Answer:
c
Step-by-step explanation:
commission is basically 3 percent of what he sells he gets, sooooo 3 percent of 3800 is 114 (3800 × .03 because change the percent to decimal) and add it to his pay :)
Answer:
D
Step-by-step explanation:
use the coordinate plane to answer the question What point is at (1,-3)
Answer:
Step-by-step explanation:
the x coordinate is to the right so your choices are J A K G and C. You know this because 1 is positive and that moves to the right.
The -3 moves 3 units below the x axis. That limits your answer to KCG
We have to assume that each square is worth one, so the answer must be C.
Which expression is equivalent to (2^1/2*2^3/4)^2?
Answer: 4
Step-by-step explanation:
Answer:
[tex]2^{\frac{5}{2}}[/tex]
Step-by-step explanation:
We have to solve the given expression [tex][(2)^{\frac{1}{2}}(2)^{\frac{3}{4}}]^{2}[/tex]
As we know [[tex]x^{a}.x^{b}=x^{a+b}[/tex]]
Now by solving the given expression by this identity
[tex][2^{\frac{1}{2}+\frac{3}{4}}]^{2}[/tex]
= [tex][2^{\frac{5}{4}}]^{2}[/tex]
= [tex]2^{\frac{(5)(2)}{4}}[/tex]
= [tex]2^{\frac{10}{4} }[/tex]
= [tex]2^{\frac{5}{2}}[/tex]
Therefore, the given expression can be represented by [tex]2^{\frac{5}{2}}[/tex].
Help with these questions, please!! I don't understand them!
Answer:
• arc PS = 40°
• arc UV = 24°
Step-by-step explanation:
There are relationships between the arcs intercepted by secant lines and the angle the secant lines make with each other. In these problems, you are expected to make use of these relationships, along with others you have learned about triangles.
The relationships are basically these:
• when the secants intersect inside the circle, the angle between them is half the sum of the intercepted arcs.
• when the secants intersect outside the circle, the angle between them is half the difference of the intercepted arcs.
__
First problem:
The angle between the secants QS and PR is shown to be 50°. Intercepted arc QR is shown to be 60°. You are asked to find the other intercepted arc, PS. Based on the above, we know ...
∠POS = (1/2)(arc PS + arc QR)
50° = (1/2)(arc PS + 60°)
Multiplying by 2, we get ...
100° = arc PS + 60°
Subtracting 60°, gives ...
40° = arc PS
__
Second problem:
We need to name a couple of points so we can describe more clearly what is going on. Call the point on arc PS where line QT intersects it point R. Call the point where line QT crosses line SU point X. (Point X is the vertex of the 99° angle.)
The relations described above tell us ...
angle W = (1/2)(arc PS - arc UV)
In this equation, we only know the value of arc PS = arc PR + arc RS = 20° + 94° = 114°.
But, we know two of the angles in triangle QWX. They are angle Q = 36° and angle X = 99°. Then angle W must be ...
angle W = 180° -36° -99° = 45°
Now, we can finish the above equation involving arc UV:
45° = (1/2)(arc PS - arc UV) . . . . . put the values we know in the secant relation
90° = 114° -arc UV
arc UV = 114° -90° = 24° . . . . . . . .solve for arc UV
Answer: i think he answered ur Q and i need points so sorry
please forgive me
Step-by-step explanation:
Ik it’s 7 in the morning but can somebody help a gal out
Answer:
10
Step-by-step explanation:
The vertical scale gives us the frequency or the number of pets under each category . From the diagram;
The number of Dogs is 11 while there is only 1 horse
The difference between this numbers will be the solution to the question posed;
11 - 1 = 10
Therefore, 10 more dogs are pets than horses
Answer: 10
Step-by-step explanation:
11 - 1
Which fraction is equivalent to seventy-five hundrths?Three fourths,three sixths,one third,orone fourth
Three forths (75%, 0.75, 3/4)
can someone check this one for me , thank you!
