Therefore, the shopkeeper made a profit of Rs. 30,000 and the profit percentage is 6.25%.
What is percent?Percent is a way of expressing a fraction or a proportion as a quantity out of 100. The term "percent" means "per hundred". So, when we say that something is 50 percent, we mean that it is 50 out of 100 or 50/100, which can also be simplified to 1/2. The symbol used to represent percent is "%". For example, if a store is offering a discount of 20%, it means that the customer can buy the item for 20% less than the original price, or in other words, the customer will pay only 80% of the original price. Percentages are used in many different areas of life, such as finance, mathematics, science, and statistics. They are used to represent proportions, changes, growth rates, and many other types of data.
Here,
The total cost of 300 bicycles is:
Cost of 1 bicycle = Rs. 1500
Cost of 300 bicycles = 1500 x 300 = Rs. 4,50,000
Transportation cost per bicycle is Rs. 75, so the total transportation cost for 300 bicycles is:
Transportation cost of 1 bicycle = Rs. 75
Transportation cost of 300 bicycles = 75 x 300 = Rs. 22,500
The total cost of purchasing 300 bicycles including transportation cost is:
Total cost = Cost of bicycles + Transportation cost
Total cost = Rs. 4,50,000 + Rs. 22,500 = Rs. 4,72,500
The shopkeeper spent Rs. 7500 on advertising.
So, the total cost of the shopkeeper is:
Total cost = Cost of bicycles + Transportation cost + Advertising cost
Total cost = Rs. 4,72,500 + Rs. 7500 = Rs. 4,80,000
The selling price of 1 bicycle is Rs. 1700, so the selling price of 300 bicycles is:
Selling price of 1 bicycle = Rs. 1700
Selling price of 300 bicycles = 1700 x 300 = Rs. 5,10,000
The profit or loss is calculated by subtracting the total cost from the total selling price:
Profit/Loss = Selling price - Total cost
Profit/Loss = Rs. 5,10,000 - Rs. 4,80,000 = Rs. 30,000
Since the shopkeeper made a profit of Rs. 30,000, we can calculate the profit percentage as follows:
Profit percentage = (Profit / Total cost) x 100
Profit percentage = (30,000 / 4,80,000) x 100
Profit percentage = 6.25%
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A triangular bandana has an area of 86 square inches. The height of the triangle is 5 3/8
inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.
An equation to find the length of the base of the triangle is 86 = ?
The length of the base of the triangle is ? inches
Answer the word problem UvU
A triangular bandana has an area of 86 square inches. The height of the triangle is 5 3/8 inches. An equation to find the length of the base of the triangle is 86 = 1/2 * b * 43/8
The length of the triangle's base is 32 inches.
We know that the formula for calculating the area of a triangle is:
1/2 * base * height = area
We also know that the triangle's height is 5 3/8 inches, which may be expressed as a mixed number:
Height = 5 + 3/8 inch = 43/8 inch
Let b be the base of the triangle.
Substituting these numbers into the area formula yields:
86 = 1/2 * b * 43/8
To find b, multiply both sides of the equation by 2/43:
86 * 2/43 = 2/43 * 1/2 * b * 43/8
4 = b/8
b = 32
As a result, the length of the triangle's base is 32 inches.
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I have 500 red balls, 500 green balls, 500 blue balls, and 500 yellow balls in a bin. What is the smallest amount of balls I need to grab so that I am sure I have grabbed 250 balls of one color?
Answer:
To ensure that you have grabbed 250 balls of one color, you need to use the Pigeonhole Principle. The worst-case scenario is that you grab 249 balls of each color, totaling 996 balls. Therefore, the smallest amount of balls you need to grab is 997, which guarantees that you have grabbed 250 balls of one color.
To explain further, let's consider the worst-case scenario where you grab 249 red balls, 249 green balls, 249 blue balls, and 249 yellow balls. This totals to 996 balls. However, if you grab just one more ball, you will have a total of 997 balls, and since there are only four colors, at least one color will have 250 balls or more. Therefore, by grabbing 997 balls, you can be sure that you have grabbed at least 250 balls of one color.
Answer:
997
Step-by-step explanation:
I multiplied 249 by 4 first. This is because I wanted to find how many balls the person could grab in total without having 250 of the same color.
249*4= 996
However, the question wants to guarantee that one color has 250.
