The correct simplification of the expression is 25x^2y^22.
How to calculate the expressionIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
x mn = x ^ m×n = xmn
xm× xn = x m+n
= (5)2(x)^2(y5)^2(y3)^4
= 25x^2y10y^12
= 25x^2y^22
Therefore, the correct simplification of the expression is 25x^2y^22.
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Choose the correct simplification of the expression (5xy5)2(y3)4.
25x2y22, 10x2y22, 25x3y14, 10x3y14
A maintenance worker needs to wax a restaurant floor shaped like the image shown. A six-sided figure. There is a horizontal base of 33 feet then another horizontal base below it of 19 feet. The longest side is to the right and is 37 feet. The top is 28 feet. There is a perpendicular from the vertex of the top to the first base of 33 that is labeled 14 feet. If the wax cost $1.67 a square foot, how much will the wax cost to cover the floor? $832.50 $1,300.10 $1,664.99 $2,600.19
If the wax was priced at $1.67 per square foot, it would cost $1,664.99 to wax the entire floor. The right answer is C.
How to calculate the area of the floor?The floor is made up of a trapezoid and a rectangle.
The area of a trapezoid can be calculated as:
A = (b₁ + b₂)/2 x h
Where b₁ and b₂ are the lengths of the bases and h is the height.
The trapezoid is 14 feet tall, and its bases are 33 feet long and (28 - 19) or 9 feet wide. Thus, its area is:
A = (33 + 9)/2 x 14
A = 294 square feet
The rectangle is 37 feet tall with a 19-foot base. Thus, its area is:
A = 19 x 37
A = 703 square feet
The area of the triangle and trapezoid together make up the overall area of the figure.
A = 294 + 703
A = 997 square feet
Finally, to find the cost of the wax, we multiply the area by the cost per square foot:
Cost = 997 * $1.67
Cost = $1664.99
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If 70% of a number is 224 and 95% of the same number is 304, find 25% of that number.
Using the information given in the problem to set up two equations and by solving them
25% of the number is 80.
What is an equation?An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two parts: the left-hand side and the right-hand side, separated by an equal sign (=). The left-hand side and right-hand side can contain variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.
According to the given informationLet's call the number we're looking for "x". We can use the information given in the problem to set up two equations:
0.7x = 224 (equation 1)
0.95x = 304 (equation 2)
We want to find 25% of the same number, which can be written as 0.25x. We can solve for x using either equation 1 or equation 2 and then plug that value into 0.25x to find the answer.
Let's solve for x using equation 2:
0.95x = 304
x = 304/0.95
x = 320
Now that we know x is 320, we can find 25% of that number:
0.25x = 0.25(320) = 80
So 25% of the number we were looking for is 80.
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To make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. TO make
the recipe taste more like banana, ; cup more banana was added to the blender. The smoothie now has 1.4 cups
of bananas. How many cups of bananas were in the original recipe?
cup
Based on the information, it can be inferred that the original recipe contained 0.9 cups of banana.
How to calculate the original amount of banana contained in the recipe?To calculate the original amount of banana contained in the smoothie recipe we must perform the following mathematical operation:
We know that the final recipe has 1.4 cups of banana and that to make it have a more intense banana flavor they added 1/2 cups of banana, that is, 0.5 cups.
According to the above, we must subtract the amount that was added to the final amount to find how much the recipe has as shown below:
1.4 drinks - 0.5 drinks = 0.9 drinks
According to the above, the original recipe would have 0.9 cups of banana.
Note: This question is incomplete. Here is the complete information:
To make a strawberry banana smoothie, a recipe calls for 1.75L cups of strawberries and some bananas. To make the recipe taste more like banana, 1/2 C cup more banana was added to the blender. The smoothie now has 1.4 cups of bananas. How many cups of bananas were in the original recipe?
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when the temperature is 35°C there are 7 million bacteria. How many millions of bacteria are there when the temperature is 38°C 
The number of millions of bacteria when the temperature is 38°C is 7, 600, 000 bacteria
What is proportion?Proportion can simply be defined as a mathematical comparison of numbers.
