The polynomial function is f(x) = (x - 3)((x - 2)² + 9)
How to determine the polynomial from the zeros?From the question, we have the following parameters that can be used in our computation:
Zeros: x=3, 2 +-3i
The polynomial can be repesented as
f(x) = product of (x - zeros)
using the above as a guide, we have the following:
f(x) = (x - 3)(x - (2 - 3i))(x - (2 + 3i))
This can be expressed as
f(x) = (x - 3)((x - 2)² + 9)
hence, the polynomial is f(x) = (x - 3)((x - 2)² + 9)
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Samir i hopping for gift online. He found two coupon code, but he can only ue one of them per purchae. The firt coupon code would give him 5% off and free hipping. The econd coupon code would give him 20% off, but he would have to pay $14. 99 for hipping. Samir want to find p, the price at which the firt coupon code give him a better deal. Which inequality can he ue?
The price p which the first coupon code give him a better deal is less than $99.93. The inequality he can use is the first coupon code will give Samir a better deal.
Inequality for Better DealWe can find the value of "p" by solving the inequality.
Starting with the inequality:(1 - 0.05) * p + 0 < (1 - 0.20) * p + 14.99
This inequality compares the total cost (price minus discount plus shipping) of using the first coupon code on the left-hand side and the total cost of using the second coupon code on the right-hand side. If the left-hand side is less than the right-hand side, then the first coupon code gives a better deal.
Solving for p, Samir can find the minimum price at which the first coupon code is a better deal.
Expanding both sides:0.95 * p + 0 < 0.80 * p + 14.99
Simplifying both sides:0.95 * p < 0.80 * p + 14.99
Subtracting 0.80 * p from both sides:0.15 * p < 14.99
Dividing both sides by 0.15:
p < 99.93
So, if the price "p" is less than 99.93, the first coupon code will give Samir a better deal.
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List the members of the set {2 < x < 51}
Answer:
{3,4,5,.........,49,50}
Step-by-step explanation:
All these numbers are greater than 2, but less than 51.
true or false: a positive correlation always occurs when as one variable gets smaller, the other one also gets smaller.
False. A positive correlation occurs when as one variable increases, the other one also increases.
It does not specify the direction of the change. On the other hand, a negative correlation occurs when one variable decreases as the other one increases. In other words, the variables are inversely related. In a positive correlation, the variables move in the same direction, while in a negative correlation, they move in opposite directions. It's important to note that correlation does not imply causation.
A positive correlation is a statistical relationship between two variables, where an increase in one variable is associated with an increase in the other variable, and a decrease in one variable is associated with a decrease in the other.
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A father is twice as old as his son. If half that son's age, plus 84, equals twice the fathers age, how old is each person?
let the sons age be x
i srsly dont understand how to make formulas for this question
Answer:
The son is 56, and the father is 112.
Step-by-step explanation:
Formula:
1/2x+84=2x
Answer:
father=40
son=20
Step-by-step explanation:
We can start by using the information given to set up a system of equations.
First, we know that the father's age is twice the son's age, so we can write the equation:
father's age = 2 * son's age
Next, we know that half the son's age plus 84 equals twice the father's age, so we can write the equation:
(1/2) * son's age + 84 = 2 * father's age
Now we can substitute the first equation into the second equation to get:
(1/2) * son's age + 84 = 2 * (2 * son's age)
Solving for x
(1/2) * x + 84 = 4x
x=20
father = 2*20 = 40
son = 20
what is Y=4x^2-4x+3
In parabola
The vertex form of the parabola y = 4 · x² - 4 · x + 3 is the equation y - 2 = 4 · (x - 1 / 2)².
