The capacitive reactance of the circuit with capacitance of 4 x 10⁻⁸ farad and the AC power source of 2 Khz is X[C] = 1.99 x 10⁻⁷ ohms.
What is Capacitance?The capacitance of a body is defined as the charge holding ability of a body. Mathematically, capacitance is the ratio of charge and potential as follows -
C = dQ/dV
Given is the total capacitance measures .04 microfarad. If the circuit is supplied by an AC power source operating at 2 kHz.
From this we can write -
Capacitance [C] = 0.04 microfarad = 4 x 10⁻⁸ farad.
Frequency of AC supply [f] = 2 KHz = 2 x 10³ Hz
The capacitive reactance is given by -
X[C] = 1/2πfC
X[C] = (1/2 x 3.14 x 2 x 10³ x 4 x 10⁻⁸)
X[C] = 1/(50.24 x 10⁻⁵)
X[C] = 0.0199 x 10⁻⁵
X[C] = 1.99 x 10⁻⁷ ohms
Therefore, the capacitive reactance of the circuit with capacitance of 4 x 10⁻⁸ farad and the AC power source of 2 Khz is X[C] = 1.99 x 10⁻⁷ ohms.
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The area of the scale model of a playground is 6 square yards. The scale model is enlarged by a scale factor of 3 to create the actual playground. What is the area of the actual playground?
The actual area of the playground is 54 square yards
How to determine the area?The given parameters are
Area of the scale model = 6 square yardsScale factor of dilation = 3The actual area of the playground is calculated as
Actual area = Area of the scale model * Scale factor of dilation^2
Substitute the known values in the above equation
So, we have
Actual area = 6 * 3^2
Evaluate the exponent
Actual area = 6 * 9
Evaluate the product
Actual area = 54
Hence, the value of the area is 54
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Find compatible numbers to find two estimates.
2518 divided by 32
Answer: 78.6875
Step-by-step explanation:
math
Which picture shows a properreflection across the red dashed line?АB
When you reflect a point across the red dashed line y = x, the x-coordinate and y-coordinate change places;
If you reflect over the red dashed line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x).
Thus, the picture that shows a proper reflection across the red dashed line is B
what is 11/15 + (- 3/5)
we have
11/15 + (- 3/5)
step 1
REmove the parenthesis
11/15-3/5
Remember that
3/5(3/3)=9/15 ------> is the same number
substitute
11/15-9/15 -----> the fractions have the same deniominator
so
(11-9)/15
2/15
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.40). What is the slope of the graph? What is the unit rate? Complete the explanation The slope is passes through the point (1 The unit rate is $ Vmin. If the graph ofa proportional relationship r), then r equals the slope and unit rate.
Let:
(x1,y1)=(0,0)
(x2,y2)=(1,3.40)
The slope is:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{3.40-0}{1-0}=\frac{3.40}{1}=3.40[/tex]The unit rate is:
[tex]\frac{3.40}{\min }[/tex]HELP!!!!!!!
they are 10 to 10. my screen isn't big enough to screenshot it.
A B C or D
The points (0, 4) , (1, 2) and (2, 0) are shown in figure.
Option 2 is true.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
In the table,
The values of x = 0 , 1 , 2
The values of y = 4 , 2 , 0
Now,
The coordinates are;
(x , y) = (0, 4) , (1, 2) and (2, 0)
Here, For the value of x shows the coordinates for x - axis.
The value of y shows the coordinates for y - axis.
So, The points (0, 4) , (1, 2) and (2, 0) are draw on the graph as given in figure.
Thus, The points (0, 4) , (1, 2) and (2, 0) are shown in figure.
Option 2 is true.
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Hello all the info I was given is right there
11.
We can determine the number of real solutions checking the number of times the graph crosses the x-axis, therefore, we can conclude from the graph that the function has 2 real solutions
Question Let f(x) = -531+4. Evaluate f(-1). Do not include 'f(-1) =' in your answer.
Note that the function f(x) = -531+4 is a function that doesn't depend on x. Hence, it is a constant function. We have that f(x) = -531+4 = -527. This means that the function assigns to any input value the number -527. So, in this case
f(-1) = -527.
Saquon Barkley lost 7 2⁄3 yards on the first play, and gained 9 5⁄8 yards on the next play. What was the total gain or loss for the running back during the first two plays?