The different types of proportion in mathematics are;
Direct ProportionInverse ProportionCompound ProportionContinued ProportionFrom the information given, we have that;
When the temperature was 35 degree Celsius, the number was 7 million
Then, we have the representation given as;
35°C = 7, 000, 000
Then 38°C = x
cross multiply, we get;
x = 7, 000, 000 × 38/35
divide the values
x = 7, 600, 000 bacteria
Hence, the value is 7, 600, 000 bacteria
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on january 28, 1986, space shuttle challenger exploded on takeoff. all seven crew members were killed. following the disaster, scientists and statisticians helped analyze what went wrong. they determined that the failure of o-ring joints in the shuttle's booster rockets was to blame. under the cold conditions that day, experts estimated that the probability that an individual o-ring joint would function properly was 0.977. but there were six of these o-ring joints, and all six had to function properly for the shuttle to launch safely. assuming that o-ring joints succeed or fail independently, find the probability that the shuttle would launch safely under similar conditions. show your work.
The probability of the shuttle launching safely under similar conditions is 0.859, or approximately 86%.
Scientists and statisticians played a crucial role in analyzing the cause of the disaster, which was eventually attributed to the failure of O-ring joints in the shuttle's booster rockets.
To understand the probability of the shuttle launching safely under similar conditions, we need to consider the probability of all six O-ring joints functioning properly. According to experts, the probability of an individual O-ring joint working in cold conditions was 0.977.
Assuming that the O-ring joints succeed or fail independently, we can use the multiplication rule of probability to calculate the probability of all six joints functioning properly.
The multiplication rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the probability of all six joints working properly is:
P(all six joints work) = P(joint 1 works) x P(joint 2 works) x P(joint 3 works) x P(joint 4 works) x P(joint 5 works) x P(joint 6 works)
Plugging in the given probability of an individual O-ring joint working in cold conditions (0.977), we get:
P(all six joints work) = 0.977 x 0.977 x 0.977 x 0.977 x 0.977 x 0.977
P(all six joints work) = 0.977⁶
P(all six joints work) = 0.859
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Please help me by determine the value of the missing angle using the inverse trig function
By applying the Pythagorean theorem to the provided question, we can say that in this triangle =>
AC =[tex]\sqrt{115}[/tex]
What exactly is a triangle?Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.
Pythagorean theorem applies here, in this triangle
AC = [tex]A^2 + B^2[/tex]
AC = [tex]\sqrt{14^2 -9^2}[/tex]
AC = [tex]\sqrt{115}[/tex]
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IM BEING TIMED PLS HURRRYYY
Use factoring to write an expression equivalent to
100x^2-49y^2
SHOW UR WORKKK
The equivalent expression is (10x - 7y)²
What are algebraic expressions?They are defined as expressions that are composed of variables, terms, coefficients, factors and constants.
They are also made up of arithmetic operations.
It is important to note that equivalent expressions are defined as expressions having the same solution but usually differ in the mood of their arrangement.
From the information given, we have that;'
100x^2-49y^2
Find the perfect squares of the values, we have;
(10x - 7y)²
Hence, the expression is (10x - 7y)²
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The quadratic expression 100x² - 49y² is equivalent to (10x - 7y)(10x + 7y)
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
Given the quadratic equation:
100x² - 49y²
Factorizing the polynomial:
100x² + 70xy - 70xy - 49y²
= 10x(10x + 7y) - 7y(10x + 7y)
= (10x - 7y)(10x + 7y)
The expression is equivalent to (10x - 7y)(10x + 7y)
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you could measure arrival delay by recording the amount of time between actual arrival time and scheduled arrival time (with positive numbers representing delays and negative numbers representing early arrivals). is this variable categorical or quantitative? if the variable is quantitative, classify it as discrete or continuous.
It is a continuous variable, as it can take on any value within a certain range (i.e., any value between a positive delay and a negative early arrival).
The variable described is quantitative, as it represents a numerical measurement of time, which is a continuous variable that can take on any value within a certain range. The range includes both positive values, representing delays, and negative values, representing early arrivals. This variable is a useful metric for tracking the performance of transportation systems or airlines, as it provides an objective measure of the amount of time a flight is delayed or arrives early. By analyzing the distribution of arrival delay times, policymakers and transportation providers can identify patterns, trends, and potential areas for improvement in their service delivery.
