The solution is, the retail price of the mattress, before the discount is $2,400. & the wholesale price, before the markup was $960
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
Part A:
Given that the mattress is sold for 50% off of the retail price, let the retail price of the mattress be x, then
50% of x = 1200
⇒ 0.5x = 1200
⇒ x = 1200 / 0.5 = 2400
Therefore, the retail price of the mattress, before the discount is $2,400.
Part B:
Given that the store marks up the retail price to 150% of the wholesale price. Let the whole sale price be p, then
(100% + 150%) of p = 2400
250% of p = 2400
2.5p = 2400
p = 2400 / 2.5 = 960.
Therefore, the wholesale price, before the markup was $960.
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The curve above is the graph of a sinusoidal function. It goes through the points
(
-
9
,
0
)
and
(
5
,
0
)
. Find a sinusoidal function that matches the given graph. If needed, you can enter
π
=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.
Answer:
Step-by-step explanation:
To find a sinusoidal function that matches the given graph, we need to find the amplitude (A), period (T), phase shift (h), and vertical shift (k) of the function.
Since the graph goes through the points (-9,0) and (5,0), we know that the maximum value of the function is located at the average of the x-values, which is -2, and that the minimum value of the function is located at the average of the x-values, which is (9+5)/2 = 7. The amplitude of the function can be found by taking half the difference of the maximum and minimum y-values, which is 0 - (-2)/2 = 1.
The period of the function can be found by taking the difference of the x-values of two consecutive maxima or minima, which is 5-(-9) = 14.
The phase shift can be found by noting the horizontal shift of the graph from its standard form, which is usually given by the equation y = A sin(x). In this case, the graph is shifted 2 units to the right, so the phase shift is 2.
The vertical shift can be found by noting the location of the midline of the graph, which is half way between the maximum and minimum y-values. In this case, the midline is at y = -1.
Putting all these values together, we can write a sinusoidal function that matches the given graph as:
f(x) = 1 sin(x + 2π/14) - 1
This function has amplitude 1, period 14, phase shift 2π/14 to the right, and a vertical shift of -1 down.
help, need answer asap
The area of the triangle is 1 square foot.
Waht is the area of the triangle?Remember that the area of a triangle of base B and height H is:
A =B*H/2
Here we can see that:
B = 3ft
H = (2/3) ft
Replacing that in the area formula we will get:
A = (3ft)*(2/3)ft/2 = 1 ft²
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ames needs to make a total of 50 deliveries this week. so far he has completed 32 of them. what percentage of the total deliveries has lamar completed?
Answer:
64%
Step-by-step explanation:
"Percent" means per hundred. So Lamar has completed 32 out of 50 deliveries.
32/50 is the same as 64/100.
64/100 is 64%
Without mental math, if you can use a calculator, divide
32÷50
You'll get 0.64, times by 100 (or move the decimal point two places to the right) to get 64%
how to draw a mind map to show the role that played in urbanisation?
By several orders of magnitude, the role that money plays in the rate of urbanization and various economic activities is significant.
What does urbanization entail?The proportion of people who live in towns and cities growing is known as urbanization. People relocate to urban areas from rural (countryside) areas, which causes urbanization (towns and cities). This typically happens when a nation is still growing.
What are urbanization's causes and effects?Urban areas can expand due to a rise in the population or because people move there. Urbanization causes habitat loss, deforestation, and freshwater extraction from the environment, which can reduce natural things and change species ranges and interactions.
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The rectangular floor of a classroom is 30 feet in length and 33 feet in width. A scale drawing of the floor has a length of 10 inches. What is the perimeter, in inches, of the floor in the scale drawing?
The perimeter of the floor in the scale drawing is 42 inches.
To find the scale factor, we can use the length of the room in the original and the scaled drawing:
scale factor = length in scale drawing / length in original = 10 inches / 30 feet
Since 1 foot = 12 inches, we can convert the length of the room to inches:
30 feet * 12 = 360 inches
So, the scale factor is 10 inches / 360 inches = 1/36.
