A mathematics class is given the following trinomial to factor using the grouping method. 6x2 + 11x - 10 Which of the following students has correctly identified the first step towards factoring this trinomial correctly

Rounded answers In Your calculations to find missing measures is given below.

Given: a = 8.72, b = 11.1, c = 11.7

Using the Law of Cosines, we can calculate angle A:

A = arccos((b2 + c2 - a2)/2bc)
A = arccos((11.12 + 11.72 - 8.722)/(2*11.1*11.7))
A = arccos(2.61/265.57)
A = arccos(0.00984)
A = 89.8°

Using the Law of Sines, we can calculate angle B:


Using the Law of Cosines, we can calculate side c:

c2 = a2 + b2 - 2abcos(C)
c2 = 8.722 + 11.12

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Yes, the set of all real numbers is uncountably infinite but "infinity" is not   a member of the set of real numbers.

Basically, The real numbers R is the set of "all the numbers" on the number line that  includes the rationals and irrationals together.

The real numbers are an uncountably infinite set – there actually are far more real numbers than there are natural numbers, and there is no way to line up the reals and the naturals so that we are assigning exactly one real number to each natural number. Hence there is no possible way of counting the number it can be considered in the category of uncountably infinite. If the domain of a function is all real numbers, you can represent this using interval notation as (−∞,∞), however "infinity" is not a member of the set of real numbers.

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Answer: 27

Step-by-step explanation:

The given equation rearranged so that the variable q is the independent variable is 12r + 4r = 3q + 7q OR 16r = 10q

From the question, we are to rearrange the given equation so that the variable q is the independent variable

From the given information,

The give equation is

−7q + 12r = 3q − 4r

Add 7q to both sides of the equation

−7q + 7q + 12r = 3q + 7q − 4r

12r = 3q + 7q − 4r

Add 4r to both sides of the equation

12r + 4r = 3q + 7q − 4r + 4r

12r + 4r = 3q + 7q

Simplifying

16r = 10q

The equation rearranged is 12r + 4r = 3q + 7q OR 16r = 10q

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Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of plotting data.

The most typical method of utilizing a chart to convey data is to graph the correlation of two additional variables. Diagrams created by hand or using a computer are also acceptable. From the origin, go three up, then 2 pieces to the right. On the reference system, it is important to display the digits for positions 2, 3, and 4. Be really explicit with your points. The pinkish squiggle with the letter P represents the value of 2.3. You must first generate a number line for each number in a collection of data to be able to create a chart.

Here,

Given :

Data gathered from hospitals is frequently used by institutions like the US Center of Disease Control (cdc).

In order to determine what data they use,

From the information provided, it is clear that they are using second-party data.

Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of charting the data.

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The angular velocity is 0.14 rad/sec.

The velocity of the Ferris wheel if it becomes disengaged from the motor and rolls away is 17.44 ft/sec.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Diameter of the Ferris wheel = 250 feet

The radius of the Ferris wheel = 125 feet

Now,

The linear velocity v = wr

Where w is the angular velocity.

The angular velocity.

w = v/r

The linear velocity v.

v = 2πr/T

v = (2 x 3.14 x 125) / 45

v = 17.44 ft/sec

The angular velocity.

w = v / r

w = 17.44/125

w = 0.14 rad/sec

Thus,

Angular velocity is 0.14 rad/sec.

The velocity of the Ferris wheel after disengaging from the motor is

17.44 ft/sec.

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Answer:

The answer would be 70

Step-by-step explanation:All you have to do is divide 840 by 12 and you get 70 Hope this helps and have a great week:)

Answer:

70

Step-by-step explanation:

This is because 840/12=70

Hope it helps you

PLS RATE AS BRAINLIEST ANSWER

Answer:

j+k=468

j=52 + j

are the correct equations

The time estimates for units 2, 3, 4, and 5, rounded to 2 decimal places, are 4.8 hours, 34.56 minutes, 4.14 minutes, and 0.48 minutes respectively.

A learning percentage is the percentage by which the time required to complete a task decreases as the number of units produced increases. In this case, the learning percentage is 88%.

To develop the time estimates for units 2, 3, 4, and 5, we can use the formula:

Time for unit n = Time for unit 1 (1 - learning percentage)⁽ⁿ⁻¹⁾

Where n is the unit number, and the learning percentage is expressed as a decimal.

