The estimate of 5/8 - 1/10 is 0.5, which is option B.
What is division in mathematics?
In mathematics, division is an arithmetic operation that is used to split a quantity into equal parts or to find the number of times one quantity is contained within another quantity. It is the inverse operation of multiplication, and is represented by the symbol "÷" or "/".
To estimate 5/8 - 1/10, we can round 5/8 to the nearest tenth, which is 0.6, and round 1/10 to the nearest tenth, which is 0.1. Then we can subtract them to get an estimate of the difference:
5/8 - 1/10 ≈ 0.6 - 0.1 = 0.5
Hence, the estimate of 5/8 - 1/10 is 0.5, which is option B.
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Brianna practices the piano 595 minutes in 5 weeks. At what rate did she practice, in minutes per day?
She practiced with a rate/speed of 17 min/day.
What is the definition of speed?
The following is the definition of speed:
The rate at which the position of an item changes in any direction.
The ratio of distance travelled to time spent travelling is described as speed. Speed is a scalar number since it has just one direction and no magnitude.
Formula for Speed
The speed formula is as follows:
s=d/t
Where,
s denotes the speed in metres per second, d the distance travelled in metres, and t the time in seconds.
Now,
Given Total time she practiced=595 minutes
Total time she practiced=5 weeks=5*7
=35 days
then rate at which she practiced per day=595/35
=17 min/day
hence,
Brianna practiced with a rate of 17 min/day.
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The sum of the digits of an odd 2 digit number is 17 what is the number
Answer:
x+y=17
y can be 1,3,5,7 or 9
Let's start at 9
x+9=17
x=8
So the burner is 89
7, 5, 3 and 1 don't work
For example In order x+7=17, x should be 10, which is a contradiction; x is the one-digit number. If 7 doesn't work, lower numbers shouldn't work as well.
Step-by-step explanation:
The scooter is being sold at a 10% discount. The original price is shown. Which methods can you use to find the new
sale price? Which method do you prefer? Explain.
Multiply $42.00 by 0.9.
Multiply $42.00 by 0.9,
then add to $42.00.
Multiply $42.00 by 0.1,
then subtract from $42.00.
Multiply $42.00 by 0.9,
then subtract from $42.00.
The preferred method to know the price of the scooter is
Multiply $42.00 by 0.9.How to find the sale priceThe question is a percentage problem
10%
= 10 percent
= 10 / 100
= 0.1
Since the problem is about discount of 10 % .
= 1 - 0.1
= 0.9
The sale price using the factor of 0.9
= $42 * 0.9
This method is more straight forward and gives the correct answer
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What is the longest increasing subsequence problem in dynamic programming?
The Longest Increasing Subsequence (LIS) problem is a classic problem in dynamic programming. Given a sequence of numbers, the problem is to find the longest subsequence in which the numbers are in increasing order. For example, given the sequence {3, 1, 5, 2, 4}, the longest increasing subsequence is {1, 2, 4}, which has length 3.
The LIS problem can be solved using dynamic programming by defining an array to store the length of the longest increasing subsequence that ends at each position in the sequence. The array is initialized to 1, and then for each position i in the sequence, the length of the longest increasing subsequence that ends at i is calculated by finding the maximum length of any subsequence that ends at a position j < i and has a smaller value than the value at i. The final solution is the maximum length of any subsequence in the array.
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the probability that a continuous random variable equals any of its values is called?
The probability that a continuous random variable equals any of its values is called Continuous probability distribution.
Continuous probability distribution:
A probability distribution in which the random variable X can take on any value (which is continuous). Since there are infinitely many possible values for X, the probability that X takes on any particular value is zero. So we often talk about a range of values [p(X >0] = 0.50).
An absolutely continuous probability distribution is a probability distribution of real numbers with an uncountable set of possible values, such as the full interval of a solid line, where the probability of any event can be expressed as an integral. More precisely, there exists a function f: R − [0, so that for each interval[ 0,∞] ⊂ R, the probability that X belongs to [a, b] is given by the integral of f over I.
