Answer:
68.9°
Step-by-step explanation:
Using Sine rule
x/sin X = y/sin Y
4.5/sin X = 4/sin 56
sin X × 4 = 4.5 × sin 56
sin X = 4.5 × sin 56/4
X = arc sin (4.5 × sin 56/4)
X = 68.85449°
Approximately = 68.9°
Tri-County G\$T selis 150,000 MWh per yeat of electrical power to Boulder at $80 per MWh, has fixed costs of $80.1 milion per yoar, and has varistele costs of $20 por MWh. If Tri-County has 1,000,000MW h of demand from its customers (other than Boulder), what will Tri-County have to charge to break even? Tri-County wit have to charge? to break oven. (Enter your response rounded to the nearest penny.)
Tri-County will have to charge approximately $83.1 per MWh to break even.
To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.
The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.
To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.
Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.
Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh
Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.
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Calculate minimum and maximum frequency for acoustic
and optic mode.
( short question (
The specific range depends on the material properties and the energy levels involved.
The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.
Acoustic Mode:
The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.
The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.
The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.
Optic Mode:
The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.
The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.
The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.
It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.
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convert the binary expansion of each of the following integers to a hexadecimal expansion. the hexadecimal notation of (0111 0111 0111 0111)2
Each group of four binary digits can be represented by a single hexadecimal digit. The hexadecimal notation of (0111 0111 0111 0111)₂ is (7777)₁₆.
To convert the binary expansion of (0111 0111 0111 0111)2 to hexadecimal, we first group the digits into groups of four starting from the right:
(0111 0111 0111 0111)2 = (7 7 7 7)16
Each group of four binary digits can be represented by a single hexadecimal digit. In this case, each group of four binary digits represents the hexadecimal digit 7. Therefore, the hexadecimal notation of (0111 0111 0111 0111)2 is (7777)16.
To convert the binary expansion (0111 0111 0111 0111)₂ to a hexadecimal expansion, you can group the binary digits into sets of four starting from the right and then convert each group to its corresponding hexadecimal value. Here's the process:
1. Group the binary digits: (0111) (0111) (0111) (0111)
2. Convert each group to hexadecimal:
- (0111)₂ = 7₁₆
- (0111)₂ = 7₁₆
- (0111)₂ = 7₁₆
- (0111)₂ = 7₁₆
Your answer: The hexadecimal notation of (0111 0111 0111 0111)₂ is (7777)₁₆.
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write mathematical equations that show how you will calculate the detected activity from the count rate due to background radiation and the sample of kcl. also write an equation that shows how you will determine the true activity of your sample
The values for R(detected), λ, and t into the equation, you can calculate the "true" count rate of your sample
To calculate the detected activity from the count rate due to background radiation and the sample of KCl, you can use the following equation:
R(detected) = R(total) - R(background)
In this equation, R(background) represents the count rate for background radiation, and R(total) represents the total count rate detected from your sample and background. By subtracting the count rate of background radiation from the total count rate, you can determine the detected count rate from your sample, R(detected).
To determine the "true" activity of your sample, you can use the following equation:
R(true) = R(detected) / (1 - exp(-λt))
In this equation, R(true) represents the "true" count rate of your sample, R(detected) represents the detected count rate from your sample, λ represents the decay constant of the radioactive isotope in your sample, and t represents the time during which the count rate is measured.
By plugging in the values for R(detected), λ, and t into the equation, you can calculate the "true" count rate of your sample, which represents the actual activity of the radioactive isotope in the sample.
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Complete question:
write a mathematical equations that show how you will calculate the detected activity from the count rate due to background radiation and the sample of KCl. also, write an equation that shows how you will determine the "true" activity of your sample. Use the following terms:
R(background) = count rate for background radiation
R(total) = total count rate detected from your sample and background
R(detected) = detected count rate from your sample less the background radiation
R(true) = the "true" count rate of your sample.
