The wavelength of the light is found to be 384.06 nm. The light is coming from the source as sodium bulb.
Define the term wavelength of the light?The distance between two crests or troughs of a light wave is known as the wavelength of light.
As a result, wavelength refers to the separation between one wave's crest or dip and the following wave. This Greek letter lambda (λ) is frequently used to represent wavelength. The word wavelength is also occasionally used to refer to modulated waves, their sinusoidal envelopes, or waves created by the interference of multiple sinusoids.For the stated question-
The wavelength of the light before refraction = 510.8 nm (air).
The refractive index of 1.33.(water).
Thus,
refractive index = wavelength of the light in air/wavelength of the light in water.
μ = λ(air) / λ(water)
1.33 = 510.8 / λ(water)
λ(water) = 510.8/1.33
λ(water) = 384.06 nm
Thus, the wavelength of the light is found to be 384.06 nm.
The light is coming from the source as sodium bulb (for wavelength of 510.8 nm.)
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Solve the system of equation and choose
4x+5y=22
2x+3y=12
Answer:The equation of the solution 4x + 5y = 22 and 2x + 3y = 12 will be (3, 2).
What is the solution of the equation?
The solution of the equation means the value of the unknown or variable.
The equations are given below.
4x + 5y = 22 …1
2x + 3y = 12 …2
The degree of the equation is one, then the equations will be the linear equation.
Multiply the equation 2 by 2, then subtract the equation 1 from 2. Then the equation will be
4x + 6y = 24
–4x – 5y = –22
6x - 5y = 24 – 22
Then simplify the equation, then the equation will be
y = 2
Substitute the value of y in equation 1, then the value of x will be
4x + 5(2) = 22
4x + 10 = 22
4x = 22 – 10
4x = 12
x = 12 / 4
x = 3
Then the equation of the solution will be (3, 2).
Step-by-step explanation:
Mrs. Jones deposited $40,000 in a bond and earned simple interest at 7% annually for two years. Calculate the interest earned at the end of the period.
The interest earned at the end of the period by Jones is $5600.
How to calculate the interest?It should be noted that the simple interest is calculated as:
= Principal × Rate × Time
In this case, Jones deposited $40,000 in a bond and earned simple interest at 7% annually for two year
The interest will be:
= Principal × Rate × Time
= $40000 × 7% × 2
= $40000 × 0.07 × 2
= $5600
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Zoe is younger than Keilantra. Their ages are consecutive odd integer Find Zoe's age if the sum of the square of Zoe's age and 4 times Keilantra's age is 125.
Currently, Zoe's age is nine years old
How to determine Zoe's age?From the question, we have the following mathematical statements:
Zoe is younger than Keilantra. Their ages are consecutive odd integer sThe sum of the square of Zoe's age and 4 times Keilantra's age is 125.The above means that:
x = y - 2
x² + 4y = 125
Where x represents Zoe's and y represents Keilantra
Make y the subject in x = y - 2
y = x + 2
So, we have
x² + 4(x + 2_ = 125
Expand
x² + 4x+ 8 = 125
Evaluate
x² + 4x - 117 = 0
Using a graphing calculator, we have
x = 9
Recall that:
x represents Zoe's
Hence, Zoe;s age is 9
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Find the nth term of this quadratic sequence
2, 8, 18, 32, 50,
Answer:
Step-by-step explanation:
From the series, 2, 8, 18, 32, 50,...
By observation and by trial and error.
The first term, n = 1 = 2*1*1 = 2
Second term, n =2, = 2*2*2 = 8
Third, n =3, = 2*3*3 = 18
Third term, n = 4, = 2*4*4 = 32
Fourth term, n =5, 2 * 5* 5 = 50
For nth term, 2 *n *n = 2n²
Therefore nth term = 2n²
I hope this helps.
A drink is made from fruit juice and soda on the ratio 1:4.
A jug contains 1750 ml of the drink.
How much soda was used to make the drink in the jar?
Answer:
it is made of 1400ml of soda
Step-by-step explanation:
Isabella and her children went into a restaurant and will buy drinks and tacos. Each drink costs $2.75 and each taco costs $2. Isabella has a total of $40 to spend on drinks and tacos. Write an inequality that would represent the possible values for the number of drinks purchased, d, and the number of tacos purchased, t.
Answer:
d=8
t=9
Step-by-step explanation:
2.75x8=$22
2x9=$18
22+18=40
d=8
t=9
Answer:
2.75d+2t <= 40
Step-by-step explanation:
What is the slope of the line that passes through the points (9, 5) and (21, -5)? Write your answer in simplest form.