[tex]P(a\leq X\leq b) = \int\limits^a_b {f(x)} \, dx[/tex]
Since this is the definition of a probability density function, an absolutely continuous probability distribution is exactly equivalent to a probability density function. In particular, the probability that X takes any single value a (i.e. a≤X≤b) is zero because integrals with the same upper and lower bounds are always zero. If the interval [a, b] is replaced by the measurable set A, then the equivalence remains valid.
P(X ∈ A) = [tex]\int\limits^a_b {f(x)} \, dx[/tex]
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What are the answers to 15,16,17 and 18 ????
The missing sides of each pair of similar triangles are listed below:
Case 15: w = 5, x = 25 / 12, y = 65 / 12, z = 169 / 12
Case 16: x = 12, y = 6√3, z = 3√5
Case 17: x = 40 / 3, y = 32 / 3
Case 18: x = 5, y = 20, z = 10√3
How to find the values associated to system of similar triangles
In this problem we find four cases of pairs of similar triangles, whose missing sides can be found by means of proportion formulas and Pythagorean theorem. Now we proceed to determine the missing lengths for each length:
Case 15
w = √(13² - 12²)
w = 5
12 / w = w / x
w² = 12 · x
x = w² / 12
x = 5² / 12
x = 25 / 12
y = √[(25 / 12)² + 5²]
y = 65 / 12
z = 12 + x
z = 169 / 12
Case 16
6 / 3 = x / 6
x = 36 / 3
x = 12
y = √(x² - 6²)
y = √(12² - 6²)
y = 6√3
z = √(3² + 6²)
z = 3√5
Case 17
y / 8 = 8 / 6
y = 8² / 6
y = 64 / 6
y = 32 / 3
x = √(8² + y²)
x = √[8² + (32 / 3)²]
x = 40 / 3
Case 18
x = √[10² - (5√3)²]
x = 5
y = x + 15
y = 20
z = √[15² + (5√3)²]
z = 10√3
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Please help. I know it’s long but I will literally do anything. Please
The slope and y - intercept of the line of best fit are 1.22 and -0.09 respectively.
What is the slope of the line of best fita.
To fill the table of the residuals, we can approach it as;
residual = food waste - number of people.
3.2 - 2 = 1.4
2.5 - 3 = -0.5
8.9 - 4 = 49
4.7 - 4 = 0.7
3.5 - 4 = -0.5
4 - 4 = 0
5.3 - 5 = 0.3
4.6 - 5 = -0.4
7.8 - 5 = 2.8
3.2 - 6 = -2.8
12 - 8 = 4
b.
The equation is given as;
y = 1.22x - 0.09
The slope of the line of best fit is 1.22
c.
The y - intercept is given as -0.99
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what is 5'2 in meters?
AS per the measurement, the value of 5'2 in meters is 1.5748 meters.
One common unit of measurement is the foot, which is often used to measure height. However, in some scientific fields, the meter is the preferred unit of measurement.
To convert 5'2 into meters, we first need to understand the relationship between feet and meters. One foot is equal to 0.3048 meters, which means that we can convert 5 feet to meters by multiplying 5 by 0.3048. This gives us 1.524 meters.
But what about the additional 2 inches? We can convert inches to meters by dividing the number of inches by 39.37 (the number of inches in a meter). In this case, 2 inches divided by 39.37 equals 0.0508 meters.
To get the total measurement in meters, we simply add the two values: 1.524 + 0.0508 = 1.5748 meters.
Therefore, 5'2 is equivalent to 1.5748 meters.
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Help please look at the pic and answer
Answer:
1 and 1/4 (1.25)
Step-by-step explanation:
So imagine you have 2 pizzas. Your friend wants to bring one home. Your pizzas are both in two pieces, and your friend wants to take one whole pizza and a half of the second one. In the first graph, that friend takes
1 and 1/2 (1/2 meaning one half) or 1.5 (.5 being half)
To get the fraction for one half you have to think:
- How many slices are there in each pizza?
