Using the quadratic formula, solve the equation below to find the two values of x.
\(8x^{2} - 35 = -18x\)
Give each value as a fraction in it's simplest form.

Answer:

an = -6n + 5.

Step-by-step explanation:

This is an arithmetic sequence with first term a1 = -1 and common difference d = -6

an = a1 + d(n-1)

an = -1 + -6(n - 1)

an = -1 -6n + 6

an = -6n + 5.

To answer the questions related to the probability of droplet sizes, we'll use the normal distribution with the given mean and variance. Let's solve each part of the question:

a. Probability that the size of a single droplet is less than 1500 μm:

To find this probability, we need to calculate the cumulative distribution function (CDF) of the normal distribution up to 1500 μm. We'll use the z-score formula:

z = (x - μ) / σ

Where:

x = droplet size (1500 μm)

μ = mean (1050 μm)

σ = standard deviation (square root of the variance, which is sqrt(22500 μm))

Calculating the z-score:

z = (1500 - 1050) / sqrt(22500)

= 450 / 150

= 3

Using the z-score table or a calculator, we can find that the cumulative probability corresponding to z = 3 is approximately 0.9987.

Therefore, the probability that the size of a single droplet is less than 1500 μm is approximately 0.9987.

b. Probability that the size of a single droplet is between 1000 and 1500 μm:

Similar to part (a), we need to calculate the cumulative probability for two values: 1000 μm and 1500 μm. Let's calculate the z-scores for both values:

For 1000 μm:

z_1000 = (1000 - 1050) / sqrt(22500)

For 1500 μm:

z_1500 = (1500 - 1050) / sqrt(22500)

Once we have the z-scores, we can find the corresponding cumulative probabilities using the z-score table or a calculator. Then, we subtract the probability for 1000 μm from the probability for 1500 μm to find the probability between the two values.

c. Characterizing the smallest 2% of all droplets:

To characterize the smallest 2% of droplets, we need to find the droplet size that corresponds to the 2nd percentile of the normal distribution. In other words, we need to find the value x such that the cumulative probability up to x is 0.02. We can use the z-score formula to solve for x:

z = (x - μ) / σ

We'll find the z-score corresponding to the cumulative probability 0.02 using the z-score table or a calculator. Then, we can rearrange the formula to solve for x:

x = z * σ + μ

d. Probability that at least one of five independently selected droplets exceeds 1500 μm:

To find this probability, we'll use the complement rule. The probability that none of the five droplets exceed 1500 μm is the complement of the probability that at least one of them exceeds 1500 μm. We can calculate this probability by subtracting the probability of none from 1. We'll use the probability obtained in part (a) for a single droplet.

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Answer:5/5x-15/x

Step-by-step explanation:

Answer: your answer should be 3x^2 + 10x -75 / 5x.

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Find common denominator

3. Combine fractions with common denominator

4.  Multiply the numbers

5. Re-order terms so constants are on the left

6. Combine exponents

7. Multiply the numbers

8. Rearrange terms

therefore hopefully giving you the answer of 3x^2 + 10x -75 / 5x.

Answer:

13A + 1

Step-by-step explanation:

Combine like terms. Like terms are terms that have the same amount of the same variable:

Set the expression:

12A + A + 2 - 1

(12A + A) + (2 - 1)

13A + 1

13A + 1 is your answer.

~

Hey there!

12a + 2 + a - 1

COMBINE the LIKE TERMS

= (12a + 1a) + (2 - 1)

= 12a + 1a + 2 - 1

= 13a + 1

Therefore, your answer is: 13a + 1

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The given statement is 1. Always true

2. Always true

3. Always true

4. Sometimes true

5. Never true

Statement 1: A line and a point are always coplanar.

Answer: Always true.

Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.

Statement 2: Congruent angles form vertical angles.

Answer: Always true.

Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.

Statement 3: Linear pairs that are congruent are right angles.

Answer: Always true.

Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.

Statement 4: The sum of angles that form a linear pair is less than 180 degrees.

Answer: Sometimes true.

Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.

Statement 5: Vertical angles are complementary.

Answer: Never true.

Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.

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The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.

To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.

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Answer:

f = 14 1/3

Step-by-step explanation:

To solve this, we can add 4 1/3 to both sides:

- 4 1/3 + 4 1/3 cancels out, while 10 + \(4\frac{1}{3}\) becomes \(14\frac{1}{3}\):

Therefore, f = \(14\frac{1}{3}\).

Applying the centroid theorem, the value of x in the given triangle in the figure is: B. 4

The point where the three median of a triangle meet is the centroid. According to the centroid theorem, the centroid is 2/3 of the distance from each midpoint of the opposite sides to each vertex of the triangle.

Based on the centroid theorem, we have:

FY = 2/3(FS)

Substitute

x = 2/3(x + 2x - 6)

x = 2/3(3x - 6)

3x = 2(3x - 6)

3x = 6x - 12

3x - 6x = -12

-3x = -12

x = -12/-3

x = 4 (option B)

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Answer:I think you can say like the most bought music in class B is alternative and the lowest one is classical and so on

Step-by-step explanation:

Slope of the given graph function is -3/2 while the y-intercept: (0, 1)

What is slope intercept?

