A cube has a volume of 125 cubic inches. What is the length of each edge? Enter your answer in the box.
Answer: 5 cm
Step-by-step explanation:
Given : The volume of a cube = 125 cubic inches.
The formula for the volume of a cube is :
[tex]V=s^3[/tex], where s is the side-length .
Substitute V= 125 in the above formula ,
[tex]125=s^3[/tex]
Taking cube root on both the sides , we get
[tex]\sqrt[3]{125}=s\\\\\Rightarrow\ s= \sqrt[3]{5^3}=5[/tex]
Hence, the side length of cube= [tex]5\ cm[/tex]
Each edge will be 5 inches.
Volume of the cube = 125 cubic inches
It should be noted that a cube's volume is gotten by multiplying the side thrice. In this case, let's say the value of each side is a. Therefore, based on the information given above:
a × a × a = 125
a³ = 125
a = 3✓125
a = 5
Therefore each edge is 5 inches.
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What is M-1/6-4m+5/6 simplified
The simplified expression is -3M + 1
How did we get the value?To simplify the expression M - (1/6) - 4M + (5/6), we can combine the like terms.
First, let's combine the terms with M:
M - 4M = -3M
Now, let's combine the constant terms:
(1/6) + (5/6) = (1 + 5)/6 = 6/6 = 1
Putting it all together, the simplified expression is:
-3M + 1
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There are k types of coupons. independently of the types of previously collected coupons, each new coupon collected is of type i with probability pi, ki =1 pi = 1. if n coupons are collected, find the expected number of distinct types that appear in this set. (that is, find the expected number of types of coupons that appear at least once in the set of n coupons.)
Let X be the expected number of distinct types of coupons in the collection of k coupons X = X1 + X2 + ……. + Xx.
Peter is a painter, and he wonders if he would have time to catch a paint bucket dropped from his ladder before it hits the ground. He drops a bucket from the top of his 9-foot ladder. The height, h, of the bucket can be represented by the equation, h= -16t^2 + 9, where the height is measured in feet from the ground, and the time since the bucket was dropped, t, is measured in seconds. After how many seconds does the bucket hit the ground? Do you think he could catch the bucket before it hits the ground.
The paint bucket dropped from the 9-foot ladder would hit the ground in approximately 0.75 seconds, according to the equation given for free fall. Given this quick time frame, it might be difficult for Peter to catch the bucket before it hits the ground.
Explanation:The situation described involves a physical phenomenon known as free fall, under the influence of gravity. In the case of the paint bucket, when it is dropped from the top of the ladder, the height h of the bucket from the ground at any time t is given by the equation h = -16t^2 + 9. The bucket hits the ground when h = 0.
To find when the bucket hits the ground, we solve the equation -16t^2 + 9 = 0 for t. Using the quadratic formula, we find the roots to be t = -0.75s and t = 0.75s. Since time cannot be negative in this situation, we discard the negative root. Thus, the bucket hits the ground after 0.75 seconds.
As to whether Peter could catch the bucket before it hits the ground, it does depend on his reflexes and agility, but generally it may be difficult to react and move quickly enough within such a brief time frame.
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help me out some one
30 POINTS: Dalton's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 200 sodas in all, 20% of which were regular. How many regular sodas did the diner serve?
Hannah wishes to find the vertex of the function x2 + 3x - 28 = 0 by completing the square. Which of the following equations may be used to identify the coordinates of the vertex?
A. (x + 1.2)2 = 30.25
B. (x + 2.25)2 = 30.5
C. (x + 2.5)2 = 30.75
D. (x + 2.75)2 = 32.5
The sum of the reciprocals of two consecutive integers is -9/20. Find the two integers
What is the value of mc011-1.jpg?
–4
–2
2
4
the pic is the .jpg
The question is unclear as it references links rather than providing a specific mathematical problem to solve. A correct answer cannot be given.
Explanation:It appears there has been a misunderstanding. The actual mathematical question has not been provided in the text. Instead, there are references to image sources, licenses, and websites that do not contain a clear mathematical question to answer. Therefore, I'm unable to provide a value or solve the equation.
The value of the expression -2(7-15)/4 simplifies to 4 after following the order of operations: first subtracting inside the brackets, then multiplying by -2, and finally dividing by 4.
Explanation:The value of the given expression -2(7-15)/4 when simplified is computed in the following steps:
Calculate the value inside the brackets: 7 - 15 = -8.Multiply this result by -2: -2 * (-8) = 16.Divide the product by 4: 16 / 4 = 4.Therefore, the value of the entire expression is 4, which corresponds to answer option d)4.
If the heights of 300 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have heights (a) greater than 72 inches, (b) less than or equal to 64 inches, (c) between 65 and 71 inches inclusive, (d) equal to 68 inches? assume the measurements to be recorded to the nearest inch.
