Total 1920 cubes can fit in the given prism.
Given that:Dimensions of prism are: [tex]2\dfrac{2}{5} = \dfrac{12}{5}[/tex] , [tex]3\dfrac{1}{5} = \dfrac{16}{5}[/tex], and 2 inches respectively.
Size of a side of given cube = 1/5 inch
To find:Number of cubes that can fit in given prism.
Calculations and explanation:This problem is all about spaces. Only that number of cube will fit, which the prism will allow to. The given prism has got some space in it(The volume), and the cubes have some size (their volume).
Since prism is a cuboid(which is mistakenly written as rectangular in the question), thus we have:
Volume of prism = multiplication of lengths of its sides = [tex]\dfrac{12}{5} \times \dfrac{16}{5} \times 2 = \dfrac{384}{25}[/tex] cubic inches
Volume of the cube = cube of its one side's length = [tex](\dfrac{1}{5})^3 = \dfrac{1}{125}[/tex] cubic inches
We will divide the total space with space amount each cube take so as to find number of cubes allowed by prism to be fitted in it.
Thus:
[tex]\text{Number of cubes} = \dfrac{\dfrac{384}{25}}{\dfrac{1}{125}} = 1920 \: \rm cubes[/tex]
Thus, in total, there can be 1920 cubes fitted in the prism.
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The rectangular prism can hold 1920 cubes with edge lengths of [tex]\frac{1}{5}[/tex] inch. This is calculated by finding the volume of the prism and dividing it by the volume of one small cube.
To find how many cubes with an edge length of [tex]\frac{1}{5}[/tex] inch fit into a rectangular prism with dimensions [tex]2\frac{2}{5}[/tex] inches, [tex]3\frac{1}{5}[/tex] inches, and 2 inches, we follow these steps:
Convert the dimensions of the prism into improper fractions:
[tex]2\frac{2}{5}[/tex] inches = [tex]\frac{12}{5}[/tex] inches[tex]3\frac{1}{5}[/tex] inches = [tex]\frac{16}{5}[/tex] inches2 inches = [tex]\frac{10}{5}[/tex] inchesCalculate the volume of the prism:
Volume = [tex]\frac{12}{5} \times \frac{16}{5} \times \frac{10}{5} = \frac{1920}{125}[/tex] cubic inchesDetermine the volume of one small cube:
Edge length of a small cube = [tex]\frac{1}{5}[/tex] inch → Volume = [tex]\left(\frac{1}{5}\right)^3[/tex] = [tex]\frac{1}{125}[/tex] cubic inchesFind the number of small cubes by dividing the volume of the prism by the volume of one small cube:
Number of cubes = [tex]\frac{1920/125}{1/125} = 1920[/tex]Thus, 1920 cubes with an edge length of [tex]\frac{1}{5}[/tex] inch can fit into the given rectangular prism.
Corrected question:
A rectangular prism measures [tex]2\frac{2}{5}[/tex] inches by [tex]3\frac{1}{5}[/tex] inches by 2 inches
How many cubes with edge length [tex]\frac{1}{5}[/tex] inch fit in the prism?
Suppose you are driving to visit a friend in another state you are driving at an average rate of 50 mph you must drive a total of 480 miles if you have already driven 130 miles how long would it take you to reach your destination?
Answer:
300 more miles
Step-by-step explanation:
because its easy NO OFFENSE SERIOULSY
classification for square root 2
Answer: It is irrational because it cannot be written as a ratio of two integers. It is not a perfect square
Step-by-step explanation:
Pedro planted 15 plants in his garden is 45 minutes. How long did it take him to plant 5 plants?
Which of the following would be a good name for the function that takes the weight of a box and returns the energy needed to lift it ?
Answer:
B
In a function, f(x), there are two parts:
x: the input value
f: the output value
What’s is 4/5•5/7 which they are both negative
Answer:
-20/35 if you simplify it would be -4/7
Step-by-step explanation:
F(x)=5x+1 g(x)= -2x+15
F(x)=5x+1
g(x)= 2x+15
5x+1=F(x)
Xx2=(5+1)
x=6x2
x=12
Fx= F12
Area of composite figure
Answer:
4x4x8x2
256
Step-by-step explanation:
Janine is analyzing spending habits of students in her high school. She finds a mean monthly discretionary expense of $70 spent on having meals out with friends the standard deviation of the distribution is five. What is the variance?
