Question I conduct a survey, and find out that the proportion of college students who are women is 0. also learn that the proportion of psychology majors is 0.1. Assume that these two variables are indepen What is the probability of randomly selecting a student who is either female or a psychology major? Rou the hundredths place.​

Answer:

Step-by-step explanation:

We can simplify the expression on the left-hand side using trigonometric identities:

tan(-A) = -tan(A) (since tan(-θ) = -tan(θ))

sin(180°+A) = -sin(A) (since sin(180°+θ) = -sin(θ))

sec(270°-A) = -cos(A) (since sec(270°-θ) = -cos(θ))

cos²(90°+A) = sin²A (since cos²(90°+θ) = sin²θ)

Substituting these values, we get:

-x.sin(A).cos(A).tan(A) = x.sin(-A) - sin²A.sin(A)

-x.sin(A).cos(A).tan(A) = -x.sin(A) - sin³A

Now, we can simplify this equation by moving all the terms to one side:

-x.sin(A).cos(A).tan(A) + x.sin(A) + sin³A = 0

Factoring out sin(A), we get:

sin(A) (-x.cos(A).tan(A) + x + sin²A) = 0

Since sin(A) ≠ 0, we can divide both sides by sin(A):

-x.cos(A).tan(A) + x + sin²A = 0

Multiplying both sides by cos(A), we get:

-x.sin(A) + x.cos²(A) + sin²A.cos(A) = 0

Using the identity cos²(θ) + sin²(θ) = 1, we can write this as:

-x.sin(A) + x(1 - sin²A) + sin²A.cos(A) = 0

Simplifying and rearranging, we get:

x = sin(A)/(cos(A) - sin²(A))

Therefore, the value of x is given by the expression sin(A)/(cos(A) - sin²(A)).

Answer:     x^2-xy-2x^2y+2xy^2+2x+2y over 2x(x - y)

Step-by-step explanation:

because im that guy

"To round the decimal number 285.429 to the nearest tenth, we need to look at the digit in the hundredths place, which is 2.

If the digit in the hundredths place is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is.

In this case, the digit in the hundredths place is 2, which is less than 5. Therefore, we leave the digit in the tenths place as it is, which is 2.

So, rounding 285.429 to the nearest tenth gives us:

285.4

Therefore, the rounded value of the decimal number 285.429 to the nearest tenth is 285.4." (ChatGPT, 2023)

Answer:

Krish saves 9 minutes by cycling to his office.

Step-by-step explanation:

Krish used to take 30 minutes to walk to his office. After he bought a new cycle, he takes only 7/10 of the time he used to take to reach the office. Let's call the new time he takes to reach the office "t" (in minutes).

We can set up a proportion to find the value of t:

30 / 1 = t / (7/10)

To solve for t, we can cross-multiply:

30 * 7/10 = t

21 = t

So, Krish now takes 21 minutes to reach his office by cycle.

To find how many minutes he saves by cycling, we can subtract the new time from the old time:

30 - 21 = 9

Krish saves 9 minutes by cycling to his office.

Using the concept of percentage, we can deduce that Kareem does not have enough money with him

To solve the questions given, we need to apply the concept of percentage on some.

a) Rounding the price of the guitar to a convenient amount, we get $180.

b) 10% of the rounded price is: 0.1 x $180 = $18.

c) 1% of the rounded price is: 0.01 x $180 = $1.80.

d) To get the estimated tax, we need to multiply the rounded price by the HST rate: 0.13 x $180 = $23.40. Dividing this by $1.80, we get approximately 13.

e) The estimated tax is $23.40.

f) Adding the estimated tax to the rounded price, we get $180 + $23.40 = $203.40.

Since Kareem has $200 cash with him, he does not have enough money to buy the guitar at the estimated price of $203.40. Therefore, the answer is NO.

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The inverse function of f(x) = (x + 5)² on the domain x >= -5 is given as follows:

[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]

The domain of the inverse function is given as follows:

x >= 0.

The function for this problem is defined as follows:

f(x) = (x + 5)² on the domain x >= -5.

