Which of the following are equivalent to x2 – 4x + 9? Select four answers.
A. (x – 3)2 – 4x
B. (3x2 – 3x + 1) – (2x2 + x – 8)
C. (x – 3)(x + 3) – 2x
D. (x – 3)2 +2x
E. (x – 5)(x + 1) +14
F. (8x2 + 2x) – (4x2 + 6x) + (9 – 3x2)

Answer: a) The probability that the system will fail during a 3-month period can be calculated as the sum of the probabilities of subsystem A and subsystem B failing, since the system fails if either one fails. The probability of subsystem A failing in 3 months is given by P(A) = 1 - e^(-0.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.0664. The probability of subsystem B failing in 3 months is given by P(B) = 1 - e^(-1.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.36. Therefore, the probability that the system will fail in 3 months is P(system) = P(A) + P(B) = 0.0664 + 0.36 = 0.4264.

b) To find the probability that there will be no more than two failures of the system during a 6-month period, we need to use the cumulative distribution function (CDF) of the Poisson distribution. Let X be the number of failures of the system in 6 months. The CDF is given by F(x) = P(X <= x) = 1 - P(X > x), where P(X > x) is the probability that there will be more than x failures. Therefore, the probability that there will be no more than two failures of the system during a 6-month period is given by F(2) = 1 - P(X > 2). We can use the formula for the Poisson distribution to find P(X > 2), which is P(X > 2) = e^(-6 * (P(A) + P(B))) * ((6 * (P(A) + P(B)))^3 / 3! + (6 * (P(A) + P(B)))^2 / 2! + 6 * (P(A) + P(B)) / 1! + 1). Plugging in the values for P(A) and P(B) from part (a), we get F(2) = 1 - e^(-6 * 0.4264) * ((6 * 0.4264)^3 / 3! + (6 * 0.4264)^2 / 2! + 6 * 0.4264 / 1! + 1) = 1 - 0.2079 = 0.7921.

c) To find the probability that the next system failure will occur within a year, we need to find the cumulative distribution function (CDF) of the time between failures, which is the sum of the time between failures of subsystem A and subsystem B. Let X be the time between failures of subsystem A, which follows an exponential distribution with rate 0.2 per month. Let Y be the time between failures of subsystem B, which also follows an exponential distribution with rate 1.2 * 0.2 = 0.24 per month. Then the CDF of the time between failures is given by F(t) = P(X + Y <= t) = 1 - P(X + Y > t0.2 * 12) * e^(-0.24 * 12) = 1 - 0.17 = 0.83. Therefore, the probability that the next system failure will occur within a year is 0.83.

Step-by-step explanation:

Triangle is a polygon with 3 sides. The record of the letters in your triangle from left to right is EGFBIHDCA.

A triangle is a polygon with 3 sides. Also, It has three vertices.

As the example is given to us, ABCDEFGHI is the record of the letters that are when seen from top to bottom, therefore, if we rotate the triangle such that the left side of the triangle is on the upper side, then the triangle we will get is given below.

Thus, the record of the letters in your triangle from left to right is EGFBIHDCA.

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The local maximum for the graph below is given at point b.

A function has a local maximum when it changes from increasing to decreasing.

For the graphed function, we have that the function is increasing until point b, and then it starts to decrease, hence the local maximum is given at point b.

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The binomial distribution P( x = 4 ) if n = 5 and p = 0.7 is 0.3602.

Binomial probability distribution determines the probability of a discrete random variable.

Given that;

Using the formula, probability mass function;

P( X = x ) = ⁿCₓPˣ( 1 - P )ⁿ⁻ˣ

P( X = x ) = ⁵Cₓ × 0.7ˣ × ( 1 - 0.7 )⁵⁻ˣ

Now for P( x = 4 )

P( X = 4 ) = ⁵C₄ × 0.7⁴ × ( 1 - 0.7 )⁵⁻⁴

P( X = 4 ) = ⁵C₄ × 0.7⁴ × ( 1 - 0.7 )

P( X = 4 ) = 5 × 0.2401 × 0.3

P( X = 4 ) = 0.3602

Therefore, the value of P( x = 4 ) is 0.3602.

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a. A rise in the unemployment rate accompanies a fall in real GDP. - Consistent

b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed. - Not consistent

c. Negative real GDP growth is associated with a fall in the unemployment rate. - Not consistent

This is consistent with the observed relationship between real GDP growth and changes in the unemployment rate. An increase in real GDP is associated with a decrease in the unemployment rate, and vice versa.

