Write and solve an equation. Make sure you show your work.
1. Tyler paid $178 to get his car repaired. He was charged $73 for parts and $35 per hour
for labor. How many hours did it take to repair his car?


Someone please show me how to do this step by step and please don’t use this as a free ticket.

The work done on a particle moving uniformly around the unit circle centered at the origin under a constant force field, f(x, y), is zero.

When a particle moves in a closed path, like a circle, the net work done by a conservative force field is always zero. In this case, the force field is constant, which means it does not change as the particle moves along the path. Since the work done by a constant force is given by the formula W = F * d * cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and the displacement vectors, we can see that the cosine of the angle will always be zero when the particle moves along the unit circle centered at the origin. This implies that the work done is zero. Thus, the work done on the particle is zero.

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a) Union of the given relations R1 and R2, R1 U R2 is {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}.

Given, R1 = {(1, 2), (2, 3), (3, 4)}R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}To find the union of two sets, we have to take all the elements in both the sets. The union of two sets A and B is the set of elements, which are in A or in B or in both. Therefore, R1 U R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}.b) Intersection of the given relations R1 and R2. The intersection of R1 and R2 is {(1, 2), (2, 3)}

The intersection of two sets A and B is the set of elements which are in A and B both. Therefore, R1 ∩ R2 = {(1, 2), (2, 3)}.c) Difference of the given relation R2 from R1. R2 - R1 is {(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}.In this case, we need to subtract the set R1 from set R2, that is R2 - R1. Therefore, R2 - R1 = {(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}.d) Difference of the given relation R1 from R2. R1 - R2 is full explanation:In this case, we need to subtract the set R2 from set R1, that is R1 - R2. Therefore, R1 - R2 is null since R2 has some elements which are not in R1. Hence the main answer is null.

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A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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Answer:

Formula for volume of sphere: V = 4/3πr³

Formula for surface area of sphere: A = 4πr²

To solve the question we must know about Logarithm.

A log function is a way to find how much a number must be raised in order to get the desired number.

\(a^c =b\)

can be written as

\(\rm{log_ab=c\)

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

\(\rm{log_{10}1000=3\)

The value of input can not be negative, the value of x is 8.

\(\rm{ log_2x+log_2(x-6)= 4\)

        \(\rm{ log_2x(x-6)= 4\)

        \( x(x-6)= 2^4\)

        \(x^2 -6x -16=0\\ x^2 -8x +2x-16=0\\ x(x-8)+2(x-8)=0\\ (x+2)(x-8) = 0\)

Equating factors against 0,

1.    \((x+2)=0\\ x=-2\)

2.     \((x-8)=0\\ x=8\)

As the value of input can not be negative, the value of x is 8.

Hence, the value of x is 8.

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Answer:

The answer is C

Step-by-step explanation:

C) x2 – 6x – 16 = 0

Answer:

Total weigh = 75g

a) so the mass of wheat and oats one protion = 75*(71/100) g = 53.25g

b) the mass of nuts in one serving = 75*(2.5/100) g = 1.875g

Step-by-step explanation:

Here I think mass = weigh, as it's not physics.

The equivalent expression of the given expression (10^5 / 54x^8)^1/3 would be equal to 5^(1/3) / 3x.

A fraction represents a part of a number or any number of equal parts.

The expression is given as

\((10x^5 / 54x^8)^{1/3}\\\\(5 / 27x^3)^{1/3}\\\\5^{1/3}/ (27x^3)^{1/3}\\\\5^{1/3} / 3x\)

This is the simplest form of expression.

Thus, the equivalent expression is 5^(1/3) / 3x.

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Answer:

D

i did the test

The table that shows the growth rate of Plant 1 which is 4 cm/week, and the graph that gives the growth rate of Plant 2 as 2 cm/week gives the correct option as C;

C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning

A proportional relationship between two variables is one in which one variable is a multiple of the other.

