What is 3+√-3 in the form a+bi?

Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

Hey! Hope this helps!

Step-by-step explanation:

Have an awesome Friday <3

Approximately 456.3 feet of fence to surround the entire circular yard.

Now, For the amount of fencing needed to surround a circular yard, we have to calculate the circumference of the circle, which is the distance around the circle.

Since, The circumference of a circle is,

⇒ C = πd,

where, C is circumference, d is diameter,

Here, the diameter of the circular yard is 145 feet,

So the radius is half of that,

r = 145/2 = 72.5 feet.

So, Using the formula, we can calculate the circumference as:

C = πd

C = 3.14 x 145

C = 456.3 feet

Therefore, Approximately 456.3 feet of fence to surround the entire circular yard.

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Answer:

9 cm

Step-by-step explanation:

y = 12 - 3

y = 9

The value of given expression  [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) is 1/5

In this question, we have been an expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9)

We need to evaluate given expression.

First we write an improper fraction as proper fraction.

1 1/5 = 6/5

So given expression becomes,

[(1 1/5−2/5)⋅(− 3/4)3]÷(−9)

=  [(6/5 − 2/5) × (− 3/4) 3] ÷ (−9)

=  [(4/5) × (-9/4)] ÷ (−9)

= (-9/5) ÷ (-9)

= 1/5

Therefore, the value of given expression  [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) is 1/5

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Answer:

I would say 100 since 256.78 is closer to 100 then 1000 or 10

Step-by-step explanation:

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graphing calculator can do a nice job of showing you what the graph looks like.

The initial factor of 4 is the value when x=0, the y-intercept. The base of 2 tells you the function value is multiplied by 2 for each unit of x to the right, and divided by 2 for each unit of x to the left. (The curve quickly goes off the top of the graph.)

The horizontal asymptote is y=0, as it is for all exponential functions (that have not been translated).

Answer:

m = 0 or slope = 0

Step-by-step explanation:

Jack and Jill went for a walk separately. Jack’s total distance in blocks, x, was thirty blocks fewer than twice Jill’s total distance in blocks, y. The difference between five times Jack’s total distance and twice Jill’s total distance is ten blocks. 10 blocks did Jack and Jill each walk. This can be solved by solving equations.

An equation is an algebraic statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 6x + 11 = 14, for instance, the two expressions 6x + 11 and 14 are separated by the symbol "equal (=)"

x= 2y -30 ............. (1)

5x-2y=10 ............. (2)

substitute x= 2y-30 into the 2nd equation

or, 5(2y-30)-2y = 10

or, 10y-150-2y=10

or, 10y -150-2y= 10

or, 8y-150=10

After adding 150 on both sides we get:

or, 8y = 160

so, y = 20  

substitute y=20 into x = 2y-30

so, x = 40-30

so x = 10 & y = 20

thus, 10 blocks did Jack and Jill each walk.

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The posterior probability of a favorable market, given the prediction of the research company, is 0.84 and the posterior probability of an unfavorable market is 0.16.

It is a branch of mathematics that deals with the occurrence of a random event.

P(A|B) = P(B|A) × P(A) / P(B)

where A and B are events, and P(A|B) is the probability of event A given that event B has occurred.

P(A) = 0.58 (the prior probability of a favorable market)

P(B|A) = 18/20 = 0.9

P(not A) = 1 - P(A)

= 1 - 0.58

= 0.42 (the prior probability of an unfavorable market)

P(B'|A') = 9/12 = 0.75

To calculate P(B), we use the law of total probability

P(B) = P(B|A) × P(A) + P(B|not A) × P(not A)

We can find P(B|not A) by subtracting P(B'| A') from 1:

P(B|A)' = 1 - P(not B|not A)

= 1 - 0.75

= 0.25

Substituting the given values, we have:

P(B) = 0.9 × 0.58 + 0.25 ×0.42

= 0.62

Let us calculate the posterior probabilities:

P(A|B) = P(B|A) × P(A) / P(B)

= 0.9× 0.58 / 0.62 = 0.84

P(A|B)' = 1 - P(A|B) = 1 - 0.84 = 0.16

Therefore, the posterior probability of a favorable market, given the prediction of the research company, is 0.84 and the posterior probability of an unfavorable market is 0.16.

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Answer:

Step-by-step explanation:

The equation of any line perpendicular to a line with an equation of x= (vertical line) will have the form y= (horizontal line). In this case, since this line passes through the y value of 3, that means that the equation is y=3.

