Answer:
\(let \: their \: points \: of \: intersection \: be \to \: x \\ since : \\ \: \overline{MN} \: intersects \: \overline{QL} \: at \: point \: x : \\ and\\ \overline{QL} \: also \: meets \: \overline{MN} \: at \: point \: x : \\ hence \: \overline{QL}\: and \: \overline{MN} \: bisects \: each \: other.\)
Consider a sample with data values of \( 10,20,21,14,18 \) and 19. Compute the mean and median. mean median
of the pth percentile: the location within the data and the actual value. The formula for f
The mean of the data values is 17. The median of the data values is 18.
To find the mean of a set of data values, we sum up all the values and divide by the total number of values. In this case, the sum of the data values is 10 + 20 + 21 + 14 + 18 + 19 = 102. Since there are 6 data values, the mean is 102/6 = 17.
The median is the middle value of a set of data when it is arranged in ascending or descending order. In this case, the data values arranged in ascending order are 10, 14, 18, 19, 20, 21. Since there are 6 values, the middle two values are 18 and 19. Therefore, the median is 18.
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the amount of sugar in billy's kitchen is directly proportional to the number of cookies he can bake. the number of cookies that billy bakes is inversely proportional to a score of his physical health (since he eats all the cookies). by what percent will billy's health score go down if his sugar resources are quadrupled?
Billy's health score go down by 75% if his sugar resources are quadrupled
Let the amount of sugar in Billy's kitchen be denoted by S and the number of cookies he can bake be denoted by C. Let his health score be denoted by H. Then we have the following relationships:
C ∝ S (directly proportional)
C ∝ 1/H (inversely proportional)
Combining these two relationships, we get:
C ∝ S/H
If S is quadrupled, then C will also quadruple according to the first relationship. However, H will decrease by some percentage x according to the second relationship. To find x, we can use the fact that C is proportional to S/H:
C = k*S/H
where k is a constant of proportionality. If S is quadrupled, then C will also quadruple, so we have:
4C = k4S/H
C = kS/(H/4)
This tells us that if S is quadrupled, then C will be divided by H/4. In other words, C/H will be divided by 4. So, the percentage decrease in H can be found as follows:
C/H → (C/H)/4 = (S/H)/(4/k) → x = 100%*(1 - 1/4) = 75%
Therefore, if Billy's sugar resources are quadrupled, his health score will go down by 75%.
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The measure of an angle is 51.6°. What is the measure of its supplementary angle?
Answer:
128.4°
Step-by-step explanation:
Supplementary angels are 180°
180°-51.6°=128.4°
What is the distance between -12 and 5?
Answer:
7
Step-by-step explanation:
PLZ TELL ME IF IM WRONG
Traingle A(1,8), M(6,8). P(2,3), is reflected over the x axis and then rotated 90degrees clockwise. What are the coordinates of its image A'M'P'?
Reflection over the x-axis transforms the point (x,y) into (x, -y), then
A(1,8) → A''(1, -8)
M(6,8) → M''(6, -8)
P(2,3) → P''(2, -3)
Rotation 90° clockwise transform the point (x, y) into (y, -x), then
A''(1, -8) → A'(-8, -1)
M''(6, -8) → M'(-8, -6)
P''(2, -3) → P'(-3, -2)
which show a set of prime factors
A. 2, 17
B. 2, 4, 5
C. 4, 11
D. 2, 25
Answer:
i think it D if no im so sorry :)
Step-by-step explanation:
Answer: A.2,17
Step-by-step explanation:
Prime numbers are those which are divisble by 1 and itself so 2,17 are
the cost per ounce of a drink, c, varies inversely as the number of ounces, n. six ounces of the drink costs 60 cents per ounce. how many cents per ounce would 9 ounces cost?
When the number of ounces is 9, the cost per ounce would be 40 cents. To solve , we can use the concept of inverse variation, which states that two variables are inversely proportional if their product remains constant.
