The frequency (F) and length (L) of a wave are related by the following formula: F x L = 3.0 x 10^10. Consider that the wavelength of violet light is 1.3 x 10^−8. What is the frequency of violet light?
A) 1.7 x 102
B) 2.3 x 102
C) 2.3 x 1018
D) 4.3 x 107
Answer:
B: 2.3 x 10^18
expination:
Substitute values into the formula.
F x L = 3.0 x 10*10
F x 1.3 x 10^−8 = 3.0 x 10^10
F = 3.0 x 10^10 1.3 x 10^−8 F = 2.3 x 10^18
These are the first sentences in the short story, "The Gift of the Magi," by O. Henry: "One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies." Model the scenario with an equation. Let q be the number of quarters, d be the number of dimes, and n be the number of nickels.
The model which represents the total amount in terms of pennies, quarters, dimes and nickel is 0.25q + 0.10d + 0.05n + 0.60
Total amount = $1 and 87 cents = $1.87Amount in pennies = 60 cents = $0.60Number of Quarters, Nickel and Dimes = q, n and d respectively 1 quarter = $0.25 ; 1 dime = $0.10 ; 1 nickel = $0.05To create a mathematical model of the total amount :
Total worth of Quarters = 0.25qTotal worth of dimes = 0.10dTotal worth of nickel = 0.05nTotal worth of pennies = $0.60Total amount = 0.25q + 0.10d + 0.05n + 0.600.25q + 0.10d + 0.05n + 0.60 = 1.87Therefore, the model which represents the total amount is 0.25q + 0.10d + 0.05n + 0.60
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Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will megan and connor have saved the same amount
Connor and Megan are separated by 50-18,5=31,5 dollars. 7,75-5,5=2,25 $ is the difference between the two saves. To save the same amount, it will take them 14 weeks.
What exactly do you mean by an equation system?Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system).
The number of equations must match the number of unknowns for a system to have a singular solution.
What function does an equation system serve?When there are multiple unknowns and there is sufficient data to set up equations in those unknowns, systems of equations are utilized to solve applications.
Generally speaking, if there are n unknowns, we require n equations set up in those unknowns.
How long will it take Megan and Connor to save the same amount of money?The number of weeks, x,
To help Megan, we have:
50+5.5x
We have these for Connor:
18.5+7.75x
For both to possess an equal sum:
50+5.5x=18.5+7.75x
How to find x?
2.25x=31.5
X=31.52.25=14.
Hence we have to save the same amount, it will take them 14 weeks.
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Suppose that you only have liability and comprehensive car insurance and you allow your roommate (who doesn't have car insurance) to drive your car to run an errand. What will likely happen if there is a single-car accident causing moderate damage to your car while your roommate is driving?
If Alicia can read 3 pages in 1 minute, how long would it take her to read 33 pages?
divide total pages by pages per minute
33 / 3 = 11 minutes
Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 204204 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions of the box be?
Which statements are true about the linear inequality y > x – 2? Check all that apply.
The slope of the line is –2.
The graph of y > x – 2 is a dashed line.
The area below the line is shaded.
One solution to the inequality is (0, 0).
The graph intercepts the y-axis at (0, –2).
The true statements about the linear inequality y > x - 2 are that the slope of the line is 1, the graph is a dashed line, the area above the line is shaded, and the graph intercepts the y-axis at (0, -2).
When analyzing the linear inequality y > x - 2, we can identify several characteristics that relate to its graph and the solutions it represents:
The slope of the line is 1, not -2. This is because the equation is in the slope-intercept form y = mx + b, where m is the slope and here m = 1.The graph of y > x - 2 is indeed a dashed line, which indicates that the line itself is not included in the set of solutions for the inequality.The area above the line is shaded because the inequality is y > x - 2, which means all the points where y is greater (above) than x-2.One solution to the inequality is not (0, 0) because when x=0 and y=0, the inequality does not hold true (0 is not greater than -2).The graph intercepts the y-axis at (0, -2), which is the point where the line crosses the y-axis. This corresponds to the b term in the equation y = mx + b.Which of the following proportions is false?
10/25=40/100
18/48=20/50
25/45=75/135
24/30=20/25
What is this equation in slope-intercept form? -3x-2y=30
Find the discount price for a cell phone that is on sale for 15% off if the original price is $75? $60.00 $63.75 $64.25 $86.25
a plumber needs to replace 20 feet of copper piping. When he gets to the supply store, the lengths are given in meters. How many meters of piping does he need to purchase
what is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line?
y= -3.5x+57.5
y= 3.5x+57.5
y= -3.5+32.5
y= -3x+57.5
Answer: The correct option is
(A) [tex]y=-3.5x+57.5.[/tex]
Step-by-step explanation: We are given to find the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line.
From the table and the scatter plot sown in the figure, we note that
the two points that are closest to the line are (5, 40) and (15, 5).
