The experimental probability that the next student to respond likes Hamlet best is 1/6 or 0.1667 as a decimal.
Calculating Experimental Probability of a Shakespeare Play Survey in an English ClassIn this problem, we are given the results of a survey conducted in an English class to determine which Shakespeare play the students liked the best. The teacher recorded the number of students who liked each of the three plays: Hamlet, Twelfth Night, and A Midsummer Night's Dream.
To calculate the experimental probability, we first need to find the total number of students who have responded to the survey so far. From the information given, we know that 2 students liked Hamlet best, 8 students liked Twelfth Night best, and 2 students liked A Midsummer Night's Dream best. Therefore, the total number of students who have responded so far is: 2 + 8 + 2 = 12
Next, we need to determine how many of these 12 students liked Hamlet best. We know from the data given that 2 students liked Hamlet best, so the number of students who liked Hamlet best is: 2
Finally, we can calculate the experimental probability that the next student to respond likes Hamlet best. We do this by dividing the number of students who liked Hamlet best (2) by the total number of students who have responded so far (12): 2/12
Simplifying this fraction, we get: 1/6
Therefore, the experimental probability that the next student to respond likes Hamlet best is 1/6 or 0.1667 as a decimal. This means that if we were to randomly select a student from the class and ask them which Shakespeare play they liked the best, there is a 1 in 6 chance that they would choose Hamlet.
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Solve for m.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
8m + 95 < -87m+5
The values of m for the given inequality should be in the interval
(-∞, -18/19).
What is meant by inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols. Typically, we use the "not equal" sign to indicate that two values are not equal. However several inequalities are utilised to compare the numbers, whether it is less than or higher than.
Given the inequality,
8m + 95 < -87m +5
We are asked to solve the inequality.
this means we have to find the value of m.
8m + 95 < -87m +5
8m + 87m < 5 - 95
95m < -90
m < -90/95
m< -18/19
Therefore the values of m for the given inequality should be in the interval (-∞, -18/19).
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Please Answer Quick!!
Therefore , the solution of the given problem of graph comes out to be
option c is correct it shows an association of the distribution of different mode of transportation among the same age of group.
What is graph ?Academics use graphs to visually represent or chart happenings or quantities in a logical manner. The interaction between a number of objects is frequently represented by a graph point. A graph is a non-linear storage structure made up of nodes, also known as vertices, and edges. The vertices, sometimes referred to as nodes, should be joined together with glue. Vertex numbers in this graph are 1, 2, 3, or 5, while edge numbers are 1, 2, 1, 3, 2, 4, etc. (2.5). (3.5). (4.5). (4.5). (4.5).
Here,
Given : A graph having choices of adult , child , teen and senior mode of transportation ,
In different age the mode of transportation preferred by among the same ages .
Thus ,
it shows an association of the distribution of different mode of transportation among the same age of group.
So , option c is the correct answer.
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An ellipse has a vertex at (–5, 0), a co-vertex at (0, 4), and a center at the origin. Which is the equation of the ellipse in standard form?
The equation of the ellipse in standard form is 16x² + 25y² = 400.
What is the standard form of the equation of an ellipse?The standard form of the equation of an ellipse centered at the origin is:
x²/a² + y²/b² = 1
where a is the distance from the center to a vertex along the x-axis, and b is the distance from the center to a co-vertex along the y-axis.
In this case, we know that the center of the ellipse is at (0,0), a vertex is at (-5,0), and a co-vertex is at (0,4).
The distance from the center to a vertex along the x-axis is the absolute value of the x-coordinate of the vertex, which is 5. So, a = 5.
The distance from the center to a co-vertex along the y-axis is the absolute value of the y-coordinate of the co-vertex, which is also 4.
So, b = 4.
Substituting these values into the standard form equation, we get:
(x²/5²) + (y²/4²) = 1
Simplifying and multiplying by 5² and 4², we get the standard form equation of the ellipse:
16x² + 25y² = 400
Therefore, the equation of the ellipse in standard form is 16x² + 25y² = 400.