- How can I make this a fraction?
- If it says “1” for a whole pizza how much is half going to be?
If there are 2 parts to one pizza, and only 1 of the 2 parts are taken, it is considered 1/2.
Another way you show “1/2” is by putting “.5 (0.5)” at the end of a number. You can find “.5” by doing “1 ÷ 2”
You divide one and two because there is 1 pizza and 2 parts of it.
Now that you know how to figure out the first one, the second one should be easy!
But.. for some reason, the “1/2 (.5)” that we got earlier of the second pizza is cut in half!
You can see that they took one full pizza, and half of “1/2” of a pizza!
There are two simple ways to find out what number “half of a half of a pizza” is!
For the first, you can count the blocks!
In this case, there are 4 blocks (4 slices), in a pizza. One pizza has all 4 blocks filled, meaning one whole pizza is taken by your friend, and only 1 block is filled in on the second pizza! You can say, for the second pizza, that your friend took “1/4” of a pizza.
You get this by seeing that out of 4 blocks that could be filled, only 1 is!
Which gives you the answer “1/4 (0.25)”
Or you could divide!
If you look you can see there are 2 parts where “1/2” was. If you want to find what half of “1/2” is, you could write the equation:
“1/2 ÷ 2”
The answer you get is also “1/4 (0.25)”
You divide “1/2” and “2” because you want to find what one of 2 parts of 1/2 is.
Now that you know that there is one full pizza and 1/4 of a pizza, your final answer comes out to be 1 and 1/4 (1.25) because you combine the two answers together.
help pls
The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
What is the value of the upper quartile?
52
53
54
56
The upper quartile of the data set is, 56.
What is mean by Addition?The process for combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
The values of 42, 44, 50, 54, and 56 are all marked by the box plot.
Hence, The value of upper quartile is,
⇒ Upper quartile = 3/4 (n + 1)
Where, n is number of terms.
Hence, We get;
⇒ Upper quartile = 3/4 (5 + 1)
= 3/4 × 6
= 4.5
≈ 5th term
Thus, The value of Upper quartile = 56
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Find the value of the variable (s)
The value of x in the right triangle is 8.7 units.
How to find the angles of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The side of a right angle triangle can be found using trigonometric ratios or Pythagoras's theorem.
Hence, let's use Pythagoras's theorem,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
x² = 10² - 5²
x² = 100 - 25
x = √75
x = 8.66025403784
Therefore,
x = 8.7 units
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Please help asap! 10 points!!!
Answer: 2 inches of rain
Step-by-step explanation:
Since Monday has rainfall of 0.50 inches and Tuesday 0.25, we can use this information to solve the final question. Since it rained on Monday the amount of it in three days, we can multiply 0.5 by 3 and get 1.5. For Tuesday it was 2 days so we can multiply 0.25 by 2 and get 0.5. Add them up and you get 2. Put the unit in inches.
What are the three first common denominators of 7/9 and 2/3
From the given information provided, the first three common denominators of 7/9 and 2/3 are 9, 18, and 27.
To find the common denominators of 7/9 and 2/3, we need to find the least common multiple (LCM) of their denominators.
The prime factorization of 9 is 3 x 3, and the prime factorization of 3 is 3.
The prime factorization of 2 is 2, and the prime factorization of 3 is 3.
The common factors are 3, so the LCM of 9 and 3 is 9.
Therefore, the common denominator of 7/9 and 2/3 is 9.
To find the next two common denominators, we can continue to find the LCM of the denominators with the added factor of 9.
The prime factorization of 18 (2 x 3 x 3) includes the prime factors of 9, so it is a common denominator.
The prime factorization of 27 (3 x 3 x 3) also includes the prime factors of 9, so it is another common denominator.