We know that
the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the given line will be
[tex]m=\dfrac{5-40}{15-5}=-\dfrac{35}{10}=-3.5.[/tex]
Since the point (5, 40) is very close to the line, so its equation will be
[tex]y-40=m(x-5)\\\\\Rightarrow y-40=-3.5(x-5)\\\\\Rightarrow y=-3.5x+17.5+40\\\\\Rightarrow y=-3.5x+57.5.[/tex]
Thus, the required equation for the linear model is [tex]y=-3.5x+57.5.[/tex]
Option (A) is CORRECT.
porfavor me pueden decir Cuanto es 2x2
Si es 2x^2, ya esta en forma simplificada, y no hay mas que le puedes hacer.
Si es 2 por 2, la respuesta es 4.
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply.
Answer:a and e
Step-by-step explanation:
Got it right
what statement describes the function f(x)=|x^4-x^3|
did u ever get the answer for this
The given function f(x) = |[tex]x^{4}[/tex] - x³| is Option A. neither even nor odd because substituting -x changes the form of the function inside the absolute value. Thus, the function does not meet the criteria for either even or odd functions.
To determine if the function f(x) = |[tex]x^{4}[/tex] - x³| is even, odd, or neither, we need to check how it behaves under the transformation x -> -x.
An even function satisfies the property f(-x) = f(x) for all x, while an odd function satisfies f(-x) = -f(x) for all x.
First, let's consider the inside of the absolute value:
If we replace x with -x, we get: f(-x) = |[tex]-x^{4}[/tex] - (-x)³| = |[tex]x^{4}[/tex] + x³|.
We see that the expression has changed, since |[tex]x^{4}[/tex] - x³| is different from |[tex]x^{4}[/tex] + x³| . Therefore, f(x) does not exhibit the properties of being either even or odd.
This means the correct answer is:
Option A. The function is neither even nor odd.
Complete question:
Which statement describes the function f(x) = the absolute value of x^4 - x^3?
A. The function is neither even nor odd.
B. The function is both even and odd.
C. The function is even.
D. The function is odd.
A ladder is leaning against a building. the distance from the bottom of the ladder to the building is 16 ft shorter than the length of the ladder. how high up side of the building is the top of the ladder if the distance is 8 ft less
What is the period, in seconds, of a simple pendulum of length 2 meters? Use the gravitational constant g = 9.8 m/s^2 and round your answer to two decimal places.
Answer:
The period, in seconds to two decimal places is, 2.84 sec
Step-by-step explanation:
Using formula:
[tex]T = 2 \pi \sqrt{\frac{l}{g}}[/tex] ......[1]
where
T represents the Time period in second
l represents the length of the pendulum/
As per the statement:
Use the gravitational constant g = 9.8 m/s^2 , length of the simple pendulum(l) = 2 meters and [tex]\pi = 3.14[/tex]
Substitute the given values we have;
[tex]T = 2\cdot 3.14 \cdot \sqrt{\frac{2}{9.8}}[/tex]
⇒[tex]T = 6.28 \cdot \sqrt{\frac{1}{4.9}}=6.28 \cdot \frac{1}{2.21359436212}= \frac{6.28}{2.21359436212} = 2.83701481512[/tex]
Therefore, the period, in seconds to two decimal places is, 2.84 sec
Answer:
2.84 seconds
Step-by-step explanation:
Write a linear equation given the point and slope or two points (-7,13);slope =2
The linear equation is y = 2x+ 27.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given:
points: (-7, 13) and slope =2
As, we know the equation of line
y= mx +b
as, the line passes through the point (-7, 13) and m= 2
13 = 2(-7) +b
13 + 14 = b
b= 27
Hence, the equation of line is y = 2x+ 27
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If the product of the slopes of two lines equals -1, then the lines ___________.
a. are the same
Write an equation in slope-point form, of the line through point j(4,1). with slope -4.
I don't get this someone help me
Karl is purchasing a $205,000 home with a 30-year mortgage at 5.5%. Because he is not making a down payment, PMI in the amount of $97.50/month is required for the first 2 years of the loan. Based on this information, what is the total cost of this loan?
Answer:
The total loan payment is:is $1,024,050
Step-by-step explanation:
To know the total cost of this loan we must sum the the purchasing the mortgage loan LM and the PMI:
L=LM+PMI
The 30-year mortgage loan of $205,000 at 5.5% interest rate can be calculated as:
LM=$205,000*(1+0.055)^30
LM=$205,000*4.984 = $1,021,710
Then for the PMI over 24 months:
PMI: $97.5* 24 = $2,340
Therefore the total loan payment is:
L= $1,021,710 + $2,340 = $1,024,050
One side of a triangle is x in., another side is 2x in., a third side is 2x in., and the perimeter is 36 in.
The expression that represents the area of this triangle is x2 + x + cm2.
1.) 4 2.) 22 3.) -12
Answer:
Step-by-step explanation:
Which of the following is the most appropriate unit to describe the rate at which a person reads?
