Each figure is filled with unit cubes. Drag 22 figures whose combined volume is equal to 45 unit cubes.
Answers
To solve this problem, what we have to do first is to calculate for the volumes of each figure. Let us start from the figure on the left going to the right. Let us call the figures 1 to 4. Formula for volume is:
V = l * w * h
Figure 1:
V1 = 4 * 3 * 1 = 12 unit cubes
Figure 2:
V2 = 3 * 2 * 3 = 18 unit cubes
Figure 3:
V3 = 2 * 2 * 4 = 16 unit cubes
Figure 4:
V4 = 3 * 3 * 3 = 27 unit cubes
The two combinations that would result in 45 total unit cubes would be:
V = V2 + V4 = 18 unit cubes + 27 unit cubes = 45 unit cubes
So the answers are:
Figure 2 and Figure 4
Related Questions
vito just put some money into a cd that pays 12.7 interest compound quarterly. according to the rule of 72,in the approximately how years will he have 4 times the amount of money that he has now
Answers
Answer:
11.34 years.
Step-by-step explanation:
We have been Vito put some money into a cd that pays 12.7 interest compound quarterly.
Since the rule of 72 states that to find the number of years it will take an amount to double, we need to divide 72 by annual interest rate.
First of all let us find the number of years it will take to double Vito's money by dividing 72 by 12.7.
[tex]\text{Time it will take to double Vito's money}=\frac{72}{12.7}[/tex]
[tex]\text{Time it will take to double Vito's money}=5.66929133858\approx 5.669[/tex]
Since it will take 5.669 years to double Vito's money, so to find the time it will take Vito to have 4 times the money, we will multiply 5.669 by 2.
[tex]\text{Time it will take to have 4 times Vito's money}=5.669*2[/tex]
[tex]\text{Time it will take to have 4 times Vito's money}=11.338\approx 11.34[/tex]
Therefore, approximately in 11.34 years Vito will have 4 times the amount of money that he has now.
81.54 is what percent of 75.5
Answers
(p/100)(75.5)=81.54
75.5p/100=81.54 multiply both sides by 100
75.5p=8154 divide both sides by 75.5
p=8154/75.5
p=108%
....
check
75.5(108/100)=81.54
75.5(1.08)=81.54
81.54=81.54
if the GCF of two numbers is 1, they are called relatively prime. Find three sets of relatively prime numbers
Answers
The GCF can be obtained by taking the prime factors of two numbers then multiplying the common prime factors. IF there are none, then the GCF is 1 and the numbers are called relatively prime.
There are a lot of relatively prime numbers. To name three sets:
3 and 19
7 and 20
15 and 28
For these sets, we see that there are no other common factors except 1. To illustrate the factors:
3 = 1, 3
19 = 1, 19
7 = 1, 7
20 = 1, 2, 2, 5
15 = 1, 3, 5
28 = 1, 2, 2, 7
So we see that only the number 1 is the factor in each set.
Final answer:
Three sets of relatively prime numbers are 9 and 16, 14 and 25, and 8 and 21, as they do not share any common prime factors other than 1.
Explanation:
If the Greatest Common Factor (GCF) of two numbers is 1, they are indeed referred to as relatively prime. To find sets of relatively prime numbers, we need to identify pairs of numbers that do not have any prime factors in common other than 1.
9 and 16: The prime factors of 9 are 3· 3, and the prime factors of 16 are 2· 2· 2· 2. They share no common prime factors, so they are relatively prime.
14 and 25: The prime factors of 14 are 2· 7, and the prime factors of 25 are 5· 5. Since they have no common factors, these numbers are also relatively prime.
8 and 21: The prime factors of 8 are 2· 2· 2, and the prime factors of 21 are 3· 7. With no prime factors in common, 8 and 21 are relatively prime.
Therefore, we have found three sets of relatively prime numbers: 9 and 16, 14 and 25, and 8 and 21.
What is the eighth term of the geometric sequence 4,-20,100,...?
Answers
The eighth term of the geometric sequence 4, -20, 100,... is 9600, calculated using the formula aₙ = arⁿ⁻¹ with a = 4, r = -5, and n = 8.
The eighth term of the geometric sequence 4, -20, 100,... is 9600.
To find the eighth term of a geometric sequence, you can use the formula: aₙ = arⁿ⁻¹, where a is the first term, r is the common ratio, and n is the term number. In this case, a = 4, r = -5, and n = 8.
Plug the values into the formula: 4 x (-5)⁸⁻¹ = 9600.
