain), where each input has exactly one output and the output can be linked to its input.

The power series expansion of the function f(x) = sin(x) about x = 0 is given by:

f(x) = \(x - x^{3/3}! + x^{5/5}! - x^{7/7}! + ...\)

To find the first four nonzero terms, we substitute x = 0 into the series and discard all the terms that are zero:

f(0) = 0 - 0 + 0 - 0 + ... = 0

f'(0) = 1 - 0 + 0 - 0 + ... = 1

f''(0) = 0 - 3!/2! + 0 + 0 + ... = -3/2

f'''(0) = 0 + 0 + 5!/3! - 0 + ... = 5/6

Therefore, the first four nonzero terms in the power series expansion of sin(x) about x = 0 are:

sin(x) ≈ \(x - x^{3/3}! + x^{5/5}! - x^{7/7}!\)

Simplifying this expression, we get:

sin(x) ≈ \(x - x^{3/6} + x^{5/120} - x^{7/5040\)

So, the correct answer is option (D) - \(x^{3/6} + x^{5/120} - x^{7/5040\).

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Answer:

A. Distributive Property

Step-by-step explanation:

The 2 is being distributed to the 5 and the 9.

Answer:

Distributive Property

Step-by-step explanation:

You are distributing 2➡️(5+9)

There are 12 cells or groups in a 3 × 4 ANOVA design.

So, the answer is option B.

This design involves three levels of one independent variable and four levels of another independent variable, resulting in 12 unique combinations or cells.

Each cell represents a specific condition or treatment group in the study, and the dependent variable is measured for each group.

ANOVA, or analysis of variance, is a statistical method used to compare means between groups to determine if there are significant differences. Understanding the number of cells or groups in the design is important for planning the study and interpreting the results accurately.

Hence,the correct answer is B.

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The exact angles between 0 and 2π radians that are coterminal to π are 3π and -π. In degrees, the coterminal angles would be 540 degrees and -180 degrees.

The angle π (pi) is equivalent to 180 degrees. To find the exact angle between 0 and 2π radians that is coterminal to π, we need to find angles that have the same initial and terminal sides as π.

Since π is equivalent to 180 degrees, we can start by adding or subtracting multiples of 2π (360 degrees) to find coterminal angles. Adding 2π to π gives us 3π, which is coterminal to π. Similarly, subtracting 2π from π gives us -π, which is also coterminal to π.

So, the exact angles between 0 and 2π radians that are coterminal to π are 3π and -π.

In degrees, the coterminal angles would be 540 degrees and -180 degrees.

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Thus, if M = $1.5 trillion, V = 7, and P = 1.05, the real output of the economy (Q) is $10 trillion.

The equation of exchange is an economic equation that relates the money supply (M) with the price level (P), the velocity of money (V), and the real output of the economy (Q). The equation is M x V = P x Q.

Using the given values of M = $1.5 trillion, V = 7, and P = 1.05, we can solve for Q by rearranging the equation as Q = M x V / P.

Plugging in the numbers, we get:

Q = ($1.5 trillion x 7) / 1.05 = $10 trillion

Therefore, if M = $1.5 trillion, V = 7, and P = 1.05, the real output of the economy (Q) is $10 trillion.

It's worth noting that the equation of exchange is a theoretical model and may not reflect actual economic conditions. In practice, changes in any one of the variables (M, V, P, or Q) can affect the others, and there may be other factors at play that influence the economy.

Nonetheless, the equation of exchange provides a useful framework for thinking about the relationship between the money supply, prices, and economic activity.

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Complete question

in the equation of exchange, if m = $1.5 trillion, v = 7, and p = 1.05, then:

Find real output.