A. Minutes per word, because the independent quantity is the minutes
B.Minutes per word, because the independent quantity is the words
C.Words per minute, because the independent quantity is the minutes
D.Words per minute, because the independent quantity is the words
A presidential candidate plans to begin her campaign by visiting the capitals in 44 of 5050 states. what is the probability that she selects the route of fourfour specific capitals? is it practical to list all of the different possible routes in order to select the one that is best?
The probability of the presidential candidate selecting a specific route of four capitals is approximately 0.00575. It is not practical to list all the different possible routes to select the best one.
Explanation:To find the probability that the presidential candidate selects a specific route of four capitals, we need to calculate the number of possible routes and divide it by the total number of routes. Since there are 44 capitals and we need to select 4, we can use the combination formula.
The number of possible routes is given by C(44,4) which is equal to 44!/(4!(44-4)!) = 44!/(4!40!) = (44*43*42*41)/(4*3*2*1) = 91,390.
The total number of routes is 50P44, which is equal to 50!/6! = (50*49*48*47...*7*6!)/(6!) = (50*49*48*47...*7) = 15,890,700.
Therefore, the probability of selecting the specific route of four capitals is 91,390/15,890,700 = 0.00575 (rounded to 5 decimal places). This means that there is a very low probability of selecting this specific route.
It is not practical to list all of the different possible routes in order to select the best one, as there are over 15 million routes. Instead, the candidate may use other criteria such as population density, political demographics, or strategic considerations to determine the best route.
Please help!
A circle has center O(−3, 1) and radius 10. Which of the following points is on the circle?
V(−3, −4)
X(5, −2)
Y(−6, 0)
Z(5, 7)
The equation K = mv2 represents the energy an object has based on its motion. The kinetic energy, K, is based on the mass of the object, m, and the velocity of the object, v. Lashandra is given K and v for 10 different objects. In order to make solving more efficient, she solves the equation for m : m = . After attempting to determine the mass of a few objects, Lashandra realizes there must be something wrong with her formula. What is Lashandra’s error? She should have multiplied by 2 instead of dividing by 2. She should have multiplied by instead of dividing by 2. She should have used the square root to move the squared term to the other side of the equation. She should have squared the K when moving the v2 to the other side of the equation.
Answer:
She should have multiplied by 2 instead of dividing by 2.
Step-by-step explanation:
Note: The given equation is incorrect and second equation is missing.
Consider the given equation is
[tex]k=\dfrac{1}{2}mv^2[/tex] ...(i)
The formula find by Lashandra is
[tex]m=\dfrac{k}{2v^2}[/tex]
We need to find the Lashandra’s error.
Multiply both sides by 2 in equation (i).
[tex]2k=mv^2[/tex]
Divide both sides by [tex]v^2[/tex].
[tex]\dfrac{2k}{v^2}=m[/tex]
It means, the formula find by Lashandra is incorrect. She should have multiplied by 2 instead of dividing by 2.
Answer:
a
Step-by-step explanation:
2021 edg
The length of a rectangle is 5 yd longer than its width. if the perimeter of the rectangle is 46 yd , find its area.
The area of the rectangle is 126 square yards.
Solving the area and perimeter of a rectangle.
The area of a rectangle is the multiplication of the length and the width. The perimeter of the rectangle is calculated by using the formula perimeter = 2(length × width).
Let the Length be (L) and the width be (w).
Length = w + 5Width = wPerimeter = 2 (length + width)
Perimeter = 2 ((w+5) +w)
Perimeter = 2w + 10 + 2w
Perimeter = 4w + 10
Since Perimeter = 46 yd, then:
46 = 4w + 10
4w = 36
w = 36/4
w = 9 yards
Length = 9 + 5 = 14 yards
The area of the rectangle is:
Area = length × width
Area = 14 yd × 9 yd
Area = 126 yd²
A rectangle is 4 cm longer than it is wide, and its area is 117 cm2 . find its dimensions.
The length and width of the rectangle are [tex]13[/tex] cm and [tex]9[/tex] cm respectively whose area is [tex]117 cm^2[/tex].
Let the width of the rectangle be [tex]x[/tex].
Then the length of the rectangle is [tex]x+4[/tex].
Area of a rectangle [tex]=[/tex] length [tex]\times[/tex] width
Area [tex]= 117 cm^2[/tex]
[tex](x+4) \times x = 117[/tex]
[tex]x^2+4x=117[/tex]
[tex]x^2+4x-117=0[/tex]
[tex]x^2+13x-9x-117=0[/tex]
[tex]x(x+13)-9(x+13)=0[/tex]
[tex](x+13)(x-9)=0[/tex]
[tex]x+13=0, x-9=0[/tex]
[tex]x=-13, x=9[/tex]
Since, length cannot be negative. So, [tex]x=-13[/tex] is not possible.
So, [tex]x=9[/tex].
And [tex]x+4=13[/tex]
So, length [tex]= 13[/tex] cm and width [tex]= 9[/tex] cm.
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