Answer:
C
Step-by-step explanation:
Using sum/difference to product identity
• sin x - sin y = 2 cos([tex]\frac{x+y}{2}[/tex]) sin ([tex]\frac{x-y}{2}[/tex])
with x = 4Θ and y = 2Θ
Then
sin(4Θ) - sin(2Θ)
= 2 cos([tex]\frac{4o+2o}{2}[/tex]) sin([tex]\frac{4o-2o}{2}[/tex])
= 2cos(3Θ)sinΘ → C
50 POINTS! NEED HELP ASAP!
Which logarithmic graph can be used to approximate the value of y in the equation 3y = 8? (6 points)
Answer:
The answer is the graph in the image.
Give brainliest if you please. :)
A logarithmic graph that can be used to approximate the value of y in the equation [tex]3^y = 8[/tex] is =: B. graph B.
In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]y = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, or base.Based on the information provided above, we can logically deduce the following equation;
[tex]3^y = 8[/tex]
By applying base 3 logarithm to boths sides of the equation, we have;
[tex]log_{3}(3^y)=log_{3}(8)\\\\ylog_{3}3=log_{3}8\\\\y=log_{3}8\\\\y\approx 1.89\\\\\\\\y=log_{3}x[/tex]
In conclusion, we can reasonably infer and logically deduce that only graph B is a logarithmic graph that can be used to approximate the value of y in the equation [tex]3^y = 8[/tex], which is approximately equal to 1.89.
Missing information:
Which logarithmic graph can be used to approximate the value of y in the equation [tex]3^y = 8[/tex]?
Deborah bought some bouquets of flowers. She wrote this equation to show the number of flowers in one bouquet. F = 6 deborah bought 4 bouquets of flowers. Which equation represents the number of flowers she has altogether? a. 4 × f = 6 b. 4 × f = 10 c. 4 × f = 4 × 6 d. 6 × f = 6 × 4
Answer:
c
Step-by-step explanation:
4×F=4×6 because if one bouquet is 6 flowers, and you had 4 bouquets youd have 4 times as many flowers
3 cards are drawn at random from a standard deck.
Find the probability that all the cards are hearts.
Find the probability that all the cards are face cards.
Note: Face cards are kings, queens, and jacks.
Find the probability that all the cards are even.
(Consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13)
The probabilities of drawing all hearts, face cards, or even cards are calculated with the formula: [tex](n/52) * ((n-1)/51) * ((n-2)/50)[/tex] where n is the total number of cards that match the desired outcome.
Explanation:The subject here is probability, specifically, how to determine the likelihood of a particular outcome when drawing cards from a standard deck. Let's deal with each probability one at a time.
The probability that all the cards are hearts: There are 13 hearts in a deck of 52 cards. So the probability that the first card is a heart is 13/52, the second is 12/51 (because one heart is already drawn), and the third is 11/50. So, the overall probability is [tex](13/52) * (12/51) * (11/50).[/tex]The probability that all the cards are face cards: There are 12 face cards (kings, queens, and jacks) in a deck. Using the same principle, the probability is [tex](12/52) * (11/51) * (10/50).[/tex]The probability that all the cards are even: The 'even' cards are 2, 4, 6, 8, 10, which have 4 of each (hearts, diamonds, spades, clubs) totaling 20 cards. So, the probability is [tex](20/52) * (19/51) * (18/50).[/tex]Learn more about Probability here:
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Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 2 of x squared, dx .
Split up the interval [0, 2] into 4 subintervals, so that
[tex][0,2]=\left[0,\dfrac12\right]\cup\left[\dfrac12,1\right]\cup\left[1,\dfrac32\right]\cup\left[\dfrac32,2\right][/tex]
Each subinterval has width [tex]\dfrac{2-0}4=\dfrac12[/tex]. The area of the trapezoid constructed on each subinterval is [tex]\dfrac{f(x_i)+f(x_{i+1})}4[/tex], i.e. the average of the values of [tex]x^2[/tex] at both endpoints of the subinterval times 1/2 over each subinterval [tex][x_i,x_{i+1}][/tex].