An electronics store is having a sale. A CD player that normally costs $49.95 is on sale for 5% off. How much is the discount
Answer:$2.50
Step-by-step explanation: You will take $49.95 times 0.05 or 5% and you get 2.497 and round that to $2.50.
What is the answer?❤️
Answer:
a=4 B i think is =20 c im not sure
Step-by-step explanation:
In the triangle shown below, which altitude length can be found without using the Distance Formula? What is the length?
Answer: a.) the altitude from N to line LM 6 units
Step-by-step explanation: Looking at the graph, you can count the units from the point N to the line, or you can find the difference between 4 and -2: 4- (-2) = 6
The altitude from N to LM is 6 units. Therefore, option A is the correct answer.
From the graph, triangle LMN is given.
What is the altitude length?The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex.
From the given graph we can see, the altitude from N to LM is 6 units.
Therefore, option A is the correct answer.
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Show your work please
Answer:
Perimeter:
\(2( \frac{2}{3} + \frac{1}{2} ) = 2( \frac{4}{6} + \frac{3}{6} ) = 2( \frac{7}{6} ) = \frac{7}{3} = 2 \frac{1}{3} \)
The perimeter is 2 1/3 inches.
Area:
\( \frac{2}{3} \times \frac{1}{2} = \frac{1}{3} \)
The area is 1/3 of a square inch.
a bag contains $4$ orange balls and $5$ purple balls. raina draws three balls out of the bag, one at a time, without replacement. what is the probability that the colors of the balls alternate?
The odds of the colors of the balls alternating without replacement are 5/18.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
Raina draws three balls out of the bag, one at a time, without replacement,
=4/9*5/8*3/7+5/9*4/8*4/7
=5/42+10/63
=35/126
=5/18
The probability that the colors of the balls alternate without replacement is 5/18.
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Natalie won 45 pieces of gum playing the
bean bag toss at the county fair. At school
she gave one to every student in her math
class. She only has 18 remaining. How
many did she give away?
my Christmas present to you
Answer:
k wat is it
Step-by-step explanation:
5. What is the slope of the line that passes through (0, 1) and (3, 7)? A -2 B -1/2 C 1/2 D 2
The slope of the line that passes through the points (0, 1) and (3, 7) include the following: D. 2.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope) = rise/run
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope) = (7 - 1)/(3 - 0)
Rate of change (slope) = 6/3
Rate of change (slope) = 2.
Based on the data points, the rate of change is the change in y-axis with respect to the x-axis and it is equal to 2.
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Suppose IQ scores were obtained for randomly selected sets of . The pairs of measurements yield , , r , P-value 0.000, and , where x represents the IQ score of the . Find the best predicted value of given that the has an IQ of ?
Use a significance level of 0.05. 20 siblings 20 x=99.42 y=97.2 =0.867 = = −21.33+1.19x y older child y older child 97 Click the icon to view the critical values of the Pearson correlation coefficient r.1 The best predicted value of is . y (Round to two decimal places as needed.) Critical Values of the Pearson Correlation Coefficient r n 0.05 α = 0.01 α = NOTE: To test H0 : 0 against H1: 0, reject H0 if the absolute value of r is greater than the critical value in the table. rho= rho≠4 0.950 0.990 5 0.878 0.959 6 0.811 0.917
The best predicted value given that a person has an IQ of 91 is 94.03.
Here, we are given that-
sample size n = 20
sample mean for the independent value x = 100.39
sample mean for the dependent value y = 103.6
coefficient of correlation r = 0.925
The general expression for representing a linear model is given by-
y = β₀ + β₁x
where β₀ is the intercept and β₁ is the slope
For the above given case, the linear model will be given as-
y = -3.34 + 1.07x
where -3.34 is the intercept and 1.07 the slope.
To find the best predicted value when X = 91, we substitute the value of x as 91 in the equation as follows-
y = -3.34 + 1.07(91)
y = 94.03
Thus, the best predicted value given that a person has an IQ of 91 is 94.03.