The student can use the normal distribution and z-scores to estimate the number of students in different height ranges. The heights were estimated to be: about 28 students over 72 inches, 28 students less or equal to 64 inches, roughly 205 students between 65 and 71 inches, and it is statistically impossible to determine exactly 68 inches from the data given.
Explanation:This question is dealing with a concept in statistics known as the normal distribution. In this context, we are asked to find the proportion of students whose heights fall into various ranges, based on a known mean and standard deviation. With a mean of 68 inches and a standard deviation of 3 inches, we can calculate the z-score for each scenario:
Greater than 72 inches: Z = (72-68)/3 = 1.33. Looking at the z-table, the proportion associated with 1.33 is 0.9082, but we want greater than, so we subtract from 1, giving approximately 0.0918, or 9.18%. Multiply this percentage by the total number of students (300) to estimate the number of students taller than 72 inches. This yields an approximate total of 27.54, but since we cannot have fractional students, we would say approximately 28 students.Less than or equal to 64 inches: Z = (64-68)/3 = -1.33. The proportion for -1.33 on the z-table is 0.0918, which we interpret as 9.18%. This would amount to approximately 27 or 28 students.Between 65 and 71 inches: Calculate two z-scores: Z1 = (65-68)/3 = -1.00 and Z2 = (71-68)/3 = 1.00. Using the z-table, we find that the proportions for z-scores of -1.00 and 1.00 are approximately 0.1587 and 0.8413. So, the proportion between these two z-scores is 0.8413 - 0.1587 = 0.6826, or 68.26%. This correlates to roughly 205 students.Equal to 68 inches: It's impossible to exactly determine the number of students who are exactly 68 inches tall from the data given. The normal distribution is a continuous distribution, and the probability of any single, specific value (like exactly 68 inches) is technically zero. However, you can determine the number of students likely to be in a small range around 68 inches.Learn more about Normal Distribution here:https://brainly.com/question/34741155
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A city's population is represented by the function P=25,000(1.0095)t , where t is time in years.
How could the function be rewritten to identify the daily growth rate of the population?
What is the approximate daily growth rate?
The daily population growth function is P=25,000((1.0095)1/365.25)t, and the daily growth rate is approximately 1.000026 or an increase of about 0.0026% per day.
Explanation:The city population growth function given, P=25,000(1.0095)t, is an exponential function. To identify the daily growth rate, we need to rewrite this function in terms of days. As there are approximately 365.25 days in a year, we substitute this into the formula for t. Hence, the daily population growth function becomes P=25,000(1.0095)t/365.25.
To find the approximate daily growth rate, we solve for the base of the exponent. Using the fact that (ab)c = abc, we can rewrite the function as P=25,000((1.0095)1/365.25)t.
Thus, the daily growth rate of the population is approximately the value of (1.0095)1/365.25, which calculates to about 1.000026, or an increase of about 0.0026% per day.
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One integer is 5 more than another. Their product is 234. Find the integers?
Final answer:
The integers in question are 13 and 18, which fulfill both conditions of one integer being 5 more than the other and their product being 234.
Explanation:
We are looking for two integers where one is 5 more than the other and their product equals 234. Let's designate the smaller integer as x. Then the larger integer can be represented as x + 5. The equation describing their product is:
x * (x + 5) = 234
Expanding this, we get:
x2 + 5x - 234 = 0
Solving this quadratic equation, we can find the values of x that satisfy the equation. The factors of 234 that have a difference of 5 are 13 and 18. So, the two integers we are looking for are 13 and 18.
Which of the following expression has a value less than 0.7? A) 0.7×4/3. B) 0.7×3/3 C) 0.7×1/3
Which of the following numbers is a factor of 49 ?
The quotient of a number and ten increased by eleven
The expression 'The quotient of a number and ten increased by eleven' is written as (x/10) + 11 in mathematical terms. Understanding the role of exponents, such as in the expression 10² equals 100, helps in grasping concepts like scientific notation, where large or small numbers are expressed as the product of a number and a power of ten, such as 1.372568 × 10⁶.
Explanation:The question 'The quotient of a number and ten increased by eleven' translates to a mathematical expression. This expression can be represented as (x/10) + 11, where 'x' is the number in question. It's a simple algebraic expression where you first divide the number by ten and then add eleven to the result.
When discussing multiplication and division by powers of 10, it's important to understand the concept of an exponent. The exponent is a raised number to the right of the 10, indicating the number of factors of 10 in the original number. For example, in the expression 10², the exponent 2 indicates that ten is multiplied by itself once, resulting in 100. This is consistent with the way our numbering system works, with each place value being ten times greater than the one to its right.