Step-by-step explanation:

Ok, so we know the bank loaned part of the $17,500 at a 4% interest rate. Lets call this loan amount x. Then the rest of the 17,500 was loaned at a 9% interest rate. Whatever this amount was, we can define it as 17,500 - x. We also know that the total interest earned was $1,100. With this information, we can form the following equation:

.04(x) + .09(17500 - x) = 1100

Multiply the .09 times the inside of the parentheses:

.04x + 1575 - .09x = 1100

Simplify:

-.05x + 1575 = 1100

-.05x = -475

x = 9500

Since x is originally the amount loaned at the 4% interest rate, we know that $9,500 was loaned at a 4% interest rate.

To figure out the other amount loaned at 9%, simply subtract 9,500 from 17,500 -- this gets us 8,000. So $8,000 was loaned at a 9% interest rate.

I hope this helps!

Noting that the tip is one among the total sum charged on the bill is the best strategy for computing the required 20% tip using fractions.

aggregate attempting to determine the whole amount, time, or quantity. The amount at issue or under investigation is very active. the overall outcome, significance, or import. a third accounting, the principal, and the interest. There are word forms for quantities, amounting, and amounted. adaptable noun A thing's quantity is how much of it there is, that however much someone have, the amount you require or how much you can get. He needs that much money to make ends meet.

given

You can use a fraction to express the percentage 20%.

This is inferred from the fact that the sign for percentage,% means to divide by 100.

Therefore, it is important to understand that 20% equals 20/100, or 1/5.

As a result, the 20% tip represents one-fifth of the total.

Noting that the tip is one among the total sum charged on the bill is the best strategy for computing the required 20% tip using fractions.

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Answer:

\(-x - y = 2\).

Step-by-step explanation:

If the slope of a line in a plane is \(m\) and the \(y\)-intercept of that line is \(b\), the slope-intercept equation of that line would be \(y = m\, x + b\).

Rearrange the equation of the given line \(-x + y = 7\) in the slope-intercept form to find the slope of this line:

\(-x + y = 7\).

\(x -x + y = x + 7\).

\(y = x + 7\).

Notice that in the slope-intercept equation of this given line, the coefficient of \(x\) is \(1\). Thus, the slope of the given line would be \(m_{1} = 1\).

Two lines in a plane are perpendicular to one another if the product of their slopes is \((-1)\). In other words, if \(m_{1}\) and \(m_{2}\) are the slopes of two lines perpendicular to each other, then \(m_{1}\, m_{2} = (-1)\).

Since \(m_{1} = 1\) for the given line, the slope of the line perpendicular to this given line would be:

\(m_{2} = (-1) / m_{1} = (-1) / 1 = -1\).

If the slope of a line in a plane is \(m\), and that line goes through the point \((x_{0},\, y_{0})\), the equation of that line in point-slope form would be:

\(y - y_{0} = m\, (x - x_{0})\).

The slope of the line in question is \(m = (-1)\). It is given that this line goes through the point \((-1,\, -1)\), where \(x_{0} = (-1)\) and \(y_{0} = (-1)\). Thus, the equation of this line in point-slope form would be:

\(y - y_{0} = m\, (x - x_{0})\).

\(y - (-1) = (-1)\, (x - (-1))\).

\(y + 1 = -(x + 1)\).

Rearrange this equation to match the format of the choices:

\(y + 1 = -x - 1\).

\(x + y = -2\).

\(-x - y = 2\).

Answer:

what is z

Step-by-step explanation:

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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For constant A to be -4 (option 1) the system of equations have exactly one real solution.

NOTE: We are working with the problem statement: Y=-3 Y=Ax2+4x-4 In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution?

We have given, y=-3

y= Ax^2+4x-4

Therefore, -3= Ax^2+4x-4

or, Ax^2+4x-1=0

For second order equation of ax^2+bx+c=0 have a solution for

x= [-b± (√b^2-4ac)]/2a]   [Ax2 + Bx + C = 0 is the Sridharacharya equation, where a, b, and c are real values and a 0. The Sridharacharya formula, which is stated as x = (-b (b2 - 4ac)) / 2a, provides the answer to the Sridharacharya equation.]

For single solution b^2-4ac=0

here, Ax^2+4x-1=0

4^2 - 4a(-1)=0

16+4a=0

a= -(16)/4

a= -4

option A is correct .

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This is only true equation when A is equal to -2. Therefore, the correct answer is B) -2.

B) -2

The given system of equations can be written as:

Y = A*x^2 + 4*x - 4

We can solve this equation by using the Quadratic Formula. The Quadratic Formula states that the solutions to the equation are given by:

x = [-b +/- sqrt(b^2-4ac)]/2a

where a, b, and c are the coefficients of the equation. In this case, a = A, b = 4, and c = -4.