So,
[tex]\displaystyle\int_0^2x^2\,\mathrm dx\approx\dfrac{0^2+\left(\frac12\right)^2}4+\dfrac{\left(\frac12\right)^2+1^2}4+\dfrac{1^2+\left(\frac32\right)^2}4+\dfrac{\left(\frac32\right)^2+2^2}4[/tex]
[tex]=\displaystyle\sum_{i=1}^4\frac{\left(\frac{i-1}2\right)^2+\left(\frac i2\right)^2}4=\frac{11}4[/tex]
Suppose your friend multipled 1.2 and 2.6 and got 31.2 as the product. Is your friend's answer reasonable? Justify your response
Answer:
no
Step-by-step explanation:
What is the simplified version of [tex](2\sqrt{5}+3)(\sqrt{5}-1)[/tex]
ANSWER
EXPLANATION
We want to simplify:
[tex](2\sqrt{5}+3)(\sqrt{5}-1)[/tex]
Recall the distributive property;
(a+b)(c+d)=a(c+d)+b(c+d)
We apply this property to get,
[tex]2\sqrt{5}(\sqrt{5}-1) + 3(\sqrt{5}-1)[/tex]
We expand to get,
[tex]2 \times 5-2 \sqrt{5} + 3\sqrt{5}-3[/tex]
This simplifies to,
[tex]10 + \sqrt{5}-3[/tex]
The simplest form of the given expression is:
[tex]7 + \sqrt{5}[/tex]
You have 1 case of soap bars and there are 150 bars in a case you use 300 bars of soap per day how many cases do you need to order to have enough for 7
Answer:
13 cases
Step-by-step explanation:
we know that
You have 1 case of soap bars
There are 150 bars in a case
You use 300 bars of soap per day ----> 2 cases per day
using proportion
Find how many cases do you need to order to have enough for 7 days
Let
x ----->the number of cases
2/1=x/7
x=2*7=14 cases
but remember that you have 1 case
so
you needed 14-1=13 cases
Find the greatest common factor of 7w and 4m 3
Answer:
Greatest common factor = 1
Step-by-step explanation:
given algebraic expressions are 7w and [tex]4m^3[/tex].
Now we need to find about what is the greatest common factor that is GCF of given algebraic expressions 7w and [tex]4m^3[/tex].
7 is a prime number so that can't be factored more.
There is no common factor of 7 and 4 except 1.
there is no common factor of w and [tex]m^3[/tex].
Hence required greatest common factor of given algebraic expressions 7w and [tex]4m^3[/tex] is 1.
Evaluate this exponential expression. 3 • (5 + 4)2 – 42 =
Final answer:
The expression 3 · (5 + 4)2 – 42 evaluates to 227, after applying the order of operations to add, square, multiply, and subtract the given numbers.
Explanation:
To evaluate the given exponential expression 3 · (5 + 4)2 – 42, we follow the order of operations, commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, we add the numbers inside the parentheses: (5 + 4), which equals 9.
Next, we raise this sum to the power of 2: 92, which is equal to 81.
Then, we calculate 42, which is 16.
Now, we multiply 3 by the result of 92: 3 · 81, giving us 243.
Lastly, we subtract 42 from this result: 243 – 16, yielding the final answer of 227.
The final result of the expression 3 · (5 + 4)2 – 42 is 227.
IQ scores are measured with a test designed so that the mean is 120 and the standard deviation is 12. Consider the group of IQ scores that are unusual. What are the z scores that separate the unusual IQ scores from those that are usual? What are the IQ scores that separate the unusual IQ scores from those that are usual? (Consider a value to be unusual if its z score is less than minus2 or greater than 2.)What are the IQ scores that separate the unusual IQ scores from those that are usual?