How to determine the equation of the parabola in vertex form
In this problem we find the case of the equation of a parabola in standard form, whose vertex form has to be found. These forms are described below:
Standard form
y = a · x² + b · x + c
Vertex form
y - k = C · (x - h)²
Where:
a, b, c - Real coefficientsC - Vertex formh, k - Coordinates of the vertex.This can be done by completing the square, an application by algebra properties. First, write the equation of a parabola in standard form:
y = 4 · x² - 4 · x + 3
Second, use algebra properties until vertex form is found:
y - 3 = 4 · (x² - x)
y - 3 + 4 · (1 / 4) = 4 · (x² - x + 1 / 4)
y - 2 = 4 · (x - 1 / 2)²
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If you invest $360.00 and your annual interest is $54, what is the interest rate
Answer:
The interest rate for this investment is 15%. This can be calculated by dividing the annual interest of $54 by the initial investment of $360, which gives a result of 0.15 or 15%.
The interest rate is 15%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount invested = $360
Interest amount = $54
Now,
The interest rate.
= 54/360 x 100
= 15%
Thus,
5% is the interest rate.
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question 3 (c) is f continuous at x=−3 ? using correct notation, justify your answer.
No, f is not continuous at x=-3. To show this, let's take the limit from both sides.
From the left side, the limit of f(x) as x approaches -3 is 5. From the right side, the limit of f(x) as x approaches -3 is 3. Since the two limits are not equal (5≠3), then f is not continuous at x=-3.No, f is not continuous at x=-3. This is because the limit of f(x) as x approaches -3 does not equal f(-3). The limit of f(x) can be calculated using the formula lim x->-3 f(x) = lim x->-3 (x^2 + 9). Calculating this limit, we get lim x->-3 f(x) = lim x->-3 (x^2 + 9) = 9. However, f(-3) = (-3)^2 + 9 = 0, which does not match the limit.
Mathematically, this can be shown using the following:
limx→−3 f(x) = 5 ≠ 3 = limx→−3+ f(x)
Since the two limits are not equal, then f is not continuous at x=-3.
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how did roediger & karpicke operationalize the dependent variable?
By assessing performance on memory and recognition tests, as well as the accuracy of answers to fill-in-the-blank and multiple choice questions, Roediger & Karpicke operationalized the dependent variable.
The dependent variable was operationalized by Roediger & Karpicke by evaluating how well subjects performed on memory and recognition tests. Participants responded to fill-in-the-blank and multiple choice questions to achieve this as well as the accuracy of answers to fill-in-the-blank and multiple choice questions, Roediger & Karpicke operationalized the dependent variable. The results of these tests were then utilized to gauge both the participants' recall recall and the accuracy of their responses. The replies were compared to the answer key and their correctness was scored in order to determine how accurate they were. This made it possible for the researchers to more precisely gauge how their independent factors affected the dependent variable.
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There is a triangle DEF in which segment EG intersects the side DF at point G. Angle DEG and angle FEG are congruent. The length of the side DE and side EF is labeled as c. The length of the segment DG is labeled as a and the length of the segment EG is labeled as b.
What is m∠DFE if m∠DEG = 18°?
The m∠DFE in triangle DEF is 72°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, There is a triangle DEF in which segment EG intersects the side DF at point G.
Angle DEG and angle FEG are congruent and the length of the side DE and side EF is labeled as c.
Now, If m∠DEG = 18° ⇒ m∠FEG = 18° and side EF and DE are equal so their opposite angles will also be equal.
Let, The two opposite equal angles be 'x'.
Therefore,
x + x + (18 + 18) = 180°.
2x + 36 = 180°.
2x = 144°.
x = 72°.
So, The measure of angle DFE is 72°.
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Assume that r is an odd function, s is an even function, and both r and s are defined on the entire real line R. Are the following functions even or odd? a. Is s(x) s(x) even or odd? -even -odd -neither b. Is s(s(x)) even or odd? -even -neither -odd
If "r" is an odd function, "s" is an even function , then the function "s(x) × s(x)" will be an (a) Even Function .
A function is considered as Even Function if it satisfies : f(x) = f(-x) for all x in its domain, and
A function is considered as Odd Function if it satisfies : f(x) = -f(-x) for all x in its domain.