The range of the function is y >= 0, as the vertex is at (-5,0) and the function is increasing over it's domain, hence the domain of the inverse function, which is the range of the original function, is given as follows:

x >= 0.

To obtain the inverse function, wee exchange x and y in the definition of the function, and then isolate y, hence:

x = (y + 5)²

[tex]y + 5 = \sqrt{x}[/tex]

[tex]y = \sqrt{x} - 5[/tex]

[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]

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Answer:

To find the cost equation, we can use the two data points given:

(100, 1400) and (400, 4100)

We can use the point-slope form of a linear equation, where the slope is the change in cost over the change in quantity:

slope = (4100 - 1400) / (400 - 100) = 2700 / 300 = 9

Using the point-slope form with the first data point:

y - 1400 = 9(x - 100)

y - 1400 = 9x - 900

y = 9x + 500

So the cost equation is y = 9x + 500.

To find the cost to manufacture 150 shoes, we can plug in x = 150 into the cost equation:

y = 9(150) + 500 = 1850

So the cost to manufacture 150 shoes is $1850.

To find the revenue function, we multiply the number of shoes sold by the price per shoe:

Revenue = price x quantity = 19x

To determine the number of items needed to break even, we need to find the quantity where revenue equals cost. Let C(x) be the cost function and R(x) be the revenue function. The break-even point occurs when:

C(x) = R(x)

9x + 500 = 19x

500 = 10x

x = 50

So the company needs to sell 50 designer shoes to break even.

Step-by-step explanation:

Answer:

Cost equation:  y = 9x + 500

It costs $1,850 to manufacture 150 shoes.

Revenue function:  R(x) = 19x

The number of items that need to be sold to break even is 50.

Step-by-step explanation:

Definition of variables

If it costs $1,400 to manufacture 100 designer shoes:

If it costs $4,100 to manufacture 400 designer shoes:

Assuming the relationship between the number of shoes and the cost to manufacture them is linear, the slope of the equation of the line the models the relationship can be found by dividing the change in y-values by the change in x-values of the two data points:

[tex]\implies \sf Slope\;(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4100-1400}{400-100}=9[/tex]

Substitute the found slope and one of the points into the point-slope form of a linear equation to create an equation that gives the total cost to manufacture the shoes in terms of the number of shoes (x):

[tex]\implies \sf y-y_1=m(x-x_1)[/tex]

[tex]\implies \sf y-1400=9(x-100)[/tex]

[tex]\implies \sf y-1400=9x-900[/tex]

[tex]\implies \sf y=9x+500[/tex]

Therefore, the cost equation is y = 9x + 500.

To calculate the cost to manufacture 150 shoes, substitute x = 150 into the cost equation:

[tex]\begin{aligned}\implies \sf y&=\sf 9(150)+500\\&= \sf 1350+500\\&= \sf 1850\end{aligned}[/tex]

Therefore, it costs $1,850 to manufacture 150 shoes.

The revenue is the income a company generates before any expenses are subtracted. Therefore, the revenue function is simply the selling price of the item multiplied by the number of items sold.

Given the product sells for $19 per item, the revenue function is:

[tex]\implies \sf R(x)=19x[/tex]

The break even point is the point at which the total revenue equals the total cost, so there is neither profit nor loss.

To determine the number of items that should be sold to break even, equate the cost equation and the revenue function and solve for x.

[tex]\begin{aligned}\sf R(x)&=\sf y\\\implies \sf19x&=\sf 9x+500\\\sf 10x&=500\\\sf x&=50\end{aligned}[/tex]

Therefore, the number of items that need to be sold to break even is 50.

Assuming that there are no other transactions or fees on the credit card, here's how to calculate the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made:

1.) Unpaid Balance: The unpaid balance is the amount of the credit card balance that remains after making the minimum monthly payment. In this case, the minimum monthly payment is $125, so the unpaid balance would be:

$5000 - $125 = $4875

2.) Interest Charge: The interest charge for unpaid balances is 18% per year. To calculate the monthly interest rate, divide the annual rate by 12:

18% / 12 = 1.5%

3.) To calculate the interest charge for the month, multiply the unpaid balance by the monthly interest rate:

$4875 x 1.5% = $73.13

So the new interest charge for the month is $73.13.