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While going through some more data from the AP Stats survey, Meghan finds some
interest correlations between student participation in sports and their grades. Of the
students surveyed, 341 played at least one sport and were on honor roll; 121 played
at least one sport but weren't on honor roll; 363 played no sports and weren't on
honor roll; and 275 played no sports and were on honor roll.
Using a two-way frequency table, determine what percentage of respondents play at
least one sport for the school.
Answer: no answer
Step-by-step explanation:
Estimate ∫20(4x2−2x)dx= using a left Reimann Summ and 4 equal subintervals
The left Riemann Sum approximation for the integral of 20(4x² - 2x)dx over the interval [0, 20] with four equal subintervals is 165250.
In calculus, the integral is a mathematical tool that allows us to find the area under a curve. It is an important concept that is used in many fields of science and engineering. One way to estimate the value of an integral is by using a Riemann Sum, which involves dividing the region under the curve into small rectangles and adding up their areas.
In this case, we will be using a left Riemann Sum with four equal subintervals to estimate the integral of 20(4x² - 2x)dx.
To use a left Riemann Sum, we need to first divide the interval of integration into equal subintervals. In this case, we have four subintervals of width
=> (b - a)/n = (20 - 0)/4 = 5.
The left endpoint of each subinterval will be used as the height of the rectangle that represents the area under the curve in that subinterval.
Next, we need to evaluate the function 20(4x² - 2x) at the left endpoints of each subinterval. These values will be used as the heights of the rectangles. The left endpoints are 0, 5, 10, and 15, so we have:
f(0) = 20(4(0)² - 2(0)) = 0
f(5) = 20(4(5)² - 2(5)) = 1900
f(10) = 20(4(10)² - 2(10)) = 7200
f(15) = 20(4(15)² - 2(15)) = 15150
We can now find the area of each rectangle by multiplying its height by its width (5). The total area is the sum of these areas:
(0)(5) + (1900)(5) + (7200)(5) + (15150)(5) = 165250
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ΔLMN ≅ ΔRST, ∠L = 49º, ∠M = 10x, ∠S = 70º, and ∠T = 4y + 9
The measure of ∠R =49, ∠T = 61 , ∠M = 70 , ∠N = 61, x = 7 and y = 13.
What are Congruent triangles?
When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent.
Given, ΔLMN ≅ ΔRST,
So, ∠L = ∠R = 49
∠M = ∠S = 70
∠N = ∠T = 4y + 9
Now, In triangle RST,
∠R + ∠S + ∠T = 180 ( sum of all angles of a triangle is 180 )
49 + 70 + ∠T = 180
∴ ∠T = 61 = ∠N
and, 4y + 9 = 61
y = 13.
Now, In triangle LMN ,
∠L + ∠M + ∠N = 180
49 + 10x + 61 = 180
10x = 70
x = 7
∴ ∠M = 70.
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2. Order the following decimals from least to greatest.
0.439
0.394
0.441
0.531
0.342
The local ferry takes cars across a bay. One day, the ferry transported a total of 610 cars over a 5 -hour period. The ferry took the same number of cars each hour. How many cars did it take each hour? Complete the bar diagram to help.
___ cars
c
c
c
c
___________
c
Answer:122 cars per hour
Step-by-step explanation:Get the total number of cars 610 get the time period 5 hours divide 610 divided by 5 equals 122 cars per hour.
Answer: the ferry took atleast 3,050 cars each hour
how do you know how adding a smaller data point will affect the mean or median if its smaller than them
When the smaller data point is included, the mean will drop when compared to the other values, but the median may increase or decrease depending on whether the collection of numbers is even or odd.
1. Calculate the original set of numbers' mean and median.
2. Include the lesser data point in the collection.
3. Determine the updated median and mean.
4. Evaluate the original mean and median in comparison to the new mean and median. Depending on whether the collection of numbers is even or odd, the median will decline while the mean will increase.
We must first determine the mean and median of the initial set of data in order to evaluate how the addition of a smaller data point will impact those values. Adding together all the values and dividing by the total number of values yields the mean. We place the middle value in the set of integers after sorting them from least to largest to determine the median. We include the new, smaller data point in the set after finding the mean and median. We next perform the same calculations as previously to determine the new mean and median. Finally, we contrast the updated mean and median with the baseline values. The median may stay the same or drop depending on whether the set of numbers is even or odd, while the mean often decreases as it is compared to other values. The mean and median of a set of numbers can therefore be significantly affected by the addition of a tiny data point.