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The following sample observations were randomly selected. (Round intermediate calculations and final answers to 2 decimal places.) x: 4 5 6 6 9 y: 3 6 5 7 7 pictureClick here for the Excel Data File 1. The regression equation is y : ______ + _____ x 2. When x is 8 this gives y: _____
The regression equation is y = 1.56 + 0.69⋅x².
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
x: 4 5 6 6 9
y: 3 6 5 7 7
Σx=28, ΣΥ=27, Σxy = 163, Σx' = 174
a = ΣΥ ΣΑΣΑ Σ ΑΥ = 27-174-28-163 = 1.558
b= 5.163 28 27 /5-174-(28)2 = 0.686
y = 1.558 + 0.686x²
Hence, The regression equation is y = 1.56 + 0.69⋅x².
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Simply expression
Please show steps
The simplified expression for this problem is given as follows:
-3(x + y) = -3x - 3y.
What is the distributive property?With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.
For this problem, the outer term -3 multiplies both of the inner terms, x and y, hence:
-3x.-3y.Hence the simplified expression is defined as follows:
-3(x + y) = -3x - 3y.
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Ann had a total of 285 red and blue beads. She used 45 red beads and 40% of the blue bead. After that,the ratio of the number of red beads to blue beads Ann had was 1:3.
[a] what fraction of blue beads did Ann use
[b] How many beads did Ann have in the end
(a) Ann used 4/10 blue beads i.e. 80.
(b) Ann had 160 beads in the end.
The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
According to mathematicians, any real number may be expressed using the four basic operations, also referred to as "arithmetic operations." The four mathematical operations that produce quotient, product, sum, and difference, respectively, are divide, multiply, add, and subtract.
(a) We are given that Ann had a total of 285 red and blue beads, and she used 45 red beads and 40% of the blue bead.
Let the red beads be x and blue beads be y
So, we get
x + y = 285
x = 285 - y
After using the beads, we get another equation as
⇒(x - 45) / (y - 0.4y) = 1/3
⇒(285 - y - 45) / (y - 0.4y) = 1/3
⇒(240 - y) / (0.6y) = 1/3
⇒720 - 3y = 0.6y
⇒720 = 3.6y
⇒y = 200
So, x = 85
Blue beads used = 40% of 200 = 80
(b) Since, Ann has used 80 blue beads and 45 red beads, so
Beads in the end = 285 - 45 - 80 = 160
Hence, Ann had 160 beads in the end.
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Can someone check my wrong answers for another excercise?
The answers to the probability problem have been stated below
How to solve the probabilityThe mean of the distribution would be 29
The standard deviation would be 8.7/√40 = 1.38
If the sample was larger, the mean would stay the same, the standard error would decrease.
3. The corresponding z score with
43.8 - 29 / 8.7
= 1.70
b. z = (43.8-29)/(8.7/√40) = 8.94
14.8 /1.38
= 10.7
c) the fisherman is more likely to catch one fish
d) z = (30.8-29)/(8.7/√40) = 1.26
= 1.8 / 1.38
= 1.304
e) He is more likely to catch 40 fishes.
4.a) Proportion in the middle = 0.95
Proportion on left and right side of normal curve = (1-0.95)/2
= 0.025
Z score at p = 0.025 using excel = NORM.S.INV(0.025) = 1.96
X1 = µ - z*σ = 29 - (1.96)*8.7
= 11.948
X2 = µ + z*σ = 29 + (1.96)*8.7
= 46.052
between 11.948 and 46.052
b)
Proportion in the middle = 0.95
Proportion on left and right side of normal curve = (1-0.95)/2 = 0.025
NORM.S.INV(0.025) = 1.96
x1 = 29 - (1.96)*8.7/√40
= 29 - 2.698
= 26.30
x2 = 29 + 2.698
= 31.698
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WILL VOTE 75 POINTSSS
Which of the following can sine squared theta over the quantity 1 plus cosine theta end quantity be simplified to?
cos θ
1 + cos θ
1 − cos θ
sin θ + tan θ
Answer:
The expression "sine squared theta over the quantity 1 plus cosine theta end quantity" can be simplified to "1 - cos θ".