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Problem 3: Four matrices are given below. B = -61 A = 1 2 3 456 C = 0 D = -3 1 (a) Is CT + D defined? If yes, compute it. If no, why not? (b) Is AB defined? If yes, what are its dimensions? If no, why
The resulting matrix will have dimensions 2 x 2, just like matrix A because the number of rows in matrix A and the number of columns in matrix B dictate the size of the resulting matrix.
(a) It is impossible to compute CT + D because the dimensions of the matrices are incompatible. The matrix C has 1 row and 2 columns, whereas the matrix T has 2 rows and 1 column.
As a result, matrix multiplication is impossible because the number of columns in the first matrix does not match the number of rows in the second matrix. So, no, CT + D is not defined.
(b) Yes, AB is defined.
The dimensions of matrix A are 2 x 2, while the dimensions of matrix B are 1 x 2. The number of columns in matrix A matches the number of rows in matrix B, so matrix multiplication is possible.
The resulting matrix will have dimensions 2 x 2, just like matrix A because the number of rows in matrix A and the number of columns in matrix B dictate the size of the resulting matrix.
So, AB is a 2 x 2 matrix.
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The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from.
The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from CHANCE .
The word "chance" describes unpredictability or the unexpected in relation to things like events that happen without a clear reason why and without human intention.
The conclusion is that chance is the tendency of people to recognize different kinds of significant patterns in a random order or sequence in addition to evaluating any kind of outcome. Because chance can also result in an underestimating of a system's conclusion or result, it is crucial to consider it when conducting an investigation.
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need help asap. low geometry grade
Answer:
x=9.3
Step-by-step explanation:
use SohCahToa
in this case u use cos
cos(41°)=7/x
x=7/cos(41)
x=9.275090953
x=9.3
Mariana made a quilt square with the design shown below.
https://cdn.app.edmentum.com/EdAssets/cfa811cb5c44407fbc5e76dd7dfc22a8?ts=635545793215170000
Which of the following best describes the shaded triangle with the given measures?
A.
obtuse isosceles triangle
B.
right scalene triangle
C.
obtuse scalene triangle
D.
right isosceles triangle
Answer:
B.
right scalene triangle
Step-by-step explanation:
Find the value of x in the equation below. 12+x = 16.7
Answer:
\( \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.7}}}}}\)
Step-by-step explanation:
\( \sf{12 + x = 16.7}\)
Move 12 to right hand side and change it's sign
\( \dashrightarrow{ \sf{x = 16.7 - 12}}\)
Subtract 12 from 16.7
\( \dashrightarrow{ \sf{4.7}}\)
Hope I helped!
Best regards!
Answer:
\(\huge\boxed{\sf x = 4.7}\)
Step-by-step explanation:
12 + x = 16.7
Subtracting 12 to both sides
x = 16.7 - 12
x = 4.7
Which ratio does NOT represent this situation?
1 point
o
3:12
9:3
8:2
1:3
Answer:
1:3
Step-by-step explanation:
3:12 is the amount of shaded circles to all circles, 8:2 is basically the same thing as 3:12 and 9:3 is the amount of shaded circles to the amount of non-shaded circles. 1:3 wouldn't work because it is not the right ratio.
In a particular country, there are two types of currency: Kabuls and Carumpts. 8 Kabuls and 2 Carumpts are worth $61.70. 3 Kabuls and 10 Carumpts are worth $31. What is the dollar value of each piece of currency?
Answer:
Kabuls = 7.5
Carumpts= 0.85
Step-by-step explanation:
Let x represent the price of kabuls
Let y represent the price of carumpts
8x + 2y= 61.70......equation 1
3x + 10y= 31.........equation 2
Multiply equation 1 by 3 and equation 2 by 8
24x + 6y= 185.1
24x + 80y= 248
-74y = -62.9
y= 62.9/74
y= 0.85
Substitute 0.85 for y in equation 1
8x + 2(0.85) = 61.70
8x + 1.7= 61.70
8x = 61.70-1.7
8x = 60
x= 60/8
x= 7.5
Hence the dollar value for kabuls is 7.5 and carumpts is 0.85
What is the slope that passes through (4,4) and (-2,8)
Answer:
hope it helps you..............