For example, to find the time estimate for unit 2:

Time for unit 2 = Time for unit 1 (1 - 0.88)⁽²⁻¹⁾

= 40 (1 - 0.88)

= 40 × 0.12 = 4.8 hours

To find the time estimate for unit 3:

Time for unit 3 = Time for unit 1 (1 - 0.88)²

= 40 (1 - 0.88)²

= 40 × 0.12²

= 0.576 hours

= 34.56 minutes

To find the time estimate for unit 4:

Time for unit 4 = Time for unit 1 * (1 - 0.88)^(4-1)

= 40 * (1 - 0.88)^3

= 40 * 0.12^3

= 0.069 hours

= 4.14 minutes

To find the time estimate for unit 5:

Time for unit 5 = Time for unit 1 * (1 - 0.88)^(5-1)

= 40 * (1 - 0.88)^4

= 40 * 0.12^4

= 0.008 hours

= 0.48 minutes

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Answer:x-5.50=20

Step-by-step explanation:

The probability that both balls removed are red is 10.7%, while the probability that the second ball removed is red is 19.0%.

(a) The conditional probability that the second ball you remove is red given that the first ball you remove is red is 2/7 or 28.6%.

P(second ball is red | first ball is red) = P(second ball is red and first ball is red) / P(first ball is red)

= (2/7) / (3/8)

= 2/7

(b) The probability that both balls that you remove are red is (3/8)*(2/7) = 6/56 or 10.7%.

P(both balls are red) = P(first ball is red) * P(second ball is red | first ball is red)

= (3/8) * (2/7)

= 6/56

(c) The probability that the second ball that you remove is red is (2/7)*(5/9) + (3/8)*(2/7) = 4/21 or 19.0%.

P(second ball is red) = P(second ball is red and first ball is red) + P(second ball is red and first ball is blue)

= (2/7)*(5/9) + (3/8)*(2/7)

= 4/21

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It is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.

To determine this:

A 95% confidence interval for a proportion gives us an estimate of the range of values where the true proportion is likely to fall. The interval (0.751, 0.863) means that we are 95% confident that the true proportion of math students who prefer to use a handheld calculator versus computer software for computations falls between 0.751 and 0.863.

Given this information, it is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.

In other words, based on the sample data and the construction of the confidence interval, there is strong evidence that the true proportion of math students who prefer to use a handheld calculator is above 75%.

It's important to note that the confidence interval is only an estimate of the true proportion, and it's possible that the true proportion is not exactly within this interval. However, the 95% confidence level means that if we were to repeat the study many times, in about 95% of the cases, the interval would contain the true proportion.

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The probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13

In the given question, suppose that you draw a card from a standard deck of cards.

We have to find the probability that the card is a face card (i.e., a jack, queen, or king) or a heart.

As we know that in a deck of cards have total 52 cards.

In which 26 cards are in heart shape.

Every different type of card have 3 face cards and have total four different type of cards. That means there are total 12 face cards.

In 26 cards of heart have total 6 face cards.

So, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart

P = (Total face cards + total heart shape card - 6 face cards)/Total cards in a deck

P = (12 + 26 - 6)/52

P = (38 - 6)/52

P = 32/52

P = 8/13

Hence, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13.

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Answer:

71.4°F

Step-by-step explanation:

The maximum is when [tex]\sin(0.24x-1.88)=1[/tex], yielding a maximum of [tex]8.6+62.8=71.4[/tex].

if a kite is also a parallelogram, then it must be a rhombus is the correct statement

Is A rhombus a parallelogram?

Also, every rhombus is considered as a parallelogram but the converse is always not true. Parallelogram: A parallelogram is a flat-shaped figure. It has four sides. The pair of opposite faces/sides of a parallelogram are parallel and congruent to each other.

The only set of two parallelograms is the third one: square and rhombus.

Parallelograms are quadrilaterals (polygons with 4 sides) whose opposite sides are parallel.

Square, rhombus and rectangle are parallelograms.

Some kites may be parallelograms but not all the kites are parallelograms and trapezoid are not parallelograms.

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Answer:

[tex]\frac{19}{13}[/tex]

Step-by-step explanation:

expressing 9.5 ÷ 6.5 as a fraction , that is

[tex]\frac{9.5}{6.5}[/tex] ( multiply numerator and denominator by 2 for whole numbers )

= [tex]\frac{9.5(2)}{6.5(2)\\}[/tex]

= [tex]\frac{19}{13}[/tex] ← in simplest form

a fraction is in simplest form when no other value but 1 will divide into the numerator and denominator.

Answer:

See below

Step-by-step explanation:

Better description of what you want.