Answer:
Variance = 25
Step-by-step explanation:
Standard deviation is the under root of variance.
Variance is the square of standard deviation.
Data:
Mean = 70
Variance = ?
Standard deviation = √variance = 5
Variance = 5²
Variance = 25.
Therefore, the variance is 25.
Final answer:
The variance of the monthly discretionary expenses on meals out with friends is 25 dollars squared.
Explanation:
To find the variance of Janine's data on the spending habits of students for meals out with friends, you'll use the squared value of the standard deviation.
Since Janine found the standard deviation to be five dollars, you simply need to square this number to find the variance.
Step-by-step Calculation:
Identify the standard deviation (denoted as σ) which is 5.Square the standard deviation to find the variance: Variance = σ² = 5².Calculate the squared value: 25.The variance of the distribution of monthly discretionary expenses on meals out is 25 dollars squared.
Consider the equation 8x + 5 = 37. Write a real-life scenario that this equation could model.
Answer:
Dave has been introduced to a new phone service. They charge a monthly fee of $5 and each phone call made out of country is $8. How much phone calls did Dave made out of country if his bill this month was 37?
The equation represents a membership of a gym, where there is a $5 charge for membership and a per month charge of $8 and x represents the number of months when the total charge becomes $37.
To imply the given equation 8x + 5 = 37 in the rel life scenario.
What is the equation?The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.
Here,
Equation 8x + 5 = 37
Let's assume that, we are in the gym and the membership charge of the gym is 5$ and after months the charge becomes $37
And gym charges $8 per month after membership where x represents the number of months when the charge becomes $37.
Thus, the way the equation is implemented in the real-life scenario is shown above.
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Line segment Z E is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y. Triangle G E F has angles with different measures. Point A is at the center. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Z, and A Y. Which must be true? Please Hurry I don't have a lot of time to finsh my test!
Answer:
C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Step-by-step explanation:
The center of insribed circle into the triangle is the point where the angle bisectors of the triangle meet.
The center of circumsribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.
Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides, so the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle. Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Answer:
c
Step-by-step explanation:
What is 7909+1044 using algorithm
Answer:
8,953
Step-by-step explanation:
line up 7,909 and 1,044 like this :
7,909
+ 1,044
then add everything
Using the addition algorithm, first you align the numbers by place value, then starting from the rightmost position, you add each place numbers together. Accordingly, 7909 + 1044 equals 8953.
Explanation:The process of adding two numbers using the additon algorithm begins with lining up the numbers by their place values. Starting from the rightmost digit, which is the one's place, you add the numbers in each corresponding place together.
In this case, Adding 7909 and 1044:
You begin with the ones place (9+4), which equals 13. You put down the 3 and carry over the 1 to the next place. After the first step the result would look like this: 790_3 with 1 carried over. Next, you add the numbers in the tens place (0+4) and the carried over 1, which equals 5. So the result after the second step would look like this: 79_53. You then move to the hundreds place. Since there is no number to add with 9, you simply carry it down. So the result after the third step would look like this: 7_953. Finally, you add the numbers in the thousands place (7+1), which equals 8. Therefore, the final result of 7909 + 1044 using the addition algorithm is 8953. Learn more about Addition Algorithm here:
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A pack of gum contains 30 sticks. If the pack of gum costs $1.79, what is the most appropriate price per stick of gum?
The most appropriate price per stick of gum should be $0.5966.
Given that,
A pack of gum contains 30 sticks. If the pack of gum costs $1.79Based on the above information, the calculation is as follows:
[tex]= 30\div 1.79[/tex]
= 0.5966
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A square room has an area of 400 square feet. What is the side length of the room?
Answer is 20
Step-by-step explanation:
The ______ is the amount of space an object contains measured in cubic units
What is the range of f(x) = c?