This is because when GDP increases, businesses are able to hire more workers, leading to a decrease in the unemployment rate. Conversely, when GDP decreases, businesses may have to lay off employees or reduce their hours, leading to an increase in the unemployment rate.

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The complete question is:

Which of the following are consistent with the observed relationship between growth in real GDP and changes in the unemployment rate as shown in Figure 8-5? Which are not?

a. A rise in the unemployment rate accompanies a fall in real GDP.

b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed.

c. Negative real GDP growth is associated with a fall in the unemployment rate.

According to the posed question, the rectangular prism's surface area would be 90 cm2.

What is a Rectangular Prism's Surface Area?

The total surface area of a rectangular prism's rectangular faces is alluded to as the prism's surface area. There are two distinct types of it: lateral surface area and total surface area. In contradiction to the lateral surface area, which only includes the lateral faces and omit the base areas, the total surface area of a rectangular prism refers to the area among all six faces.

Given, W = 3 cm, L = 6 cm, and H = 3 cm

surface area = 2 (WL + LH + HW)

                     = 2 (18 + 18 + 9)

                      = 2× 45 = 90 cm².

Consequently, the rectangular prism's surface area is 90 cm².

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Answer:

a -3.9

Step-by-step explanation:

Subtract 13 from both sides which makes it -19 > 5x. then divide by 5 on both sides

Answer:

ummmm i would say unbiased fam only bc i love ice cream and i always wonder whichwtch one does people like more.

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

They both dont touch and go in the sam direction

Answer:

Below

Step-by-step explanation:

It APPEARS that First and last choices are true.....the lines do not cross in the picture...BUT you cannot say for SURE they are parallel  without more information about the angles at  D E H and I    ....or markings

The statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

In relation to the original function f, the inverse function is denoted by the symbol f⁻¹, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.

We know that inverse of function is NOT the reciprocal of f. The composition of the function f and the reciprocal function f inverse gives the domain value of x.

Hence, the statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

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An absolute value inequality that expresses the actual temperature in your city, given that the average January temperature is 45° F and the temperature can vary up to 5° F warmer or colder, would be: | x - 45 | ≤ 5.

Where x represents the actual temperature in degrees Fahrenheit.

An inequality with an absolute value expression is referred to as an absolute value inequality. A quantity is enclosed in vertical bars (| |), which stand for the distance between that quantity and zero on the number line, to indicate an absolute value statement. The absolute value of an integer is always positive, hence regardless of the sign of x, |x| indicates the distance of x from zero.

Finding all feasible values of the variable that meet the inequality is the goal when resolving an absolute value inequality. To accomplish this, we first isolate the expression defining the absolute value, and then divide the inequality into two cases, one for positive and one for negative expressions defining the absolute value. Then, we resolve each case separately and combine the solutions.

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Size of the house should be 2900 ft².

Correct option is B.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

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"When solving an inequality, if you the coefficient is negative, as in-3x > 9, the inequality" statement becomes: true

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers. The equals sign in the equation-like phrase 7x 4 > 2x + 5 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 7x 4, is larger than the right part, 2x + 5, in the equation. Finding the values of x for which the inequality holds true will be of importance to us.

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The given conclusion "(x + 2)² = (x² + 2)" is false.

The two set representation methods are -

Given is the set A{1, 2, 3}.

(x + 2)² should be equal to (x² + 2) for all x ∈ A.

We can write -

(1 + 2)² = 1² + 2

9 ≠ 3

Therefore, the given conclusion "(x + 2)² = (x² + 2)" is false.

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{Question in english -

For all x in A: {1, 2, 3}, (x + 2)² is equal to (x² + 2). True or false?}

To find the x-intercept of the equation 3x + 5y = 9, we set y = 0 and solve for x.When y = 0, the equation becomes 3x + 5(0) = 9, which simplifies to 3x = 9.Solving for x, we get x = 3.The x-intercept of the equation 3x + 5y = 9 is (3, 0).

What is x-intercept ?

An x-intercept is a point where a graph or a line crosses the x-axis. It is the value of the independent variable (x) when the dependent variable (y) is equal to zero. In other words, it is the point at which a function or equation intersects the x-axis, and its coordinates are of the form (x, 0). To find the x-intercept of a graph or equation, you can set y=0 and solve for x.

To find the x-intercept of the equation 3x + 5y = 9, we need to set y = 0 and solve for x.

So, we have:

3x + 5(0) = 9

3x = 9

x = 3

Therefore, the x-intercept of the equation 3x + 5y = 9 is (3,0), which means the point where the line intersects the x-axis is (3,0).