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The complete question is
how do you know how adding a smaller data point will affect the mean or median if its smaller than them other value.
How you would solve a problem with variables on both sides of the equation?
Answer:
im him
Step-by-step explanation:
shawna knows that a correlation between calories of sweeteners consumed and mortality rates among women does not, in itself, mean that drinking more soft drinks will lead to a higher chance of her dying. which of the following would not be a lurking variable in the above scenario? a.) shawna's weight b.) the time of day shawna exercises c.) the number of soft drink brands available for purchase d.) the amount of caffeine available in soft drinks
Answer: Musical preferences
A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely your musical preferences affect mortality or how much sweetener you consume.
The number of soft drink brands available for purchase is not a lurking variable in this scenario. Correct option is C.
The statement is asking which of the given variables is not a lurking variable in the scenario where Shawna is considering the correlation between the calories of sweeteners consumed and the mortality rates among women, and is trying to determine whether drinking more soft drinks will lead to a higher chance of her dying.
A lurking variable is a variable that is not included in the analysis, but has an effect on the relationship between the variables being studied. In this case, the variables being studied are the calories of sweeteners consumed and the mortality rates among women, and the effect of drinking more soft drinks on the chances of dying.
Out of the given variables, the number of soft drink brands available for purchase would not be a lurking variable, as it does not have an effect on the relationship being studied.
Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could all potentially have an effect on the relationship being studied, either as confounding variables or moderators.
For example, Shawna's weight could be a confounding variable, as it is associated with both sweetener consumption and mortality rates. The time of day she exercises could be a moderator, as exercise may affect the metabolism of sweeteners and caffeine, which could in turn affect mortality rates.
The amount of caffeine available in soft drinks could be a confounding variable, as caffeine consumption is associated with both sweetener consumption and mortality rates.
In summary, the number of soft drink brands available for purchase is not a lurking variable in this scenario, while Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could potentially be confounding variables or moderators that need to be accounted for in the analysis.
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What information is in the text but not in the graph?
Answer:
B. More money was given than expected in 1994
Step-by-step explanation:
Nowhere is it mentioned what amount was expected as donations. Only actual amounts received are shown on the graph
Hence this is an assumption and not necessarily fact
Ethan is planning for his retirement. He has narrowed it down to two investment options. The first is an IRA where monthly payments are made, in the amount of $416.66, for 30 years. The second is a Roth IRA where annual payments are made, in the amount of $5000, for 30 years. If both compound interest at a rate of 2.5%, determine which account will yield the largest future value for Ethan, and how much greater that value will be than that of the other account. Round your final answer to the nearest cent.
The Roth IRA will provide Ethan with the most future benefit, with the IRA valued at $195,902.08 and the Roth at $211,633.75. The difference in the future value of the two accounts is $15,731.67.
What is an investment?A purchase made with the intention of creating income or capital growth is known as an investment. An asset's value increasing over time is referred to as appreciation. When a person invests in a thing, they do not intend to utilise it as a source of immediate consumption, but rather as a tool for future economic growth.
The Roth IRA will provide Ethan with the most future benefit. The IRA will be valued $195,902.08 after 30 years, while the Roth IRA will be worth $211,633.75. As a result, the Roth IRA is valued $15,731.67 more than the IRA.
To determine the IRA's future value, use the formula FV = P(1+r)n, where P is the monthly payment, r is the interest rate, and n is the number of periods (in this case, 30 years). With our data in, we get: FV = 416.66(1+0.025)30 = $195,902.08.
We may apply the same approach to compute the future value of the Roth IRA, but with a $5,000 yearly payout. With our values in, we get: FV = 5000(1+0.025)30 = $211,633.75.
The difference in the future value of the two accounts is $15,731.67, which is the amount that the Roth IRA will be worth more than the IRA.
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two messenger services deliver to a small town. service a has 75% of all the scheduled deliveries, and service b has the remaining 25%. their on-time rates are 80% and 60% respectively. calculate the probability that a package is delivered on time.