If Saquon Barkley lost [tex]7\frac{2}{3}[/tex] yards on the first play, and gained [tex]9\frac{5}{8}[/tex] yards on the next play, then the total gain for the running during the first two plays is [tex]1\frac{23}{24}[/tex] yards
The amount he lost on the first play = [tex]7\frac{2}{3}[/tex] yards
Convert the mixed fraction to the simple fraction
[tex]7\frac{2}{3}[/tex] yards = 23/3 yards
The amount he gained on the second play = [tex]9\frac{5}{8}[/tex] yards
Convert the mixed fraction to the simple fraction
[tex]9\frac{5}{8}[/tex] yards = 77/8 yards
The total gain for the running during the first two plays = The amount he gained on the next play - The amount he lost on the first play
Substitute the values in the equation
= 77/8 - 23/3
= 47/24 yards
Convert the simple fraction to the mixed fraction
47/24 yards = [tex]1\frac{23}{24}[/tex] yards
Hence, if Saquon Barkley lost [tex]7\frac{2}{3}[/tex] yards on the first play, and gained [tex]9\frac{5}{8}[/tex] yards on the next play, then the total gain for the running during the first two plays is [tex]1\frac{23}{24}[/tex] yards.
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a hotel manager has 12 diferent promotional events,plans to run 4 weeks, how many events can she run
Answer: 3 per week.
Step-by-step explanation: 3 x 4 = 12.
The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would liketo travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket
We have that the price of a train ticket has an initial fee of $5 and $2.75 per stop.
Then, we can represent this using the next inequality:
[tex]5+2.75\cdot S\leq21[/tex]In the inequality, we have some restrictions:
• Julia only has $21, no more than that.
,• In the inequality, we need to talk about the same units. If we have units in money on one side of the inequality, we need to have the same units on the other side of the inequality.
,•
Therefore, the scenario can be described by the inequality presented in the first option (option A).
Find the quotient.0.56/−0.7
ANSWER
-0.8
EXPLANATION
The division between a positive number and a negative number gives as a result a negative number. With this in mind, we can do the division as if the numbers were both positive and then add the minus sign to the result:
Adding the minus sign, the result is -0.8
2f = -12f=??[tex]2f = - 12 \\ \\ f = [/tex]
Given:
2f = -12
We are required to find the value of f.
To find f, divide both sides of the equation by 2.
We have:
[tex]\begin{gathered} \frac{2f}{2}=-\frac{12}{2} \\ \\ f\text{ = -6} \end{gathered}[/tex]ANSWER:
f = -6
Alyssa paints 3 walls blue. Each of the walls is 8.3 feet tall and 7.5 feet wide. Round the length and width to the nearest whole number. Then estimate the area that Alyssa will paint. Write equations to show your work. Once, you have done everything find the exact area. Write equations to show your work. Then, compare your estimate to the exact answer. Why is your answer reasonable?
The equation to show the area Allysa will paint is Area = 3(Height x Width) = 3( 8.3ft * 7.5ft) and the area is 186.75 ft²
How to solve Algebraic Word Problems?We are given the dimensions of wall as 8.3ft by 7.5ft.
Thus;Height of wall = 8.3 ft
Width of wall = 7.5 ft
Now, there are total 3 walls in the bedroom to be painted blue.
The formula to calculate the area of one wall is;
A = Height x WidthFormula to calculate the area of four walls will be;
Area = 3(Height x Width) = 3( 8.3ft * 7.5ft)
= 3 (62.25 ft²)= 186.75 ft²
Thus, an area that Alyssa will paint = 186.75 ft²
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In the expression 5^2, the 2 represents the _________________.
A: product
B: sum
C: base
D: exponent
The number, 2, in the given expression represents the exponent. The correct option is D: exponent
The exponent in a mathematical expressionFrom the question, we are to determine what the number, 2, represents in the given expression
The given expression is
5^2
That is,
5²
An exponent is a number or letter written above and to the right of a mathematical expression called the base
In the given expression, the number 2 is written above and to the right of 5. The number 5 is the base in the expression.
Thus,
The 2 represents the exponent
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Is this the right answer to the question. Not 100% sure.