4.) Purchasing Power: Purchasing power refers to the amount of credit that is available on the credit card after making the minimum monthly payment and accounting for any interest charges. To calculate the purchasing power, subtract the unpaid balance and interest charge from the credit limit:

$5000 - $4875 - $73.13 = $51.87

So the purchasing power on the credit card after the minimum monthly payment is made is $51.87.

The joint frequencies are the cells where the categories for two variables in a two-way frequency table intersect, while the marginal frequencies are the sums of the row or column in a two-way frequency table.

Joint frequencies represent the frequency counts of each combination of categories for two variables, while marginal frequencies represent the frequency counts of each category for one variable, regardless of the other variable.

For example, in a two-way frequency table of gender and political affiliation, the joint frequency for "Male" and "Republican" would represent the number of individuals who are both male and Republican.

The marginal frequency for "Male" would represent the total number of males in the sample, regardless of their political affiliation. The marginal frequency for "Republican" would represent the total number of individuals who identify as Republican, regardless of their gender.

Understanding the difference between joint and marginal frequencies is important for analyzing the relationship between two variables and identifying any patterns or trends.

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Answer:

To convert kilometers to miles, we can use the conversion factor 1 km = 0.621371 miles.

First, let's convert the total distance of 5.632704 km to miles:

5.632704 km * 0.621371 miles/km = 3.497672 miles

Next, let's convert the distance already hiked, 4.425969 km, to miles:

4.425969 km * 0.621371 miles/km = 2.746203 miles

To find out how many miles Lisa has left, we can subtract the distance already hiked from the total distance:

3.497672 miles - 2.746203 miles = 0.751469 miles

So Lisa has 0.751469 miles left to hike.

Step-by-step explanation:

Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:

12x = 500

x = 500/12

x = 41.67

x≅ 42

Julia needs to buy 42 packets

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Answer:

D

Step-by-step explanation:

..

Answer:

[tex]\textsf{Degree:}\quad 6[/tex]

[tex]\textsf{Leading\;coefficient:}\quad \dfrac{1}{3456}[/tex]

[tex]\textsf{Zeroes:}\quad -6, 2, 5, 8[/tex]

[tex]\textsf{Factors:}\quad (x + 6), (x - 2), (x - 5), (x - 8)[/tex]

[tex]\textsf{Factors\;with\;multiplicity:}\quad (x + 6)^3(x - 2)(x - 5)(x - 8)[/tex]

[tex]\textsf{Equation\;of\;function:}\quad f(x)=\dfrac{1}{3456}(x+6)^3(x-2)(x-5)(x-8)[/tex]

Step-by-step explanation:

The zeroes are the x-values of the points where the function crosses the x-axis, so the x-values when f(x) = 0.

Therefore, the zeroes of the given function are:

[tex]\hrulefill[/tex]

According to the factor theorem, if f(x) is a polynomial, and f(a) = 0, then (x - a) is a factor of f(x). Therefore, the factors of the function are the x-values that satisfy f(x) = 0.

Therefore, the factors of the given function are:

[tex]\hrulefill[/tex]

The multiplicity of a factor is the number of times the factor appears in the factored form of the equation of the polynomial.

If the behaviour of the x-intercept is like that of a line, i.e. the curve passes directly through the intercept, its multiplicity is one.

Therefore, the factors (x - 2), (x - 5) and (x - 8) have multiplicity one.

The behaviour of the x-intercept at x = -6 is like that of a cubic function (S-shape). There, this zero has multiplicity 3: (x + 6)³.