Service a has 75% of all the scheduled deliveries, and service b has the remaining 25%, their on-time rates are 80% and 60% respectively, the probability that a package is delivered on time is 0.75 or 75%.
To calculate the probability that a package is delivered on time, we need to use the law of total probability and the probabilities of on-time delivery for each messenger service.
Let A denote the event that a package is delivered by Service A, and B denote the event that a package is delivered by Service B. Then, we have:
P(on-time delivery) = P(on-time delivery | A) * P(A) + P(on-time delivery | B) * P(B)
where P(on-time delivery | A) is the probability that a package is delivered on time given that it was sent through Service A, and P(A) is the probability that a package is sent through Service A.
Similarly, P(on-time delivery | B) is the probability that a package is delivered on time given that it was sent through Service B, and P(B) is the probability that a package is sent through Service B.
From the information given in the question, we know that P(A) = 0.75, P(B) = 0.25, P(on-time delivery | A) = 0.8, and P(on-time delivery | B) = 0.6. Substituting these values into the above formula, we get:
P(on-time delivery) = 0.8 * 0.75 + 0.6 * 0.25
= 0.6 + 0.15
= 0.75
Intuitively, this result makes sense because Service A, which has a higher on-time rate and delivers 75% of the packages, dominates the total probability of on-time delivery. However, the contribution of Service B cannot be ignored completely and reduces the overall on-time rate slightly.
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The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool
Answer:
Step-by-step explanation:
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The actual distance between the basketball court and the pool is 37.5 feet
Distance refers to the amount of space between two objects or points. It is a measure of how far apart two things are from each other.
The scale of the model is 3 inches = 5 feet. This means that every 3 inches on the model represents 5 feet in actual size. We are given that the distance between the basketball court and the pool on the model is 22.5 inches. To find the actual distance between these areas, we need to use the scale.
We can start by setting up a proportion using the scale. We know that 3 inches on the model represents 5 feet in actual size. Therefore, we can say that:
3 inches / 5 feet = 22.5 inches / x
We are trying to solve for x, which represents the actual distance between the basketball court and the pool. To solve for x, we can cross-multiply and simplify the equation:
3 inches x x = 5 feet x 22.5 inches
3x = 112.5
x = 37.5 feet
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Complete Question:
The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool?
Rewrite in simplest radical form
The simplest radical form is x⁵.
What is radical form?Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.
The given radical form is [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex].
The radical and root of a number are the same thing.
Simplifying a radical eliminates the square roots, cube roots, fourth roots, etc.
In the given expression, 1/6 is the 6th root, in both numerator and denominator cancel out 6th root x.
That is, [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex] =x⁵ ([tex]x^{\frac{1}{6} }[/tex] in the denominator is gets cancelled with [tex]x^{\frac{1}{6} }[/tex] in the numerator)
Therefore, the simplest radical form is x⁵.
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what is the cost of fencing a circular garden of radius 28 with five rounds of wire if the wire cost Rupees 50 per metre.
Answer:
7,000 Rupees
Step-by-step explanation:
3. A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150
yards from the center of the green. Whilestanding on the marker facing the green, the golfer turns
110 toward his ball. He then paces off 35 yards to hit his ball. See figure. How far is the ball from the
center of the green? Round to the nearest yard
We can use the Pythagorean theorem to solve this problem. Let's call the distance from the ball to the center of the green "d". We know that the marker is 150 yards from the center of the green, and the golfer has paced off 35 yards in a direction 110 degrees from the marker.
Let's use x to represent the horizontal distance from the marker to the ball, and y to represent the vertical distance from the marker to the ball. Then, we have:
x = 35 * cos(110)
y = 35 * sin(110)
Using the Pythagorean theorem, we can find the distance "d" from the ball to the center of the green:
d^2 = x^2 + (y + 150)^2
Plugging in the values for x and y, we get:
d^2 = 35^2 * cos(110)^2 + (35 * sin(110) + 150)^2
d^2 = 1225 + (150 + 35 * sin(110))^2
Using a calculator, we can find that sin(110) = 0.939, so:
d^2 = 1225 + (150 + 31.65)^2
d^2 = 1225 + (181.65)^2
d^2 = 1225 + 32762.7225
Taking the square root of both sides:
d = sqrt(1225 + 32762.7225)
d = sqrt(33987.7225)
d = 183.83
Rounding to the nearest yard:
d = 184 yards
So, the ball is 184 yards from the center of the green.
a rectangular piece of cardbord of dimensions 42 cm multiplaced by 32 is used to make a box.squares of size 6 x 6cm are cut out from all four corners.the remaining portion is folder to make a box.the inner surface of the box are painted.find the total area of the painting surfaces
The area of the rectangular piece to be painted after cutting will be 1200 cm².