Let's denote the cost per ounce as C and the number of ounces as N. According to the problem, we know that when N = 6, C = 60 cents per ounce. Using the inverse variation equation, we have: C × N = k, where k is the constant of variation. Substituting the given values, we get: 60 × 6 = k; k = 360.
Now, we can find the cost per ounce when N = 9: C × 9 = 360. Dividing both sides by 9, we have: C = 360 / 9; C = 40. Therefore, when the number of ounces is 9, the cost per ounce would be 40 cents.
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Someone plz help me
Answer:
16 is the answer hope i helped!
Step-by-step explanation:
Answer:
i think it c
:D
Step-by-step explanation:
Consider the series one-fourth, startfraction 1 over 16 endfraction startfraction 1 over 64 endfraction startfraction 1 over 256 endfraction ellipsis which expression defines sn?
The expression that defines sn is startfraction 1 over 4 raised to the power of (n + 2) endfraction.
The series is given as: one-fourth, startfraction 1 over 16 endfraction, startfraction 1 over 64 endfraction, startfraction 1 over 256 endfraction, ellipsis.
To find the expression that defines sn, we can observe the pattern in the series.
The numerator of each term is always 1, and the denominator follows the pattern of powers of 4.
So, the nth term of the series can be written as startfraction 1 over 4 raised to the power of (n + 2) endfraction.
Therefore, the expression that defines sn is startfraction 1 over 4 raised to the power of (n + 2) endfraction.
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Pls. Help find these answers?!
Answer:
12
Step-by-step explanation:
Answer:
1) 12 boxes
2) 3, 6, 12
3) 12
4) 110 degrees
Step-by-step explanation:
1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.
Length: 4 boxes
Width: 3 boxes
4 x 3 = 12
12 boxes
2)
10% of 30 is 0.1 times 30.
0.1 x 30 = 30/10 = 3
20% of 30 is 0.2 times 20.
0.2 x 30 = 30/5 = 6
40% of 30 is 0.4 times 20.
0.4 x 30 = 30/2.5 = 12
3) Count the cubes. Reminder there are 2 boxes you cannot see.
Top Layer: 2
Middle Layer: 4
Back Bottom Layer: 4
Front Bottom Layer: 2
2 + 4 + 4 + 2 = 12
4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.
180/18 (The angle of each section)
10
11 Sections
10 x 11 = 110
Congruent angles have the same number of?
Answer:
congruent angles have same number of shape and size
consider the following special divergent series below:
student submitted image, transcription available below
different between each n is 1. (ex- 1/1+1/2+1/3...)
In MATLAB, using FOR LOOPS ONLY calculate the total sum of the first 750 terms.
USING FOR LOOPS!!!
use Matlab code
Here's a MATLAB code that calculates the total sum of the first 750 terms of the series using only for loops.
```matlab
% Initialize the total sum
totalSum = 0;
% Iterate from n = 1 to n = 750
for n = 1:750
% Calculate the term of the series for the current n
term = 1/n;
% Add the current term to the total sum
totalSum = totalSum + term;
end
% Display the total sum
disp(['Total sum of the first 750 terms: ' num2str(totalSum)]);
```
This code iterates from n = 1 to n = 750 and calculates the term of the series for each n as 1/n. It then adds each term to the total sum using the for loop. Finally, it displays the total sum of the first 750 terms.
Please note that the series you provided, 1/1 + 1/2 + 1/3 + ..., is the harmonic series, which is a well-known divergent series. As the number of terms increases, the series sum grows without bound.
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the mean monthly electric bill for 71 residents of the local apartment complex is $62. what is the best point estimate for the mean monthly electric bill for all residents of the local apartment complex?
If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .
In the question ,
it is given that ,
the number of residents in the local apartment complex is = 71
the mean electric bill for the 71 residents = $62 ;
we know that the sample mean is itself called as the best point estimate ;
So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of local apartment complex which is given as $62 .
Therefore , the best point estimate is $62 .