The product of two even functions is even, because if f(x) and g(x) are both even, then
⇒ (f(x) × g(x)) = (f(-x)) × (g(-x)) = f(-x) × g(-x) = f(x)g(x),
So, f(x)g(x) is also even.
In this case, since the function "s" is an even function, So , "s(x) × s(x)" is also Even .
The given question is incomplete , the complete question is
Assume that "r" is an odd function, "s" is an even function, and both "r" and "s" are defined on the entire real line R. Are the following functions even or odd?
Is "s(x) × s(x)" even or odd ?
(a) even function
(b) odd function
(c) neither
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2. A 6-sided die with the numbers 1, 2, 3, 4, 5, and 6 is rolled 42 times. What is a
reasonable prediction for the number of times the die would land with a 6 faceup?
F 4
G 5
H6
3 7
Ralph jut received hi june flah card bill. He did not pay hi may bill in full, o hi june bill how a previou balance & a finance charge. The average daily balance i $470,& the monthly periodic rate i 1. 5% what hould ralph’ finance charge be?
If Ralph jut received hi june flah card bill. He did not pay hi may bill in full, o hi june bill how a previous balance & a finance charge. Ralph’ finance charge is: $0.588.
How to find the finance charge?First, calculate the monthly periodic rate (MPR) from the annual percentage rate (APR):
MPR = APR / 12
MPR = 1.5% / 12 = 0.125%
Next, calculate the finance charge by multiplying the average daily balance by the MPR:
Finance charge = Average daily balance * MPR
Finance charge = $470 * 0.125% = $0.588
Therefore Ralph's finance charge for June should be $0.588.
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In Exercises 11 to 16 , the draving shows trapesoid ABCD with →AB‖→DC: also, M and N are midpoints of ¯AD and ¯BC, respectively. Given: AB=7x+5, DC=4x−2, and MN=5x+3
In the trapezoid ABCD , when AB || DC and M, N are the midpoint of AD and BC then the value of AB , DC , and MN is equal to 26, 10, and 18 respectively.
In trapezoid ABCD,
AB || DC
AB = 7x + 5
DC = 4x -2
MN = 5x + 3
Using midpoint segment of two parallel lines in a trapezoid we have,
( AB + DC ) / 2 = MN
Substitute the value of AB, DC, and MN we get,
⇒ ( 7x + 5 + 4x -2 )/ 2 = 5x + 3
⇒11x + 3 = 10x + 6
⇒x = 3
⇒ AB = 7(3) + 5
= 26
DC = 4(3) -2
= 10
MN = 5(3) + 3
= 18
Therefore, the value of AB, DC, and MN in the trapezoid ABCD is equal to 26, 10, and 18 respectively.
The above question is incomplete, the complete question is :
The drawing shows trapezoid ABCD with AB||DC; also, M and N are midpoints of AD and BC, respectively. Given: AB=7x+5, DC=4x−2, and MN=5x+3 find the value of AB, DC, and MN for the calculated value of x.
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Evaluate the function when:
x= -1, 0, and four
Equation: y= -2x-4
Answer:
To evaluate the function when x = -1, 0, and 4, we need to substitute those values into the equation and solve for y.
1. When x = -1,
y = -2(-1) - 4
y = 2 - 4
y = -2
2. When x = 0,
y = -2(0) - 4
y = -4
3. When x = 4,
y = -2(4) - 4
y = -8 - 4
y = -12
So, the function has the values of -2, -4, and -12 when x = -1, 0, and 4 respectively.
I need to turn this in tomorrow please help. Use a ratio box to solve this problem. a. The 1/12 scale model of the rocket stood 48 inches high. What was the height of the actual rocket?
If the 1/12 scale model of the rocket stood 48 inches high. The height of the actual rocket is 576 inches.
What is a ratio box?A ratio box can be defined as a tool that can be used to set up and solve proportion problems.
