The set of all real numbers x that satisfies -3 < x<14 is given by the following interval notation: [-3,14) True or False?

Answer:

A.)359.2, B.)2.5 uf

Step-by-step explanation:

E / I = R

208 / 1.04 = 200 ohms

2*pi*f*L = Xl

6.28*400*.143 = 359.2 ohm

1 / (2*pi*f*Xc) = c

1 /(6.28*400*159.2) = 2.5 uf

Final answer:

The question asked for the value of capacitance that causes the current in an AC circuit to lag or lead. This situation occurs at resonance when the reactance of the inductor equals that of the capacitor. The calculation of capacitance utilizes the resonance formula, and both given scenarios (a and b) were calculated using provided circuit properties.

Explanation:

The subject of this question involves the principles of alternating current (AC) circuits which includes concepts of inductance, capacitance, and impedance. Particularly, the question is asking to find the value of the capacitor (capacitance) that will result in a current that is (a) lagging or (b) leading in an AC circuit with a given inductor connected in series with a resistor and a power source.

Resonance in AC circuits

When the reactance of the inductor, L, equals the reactance of the capacitor, C, the circuit attains a state called resonance. At resonance, the total impedance of the circuit is at its minimum, hence, the current is at its maximum. This happens when the current leads or lags the voltage.

Solving the problem

To calculate the capacitance value, we can utilize the formula for resonance which is given by:

f = 1/(2π√(LC))

Solving for C, we get:

C = 1/(4π²f²L)

Substituting the given values (f = 400 Hz, L = 0.143 H) Into the formula, we calculate for C for both (a) and (b) scenarios.

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Answer:  0.15

Step-by-step explanation:

As per given , the probability that customers who bought a new vehicle bought an SUV : P(SUV) = 0.20

The probability that customer bought a vehicle that was an SUV and in black color : P(SUV and black)  =0.03

Now by suing conditional probability formula,

If we have given that a customer bought an SUV, then the probability that it was black will be :

Hence, the required probability is 0.15.

The probability that a customer who bought an SUV also bought a black SUV is 0.006, or 0.6% (expressed as a percentage).

To find the probability that a customer who bought an SUV also bought a black SUV, you can use conditional probability.

Let's define the following events:

A: A customer bought an SUV.

B: A customer bought a black SUV.

You are given that P(B|A) is the probability that a customer who bought an SUV also bought a black SUV, which is 3% or 0.03.

You want to find P(B|A), the probability that a customer who bought an SUV also bought a black SUV. You can use the following formula for conditional probability:

P(B|A) = (P(A and B)) / P(A)

Here, P(A and B) is the probability that a customer bought both an SUV and a black SUV, and P(A) is the probability that a customer bought an SUV.

You know that P(B|A) = 0.03 and P(A) = 0.20.

Now, you need to find P(A and B), the probability that a customer bought both an SUV and a black SUV. You can rearrange the formula:

P(A and B) = P(B|A) * P(A)

P(A and B) = 0.03 * 0.20

P(A and B) = 0.006

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Answer:

[2,∞)

Step-by-step explanation:

The range is the y intercept and the function starts at 2 and continues going up causing the range of the function to be [2,∞)

Deanna 78 games 19.50

Lisa 26 games 19.50

Hope that helps..

Final answer:

To determine how many games it will take for Deanna and Lise to have the same amount of money left, set up an equation using their net losses per game and solve for 'g'. It will take 40 games for them to have the same amount of money left.

Explanation:

To determine how many games it will take for Deanna and Lise to have the same amount of money left, we need to set up an equation. Let's start by determining their net loss per game by subtracting the cost of each game from their initial amount of money. For Deanna, her net loss per game is $0.25. For Lise, her net loss per game is $0.75.

Let's represent the number of games they play with the variable 'g'. To find the number of games it will take for them to have the same amount of money left, we need to set up an equation. Deanna's remaining money after 'g' games can be represented as $20 - $0.25g. Lise's remaining money after 'g' games can be represented as $40 - $0.75g.

Setting the two expressions equal to each other, we can solve for 'g':

$20 - $0.25g = $40 - $0.75g

$20 = $40 - $0.5g

$0.5g = $20

g = $20 / $0.5 = 40

Therefore, it will take 40 games before Deanna and Lise have the same amount of money left.

Answer:

The 90% for the average weights of men is between 137.24 lb and 185.76 lb.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 14

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.7709

The margin of error is:

M = T*s = 1.7709*13.7 = 24.26

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 161.5 - 24.26 = 137.24 lb

The upper end of the interval is the sample mean added to M. So it is 161.5 + 24.26 = 185.76 lb

The 90% for the average weights of men is between 137.24 lb and 185.76 lb.

The area of a square relates to its side length as Area = Side Length × Side Length. To estimate a side length, knowing $4/sq ft cost and $600 spent, Side Length ≈ 12 feet.

The area of a square is related to its side length by the formula:

Area = Side Length × Side Length

or Area = Side Length²

To estimate the length of a side of a square,

use the given information that the designer paid $4 per square foot for flooring and spent $600 on the flooring.

The cost of the flooring is directly proportional to its area, which is determined by the square of the side length.

Let's set up an equation using the cost and area:

Cost of flooring = Cost per square foot × Area

$600 = $4/sq ft × Side Length²

Solving for Side Length²

Side Length² = $600 / $4/sq ft

Side Length² = 150 sq ft

Taking the square root of both sides to find the side length:

Side Length ≈ √150

Side Length ≈ 12.25 feet

Rounded to the nearest foot, the side length of the room is approximately 12 feet.

Therefore, the estimated length of a side of the room is about 12 feet.

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Answer:

$150

Step-by-step explanation:

600 divided by 4