O
{0}
0 (-00,00)
{c}
[0, 0)
To add or subtract fractions with different denominators first find the equivalent fractions with a _ denominator
Answer: Common
Step-by-step explanation:
The answer is with a multiplication of denominators, because when you multiply the denominator of one fraction with the denominator of the other fraction, we will get product which could divide between both denominator
for example if you have the following equation:
2/3+2/4
and you multiply 3*4 =12
and you can use it to complete the equation as a common denominator
how to convert 1 years 6 months into 1.5 years
Step-by-step explanation:
6 months = 0.5 years (6/12)
1 year + 0.5 years = 1.5 years
A superhero recently asked his nemesis how many cats she has. She answered with a riddle: "Five dash sixths of my cats plus two."
How many cats does the nemesis have?
On a number line, will the square root of 20 be closer to 4.4 or 4.5
Answer: 4.5 would be closer
Step-by-step explanation: 4.4x4.4 is 19.36 which is about 64 points away and 4.5x4.5 is 20.25 which is 25 points away
Answer:
4.5
Step-by-step explanation:
Nearest of square root of 20
[tex]\sqrt{20}[/tex]
To choose closer from two numbers 4.4 or 4.5
First we find the square of both number.
Square of 4.4
[tex]4.4^2 = 19.36[/tex]
Square of 4.5
[tex]4.5^2=20.25[/tex]
Now compare the closer number from 20
Difference of, 20.25 - 20 = 0.25
Difference of, 20-19.36 = 0.64
As we know, 0.25<0.64
Hence, On number line square root closer to 4.5
6895 round to nearest thousand
Answer:
7000
Step-by-step explanation:
What is 2/3 written as a sum of unit fractions with the denominator of nine
Answer:
Step-by-step explanation:
2/3 = 6/9 because to get to nine from three you need to multiply by three so you multiply the 2 by three to and you get 6 so the answer is 6/9
2/3 written as a sum of unit fractions with the denominator of nine is 6/9.
What is an equivalent fraction?Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.
The given fraction is 2/3.
2/3 written as a sum of unit fractions with the denominator of nine
Now, multiply both numerator and denominator by 3
2×3/3×3
= 6/9
Therefore, 2/3 written as a sum of unit fractions with the denominator of nine is 6/9.
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You are competing in a race. The table shows the times from last year's race you want your time to be last year's median time with an absolute
deviation of at most 5 minutes. Complete the inequality to represent the time in minutes) you hope to achieve
Answer:
[tex]27\leq x \leq37[/tex]
Step-by-step explanation:
Let's arrange the numbers from least to greatest:
20, 25, 27, 28, 31, 32, 32, 38, 40, 40, 42, 48
The median is the "middle" number when arranged from least to greatest.
There are 12 numbers, so the middle number would be "average" of 6th and 7th terms.
6th term = 32
7th term = 32
Average = (32+32)/2 = 32
Hence, median = 32
Absolute deviation of 5 minutes means 5 minutes less or greater than the median, 32.
So, 32 - 5 = 27 & 32 + 5 = 37
Hence [tex]27\leq x \leq37[/tex]
To find the inequality range for race times, we must first arrange the times and find the median, which is 32 minutes. The desired race time with an absolute deviation of at most 5 minutes from the median results in the inequality 27 ≤ x ≤ 37.
Explanation:
To solve this problem, we need to arrange the given race times in order and find the median. Once we find the median, we can set up an inequality that represents a race time within 5 minutes more or less than this median time.
First, we arrange the race times in ascending order: 20, 31, 27, 32, 25, 42, 48, 28, 40, 38, 32. After putting them in the proper order (20, 25, 27, 28, 31, 32, 32, 38, 40, 42, 48), we find that the median, which is the middle value, is 32 minutes since there are 11 times, and the 6th time is the median.
Next, we want to have a race time with an absolute deviation of at most 5 minutes from the median (32 minutes). This gives us the inequality 27 ≤ x ≤ 37. So, the time you hope to achieve in the race is between 27 and 37 minutes.
what the answer tonthis question 10x=-4(2x-9)
10x = 4(2x -9)
10x = 8x - 36
10x - 8x = -36 - 8x
2x = -36
2x ÷ 2 = -36 ÷ 2
x = -18
If you need a better explanation just as in the comments.
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equation?
25-5x=5(-x + 5)
Select all that apply.