Answer:
-5/6
Step-by-step explanation:
1. Label X1 AND Y1 and X2 AND Y2 (9(x1),5(x2)) (21(x2),-5(y2))
2. Use this formula [tex]\frac{y2-y1}{x2-x1}[/tex]=slope
3. Plug the numbers into the formula [tex]\frac{-5-5}{21-9}[/tex][tex]= - \frac{10}{12}[/tex]
4. Find the simplest form.
[tex]slope= - \frac{5}{6}[/tex]
Find the sum of all positive integers such that their expression in base 7 digits is the reverse of their expression in base 16 digits. Express your answer in base 10.
The sum of all positive integers such that their expression in base 7 digits is the reverse of their expression in base 16 digits is 58.
What is meant by positive integer?Natural numbers are numbers used in mathematics for counting (as in "there are six coins on the table") and ranking (as in "this is the third largest city in the country"). Cardinal numbers are used for counting, and ordinal numbers are used for ordering. Natural numbers, which have no mathematical features, are sometimes employed as labels.
When the number is a 1 digit number (1 digit number in base 7)- the numerals 0, 1, 2, 3, 4, 5, and 6
When the number is a 2 digit number=a×7+b=b×16+a / subtract (a+b) a×6=15×b / divide by 3 2a=5b indicating an is divisible by 5 meaning a=5 (since if a=0 then b=0 and the phrase ab is not defined because the digit that indicates the highest number in a given number cannot be 0) meaning b=2. So there is just one two-digit number=52 (in base 7)=37. (in base 10).
When the number is three digits, subtract (a+c+7b) 48a=255c+9b / divide by three 16a=85c+3b. c cannot be 0 because this indicates that the expression cba is not defined.
If c=1, 16a=85+3b
There are no answers to that problem. If c>1, this suggests that 16a=85c+3b>=170, implying that a>6. This, however, is not possible! As a result, there is no solution.
As a result, the sum of all positive integers is 58.
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What is the slope of this non-vertical line?
Answer:
THE SLOPE IS 16
Answer: The slope is 16/1 which is just 16.
Step-by-step explanation:
giving 60 point if u do
The percentage error of Bob’s measurement to the nearest tenth of a percent is 3.87%
The percentage error is The difference between the estimated value and the actual value in relation to the actual value is given as a percentage. Analyst use this formula to determine how big is the error in a relation to true value.
Here, given that
The experimental volume of liquid is 18.8 ml, and the actual volume of liquid is 18.1 ml
i.e. exprimental volume=18.8 mL
and, actual volume=18.1 mL
Now, we will calculate the percentage error
So,
percentage error=((Exprimental value-Actual value)/(Actual value))∙100
percntage error=((18.8-18.1))/18.1∙100
percentage error=0.7/18.1∙100
percentage error=0.0387∙100
percentage error=3.87%
Thus,
We got percentage error of 3.87% in measurement
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Work out the values of A and B in these equivalent ratios.
A: 6:7 = 8:24: B
A =
B =
The value of A is 32.
The value of B is 28.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
A : 6 : 7 = 8 : 24 : B
This means,
6 units = 2432
1 units = 24/6
1 units = 4
Now,
The value of A.
A = 8 units
1 unit = 4
8 units = 8 x 4 = 32
The value of B.
B = 7 units
1 unit = 4
7 units = 7 x 4 = 28
Thus,
A = 32
B = 28
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Use mental math to solve the equation. x - 15 = 19
Answer: x = 34
Step-by-step explanation:
Add 19 and 15 in your head. 9 + 5 = 14. Now, add 10 + 10 + 14. This gives 34.
What are 3 congruent segments?.
The same circle's radii. parallelogram, rectangle, square, and rhombus opposite sides, sides of a triangle with equal sides.
What is congruent segments?
Segments of the same length are said to be congruent. Collinear points are those that share a line. A mathematical assertion that can be validated is known as a theorem. A point that divides a segment into two congruent segments is the segment's midpoint.
Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments.
When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments.
The congruent segments continue to be congruent even after being turned, flipped, or rotated. Congruence between any two congruent line segments is represented by the symbol.
the same circle's radii.parallelogram, rectangle, square, and rhombus opposite sides.sides of a triangle with equal sides.Look at the illustration below that shows congruent line segments:
Here, the double vertical bars on each line segment, PQ and XY, represent their equality, resulting in the line segment PQ ≅ XY.
We shall examine the congruent line segments' qualities in order to learn more about them. Congruent lines in geometry possess the following characteristics:
(i) Reflexive
(ii) Symmetric
(iii) Transitive
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What is the graph of y-2=-3(x-1)?
The graph of y-2=-3(x-1) is shown in the figure below;
How to plot a graph of given function?Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, needs some skill and some mathematical concepts to understand.