The possible table in the question is presented as follows;

Plant 1

The values on the graph are;

Plant 2

The rate, r1, of growth of Plant 1 is therefore;

r1 = 8 cm/(2 weeks) = 4 cm/week

The rate, of growth, r2, of plant 2 is found as follows;

r2 = 4 cm/(2 weeks) = 2 cm/week

Given that Plant 1 grows faster at 4 cm/week, than Plant 2, that grows at 2 cm/week, the correct statement is since Plant 1 grows 4 cm/week and Plant 2 grows 2 cm/week, Plant 1 grows more per day.

The correct option is therefore;

C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning

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The percent decrease of speed is given as 20%. Speed after the decrease is 48 miles per hour. So the initial speed will be 60 mph.

Percentage can be defined as the fraction of a number with 100.

10% means 10/100.

Here the percentage decrease is given as 20%.

So, let x be the initial speed.

Decrease in speed = 20% × x= 20/100× x = 0.20x

20% is decreased from the initial velocity x to reach 48 mph

x - 0.20x = 48

0.80x = 48

x = 48/0.80 = 60

So the actual speed from university A to university B was 60 mph.

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If deion saves 15% of his paycheck every month. last month he saved $219. then his paycheckwould have been $1460

deion saves 15% of his paycheck every month. last month he saved $219. how much was his paycheck

Let his paycheck be p

Then 15 % of p is equal to 219

(15/100 ) p = 219

p = 219 (100/15)

p = 1460

Therefore, if deion saves 15% of his paycheck every month. last month he saved $219. then his paycheck would have been $1460

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The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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The value of z such that 0.15 of the area lies to the right of z can be found using the standard normal distribution table or a statistical calculator.

First, we need to determine the area to the left of z, which is 1 - 0.15 = 0.85. This is the area under the standard normal curve up to z.

Next, we need to find the corresponding z-score for this area. We can use the inverse normal distribution function, which is available in most statistical calculators. Alternatively, we can use the standard normal distribution table to find the value of z that corresponds to an area of 0.85.

Using the standard normal distribution table, we can look up the area 0.85 in the body of the table or the cumulative area column. The corresponding z-score is 1.04. This means that 85% of the area under the standard normal curve lies to the left of z = 1.04, and 15% of the area lies to the right of z = 1.04.

Therefore, the value of z such that 0.15 of the area lies to the right of z is z = 1.04, rounded to two decimal places. This means that if we have a standard normal distribution with a mean of 0 and a standard deviation of 1, then approximately 15% of the values will be greater than 1.04 standard deviations above the mean.

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Answer:

0.1356 g

Step-by-step explanation:

The formula for density is, \(\rho ={\frac {m}{V}}\), so we can plug in our values and solve for m, the mass.

\(\rho ={\frac {m}{V}}\)

1.2x10⁻²= \(\frac{m}{11.3} \)

m= 0.1356 g

Answer:

Length in feet = X - 80

Step-by-step explanation:

A = width x length

A/width = length

(x^2 -100x + 1600) /( x - 20) = length

(x - 20) (x - 80) / (x - 20) = length

x - 80 = length

x - 80 = length

Answer: 84.

Step-by-step explanation: If you add the width 5cm and 2cm, it gives you 7cm, then length x width so 12x7= 84(cm).

If I am wrong, I am truly sorry, I haven't done area in a long time.

The population of interest is: A. all people in Emerald, Queensland.

The population of interest refers to the group of individuals that the research is trying to draw inferences about. In this case, the international fast food chain is looking to assess the level of interest in opening a franchise in Emerald, Queensland.

Therefore, the population of interest is all people who live in Emerald, Queensland, as they are the group that the research is trying to understand. The sample of 100 addresses that the research firm selected is just a subset of this population and the questionnaires are being sent to them to infer about the entire population.

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Answer:

no you can only use side side side when all of your triangles are equilateral triangles

Step-by-step explanation:

To calculate the company's annual holding cost, we need to multiply the annual average inventory by the holding cost per unit.

First, we need to calculate the annual average inventory. The formula for the average inventory is (Q/2), where Q represents the order quantity.