Answer:
Yes, you are correct. Lines l and m are parallel, so corresponding angles are congruent. It does follow that x = 60.
Given a triangle with a = 1, A = 17°, and B = 32°, what is the length of c? Round to the nearesttenth.
a=1
A=17°
B=32°
c=?
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex][tex]C=180-17-32=131[/tex][tex]\frac{1}{\sin 17}=\frac{c}{\sin 131}[/tex][tex]\frac{1}{0.2924}\cdot0.7547=c[/tex][tex]2.58=c[/tex]negative 45 minus negative 19
Answer:
-26
Step-by-step explanation:
Answer:
The answer to this problem is -26
The function g is defined as follows.
g(x)=x² +1
If the graph of g is translated vertically upward by 4 units, it becomes the graph of a function h.
Find the expression for h (x).
Answer:
Use that steps to find your answer
Answer:
h(x) = g(x) + 5 = x² + 5
Step-by-step explanation:
Since the graph is translated vertically upward by 4 units, there is no change in the x values; for the same x value the new y value is +4 times the old y value
This is a multi-part Item. Make note of your answer(s) to this part for use in the remaining part(s).Kara and Nathan participated in a 60-minute maze race.Kara:32 minutesNathan:40 minutesPart AUse ratio notation and decimal notation to describe the relationship between Kara's time and the total time of the race.Enter the correct answers in the box. For the decimal, enter the digit that repeats 3 times.Hint(s): Write the ratio of Kara's time over the total time.Use long division to write the fraction as a decimal.ratio:decimal:
Answer:
Kara's rate over the total time is 0.5333
Step-by-step explanation:
Kara finished the race in 32 minutes.
The total duration of the race was 60 minutes.
So the ratio is:
32/60 = 16/30 = 8/15 = 0.5333
Kara's rate over the total time is 0.5333
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6?
Drag each choice into the boxes to correctly complete the table.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Parallel Perpendicular Neither
y=−12x−5−2x+y=−4−x+2y=2x+2y=−2
Answer:
Step-by-step explanation:Base line: x + 2y = 6
Parallel: Continous, never touching
Perpendicular: Create a right angle when touching
y= -1/2x -5 : Parallel
-2x+y=-4 : Pependicular
-x+2y=2 : Neither
x+2y=-2 : Parallel
Use the graph below for this question: graph of parabola going through 2, negative 3 and 3, negative 1. What is the average rate of change from x = 2 to x = 3? (1 point) a) 2 b) 3 c) 0 d)5
From x = 2 to x = 3 the average rate of change is 2.
The graph of the parabola passes through 2, negative 3 and 3, negative 1 or ( 2, - 3) and ( 3, - 1 ).
Let's say y = f(x) represents the function of the parabola.
Then f( 2 ) = - 3 and f( 3 ) = - 1
Now, for a function y = f(x) the average rate of change from x = a to x = b is given by the expression [ f( b ) - f( a ) ] / ( b - a)
When x changes from x = 2 to x = 3,
The average rate of change will be:
[ f( 3 ) - f( 2 ) ] / ( 3 - 2 ) = [ - 1 - ( - 3 ) ] / 1 = 2
The average rate of change from x = 2 to x = 3 is 2.
The correct option is (a).
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A scientist begins with 100 milligrams of a radioactive substance, which decays exponentially.after 9 hours 55mg of the substance remains How many milligrams will remain after 21 hours? Round the answer to the nearest whole number and include units
We have that the general expression for a function with exponential growth or decay is:
[tex]f(t)=ab^t[/tex]where 'a' represents the initial value, 'b' represents the growth or decay and t represents the time.
In this case, we have that a = 100, since that is the initial population (100 mg of radioactive substance). Also, since we have that after 9 hours, 55 mg of the substance remains, we have the following equation:
[tex]f(9)=55[/tex]now, given the exponential function, with a = 100, we have:
[tex]f(t)=100b^t[/tex]then, combining both expressions, we get:
[tex]f(9)=100b^9=55[/tex]solving for b, we have:
[tex]\begin{gathered} 100b^9=55 \\ \Rightarrow b^9=\frac{55}{100} \\ \Rightarrow b=\sqrt[9]{\frac{55}{100}}=0.935 \\ b=.935 \end{gathered}[/tex]then, the function is defined as follows:
[tex]f(t)=100\cdot(0.935)^t[/tex]finally, to find out how many milligrams will remain after 21 hours, we can make t = 21 and evaluate the function:
[tex]\begin{gathered} t=21 \\ \Rightarrow f(21)=100(0.935)^{21}=24.38 \\ f(21)=24.38mg \end{gathered}[/tex]therefore, there will be 24.38mg after 21 hours
Do the ratios 3 4 and 7 8 form a proportion?
no
No, the ratios are not proportional because they are not equivalent.