How is inductive reasoning used in geometry?
Answers
Answer:
Inductive reasoning draws general conclusions from specific details / observations - in other words, going from specific --> general.
Example:
Specific: I break out when I eat peanuts.
Observation: This is a symptom of being allergic.
General Conclusion: I am allergic to peanuts.
hope this helps! <3
Final answer:
Inductive reasoning in geometry involves observing patterns in specific instances and formulating general rules or hypotheses, such as the sum of angles in a triangle or the properties of parallel lines intersected by a transversal.
Explanation:
Inductive reasoning in geometry is used to derive broad generalizations from specific observations or instances. One way inductive reasoning is applied is by observing patterns or properties in a set of geometric figures and then formulating a hypothesis or general rule that applies to all similar figures. For example, after measuring the angles of several triangles and finding that they always add up to 180 degrees, one might assume that all triangles have this property. Another example is when looking at multiple parallel lines cut by a transversal and noticing the corresponding angles are equal, thus generalizing that this is the case for any parallel lines intersected by a transversal.
Scientists, including mathematicians, use inductive reasoning to construct hypotheses, which are then tested using deductive reasoning. The conclusions drawn from inductive reasoning may not always be correct, but they are essential for advancing scientific and mathematical knowledge by suggesting relationships and rules that can be rigorously tested.
A furniture store is having a going-out-of-business sale. Two hours after opening, there are 415 sofas still available. Three hours later, there are 301 sofas available. How many hours will the store have to stay open to sell the entire inventory? Assume the sales rate is constant and round your answer to the nearest whole hour.
Answers
x(t) = a + bt
where
x = number of sofas remaining after t hours from opening,
a, b are constants.
When t = 2 hours, x = 415. Therefore
a + 2b = 415 (1)
Three hours later (t = 2 +3 = 5), there are 301 sofas left.
Therefore
a + 5b = 301 (2)
Subtract (2) from (1).
-3b = 415 - 301 = 114
b = -38
From (1), obtain
a = 415 - 2*(-38) = 491
The required function is
x(t) = 491 - 38t
When all sofas are sold, x=0. Therefore the time required to complete the sale is given by
491 - 38t = 0
38t = 491
t = 12.92 hours
Answer:
The time required to sell the inventory is 13 hours (nearest whole hour)
A league of 19 teams is playing a "round-robin" style tournament, where each team plays every other team exactly once. How many games total need to be played? Justify your answer using a graph model—say what the vertices and edges of your graph represent, and what (if any) theorems you use. (Upload your file below.)
Answers
f(x) = 2/3 x -5 what is the value f(6)?
Answers
f(6)=4-5
f(6)=-1
Final answer: f(6)= -1
The surface areas of two similar solids are 340 yd2 and 1,158 yd2. The volume of the larger solid is 1,712 yd3. What is the volume of the smaller solid?
Answers
Let us say that,
1 = smaller solid
2 = larger solid
We must remember that the surface area of an object is proportional to the square of their sides, therefore,
SA = k s^2
where k is the constant of proportionality.
By taking the ratio of the 2 similar solids:
SA2 / SA1 = k s2^2 / k s1^2
SA2 / SA1 = s2^2 / s1^2
sqrt (SA2 / SA1) = s2 / s1
s2 / s1 = sqrt (1158 / 340)
While the volume of an object is proportional to the cube of
their sides, therefore:
V = k’ s^3
where k’ is the constant of proportionality.
By taking the ratio of the 2 similar solids:
V2 / V1 = k’ s2^3/ k’ s1^3
V2 / V1 = s2^3/ s1^3
1712 / V1 = [sqrt (1158 / 340)]^3
1712/V1 = 6.28556705
V1 = 272.37 yd^3
A tree is 6 feet 4 inches tall. How tall is it in inches?
Answers
The number of inches in 6 feet 4 inches tall is 76 inches.
Given that, a tree is 6 feet 4 inches tall.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 feet = 12 inches
So, 6 feet = 6×12
= 72 inches
Now, in inches = 72+4
= 76 inches
Therefore, the number of inches in 6 feet 4 inches tall is 76 inches.
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Rewrite sin 15 degree in terms of a 75 degree angle and in terms of the reciprocal of a trigonometric function.