So I did 996+1=997. (which means there could be: 249 red, 249 yellow, 249 green, and 250 blue)
This means that every other color could be at 249, but one would guarantee to be at 250 with 997 pulls
What is the answer for this question?
The figure similar to figure E after dilation is figure F.
What are transformations?The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
We know that when a figure is dilated the ratio of their sides are same, that is they are proportional.
From the graph we observe that the line passes through the point F and E. Thus, the sides of the figure are proportional or in linear relation with each other.
Hence, the figure similar to figure E after dilation is figure F.
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1 point) Solve the equation x²−4x−21=0 byfactoring.The solutions are x1=and x2=with x1
The solutions of x1 = 7 and x2 = -3 with x1 through solving the quadratic equation x²−4x−21=0 by factoring
The equation :x² - 4x - 21 = 0, solve it by factoring it.The first step is to find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3.So, we rewrite the equation using -7 and 3 instead of -4x:x² - 7x + 3x - 21 = 0.
Group the first two terms and the last two terms: x(x - 7) + 3(x - 7) = 0.
Factor out the common factor of (x - 7): (x - 7)(x + 3) = 0.
Now, we have two factors that when multiplied, give us zero. This means that either (x - 7) = 0 or (x + 3) = 0.
Solving for x, we get: x = 7 or x = -3.
The solutions are x1 = 7 and x2 = -3.The equation x² - 4x - 21 = 0 can be solved by factoring it. To factor this equation, we first find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3. Then we rewrite the equation using -7 and 3 instead of -4x.
The resulting equation is x² - 7x + 3x - 21 = 0.
Next, we group the first two terms and the last two terms to get x(x - 7) + 3(x - 7) = 0.
We factor out the common factor of (x - 7) to get (x - 7)(x + 3) = 0.
We then solve for x to get x = 7 or x = -3. Therefore, the solutions are x1 = 7 and x2 = -3.
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The city underpass renovation can be finished by 34 men in 40 days. If 9 of them withdraw before the work started, how many days are they going to finish the work?
It will take 55 days to finish the renovation with 25 men.
If 34 men can finish the renovation in 40 days, we can say that the number of men is inversely proportional to the number of days needed to finish the work. Therefore, we can write:
Number of men × Number of days = Constant
We can find the value of the constant by using the given information:
34 men × 40 days = 1360
This means that the constant is equal to 1360.
If 9 men withdraw before the work started, then the number of men who will work on the renovation is 34 - 9 = 25.
We can now use the constant to find the number of days needed to finish the renovation with 25 men:
25 men × Number of days = 1360
Number of days = 1360 ÷ 25
Number of days = 54.4
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Find the value of the indicated trigonometric ratio.
The value of tan α is [tex]\frac{3}{4}[/tex] . This value has been obtained by using the concept of trigonometry.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the study of right-angle triangles, which even includes their sides, angles, and relationships.
We know that the value of tan α is the ratio of a triangle's base to the triangle's perpendicular.
In the question, we are given that the base is 15 and the perpendicular is 20.
So, from the above information, we get the value as
⇒tan α = [tex]\frac{15}{20}[/tex]
⇒tan α = [tex]\frac{3}{4}[/tex]
Hence, the value of tan α is [tex]\frac{3}{4}[/tex] .
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For Bracken to break even (suffer no loss and earn no profit) over the passage of 3 years, about how many people among the
1,000 insured people can file a claim for a surgical procedure?
A. 10
B. 14
C. 16
D. 17
E. 20
About 16 people among the 1,000 insured people can file a claim for a surgical procedure.
define profitProfit is the financial gain earned by a business or an individual after deducting all the expenses and costs associated with generating that revenue. It represents the difference between the total revenue earned and the total expenses incurred.
The total amount collected in premiums over 3 years for Bracken is:
$100 x 1,000 x 3 = $300,000
Assuming x people among the 1,000 insured people file a claim for a surgical procedure, the total amount paid out in claims by Bracken would be:
$25,000 x x = $25,000x
The total deductible paid by the claimants would be:
$3,500 x x = $3,500x
So, the total amount paid out by Bracken would be:
$25,000x + $3,500x = $28,500x
For Bracken to break even, the total amount collected in premiums should be equal to the total amount paid out in claims plus the deductible for 3 years.