Answer:
Step-by-step explanation:
The speed of a runner increased steadily during the first three seconds of a race. her speed at half-second intervals is given in the table. find lower and upper estimates for the distance that she traveled during these three seconds.
t(s) 0 0.5 1.0 1.5 2.0 2.5 3.0
V (ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2
She can only move a certain distance in three seconds, with a lower distance of 33.45 feet and a upper distance of 43.45 feet.
The first three seconds of a race saw a runner's speed rapidly grow.
The time is therefore 3 seconds.
The table provides her speed at half-second intervals.
We are aware,
Speed = Distance / Time
Similarly
Distance = Speed × Time
t equals 0.5 seconds
Then, the lower distance traveled overall is equal to 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).
Terms are multiplied and added.
= 0.5 × 66.9
= 33.45 feet
The upper distance traveled is equal to 0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)
= 0.5 × 86.9
= 43.45 feet
As a result, Her lower distance in three seconds is therefore 33.45 feet, and her upper distance in three seconds is 43.45 feet.
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solve the formula A= pi r^2 for r
Answer:
sqrt(A/pi)= r
Step-by-step explanation:
A= pi r^2
Divide each side by pi
A/pi= pi r^2/pi
A/pi= r^2
Take the square root of each side
sqrt(A/pi)= sqrt( r^2)
sqrt(A/pi)= r
The value of r after solving A=pi\(r^{2}\) is \(\sqrt{A/Pi}\).
What is a Formula?A mathematical relationship or rule expressed in symbols.
How to solve a formula?We have been giving the following formula and we have to solve it for r means we have to find the value of r.
A=pi\(r^{2}\)
A/pi=\(r^{2}\)
r=\(\sqrt{A/Pi}\)
Hence the value after solving the formula A=Pi\(r^{2}\) is \(\sqrt{A/Pi}\)
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A food vending truck made a bar graph showing their revenue for four days last week. Which of the following is closest to the range of sales for the four-day period?
A.
$450
B.
$50
C.
$2,300
D.
$250
The is closest to the range of sales for the four-day period is $5,500 (Option A)
How is this so?Taking a look at the graph we can see that in May, there were about 5,500 dollars in sales.
In June, there were 8,000 dollars in sales.
In July, there were about 2,500 dollars in sales.
In August, there were 6,000 dollars in sales.
To find the range, subtract the smallest amount from the largest amount.
$8,000 - $2,500 = $5,500
Therefore, the range is $5,500. So we are right to state that Option A is the answer.
Note that the principle of range here remains the same across board.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
A company made a bar graph showing the amount of sales for each month in thousands of dollars. Which of the following is closest to the range of sales for the four-month period?
A. $5,500
B. $3,000
C. $500
D. $2,500
See attached image.
Suppose the linear approximation for a function f(x) at a = 3 is given by the tangent line y = −2x + 12. What are f(3) and f '(3)? f(3) = f '(3) = If g(x) =[f(x)]2 , find the linear approximation for g(x) at a = 3, L(x) = _____
The linear approximation for g(x) at a = 3 is L(x) = -24x + 108.
The equation of the tangent line to a function f(x) at a point x = a is given by: y = f(a) + f'(a)(x - a)
In this case, the linear approximation for f(x) at a = 3 is given by the tangent line:
y = -2x + 12
Comparing this to the equation of the tangent line, we have:
f(a) = -2a + 12 = -2(3) + 12 = 6
f'(a) = -2
Therefore, f(3) = 6 and f'(3) = -2.