To verify, we can graph the equation and see that the point (3,0) is indeed on the x-axis.

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The average rent of a one-bedroom apartment in Brooklyn is estimated to be $2,836.69 in 2023 after the 2.5% increase in both 2022 and 2023

What is the percentage increase?

Percentage increase is a measure of how much a value or quantity has increased relative to its original value, expressed as a percentage.

To calculate the percentage increase, you can use the following formula:

Percentage increase = (New value - Old value) / Old value x 100%

If the average rent of a one-bedroom apartment in Brooklyn is $2,700 in 2021, and it increases by 2.5% in both 2022 and 2023, we can calculate the average rent in 2023 as follows:

Calculate the increase in rent due to the 2.5% increase in 2022:

2.5% of $2,700 = 0.025 x $2,700 = $67.50

The new rent in 2022 will be $2,700 + $67.50 = $2,767.50

Calculate the increase in rent due to the 2.5% increase in 2023:

2.5% of $2,767.50 = 0.025 x $2,767.50 = $69.19

The new rent in 2023 will be $2,767.50 + $69.19 = $2,836.69

Therefore, the average rent of a one-bedroom apartment in Brooklyn is estimated to be $2,836.69 in 2023 after the 2.5% increase in both 2022 and 2023.

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The copy machine make 44 copies per minute.

The unitary method is the method of solving a problem by the first value of a single unit and than finding the value of single unit by multiplying. Unitary method is a technique by which we can find the value of a single unit from the value of multiple data and also the value of more than one unit from the value of single unit. This is a method that we use for most of the calculations in mathematics;

We are given that Time copy machine take= 4min 15sec

Number of copies=187

Now, 1min=60sec

4min=240sec

Total time=240+15 =255sec

Therefore, 255sec=187copies

60sec= 187 x 60/255

=44

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C - this equation is simplified to a numeric identity. the variable has infinite solutions.

8k - 14 = -4k + 10 + 12(k - 2) --> use distributive property

8k - 14 = -4k + 10 + 12k -24 --> combine like terms

8k - 14 = 8k -14 --> combine like to each side

8k - 8k = -14 + 14 --> simplify

0 = 0

note, the variable cancels out, therefore there is no identity and ANY numeroc value can be used, as ant value will cancel itself out.

this means there is an infinite numbers of solutions.

When x changes from 2 to 5, the average velocity (or average rate of change of y with respect to x) is 9.33 m/s. When x changes from 2 to 2 + h, the average velocity is 2 + hm/s.

Average speed is determined by dividing the total distance you travelled by the total time, whereas average velocity is determined by dividing your displacement (a vector Throughout the entire period, position to your finish position).

(A) The following formula is used to get the average velocity when x changes from 2 to 5:

value of y at x = 2

= 2²+2 = 6 m

value of y at x = 5

= 5²+5 = 30 m

displacement equals 30 – 6 = 24 m.

Time is 5 - 2 = 3 seconds.

average velocity

= displacement /Time duration

= 24/3 = m/s

B) Value of y at x = 2 = 5 for x changing from x to x plus ie for minimal change in x.

Displacement during a little change in x will be 0 because the value of y will once again be 5.

C )  

y(x) = x² + x

dy / dx = 2x + 1

dy / dx  represents instantaneous  velocity

so when x = 2

instantaneous velocity = 2 x 2 +1

= 5 m /s

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Answer:

simple interest is $6.8

Miguel pay the amount to Julio at the end of 6​ months was $206.8

Step-by-step explanation:

Given : Miguel Rodriguez borrowed ​$200 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.8​%.

To Find : ​a) How much will the interest amount​ to?

​b) What amount must Miguel pay Julio at the end of 6​ months?

Solution :

Formula for simple interest :

Where rate is in decimal

Time is in years

So, rate of interest = 6.8 % = 0.068

Time = 6 months = 6/12=0.5

Principal = $200

Thus= 200x0.068x0.5=6.8

[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank [tex]\frac{1}{2}[/tex] glass each.

Meaning of fraction = An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

Annie made 4 glasses of juice

To find = fraction of juice that was left

Total glasses of juice = 4

Her 5 friends drank 1/2 glass each

= 5 × [tex]\frac{1}{2}[/tex]

= [tex]\frac{5}{2}[/tex]

Fraction of juice that left,

5 - [tex]\frac{5}{2}[/tex]

Subtracting by taking LCM,

= [tex]\frac{10 - 5}{2}[/tex]

= [tex]\frac{5}{2}[/tex]

[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank 1/2 glass each.