[tex]\hrulefill[/tex]

So far we have found the zeros, factors and their multiplicities, so we can write a factored form of the function:

[tex]\implies f(x)=a(x+6)^3(x-2)(x-5)(x-8)[/tex]

The degree of the function is the highest exponent value of the variables in the polynomial. Therefore, to find the degree of the function, simply sum the exponents of the factors:

[tex]\implies \textsf{Degree}=3 + 1 + 1 + 1 = 6[/tex]

Therefore, the degree of the function is 6.

[tex]\hrulefill[/tex]

From inspection of the given graph, the y-intercept is (0, -5).

Therefore, to find the leading coefficient (value of a), substitute (0, -5) into the equation and solve for a:

[tex]\begin{aligned}\implies f(0)=a(0+6)^3(0-2)(0-5)(0-8)&=-5\\a(216)(-2)(-5)(-8)&=-5\\-17280a&=-5\\a&=\dfrac{1}{3456}\end{aligned}[/tex]

Therefore, the leading coefficient of the function is 1/3456.

[tex]\hrulefill[/tex]

Putting everything together, the function in factored form is:

[tex]f(x)=\dfrac{1}{3456}(x+6)^3(x-2)(x-5)(x-8)[/tex]

In standard form:

[tex]f(x)=\dfrac{1}{3456}x^6+\dfrac{1}{1152}x^5-\dfrac{1}{36}x^4-\dfrac{37}{432}x^3+\dfrac{17}{24}x^2+\dfrac{13}{8}x-5[/tex]

Using square process method, we can get the values of x to be 12 and 6.

The formula a (x + m)2 + n = a (x + m)2 + n is the simplest to remember while learning how to complete the square technique.

The following formulas can be used to compute m and n in this situation: m = b/2a and n = c - (b2/4a).

From the question,

x² - 18x + 72= 0

⇒ x² - 18x = -72

Complete the square by adding the half of the square of the coefficient of x to both sides of the expression as shown:

⇒ x² - 18x + (18/2) ² = -72 + (18/2) ²

⇒ x² - 18x + 9² = -72 + 81

⇒ (x-9) ² = 9

⇒ x-9 = ± 3

So, values of x are:

x = 3 + 9

= 12

x = -3 + 9

= 6

Therefore, the values of x are 12 and 6.

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To solve the exponential equation 4^(3+x) = 25 for x, we need to use logarithms. We can use any base of the logarithm to solve this equation. However, some bases may be more convenient or easier to use than others. The possible bases of the logarithm that we can use to solve this equation are:

Log base 4: If we take the logarithm of both sides of the equation with base 4, we get:

log₄(4^(3+x)) = log₄(25)

(3+x)log₄(4) = log₄(25)

3+x = log₄(25)/log₄(4)

3+x = 2.3219

x ≈ -0.6781

Log base 25: If we take the logarithm of both sides of the equation with base 25, we get:

log₂₅(4^(3+x)) = log₂₅(25)

(3+x)log₂₅(4) = 1

3+x = 1/log₂₅(4)

3+x = 1/1.3219

x ≈ -1.6781

Log base x: If we take the logarithm of both sides of the equation with base x, we get:

logₓ(4^(3+x)) = logₓ(25)

(3+x)logₓ(4) = logₓ(25)

3+x = logₓ(25)/logₓ(4)

3+x = log₄(25)/log₄(x)

x = log₄(25)/log₄(x) - 3

Log base 10: If we take the logarithm of both sides of the equation with base 10, we get:

log₁₀(4^(3+x)) = log₁₀(25)

(3+x)log₁₀(4) = log₁₀(25)

3+x = log₁₀(25)/log₁₀(4)

3+x = 1.3979

x ≈ -1.6021

Therefore, we can use any of the above logarithm bases to solve for x in the given equation.

By answering the above question, we may state that The chance of probability drawing a non-red marble is just the probability of drawing a non-red marble. As a result, the probability is 209/210.

Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.

The likelihood of drawing a red marble is 210, which indicates that one red marble is drawn out of every 210 in the jar. This probability may be expressed as a fraction:

P(Red) = 1/210

The likelihood of drawing a non-red marble is the inverse of the probability of drawing a red marble:

P(Not Red) = 1 minus P(Red) = 1 minus 1/210 = 209/210

As a result, the chance of drawing a marble that is not red is 209/210.