Answers
[tex]\bf \cfrac{\sqrt{2}}{2}\cdot \cfrac{\sqrt{3}}{2}-\cfrac{\sqrt{2}}{2}\cdot \cfrac{1}{2}\implies \cfrac{\sqrt{6}}{4}-\cfrac{\sqrt{2}}{4}\implies \cfrac{\sqrt{6}-\sqrt{2}}{4}\\\\ -------------------------------\\\\ csc(15^o)=\cfrac{1}{sin(15^o)}\implies csc(15^o)=\cfrac{1}{\frac{\sqrt{6}-\sqrt{2}}{4}} \\\\\\ csc(15^o)=\cfrac{4}{\sqrt{6}-\sqrt{2}}[/tex]
and now, we can rationalize the denominator by using its conjugate and difference of squares.
[tex]\bf \cfrac{4}{\sqrt{6}-\sqrt{2}}\cdot \cfrac{\sqrt{6}+\sqrt{2}}{\sqrt{6}+\sqrt{2}}\implies \cfrac{4(\sqrt{6}+\sqrt{2})}{(\sqrt{6}-\sqrt{2})(\sqrt{6}+\sqrt{2})} \\\\\\ \cfrac{4(\sqrt{6}+\sqrt{2})}{(\sqrt{6})^2-(\sqrt{2})^2}\implies \cfrac{4(\sqrt{6}+\sqrt{2})}{6-2}\implies \boxed{\sqrt{6}+\sqrt{2}}[/tex]
Six years from today you need $10,000. you plan to deposit $1,500 annually, with the first payment to be made a year from today, in an account that pays an 8% effective annual rate. your last deposit, which will occur at the end of year 6, will be for less than $1,500 if less is needed to reach $10,000. how large will your last payment be?
Answers
We calculate the future value of the 6 annual deposits of $1500 at 8%:
F=1500(1.08^6-1)/(0.08)=11003.89
Since the last payment is due on the day of withdrawal, he would have paid $1500 to get back $11003.89, i.e. with an excess of 1003.89.
Therefore his last payment is 1500-1003.89=$496.11
Amount of last payment is approximately $497
Given that;
Number of year = 6 year
Annual deposit = $1,500
Annual rate = 8% = 0.08
Find:
Amount of last payment
Computation:
[tex]Future\ value = Annual\ deposit[(1+r)^n - 1]/r[/tex]
[tex]Future\ value\ of\ the\ 6\ annual\ deposits = 1500[\frac{(1+0.08)^6 - 1}{0.08}][/tex]
[tex]Future\ value\ of\ the\ 6\ annual\ deposits = 1500[(1.08)^6 - 1]/0.08\\\\Future value of the 6 annual deposits = 1500[0.58687]/0.08[/tex]
Future value of the 6 annual deposits = 11,003.25
Future value of the 6 annual deposits = $11,003 (Approx.)
Extra payment = 11,003 - 10,000
Extra payment = $1,003
So,
Amount of last payment = 1,500-1,003
Amount of last payment = $497
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A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x) =x^2-320x+40,052 . What is the minimum unit cost? Do not round your answer.
Answers
the lowest point, or lowest cost value, it reaches, is the U-turn point, or vertex
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llccll} y = &{{ 1}}x^2&{{ -320}}x&{{ +40052}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so, the lowest cost is at [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex]
4.4 mi/h how many ft/s
Answers
Answer:
about 6.45 ft/s
Step-by-step explanation:
The conversion factor for mph to fps is ...
1 mph = 22/15 fps
Multiplying by 4.4 gives ...
4.4 mph = 96.8/15 fps = 484/75 fps = 6 34/75 fps
≈ 6.4533333... ft per second
Write the ratio of 4 teachers to 134 students in simplest form.?
Answers
So it would be 2 teachers to 67 students
divide 134/4 = 33.5 that would be 1/33.5
since you can't have .5 student, multiply each side by 2
33.5*2 = 67
so 2/67 would be the simplest form using whole numbers
Find the amount of time to the nearest day it would take a deposit of $1300 to grow to 1 million at 17% compounded continuously. The amount of time it would take to grow the deposit to $1 million is____ years ___ days
Answers
[tex]\bf 1000000=1300e^{0.17t}\implies \cfrac{1000000}{1300}=e^{0.17t}\implies \cfrac{10000}{13}=e^{0.17t} \\\\\\ ln\left( \frac{1000000}{1300} \right)=ln(e^{0.17t})\implies ln\left( \frac{1000000}{1300} \right)=0.17t \\\\\\ \cfrac{ln\left( \frac{1000000}{1300} \right)}{0.17}=t\impliedby years[/tex]
now, how many days? simply multiply t * 365.