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The function for the given zeros is f(x)=2x³-8x²+8x-32.

The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.

Given that, n=3.

x=4 and x=2i

We then know that the third root must be x=-2i

Now, f(x)=a(x-4)(x-2i)(x+2i)

= a(x-4)(x²-(-2i)²)

= a(x-4)(x²-(-4))

= a(x-4)(x²+4)

= ax²(x-4)+4(x-4)

f(x)= a(x³-4x²+4x-16)

f(1)=a(1³-4×1²+4×1-16)

-30=a(1-4+4-16)

a=2

Now, f(x)=2(x³-4x²+4x-16)

f(x)=2x³-8x²+8x-32

Therefore, the function is f(x)=2x³-8x²+8x-32.

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The concept of exponential growth function is discussed below.

An exponential function is of the form -

y = A(B)ˣ

Given is to explain exponential growth.

Exponential growth of a quantity happens if the rate of instantaneous change is directly proportional to the quantity itself. The general exponential function is -

y = A(B)ˣ

More specifically -

[tex]$f(x)=a(1+r)^{x}[/tex]

where -

f(x) = exponential growth function

{a} = initial amount

{r} = growth rate

{x} = number of time intervals

Therefore, the concept of exponential growth function is discussed above.

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{Question in english -

What is exponential growth?}

Possible answers are:

3

4

5

6

7

8

9

Joe was given  $329 for an overnight trip because he drove a distance of 220 miles

How to solve Word Problems ?

Five Easy Steps to Solving Word Problems (WASSP)

Given Data

Amount rep receive = $175

Added amount per mile driven = $0.70

Reimbursed/Total  = $329

The Mathematical relation for this scenario is

Total amount = Amount Receive+ 0.7*Distance driven

let the distance driven be x

Substituting our given data into the relation we have

329= 175+ 0.7*x

329-175 = 0.7x

154 = 0.7x

divide both sides by 0.7

x = 154/0.7

x = 220miles

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Shipping Central charges $0.51 more than Globe Delivery for any given weight of the package.

The cost for shipping a package that weighs x pounds from Boise to Los Angeles is shown below.

Company                    Cost ($)

Shipping Central        3x+3.50

Globe Delivery          2x + 2.99

To determine the amount more Shipping Central charges than Globe Delivery, you can subtract the cost function for Globe Delivery from the cost function for Shipping Central.

The difference between the two cost functions is:

3x + 3.50 - (2x + 2.99) = x + 0.51 = $0.51 + x

This means that, for any given weight of the package, Shipping Central charges $0.51 more than Globe Delivery.

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Answer:

3.4 x 10⁻²  kg · m²/s²

Step-by-step explanation:

[tex]3.4\times \:10^5=340000[/tex]

The numerator is in g.cm² and the denominator is the same s²

So we only need to convert the numerator from g.cm² to kg.m²

1 kg = 1000 grams = 10³ grams
1 gm = 1/10³ kg
1 gm = 10⁻³ kg

1 m = 100 cm = 10² cm

1 m² = 100² cm² = (10²)² = 10⁴ cm²

Or 1 cm² = 1/10⁴ cm² = 10⁻⁴ cm²

Therefore to convert g · cm² to kg · m² we multiply by

(10⁻³)  · (10⁻⁴) = 10⁻⁷

Therefore 3.4 x 10⁵ g · cm² =  3.4 x 10⁵ x 10⁻⁷ kg · m²

= 3.4 x 10⁻² kg · m²/s²

Answer:

3

Step-by-step explanation:

Parenthesis

Exponent

Division

Multiplication

Addition

Subtraction

(1.3+0.2) ÷ 5+2.7

paranthesis first

1.5 ÷ 5 + 2.7

Division next

0.3 +2.7= 3

The distance from the apex, or top of the pyramid, to each vertex of base is 10.9.

A right rectangular pyramid is a pyramid, with four slant sides, and a rectangular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Given that;

Altitude of pyramid= 10

Each side base of pyramid= 6

Now,

So using pythagorean theorem,

x2=y2+(10)2....1

with y half of the length of the diagonal of the base.

2y=length of the diagnol

and (2y)2 = 72

4y2=72

y = 3√2.

So substitute y in eq1 and get x

( 3√2)2+(10)2=(x)2

(x)2=118

x=10.86.

x≈10.9

Therefore, the side of  right square pyramid will be 10.9.

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