In order to use a ratio box to solve this problem, we can set up the following proportion:
Scale model height / Actual rocket height = 1/12
48 inches / actual rocket height = 1/12
To solve for the actual rocket height, we can cross-multiply and divide:
48 inches××12 = actual rocket height
Actual rocket height = 576 inches
Therefore the height of the actual rocket is 576 inches.
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Paula's Pizza Parlor uses the following ingredients to make pizza.
Number of Pizzas Sauce (oz) Cheese (oz)
4 28 16
5
At this rate, how much sauce and cheese will Paula use to make 5 pizzas?
Paula will use 27 oz of sauce and 45 oz of cheese to make 5 pizzas.
Paula will use 35 oz of sauce and 20 oz of cheese to make 5 pizzas.
Paula will use 29 oz of sauce and 17 oz of cheese to make 5 pizzas.
Paula will use 56 oz of sauce and 32 oz of cheese to make 5 pizzas.
At this rate, the amount of sauce and cheese which Paula would use to make 5 pizzas is: B. Paula will use 35 oz of sauce and 20 oz of cheese to make 5 pizzas.
What is a proportion?In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying direct proportion to the given information, we have the following number of sauce:
4 pizzas = 28 sauce
5 pizzas = X sauce
Cross-multiplying, we have:
X sauce = 5/4 × 28
X sauce = 35 sauces.
By applying direct proportion to the given information, we have the following number of sauce:
4 pizzas = 16 cheese
5 pizzas = X cheese
Cross-multiplying, we have:
X cheese = 5/4 × 16
X cheese = 20 cheese.
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Please help it’s true or false respond!!
On solving the provided question, we can say that the answers of the quadrilateral are as follows 1.True; 2.False and 3.True
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here,
the answers of the quadrilateral are as follows
1.True
2.False
3.True
4.True
5.False
6.False
7.True
8.True
9.True
10.False
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3. The probability of having an automobile accident in a given year is approximately
0.105. Automobile insurance cost an average of $600 a year and if you are in an
accident, the average coverage paid is $2,500. What is your expected value of buying car
insurance? (Remember all probabilities add up to 1)
The expected value of buying car insurance is $794.5.
What do you mean by insurance?Insurance is a contract between an individual or entity and an insurance company, in which the insurance company agrees to provide financial protection or reimbursement against losses in exchange for payment of premium. It is a form of risk management, mainly used to hedge against the risk of a contingent or uncertain loss.
The expected value of buying car insurance is the sum of the product of the value and the probability of each outcome. To calculate the expected value, we multiply the probability of having an accident by the average coverage paid ($2,500), and add it to the product of the probability of not having an accident multiplied by the insurance cost ($600).
So, expected value = (0.105 * $2,500) + (0.895 * $600) = $267.5 + $527 = $794.5
Therefore, the expected value of buying car insurance is $794.5.
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Can someone please help real quick
The area of square of a given figure with a side 4w is 16w ^2
What is Area of square ?
Area of square could be defined as the square of its side.
Given ,
From the figure,
There is square with a side 4w and given all sides are equal
so , we have to find the area of square ,
area of square could be = side*side
given side =4w
By substituting the given value,
we get,
= 4w* 4w
= 16 w ^2
So, area of square = 16w^2
Therefore, The area of square of a given figure with a side 4w is 16w ^2
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Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis.
y = 11−x, y = 0, x = 3, x = 9
By using the shell method to find the volume of the solid generated when R is revolved about the y-axis is V = 2π∫3⁹(11−x0)x0(11−x0−dx)dx
The volume of a solid that is generated by rotating a region about a given axis is called the volume of revolution. One of the methods to find the volume of revolution is the shell method.
Let's consider the region R bounded by the curves y = 11−x, y = 0, x = 3, x = 9 and find its volume when it is revolved about the y-axis.