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I really really need help on this
The inequalities representing the two lines are y ≤ 3x + 8 and y < - 2x - 8.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The two lines can be obtained by identifying the points.
(0, - 8) and (1, - 10) are the points of the non-dotted line.
So, m = (- 10 + 8)/(1 - 0).
m = - 2.
Now, - 8 = 0(-2) + b.
b = - 8.
y = - 2x - 8.
The points for the dotted line are, (0, 8) and (1, 11).
m = (11 - 8)/(1 - 0).
m = 3
8 = 3(0) + b.
b = 8.
y = 3x + 8.
The dotted line is y ≤ 3x + 8 and the non-dotted line is y < - 2x - 8.
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q es un diagrama circular
A circular diagram is a pie chart.
What is a pie chart?A pie chart is a circular statistical graph used to display data.
The chart is divided into slices, with each slice representing a category or proportion of the data.
Pie charts are commonly used to show percentages or fractions of a whole.
We have,
A circular diagram.
A circular diagram is commonly referred to as a pie chart.
It is a type of graph that represents data in a circular format, with each section of the chart representing a different category or value.
The size of each section is proportional to the value it represents, and the total sum of all sections is equal to 100%.
Example:
From the pie chart,
The total color is 100.
The number of each color.
Green = 25/100 x 100 = 25
Blue = 35/100 x 100 = 35
Red = 10/100 x 100 = 10
White = 15/100 x 100 = 15
Orange = 15/10 x 100 = 15
Thus,
A circular diagram is a pie chart.
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The complete question in Englsih.
What is a circular diagram.
if the matrix M is a linear combination of the matrices Mi, M2 and M3:M = [2 3 ] [1 2 ]M1 = [ 2 2 ][ 1 1 ] M2 = [ -1 1 ][ 2 1 ]M3 = [ 1 2 ] [ 3 1 ]if so, determine scalars c1, c2, c3 such that c1M1 + c2M2 +C2M3 = M.
The scalars c1 = 2/5, c2 = -3/5, and c3 = -8/5 satisfy the equation:
c1M1 + c2M2 + c3M3 = [ 2 3 ][ 1 2 ]
We want to find the scalars c1, c2, and c3 such that:
c1M1 + c2M2 + c3M3 = M
Substituting the given matrices:
c1[ 2 2 ] c2[ -1 1 ] c3[ 1 2 ] [ 2 3 ]
[ 1 1 ] [ 2 1 ] [ 3 1 ] [ 1 2 ]
Multiplying each scalar by its corresponding matrix:
[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ]
[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ]
Setting the result equal to M:
[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ] = [ 2 3 ]
[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ] [ 1 2 ]
This gives us two equations:
2c1 - c2 + c3 = 2
2c1 + 2c2 + 3c3 = 3
c1 + 2c2 + 3c3 = 1
c1 + c2 + 2c3 = 2
We can solve this system of equations using any method we prefer, such as elimination or substitution. Here, we will use elimination.
Subtracting the first equation from the second, we get:
3c2 + 4c3 = 1
Subtracting the third equation from fourth, we get:
c2 - c3 = 1
Multiplying second equation by 2, we get:
4c1 + 4c2 + 6c3 = 6
Subtracting first equation from this, we get:
5c2 + 5c3 = 4
Now we have three equations for c2 and c3:
3c2 + 4c3 = 1
c2 - c3 = 1
5c2 + 5c3 = 4
Solving for c2 and c3 using elimination, we get:
c2 = -3/5
c3 = -8/5
Substituting these values into the third equation, we get:
c1 = 2/5
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he scatterplot provided shows the gestations periods and life expectancies for several animal species. The plot contains two points that may be of concern. The point in the upper right corner of this scatterplot is for elephants, and the other point at the far right is for hippos.
a) By removing one of these points, we could make the association appear to be stronger. Which point? Explain.
b) Would the slope of the line increase or decrease?
c) Should we just keep removing animals to increase the strength of the model? Explain.
d) The slope of the scatterplot's regression line is 15.5. If we remove elephants from the scatterplot, the slope of the regression line becomes 11.6 days per year. Do you think elephants were an influential point? Explain.
