Therefore, the sphere described here cannot hold all of the water from the cylinder.
What is diameter?Diameter is a straight line passing through the center of a circle or a sphere, and connecting two points on its circumference. It is the longest distance between any two points on a circle or a sphere, and it is equal to twice the radius. In other words, if you know the diameter of a circle or a sphere, you can find its radius by dividing the diameter by 2, and vice versa, if you know the radius, you can find the diameter by multiplying the radius by 2.
The volume of the cylinder can be calculated as follows:
Radius of cylinder = Diameter[tex]/2 = 3/2 = 1.5 cm[/tex]
Volume of cylinder[tex]= \pi r^2h = \pi (1.5)^2(8) = 56.55 cm^3[/tex]
To determine if a sphere with a radius of 2 cm can hold all of the water from the cylinder, we can calculate its volume as follows:
Volume of sphere [tex]= 4/3\pi r^3 = 4/3\pi (2)^3 = 33.51 cm^3[/tex]
Since the volume of the cylinder is greater than the volume of the sphere, the sphere cannot hold all of the water from the cylinder. Therefore, the sphere described here cannot hold all of the water from the cylinder.
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I need help with this question
The length of the leg of the triangle (hypotenuse, opposite side, adjacent side) are 10, 17, and 5 respectively.
How to round the number to nearest whole number?To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If this digit is less than 5 (1, 2, 3, 4) we don't have to do anything, but if the digit is 5 or greater (5, 6, 7, 8, 9) we must round up.
To find the length of each leg we need to consider the angle BAC.
[tex]sin60 = \frac{opposite side}{hypotenuse} =\frac{BC}{10}[/tex]
[tex]\frac{\sqrt{3} }{2} = \frac{BC}{10}\\ BC = \frac{\sqrt{3} }{2} * 10\\ BC = \sqrt{3} * 10\\ BC = 17.32 = 17[/tex]
[tex]cos60 = \frac{adjacent side}{hypotenuse} \\\frac{1}{2} = \frac{AB}{10} \\AB = \frac{1}{2} *10\\AB = 5[/tex]
Therefore the length of the leg of triangle are 17 and 5.
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Tamekia and Marsha mow lawns during the summer to earn money. Tamekia determined that she can earn between $6.00 and $6.25 per hour. Marsha estimates that she earns between $7.50 and $8.00 per hour. About how much more money will Marsha earn than Tamekia if they each work 22 hours?
Marsha would earn about $35.75 more than Tamekia if they each work 22 hours.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.
To estimate the difference in earnings between Tamekia and Marsha, we can find the average hourly rates for each and use them to calculate an approximate earnings difference.
For Tamekia:
The hourly rate is between $6.00 and $6.25.
The average hourly rate is approximately $(6.00 + 6.25) / 2 = $6.125.
For Marsha:
The hourly rate is between $7.50 and $8.00.
The average hourly rate is approximately $(7.50 + 8.00) / 2 = $7.75.
If they each work 22 hours, Tamekia would earn approximately $6.125 x 22 = $134.75, and Marsha would earn approximately $7.75 x 22 = $170.50.
The difference in earnings between Marsha and Tamekia would be approximately $170.50 - $134.75 = $35.75.
Therefore, Marsha would earn about $35.75 more than Tamekia if they each work 22 hours.
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Find the area of the Trapezoid
16.6 mi
6.7 mi
13.1 mi
18.5 mi
please explain I'll mark brainlisest
Answer:
The area of the trapezoid is 165.06mi.
Step-by-step explanation:
We can find the area of a trapezoid by the following formula:
[tex]\boxed{A_T = \frac{(B + b) \cdot h}{2} }[/tex]
[tex]A_T[/tex] is the area of the trapezoid (in our case, it is what we want to find)[tex]B[/tex] is the biggest base (in our case, the biggest base is 18.5 mi)[tex]b[/tex] is the smallest base (in our case, the smallest base is 6.7 mi)[tex]h[/tex] is the height (in our case, the base height is 13.1 mi)Note: Base are the parallel sides of the trapezium.