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a) z 0.03
. Note z 0.03
is that value such that P(Z≥z 0.03
)=0.03. (b) A random sample of size 36 is taken from a population with standard deviation σ=12. If the sample mean is X
ˉ
=75, construct: i. 90% confidence interval for the population mean μ. ii. 96% confidence interval for the population mean μ.
(a) To find the value of z 0.03, we use a standard normal distribution table or calculator. From the table, we find that the z-score corresponding to a right-tailed probability of 0.03 is approximately 1.88. Therefore, z 0.03 = 1.88.
(b) Given a random sample of size n = 36 from a population with standard deviation σ = 12 and sample mean X = 75, we can construct confidence intervals for the population mean μ using the t-distribution since the population standard deviation is unknown.
i. To construct a 90% confidence interval for μ, we first need to find the t-value with degrees of freedom (df) = n - 1 and a cumulative probability of (1 - 0.90)/2 = 0.05 in each tail of the distribution. Using a t-distribution table or calculator with df = 35, we find that the t-value is approximately 1.69.
The margin of error (ME) is then calculated as ME = tα/2 * (σ/√n), where tα/2 is the critical value for the desired level of confidence, σ is the population standard deviation, and n is the sample size.
Substituting the values, we get ME = 1.69 * (12/√36) = 6.08
The confidence interval is then calculated as (X - ME, X + ME) or (75 - 6.08, 75 + 6.08), which simplifies to (68.92, 81.08). Therefore, we are 90% confident that the true population mean falls within this interval.
ii. To construct a 96% confidence interval for μ, we follow similar steps as above but with a different t-value and margin of error.
Using a t-distribution table or calculator with df = 35, we find that the t-value is approximately 2.03 for a cumulative probability of (1 - 0.96)/2 = 0.02 in each tail of the distribution.
The margin of error is then calculated as ME = 2.03 * (12/√36) = 7.32
The confidence interval is (X - ME, X + ME) or (75 - 7.32, 75 + 7.32), which simplifies to (67.68, 82.32). Therefore, we are 96% confident that the true population mean falls within this interval.
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If a = 7, what is the value of the expression 2(a + 8)?
Answer:
30
Step-by-step explanation:
2(a + 8)
Let a = 7
2(7 + 8)
Using PEMDAS, lets add first because this is inside the parentheses.
2(15)
Now multiply,
30
Answer:
You replace the a with 7.
2(a + 8)
2(7 + 8)We solve the brackets (according to the BODMAS rule) and simplify.
2(15)30.In the diagram below, what is the relationship between the number of triangles and the perimeter?
The perimeter "P" is equal to the length of the base of one triangle multiplied by the "n" number of triangles in the figure plus two times the length of another side. The equation for the perimeter is P = 5n + 14.
We are given triangles. The triangles are arranged in a certain pattern. The length of the base of each triangle is equal to 5 units. The length of the other two sides is 7 units each. We conclude that all the triangles are isosceles. We need to find the relationship between the number of triangles and the perimeter of the figure. Let the perimeter of the figure having "n" number of triangles be represented by the variable "P".
P(1) = 14 + 5(1)
P(2) = 14 + 5(2)
P(3) = 14 + 5(3)
We can see and continue the pattern. The relationship between the perimeter and the number of triangles is given below.
P(n) = 14 + 5n
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Answer:
Step-by-step explanation:
14
PQ= RQ and PS= RS a=?
The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.
What are interior angles?In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.
Given:
The length of the segment PQ is equal to the length of the segment RQ.The length of the segment PS is equal to the length of the segment RS.The following steps can be used in order to determine the measure of angle a:
Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.
Step 2 - Apply the sum of interior angle property on triangle PQR.
\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)
\(\angle\text{Q}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-60\)
\(\angle\text{R}=60^\circ\)
Step 3 - Now, apply the sum of interior angle property on triangle PSR.
\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)
\(\angle\text{S}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-90\)
\(\angle\text{R}=45^\circ\)
Step 4 - Now, the measure of angle a is calculated as:
\(\angle\text{a}=60-45\)
\(\angle\text{a}=15\)
The measure of angle a is 15 degrees.