Points for Elephant powerful. When we remove the point for elephant, the slope line will drop, and we shouldn't just keep eliminating animals.
a) The link between gestation lengths and life expectancies would seem larger if the point for elephants in the scatterplot's upper right corner were removed. This is due to the elephant data point's status as an outlier, which means that it differs significantly from the scatterplot's other points and can significantly affect the regression line.
b) If the elephant point is eliminated, the slope of the line will decrease. This is due to the elephant point's long gestation time and long life span, which contribute to the regression line's greater slope.
c) No, we shouldn't keep eliminating creatures to make the model more robust. While the strength of the link between the variables can be strengthened by deleting outliers like the elephant point, it's critical to remember that each data point reflects a genuine observation.
d) Elephants undoubtedly had some influence. The elephant point had a considerable impact on the link between gestation times and life expectancies, as shown by the fact that deleting it resulted in a reduction in the slope of the regression line.
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in a party, 10 soft drinks are required for every 12 guests. If there are 252 guests, how many soft drinks are required?
Answer:
To find your answer, you will divide 252 by 123, and then multiply it by 10:
252 / 12 = 21
21 * 10 = 210
210 soft drinks are required.
Step-by-step explanation:
Hope it helps! =D
The sum of the angle measures of a polygon with n sides is given. Find n.
For sum of all angles of polygon=900°, no. of sides will be 7.
What exactly is a polygon?
Polygons are two-dimensional geometric objects that have the same number of sides on all sides. The sides of a polygon are made up of straight line segments linked end to end. As a result, the line segments of a polygon are referred to as sides or edges. The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result. A triangle of a polygon. A circle is a planar figure, however it is not regarded a polygon since it is curved and lacks sides and angles. As a result, we may argue that all polygons are 2d forms, but not all two-dimensional figures are polygons.
For a polygon with n no. of sides
sum of all interior angles=(n-2)*180°
Now,
As given the sum of all angles=900°
then number of sides of a polygon will be
(n-2)*180=900
n-2=5
n=7
Hence,
For sum of all angles of polygon=900°, no. of sides will be 7.
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where are the most densely populated areas of japan with over 1000 people per kilometer?
Furthermore, Tokyo Metropolis had the highest population density among Japan's prefectures, with 6,402.6 people per square kilometer. This one was nearly 18.9 times greater than that of the state median (338.2 persons per square kilometer). In 2020, Japan had 12 cities with an inhabitants of one thousand or maybe more.
What is the world's biggest and densetly populated Japanese island?
It is home to approximately 104 million people (2010), or more than 80% of the Japanese population. Honshu is the most highly populated island (429 people per km2) along with the most economically prosperous nation on the island.
Which two towns are situated in Japan's most densely populated areas?
Osaka, Kobe, and Kyoto make up Japan's most highly populated region, with each capital of a prefecture. This region is commonly referred to as the Kansai region.
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y=20(1+0.025)^x growth or decay
The given function[tex]Y=20(1+0.025)^x[/tex] is an exponential gr.
What is an exponential function?
An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is the input variable. These functions are commonly used to model situations that involve continuous growth or decay.
In the given example you provided[tex]Y=20(1+0.025)^x[/tex] represents growth because the base of the exponential term, 1+0.025, is greater than 1. As x increases, the exponential term gets larger and the value of y increases, which indicates growth.
Hence, the given function,[tex]Y=20(1+0.025)^x[/tex] is exponential growth.
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Write the solution set of the given homogeneous system in parametric vector form.3x1+3x2+6x3=0−6x1−6x2−12x3=0−4x2+4x3=03x1+3x2+6x3=0−6x1−6x2−12x3=0−4x2+4x3=0 where the solution set is x=⎡⎢⎣x1x2x3⎤⎥⎦x=[x1x2x3]
The solution set of the given homogeneous system in parametric vector form is x = (0, 0, t), where t is a real number
Vectors are an important mathematical tool for representing complex data and equations. In this problem, we are given a homogeneous system of equations and asked to write the solution set in parametric vector form.