It would take approximately 39 years and 183 days for the deposit to grow to $1 million.
Use the concept of compound interest defined as:
The interest that is computed using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given that,
Initial deposit: $1300
Target amount: $1 million
Interest rate: 17%
Compounding: Continuous
Time to calculate: To the nearest day
To find the amount of time it would take,
Use the formula:
[tex]t = \dfrac{ln(\frac{M}{P})}{r}[/tex]
Where,
t = time in years
M = final amount ($1 million)
P = initial deposit ($1300)
r = interest rate (17% or 0.17)
Find the natural logarithm of the ratio M/P:
ln(1,000,000 / 1,300) ≈ 6.64
Divide the result by the interest rate:
t = 6.64 / 0.17
t ≈ 39.05 years
So, it would take approximately 39 years to grow the deposit to $1 million.
To determine the number of days,
Multiply the decimal part of the years by 365 (assuming a non-leap year):
0.05 x 365 ≈ 183 days
Hence,
Rounding to the nearest day, it would take approximately 39 years and 183 days for the deposit to grow to $1 million.
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The equation y = ax describes the graph of a line. If the valise of a is positive , the line:
Answers
like: y=5x, y=-14x, y=-7x, y=(1/2)x etc,
then this equation represents a line.
If :
i) a>0, the line is increasing
ii)a<0, the line is decreasing
iii) a= 0, then y=ax becomes y=0, which is the equation of the x-axis.
Answer: the line is increasing, that is it rises continuously as it moves to the right.
For what value of a does 9=(1/27)^a+3
Answers
[Note: Please review rules of PEMDAS.
The question posted as is means
9=[(1/27)^a]+3 which is probably not what you mean. It has been interpreted with (a+3) as the exponent, please check.]
Need to find value of a that satisfies above.
We will first isolate a in order to solve for its value.
9=(1/27)^(a+3)
Switch unknown to the left
(1/27)^(a+3) = 9
Since both 27 and 9 are powers of 3, we can take log to base 3.
take log (base 3) on both sides, applying rule of logarithm of exponents.
(a+3)log_3(1/27)=log_3(9)
(a+3)log_3(3^(-3))=log_3(3^2)
Apply definition of logarithm [log_a(a^k)=k]
(a+3)(-3)=2
(a+3)=-2/3
a=-3 2/3=-11/3
Check: (1/27)^(-11/3+3)=(1/27)^(-2/3)=(3^(-3))^(-2/3)=3^(-3(-2/3))=3^2=9 ok
Answer: a=-11/3 or a=-3.667 (approx.)
The value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3
Solving indical equationsThe given equation is:
[tex]9=(\frac{1}{27})^{a+3}[/tex]
This can be rewritten as:
[tex]9=27^{-1(a+3)}[/tex]
Which can be further simplified as:
[tex]3^2=3^{-3(a+3)}[/tex]
Since the bases are equal, they cancel out
The equation becomes:
2 = -3(a + 3)
2 = -3a - 9
2+9 = -3a
-3a = 11
a = -11/3
Therefore, the value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3
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(1 point) suppose that the trace of a 2×22×2 matrix aa is tr(a)=−4tr(a)=−4, and the determinant is det(a)=0det(a)=0. find the eigenvalues of aa.
Answers
[tex]\mathbf A=\begin{bmatrix}a&b\\c&d\end{cases}[/tex]
with [tex]\mathrm{tr}\,\mathbf A=a+d=-4[/tex] and [tex]\det\mathbf A=ad-bc=0[/tex]. We can find the eigenvalues of [tex]\mathbf A[/tex] in the usual way, by taking the determinant of [tex]\mathbf A-\lambda\mathbf I[/tex] and setting it equal to 0.
[tex]\begin{vmatrix}a-\lambda&b\\c&d-\lambda\end{vmatrix}=(a-\lambda)(d-\lambda)-bc=\lambda^2-(a+d)\lambda+(ad-bc)[/tex]
and we observe that the characteristic polynomial has linear coefficient [tex]-\mathrm{tr}\,\mathbf A[/tex] and constant coefficient [tex]\det\mathbf A[/tex]. Thus in this case we have the characteristic polynomial equation,
[tex]\lambda^2+4\lambda=\lambda(\lambda+4)=0\implies\lambda_1=0,\lambda_2=-4[/tex]
the slope of a line is 2/3. what is the slope of a line that is perpendicular to this line? Type a numerical answer in the space provided. do not include spaces in your answer. if necessary, use the / key to represent a fraction bar and only type improper fractions (no mixed numbers).