$300,000 = $28,500x + $3,500(1,000 - x)
Simplifying and solving for x, we get:
x = 16
Therefore, about 16 people among the 1,000 insured people can file a claim for a surgical procedure for Bracken to break even over the passage of 3 years.
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The complete question is:
Atrap and Bracken are two rival insurance companies. Atrap and Bracken have premiums of $150 and $100 and deductibles of $2,500 and $3,500 respectively. The average expense of surgery is $25,000. For Bracken to break even (suffer no loss and earn no profit) over the passage of 3 years, about how many people among the 1,000 insured people can file a claim for a surgical procedure?
a -10
b- 14
c- 16
d- 17
e- 20
Consider the figure below.
What are the coordinates of Point S after a dilation with the center at the origin and a scale factor of 12?
Responses
(2,−1)
( 2 , − 1 )
(4,−2)
( 4 , − 2 )
(8,−4)
( 8 , − 4 )
(16,−8)
On solving the question we have that As a result, the coordinates of coordinates point S after dilation with the origin as the Centre and a scale factor of 12 are (24, 12). Option (D) (16,-8), however, is incorrect.
what are coordinates?In geometry, a coordinate system is a method that uses one or more numbers or coordinates to determine the precise location of points or other physical objects on a basis, such as Reference frame. Pairs of figures called coordinates are employed in order to locate a point or item on a double plane. The x and y parameters of a location on a 2D plane are two integers that describe its position. a set of digits which represent precise positions. In most cases, the figure has two numbers. The first number represents the front-to-back distance, while the second column represents the top-to-bottom distance. As in (12.5), there are 12 divisions below and 5 units above.
To determine the image of point S after dilation with the origin as the centre and a scale factor of 12, multiply S's coordinates by the scale factor of 12.
As a result, the coordinates of point S after dilation are as follows:
S' = (12 × 2, 12 × −1)
S' = (24, −12)
As a result, the coordinates of point S after dilation with the origin as the centre and a scale factor of 12 are (24, 12).
Option (D) (16,-8), however, is incorrect.
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What fraction of the sweaters cost $50 or less?
Please help I will award brainliest
if there are 6 consecutive numbers and 10 is the smallest one, what is their sum?
Hence, 75 is the result of adding the six consecutive integers starting at 10.
What are consecutive numbers?Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference.
We can find the sum of these numbers by adding them up if there are six consecutive numbers and 10 is the smallest one.
The six numbers in order are x, x+1, x+2, x+3, x+4, and x+5. We are aware that x equals 10 because 10 is the smallest number.
The six numbers are therefore 10, 11, 12, 13, 14, and 15.
We simply put them together to determine their sum:
10 + 11 + 12 + 13 + 14 + 15 = 75
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work out the length and width
Answer:
The dimensions of the rectangle are 5 by 24.
Step-by-step explanation:
Sometimes it's easy to finish solving the system and think that the x and y coordinates are your answer. Remember what the question is asking for - the dimensions of the rectangle.
please help with this Pythagorean theorem problem!
Answer:
5
Step-by-step explanation:
3^2+4^2
9+16=25
sqrt25
Write all the factors of 15 .
Use commas to separate them.
Answer: 1, 3, 5 and 15
Step-by-step explanation:
trust me bro
I NEED HELP ON THIS ASAp!
A graph of each inequality is shown in the grid below.
A shape which the solution region represent is a rectangle.
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;
0.4r ≤ 120 .....equation 1.
r ≥ 4(360/5) .....equation 2.
By evaluating the given system of inequalities, we have;
r ≤ 120/0.4
r ≤ 300
r ≥ 4(360/5)
r ≥ 4(72)
r ≥ 288
By combining the system of inequalities, we have:
288 ≤ r ≤ 300
Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region between the solid line, and the point of intersection of the lines on the graph representing each.
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1 point) The polynomialf(x)=(5−x)(x+4)(7x+3)2f(x)=(5−x)(x+4)(7x+3)2 hasdegree=leading coefficient=constant coefficient=
The polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has a degree of 2, a leading coefficient of 49, and a constant coefficient of 60.
The polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has the following degree, leading coefficient, and constant coefficient:
Degree: The degree of a polynomial is the maximum degree of any term in it.
Here, the term of highest degree is (7x + 3)2 which has a degree of 2.
Therefore, the degree of the polynomial is 2. Leading coefficient: The leading coefficient of a polynomial is the coefficient of the term of highest degree.