The chance of drawing a non-red marble is just the probability of drawing a non-red marble. As a result, the probability is 209/210.

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Answer:

10

Step-by-step explanation:

362/6 = 60R2

461/6 = 76R5

2761/6 = 460R1

2x5x1 = 10

Solving the quadratic equation we can see that the object will be 6.5 seconds falling down.

We know that the height is modeled by the quadratic equation

h=-16t²+676

The object will reach the ground when the height is zero, so we need to solve:

-16t²+676 = 0

Solving this for t we will get:

16t² = 676

t² = 676/16

t = √(676/16)

t = 6.5

The object will be 6.5 seconds falling down.

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Answer:

-41 is the ANS.

Step-by-step explanation:

9-25*2

9-50

-41

Answer:

Childrens books

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve for which type of book covers the most space, we need to first convert 25% from a percentage to a fraction.

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If percentages are fractions of 100, then 25% as a fraction would look like this:

We can do the same to 0.3, although it isn't a percentage.

Now, we need to convert the fractions ([tex]\frac{25}{100}[/tex], [tex]\frac{30}{100}[/tex], [tex]\frac{7}{20}[/tex]) to have a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To make [tex]\frac{7}{20}[/tex] have a denominator of 100, we can multiply the 20 by 5 to get 100.

Now the fraction is [tex]\frac{35}{100}[/tex].

The three fractions given are:

The larges given fraction is [tex]\frac{35}{100}[/tex] meaning that the children's books cover the most shelf space in the store.

19/100 into decimals is 0,19

To write a fraction based on 10/100/1000... you must move the decimal point to the left the number of times equivalent to the number of zeros in the base.
In this case, base 100 has two zeros. Then move two squares to the left.

[tex]\begin{array}{l}\bf 19\\\sf {0}{,}\!\overset{\overset{2}{\curvearrowleft}}{1}\!\overset{\overset{1}{\curvearrowleft}}{9}\\\\\bf \dfrac{19}{100}=0{,}19\end{array}[/tex]

Did you see how easy the conversion was under these circumstances?

If you have any question about this solution, you can ask me in the comments :)

The minimum annual interest rate for Kyoko to reach her goal, using daily compounding, is 9.903%.

The interest rate is computed using an online finance calculator that sets the following parameters.

The compounding period involved is 2,555 days for 7 years, based on the assumption that there are 365 days in a year.

N (# of periods) = 2555 days (7 years x 365 days)

PV (Present Value) = $10,000

PMT (Periodic Payment) = $-0

FV (Future Value) = $-20000

Results:

I/Y = 9.903% if interest compound 365 times per year (APR)

I/Y = 10.409% if interest compound once per year (APY)

I/period = 0.027% interest per period

Total Interest = $10,000.00

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Answer:

1 product

Step-by-step explanation:

Given the equation that shows how the time required to complete an online shopping transaction is related to the number of products being purchased as;

t = 24p + 27

t represents the time required to complete the transaction

p is the product purchased

If it takes 51 seconds to complete a transaction, to get the amount of product purchased, we will substitute t = 51 into the expression and find p as shown;

51 = 24p + 27

Substract 27 from both sides

51-27 = 24p + 27 - 27

24 = 24p

24p= 24

p = 24/24

p = 1

Hence only 1 product is being purchased

Answer:

80

Step-by-step explanation:

The variable "n" is not defined, but rather "k" is used in the summation. Assuming that "n" was meant to be "k", the expression should be:

s4 = ∑ k=1 to 4 of 2(3^(k-1))

To evaluate this expression, we need to substitute each value of k from 1 to 4 into the expression 2(3^(k-1)), and then sum up the results.

Starting with k = 1:

2(3^(1-1)) = 2(3^0) = 2(1) = 2

Moving on to k = 2:

2(3^(2-1)) = 2(3^1) = 2(3) = 6

Next, k = 3:

2(3^(3-1)) = 2(3^2) = 2(9) = 18

Finally, k = 4:

2(3^(4-1)) = 2(3^3) = 2(27) = 54

Now we add up these four results:

s4 = 2 + 6 + 18 + 54 = 80

Therefore, the value of s4 is 80.