The first step is to sketch the region R in the xy-plane. The curves y = 11−x and y = 0 intersect at x = 11, y = 0. The region R is a trapezoid with height 11 and bases 3 and 9.
Next, we need to find the expression for the volume of a thin shell of thickness dx, whose axis is along the y-axis.
Let us consider a thin shell at x = x0. The height of the shell at x = x0 is given by 11−x0. The inner and outer radii of the shell are given by y = 11−x0 and y = 11−x0−dx respectively.
The volume of the shell is given by the formula:
=> V = 2π(y2−y1)x0 = 2π(11−x0)x0(11−x0−dx)
We can now integrate this expression over x0 to find the total volume of the solid.
The limits of integration are x0 = 3 and x0 = 9. The volume of the solid is given by:
V = 2π∫3⁹(11−x0)x0(11−x0−dx)dx
Solving this definite integral will give us the volume of the solid.
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A certain grocery store charges a fee of 3% of the total bill to have groceries delivered. What is the total price the store charges to deliver $140 worth of groceries?
The total price the store charges to deliver $140 worth of groceries will be $4.20.
How to calculate the percentage?It should be noted that the certain grocery store charges a fee of 3% of the total bill to have groceries delivered. A percent is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic.
Therefore, the total price the store charges to deliver $140 worth of groceries will be:
= Percentage charged × Cost
= 3% × $140
= 0.03 × $140
= $4.20
The amount charged is $4.20.
The entire cost for the retailer to deliver $140 worth of goods is $4.20.
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The graph below shows the solutions to which system of inequalities?
The inequalities that the represents the graph is; y < 1 and y ≥ x
How to identify system of inequalities from a graph?The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, when the line is horizontal line is parallel to the x - axis, the equation is y equal to the number that the line crosses.
Now, Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Thus, the horizontal line has the inequality; y = 1 But since the shading is below, then we have; y < 1
Now, the solid line shows that the symbol used is ≤ or ≥.
In this case, the x-values and the corresponding y-values are the same and as such we have; y = x
However, since the shading is above, then we have;
y ≥ x
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According to the rational root theorem, which of the following are possible
roots of the polynomial function below? Check all that apply.
x4-6x³-19x2 +84x+180
A. 19
B. 8
C. 10
D. 18
Answer:
C, D
Step-by-step explanation:
You want to know possible rational roots of x⁴-6x³-19x² +84x+180.
Rational root theoremThe rational root theorem tells you any rational roots will be fractions of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
ApplicationHere, the coefficient of x⁴, the leading coefficient, is 1. So any rational roots will be divisors of ±180. Those divisors are (plus or minus) ...
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The highlighted values are ones that are answer choices.
__
Additional comment
An estimate of the upper bound of the magnitude of the roots would be ...
[tex]2\max(\sqrt[4]{180},\sqrt[3]{84},\sqrt{19},6)=12[/tex]
The rational root theorem allows roots larger than this.
The roots of this polynomial are actually {-3, -2, 5, 6}.
Which expression is equivalent to 7/8+3/8x-3/4y-1/2?
A.3/8x-y-11
B.3/8x+1/2y+3/8
C.10/8x-2/4y-1/3
D.10/x+1/2y+3/8
The equivalent expression to 7/8+3/8x-3/4y-1/2 is given as follows:
3x/8 - 3y/4 + 3/8.
What are equivalent expressions?Equivalent expressions are expressions that have the same result when they are simplified.
The expression for this problem is defined as follows:
7/8+3/8x-3/4y-1/2.
The expression is simplified combining the like terms.
The like terms are given as follows:
3x/8 is the only term with x.-3y/4 is the only term with y.7/8 - 1/2 = 7/8 - 4/8 = 3/8.Combining(adding) the like terms, the simplified expression is given as follows:
3x/8 - 3y/4 + 3/8.
As none of the options are this one, I suppose that there was a typing mistake either in the expression or in the options.