Now, let's change the values in the previous formula:
[tex]A_T = \frac{(B + b) \cdot h}{2}\\\\A_T = \frac{(6.7 + 18.5) \cdot 13.1}{2}\\\\A_T = \frac{25.2 \cdot 13.1}{2}\\\\A_T = \frac{330.12}{2}\\\\A_T = 165.06[/tex]
Therefore, the area of this trapezoid is 165.06 mi.
I hope I've helped.
Happy studying! =D
4x7x2 1\2 I really need a good answer
Answer:
70
Step-by-step explanation:
Hello there! Let's work this through:
Firstly, we might want to simply 2 1/2 into 5/2, for simplification.
So, we now have 4 * 7 * 5/2
Simplifying we have [tex]\frac{4*7*5}{2}[/tex]
We see that we can easily simplify 4/2 into 2 * 7 * 5
Further simplifying we get 10*7
Last bit and we get our answer of 70
From here we get 2
Find the perimeter of the triangle
first off, something noteworthy is that we have two angles of 60°, that means that the angle atop is also 60°, so we really have an equilateral triangle, with an altitude or height as shown above, so
[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{15} \end{cases}\implies 4\sqrt{15}=\cfrac{s\sqrt{3}}{2}\implies 8\sqrt{15}=s\sqrt{3} \\\\\\ \cfrac{8\sqrt{15}}{\sqrt{3}}=s\implies \cfrac{8\sqrt{2\cdot 3}}{\sqrt{3}}=s\implies \cfrac{8\sqrt{2}\cdot \sqrt{3}}{\sqrt{3}}=s\implies 8\sqrt{2}=s \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{\LARGE perimeter} }{8\sqrt{2}~~ + ~~8\sqrt{2}~~ + ~~8\sqrt{2}}\implies 24\sqrt{2}[/tex]
Please answer the question correctly my test is due in 30 mins please help
The value of x is 14.
What is the triangle?
A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.
The sum of the angles in a triangle is 180°, so we can set up an equation:
(4x+3) + 76 + (4x-11) = 180
Simplifying and solving for x:
8x + 68 = 180
8x = 112
x = 14
Therefore, the value of x is 14.
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MidSegment theorem Someone please Solve for X For TOP and BOTTOM Question!
Will Give Brainiest and 5 Stars and Thumbs up and Comment.
The value of x on the first image is 5 and in the second image is 17.
What is Triangle?Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees which is called interior angles.
According to the given information:
In fig 1, by midsegment theorem,
[tex]x+8 = \frac{1}{2} (3x+11)[/tex]
on simplifying
[tex]2x+16=3x+11\\3x-2x = 16-11\\x = 5[/tex]
In fig 1, by midsegment theorem,[tex]x+5=\frac{1}{2} (3x-7)[/tex]
on simplifying
[tex]2x+10 = 3x-7\\3x-2x = 10+7\\x = 17[/tex]
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Angel's net pay is 68%of her gross pay of $59, 600 per year. What is her monthly net pay? Show your work!
Answer:To find Angel's monthly net pay, we can use the following steps:
Calculate Angel's annual net pay:
Her net pay is 68% of her gross pay, so we can find her net pay by multiplying her gross pay by 0.68:
Net pay = Gross pay x 0.68
Net pay = $59,600 x 0.68
Net pay = $40,648
Divide Angel's annual net pay by 12 to find her monthly net pay:
Monthly net pay = Annual net pay / 12
Monthly net pay = $40,648 / 12
Monthly net pay = $3,387.33 (rounded to two decimal places)
Therefore, Angel's monthly net pay is $3,387.33.
Step-by-step explanation:
Jim takes an hour to fold the weekly washing for his family. His older sister Sara can do the same job in half the time. How many minutes would it take them to fold the washing together if they continue to fold at their own rates?