To find the length of the room in the scaled drawing, we can use the scale factor:
length in scale drawing = scale factor * length in original = (1/36) * 360 inches = 10 inches
And the width in the scaled drawing would be:
width in scale drawing = scale factor * width in original = (1/36) * 33 feet * 12 inches/foot = (1/36) * 396 inches = 11 inches
Finally, to find the perimeter of the room in the scaled drawing, we add up the lengths of all four sides:
perimeter = 2 * (length in scale drawing) + 2 * (width in scale drawing) = 2 * 10 inches + 2 * 11 inches = 20 inches + 22 inches = 42 inches.
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Pleeeeeeeeeeeease answer this for me I’ll give brainly pls pls pls pls
Answer: S=V cubed
Step-by-step explanation:
Answer: A. S = cube of V
Step-by-step explanation:
Cube both sides of the equation to single s out
What is the value of w-1(3)?
-0. 75
-0. 2
5
8
The value of [tex]w^{-1}(3)[/tex] is -0.75
We know that the function is a well defined relation between input and output values in which each input is related to exactly one output.
An inverse function is nothing but a function that returns the original value for which a function has given the output.
If two functions f and g are inverse functions, then f(x) = y if and only if g(y) = x
Here, the table of values for function is:
x w(x)
-3 8
-0.75 3
3 0.2
6.5 -3
7 1
From above table we can observe that for input x = -0.75, the value of function w(x) is 3
This means, that the inverse of 3 for function w is -0.75
Therefore, [tex]w^{-1}(3)[/tex] = -0.75
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Find the complete question below.
Given the set of data below, which measure(s) will change if the outlier is removed?
4, 7, 9, 9, 10
mode
median
mean
range
If the outlier is removed, the following measures will change:
mean
range
Understanding mean and rangea) Mean: Mean is the average of a set of numerical values. It is calculated by summing up all the values in the set and then dividing the sum by the number of values. The mean is a measure of central tendency and represents the typical value of a set of data.
b) Range: Range is a measure of dispersion and represents the difference between the largest and smallest values in a set of numerical data. It provides a quick and simple way to understand the spread of the data, and the difference between the extreme values. The range is calculated by subtracting the smallest value in the set from the largest value.
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Express 20cm to 15m
to the lowest form
Answer:
Step-by-step explanation:
To convert 20 cm to meters, we divide by 100, because 1 meter = 100 centimeters.
So, 20 cm = 20/100 m = 0.2 m
To convert 0.2 m to meters in the lowest form, we divide by 15, because 1 meter = 15 units.
So, 0.2 m = 0.2/15 m = 0.013 m
So the final answer is 0.013 m.
height of a cuboid is three-fourths of its length,breadth is 4 cm and total surface area is 608,finds the length and height of the cuboid.
Height of a cuboid is three-fourths of its length,breadth is 4 cm and total surface area is 608.
the length of the cuboid is 24 cm and its height is 18 cm.
Let us denote the length of the cuboid as "l" and the height of the cuboid as "h".
Based on the facts provided, we may conclude:
h = (3/4)l
Furthermore, the total surface area is 608, which may be computed as follows:
608 = 2(lb + bh + lh)
Extending the formula and changing the value of h:
608 = 2(lb + bh + l(3/4)l)
2(lb + 4h + (3/4)l^2) = 608
Now that we have the equation, we can solve for l by substituting the values of b (breadth) and h (height):
2(4l + 4h + (3/4)l^2) = 608
8l + 8h + (3/2)l^2 = 304
(3/2)l^2 + 8l + 8h = 304
We can now solve for l using the quadratic formula:
l = (-8 ± √(8^2 - 4 * (3/2) * (304 - 8h))) / (2 * (3/2))
Because h = (3/4)l, we may simplify by substituting this formula for h:
l = (-8 ± √(8^2 - 4 * (3/2) * (304 - 3l))) / (2 * (3/2))
Expanding the square root:
l = (-8 ± √(64 + 12l)) / 3
When we solve for l, we get:
l = 24
Finally, for h, substitute the value of l into the equation:
h = (3/4) * 24 = 18
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PLEASE HELP PLEASE !!!!