To find the linear approximation for g(x) = [f(x)]^2 at a = 3, we can use the chain rule:
g'(x) = 2f(x)f'(x)
At a = 3, we have:
g(3) = [f(3)]^2 = 6^2 = 36
g'(3) = 2f(3)f'(3) = 2(6)(-2) = -24
The equation of the tangent line to g(x) at a = 3 is then: y = g(3) + g'(3)(x - 3)
Substituting in the values we found, we get:
y = 36 - 24(x - 3) = -24x + 108
Therefore, the linear approximation for g(x) at a = 3 is L(x) = -24x + 108.
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Are the lines parallel, perpendicular, or neither?
One line passes through the points (3, 2) and (6, 8), and the other line passes through the points (0, 2) and (2, 6).
Answer:
Parallel
Step-by-step explanation:
Slope of line 1:
y2 - y1 / x2 - x1
8 - 2 / 6 - 3
6/3
= 2
Slope of line 2:
y2 - y1 / x2 - x1
6 - 2 / 2 - 0
4/2
= 2
- Since the slope is the same, both the lines are parallel.
i need help
I'm doin
Answer:
graph A
Hope that helps!
Answer: Graph a
Step-by-step explanation: The points in graph A match the table provided. The points (-2,2), (-1,3), and (0,4) are all on the line in graph A. If the line continued it would pass through (1,5).
On a coordinate plane, a curved line with minimum values of (negative 0.5, negative 7) and (2.5, negative 1), and a maximum value of (1.5, 1), crosses the x-axis at (negative 1, 0), (1, 0), and (3, 0), and crosses the y-axis at (0, negative 6). Which interval for the graphed function contains the local maximum?
The interval for the graphed function that contains the local maximum is from (negative 0.5, negative 7) to (1.5, 1).
To find the interval for the graphed function that contains the local maximum, we need to use the given minimum and maximum values. The minimum values are (negative 0.5, negative 7) and (2.5, negative 1), and the maximum value is (1.5, 1). We need to determine the x-axis and y-axis crossings. The x-axis crossings are (negative 1, 0), (1, 0), and (3, 0), and the y-axis crossing is (0, negative 6). To find the interval, we need to find the lowest x-coordinate and the highest y-coordinate of the given values. The lowest x-coordinate is (negative 0.5, negative 7) and the highest y-coordinate is (1.5, 1). Thus, the interval for the graphed function that contains the local maximum is from (negative 0.5, negative 7) to (1.5, 1).
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In a school of 2000 students, the ratio of teachers to students is 3:80.Some teachers join the school and the ratio changes to 1:20.Find the number of teachers who joined the school.
In a school of 2000 students, the ratio of teachers to students is 3:80. This means there are 3 teachers for every 80 students.
Thus, 25 teachers joined the school.
Let the number of teachers be x and students be y.
Then, according to the given ratio, we have the equation:
\(\frac{x}{y}=\frac{3}{80}$$\)
Multiplying both sides by 80y, we get:
80x=3y
Thus, we know that there are 3/80 teachers per student.
Now let's consider the new ratio, which is 1:20.
This means there is 1 teacher for every 20 students.
We can set up another equation based on this ratio:
\(\frac{x+a}{y}= \frac{1}{20}$$\)
where a is the number of teachers who joined the school. Multiplying both sides by 20y, we get:
20(x+a)=y
Now we have two equations:
\(80x=3y\)
20(x+a)=y
We can solve for a by substituting y in the second equation with the expression we get from the first equation:
20(x+a)=80x/3
x+a=4x/3
a = x/3
Therefore, the number of teachers who joined the school is x/3.
We know that the initial ratio of teachers to students is 3:80.
So the initial number of teachers x can be calculated by:
\(\frac{x}{2000}=\frac{3}{80}$$\)
\(x=\frac{3}{80} \times 2000$$\)
x=75
Thus, the number of teachers who joined the school is:
a = x/3
= 75/3
=25
Therefore, 25 teachers joined the school.
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A shirt regularly priced at $36.00 was on sale for 25% off.
What was the sale price?
A. $9.00
B. $24.00
C. $27.00
D. $48.00
E. None correct