Answer:
Let's start by finding out how long it takes Jim to fold the washing in minutes. Since there are 60 minutes in an hour, Jim takes 60 minutes to fold the washing. Sara can do the same job in half the time, so she takes 30 minutes to fold the washing. To find out how long it would take them to fold the washing together, we can use the formula: Time = (Work) / (Rate) In this case, the "work" is folding the washing, and the "rate" is how long it takes each person to do the work. We can add their rates together to get the combined rate: Combined rate = Jim's rate + Sara's rate Combined rate = 1/60 + 1/30 To add these fractions, we need to find a common denominator, which is 60:
4. is the linear separable svm always applicable in case of noise in the training data? if no, how can be svm modified in order to deal with noisy training data?
The linear separable SVM is not always applicable in case of noise in the training data. When dealing with noisy training data, the performance of a linear separable SVM can be negatively affected, as it tries to find a perfect separation between the classes, which may not be possible in noisy data.
To deal with noisy training data, SVM can be modified by introducing a "soft margin" approach, which allows some flexibility in class separation. This is achieved by using a parameter called C (cost parameter), which controls the trade-off between achieving a wider margin and minimizing classification errors. A higher value of C results in a smaller margin but fewer classification errors, making the model more sensitive to noise. A lower value of C results in a larger margin, allowing more classification errors but providing better generalization to handle noise.
Choosing the appropriate value for C is crucial for the SVM model's performance. Additionally, nonlinear kernel functions, such as the radial basis function (RBF) kernel, can be used instead of a linear kernel to map the data into a higher-dimensional space. This allows the SVM to find more complex decision boundaries, which can better handle noisy data.
In summary, to deal with noisy training data in SVM, one can use the soft margin approach by adjusting the cost parameter (C) and opt for nonlinear kernel functions like RBF, enabling the model to generalize better and handle noise effectively.
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Compute |1-|2-|3-|4-|5|||||.
The value of the expression |1-|2-|3-|4-|5 is 1.
Expression calculation.
We can solve this expression by working from the inside out. Starting from the innermost absolute value, we have:
|5| = 5
Next, we move outward to the next absolute value:
|4-5| = |-1| = 1
Continuing outward:
|3-1| = |2| = 2
|2-2| = |0| = 0
Finally, we have:
|1-0| = |1| = 1
Therefore, the value of the expression is 1.
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solomons studied circadian rhythms in a sample of 45 pregnant women consecutively admitted to a hospital in the first 6 months of 2021 because of severe preeclampsia. what type of sampling is this?
Solomon's study on circadian rhythms in a sample of 45 pregnant women admitted to a hospital in the first 6 months of 2021 due to severe preeclampsia is an example of consecutive sampling.
Consecutive sampling, also known as continuous or complete sampling, is a non-probability sampling method.
In this approach, researchers collect data from every subject that meets the eligibility criteria within a specific time frame.
In Solomon's study, the eligibility criteria were pregnant women admitted to the hospital with severe preeclampsia during the first 6 months of 2021.
By including all eligible subjects during this period, Solomon ensured that the sample was representative of the population under study.
The consecutive sampling method has several advantages, including ease of implementation and the potential for a relatively large sample size.
Additionally, it can provide a comprehensive view of the population during the specified time frame.
However, it may be susceptible to biases if there is a change in the population over time, or if the subjects who meet the eligibility criteria within the given period are not representative of the overall population.
In summary, Solomon's study on circadian rhythms in pregnant women with severe preeclampsia used consecutive sampling, a non-probability sampling method that involves collecting data from every subject meeting the eligibility criteria within a specific time frame.
This method is straightforward to implement and can yield a large sample size, but it may be susceptible to biases if the sample is not representative of the overall population.
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The diagram below shows part of the graph of y= ax+b/x+c
The y-intercept is (0,-4).
The vertical asymptote is x= -2.
The horizontal asymptote is y=3.
Find the value of b
The value of b, given the graph, the vertical and horizontal asymptote, would be - 8 .
How to find the value of b ?At the y-intercept, x = 0. We can plug this into the equation and solve for y:
-4 = (a(0) + b) / (0 + c)
-4 = b / c
The vertical asymptote occurs when the denominator is equal to 0:
x + c = 0
x = -2
Thus, c = 2.