A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes. What is the approximate arc length, rounded to the nearest hundredth, between each spoke? Use 3.14 for. SHOW UR WORK
Answer:
56.52mm
Step-by-step explanation:
first we need to find the circumference of the wheel, which equals 2*pi*r
then we divide the circumference by 25 since the wheel is split into 25 arcs by the 25 spokes, so our answer is:
2(3.14)(225)/(25) = 56.52mm
from january 2014 to january 2019 the doubling time for the number of wikipedia articles during this time period is
The doubling time for the number of Wikipedia articles during this period is 346.56 days.
So, based on the question, we need to find t. And the condition required to find t will be -
N(t) = 2 [tex] N_{0} [/tex]
So, keeping the value of N (t) in the equation mentioned in question.
[tex] N_{0} [/tex] [tex] {e}^{t/500} [/tex] = 2 [tex] N_{0} [/tex]
Cancel [tex] N_{0} [/tex] on both sides of the equation
[tex] {e}^{t/500} [/tex] = 2
Taking log in both sides of the equation and generating equation according to the rule
t/500 = ln 2
t = 500 × ln 2
Performing multiplication on Right Hand Side of the equation
t = 346.57
Thus, the time period is 346.57 days
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The complete question is attached in the figure.
at 5:45 p.m., a jet is located 108 mi due east of a city. a second jet is located 214 mi due north of the city. to the nearest tenth of a mile, what is the distance between the two jets?
The distance between the two jet when one is in the 108miles of east and second one 214miles in the north is equal to 239.7 miles ( nearest tenth ).
Location of the first jet at 5:45 p.m. is :
= 108 miles in the east of the city.
Location of the second jet at 5:45 p.m. is :
= 214 miles in the north of the city.
Let 'x' miles be the distance between the jets.
East and north from a city forms a right angled triangle.
'x' represents the hypotenuse.
Using Pythagoras theorem we have,
x² = 108² + 214²
⇒ x² = 11664 + 45796
⇒x² = 57460
⇒ x = 239.708 miles
⇒ x = 239.7 miles (nearest tenth )
Therefore, the distance between the two jets as per given condition is equal to 239.7 miles
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25 POINTS. HELP W THE EQUATION TYSM
Step-by-step explanation:
cubing on both sides,
(-4)³= ³√(9x-1)³
-64=9x-1
-64+1=9x
-63=9x
-63/9=x
x=-7
WRITING Write the
Parallelogram Opposite
Sides Theorem and the
Parallelogram Opposite
Sides Converse as a
biconditional statement.
The Parallelogram Opposite Sides Theorem and the Parallelogram Opposite Sides Converse as a biconditional statement is, If the opposite sides of a parallelogram are equal in length, then the parallelogram is a rectangle and If the parallelogram is a rectangle, then the opposite sides are equal in length.
What is a parallelogram?
Parallelogram is a quadrilateral with opposite sides parallel and equal and opposite angle are equal.
The Parallelogram Opposite Sides Theorem and the Parallelogram Opposite Sides Converse can be stated as a biconditional statement as follows:
For any parallelogram, the opposite sides are equal in length if and only if the parallelogram is a rectangle.
In other words,
(1) If the opposite sides of a parallelogram are equal in length, then the parallelogram is a rectangle.
(2) If the parallelogram is a rectangle, then the opposite sides are equal in length.
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Given f(x) = 4* and its inverse f-¹ (z) = log4z. If f (6) = 4096, then f-¹ (4096) = |
-L
(Just type answer, no spaces)
help please
The numeric value of the inverse function at x = 4096 is given as follows:
f-¹ (4096) = 6.
How to find the inverse function?To find the inverse function, we exchange x and y in the original function, then isolate y.
The transformation rule for each point on the inverse function, compared to the original function, is given as follows:
(x,y) -> (y,x).
f(6) = 4096, hence the point on the function is:
(6, 4096).
Then the point on the inverse will be of:
(4096, 6).
Meaning that:
f-¹ (4096) = 6.