D)

3 - 2(s - 1) = 13 + 6s  Distribute the -2

3 -2s + 2 = 13 + 6s  Combine like terms

5 - 2s = 13 + 6s  Add 2s to both sides

5 - 2s + 2s = 13 + 6s + 2s

5 = 13 + 8s  Subtract 13 from both sides

5 - 13 = 13 - 13 + 8s

-8 = 8s  Divide both sides by 8

[tex]\frac{-8}{8}[/tex] = [tex]\frac{8s}{8}[/tex]

-1 = s

E)

2(n + 9) = -6 (2n-5) + 8  Distribute the 2 nd the -6

2n + 18 = -12n + 30 + 8  Combine like terms

2n + 18 = -12n + 38  Add 12n to both sides

2n + 12n + 18 = -12n + 12n + 38

14n + 18 = 38  Subtract 18 from both sides

14n + 18 - 18 = 38 - 18

14n = 20  Divide both sides by 14

[tex]\frac{14n}{14}[/tex] = [tex]\frac{20}{14}[/tex]

n = [tex]\frac{20}{14}[/tex]  Divide the numerator and denominator by 2 to simplify

n = [tex]\frac{10}{7}[/tex]

F)

5(4k -3) -5k = 10 +2(3k + 1)  Distribute the 5 and the 2

20k -15 - 5k = 10 +6k +2  Combine like terms

15k - 15 = 12 + 6k  Subtract 6k from both sides

15k - 6k - 15 = 12 + 6k -6k

9k -15 = 12  Add 15 to both sides

9k - 15 + 15 = 12 + 15

9k = 27  Divide both sides by 9

[tex]\frac{9k}{9}[/tex] = [tex]\frac{27}{9}[/tex]

k = 3

The coin will be worth $299.23 in 11 years when increasing at the rate of 11% Option A is the correct answer.

A steady rate of expansion that is proportionate to the quantity's current size is referred to as exponential growth. In other words, a quantity expands more quickly the larger it is. The exponential function, which has the formula y = ab raised to x, can be used to mathematically represent exponential growth. Here, "a" stands for the beginning quantity or value, "b" is the growth factor or base, and "x" stands for the duration or number of growth periods. Population expansion, compound interest, and the spread of infectious illnesses are a few examples of real-world processes that show exponential growth.

The exponential growth is given by the formula:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

For the given situation we have:  (P) = $115, the interest rate (r) = 11% or 0.11, and the number of years (t) = 11.

Thus,

[tex]A = $115(1 + 0.11/1)^{(1*11)}\\A = $115(1.11)^{11}[/tex]

A = $299.23

Hence, the coin will be worth $299.23 in 11 years. Option A is the correct answer.

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T3(x) = x - x^2/2 + x^3/6.

The Taylor polynomial of degree 3 for the function f(x) = x + e^-x centered at a = 0 is given by:

T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3

= 1 + (-1 + 1)x + (e^-0 - (-1)(-1)e^-0)x^2/2! + (0 + (-1)(-1)(-1)e^-0)x^3/3!

= x - x^2/2 + x^3/6

So T3(x) = x - x^2/2 + x^3/6.

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.

The nth Taylor polynomial of the function is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series. Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem. If a function's Taylor series is converging, its total is the upper bound of the Taylor polynomials' infinite sequence. A function's Taylor series sum may not match.

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Among all the given statements for quadrilateral and parallelogram, none of the statements is true.

A rhombus is a quadrilateral with all sides of equal length, while a parallelogram is a quadrilateral with opposite sides parallel and equal in length.

(a) a quadrilateral is a parallelogram if it is a rhombus.

False, A rhombus is a quadrilateral with all sides of equal length and opposite sides parallel, so it is a parallelogram but not all parallelograms are rhombus.

(b) a quadrilateral is a rhombus if it is a parallelogram.

False, A parallelogram is a quadrilateral with opposite sides parallel and equal in length, so it may be a rhombus but not all parallelograms are rhombus.

(c) a quadrilateral is a parallelogram if and only if it is a rhombus.

False, A rhombus is a quadrilateral with all sides of equal length and opposite sides parallel, so it is a parallelogram but not all parallelograms are rhombus.

(d) a quadrilateral is a rhombus if and only if it is a parallelogram.

False, A parallelogram is a quadrilateral with opposite sides parallel and equal in length, so it may be a rhombus but not all parallelograms are rhombus.

Hence none of the above statements is true.

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Answer:

simple 5×-5 the answer divide by -5

The probability that both lights showed red is given as follows:

3/5.

A probability is obtained by the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have to find the correct nodes in the tree that result in both crossings red, and their probabilities.

For the first crossing, the probability of red is given as follows:

4/5.

For the second crossing, the probability of red is given as follows:

3/4.

Hence the probability of red in both lights is given as follows:

4/5 x 3/4 = 3/5.

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The midpoint of the given line segment can be determined by using the formula ( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ] .

As given in the question,

Let the two endpoints of the given line segment be A(x₁ , y₁) and B(x₂ ,y₂).