Here, the term of highest degree is (7x + 3)2 and it has a coefficient of 49.
Therefore, the leading coefficient of the polynomial is 49. Constant coefficient: The constant coefficient of a polynomial is the coefficient of the term of degree 0.
Here, there is only one such term, which is the constant term 60 (obtained by multiplying the constant terms of each factor: 5 × 4 × 9).
Therefore, the constant coefficient of the polynomial is 60.
Therefore, the polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has a degree of 2, a leading coefficient of 49, and a constant coefficient of 60.
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Two joggers, one averaging 8 mph and one averaging 4 mph, start from a designated initial point. The slower jogger arrives at the end of the run 35 minutes after the other jogger. Find the distance of the run
The distance of the run is about 7.33 miles.
Let's anticipate that the distance of the run is "d" miles.
We realize that time = distance ÷ velocity.
For the first jogger who averages 8 mph, the time taken to finish the run may be represented as:
t = d ÷ 8
For the second jogger who averages 4 mph, the time taken to complete the same run may be represented as:
t + 35/60 = d ÷ 4
We can simplify this equation by substituting the value of "t" from the first equation:
d ÷ 8 + 35/60 = d ÷ 4
.
Multiplying each aspects through 24 (LCM of 8 and 4), we get:
3D + 7 = 6d
Simplifying this, we get:
d = 7.33 miles (rounded to two decimal locations)
Therefore, the distance of the run is about 7.33 miles.
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Label the drawing or write the segment
The side opposite to angle B is AC. The side adjacent to angle B is BC. The hypotenuse is segment AB.
What is adjacent side and hypotenuse?A pair of sides are referred to as neighboring if they have a shared angle. The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, lies opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles.
From the figure we observe that the side opposite to angle B is AC.
The angle adjacent to angle B is BC.
The hypotenuse is segment AB.
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What is the multiplicative rate of change of the
function?
1/3
2/3
2
9
The multiplicative rate of change of a function is calculated by taking the ratio of the change in the output to the change in the input, which in this case would be 2.
The multiplicative rate of change of a function is the rate at which the output of the function changes in relation to the input. It is calculated by taking the ratio of the change in the output to the change in the input. The formula for this is:
Multiplicative Rate of Change = (Change in Output)/(Change in Input)
For example, if a function f(x) has an input of 3 and an output of 9, then the multiplicative rate of change of the function would be 2. This can be calculated by taking the difference between the output and the input, which is 9 - 3 = 6, and dividing it by the difference between the input and the output, which is 3 - 0 = 3. Thus, the multiplicative rate of change of the function is 6/3 = 2.
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complete question:
What is the multiplicative rate of change of the function f(x) = 3x?
Please help
A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is h(t)=16t^2-100
T= 2. 5 seconds
t = 10 seconds
t = 12. 5 seconds
t = 6. 25 seconds
When "down" is positive and air friction is disregarded, the time it takes for the rock to touch the ground may be calculated using the formula [tex]h(t)=16t2-100[/tex] to be roughly 6.25 seconds.
the formula[tex]h(t)=16t2 - 100[/tex]when a rock is dropped from a height of 100 feet, and assuming that "down" is positive and air friction is neglected, represents the height of the rock at time t in seconds.
As the rock will land at the value of t when h(t) = 0, we must determine that value in order to determine how long it takes for the rock to land.
When we set h(t) to 0 we obtain 0 = 16t2 - 100.
[tex]16t^2 = 100 \st^2 = 100/16 \st^2 = 6.25 \st = ±√6.25[/tex]
The only viable answer in this case is[tex]t = 6.25 = 2.5[/tex] seconds since time cannot be negative. As a result, there was a 2.5 second delay between when the rock was dropped and when it landed.
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Pls aswer!!!
and give simple workingout
Answer:
-4+3n (if first value corresponds to n=0)
or
-7+3n (if first value corresponds to n=1)
Step-by-step explanation:
Notice form each term you just need to add 3
For example, the first term is -4, then the second is -4+3=-1
then the third is -4+3+3=2
So you can start from -4 and 3 for each value.
If n=0 is the start value the sequence will be -4+3n
if the first term is n=1 the sequence will be -4+3(n-1)=-7+3n
So depends if your sequence starts from n=1 or n=0 (which is usually just a convention)
A number is called ‘interesting’ if it is divisible by 11,111. How many 10-digit interesting numbers are there?