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Evaluate 6+ 4/a + 3/b then a=4 and b=3
Answer:
The answer would be 8.
Step-by-step explanation:
Here the given expression,
6 + 4/a + 3/b
By substituting a = 4 and b = 3 in the above expression,
We get,
6 + 4/4 + 3/3
= 6 + 1 + 1
= 8
Therefore, the value of the given expression would be 8.
Answer: 8
Step-by-step explanation: Plug in a =4 and b=3 into 6+4/a +b/3 6 + 4/4 + 3/3= 6 + 1 + 1= 8
help me on this question please
Answer:
62
Step-by-step explanation:
you have to work out the surface area of a cuboid by:
3×2=6
5×3=15
5×2=10
sum of all the areas is 31
then times it by 2 which is 62
you don t really have to pay attention to the net, apart from the 2cm because you don t want to use it twice in the calculation.
Isla has 225 trading cards and Lily has 180 trading cards. a) Calculate the number of Isla's trading cards as a percentage of the number of Lily's trading cards. b) Calculate the number of Lily's trading cards as a percentage of the number of Isla's trading cards. Give your answers to the nearest 1%.
(a) Isla's trading cards are 125% of Lily's trading cards.
(b) Lily's trading cards are 80% of Isla's trading cards.
Given that,
There are 225 trading cards and Lily has 180 trading cards.
To calculate the percentage of Isla's trading cards compared to Lily's,
We can use this formula:
⇒ Isla's trading cards / Lily's trading cards x 100%
Plugging in the values we get:
⇒ (225 / 180) x 100% = 125%
Therefore,
Isla's trading cards are 125% of Lily's trading cards.
b) To calculate the percentage of Lily's trading cards compared to Isla's, we can use the formula:
⇒ Lily's trading cards / Isla's trading cards x 100%
Plugging in the values we get:
(180 / 225) x 100% = 80%
Therefore,
Lily's trading cards are 80% of Isla's trading cards.
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Angle CCC is inscribed in circle OOO.
\overline{AB}
AB
start overline, A, B, end overline is a diameter of circle OOO.
What is the measure of \angle B∠Bangle, B?
^\circ
∘
degrees
Answer:Angle B is 44 Degrees
Step-by-step explanation: Angle C intersects the circle at the endpoints of a diameter, it intercepts an arc of 180 degrees
The measure of an inscribed angle is half the measure of its intercepted arc, so we know that the measure of angle C is 90 degrees
The angles of triangle ABC must add up to 180 degrees
m∠A+m∠B+m∠C=180
46+m∠B+90=180
m∠B+136=180
m∠B=44
The measure of Angle B in the given diagram is 44 Degrees
Angle C intersects the circle at the endpoints of a diameter, it intercepts an arc of 180 degrees
The measure of an inscribed angle is half the measure of its intercepted arc, so we know that the measure of angle C is 90 degrees
What is the sum of the angles in a triangle?The angles of triangle ABC must add up to 180 degrees.
The total sum of the angle in triangles is180 degrees.
m∠A+m∠B+m∠C=180
46+m∠B+90=180
m∠B+136=180
m∠B=44
Therefore, The measure of Angle B in the given diagram is 44 Degrees.
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Question content area top
Part 1
Write an equivalent expression without parentheses. Then simplify the result.
m−(8−3m)
using exponents, On simplifying the equation, we get =4m+8.
The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.
What is the main objective of simplification?Work simplification is to develop better work processes that boost output while cutting waste and costs.
What does simplifying mean in algebra?Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.
Given equation,
m-(8-3m)
=m-8+3m
=4m+8
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Evaluate j(-1) given j(x)=2x4-x³-35x²+16x+48.
Explain what your answer tells you about x + 1 as
a factor.
Algebraically find the remaining zeros of j(x).