Answer:

Step-by-step explanation:

In quadrilateral ABCD, we have:

AB is parallel to DC

AD is parallel to BC

AC = 40 in (given)

BD = 50 in (given)

AB = 25 in (given)

We can use the fact that opposite sides of a parallelogram are equal in length to find the length of CD:

CD = AB = 25 in

Next, we can use the fact that the diagonals of a quadrilateral bisect each other to find the length of AO and OC:

AO = BO = BD/2 = 50/2 = 25 in

OC = OD = AC/2 = 40/2 = 20 in

Now we can use the triangle inequality to find the perimeter of triangle COD:

CO + OD + CD > OC

CO + 20 + 25 > 20

CO + 45 > 20

CO > -25

CO + OC > CO

CO + 20 > 0

CO > -20

CO + CD > OD

CO + 25 > 20

CO > -5

Therefore, the possible range of values for CO is:

-20 < CO < -5

However, since lengths cannot be negative, we can take the absolute value of CO to get:

5 < CO < 20

So the perimeter of triangle COD is:

CO + OD + CD = CO + 20 + 25 = CO + 45

Substituting the possible range of values for CO, we get:

5 + 45 < CO + 45 < 20 + 45

50 < CO + 45 < 65

So the perimeter of triangle COD is between 50 in and 65 in.

Therefore, the perimeter of triangle COD is between 50 in and 65 in, but the exact value depends on the length of CO, which is between 5 in and 20 in.

The correct option to determine the value of volume of solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.

One of the three-dimensional shapes that can be created with six pairs with parallel lines is a rectangular prism. Three-dimensional shapes in this category include cubes and cuboids. Prisms come in a variety of classifications based on the base.

Volume of rectangular prism = length * width * height

rectangular prism A:

length =  10 in.

Width =  3 in.

height = 6 in.

rectangular prism B:

length =  4 in.

Width =  3 in.

height = 6 in.

Thus,

volume of the solid = volume of rectangular prism A + volume of rectangular prism A

volume of the solid = 10*3*6 + 4*3*6

Thus, the correct option to determine the value of  volume of the solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.

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The given inequality 2x² 25x + 33 < 0 has been proved by using properties of parallelogram.

The formula A = bh, where b is the parallelogram's base and h is its height, determines the area of a parallelogram.

Let's use x + 6 cm for the parallelogram's base and 2x + 3 cm for its height in the diagram. The parallelogram's area can therefore be represented as follows:

A = (x + 6)(2x + 3)

By extending this phrase, we get:

A = 2x² + 15x + 18x + 18

A = 2x² + 33x + 18

We now know that the parallelogram's area is more than 10.5 cm2. As a result, we can create the disparity shown below:

2x² + 33x + 18 > 10.5

By taking away 10.5 from both sides, we arrive at:

2x² + 33x + 18 - 10.5 > 0

By condensing the left side, we obtain:

2x² + 22.5x + 7.5 > 0

When we multiply both sides by 2, we obtain:

4x² + 45x + 15 > 0

By taking 3 away from both sides, we arrive at:

4x² + 45x + 12 < 0

As a result, we have demonstrated that 2x² 25x + 33 < 0.

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Step-by-step explanation:

45+6x+15=180

60+6x=180

6x=180-60

6x/6=120/6

X=20

The value of x from the same side interior angles in a parallel lines is x = 20

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Given data ,

Let the parallel lines be represented as A and B

Now , the measures of angles are

p = 45°

And , q = ( 6x + 15 )°

where p and q are same side interior angles

And , the same side interior angles add up to 180°

On simplifying , we get

45 + 6x + 15 = 180

6x + 60 = 180

Subtracting 60 on both sides , we get

6x = 120

Divide by 6 on both sides , we get

x = 20

Hence , the angles in parallel lines are solved and x = 20

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