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Solve for X. Find the length of angle
Answer:2
Step-by-step explanation:
4*(4+2)=2*(2x+5+3)
4*6=2*(2x+8)
24=4x+16
4x=8
x=2
What is the midpoint of the segment shown below O A (-7/2, 3/2) O B. (-7,3) O c. (-7/2, 3) O D. (-7,3/2)
Answer:
B.
Step-by-step explanation:
The midpoint of a line segment is found by taking the average of the x-coordinates and the y-coordinates of the endpoints of the segment.
The midpoint of segment AB can be found as follows:
Midpoint of AB = ((-7/2 + -7)/2, (3/2 + 3)/2) = (-7, 3)
Since the midpoint of AB is the same as point B, we can conclude that the midpoint of segment AB is (-7, 3).
Naomi is using pairs of numbers from the set below to find sums, differences, products, and quotients
-6 2.7 -2/3 4 1/5 -5.1
Determine whether each statement about Naomi's calculations is true.
Select True or False for each statement.
The greatest possible sum of two numbers is 6.9.
The least possible difference of two numbers is -11.1. 0
The greatest possible product of two numbers is 11.34
The least possible quotient of two numbers is -6.3
The greatest possible sum of two number is 6.7. Naomi's statement is false.
The least possible difference between two number is -10 Naomi's statement is false
The greatest product of two number in the set is 30.6. Naomi's statement is false
The least possible quotient of two numbers from the set is -6. Naomi statement is false
What are mathematical operations?In mathematics, an operation is a function which takes zero or more input values to a well-defined output value. The number of operands is the arity of the operation.
The greatest possible sum = 4+2.7 = 6.7
The least possible difference = -6-4 = -10
The greatest possible product = -6×-5.1 = 30.6
The least possible quotient = 4÷ -2/3 = -12/2 = -6
Therefore all Naomi's statement are false.
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The maximum weight, w, that a stepladder can hold is 250 pounds. Which inequality represents this situation?
O w ≥ 250
w > 250
O w ≤ 250
w < 250
Answer: C
Step-by-step explanation:
Just look for the less than or equal to sign
A group of volunteers tagged and released 29 owls as part of a research project. Later, the researchers counted 902 owls, 11 of which had tags. To the nearest whole number, what is the best estimate for the owl population?
The best estimate for the owl population is 2,378.
The population of the owl can be estimated using the concept of proportion. Proportion refers to a mathematical comparison between two numbers. According to the concept, if two sets of given numbers are increasing or decreasing in the same ratio, hence the ratios are said to be directly proportional to each other.
Based on the provided information, 29 owls are tagged and released as part of a research project. Assume that the total number of owl populations is x. At the later time, researchers counted 902 owls and found the 11 were tag. Hence, there are 18 tagged owls which are not accounted for. Assuming that the proportional of tagged owls to number of owls counted applies to the remaining population, the total number of owls can be best estimated as:
x = (902/11)*29 = 2,378
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for each positive integer n, what is the largest value of p such that zero is the most likely number of successes in n independent trials with success probability p?
The largest value of success probability p with zero as most likely number of success with n independent trials is equal to 1 / ( n + 1 ).
Probability of success is equal to p
Probability of failure is equal to ( 1 - p)
Number of trials is positive integer n
Condition for 'n' independent trials :
Zero is most likely number of success
⇒ P(0) ≥ P(1)
⇒ ⁿC₀ p⁰ ( 1 - p )ⁿ⁻⁰ ≥ ⁿC₁ p¹ ( 1 - p )ⁿ⁻¹
⇒ ( 1 - p )ⁿ ≥ np ( 1 - p )ⁿ⁻¹
⇒( 1 - p ) ≥ np
⇒ np + p ≤ 1
⇒ p ≤ 1 / ( n + 1 )
Largest value of p is equal to 1 / ( n + 1 ).
Therefore, the largest value of success probability p with n independent trials is equal to 1 / ( n + 1 ).
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Melissa ate 1/2 of her salad for lunch and ate 4/9 of he salad for dinner. How much of her salad did she eat?