Given:

Annual requirements (Demand) = 7500 units

Ordering cost = BD 12

Order quantity (Q) = 150, 300, 45000 (Assuming these are different order quantities)

Holding cost per unit = BD 0.5

For each order quantity, we can calculate the annual average inventory using the formula (Q/2). Then, we multiply the average inventory by the holding cost per unit.

For order quantity Q = 150:

Average Inventory = Q/2 = 150/2 = 75 units

Holding Cost = Average Inventory * Holding cost per unit = 75 * 0.5 = BD 37.5

For order quantity Q = 300:

Average Inventory = Q/2 = 300/2 = 150 units

Holding Cost = Average Inventory * Holding cost per unit = 150 * 0.5 = BD 75

For order quantity Q = 45000:

Average Inventory = Q/2 = 45000/2 = 22500 units

Holding Cost = Average Inventory * Holding cost per unit = 22500 * 0.5 = BD 11250. Now, we sum up the holding costs for each order quantity:

Annual Holding Cost = BD 37.5 + BD 75 + BD 11250 = BD 11362.5 Therefore, the company's annual holding cost is BD 11362.5.

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a. The recursive formula for the number of tulips Marko has is: \(Tn = Tn-1 + 5\), where Tn is the number of tulips in year n and Tn-1 is the number of tulips in year n-1.

b. The explicit formula for the number of tulips Marko has is: Tn = 20 + 5n, where Tn is the number of tulips in year n and n is the number of years since Marko started planting.

c. If this trend continues, there will be 90 tulips in 10 years.

d. If this trend continues, it will take Marko 40 years to have 200 tulips.

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Answer:

316,800,000 feet

Step-by-step explanation:

Answer

one line is points (-9,4 ) (1,-2) and both cross over each at (3,4)

Step-by-step explanation:

Honors algebra was a tragic year

Answer:

x = -6

Step-by-step explanation:

Distribute the 2 into the brackets:

2x + 10 = -2

leave the 2x alone on one side:

2x = -2 -10

2x = -12

divide both sides by 2:

x = -6

Answer:

6/23

Step-by-step explanation:

The design features intended to improve access to public transport for people with mobility impairments are:

E. A, B, and C

These include:

A. Tactile Ground Surface Indicators (TGSI): These are textured surfaces on the ground that provide tactile cues to assist individuals with visual impairments in navigating their way to and within public transport stations.

B. Ramps and/or lifts to station platforms: These features provide accessibility for individuals using wheelchairs or other mobility devices by eliminating barriers such as stairs and providing a smooth transition between the platform and the vehicle.

C. "Kneeling buses" that allow for level bus boarding: Kneeling buses have the ability to lower the vehicle closer to curb level, making it easier for individuals with mobility impairments to board and disembark from buses.

These design features aim to create inclusive and accessible public transportation systems, ensuring that individuals with mobility impairments can independently and safely use public transport services.

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A neutral solution contains equal concentrations of [H3O+] and [OH-].

This is because the concentration of these ions determines the acidity or basicity of a solution. In a neutral solution, the pH is 7.0 and the [H3O+] and [OH-] concentrations are both 1.0 x 10^-7 M. If the pH is lower than 7.0, the solution is acidic and [H3O+] is greater than [OH-]. Conversely, if the pH is higher than 7.0, the solution is basic and [OH-] is greater than [H3O+]. It is important to note that the concentration of these ions can change with temperature and other factors, leading to changes in acidity or basicity. Neutral solutions contain equal concentrations of [H3O+] and [OH-] ions. In these solutions, the balance between acidic and basic species is maintained, resulting in a pH of 7 at 25°C. This equilibrium is important for maintaining stable chemical conditions in various systems, including biological and environmental processes. Examples of neutral solutions include pure water and other substances with equal amounts of acidic and basic components.

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Answer:

1. 1/2

2. 1/5

Step-by-step explanation:

I used a calculator!

Answer:

1.3/6 or 1/2

2.1/5

Step-by-step explanation:

Just write that out, thats all the steps there is, 3/6 simplifies to 1/2 because they're equivalent