The homogeneous system consists of three equations: 3x₁ + 3x₂ + 6x₃ = 0, -6x₁ - 6x₂ - 12x₃ = 0, and -4x₂ + 4x₃ = 0. To solve this system, we need to use linear algebra techniques, such as Gaussian elimination, to find the solution set.
By using Gaussian elimination, we can reduce the system to a simpler system, which has the form x₁ = 0, x₂ = 0, and x₃ = t, where t is a real number. This can be written as a parametric vector form as x = (0, 0, t).
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what is the mean value of the following scores: 12, 25, 15, 27, 32, 8?
The mean value of the scores is 19.83, based on their sum and quantity of numbers.
The mean or average is calculated using the formula -
Mean = sum of all the numbers ÷ quantity of numbers.
We see that there are six numbers and hence the quantity of numbers will be 6.
Sum of all the numbers = 12 + 25 + 15 + 27 + 32 + 8
Performing addition on Right Hand Side of the equation
Sum of all the numbers = 119
Now calculating the mean of the scores by keeping the values in formula -
Mean = 119/6
Performing division on Right Hand Side of the equation
Mean of scores = 19.83
Hence, the average of scores is 19.83.
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What is 6 ft 6 ft in inches?
We converted the measurement of 6 ft x 6 ft to inches using a conversion factor of 12 inches per foot, resulting in a total area of 5,184 square inches.
Measurement is an important aspect of our daily lives, and it involves quantifying the size, length, or dimensions of an object or space. Different units of measurement are used to express the size or length of an object, depending on the context or purpose.
The measurement of 6 ft x 6 ft is the size or area of a square-shaped object, where each side is 6 ft long. To convert this measurement to inches, we need to use a conversion factor that relates feet to inches. One foot is equal to 12 inches, so we can multiply each side of the square by 12 to get the corresponding measurement in inches.
6 ft x 12 inches/ft = 72 inches
Therefore, the measurement of 6 ft x 6 ft in inches is 72 inches x 72 inches, which equals 5,184 square inches. This means that if we had a square-shaped object with sides measuring 6 feet, the total area of the object would be 5,184 square inches.
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Write the logarithmic expression as a single logarithm.
1/2(log₂x + log ₂y) - 5 log ₂(x+6)
Answer:
We can use the following logarithmic identities to simplify the expression:
log a + log b = log (ab)
log a - log b = log (a/b)
n log a = log (a^n)
Using these identities, we can simplify the expression as follows:
1/2(log₂x + log₂y) - 5 log₂(x+6)
= 1/2 log₂(xy) - log₂(x+6)^5 (using the first two identities)
= log₂[(xy)^(1/2)/(x+6)^5] (using the third identity to combine the logarithms)
Therefore, the simplified expression is:
log₂[(xy)^(1/2)/(x+6)^5]
Step-by-step explanation:
your friend bought a new pair of shoes. He said the regular price was 75$ but that he got them for a 40% discount. What is the sale price of the shoes?
The sale price of the shoes is $45.
Your friend bought a new pair of shoes that had a regular price of $75. The regular price is the original or full price of the item before any discounts or promotions are applied.
Your friend said that he got a 40% discount on the shoes. A discount is a reduction in price from the regular price, often as a promotion or incentive to encourage customers to purchase the item. In this case, the discount is 40% of the regular price.
To calculate the sale price of the shoes, we need to subtract the discount amount from the regular price. The discount amount is 40% of $75, which is:
Discount amount = 40% x $75
Discount amount = $30
Now, we can find the sale price by subtracting the discount amount from the regular price:
Sale price = Regular price - Discount amount
Sale price = $75 - $30
Sale price = $45
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Find the area of the surface generated when the given curve is revolved about the given axis. y=1/16(e^8x+e^−8x),
for
−3≤x≤3;
about the x-axis The surface area is
square units.