As per midpoint concept it divides the given line segment in the equal ratio.

let the given line segment AB divided in the equal ratio of n : n

Consider the coordinates of the required mid point be ( x , y ) :

using midpoint formula we have :

( x , y ) =  [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ]

If the point divides the given line segment in the ratio 2 : 2

The required midpoint is given by

(x ,y ) = [ (2x₁ + 2x₂ )/2(2) , (2y₁ + 2y₂ )/2(2)]

        =  [ (x₁ + x₂ )/2 ) , (y₁ + y₂ )/2 ]

Therefore, the required midpoint which divides the given line segment into equal parts is ( x , y ) =  [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ].

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The particular solution of y = f(x) to the given differential equation [tex]\frac{dy}{dx} = y (xlnx)[/tex] with the initial condition f(1) = 4 is [tex]y = 4e^{\frac{1}{2}x^{2} lnx } - \frac{1}{4} x^{2} + \frac{1}{4}[/tex].

dy/dx = y(x lnx)

1/y dy = x lnx dx      Eqn (1)

Let u =  lnx, dv = x dx

Differentiate u = lnx

du = 1/x dx

Integrate dv = x dx

v = (1/x)x²

Now, integrate equation(1), we get

∫1/y dy = ∫x lnx dx

ln y = 1/2 x² ln x - 1/4 x² + C       Eqn (2)

Now, put the value of x and y to calculate the value of C

ln 4 = 1/2 ln 1 - 1/4 + C

ln 4 + 1/4 = C

Put the value of C in equation (2), and we get

ln y = 1/2 x² ln x - 1/4 x² + ln 4 + 1/4

[tex]y = 4e^{\frac{1}{2}x^{2} lnx } - \frac{1}{4} x^{2} + \frac{1}{4}[/tex]

--The given question is incorrect, the correct question is

''Find the particular solution y = f (x) to the given differential equation [tex]\frac{dy}{dx} = y (xlnx)[/tex] with the initial condition f(1) = 4."--

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William should use 0.625 pounds of peanuts, and 0.375 pounds of cashews in the mixture.

Given that,

The selling price of peanuts= $2.40

The selling price of cashews= $3.20

Let x be the amount of that pound composed of peanuts. (1-x) of that pound is composed of cashews.

The total price of such a pound mix is 2.4x + 3.2(1-x) = 2.7

2.4x + 3.2(1-x) = 2.7

2.4x + 3.2 - 3.2x = 2.7

-0.8x + 3.2 = 2.7

-0.8x = -0.5

x = 5/8 = 0.625 pounds of peanuts, and 1-5/8=3/8= 0.375 pounds of cashews.

Thus, William should use 0.625 pounds of peanuts, and 0.375 pounds of cashews in the mixture.

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Answer:

see below

Step-by-step explanation:

1. -2/3x [tex]\geq[/tex] 7

first, we need to divide -2/3 from x and 7 to get x alone, we also need to flip the inequality sign since we are dividing by a negative

x [tex]\leq[/tex] 21/2

or x [tex]\leq[/tex] 10 1/2

2. 32 > 23 - x

first, rearrange the inequality

32 + x > 23

subtract 32 from both sides

x > -9

3. 2 (x + 6) < 10

divide both sides by 2

x + 6 < 5

subtract 6 from both sides

x < -1

4. 15 - 4x [tex]\leq[/tex] 3x - 6

rearrange the equation

-4x + 3x [tex]\leq[/tex] - 15 - 6

-7x [tex]\leq[/tex] - 21

multiply both sides by -1 and reverse the inequality sign

7x [tex]\geq[/tex] 21

divide both by 7

x [tex]\geq[/tex] 3

im super sorry but im not sure how to help you with the graphing :(

Answer:

The 6th one is x=70 and <BCX=145

Answer: $26.094 an hour

Step-by-step explanation:

First, add up the total hours:

10 + 3 + 15 + 4 = 32

Now, add up the total amount charged:

340 + 495 = 835

Now, divide the amount charged by the number of hours:

835 / 32 = *26.094

* or 26.09375 if it needs to be exact.

The number of doors in one-story building are 8 and the number of doors in two-story building are 12.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, an employee at a construction company is ordering interior doors for some new houses that are being built.

Let the number of doors in one-story houses be x and the number of doors in two-story houses be y.

There are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors.

Here, 6x+2y=72 -------(I)

On the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors.

5x+7y=124 -------(II)

Multiply equation (I) by 7, we get

42x+14y=504  -------(III)

Multiply equation (II) by 2, we get

10x+14y=248 -------(IV)

Subtract equation (IV) from (III), we get

32x=256

x=8

Substitute x=8 in equation (I), we get

48+2y=72

2y=24

y=12

Therefore, the number of doors in one-story building are 8 and the number of doors in two-story building are 12.

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