Given;
y-2= -3(x-1)
When x=0
y-2= -3(0-1)
y-2=0
y=0
When y=0
0-2= -3(x-1)
x=1.667
Hence, the graph of these coordinates is as follows;
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I. The cost of hiring a mover is based on the distance traveled and the total weight of the objects moved.
II. The amount of time needed to paint a house decreases as the number of painters increases.
III. The income of a worker who gets paid an hourly wage depends on the number of hours worked.
The proportional relationships for each case are described as follows:
I. Direct proportional relationship.
II. Inverse proportional relationship.
III. Direct proportional relationship.
How to classify proportional relationships?There are two ways to classify proportional relationships, and these two ways are listed as follows:
Direct proportional relationship.Inverse proportional relationship.These two classifications are described as follows:
Direct proportional relationship: as the input increases, the output also increases.Inverse proportional relationship: as the input increases, the output decreases.Then the only inverse proportional relationship is given by item ii, where it is said that the time decreases and the number of workers increases.
Missing InformationThree relationships are described below: I. The cost of hiring a mover is based on the distance traveled and the total weight of the objects moved. II. The amount of time needed to paint a house decreases as the number of painters increases. III. The income of a worker who gets paid an hourly wage depends on the number of hours worked. What type of variation describes each relationship?
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Harold throw a baeball up at 24. 3m/. He take a photo at 3. 1 econd into the flight. What i the velocity of the baeball at 3. 1 econd into the flight?
The velocity of the baseball at 3.1 seconds into the flight is 7.84m/s.
What is velocity?
Velocity simply implies the speed and the direction at which an object is moving.
Since Harold throws a baseball up at 24.3m/s and he takes a photo at 3.1 seconds into the flight.
The velocity of the baseball will be:
Velocity = Distance / time
Velocity = 24.3 / 3.1
Velocity = 7.84 m/s
The velocity is 7.84 m/s.
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The baseball's speed is 7.84 m/s at 3.1 seconds into its flight.
What is velocity?
Simple definition: Velocity denotes the movement of an object's speed and direction.
Since Harold launches a baseball at a speed of 24.3 meters per second and snaps a picture 3.1 seconds into the flight.
The velocity of the baseball will be:
Velocity = Distance / time
Velocity = 24.3 / 3.1
Velocity = 7.84 m/s
The velocity is 7.84 m/s.
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a spinner has eight equally sized regions labeled from 1 to 8. we spin the spinner twice. what is the probability that the first spin is no more than 6 and the second spin is no less than 7? write your answer as a simplified fraction.
Probability of both = 6/8 * 2/8 = 12/64 which reduces to 3/16.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
probability that first spin is grey = 6/8probability that second spin is blue = 2/8probability of both = 6/8 * 2/8 = 12/64 which reduces to 3/16learn more about probability click here:
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-2 > v - 1.4 Solve the inequality for v.
Simplify your answer as much as possible.
Solution to the inequality is V < 0.6
Inequality,In mathematics, inequality is the relationship between two values that are not equal
Add 1.4 to both sides of equation -2 > v - 1.4
-2+1.4 > v -1.4 +1.4
- 0.6 > v
Move the variable to the left and flip the inequality because of the negative
V < 0.6
Therefore, the solution for the inequality is V < 0.6
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To pay for a home improvement project that totals $16,000, Genesis is choosing between taking out a simple interest bank loan at 8% for 3 years or paying with a credit card that compounds monthly at an annual rate of 15% for 7 years. Which plan would give Genesis the lowest monthly payment?
A. The monthly credit card payment would be $511.11, which is lower than the monthly payment on the bank loan.
B. The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.
C. The monthly payment on a bank loan would be $551.11, which is lower than the monthly credit card payment.
D. The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
What is simple interest?The simple interest earned can be calculated by using this formula
A = P(1 + rt)
A is the future value.
P is the principal value.
r is the interest rate.
t is the time.
Now Substituting the values into the formula, we have,
A = 16,000[1 + (0.08 × 3)]
A = 16,000[1 + 0.24]
A = 16,000× 1.24
Future value, A = $19,840.
Following that, we will compute the monthly payment over a 36-month period as follows:
Monthly payment = Future value/Time
Monthly payment = 19,840/36
Monthly payment = $551.11
Similarly, we will compute the credit card's compound interest:
A = 16000[1 + (0.15/12)]⁽¹² ˣ ⁷⁾
A = 16000[1 + 0.025]⁸⁴
A = 16000× 1.025⁸⁴
A = 9000 × 3.49258954
Future value, A = $45425.80
Following that, we will compute the monthly payment over an 84-month period as follows;
Monthly payment = Future value/Time
Monthly payment = 45425.80/84
Monthly payment = $540.78.
Thus, the monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
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find the LCM (Least Common Factor) of each set of numbers. Use ladder diagram.