A trapezoid has a base of 5 millimeters,
another base of 7 millimeters, and a height
of 6 millimeters. Explain how the area of the
trapezoid will change if the height and both
bases are doubled.
The area will rise by a factor of four if we double the base and height of a trapezoid.
Explain about the trapezoid?A quadrilateral with a single set of parallel sides is referred to as a trapezoid. The parallel and non-parallel sides are referred to as bases and legs, respectively. The distance between the bases of a trapezoid measured perpendicularly is its height.
The formula for a trapezoid's area is:
Area is equal to (base1+base2)*height / 2.
Considering that the height is 6 millimeters, the first base is 5 millimeters, and the secondary base is 7 millimeters, we may determine the trapezoid's initial area as follows:
Area = 1/2 *(5 + 7)* 6 = 36 sq. mm
Doubling the height and both bases:
New base 1 = 2 * 5 = 10 mm
New base 2 = 2 * 7 = 14 mm
New height = 2 * 6 = 12 mm
The new area of such trapezoid can be calculated using the same formula:
New Area = 1/2* (10 + 14) * 12 = 144 sq. mm
When we compare the new area to the old area, we are able to see that the new area has been four times bigger.
So, if the base and height of just a trapezoid are both doubled, the area will grow by a factor four.
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A cylinder has a volume of 1 1/16 inches3 and a radius of 1/4 inches . What is the height of a cylinder?
119/12 inches
119/22 inches
119/44 inches
119/56 inches
Therefore , the solution of the given problem of volume comes out to be the cylinder's height is roughly 5.353 inches, which is the nearest to 119/22 inches.
Describe volume.The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Cubic measurements are denoted by the characters cm3 and in3. To determine an item's size, you could use its bulk, though. The object's weight is typically transformed into mass units like grammes and kilos.
Here,
The formula for a cylinder's capacity can be used to calculate the height:
=> V = πr^2h
where the volume is V, the radius is r, and the height is h.
Inputting the numbers provided yields:
=> 1 1/16 = π(1/4)^2h
Simplifying:
=> 1.0625 = π(1/16)h
=> 1.0625 = (π/16)h
Adding 16/ to both sides:
=> h = (16/π) x 1.0625
=> h = 16.8125/π
=> h ≈ 5.3529
=> H = 5.353 inches is the result of rounding to the closest thousandth.
As a result, the cylinder's height is roughly 5.353 inches, which is the nearest to 119/22 inches.
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Please Urgent! Find the EXACT value of tan(A-B) if cscA= -17/15where A is in Quadrant III and sinB=12/13 where B is in Quadrant I.Assume all angles are measured from standard position.tan(A-B) = ?
The value of tan(A - B) will be 15/8.
As mentioned, cscA= -17/15 and A is in Quadrant III and sinB=12/13 where B is in Quadrant I To find tan(A - B), we need to have the values of sin (A - B) and cos (A - B).We know that, sin(A - B) = sinAcosB - cosAsinB and cos(A - B) = cosAcosB + sinAsinB.Since we have the values of sinA, cosA, and sinB, let's find the values of cosA and cosB.First, let's find cosA. We know that cscA = 1/sinA. Therefore, sinA = -15/17.Since A is in Quadrant III, sinA < 0, cosA < 0, and tanA > 0.
By using the Pythagorean identity sin^2A + cos^2A = 1, we get cosA = -8/17.Next, let's find cosB. We know that sin^2B + cos^2B = 1.
Therefore, cosB = sqrt(1 - sin^2B) = 5/13.
Since B is in Quadrant I, sinB > 0, cosB > 0, and tanB > 0.
Now, we have sinA, cosA, sinB, and cosB.
Using the values of sinA, cosA, sinB, and cosB, let's find sin(A - B) and cos(A - B).
sin(A - B) = sinAcosB - cosAsinB= (-15/17)(12/13) - (-8/17)(5/13)= -180/221
cos(A - B) = cosAcosB + sinAsinB= (-8/17)(12/13) + (-15/17)(5/13)= -96/221
Finally, tan(A - B) = sin(A - B) / cos(A - B)= (-180/221) / (-96/221)= 15/8. Therefore, tan(A - B) = 15/8.
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A poster storage tube in the shape of a cylinder has a diameter of inches and a volume ofcubic inches.