The horizontal asymptote occurs when the limit of the function as x approaches infinity is equal to a constant value:
y = a/c
3 = a/2
a = 3 * 2
= 6
The value of b would therefore be:
-4 = b / 2
b = -8
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jacob was researching the number of hours the average adult sleeps each night. he collected data from five individuals: subject hours of sleep subject 1 6 subject 2 6.5 subject 3 6 subject 4 7.5 subject 5 5 using the data above, what is the standard error of the sample mean? answer choices are rounded to the hundredths place. a.) 0.74 b.) 0.41 c.) 6.10 d.) 0.15
When collecting data for research, it is important to determine the error range of the data set. In the given question, Jacob was researching the number of hours the average adult sleeps each night. He collected data from five individuals.
The data collected by Jacob is as follows:Subject 1: 6 hours of sleepSubject 2: 6.5 hours of sleepSubject 3: 6 hours of sleep Subject 4: 7.5 hours of sleepSubject 5: 5 hours of sleepWe have to find the standard error of the sample mean. The formula for the standard error of the sample mean is:Standard Error = s / sqrt (n)Where,s = the sample standard deviation,n = the sample size.
For the given data set, the sample size is 5. The sample mean can be calculated as:(6 + 6.5 + 6 + 7.5 + 5) / 5 = 6.2The sample standard deviation can be calculated as:√[((6 - 6.2)² + (6.5 - 6.2)² + (6 - 6.2)² + (7.5 - 6.2)² + (5 - 6.2)²) / 4]≈ 1.306The standard error of the sample mean can be calculated as:Standard Error = 1.306 / sqrt (5)≈ 0.58Therefore, the standard error of the sample mean is 0.58. None of the options given in the question is closest to the calculated value. Hence, none of the options is the correct answer.
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Ms. Switer needs to buy sod for the front lawn of her new house . if the lawn measures 36 2/3 ft by 45 1/6 ft, how many square feet of sod will she need
Ms. Switer will need approximately 2981.388 square feet of sod for her front lawn.
What is Area?Area is the measure of the amount of space inside a two-dimensional (2D) flat surface or shape, such as a rectangle, circle, or triangle. It is typically measured in square units, such as square meters or square feet. The formula for finding the area of a shape varies depending on the shape itself.
To find out how many square feet of sod Ms. Switer will need, we need to find the area of the lawn. The formula for the area of a rectangle is length x width. Therefore, the area of Ms. Switer's lawn is:
Area = Length x Width
Area = (36 2/3 ft) x (45 1/6 ft)
Area = (110/3 ft) x (271/6 ft)
Area = 2981.388... square feet (rounded to three decimal places)
Therefore, Ms. Switer will need approximately 2981.388 square feet of sod for her front lawn.
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can someone help with this question?!?! need the answer ASAP !!
Radian measure of an angle is defined to be the ratio of arc length to the radius of the circle. The length of the arc if a 60 degree angle is 1.0476. Therefore, the radian of the 60 degrees angle is 1.0476.
What is the radian measure of an arcRadian measure of an angle is defined to be the ratio of arc length to the radius of the circle.
Arc length of sector of circle = (θ/360°) × 2πr
Arc length of sector of circle = (60°/360°) × 2 × 22/7 × 1
Arc length of sector of circle = 1.0476
radian measure of angle 60° = 1.04756/1
radian measure of angle 60° = 1.04756
In conclusion, radian measure of an angle is defined to be the ratio of arc length to the radius of the circle. The length of the arc if a 60 degree angle is 1.0476. Therefore, the radian of the 60 degrees angle is 1.0476.
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(Correct answer gets brainliest) Here is a prism with a pentagonal base. The height is 8 cm
Step-by-step explanation:
Endplate area * depth = volume
Endplate area is a composite area:
rectangle 2x 7 = 14 cm^2
and trapezoid area = height x average of bases = 3 x (3+7)/2 = 15 cm^2
total endplate area = 29 cm ^2
29cm^2 * depth = volume
29 * 8 = 232 cm^3
You have a jar of 20 jellybeans, and 4 are red. Which fraction represents the probability that you will pick a red jellybean out of the jar?