What is the definition of a rectangle?
Rectangles are four-sided polygons with 90-degree internal angles. Two sides meet at right angles at each corner or vertex. The rectangle is distinguished from the square by the fact that its opposite sides are of equal length.
If one side of a rectangle is 20 cm long, the opposite side is also 20 cm long.
A rectangle has two intersecting diagonals. The length of both diagonals is the same.
The perimeter is defined as P = 2 (Length + Width).
Area of a Rectangle=Length*Breadth
Now,
Length of cardboard=42cm
breadth=32 cm
Area of cardboard=42*32=1344cm²
Area of square to be cut=6*6=36cm²
and total 4 squares are cut
Then the area of the box that is made to be painted is =1344*4*36
=1200 cm²
hence,
The area of the rectangular piece to be painted after cutting will be 1200 cm².
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9. Si a=1/2, b=1/3, entonces
a) 1/2
b) 6/5
a+b
es igual a:
c) 1/6
d) 6
Answer:
5/6 (No option is suitable)
Step-by-step explanation:
Given information,
→ a = 1/2
→ b = 1/3
We have to find,
→ a + b
Let's solve the problem,
→ (1/2) + (1/3)
→ (3/6) + (2/6)
→ (3 + 2)/6
→ 5/6
Hence, the answer is 5/6.
Robin rides her bike 3 miles to school. She rides home a different way that is 4 miles long. This week, Robin rode to school and back 5 times.
Robin ride her bike this week 35 miles.
Robin rides her bike 3 miles to school.
She rides home a different way that is 4 miles long.
This week, Robin rode to school and back 5 times.
For one time ride to school from house = Rode to School + Rode To home
For one time ride to school from house = 3 + 4
For one time ride to school from house = 7
Robin rides total of 5 times.
So, For five time ride to school from house = 5 × For one time ride to school from house
For five time ride to school from house = 5 × 7
For five time ride to school from house = 35 miles
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The complete question is:
Robin rides her bike 3 miles to school. She rides home a different way that is 4 miles long. This week, Robin rode to school and back 5 times. How many miles did Robin ride her bike this week?
6. there are many cones with a volume of cubic inches. the height in inches of one of these cones is a function of its radius in inches where . a. what is the height of one of these cones if its radius is 2 inches? b. what is the height of one of these cones if its radius is 3 inches? c. what is the height of one of these cones if its radius is 6 inches?
In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.
[tex]\text{Height } = h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]
The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone.
If we rearrange this formula to solve for h, we get h = 3V / (πr²). This means that the height of a cone is directly proportional to the volume and inversely proportional to the square of the radius.
a. If the radius of a cone is 2 inches and its volume is given, we can find its height by plugging in the values of V and r into the formula for h.
[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]
b. Similarly, if the radius is 3 inches, the height would be:
[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (3^2)} = \frac{3V}{9\pi}[/tex]
c. If the radius is 6 inches, the height would be:
[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (6^2)} = \frac{3V}{36\pi}[/tex]
In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.
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Lavonne sold 4 times as many raffle tickets as Kenneth. Lavonne sold 56 raffle tickets. Write an equation with a variable and solve the equation to find how many tickets Kenneth sold
Equation: 4x = 56
Answer: 14 tickets
Step-by-step explanation:
4x = 56
Lavonne's tickets sold 4 times as many as Kenneth's. This means we would need to multiply Kennneth's ticket by 4 to equal Lavonne's.
4x/4 = 56/4
Now you need to solve the equation by isolating x. Here you have to divide both sides by 4.
x = 14
Kenneth sold 14 tickets.
4(14) = 56
A piece of sheet metal has dimensions 3 3/4ft x 4 2/3ft. What is the area in square inches?
amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Step-by-step explanation:
The time difference between 1:25 and 1:50 is 25 min