Answer:
Step-by-step explanation:
Here a score is considered to be "unusual" if higher than 2 std. dev. from the mean OR lower than 2 std. dev. from the mean.
Thus, any score lower than (120 - 2[12]), or 96, or higher than (120 + 2[12] ), or 144, is considered to be "unusual."
someone please help me i'll mark you brainliest
The Quotient is 8 and you would simplify if that's an option
if its not then I will tell you what else it could be
Answer:
Step-by-step explanation:
"What is the sum of 4/5 and 1/10, and how do I show that in this illustration?"
The result of this addition is 8/10 + 1/10, or 9/10; this is "the quotient" desired.
In the graph, we could divide each rectangle vertically, so that each half of each rectangle represents 1/10. Adding 8 and 1 of these newly-drawn rectangles results in 9 such rectangles, which corresponds to 9/10 as the sum of the two fractions.
This is part of an invoice that Sharon Niles received for a shipment of items. What is the last day Sharon can take advantage of the EOM discount?
A. April 18, 2012
B. May 10, 2012
C. May 8, 2012
D. April 30, 2012
assuming 7/10 eom means 7 - 10 days after, your answer would be A. April 18th, 2012.
Answer:
Option A. April 18,2012.
Step-by-step explanation:
This invoice of stationary is dated 8 April 2012, and terms written on it 7/10 EOM.
It means 7% discount of the payment within 10 days or full payment at the End of the Month (EOM)
Therefore, the last day Sharon can take advantage is 10 days after the date of invoice.
Date of invoice = April 8, 2012
after 10 days = April 18, 2012
Option A. is the correct answer.
X2 - 4x + 4 A. 4(x2 - x + 1) B. (x - 2)(x + 2) C. (x + 2)(x + 2) D. (x - 2)(x - 2)
Answer:
D. (x - 2)(x - 2)
Step-by-step explanation:
x² - 4x + 4 = (x -2)(x -2)
___
The expression matches the form ...
(a +b)² + a² +2ab +b²
where a = x and b = -2
George is drafting his dissertation paper for his doctoral program. The graph below shows the line of best fit for the data recorded on the number of
pages of the dissertation written as a function of the number of hours George spends on the draft each week.
Answers and Graph are in the picture(s)
Answer: the answer to your question is D i graphed them all that one is correct D
The equation of the line will be y = 2/3 x + 4.
What is the equation of a line passing through two points?Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by
[tex]\rm (y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
George is drafting his dissertation paper for his doctoral program.
The graph below shows the line of best fit for the data recorded on the number of pages of the dissertation writing as a function of the number of hours George spends on the draft each week.
(x₁, y₁) → (0, 4)
(x₂, y₂) → (6, 2)
Then the equation of the line will be
y - 4 = [(6 - 4) / (3 - 0)] (x - 0)
y - 4 = 2/3 x
y = 2/3 x + 4
Then the correct option is D.
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Enter a recursive rule for the geometric sequence.
10, −80, 640, −5120, ...
Answer:
an = 10 (-8)^(n-1)
Step-by-step explanation:
In a geometric series, each term is multiplied by a common ratio to get the next term. Such that:
an = a₁ (r)^(n-1)
Here, the first term, a₁, is 10. The common ratio, r, is -8, because each term is multiplied by -8 to get the next term. So:
an = 10 (-8)^(n-1)
Your answer is correct, well done!
The recursive rule of the geometric sequence is [tex]a_{n+1}= -8a_n[/tex] where a1 = 10
How to determine the recursive rule?The geometric sequence is given as:
10, −80, 640, −5120, ...