Answer: you will have 20 percent chance of finding a red jelly bean
4 jelly beans out of 20 are going to be red.
20-4=16
16/20=80%
1-0.8=.2
20%
Step-by-step explanation:
Natalie bought a book that was 25% off. The discount book was 18 dolars. What was the original price of the book
Answer:
If the book was 25% off and the discounted price was $18, then 75% of the original price was $18.
In other words, 0.75 * Original Price = $18
Solving for Original Price, we get:
Original Price = $18 / 0.75
Original Price = $24
Therefore, the original price of the book was $24.
Step-by-step explanation:
Jessica is reading a story book. She reads 30 pages of the book per day. After three days of reading, 5/8 of the book are left. How many pages are in the book?
Compare / Contrast
Jamie read 90 pages of a book in 2 days. If the book has 225 pages in it, what portion of the book does she read each day?
How many days will it take Jamie to finish the book?
Jamie will therefore need five days to complete the book as a result, P – 90 pages equals 3/8 of the book.
what is unitary method ?A mathematical strategy for resolving proportionality issues is the unitary method. Finding the price of one unit is the first step, and utilizing that value to determine the value of yet another quantity with a different quantity is the second. Consider being told, for instance, that an automobile drives 300 kilometres in 5 hours. You are able to employ the unitary technique as shown below to determine how far the car drives in eight hours. For example, 1 hour is equal to 300/5, or 60 miles. To calculate the value of eight hours, use this value: Since 8 hours are equal to 8/1 units, 480 miles are covered in 8 hours.
given
Let P represent the book's total number of pages.
Jessica reads 30 pages per day, which translates to 330 pages after 3 days, or 90 pages total.
5/8 of the book is still to be read, which indicates that 3/8 of it has already been. As a result, P – 90 pages equals 3/8 of the book.
Divide both sides by 5, and you get:
P = 144
The book thus has 144 pages.
Regarding the second query:
She reads 45 pages per 225 pages, or 1/5 of the book.
We divide the total number of pages by the average number of pages Jamie reads each day to determine the number of days Jamie will need to finish the book.
Jamie will therefore need five days to complete the book as a result, P – 90 pages equals 3/8 of the book.
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Find the values of x and y when the smaller triangle has an area of 45 cm².
PLS PLS PLS HELP
Given two similar triangles
The corresponding sides are proportions
So,
[tex]\dfrac{x}{y} =\dfrac{20}{90} =\dfrac{2}{9}[/tex]
So, the relation between x and y will be:
[tex]x=\dfrac{2}{9} y[/tex]
The area of the smaller triangle = 45 cm²
So, area =
[tex]\dfrac{1}{2} x\times y=45[/tex]
Substitute with x into the equation of the area to find the value of y
[tex]\dfrac{1}{2} \times\dfrac{2}{9} y\times y=45[/tex]
[tex]y^2=\dfrac{45\times1\times9}{2} =\dfrac{405}{2}=202.5[/tex]
[tex]y=\sqrt{202.5}[/tex]
Substitute with y into x
[tex]x=\dfrac{2}{9} \times\sqrt{202.5} =\frac{2\sqrt{202.5} }{9}[/tex]
So, the answer will be:
[tex]x=\frac{2\sqrt{202.5} }{9}[/tex]
[tex]y=\sqrt{202.5}[/tex]
Which mineral is ranked highest on the Mohs scale and very difficult to scratch?
gt the size of bass caught in strawberry lake is normally distributed with a mean of 11 inches and a standard deviation of 3 inches. suppose you catch 4 fish. what is the probability the average size of the fish you caught is more than 13 inches?
The probability that the average size of the fish you caught is more than 13 inches is approximately 0.0918
We can solve this problem by using the Central Limit Theorem, which states that the sample mean of a sufficiently large sample size will be normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we are given that the population mean is 11 inches and the population standard deviation is 3 inches. We are also given that we have a sample size of 4.
First, we need to calculate the standard error of the mean (SE) using the formula
SE = σ / sqrt(n)
where σ is the population standard deviation and n is the sample size.