In this problem, the lower limit of integral is -3 and the upper limit of integration is 3.
We can use the formula for the surface area of a solid of revolution generated by a curve revolving around a given axis. The formula is S = 2π ∫ a b y dx, where a and b are the lower and upper limits of integration, and y is the height of the curve at x. In this problem, the lower limit of integration is -3 and the upper limit of integration is 3. Substituting y = 1/16(e^8x + e^-8x) into the equation gives S = 2π ∫ -3 3 (1/16(e^8x+e^-8x)) dx. Integral this expression gives S = 10512π.
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1.Find the lateral area of a cone with a radius of 7 ft. and a slant height of 13 ft. Use 3.14 for ð and round to the nearest tenth. 439.6 ft2 324.5 ft2 571.5 ft2 285.7 ft2 2.Find the surface area of a square pyramid with a base length of 24 cm and a height of 16 cm. 1056 cm2 1536 cm2 816 cm2 1344 cm2 3.Find the volume of a rectangular prism with the following dimensions: Length = 5 mm Base = 7 mm Height = 3 mm 142 mm2 105 mm2 126 mm2 130 mm2 4.Find the volume of a square pyramid with a base length of 9 cm and a height of 4 cm. 324 cm3 108 cm3 36 cm3 152 cm3 5.Find the volume of a cone with a radius of 10 mm and a height of 6 mm. 628 mm3 600 mm3 1,884 mm3 1,254 mm3 1.D 2.C 3.? 4.? 5.?
All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.
What in math is a volume?In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.
By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.
(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:
L = π(7)(13) ≈ 285.7 ft²
Rounding to the nearest tenth, the answer is 285.7 ft².
(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:
B = (24)² = 576 cm²
The perimeter of the base is 4 times the base length, so we have:
P = 4(24) = 96 cm
Now we can use the formula to find the surface area:
A = 576 + (1/2)(96)(16) = 1056 cm²
Therefore, the surface area of the square pyramid is 1056 cm².
(3) The volume of a rectangular prism can be calculated using the formula V = lwh,
where
l is the length
w is the base
h is the height
V is the volume.
Substituting the given values, we have:
V = (5)(7)(3) = 105 mm³
Therefore, the volume of the rectangular prism is 105 mm³.
(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:
B = (9)² = 81 cm²
Now we can use the formula to find the volume:
V = (1/3)(81)(4) = 108 cm³
Therefore, the volume of the square pyramid is 108 cm³.
(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:
V = (1/3)π(10)²(6) ≈ 628.3 mm³
Rounding to the nearest whole number, the answer is 628 mm³.
Therefore, the volume of the cone is 628 mm³.
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The ratio if the sides of two similar triangles 2:3. The area of the smaller is triangle 36cm2(squared). Find the area of the larger triangle?
The requried area of the larger triangle is 81 cm².
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not greater than 180°.
Here,
When two triangles are similar, the ratio of their corresponding sides is the same, and the ratio of their areas is equal to the square of this side ratio.
In this case, the ratio of the sides of the larger triangle to the sides of the smaller triangle is 3/2 (since it is given that the ratio of the sides is 2:3). Therefore, the ratio of the areas of the larger triangle to the area of the smaller triangle is (3/2)² = 9/4.
Given that the area of the smaller triangle is 36 cm^2, we can use the area ratio to find the area of the larger triangle:
Area of larger triangle = (9/4) × (Area of smaller triangle)
= (9/4) × 36 cm²
= 81 cm²
Therefore, the area of the larger triangle is 81 cm².
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I need help on progress learn I’m in the 7th grade any volunteers to help me get done with 4x4 in iss
Answer: 16
Step-by-step explanation: Basic multiplication
4+4=8
4+4=8
8+8=16 [16!]