Answer:
1 - cos θ
Step-by-step explanation:
Fill in the blanks:
1) if tan x=0, then tan(-x)= ___
2) If sin x= 0.3, then sin(-x)= ____
3) If cos x= 0.3, then cos(-x)= ____
4) If tan x= -2, the tan (pi+x)= ____
The values are :
tan(-x) = 0sin(-x) = -0.3cos(-x) =0.3tan(pie + x) = 2What is trigonometry ?
Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and the trigonometric functions such as sine, cosine, and tangent. It is based on the study of the geometric properties of triangles and is used extensively in fields such as physics, engineering, architecture, and astronomy.
In trigonometry, the relationships between the sides and angles of a triangle are expressed using the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios between the sides of a right triangle, where one angle is 90 degrees. Trigonometric functions can also be defined for any angle, not just those in a right triangle, using the unit circle or other methods.
Trigonometry has many practical applications, such as in navigation, surveying, and the design of structures such as bridges and buildings. It is also used extensively in science and engineering, particularly in fields such as physics, mechanics, and electromagnetics.
If tan x = 0, then tan(-x) = 0.
The tangent function is an odd function, which means that tan(-x) = -tan(x). However, since tan x = 0, this means that -tan(x) = 0 as well. Therefore, tan(-x) = 0.
If sin x = 0.3, then sin(-x) = -0.3.
The sine function is an odd function, which means that sin(-x) = -sin(x). Since sin x = 0.3, this means that -sin(x) = -0.3. Therefore, sin(-x) = -0.3.
If cos x = 0.3, then cos(-x) = 0.3.
The cosine function is an even function, which means that cos(-x) = cos(x). Since cos x = 0.3, this means that cos(-x) = 0.3 as well.
If tan x = -2, then tan(pi+x) = tan(pi + atan(-2)) = tan(2.0344 + pi) = -2.
To find tan(pi + x), we need to use the identity tan(a + pi) = -tan(a). In this case, a = atan(-2), which is the inverse tangent of -2. Using a calculator or a table, we can find that a is approximately 2.0344 radians. Therefore, tan(pi + x) = -tan(2.0344) = -(-2) = 2.
Hence, values are
tan(-x) = 0sin(-x) = -0.3cos(-x) =0.3tan(pie + x) = 2To know more about trigonometry visit :
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classify the following as point , line , and or plane ________1 Corner of a Vaccinatopn room ________2 Face mask ________3 Long chain of children for pediatric vaccination
1. Point - Corner of a Vaccination room
2. Plane - Face mask
3. Line - The long chain of children for pediatric vaccination
What are points, lines, and planes:Point:
A point is represented as a "dot" on paper. There will be no length, width, or height existing for a point. It simply identifies a certain position. Zero dimensions apply to it.
Line:
The line is a one-dimensional shape in geometry. A line, thus, has length but neither width nor height. In any direction, a line never stops. Two end points of lines act as the fundamental determinants of a line.
Plane:
The coordinate plane, which is used to plot points in algebra, is an example of a plane. The number lines on the coordinate plane stretch eternally from left to right and from up to down, respectively. The coordinate plane cannot be seen entirely.
Here we have
Corner of a Vaccination room, Face mask, The long chain of children for pediatric vaccination
Where
The corner of a Vaccination room represents a point.
Face mask represents a plane
The long chain of children for pediatric vaccination represents a line.
Therefore,
1. Point - Corner of a Vaccination room
2. Plane - Face mask
3. Line - The long chain of children for pediatric vaccination
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g five cards are dealt from a standard deck of playing cards.what is the probability that the you dealt 5 cards from same suit.
Answer:
the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
Step-by-step explanation:
The total number of ways to choose 5 cards from a deck of 52 cards is given by the combination formula:
C(52, 5) = 52! / (5! (52 - 5)!) = 2,598,960
Now, we need to count the number of ways of choosing 5 cards from the same suit. There are 4 suits in a deck of cards (hearts, diamonds, clubs, and spades), so we need to count the number of ways to choose 5 cards from each of these suits and add them up.
For each suit, the number of ways of choosing 5 cards from that suit is given by the combination formula:
C(13, 5) = 13! / (5! (13 - 5)!) = 1,287
So the total number of ways of choosing 5 cards from the same suit is:
4 * 1,287 = 5,148
Therefore, the probability of getting 5 cards from the same suit is:
5,148 / 2,598,960 ≈ 0.00198
So the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
Use equivalent ratios to find the unknown vaule step by step 7/11= 28/44
Answer:
7:11
28:44
Step-by-step explanation:
Multiply both sides by 4.
An open cardboard box is 20 cm long, 12 cm
wide and 8 cm deep (Fig. 14.9). Calculate
the total area of cardboard in the box.
The Total Surface area of cardboard in the box is 992 cm².
What is Total Surface Area?The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.
Given:
length= 20 cm
width = 12 cm
height= 8 cm
So, the TSA of Cuboid
= 2(lw + wh + lh)
=2( 20 x 12 + 12 x 8 + 8 x 20)
=2( 240 + 96 + 160)
= 2(496)
= 992 cm²
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Return on Total Assets
A company reports the following income statement and
balance sheet information for the current year:
Net income
Interest expense
Average total assets
$386,760
68,250
5,230,000
Determine the return on total assets. If required, round
the answer to one decimal place.
6, Incorrect
The return on total assets (ROTA) can be calculated using the formula:
ROTA = Net Income / Average Total Assets
Using the given information, we have:
ROTA = $386,760 / $5,230,000 = 0.0739 or 7.39%
Therefore, the return on total assets for the company is 7.39%. Note that this answer is rounded to two decimal places.
What is the future value of $2,500 deposited for one year earning a 14 percent interest rate annually
Answer: $2,850
Step-by-step explanation:
Hope this helped you. Brainliest if possible! :D
I also answered first! (Please don't copy my answer for anyone that answer this question!) :D
Describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak linear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
The correct statement regarding the association of the time the player spent practicing and the number of points he scored in the game is given as follows:
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
How to describe the association?The more the player practices, the better he/she performs, that is, the more points are scored, hence the number of points increases as the number of hours practiced increase.
However, there reaches a certain threshold where the player is as good as possible, hence the points tend to stabilize, meaning that there is a nonlinear association between the variables.
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Can you help me find the point of intersection for the question in the picture attached?
Answer:
The ordered pair that is a solution is (2, 10)
Step-by-step explanation:
2x + 6 = 4x + 2 Subtract 2x from both sides
2x - 2x + 6 = 4x - 2x + 2
6 = 2x + 2 Subtract 2 from both sides
6 - 2 = 2x + 2 -2
4 = 2x Divide both sides by 2
2 = x
Substitute 2 for x in either of the two original equations.
y = 2x + 6
y = 2(2) + 6
y = 4 + 6
y = 10
The ordered pair that is a solution is (2, 10)
A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree. Approximately how high up the tree does the top of the pole reach? responses 1. 9 feet 1. 9 feet 7. 0 feet 7. 0 feet 12. 7 feet 12. 7 feet 17. 0 feet.
If A 15-foot pole is leaning against a tree and bottom of the pole is 8 feet away from the bottom of the tree. then the top of the pole reaches option (C) 12.7 feet
We can use the Pythagorean theorem to solve this problem. Let's call the height we're trying to find "x". Then, we have a right triangle where the pole is the hypotenuse, the distance from the bottom of the pole to the tree is one leg, and the height we're trying to find is the other leg. Using the Pythagorean theorem, we have:
15^2 = 8^2 + x^2
225 = 64 + x^2
Group the like terms
161 = x^2
x ≈ 12.7 feet
Therefore, the correct option is (c) 12.7 feet
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Antonio has 3 different colored shirts, he wants to share them with his 2 brothers. How many times can all 3 boys trade shirts without wearing them twice?
Answer:
6 times
HOPE THE ANSWER HELPS
(a) Select each constant that is definitely positive.
(b) Select each constant that is definitely between 0 and 1.
(c) Select each constant that could be between 0 and 1 or is definitely between 0 and 1.
(d) Which two of these constants are definitely equal?
(e) Which one of the following pairs of constants could be equal?
The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.
What is an exponent?Let 'a' is the leading coefficient and 'b' is the factor.
The exponent is given as,
y = a(b)ˣ
Some points regarding the exponent function:
If the value of 'b' is greater than one, then the graph will be increasing in nature.If the value of 'b' is less than one, then the graph will be decreasing in nature.If the value of 'b' is equal to one, then the graph will be constant in nature.If 'a' is positive, the graph will be above the line.If 'a' is negative, the graph will be below the line.If 'a' is the same for two exponent equations, then the graph has the same y-intercept.The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.
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Can someone please help.
The sinusoidal function is y = 2sin(2x) - 1
How to determine the sinusoidal functionThe general form of a sinusoidal function is given by:
y = A sin(Bx + C) + D
where:
A is the amplitudeB is the frequencyC is the phase shiftD is the vertical shiftWe know that the period is π and the amplitude is 2.
So, we have
A = 2
B = (2π)/(π) = 2
So, we have
y = 2sin(2x + C) + D
The point (-11π/4, 1) implies that, the function is shifted down by 1 unit
So, we have
y = 2sin(2x) - 1
Hence, the function is y = 2sin(2x) - 1
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Toby is buying milk. He needs 3 liters. A half-liter of costs $2.43. A 250 -milliliter container of costs $1.42. What should Toby buy so he gets 3 liters at the lowest price?
Answer:
6 half-liter
Step-by-step explanation:
To get 3 liters of milk, Toby has two options:
Option 1: Buy 6 half-liter containers
The cost of one half-liter container is $2.43, so the cost of six such containers is 6 x $2.43 = $14.58.
Option 2: Buy 12 250-milliliter containers
The cost of one 250-milliliter container is $1.42, which is equivalent to $5.68 per liter (since 1 liter is equal to 4 250-milliliter containers). Therefore, the cost of 3 liters (which is equivalent to 12 250-milliliter containers) is 12 x $1.42 = $17.04.
Therefore, Toby should buy 6 half-liter containers as it is the cheaper option.
In one season, a basketball player missed 50% of her free throws. How many free throws did she attempt if she made 183 free throws?
Answer:
Step-by-step explanation:
50% of 366 is 183, therefore your answer is 366.
41 is what percent of 120
Answer: Approximately 34.17%.
Step-by-step explanation: Let's divide 41 by 120. Doing so, we get 0.3466666 looping forever. We can simplify that to .3417, and then turn that into a percentage giving us 34.17%
After a 27% decrease the value of a game card was now on sale for $34.00. What was the original price?
The original price of the game card was approximately $46.58.
What purpose does a game serve?When the game can be effectively described by a numerical "characteristic function," such as v(S), which expresses how much any coalition S of players may win with certainty, regardless of the behaviour of the other players, then we can most readily determine the value of the game.
Let x represent the game card's initial cost. So 1 - 0.27 = 0.73, the price would be 0.73x after a 27% drop.
We are aware that 34.00 = 0.73x. We can divide both sides by 0.73 to find x:
x = 34.00 ÷ 0.73
x ≈ 46.58
Thus, the game card's initial cost was only about $46.58.
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In AOPQ, p = 6.3 cm, m/O=149° and m/P=29°. Find the length of q, to the nearest
10th of a centimeter.
The length of q is approximately is 0.4 cm.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To solve for the length of q in triangle AOPQ, we can use the law of sines, which states:
a/sin A = b/sin B = c/sin C
where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.
In triangle AOPQ, we know that:
Side p = 6.3 cm (opposite angle P)
Angle O = 149° (opposite side q)
Angle P = 29° (opposite side p)
Let use angle sum property of triangles to find the measure of angle Q:
Angle Q = 180° - Angle O - Angle P
Angle Q = 180° - 149° - 29°
Angle Q = 2°
Now we can use the law of sines to solve for the length of q:
q/sin Q = p/sin P
q/sin(2°) = 6.3/sin(29°)
q = sin(2°) × (6.3/sin(29°))
q=0.034 × (6.3/0.484)
q = 0.442 cm
Therefore, the length of q is approximately is 0.4 cm.
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Raj encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear
25
c-1² ₂]
text code for each letter by the matrix C=
85
38 46
location of spaces after you decode the text.
representing the encoded text is
to get a matrix that represents the encoded text. The matrix
111 135 111 95
101 153
55 45 41 44 64
4
What is the secret phrase? Determine the
The solution is, the answer is: The color is blue (D).
What is matrix?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
here, we have,
Our matrix C is the encoder. Let X be our secret message and let B be our encoded message. Therefore the relationship between the 3 can be represented as:
CX = B
So we want to solve for X (our secret message). So using matrix algebra:
X = C^-1*B
where C^-1 is the inverse of C.
C^-1 = | 3 -2 |
|4 -3 |
So we take C^-1 and multiply it by matrix B to get X. Matrix B is already given to us. So just multiply those two. I used a calculator to get:
X = | 20 8 5 3 15 12 15 |
| 18 9 19 2 12 21 5 |
And since A = 1, B = 2, C = 3, etc....
We decode our message and it says:
X = | T H E C O L O |
| R I S B L U E |
So the answer is: The color is blue (D)
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Answer: D
Step-by-step explanation:
Jack and Glen share a 30-ounce box of cereal. By the end of the week, Jack has eaten
1
10
of the box, and Glen has eaten
2
5
of the box of cereal. How many ounces are left in the box?
Answer:
15 oz
Step-by-step explanation:
1/10 of 30 = 30/10 = 3 oz
2/5 of 30 = 30 * 2/5 = 60/5 = 12 oz
add those up to get 3 + 12 = 15 oz eaten
there are thus 30-15 = 15 oz left in the box
Approximate the area between the x-axis and the graph of f(x) = x² + 3 over the interval [0, 2]
by calculating the sum of the areas of 4 rectangles with equal widths along the interval. The
rectangles should be placed on the x-axis and the heights should be the function values at the right
endpoint of each subinterval, as shown below.
The approximate area between the x-axis and the graph of f(x) =x² +3
over the interval [0, 2] is 9.75.
What is interval in function?introducing intervals, bounded collections of numerical values that are highly helpful in explaining domain and range. To demonstrate where a value lies in relation to two endpoints, we can use interval notation.
To approximate the area between the x-axis and the graph of
f(x) = x² + 3 over the interval [0, 2].
The heights of the rectangles in the right rectangle method are determined by the function's value at the right endpoint of each subinterval. The right endpoints of each subinterval would be 0.5, 1, 1.5, and 2 if the range [0, 2] were divided into 4 equal subintervals, each of width 0.5.
The height of the first rectangle
f(0.5) = 0.5² + 3
f(0.5) = 3.25
and, the height of the second rectangle
f(1) = 1² + 3
f(1) = 4
and, the height of the third rectangle
f(1.5) = 1.5² + 3
f(1.5) = 5.25
and, the height of the fourth rectangle
f(2) = 2² + 3
f(2) = 7
So, sum of the areas of the rectangles
= (0.5) × (3.25+4+5.25+7)
= (0.5) × 19.5
= 9.75
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An electrician purchases some outdoor lighting for a customer at a wholesale price of $950.40. The customer would
have paid the retail price of $1320. What was the wholesale discount?
(Type a whole number or an exact decimal of the decimal does not terminate round to one decimal place)
Answer:
the wholesale discount is 28%.
Step-by-step explanation:
To find the wholesale discount, we need to calculate the difference between the retail price and the wholesale price as a percentage of the retail price. We can use the following formula:
Wholesale discount = ((Retail price - Wholesale price) / Retail price) x 100%
Substituting the given values into the formula, we get:
Wholesale discount = ((1320 - 950.40) / 1320) x 100%
Wholesale discount = (369.60 / 1320) x 100%
Wholesale discount = 0.28 x 100%
Therefore, the wholesale discount is 28%.
To write the answer as a whole number or an exact decimal, we can multiply 0.28 by 100 to get:
Wholesale discount = 28%
So the wholesale discount is 28%.