SE = 3 / sqrt(4) = 1.5
Next, we need to standardize the sample mean using the formula
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.
z = (13 - 11) / 1.5 = 1.33
Finally, we can use a standard normal distribution table or calculator to find the probability that a standard normal variable is greater than 1.33. The probability is approximately 0.0918.
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-2x+y=4
graph
find slope
y-intercept
Answer:
slope is 2
y-intercept is (0,4)
yk i got u
Answer: x=
2
y−4
−2x+y=4
Subtract y from both sides.
−2x=4−y
Divide both sides by −2.
−2
−2x
=
−2
4−y
Dividing by −2 undoes the multiplication by −2.
x=
−2
4−y
Divide 4−y by −2.
x=
2
y
−2
Step-by-step explanation:
PLEASE GIVE ME BRAINLIEST
If you flatten a tissue box, you will get the net below, where he white rectangle is the top opening, find the surface area of the box, in square inches.
Answer: 185.64 inches
The surface area of the box is 185.64 square inches.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
To find the surface area of the box, we need to calculate the area of each face and then add them up.
The four faces are rectangles with dimensions 8.8 inches by 4.3 inches, so their area is 4(8.8)(4.3) = 151.36 square inches.
The other area can be described as 2(4.3)(4.3) =36.98 square inches.
Finally, we need to account for the rectangular tear on one of the sides, which has dimensions of 0.5 inches by 5.4 inches. This tear creates an additional face with area (0.5)(5.4) = 2.7 square inches.
Therefore, the total surface area of the tissue box is:
151.36 + 36.98 - 2.7 = 185.64 square inches.
Hence, the surface area of the box is 185.64 square inches.
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The perimeter of a rectangular ink pad is 28 centimetres. The area is 40 square centimetres. What are the dimensions of the ink pad
The area of the rectangle in terms of b is 11b - b², and the perimeter is always 22, regardless of the value of b.
What is rectangle?A rectangle is a four-sided flat shape with opposite sides that are equal in length and parallel to each other. It has four right angles (90-degree angles) at each corner. The two sides that are parallel to each other are called the length, and the other two sides are called the width.
The area of a rectangle is found by multiplying its length and width, and its perimeter is the sum of the lengths of all four sides. Rectangles are common in everyday life and can be found in many different contexts, such as books, doors, windows, and electronic screens.
According to given information,
Let's assume that the length of the rectangle is 'l' and the width is 'b'.
The area of a rectangle is given by the formula A = lb, where A is the area, l is the length, and b is the width.
The perimeter of a rectangle is given by the formula P = 2(l + b), where P is the perimeter, l is the length, and b is the width.
So, the area of the rectangle is:
A = lb = 28
And the perimeter of the rectangle is:
P = 2(l + b) = 40
P = (l+b) = 20
l= 20 -b
Now, we can substitute l = 20 - b into these formulas:
A = (20 - b)b
P = 2(20 - b + b)
Simplifying, we get:
A = 40b - b²
P= 40
So, the area of the rectangle in terms of b is 11b - b², and the perimeter is always 22, regardless of the value of b.
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The length of the rectangle is 10 cm and breadth of the rectangle is 4 cm.
What is rectangle?
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
The longer parallel sides are called length(l) and two shorter sides are called breadth(b).
Perimeter of a rectangle is 2(l+b).
Area of rectangle is l*b.
2(l+b)=28
L+b=28/2=14
L=14-b .....eq(1)
L*b=40
(14-b)b=40
14b-b^2=40
b^2-14b+40=0
b^2-10b-4b+40=0
b(b-10)-4(b-10)=0
(b-10)(b-4)=0
Either b=10 or b=4
If b=10 then l =4 but length can't be shorter than the breadth so b=4cm and l=10 cm is the answer.
suppose you have a circle for which you select 3 random points along its perimeter. if you were to form a triangle using these 3 points, what are the odds the center of the circle would be contained within this triangle?
The probability of the center of a circle being contained within a randomly formed triangle using three points along its perimeter is 1/4 or 25%. This probability remains the same for any size of the circle.