Finding the equation of a straight line in the coordinate plane is done using the slope intercept form. The connection that any point's coordinates on the line must satisfy is the equation of a straight line. Any point that is not on the line will not have coordinates that satisfy. The answer to this equation is simple to determine.

To Find :  equation of the line, in slope-intercept form

Solution:

Standard/ general form of equation of line in 2 variables is

Ax + By + C = 0

Slope intercept form is

y = mx + c

intercept form is

x/a  + y/b   = 1

Slope intercept form is

y = mx + c

m = Slope = -3/2

c = y intercept  =  1  

y  = (-3/2)x  + 1

equation of the line, in slope-intercept form is   y  = (-3/2)x  + 1.

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Answer: The slope is -3

Step-by-step explanation: 12 / -4 = 3 / -1 = -3

I hope this helps! :)

The sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.

The sum in expanded form is given by the expression 23 / (i + 23), where i varies from 1 to 6.

The sum in expanded form can be calculated by substituting the values of i from 1 to 6 into the expression 23 / (i + 23) and summing them up.

When i = 1, the expression becomes 23 / (1 + 23) = 23 / 24.

When i = 2, the expression becomes 23 / (2 + 23) = 23 / 25.

When i = 3, the expression becomes 23 / (3 + 23) = 23 / 26.

When i = 4, the expression becomes 23 / (4 + 23) = 23 / 27.

When i = 5, the expression becomes 23 / (5 + 23) = 23 / 28.

When i = 6, the expression becomes 23 / (6 + 23) = 23 / 29.

Therefore, the sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.

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The sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.

The sum in expanded form is given by the expression 23 / (i + 23), where i varies from 1 to 6.

The sum in expanded form can be calculated by substituting the values of i from 1 to 6 into the expression 23 / (i + 23) and summing them up.

When i = 1, the expression becomes 23 / (1 + 23) = 23 / 24.

When i = 2, the expression becomes 23 / (2 + 23) = 23 / 25.

When i = 3, the expression becomes 23 / (3 + 23) = 23 / 26.

When i = 4, the expression becomes 23 / (4 + 23) = 23 / 27.

When i = 5, the expression becomes 23 / (5 + 23) = 23 / 28.

When i = 6, the expression becomes 23 / (6 + 23) = 23 / 29.

Therefore, the sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.

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Answer:

17 + 2i

Step-by-step explanation:

Given

(2 - 3i) + 5i(1 - 3i) ← distribute both parenthesis

= 2 - 3i + 5i - 15i²  [ i² = - 1 ]

= 2 + 2i + 15

= 17 + 2i ← in standard form

The standard form of a complex number (2 − 3i) + 5i(1 − 3i) is 17 + 2i.

A complex number is a component of a number system that includes the imaginary unit, represented by the letter i as an extension of the real numbers.

Given:

(2−3i) + 5i(1−3i)

Use the distributive property and expand the expression,

(2 − 3i + 5i - 15i²)

2 + 2i - 15(-1)           [i² = - 1]

2i + 17

Therefore, the standard form of a complex number (2 − 3i) + 5i(1 − 3i) is 17 + 2i.

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The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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Answer:

Below.

Step-by-step explanation:

Each kg is 100 grams so?

4x100=400 grams.

Answer:

4000 grams.

Step-by-step explanation:

There are 1000 grams to 1 kilogram. The prefix, kilo- , means one thousand.

Change 4 kg to grams:

4 kg x (1000 g/1 kg) = 4000 grams.

~

Answer:

h(8) = 2

Step-by-step explanation:

substitute x = 8 into h(x) , that is

h(8) = 2(8 - 7) = 2(1) = 2

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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(a) The given problem can be written as:
Minimize: \(3X^2 - 22X + 2XY + Y^2 - 16Y + 60\)
(b) Subject to: \(X + 5Y ≤ 8\)

(c) We can find the difference between the new optimal objective function value and our estimated change.

a. To find the minimum solution to the given problem, we need to solve the optimization problem by minimizing the objective function subject to the constraint.

The given problem can be written as:
Minimize: \(3X^2 - 22X + 2XY + Y^2 - 16Y + 60\)
Subject to: \(X + 5Y ≤ 8\)

To find the minimum solution, we need to solve this problem using optimization techniques like linear programming or calculus.

b. If the right-hand side of the constraint is increased from 8 to 9, we need to analyze the change in the objective function.

To do that, we can find the difference between the objective function value at the new solution and the old solution.

c. Re-solving the problem with a new right-hand side of 9 will give us a new optimal objective function value.

To compare the actual change with our estimate, we can find the difference between the new optimal objective function value and our estimated change.

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The time spent on homework will be naturally more an explanatory variable and exam grade a response variable.