Answer:
17/18
Step-by-step explanation:
We know
Melissa ate 1/2 of her salad for lunch and ate 4/9 of the salad for dinner.
How much of her salad did she eat?
We take
1/2 + 4/9 = 9/18 + 8/18 = 17/18
So, Melissa ate 17/18 of her salad.
____is one thousanth less than 92.162
92.161 is one thousanth less than 92.162
How to complete the blankFrom the question, we have the following parameters that can be used in our computation:
____is one thousanth less than 92.162
Complete the blank with a variable
So, we have
x is one thousanth less than 92.162
Express as an equation
x = 92.162 - 0.001
Evaluate
x = 92.161
Hence, the expression in the blank is 92.161
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20% of all the children in a class are left-handed. 4 children are left handed. How many children are there in a class altogether?
Answer: 20 children in total.
Step-by-step explanation: If you do 20% of 20 you get 4.
20
let the total children be x
therefore 20/100 × x =4
x = 400/10
x =20
Find the slope and y-intercept of the graph of the equation.
Answer:
The slope: 4
Y-intercept: 9
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
In this case y = 4x + 9
m = 4
b = 9
So,
The slope: 4
Y-intercept: 9
Answer:
Slope: 4/1 or 4
Y-Intercept: 9
Step-by-step explanation:
y = mx + b is the Slope Intercept Formula. 'm' in the formula stands for rate of change in y/x, which is practically slope. 'b' in the formula is where the line crossed the y line. It's where it intercepts with y.
I NEEP HELP!!! If you don’t know the answer and you reply I’m going to report you so pls don’t!
Can someone please explain how to group terms in maths (I'm really struggling here )
Answer:
Step-by-step explanation:
Grouping terms in mathematics refers to the process of combining like terms, which are terms that have the same variable raised to the same power.
For example, consider the expression 2x + 3x. The terms 2x and 3x are like terms because they both have the variable x, so they can be grouped together:
2x + 3x = (2 + 3)x = 5x
When grouping terms, it's important to simplify each group of like terms before combining them. For example, consider the expression 2x^2 + 3x^2 + 4x^3. The terms 2x^2 and 3x^2 are like terms because they both have x raised to the power of 2, but they are not like terms with 4x^3 because it has x raised to a different power. To group the terms correctly, we simplify each group of like terms first:
2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2
2x^2 + 3x^2 + 4x^3 = 5x^2 + 4x^3
Once all like terms are grouped and simplified, the expression can be simplified further by combining the groups of like terms:
5x^2 + 4x^3 = 5x^2 + 4x^3
This final expression is the simplified form of the original expression.
If ac=36 and bc=18 find ad
the dimension of The diagonal ad of the rectangle will be 40.24 units.
What is a polygon?In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:
• Triangle
• Quadrilateral
• Pentagon
• Hexagon
and so on
Given data of a quadrilateral. Since the type of quadrilateral is not provided.
we will assume it to be a rectangle as shown in the figure.
From the general formula of diagonal:
Diagonal = √sum of the square of sides
Thus,
Diagonal (ad) = √(36² + 18²)
ad = 40.24
Therefore the dimension of The diagonal ad of the rectangle will be 40.24 units.
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The speed, s, of the current in a certain whirlpool is modeled by x = StartFraction 300 Over d EndFraction, where d is the distance from the center of the whirlpool. Which statement is true?
As you move closer to the center of the whirlpool, the speed of the current approaches 0.
As you move closer to the center of the whirlpool, the speed of the current approaches 1.
As you move closer to the center of the whirlpool, the speed of the current approaches infinity.
As you move closer to the center of the whirlpool, the speed of the current approaches 300
The correct statement regarding the function is given as follows:
As you move closer to the center of the whirlpool, the speed of the current approaches infinity.
How to interpret the function?The function for this problem is defined as follows:
s = 300/d.
In which:
s is the speed of the current.d is the distance to the center.As d approaches 0, the equation has the following format:
s = 300/0.
The division by a number that is very close to zero means that the output assumes a value close to infinity, hence the third option is the correct option in the context of this problem.
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