The probability that the center of the circle is contained within the triangle formed by selecting three random points along its perimeter is 1/4 or 25%. This is because any triangle that contains the center of the circle must have all of its vertices on the circumference of a smaller circle with half the radius of the original circle. The probability of selecting three random points on the circumference of this smaller circle is 1/4 or 25%.
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The school is designing a new classroom that will have the shape shown. If they need to order carpet for the room, approximate how much should they order. Responses A 2525 B 22 C 55 D 3
The area of carpet the school need to order for the room, the school is designing the new classroom shown in the figure is 5 sq. cm
What is area?
Area is the region covered by the two dimensional shapes like square, rectangle, rhombus, triangle, circle etc. The area of square is given by side x side. The rectangle area is found by length times width.
Here the coordinates of the given quadrilateral are, A(2,2); B(1,4); C(3,5); D(4,3)
To identify the type of quadrilateral we need to find the distance between the points: Distance formula=[tex]\sqrt{(X-x)^{2}+(Y-y)^{2} }[/tex]
AB=[tex]\sqrt{(1-2)^{2}+(4-2)^{2} }[/tex]
=[tex]\sqrt{5}[/tex]
BC=[tex]\sqrt{(3-1)^{2} +(5-4)^{2} }[/tex]
=[tex]\sqrt{5}[/tex]
CD=[tex]\sqrt{(4-3)^{2} +(3-5)^{2} }[/tex]
=[tex]\sqrt{5}[/tex]
DA=[tex]\sqrt{4-3)^{2} +(3-2)^{2} }[/tex]
=[tex]\sqrt{5}[/tex]
As length of all sides are equal, it can be rhombus or a square.
Now length of diagonals,
AC=[tex]\sqrt{(3-2)^{2} +(5-2)^{2} }[/tex]
=[tex]\sqrt{10}[/tex]
BD=[tex]\sqrt{(4-1)^{2} +(3-4)^{2} }[/tex]
=[tex]\sqrt{10}[/tex]
As the length of diagonals are equal, the given quadrilateral is a square.
Area of square= side x side
=[tex]\sqrt{5}[/tex] x [tex]\sqrt{5}[/tex]
= 5 sq. units
∴The area of carpet to be ordered is 5 sq. units
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Arun has three fraction cards.He puts them in order, starting with the smallest.
-8/9 -29/36 -13/18
Arun says . I think that on a number line -29/36 is exactly halfway between -8/9 and -13/18
Q.a Is arun correct ? explain your answer
Q.b On a number line , work out which fraction is exactly halfway between -1 3/4
and -11/6
Answer: Q.a Arun thinks that -29/36 is exactly halfway between -8/9 and -13/18. We can check if this is true by finding the midpoint between -8/9 and -13/18 and seeing if it equals -29/36.
To find the midpoint between two numbers, we take the average of the two numbers. So the midpoint between -8/9 and -13/18 is:
((-8/9) + (-13/18))/2 = (-16/18 + (-13/18))/2 = -29/36
Since -29/36 is the same as the midpoint, Arun is correct.
Q.b To find the fraction exactly halfway between -1 3/4 and -11/6, we can start by converting the mixed number to an improper fraction:
-1 3/4 = -7/4
-11/6
To find the midpoint between -7/4 and -11/6, we take the average:
((-7/4) + (-11/6))/2 = (-21/12 + (-22/12))/2 = -43/24
Therefore, -43/24 is the fraction exactly halfway between -1 3/4 and -11/6 on the number line.
Step-by-step explanation:
I need help with this
The two streets that are the legs of the Triangle are Streets A and B.
The length of C street can be found to be 3. 61 miles.
If Dan can bike 4 miles in half an hour, then he can make the trip to Sarah's house in 30 minutes.
How to find the length ?The length of C street can be found using the Pythagorean Theorem which is:
Length C ² = Leg A ² + Leg B²
This means the length of C street is:
Length C ² = 2 ² + 3 ²
Length C ² = 13
Length C = √ 13
= 3. 61 miles
This means that Dan can get to Sarah's house in 30 minutes if he is going at 4 miles per half hour.
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