Answers
Find the number of interest periods required to achieve the conditions set forth. A = $5,000 P = $2,000 interest is 5% compounded semiannually
Answers
A=p (1+r/k)^n
A 5000
P 2000
R interest rate 0.05
K compounded semiannually 2
N number of interest periods=kt= 2t
5000=2000 (1+0.05/2)^2t
Solve for t
5000/2000=(1+0.05/2)^2t
Log (5000/2000)=2t×log (1+0.05/2)
2t=Log (5000/2000)÷log (1+0.05/2)
T=(log(5,000÷2,000)÷log(1+0.05÷2))÷2
T=18.55 years round your answer to get 19 years
So the number of interest periods required to achieve the conditions set forth is
N=kt
N=2×19
N=38
Which is least? 0.105 0.501 0.015 or 0.15
Answers
Because it is the farthest away from the one's place.
The lowest decimal number from 0.105, 0.501, 0.015, and 0.15 is 0.015. This is because when we compare the numbers from left to right, 0.015 has the smallest digit (0) at the second decimal place which is the hundredths place.
Explanation:To determine which decimal number is the lowest, it's helpful to compare these numbers digit by digit from the left. The four numbers are 0.105, 0.501, 0.015, and 0.15. Each of them starts with 0. The second digit of 0.105, 0.501, and 0.15 is 1, but the second digit for 0.015 is 0. So, 0.015 is the lowest number because it has the smallest digit (0) in the second decimal place (hundredths place). Remember, these numbers are read as decimals and not as whole numbers, so the digit at each decimal place has a different significance.
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There are 9 more pencils then pens in a container. There are 25 writing utensils in the container in all. How many pens are there in the container?
Answers
let x the number of pencils
y the number of pens
From the statement, 9 more pencils then pens in a container,
x = y + 9
From the statement, there are 25 writing utensils in the container in all,
x + y = 25
We use substitution method to calculate for x and y,
y + 9 + y = 25
2y = 16
y = 8
x = 17
Therefore, there are 8 pens in the container and 17 pencils.
which number is a factor of 20, but not a multiple of 2? 12, 5, 10 or 4?
Answers
20/4 = 5 however,
2 x 2.5 = 5 (it doesn't work, cannot have decimals)
so 5 is your answer
hope this helps
So 1 or 20 is that number
The Canadian $1 coin has a diameter of 26.5 mm.what is the circumference of the coin?use 3.14 for pie
Answers
circumference = diameter x PI
26.5*3.14 = 83.21 mm
Answer: 83.21 mm
Step-by-step explanation:
The circumference of a circle is given by :-
[tex]\text{Circumference }=\pi d[/tex]
Given : The Canadian $1 coin has a diameter of 26.5 mm.
Then , the circumference of the coin will be :-
[tex]\text{Circumference of coin}=\pi (26.5)=(3.14)(26.5)\\\\\Rightarrow\text{Circumference of coin}=83.21\text{ mm}[/tex]
Hence, the circumference of the coin is 83.21 mm
Would you measure walls using inches or yards
Answers
can someone pls answer
Answers
9y = -11x +36
y = -11/9 +4
y = 4
Two parallel lines are crossed by a transversal. What is the value of x?
A. x = 12
B. x = 14
C. x = 22
D. x = 24
Answers
5x + 120 = 180
5x = 180 - 120
5x = 60
x = 60/5
x = 12
Answer
x = 12
Explanation
The two given angles are supplementary angles. That means that the add up to 180 degrees.
(5x + 5) + 115 = 180
5x +5 + 115 = 180
5x + 120 = 180
5x= 180 - 120
5x = 60
x = 12
A Way to write numbers by using the digits 0-9, with each digit havin a place value
______ ?
Answers
This way is the common way we usually use to write numbers. Other ways include the written form and the expanded form.
Take 100 as an example:
Standard form : 100
Written form : one hundred
Expanded form : 50 + 30 + 20
what is the least common multiple of 20 and 52
Answers
hope this helps:)
The least common multiple of 20 and 52 is, 420
What is Least common multiple?The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Given that;
The numbers are,
⇒ 20 and 52
Now, The factors of numbers are,
⇒ 20 = 2 × 2 × 5
⇒ 42 = 2 × 3 × 7
Hence, The least common multiple of 20 and 52 is,
⇒ LCM of {20, 52} = 2 × 2 × 5 × 3 × 7
= 420
Thus, The least common multiple of 20 and 52 is, 420
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