A: there is no solution
B: x= all real numbers
C: x=0
D: x=5
Given the sequence below, and that sequence has a domain of n 2 1, find the third
term.
f(n) = 3n+2
Answer:
11Step-by-step explanation:
f(n) = 3n + 2, n ≥ 1
Substitute n = 3:
f(3) = 3(3) + 2 = 9 + 2 = 11
The third term of the sequence is 11 given that that the sequence has a domain of n ≥ 1 and f(n) = 3n + 2. This can be obtained by substituting 3 in the sequence since we have to find the third term.
What is a sequence ?Sequence is an ordered list of terms with a specific order.For example, 3, 7, 11, 15, ...Calculate the third term :
Given that, the sequence ⇒ f(n) = 3n + 2
Since n ≥ 1, first term will be ⇒ f(1) = 3(1) + 2 = 5
Second term will be f(2) = 3(2) + 2 = 8
Third term will be f(3) = 3(3) + 2 = 11
Thus the sequence is 5, 8, 11, ... and the third term is 11.
Hence the third term of the sequence is 11 given that that the sequence has a domain of n ≥ 1 and f(n) = 3n + 2.
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solve 2x-3|x+1|=-2x-11
Hey!
----------------------------------------------------
Solution:
2x - 3|x + 1| = -2x - 11
2x - 3|x + 1| + (-2x) = -2x - 11 + (-2x)
-3|x + 1| = -4x - 11
-3|x + 1|/-3 = -4x - 11/-3
|x + 1| = 4/3x + 11/3
x + 1 = -(4/3x + 11/3)
x + 1 + 4/3x = 4/3 + -11/3 + 4/3x
7/3x + 1 = -11/3
7/3x + 1 - 1 = -11/3 - 1
7/3x = -14/3
7/3x * 3/7 = -14/3 * 3/7
x = -2
----------------------------------------------------
Check:
2(-2) - 3|-2 + 1| = -2(-2) - 11
(-4) - 3|-1| = (4) - 11
(-4) - 3 = (4) - 11
-7 = -7
----------------------------------------------------
Answer:
x = -2
----------------------------------------------------
Hope This Helped! Good Luck!
two angels are complementary one angle measures 3more than twice the other.
Answer:
29° and 61°
Step-by-step explanation:
Complementary angles sum to 90°
let one angle be x then the other angles = 2x + 3
Sum the angles and equate to 90
x + 2x + 3 = 90, that is
3x + 3 = 90 ( subtract 3 from both sides )
3x = 87 ( divide both sides by 3 )
x = 29
and 2x + 3 = (2 × 29) + 3 = 58 + 3 = 61
The two angles are 29° and 61°
1. Find the sum.
109.526 + 36.42
Also show the work please
Answer:
Step-by-step explanation:
Choose the replacement for x and y that makes this equation a true statement: 2x + 55y = −214
A.
x = −3 and y = −4
B.
x = −4 and y = 3
C.
x = 3 and y = −4
D.
x = 4 and y = 4
Answer: C
Step-by-step explanation:
2x3= 6
55 x -4= -220
6 + -220= -214
A vector has an x-component equal to 0.15 and a y-component is equal to 1.22 calculate the vectors direction relative to the positive x-axis
Answer:
The vector direction is 83.0° relative to the positive x-axis
Step-by-step explanation:
* Lets explain how to find the direction of a vector
- A vector is a quantity which has both magnitude and direction
- The vector has two components x-component and y-component
- The x-component = v cos Ф , and the y-component = v sin Ф,
where Ф is the angle between the vector and the positive part
of the x-axis
- The magnitude of the vector = [tex]\sqrt{x^{2}+y^{2}}[/tex]
- The direction of the vector = [tex]tan^{-1}(\frac{y}{x})[/tex]
* Lets solve the problem
∵ x-component of the vector = 0.15
∵ y-component of the vector = 1.22
- Both x-component and y-component are positive
∴ Ф will be between 0° and 90°
∵ The direction of the vector = [tex]tan^{-1}(\frac{y}{x})[/tex]
∴ The direction of the vector = [tex]tan^{-1}(\frac{1.22}{0.15})[/tex]
∴ The direction of the vector = 83.0°
* The vector direction is 83.0° relative to the positive x-axis