What is the height of the poster storage tube in inches?
ANSWER IS ON VERY BOTTOM.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. We are given the diameter of the cylinder, which is 4 inches, so the radius is half of that, or 2 inches. We are also given the volume of the cylinder, which is V = cubic inches.
Substituting these values into the formula, we get:
cubic inches = π(2 inches)^2h
Simplifying, we have:
cubic inches = 4πh
To solve for h, we can divide both sides by 4π:
h = cubic inches / 4π
Using a calculator to evaluate this expression, we get:
h = 5.027 inches (rounded to three decimal places)
Therefore, the height of the poster storage tube is approximately 5.027 inches.
The height of the poster storage tube in inches is 40 inches.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
A poster storage tube in the shape of a cylinder.
Volume = 122.5π inches³
Diameter = 3.5 inches
Radius = Diameter / 2 = 1.75 inches
Volume of the cylinder = π r² h
where r is the radius of the base and h is the height of the cylinder.
Substituting,
π (1.75)² h = 122.5π
(1.75)² h = 122.5
h = 122.5 / (1.75)²
h = 40 inches
Hence the height of the cylinder is 40 inches.
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The complete question is as follows :
A poster storage tube in the shape of a cylinder has a diameter of 3.5 inches and a volume of 122.5 (pi) cubic inches. What is the height of the poster storage tube in inches?
can someone help with this please !!
The equation of the line that is perpendicular to the equation is y = -1/5x
What is the slope and y - interceptThe given line has a slope of 5, which means that any line perpendicular to it will have a slope that is the negative reciprocal of 5. The negative reciprocal of 5 is -1/5.
Let m be the slope of the line perpendicular to y = 5x - 2. Then, the equation of this line can be written in point-slope form as:
y - y1 = m(x - x1)
where (x1, y1) is the point where the line passes through, which is the origin in this case. So, we have:
y - 0 = (-1/5)(x - 0)
Simplifying this equation, we get:
y = (-1/5)x
Therefore, the line perpendicular to y = 5x - 2 and passing through the origin has a slope of -1/5 and a y-intercept of 0. Its equation is y = (-1/5)x.
Learn more on equation of perpendicular line here;
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4.) You decide to paint your room, too.
Your room has 300 square feet of wall space to paint. Sam says it took her 10 minutes to paint 25 square feet. At this rate, how many hours would it take Sam to paint your room?
Answer: 2 hours
Step-by-step explanation: (10 min) / (25 square feet) = (X minutes) / (300 square feet)
Cross-multiply to solve, as we always do with proportions:
10 * 300 = 25 * x
3000 = 25X
3000/25 = 25X /25
120 = X
120 minutes * (1 hour / 60 minutes) = 2 hours
1. 3 students are running for a class president in a class of 70 students. How many different vote counts are possible if some student(s) do not vote.
2. In how many ways can we distribute 7 pieces of identical taffy and 8 pieces of identical licorice to 5 kids such that each kid recieves exactly 3 pieces of candy.
1. I am completely stuck. I have thought of using the "hockey stick identity", but I do not fully understand how. Thanks!
2. I tried listing out all of the possible cases, but there were way too much.
Answer:
Q1: no idea
Q2: 2 kids get 2 pieces of taffy and 1 piece of licorice and the other three get 2 pieces of licorice and 1 piece of taffy.
Step-by-step explanation:
question 2 is quite obvious but no one can get the same amount of everything so the answer that i gave makes the most sense.
A cylinder has a diameter of 10 inches and a height of 18 inches what is the volume of the cylinder
if it has a diameter of 10, that means its radius is half that or 5.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=18 \end{cases}\implies V=\pi (5)^2(18)\implies V\approx 1413.72~in^3[/tex]
What whole number is nearest to each square root? √22
Step-by-step explanation:
The square root of 22 is an irrational number, which means it cannot be expressed exactly as a finite decimal or a fraction. However, we can approximate it by finding the whole number that is closest to it.
To do this, we can use a calculator or estimation. For example, we can guess that the square root of 22 is between 4 and 5, since 4 squared is 16 and 5 squared is 25. Then we can try averaging these two numbers:
(4 + 5) / 2 = 4.5
This means that 4.5 is an approximate value of the square root of 22. The nearest whole number to 4.5 is 5, so we can say that the whole number nearest to the square root of 22 is 5.