We are given a table which has the values of the "x" column and the corresponding "y" column.The values in the "x" column are 3 and 7.The values in the "y" column are 4 and 8.The ratio of the first corresponding values in each column is 3/4 = 0.75.The ratio of the second corresponding values in each column is 7/8 = 0.875.The ratios for all the corresponding values in the table are not equivalent.Hence, they are not proportional because the ratios are not equivalent to a single value.To learn more about ratio, visit :
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Angela purchase a shirt for $14.65 a pair of jeans for $21.99 and she was charged $2.93 tax how much change should she receive if she paid with a $50 bill
The cost of the shirt = $14.65
The cost of the pair of jeans = $21.99
Tax = $2.93
Amount paid = $50
Change = Amount paid - (Cost of shirt + Cost of jeans + tax)
Change = 50 - (14.65 + 21.99 + 2.93)
Change = 50 - 39.57
Change = $10.43
HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answer:
(3.11), (310/100),(1/3),(3/10),(2/-3) Hope I helped
Step-by-step explanation:
310/100 when divided gives us 3 10/100 or in simple form 3.1
1/3 is the smallest rational number but in simple form it is equal to 0.3(3) never ending multiplication of 3
3.11 is displayed in simple form so there is no need to change the number
3/10 can be displayed in simple form as 0.3( remember when dividing by a multiplication of 10 move the decimal point to the left of the lumber by the amount of zeros)
2/-3 since we are dividing the number by a negative number the result will end up in the negatives so lets think of it as 2/3 and later add the negative sign. 2/3 is equal to 0.6(6) and since we are dividing by a negative the result will be -0.6(6)
Make the following conversions. Round your answers to 2 decimal places, where necessary.5 hours 10 minutes toa. Minutes: ? minb. Hours: ? hr
Let's do the math for this question.
The bedroom floor is in the shape of a rectangle. It is 14 feet long and 16 feet wide. Your client has requested that you install either oak flooring or maple flooring. The oak flooring costs $5.25 per square foot for materials. The maple flooring costs $7.00 per square foot for materials. The cost you charge for labor will be the same for either flooring options.
How much money will your client save if you install oak flooring instead of maple flooring?
========================================================
Explanation:
The room is 14 ft by 16 ft.
The floor area is 14*16 = 224 sq ft.
Since oak costs $5.25 per sq ft, this means the total cost of an oak floor is 5.25*224 = 1176 dollars.
Meanwhile, maple flooring will have a total cost of 7*224 = 1568 dollars
If you go with the cheaper option (oak), then the savings is 1568-1176 = 392
----------
Alternative Route:
The difference in per sq ft costs is 7.00-5.25 = 1.75, meaning you save $1.75 per sq ft if you go with the cheaper option.
Multiply this with the total floor area to get 1.75*224 = 392
Simplify the expression
10 - 2(-10x + 7)
Answer: 20x - 4
Step-by-step explanation:
10 - 2(-10x+7)
Distribute the -2:
10 + 20x -14
Combine Like Terms:
20x - 4
elenas bed measures 3‘ x 6‘ on the scale drawing what are the actual measurements of her bed
Using proportions, supposing a scale of 1 inch = 3 feet, the actual measurements of her bed are given by: 9 ft x 18 ft.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division, from the relations built in the problem.
One example of application of proportions is for scale problems, as the actual scale and the drawing length are compared to find the actual length of the object drawn.
In the context of this problem, the scale is given by:
1 inch = 3 feet.
The drawn length of the bed is given by:
3 inches x 6 inches.
Hence the actual length is given by:
9 feet x 18 feet.
As:
3 x 3 = 9.6 x 3 = 18.What is the missing information?The scale of the drawing is missing, hence we are going to suppose that it is 1 inch = 3 feet.
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