HELP PLS
Answer: look at the images for the answer and the solution
Step-by-step explanation:
o study the effectiveness of a certain adult reading program, researchers will select a random sample of adults who are eligible for the program. The selected adults will be given a pretest before beginning the program and a posttest after completing the program. The difference in the number of correct answers on the pretest and the number of correct answers on the posttest will be recorded for each adult in the sample.
Which of the following is the most appropriate inference procedure for the researchers to use to analyze the results?
A one-sample t-interval for a population mean
A matched-pairs t-interval for a population mean difference
The center remains constant, and the area in the tails of the distribution increases.
The most appropriate inference procedure for the researchers to use to analyze the results is a matched-pairs t-interval for a population mean difference.
Determine the population mean difference?A matched-pairs t-interval for a population mean difference is suitable for this study because it involves comparing the pretest and posttest scores of the same individuals.
The researchers are interested in determining whether there is a significant difference in the number of correct answers before and after the adult reading program.
By using a matched-pairs t-interval, the researchers can analyze the mean difference in scores and determine the range within which the true population mean difference is likely to fall. This inference procedure takes into account the paired nature of the data, accounting for individual differences and increasing the precision of the estimate.
It is important to use this procedure as it considers the correlation between the pretest and posttest scores for each individual, providing a more accurate assessment of the program's effectiveness.
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Solve the system by using matrix reduction. W+ x - y - 6z= -5 2w + 3x + 2y + 112 = 10 2w + x + 2y + 5z = 2 X= X= y = Select the correct choice below and fill in any answer boxes to complete your choice. A. The unique solution is w= y= , and z= 1. (Simplify your answers.) B. The system has infinitely many solutions. The solutions are of the form w= and z=r, where r is any real number. (Simplify your answers. Type expressions using r as the variable. Do not factor.) C. The system has infinitely many solutions. The solutions are of the form w= I, , y=r, and z=s, where r and s are any real numbers. (Simplify your answers. Type expressions using r and s as the variables. Do not factor.) D. The system has infinitely many solutions. The solutions are of the form w= ,x=r, y=s, and z = t, where r, s, and t are any real numbers. (Simplify your answer. Type an expression using r, s, and t as the variables. Do not factor.) O E. There is no solution. X=
The correct choice is:
A. The unique solution is w = -13.25, y = 0.25, and z = 3.75.
To solve the system using matrix reduction, let's write the system of equations in matrix form:
[A|B] = [w x y z | C]
The augmented matrix is:
[1 1 -1 -6 | -5]
[2 3 2 1 | 12]
[2 1 2 5 | 2]
Now, we'll perform row operations to reduce the matrix to row-echelon form:
R2 = R2 - 2R1
[1 1 -1 -6 | -5]
[0 1 4 13 | 22]
[2 1 2 5 | 2]
R3 = R3 - 2R1
[1 1 -1 -6 | -5]
[0 1 4 13 | 22]
[0 -1 4 17 | 12]
R3 = R3 + R2
[1 1 -1 -6 | -5]
[0 1 4 13 | 22]
[0 0 8 30 | 34]
Now, let's perform back substitution to solve for the variables:
R3 = R3/8
[1 1 -1 -6 | -5]
[0 1 4 13 | 22]
[0 0 1 3.75 | 4.25]
R2 = R2 - 4R3
[1 1 -1 -6 | -5]
[0 1 0 0.25 | 12.5]
[0 0 1 3.75 | 4.25]
R1 = R1 + R3
[1 1 0 -2.25 | -0.75]
[0 1 0 0.25 | 12.5]
[0 0 1 3.75 | 4.25]
R1 = R1 - R2
[1 0 0 -2.5 | -13.25]
[0 1 0 0.25 | 12.5]
[0 0 1 3.75 | 4.25]
Now, we have the row-echelon form of the matrix. The last column represents the values of the variables w, x, y, z.
From the reduced matrix, we can see that w = -13.25, x = 12.5, y = 0.25, and z = 3.75.