The Linear equation for a scatter plot y = mx+b has two variables i.e., a Dependent Variable [Y] and an Independent variable [X] .

A student who spends more time on his work and do it nicely will automatically get good exam grade . On the other side, a student who did'nt dedicate much time to the homework and carelessly does it , will obviously score a low exam grade.We can see that the exam grade is dependent on the time spent on the homework which naturally makes exam grade a response variable and time spent on home a independent thus an explanatory variable.

Hence, the time spent on homework will be naturally more an explanatory variable and exam grade a response variable.

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C. Multiplication property

Properties of equality and congruence are properties that show how equations or shapes can be changed but remain equal.

Properties of Equality

Since this question deals with an equation, not a shape, the properties of equality will be used. The most common properties of equality include:

The important thing to note is that whatever is done to one side, must be done to both. No matter what operation it is, if you change the equation you must change both sides equally.

Solving for X

To find the correct property, we need to solve for x. Do this by isolating the variable.

First, let's rewrite the equation.

Now, we need to find a way to isolate the variable. To isolate x, we need to get rid of the denominator, 5. Do this by multiplying both sides by 5. This will cancel out the denominator on the left side. Remember to multiply on both sides.

Then, simplify the equation

To solve this equation, we multiplied both sides by the same number. This matches the definition of the multiplication property of equality, so that must be the correct answer.

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Answer:Answer

Step-by-step explanation:

For the first part, divide 46.54 by 5.2

46.54/5.2=8.95

$8.95 per pound

For the second part if he buys half as much, its half of 5.2 plus 5.2. Now use similar steps that I used in the first part to solve for your problem.

I got $97.50, but i am not 100% sure if it is correct, so try give it a try.

1) Notice that, in this case, the center is at (0,0) the focus at (0,4) and the Vertex is at (0,7)

2) Since the focus is at the y-axis, and the center is at the origin we can start from the following formula:

Step-by-step explanation:

Let the first number be x and the second y

x+y=100

(x-12)+y

The investment problem is modeled by an initial value problem (IVP) where the rate of change of the investment is determined by the initial investment, monthly deposits, and the interest rate.

a) The investment problem can be modeled by an initial value problem where the rate of change of the investment, y(t), is given by the initial investment, monthly deposits, and the interest rate. The IVP can be written as:

dy/dt = 0.09y + 200, y(0) = 500.

b) To solve the IVP, we can use an integrating factor to rewrite the equation in the form dy/dt + P(t)y = Q(t), where P(t) = 0.09 and Q(t) = 200. Solving this linear first-order differential equation, we obtain the solution for y(t).

c) To find the value of the investment after 2 years, we substitute t = 2 into the obtained solution for y(t) and calculate the corresponding value.

d) After 2 years, the monthly deposit increases to $300. To find the value of the investment a year later, we substitute t = 3 into the solution and calculate the value accordingly.

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If you just want to conduct a flyby and aren't planning to stay, it will take you approximately 600 days, and if you want to enter orbit, it will take you about 2,000 days.

Astronomical distances are expressed in terms of a light-year, which is also spelt light year. Its length is approximately 9.46 trillion kilometers, or 5.88 trillion miles.

NASA's Pioneer 10 was the first spacecraft to ever travel across the distance between the Earth and Jupiter. On March 3, 1972, it was launched, and on December 3, 1973, it arrived. There were 640 days of flight time altogether.

However, Pioneer 10 was passing by while en route to study the outer solar system. Before NASA lost communication with it, the spacecraft traveled another 11 years into deep space after approaching the planet at a distance of 130,000 kilometers, where it snapped the first-ever close-up images of Jupiter.

Pioneer 11 launched and touched down one year later. It traveled there in 606 days, flying by Jupiter at a considerably closer distance (21,000 kilometers), and also stopped by Saturn.

The Voyager spacecraft arrived next. Voyager 1 arrived on March 5, 1979, in only 546 days, and Voyager 2 took 688 days.

Consequently, it will take between 550 and 650 days to complete a flyby.

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Utilizando proporciones, hay que el pick-up más grande carga 5250 kg.

El peso que cargan tres pick-ups están en la razón de 2:6:7

La regla de três es:

\(\frac{2}{15}\) - 1500 kg

\(\frac{7}{15}\) - x kg

Aplicando multiplicación cruzada:

\(\frac{2x}{15} = \frac{1500(7)}{15}\)

\(2x = 1500(7)\)

\(x = \frac{1500(7)}{2}\)

\(x = 5250\)

El pick-up más grande carga 5250 kg.

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Answer:

Step-by-step explanation:

Draw a picture. Seriously, this time you need to, so you can see that PS is the hypotenuse of a right triangle with legs of length 3 and 4 .

PS = √(3² + 4²) = 5

Perimeter = PQ + QR + RS + PS = 9 + 4 + 6 + 5 = 24 cm

Answer:

Yes

Step-by-step explanation:

y = x has the inverse x = y