1. 28,40
2. 180,345
Answer:
1. 280
2. 4140
Step-by-step explanation:
The winner of an egg-eating contest ate 132 eggs in 11 minutes
What is the unit rate?
Answer:
12 eggs
Step-by-step explanation:
divide 132 by 11. hope this helped :)
Answer:
12 eggs per minute
Step-by-step explanation:
To find the unit rate, take the number of eggs and divide by the number of minutes
132eggs / 11 minutes
12 eggs per minute
I need help with 9-11. I really don’t understand this, please help me!!!
Answer: 9-11 = -2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
11 - 9 = 2
2 -----> -2
OR
9 - 11 = -2
pls send the correct answer
Answer:
Angles I and E are congruent
Step-by-step explanation:
Remember, you can split the kite in half and see it for yourself
Janice currently has 26 marbles and is collecting 3 per week. Oliver currently has 10 marbles and is collecting 5 per week. how many weeks will it take so that janice and oliver have the same amount of marbles?
For, Janice and Oliver have the same number of marbles, it will take 8 weeks.
Define algebraic equation.A term in an algebraic expression that is referred to as a linear expression is either a constant or a variable raised to the first power. Or, to put it another way, none of the exponents can be higher than 1.
Positive or negative numbers can be used as coefficients in linear equations. It matters what the exponent is. When one variable in the equation is raised to a power greater than 1, the entire equation becomes nonlinear.
Given,
Oliver presently has 10 marbles and is collecting 5 per week, whereas Janice currently has 26 marbles and is adding 3 each week.
Let x be the number of weeks.
This implies,
Algebraic equation,
26 + 3x = 10 + 5x
26 - 10 = 5x - 3x
16 = 2x
x = 16/2
x = 8
So that Janice and Oliver have the same number of marbles, it will take 8 weeks.
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how to solve long devision
Answer:
Step-by-step explanation:
By putting suitable signs + , − , × , ÷ , ( , ) in-between the digits 4 4 4 many numbers can be generated, for example, 4 − (4 ÷ 4) = 3. Which of the following numbers can be generated this way?
These are the numbers that can be generated which are 3, 5, 4, 1/4, -11, 20, -8, 64, 1/2, etc.
What is arithematic operartions?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
signs + , − , × , ÷ , ( , )
the digits 4 4 4
By putting suitable signs + , − , × , ÷ , ( , ) in-between the digits 4 4 4
4 − (4 ÷ 4) = 3.
4 + (4 ÷ 4) = 5.
4 × (4 ÷ 4) = 4.
4 ÷ (4 × 4) = 1/4.
4 - (4 × 4) = -11.
4 + (4 × 4) = 20.
4 - (4 + 4) = -8.
4 × (4 + 4) = 64.
4 ÷ (4 + 4) = 1/2.
Hence, these are the numbers that can be generated which are 3, 5, 4, 1/4, -11, 20, -8, 64, 1/2, etc.
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Victoria deposited $5000 Into a savings account that earns an annual simple interest rate of 0.3%. To the nearest tenth of a year, how long will it take for the account to reach $5500?
? year(s)
The account will reach $5500 after approximately 33.3 years have passed.
The simple interest formula is I = P x r x t, where I is the interest earned, P is the principal (the initial amount of money deposited), r is the annual interest rate, and t is the time in years.
You can rearrange this formula to solve for t: t = I / (P x r).
In this case, I = $500 (the difference between the final balance and the initial balance), P = $5000 (the initial amount deposited), and r = 0.3% (the annual interest rate).
Plugging these values into the formula, we get:
t = $500 / ($5000 x 0.3%)
t = $500 / ($5000 x 0.003)
t = $500 / $15
t = 33.333...
To the nearest tenth of a year, it will take approximately 33.3 years for the account to reach $5500.
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Franklin has a grade of 60 and wants to raise it to 80. What percent increase is this?
Answer:
33.4%
Step-by-step explanation:
60+33.4%=80
60x1.334=80
If p is false and q is true, find the truth value of:
¬(p∧q)
What is parallel line class 4?.
Coplanar, straight lines that just don't cross at any point are considered parallel lines in geometry. Parallel planes were also planes that never cross each other in the same three-dimensional space.
What are lines that are parallel and perpendicular?If two lines are in the same plane and never cross, they are said to be parallel. They are equidistant lines, which means that their separation is constant. The symbol || is used to depict parallel lines. For instance, the symbol AB || CD denotes the parallelism of the line segments AB and CD. On the other hand, two straight lines are said to be perpendicular if they cross at a 90° angle.
A description line is what?A line has length but no breadth, making it a one-dimensional object. A line is made up of several points that continue indefinitely in opposing directions. His two points in a 2D plane serve as the basis for this. Collinear points are two points that are located on the same line.
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