Substituting these values into the equation, we get:

x = [-4 +/- sqrt(4^2-4*A*(-4))]/2A

Simplifying this, we get:

x = [-4 +/- sqrt(16 + 16A)]/2A

For the system of equations to have two real solutions, the value of the square root must be greater than or equal to zero. This means that 16 + 16A must be greater than or equal to zero.

This is only true when A is equal to -2. Therefore, the correct answer is B) -2.

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\(\text{Hello! :)}\)

\(\large\boxed{A. 7 / 18}\)

\(\text{Convert 2 4/7 into an improper fraction:}\\\\2*7 + 4 = 18 \\\\\text{(To find the numerator of the fraction)}\\\\\text{Fraction in improper form: 18/7}\\\\\text{Reciprocal of fraction: Swap numerator and denominator:}\\\\18/7 \text{ becomes } 7 / 18\)

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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The statements that are true are:

Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.

Clayton could negate both the x and y values in the points to find the points of the image.

C’ will move because all points move in a reflection.

The image and the pre-image will be congruent triangles.

The image and pre-image will not have the same orientation because reflections flip figures.

Options A, B, D, E, and F.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Clayton could use the relationship (x, y) → (y, x) to find the points of the image.

This is the y = x reflection rule.

This is true.

Clayton could negate both the x and y values in the points to find the points of the image.

Reflection of (x, y) along the x-axis and y-axis consecutively will give us

(-x, -y).

This is true.

C’ will remain in the same location as C because it is on the line of reflection.

This is not true.

C’ will move because all points move in a reflection.

This is true.

The image and the pre-image will be congruent triangles.

This is true.

The image and pre-image will not have the same orientation because reflections flip figures.

This is true.

Thus,

All statements are true except the statement:

C’ will remain in the same location as C because it is on the line of reflection.

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\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}\)

The total cost function is given by f(x). The reasonable domain for the function f(x) here is all the rational numbers.

The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. To put it another way, a number is considered rational if it can be written as a fraction in which the numerator and denominator are both integers.

The letter Q stands for the collection of rational numbers. It should be emphasised that rational numbers also contain whole numbers, integers, decimals, and natural numbers.

Here in the given question,

The domain of the function is the values for which the function is satisfied.

Here in this case the domain of the function are all rational numbers as they include decimal and whole numbers.

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Answer:

\( m=\frac{y_2 -y_1}{x_2 -x_1}\)

And replacing we got:

\( m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}\)

And we can use one of the points in order to find the intercept like this:

\( -3= \frac{2}{3} (-3) +b\)

\( b =-3 +2=-1\)

And the equation would be given by:

\( y= \frac{2}{3}x -1\)

Step-by-step explanation:

We want an equation given by:

\( y=mx+b\)

where m i the slope and b the intercept

We have the following two points given:

\( (x_1 = -3, y_1 =-3), (x_2=3, y_2 =1)\)

We can find the slope with this formula:

\( m=\frac{y_2 -y_1}{x_2 -x_1}\)

And replacing we got:

\( m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}\)

And we can use one of the points in order to find the intercept like this:

\( -3= \frac{2}{3} (-3) +b\)

\( b =-3 +2=-1\)

And the equation would be given by:

\( y= \frac{2}{3}x -1\)

Answer:

False

Step-by-step explanation:

When the Ftest is used to test the overall significance of a multiple regression model, it evaluates the significance of independent variables to the outcome of the regression model. The null hypothesis of an Ftest when used for multiple regression is that, the independent variables aren't significant in the outcome of the regression model while the alternative Hypothesis claims that the independent variables are significant .

For the overall significance evaluation, once one of the independent variables proves significant, then the overall Ftest is significant, that is it does not require that all individual independent variables are significant. The null only stands when all the independent variables are insignificant.

Therefore, the overall Ftest for significance isn't enough to prove that all individual. Independent variables are significant when the null is rejected.

Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.

The equation can be set up as follows:

0.80x + 0.55(600 - x) = 0.60(600)

Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.

By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.

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Let x=amount of 80% solution needed

Then 600-x=amount of 30% solution needed

Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:

0.80x+0.30(600-x)=0.40*600 get rid of parens

0.80x+180-0.30x=240 subtract 180 from each side

0.80x+180-180-0.30x=240-180 collect like terms

0.50x=60 divide each side by 0.50

x=120 ml---------------------amount of 80% solution needed

600-x=600-120=480 ml---------------amount of 30% solution needed

CK

120*0.80+480*0.30=0.40*600

96+144=240

240=240

The y-intercept of the linear function means that her initial distance from the finish line is of 10 kilometers.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 10, hence the intercept b is given as follows:

b = 10.

The y-values represent the distance in the context of this problem, hence the initial distance is of 10 km.

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