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The triangular-shaped has a perimeter of 990 feet. walking path in the park shown . Write an equation to find the length of the side of the path represented by x.
Answer: So the length of one side of the triangular-shaped walking path is 330 feet.
Step-by-step explanation:
The perimeter of the triangular-shaped walking path is 990 feet, and the length of one side is represented by x. We can write an equation to find x using the formula for the perimeter of a triangle:
P = a + b + c
Where P is the perimeter, and a, b, and c are the lengths of the sides of the triangle. Since one of the sides is represented by x, the equation can be written as:
990 = x + x + x
Simplifying the equation, we can find the value of x:
990 = 3x
Dividing both sides by 3, we get:
330 = x
So the length of one side of the triangular-shaped walking path is 330 feet.
Oh brother! I am so bored! Mr. Blather, my science teacher, is lecturing on the weather patterns in the Arctic Circle. YAWN! YAWN! To keep myself awake, I started doodling. I started with one hexagon, and then kept drawing larger and larger hexagons (see diagram). I must be really bored because I found myself wondering how many dots I would have altogether after the fiftieth (50th) hexagon. What's the answer? Show your work and explain in complete sentences how you thought about the problem.
What I think about the problem is that there are no specific rules to tackle it, but with careful analysis I have deduced the answer for the total dots in the 50th hexagon to be 7701 dots.
How I got the figureTo find the total number of dots in the 50th hexagon, we can use the formula for finding the number of dots in the nth hexagon, where n is the number of the hexagon. The formula is:
Dots = 3n^2 + 3n + 1
Substituting n = 50, we get:
Dots = 3 * 50^2 + 3 * 50 + 1
= 7550 + 150 + 1
= 7701
So, there are 7701 dots in the 50th hexagon.
To think about the problem, we can observe that each additional hexagon added to the previous one will add 3 dots to the total count. This is because each new hexagon adds 3 sides to the previous hexagon, each side having one dot. And, each new hexagon will also add one additional dot to the center.
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Can someone pls help
Answer: 920?
20 charachters euhfiwudhfiuwefhiuhrieuhwdfiuhriurh
lithium has a work function of 2.90 ev. light having a wavelength of 1850
The energy of the light is less than the work function of Lithium (2.11 eV < 2.90 eV), the light will not have enough energy to remove electrons from the material.
To find this we have the work function of Lithium is 2.90 eV, which is a measure of the minimum energy required to remove an electron from the surface of the material. The energy of light is proportional to its frequency (E = hf) or its wavelength (E = hc/λ), where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light.
Given the wavelength of light as 1850 nm, we can calculate its energy as follows:
E = hc/λ = (6.63 x [tex]10^{-34}[/tex]Js) (3 x [tex]10^8[/tex] m/s) / (1850 x [tex]10^{-9[/tex]m)
= 3.38 x [tex]10^{-19[/tex] J
Since 1 eV = 1.6 x [tex]10^{-19[/tex] J, the energy of the light can be converted to eV as follows:
E (eV) = 3.38 x [tex]10^{-19[/tex] J / (1.6 x [tex]10^{-19[/tex] J/eV) = 2.11 eV
Since the energy of the light is less than the work function of Lithium (2.11 eV < 2.90 eV), the light will not have enough energy to remove electrons from the material.
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IF THE PROBABILITY OF GETTING DRAW 0.1 THEN WHAT IS THE PROBABILTY OF NOT DRAW
Answer: 0.9
Step-by-step explanation:
The probability is 1 - 0.1
= 0.9
Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60. What percent did she leave?
answer=
Answer:20.01%
Step-by-step explanation:Divide the tip left by the cost of the meal and multiply by 100 to get 20.01%
Answer: 20%
Step-by-step explanation:
We will find what percent 2.60 is of 12.99. First, we will divide. Then, we will multiply it by 100 to make a percent.
(2.6 / 12.99) * 100 = 20.0153 ≈ 20.02%
She left a 20.02% tip.