Therefore, the unique solution to the system is w = -13.25, x = 12.5, y = 0.25, and z = 3.75.
The correct choice is:
A. The unique solution is w = -13.25, y = 0.25, and z = 3.75.
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Some of them needs to be simplify and remember it needs to be shown by Polynomials
1. A simplified expression for the volume of the above prism is 15x³ cubic units.
2. Destiny made her mistake in step 1, and the correct solution with steps is shown below.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular prism = 3x × 5x × x
Volume of rectangular prism = 15x³ cubic units.
Question 2.
Given the following expression, \(\frac{5(x+2)-(8-x)}{2}\)
Step 1: we would open the bracket;
\(\frac{5x\;+\;10\;-\;8\;+\;x}{2}\)
Step 2: we would collect like-terms and evaluate;
\(\frac{5x\;+\;x\;+\;10\;-\;8}{2}\\\\\frac{6x\;+\;2}{2}\)
Step 3: we would split;
\(\frac{6x}{2}+ \frac{2}{2}\)
Step 4: we would divide;
3x + 1
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The measure of an angle is 2 times the measure of its supplement. Tina writes an equation and finds the correct measure of each angle. Which shows the equation Tina could have written and the angle measures she could have found? A 2x + x = 90 ; 60°and 30° b (x+2) +x = 90; 44° and 46° c (x+2) + x = 180; 89° and 91° d 2x + x = 180: 60°and 120°
Answer: d.
2x + x = 180: 60°and 120°
Step-by-step explanation:
Let x= one of the supplements. (smaller)
As per given , measure of second angle = 2x
We know that,
The sum of two supplements = 180 degrees
Then,
smaller angle + larger angle =180°
i.e. x+2x = 180°
3x= 180°
x=60°
then, 2x = 2 (60°) = 120°
hence, the correct option is d.
2x + x = 180: 60°and 120°
The Zeeman effect splits a spectral at frequency f 0
into three components: a central line at f 0
and two offset lines at frequencies f 0
±eB/(4πm e
). What are the wavelengths of the three components of the Hα line at λ 0
=6562.81 A
˚
due to the magnetic field in a typical sunspot?
The wavelengths of the three components of the Hα line due to the magnetic field in a typical sunspot are as follows:
1. Central Line: The wavelength of the central line remains unchanged and is equal to the original wavelength of the Hα line, which is 6562.81 Å.
2. Offset Line 1: The first offset line occurs at a higher frequency and shorter wavelength than the central line. It is given by λ = λ0 - Δλ, where Δλ is the change in wavelength. In this case, Δλ is determined by the Zeeman effect equation: Δλ = eB/(4πm_e), where e is the charge of an electron, B is the magnetic field strength, and m_e is the electron mass. By substituting the values and using the relationship between wavelength and frequency (λ = c/f, where c is the speed of light), the corresponding wavelength of the first offset line can be calculated.
3. Offset Line 2: The second offset line occurs at a lower frequency and longer wavelength than the central line. It is given by λ = λ0 + Δλ, where Δλ is determined as explained above. By substituting the values and using the relationship between wavelength and frequency, the corresponding wavelength of the second offset line can be calculated.
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A vase contains 60 marbles, all of which are red or orange. if the ratio of red marbles to orange ones is 1:5, what is the total number of red marbles in the vase?
The total number of red marbles in the vase are 10.
What is the ratio?A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.
The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.
Now, according to the question;
Let 'x' be the red marbles in the vase.
Let 'y' be the orange marbles in the vase.
The total number of marbles in the vase are 60
x + y = 60 (equation 1)
The ratio of red marbles to orange ones is 1:5.
Thus, x/y = 1/5
cross multiplying;
5x = y
or y = 5x
substitute the value of y in equation 1;
x + y = 60 (equation 1)
x + 5x = 60
6x = 60
x = 10 (red marbles)
Thus, the number of red marbles in the vase are 10.
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How do you add this expression? -1/2 + 2/7
Answer:
You can't
Step-by-step explanation: