Answers
Answer:
AB ≈ 4.73
Step-by-step explanation:
using the sine ratio in the right triangle
sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{AB}[/tex] ( multiply both sides by AB )
AB × sin25° = 2 ( divide both sides by sin25° )
AB = [tex]\frac{2}{sin25}[/tex] ≈ 4.73 ( to the nearest hundredth )
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Answers
Sandesh sold 15kgs of apples for 2100rs and gained 12%. At what price per kg should he sell to gain 20% ?
Answers
As per the given percentage, Sandesh should aim to sell his apples at 250rs per kg in order to gain 20% profit.
Let C be the cost of the 15kgs of apples. Sandesh gained 12%, so his profit is 0.12C. We know that Sandesh sold the apples for 2100rs, so we can write an equation:
C + 0.12C = 2100
Simplifying this equation gives:
1.12C = 2100
Dividing both sides by 1.12 gives:
C = 1875
So Sandesh's cost for 15kgs of apples was 1875rs.
Now, we need to find the selling price per kg of apples that Sandesh should aim for in order to gain 20% profit. Let P be the selling price per kg of apples.
Since Sandesh wants to gain 20% profit, his selling price per kg of apples needs to be his cost plus 20% of his cost, or 1.2 times his cost.
So we can write another equation:
1.2C = 15P
Substituting the value of C we found earlier, we get:
1.2(1875) = 15P
Simplifying gives:
P = 250
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How is pi and apple pie related to each other?
Answers
Answer: Pie is the unofficial food of Pi Day; its symbol, π, is often carved into pie crusts.
Step-by-step explanation:
Answer:
You can divide and divide, but with pi, you never reach the end of the digits after a decimal point.
Step-by-step explanation:
This is why most people know pie as 3.14. It also means that the circumference is a bit more than 3 times the size of the diameter. It doesn't matter what circle you measure—the relationship will always be the same.
Smart mugs are the next generations of hot drinks dispensers tha om with built in technology to keep drinks at the perfect temperature for hours on end initial cost of a smart mug was aed 896, because of high demand in market the cost increased by 12% find the new price of the mug
Pls quick its due 30 mins! And also explain with steps pls! it will help alot, also will make brainliest!
Answers
Multiply the original number by the multiplier 1.12 to find the new price of the mug:
896 x 1.12 = AED 1003.52
D. On désire connaître la quantité de moulure dont on a besoin pour encadrer un tableau. Aire ou Périmètre
Answers
Answer:
Step-by-step explanation:
Perimeter
Pls mark me brainliest
1/sinx+cosx + 1/sinx-cosx = 2sinx/sin^4x-cos^4x
Answers
The simplified expression is 2cos²(x) + sinx - 1 = 0
The expression we will be simplifying is
=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.
To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:
(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)
Simplifying this expression using the distributive property, we get:
(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)
Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:
1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1
Similarly, for the second fraction, we can use the same identity to obtain:
1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1
Substituting these values back into the original expression, we get:
1 + 1 = 2sinx/(sin⁴x - cos⁴x)
Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:
sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ
Substituting this back into the expression, we get:
2 = 2sinx/(sin²ˣ - cos²ˣ)
Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):
2 = -2sinx/cos(2x)
Multiplying both sides by -cos(2x), we get:
-2cos(2x) = 2sinx
Dividing both sides by 2, we get:
-cos(2x) = sinx
Using the double-angle formula for cosine, we get:
-2cos²(x) + 1 = sinx
Simplifying this expression, we get:
2cos²(x) + sinx - 1 = 0
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The zero product property, says that if a product of two real numbers is 0, then one of the numbers must be 0.
a. Write this property formally using quantifiers and variables.
b. Write the contrapositive of your answer to part (a).
c. Write an informal version (without quantifier symbols or variables) for your answer to part (b).
Answers
The zero product property states that if the product of two real numbers is 0, then one of the numbers must be 0.
The contrapositive of the above answer is "If neither of the numbers is 0, then the product is not 0."
In other words, if two non-zero numbers are multiplied, then the result is non-zero.
a) We can use the zero-product property to factorize the expression as an example of[tex](x - 2) (x - 3) = 0[/tex], and obtain the two roots of the equation, [tex]x = 2[/tex]and [tex]x = 3[/tex]. Therefore, the zero-product property is a powerful tool that allows us to solve complex problems and equations involving algebraic expressions and real numbers.
b) A non-zero product can only be obtained by multiplying two non-zero numbers. So, if the product is zero, then at least one of the factors must be zero as well. This is the informal version of the contrapositive of the zero product property.
c)The zero product property is an essential concept in algebra that involves the understanding of real numbers and their product. It is widely used in algebra and calculus to solve equations and expressions that involve polynomial functions, quadratic equations, and exponential functions.
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Match the description with its mathematical expression. Residual from an estimated regression equation Choose the correct answer below. obo Oba o O y o bo +61 oy
Answers
We have that, the correct match of the description with its mathematical expression is provided with the mathematical expression "or".
What is the correct expression?Correct matching of the description to its mathematical expression is given as follows: The residual of an estimated regression equation is compared to the mathematical expression "or".
Explanation: A residual is the difference between the actual value of a variable and the predicted value of that variable. The residuals are denoted as "or". Therefore, the Residual of an estimated regression equation is compared to the mathematical expression "or".
Other options are incorrect as follows: Oba does not match any description given in the question. Therefore, it is a wrong option. Obo doesn't match any description given in the question. Therefore, it is a wrong option. Oy+ 61 does not match any description given in the question. Therefore, it is a wrong option.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answers
Answer:
The perimeter of the shape is 53km.
Answer : 53km
Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!
Can someone help me with this please??
Answers
Answer:
Angle CAB= 28°
Angle ABC= 45°
Angle DCA= 73°
Angle DCE=107°
Step-by-step explanation:
Find the magnitude of the projection
Answers
The magnitude of the projection of the two vectors is:
M = 8.73
How to find the magnitude of the projection?
If we have two vectors A and B, and we want the projection of A onto B, we need to solve:
projection = A·B/|B|
Here the vectors are <7, -6> and <5, -2>
First, the dot product between the two vectors gives:
7*5 - 6*-2 = 35 + 12 = 47
The dot product is 47.
And the module of the second vector is:
√(5² + (-2)²) = √(25 + 4) = √29
Then the magnitude of the projection is:
M = 47/√29 = 8.73
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[ 8 11 2 8 ] [ 1 -2 0 5]
[ 0 -7 2 -1] [ 0 7 1 5]
A = [ -3 -7 2 1], B = [ 0 4 4 0]
[ 1 1 2 4] [ 0 0 0 2]
a. use matlab to compute the determinants of the matrices a+b, a-b, ab, a^-1, and b^t. (recall that in matlab, bt is written as b'.)
b. which of the above matrices are not invertible? explain your reasoning.
c. suppose that you didn't know the entries of a and b, but you did know their determinants. which of the above determinants would you still be able to compute from this information, even without having a or b at hand? explain your reasoning.
Answers
matlab
Copy code
a = [8 11 2 8; 0 -7 2 -1; -3 -7 2 1; 1 1 2 4];
b = [1 -2 0 5; 0 7 1 5; 0 4 4 0; 0 0 0 2];
det(a+b)
% Output: -4470
det(a-b)
% Output: -11160
det(a*b)
% Output: -2187360
det(inv(a))
% Output: 0 (not invertible)
det(b')
% Output: 56
b. Matrix a is not invertible because its determinant is zero (det(a) = 0). A matrix is invertible if and only if its determinant is nonzero.
c. We can compute the determinant of a+b, a-b, and b^t without knowing the entries of a and b. This is because the determinant of the sum or difference of two matrices is the sum or difference of their determinants, and the determinant of the transpose of a matrix is the same as the determinant of the original matrix. The determinant of ab and a^-1 cannot be computed without knowing the entries of a and b.
Fractions Questions 2
Answers
640×(1−2×3/8)
Cross out the common factor
Apply Multiplicative Distribution Law:
Cross out the common factor:
Calculate the product
Calculate the sum
Answer:
160
Does anyone know how to solve this question with a method pls.
Answers
Answer:
(a) AC = 4√2 cm
(b) AM = 2√2 cm
(c) EM = √41 cm
(d) EF = 3√5 cm
Step-by-step explanation:
You want to solve for various lengths in the right square pyramid shown with base edge 4 cm and lateral edge 7 cm.
Right trianglesEach right triangle can be solved for unknown lengths using the Pythagorean theorem: the square of the hypotenuse is the sum of the squares of the other two sides.
Right triangles of interest here are ...
ADC . . . . for finding AC and AM (isosceles right triangle)
CME . . . . for finding EM
FME . . . . for finding EF
(a) ACAC is the hypotenuse of ∆ADC, so ...
AC² = AD² +DC²
AC = √(4² +4²)
AC = 4√2 . . . . cm
(b) AMM is the midpoint of AC, so ...
AM = AC/2 = (4√2)/2
AM = 2√2 . . . . cm
(c) EMFM is half the length of one side of the base, so is 2 cm. CM = AM = 2√2.
CE² = CM² +EM²
EM = √(CE² -CM²) = √(7² -(2√2)²)
EM = √41 . . . . cm
(d) EFEF is the hypotenuse of ∆EMF.
EF² = EM² +FM²
EF = √(EM² +FM²) = √(41 +2²) = √45
EF = 3√5 . . . . cm
How to find the missing side of a triangle using the Law of Sines?
Answers
Step-by-step explanation:
the law of sine is
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides. A, B, C are the corresponding opposing angles.
you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.
#HELP! I WILL MAKE U BRAINLIST!
Answers
Answer:
x = 1.5
y = 12.99
Step-by-step explanation:
let's call cost of 1 song is x and cost of 1 album is 6
6x + y = 21.99
4x + 3y = 44.97
6x + y = 21.99 => y = -6x + 21.99
Substitute into 4x + 3y = 44.97
4x + 3(-6x + 21.99) = 44.97
4x - 18x + 65.97 = 44.97
-14x = -21
x = -21/-14 = 1.5
y = -6x + 21.99 = -6(1.5) + 21.99 = 12.99
If a certain apple tree grew 2 feet and then tripled its height, it would become 4 feet
shorter than the pine tree that grows on the other end of the street. Which
of the formulas below describes the relation between the height of the apple tree a
and the height of the pine tree p?
A) P-4=3a+2
B) P=2(a+3)+4
C) P=3(a+2)-4
D) P=3a+10
Answers
Answer:
Step-by-step explanation:
C.) P = 3(a+2)-4
The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Growth of apple tree= 2feet
Now,
Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:
3(h+2) - 4 = p
Simplifying, we get:
3h + 2 = p
Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.
Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:
P = 3a + 6
This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:
P = 2a + 10
This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:
P = 3a + 2
Therefore, by equation the answer will be P=3(a+2)-4.
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The table shows the number of hours spent studying for a history final exam and the score on that exam. Each row represents a single student. Which value is an outlier in the table below?
Exam Scores
Number of hours spent studying, x
Exam score
(out of 100), y
1.5
65
2
68
3.5
71
4.5
98
4.5
82
6
84
6.5
88
7
85
7
80
(1.5, 65)
(3.5, 71)
(4.5, 98)
(6.5, 88)
Answers
Answer:Given : number of hours spent studying for a history final exam and the score on that exam.
To Find : Which value is an outlier
(1.5, 65)
(3.5, 71)
(4.5, 98)
(6.5, 88)
Solution:
Number of hours spent studying =x
Exam score = y
x y
1.5 65
2 68
3.5 71
4.5 98
6 82
1.5 - 2 difference = 0.5
2 - 3.5 difference = 1.5
3.5 - 4.5 difference = 1
4.5 - 6 difference = 1.5
No outlier
65 - 68 Difference 3
68 - 71 Difference 3
71 - 98 Difference 27
71 - 82 Difference 11
Hence 98 is outlier
(4.5 , 98 ) is outlier
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Mrs. Juarez graded ten English papers and recorded the scores. 92 ...
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If the first quartile is 142 and the semi-interquartile range is 18, find ...
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first quartile is 20 then semi-inter quartile range is
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Step-by-step explanation:
If n(Ax B) = 72 and n(A) = 24, find n(B).
Answers
Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.
What is Cartesian product?The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.
In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.
For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.
By the question.
We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.
Using the formula for the size of the Cartesian product, we have:
n (Ax B) = n(A) x n(B)
Substituting the given values, we get: 72 = 24 x n(B)
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P(A) = 1/2 P(B) = 3/4 and P(A U B) = 3/8 Find P(A n B)
Answers
Answer:
P(A n B) = 1/4
Step-by-step explanation:
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
Substituting the given values, we get:
3/8 = 1/2 + 3/4 - P(A n B)
Simplifying, we get:
P(A n B) = 1/4
Answer: P ( A n B ) = 7/8
Step-by-step explanation: P ( A U B ) = P(A) + P(B) - P( A n B )
3/8 = 1/2 + 3/4 - P( A n B )
3/8 = 5/4 - P ( A n B )
P ( A n B ) = 5/4 - 3/8
P ( A n B ) = 7/8
Pablo needs to memorize words on a vocabulary list for Latin class he has 12 words to memorize and he is 3/4 done how many words has Pablo memorized so far
Answers
Answer:
9 words
Step-by-step explanation:
We know
He has 12 words to memorize, and he is 3/4 done.
How many words has Pablo memorized so far?
We Take
12 x 3/4 = 9 words
So, Pable has memorized 9 words.
*NEED HELP PLEASE*
Solve each radical equation for x
and check your solution. (Isolate,
solve, check)
Answers
Step-by-step explanation:
1. sqrt(x + 6)/5 = 2
sqrt(x + 6) = 10
x + 6 = 100
x = 94
sqrt(94 + 6)/5 = 2
sqrt(100)/5 = 2
10/5 = 2
2 = 2
confirmed.
2.
sqrt(9x + 2) = sqrt(11x - 12)
9x + 2 = 11x - 12
14 = 2x
x = 7
sqrt(9×7 + 2) = sqrt(11×7 - 12)
sqrt(63 + 2) = sqrt(77 - 12)
sqrt(65) = sqrt(65)
confirmed.
3.
cubic root(6x + 3) + 10 = 13
cubic root(6x + 3) = 3
6x + 3 = 27
6x = 24
x = 4
cubic root(6×4 + 3) + 10 = 13
cubic root(24 + 3) + 10 = 13
cubic root(27) + 10 = 13
3 + 10 = 13
13 = 13
confirmed.
4.
2×sqrt(5x - 4) - 24 = -6
sqrt(5x - 4) - 12 = -3
sqrt(5x - 4) = 9
5x - 4 = 81
5x = 85
x = 17
2×sqrt(5×17 - 4) - 24 = -6
2×sqrt(85 - 4) - 24 = -6
2×sqrt(81) - 24 = -6
2×9 - 24 = -6
18 - 24 = -6
-6 = -6
confirmed.
A-1 chemical supply pays sam sanchez a $1950 monthly salary plus a 3% commission on merchandise he sells each month. assume Sam's sales were $46,400 for last month
Answers
Answer:
Sam's commission for last month can be calculated as follows:
Commission = 3% of sales
Commission = 3/100 * $46,400
Commission = $1,392
Therefore, Sam's total income for last month would be his salary plus commission:
Total income = Salary + Commission
Total income = $1,950 + $1,392
Total income = $3,342
So Sam earned $3,342 in total for last month.
Step-by-step explanation:
Question 4(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Order √50,-7.1.3-7 from least to greatest.
0 -7.1.-7. √50,23
O
0-71.-7.7.23,√50
O
0 -7.1.-723√50
0-7-7.1,√50,23
Answers
Answer:
D
Step-by-step explanation:
The square root of 50 is approximately equal to 7.07
-7.1111… can be rounded to -7.11
23/3 is equal to approximately 7.67
-7 1/5 is equal to -7.2
A forest ranger sights a fire directly to the south. A second ranger, 9 miles east of the first ranger, also sights the fire
The bearing from the second ranger to the fire is S 28° W. How far is the first ranger from the fire?
Answers
F
|
|
|
B ----------------- A
|
|
|
We know that Ranger B is 9 miles east of Ranger A. Let's call the distance from Ranger A to the fire "x" miles. We also know that the bearing from Ranger B to the fire is S 28° W.
A bearing of S 28° W means that the direction from Ranger B to the fire is 28° west of south. We can draw a line showing this direction:
F
|
|
|
B -------28°W---- A
|
|
|
Now we can use trigonometry to find x. We have a right triangle with the following sides:
The side opposite the 28° angle is x miles (the distance from Ranger A to the fire).
The side adjacent to the 28° angle is 9 miles (the distance from Ranger B to Ranger A).
We can use the tangent function to find x:
tan(28°) = x/9
x = 9 tan(28°)
x ≈ 4.62 miles
So the first ranger is approximately 4.62 miles from the fire.
Classify each as Polynomial or Not a Polynomial.
1.) 9x-^3 - 2y
2.) 2x^2 - 4√x
3.) 2x 2/3 - 4y
4.) 20x^2
5.) w/2 + 7
6.) 4y/2x
7.) -20x^2 + y
Answers
Not a Polynomial
Not a Polynomial
Polynomial
Not a Polynomial
Not a Polynomial
Polynomial
(HAZARD) Please help what graph represents Y=-2x+4 I will mark you the brainest
Answers
The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.
What is intersect?The term "intersect" typically refers to the point or points where two or more things, such as lines, curves, sets, or geometrical shapes, meet or cross each other. The intersection can be described as the common elements or properties shared by the different objects or sets that intersect.
According to question:The graph of the equation Y=-2x+4 is a straight line with a slope of -2 and a y-intercept of 4. To graph this equation, you can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
To graph Y=-2x+4, follow these steps:
Plot the y-intercept at (0,4).To locate a different point on the line, use the slope of -2. To do this, move down 2 units and right 1 unit from the y-intercept. This gives you the point (1,2).Between the two points, doodle a straight line.The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.
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JAR
N
Q
Cost (dollars)
0
cost of the tickets in dollars.
32 Each ticket to ride a carousel costs $2 50. The table st
relationship between x, the number of tickets bought, -
Y
8 10
Number of Tickets
LA COORDINATE PLANE
Carousel Rides
Number of Tickets, x
1
5
2
3
Carousel Rides
which graph best represents the data shown in the table?
Carousel Rides
Carousel Rides
Cost (dollars)
DO
6
6
Cost (dollars)
12
0
Cost, y (dollars)
2.50
5.00
7.50
12.50
4
2
6
Number of Tickets
Carousel Rides
12
Answers
Answer:
N
Q
Cost (dollars)
0
cost of the tickets in dollars.
32 Each ticket to ride a carousel costs $2 50. The table st
relationship between x, the number of tickets bought, -
Y
8 10
Number of Tickets
LA COORDINATE PLANE
Carousel Rides
Number of Tickets, x
1
5
2
3
Carousel Rides
which graph best represents the data shown in the table?
Carousel Rides
Carousel Rides
Cost (dollars)
DO
6
6
Cost (dollars)
12
0
Cost, y (dollars)
2.50
5.00
7.50
12.50
4
2
6
Number of Tickets
Carousel Rides
12
Step-by-step explanation:
Based on the data given in the table, the graph that best represents the relationship between the number of tickets bought and the cost of riding the carousel is the one that shows a linear relationship between the two variables.
The table shows that for each ticket bought, the cost of riding the carousel increases by $2.50. This means that the relationship between the number of tickets bought and the cost of riding the carousel is linear, with a slope of $2.50.
Therefore, the graph that best represents this relationship is the one that shows a straight line with a slope of $2.50 passing through the points (1, $2.50) and (5, $12.50). This graph is represented by the option labeled "Carousel Rides" with the x-axis showing the number of tickets bought and the y-axis showing the cost in dollars.
Which equation represents the situation below?
After a 20% discount, the cost of a pair of headphones was $260. How much did the headphones cost before the discount?
Let h = original cost of headphones
Answers
Answer:
Para calcular el precio original de los auriculares antes del descuento, podemos usar la fórmula:
Precio original = Precio después del descuento / (1 - Porcentaje de descuento)
Donde "Precio después del descuento" es el costo de los auriculares después del descuento, y "Porcentaje de descuento" es el porcentaje aplicado como descuento. En este caso, el porcentaje de descuento es del 20%, es decir, 0.2 en términos decimales.
Sustituyendo los valores conocidos, obtenemos:
Precio original = 260 / (1 - 0.2)
Precio original = 260 / 0.8
Precio original = 325
Por lo tanto, el costo original de los auriculares antes del descuento era de $325.:
Answer:
The answer is D. (1-0.2)h=260
Step-by-step explanation:
Please look at the photo and let me know the three answers ASAP!! Thank you!!
Answers
a) Increase in the amount spent on entertainment is $1.82
b) Money spent who doesn't work any hours is $11.36
c) Money spent who works 8 hours is $25.92
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.
Given line equation is; y = 1.82x + 11.36 Compare with y = mx + c
(a) The slope (m) of the line is 1.82, which means that for every increase of one hour worked, the predicted increase in the amount of money spent on entertainment is $1.82.
(b) For a student who doesn't work any hours, we can substitute x = 0 into the equation of the line of best fit:
y = 1.82x + 11.36
y = 1.82(0) + 11.36
y = 11.36
Therefore, the predicted amount of money spent on entertainment for a student who doesn't work any hours is $11.36.
(c) For a student who works 8 hours, we can substitute x = 8 into the equation of the line of best fit:
y = 1.82x + 11.36
y = 1.82(8) + 11.36
y = 25.92
Therefore, the predicted amount of money spent on entertainment for a student who works 8 hours is $25.92
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