The utility of using exponents is highlighted in scientific notation, which simplifies large or small numbers by representing them as a product of a number and a power of ten. This is particularly useful in fields like science and engineering, where very large or very small numbers are common. For example, the number 1,372,568 can be written in scientific notation as 1.372568 × 10⁶, representing the number as a manageable base multiplied by ten raised to the sixth power.
an electrician cuts a 136-ft piece of cable. one piece is 16 feet less than 3 times the length of the other piece. Find the length of each piece.
1st piece = x
2nd piece = 3x-16
x +3x-16 = 136
4x-16 = 136
4x = 152
x = 152/4 = 38
1st piece = 38 feet
2nd piece = 136 -38 = 98 feet
Sonny substituted 5 for x in the proportion 16/x=48/15 and cross multiplied to get 240=240. Why is this?
A.because the cross sums of the proportion are equal
B.because the cross differences of the proportion are equal
C.because the cross products of the proportion are equal
D.because the cross quotients of the proportion are equal
the answer is c i just took the test
Answer:
i agree c
Step-by-step explanation:
because 16 times 15 = 240
and 48 times 5 =240
Joe and Ella combine their photos. Then they put an equal number on each page of an 8-page photo album. How many photos are on each page?
write the following decimal as a fraction or mixed number in lowest terms 0.85
If I Row my canoe at 5 mph and I travel upstream at 3 mph, how fast will I be traveling downstream if I am rowing at the same rate ?
Only the Fahrenheit one plz
Can anyone figure this out for me please? It would be greatly appreciated.
How can you decompose the composite figure to determine its area?
Answer:
D. As a semicircle, a trapezoid and two rectangles.
Step-by-step explanation:
Please find the attachment.
We have been given a composite figure. We are asked to decompose our given figure to determine its area.
Upon looking at attachment for our given composite figure, we can see that it consists one semicircle on top, one trapezoid in middle and two rectangles on bottom. So we can decompose our composite figure as a semicircle, a trapezoid and two rectangles.
Therefore, option D is the correct choice.
number that can be divided evenly by only itself and by the number 1 is called which of the following? Prime Variable Prime Term Prime Multiple Prime Factor
What is the slope of the line tangent to the curve 3y^2-2x^2=6-2xy at the point (3 2)?
1 point) use the inner product ⟨f,g⟩=∫10f(x)g(x)dx ⟨f,g⟩=∫01f(x)g(x)dx in the vector space c0[0,1]c0[0,1] of continuous functions on the domain [0,1][0,1] to find ⟨f,g⟩⟨f,g⟩, ‖f‖‖f‖, ‖g‖‖g‖, and the angle αf,gαf,g between f(x)f(x) and g(x)g(x) for f(x)=10x2−3 and g(x)=6x−9.
The norms and the inner product of f and g can be calculated using the given inner product definition and the knowledge that the norm of a vector (here, function) is the square root of its inner product with itself. Then, the cosine of the angle between f and g can be found by dividing their inner product by the product of their norms.
Explanation:The problem is asking us to compute certain components in the context of a vector space of continuous functions, namely inner product ⟨f,g⟩, norms ‖f‖, ‖g‖, and angle between them for f(x) and g(x). Since the functions are given as f(x)=10x^2-3 and g(x)=6x-9, these can be used in the provided inner product definition ⟨f,g⟩=∫from 0 to 1f(x)g(x)dx.
The norm of a vector, in this case, the function f or g, is the square root of the inner product of the function with itself. The cosine of the angle α between the functions f and g is given by the ratio of the inner product of f and g to the product of their norms.
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An object is traveling at a steady speed of 8 2/3 miles per hour. How long will it take the object to travel to 5 1/5 miles
Answer:
The answer is 36 minutes
Step-by-step explanation:
Distance is speed multiplied by time. ( when we have steady speed )
Distance=speed* time
We are looking for time.
Time=Distance /speed
Distance= 5 1/5 miles=5,20
Speed=8 2/3 miles=8,66
T=5.20/8.66666=0,60
1 hour is 60 minutes
T=0,60/60 minutes=36 minutes
The time that it'll take the object to travel in 5 1/5 miles is 36 minutes
Note that 1 hour = 60 minutes Since the object is traveling at a steady speed of 8 2/3 miles.
Let the time taken for the object be represented by x. The equation to solve the question will be:
5 1/5 / 8 2/3 = x / 60
Cross multiply
(8 2/3 × x) = (5 1/5 × 60)
8 2/3x = 312
x = 312/ 8.67
x = 36
Therefore, the time that it'll take the object to travel in 5 1/5 miles is 36 minutes.
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You anticipate that a $2000 investment in a local business will pay an average of 4% interest in each of the next 5 years. Determine to the nearest dollar the amount of the investment at the end of 5 years.
solve the system of linear equations. separate the x- and y- values with a coma.
14x-4y=74
7x-7y=7
There are 44 colas and 22 lemon lime soda is in the cooler. Whatis the ratio of colas to lemon lime sodas?