Start by calculating the common ratio (r)
[tex]r = \frac{a_{n-1}}{a_n}[/tex]
Substitute 2 for n
[tex]r = \frac{a_{2}}{a_1}[/tex]
Substitute known values
[tex]r = \frac{-80}{10}[/tex]
Evaluate the quotient
[tex]r = -8[/tex]
Substitute -8 for r in [tex]r = \frac{a_{n+1}}{a_n}[/tex]
[tex]-8 = \frac{a_{n+1}}{a_n}[/tex]
Cross multiply
[tex]a_{n+1}= -8a_n[/tex]
Hence, the recursive rule of the geometric sequence is [tex]a_{n+1}= -8a_n[/tex] where a1 = 10
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EASY POINTS! What is the subtotal for the building materials in the bill? The subtotal should be the cost of the materials only. Don't add taxes or subtract any discounts.
A. $1,358.00
B. $1,658.00
C. $639.00
D. $239.69
Answer:
D. :)
Step-by-step explanation:
The total cost of materials is $1658
How to find the total cost?
Total cost is defined as the addition of the cost of individual material.
Cost of material=Cost*Number of pieces
Cost of:
Lumber= 20*16.69Material A=2*20.78Material B=2*15.58Material C=6*21.38Material D=118*6.60Brick=500*0.22Pipe=10*8.44Hammer drill=1*150Adding them up: 20*16.69+2*20.78+2*15.58+6*21.38+118*6.60+500*0.22+10*8.44+1*150
=$1658
Therefore, The subtotal of costs of material is $1658.
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find the ordered triple to represent u in u=3v-2/3w +2z if v=(4,-3,5) w=(2,6,-1) and z=(3,0,4)
Answer:
u=(14/3 ,-13,23/3)
Step-by-step explanation:
Given
u=3v-2/3 w+2z
And
v=(4,-3,5)
w=(2,6,-1)
z=(3,0,4)
Putting the values of v,w and z
u=3(4,-3,5)-2/3 (2,6,-1)+2(3,0,4)
u=(12,-9,15)-(4/3,12/3,-2/3)+(6,0,8)
=(12,-9,15)-(4/3,4,-2/3)+(6,0,8)
We will perform the addition first..
=(12,-9,15)-(4/3+6 ,4+0,-2/3+8)
= (12,-9,15)-(22/3,4,22/3)
Subtraction will give us:
=(12-22/3 ,-9-4 ,15-22/3)
=(14/3 ,-13,23/3)
Final Answer:
The ordered triple for vector u is then [tex]\( u = (17\frac{2}{3}, -13, 23\frac{2}{3}) \)[/tex]
Explanation:
To find the ordered triple that represents the vector u in the equation [tex]\( u = 3v - \frac{2}{3}w + 2z \)[/tex], we need to perform the vector operations on v = (4, -3, 5), w = (2, 6, -1) , and z = (3, 0, 4).
Step 1: Multiply vector v by 3.
[tex]\[ 3v = 3 * (4, -3, 5) = (3*4, 3*(-3), 3*5) = (12, -9, 15) \][/tex]
Step 2: Multiply vector w by [tex]\( -\frac{2}{3} \)[/tex].
[tex]\[ -\frac{2}{3}w = -\frac{2}{3} * (2, 6, -1) = (-\frac{2}{3}*2, -\frac{2}{3}*6, -\frac{2}{3}*(-1)) = (-\frac{4}{3}, -\frac{12}{3}, \frac{2}{3}) \\\\\[ -\frac{2}{3}w = (-\frac{4}{3}, -4, \frac{2}{3}) \\\\\[ -\frac{2}{3}w = (-1\frac{1}{3}, -4, \frac{2}{3}) \][/tex]
Step 3: Multiply vector \( z \) by 2.
[tex]\[ 2z = 2 * (3, 0, 4) = (2*3, 2*0, 2*4) = (6, 0, 8) \][/tex]
Step 4: Add the resulting vectors from steps 1, 2, and 3.
We add the corresponding components from each vector:
[tex]\[ (12, -9, 15) + (-1\frac{1}{3}, -4, \frac{2}{3}) + (6, 0, 8) \][/tex]
To add these, perform the addition component-wise:
- For the first component:
[tex]\[ 12 + (-1\frac{1}{3}) + 6 = 12 - 1\frac{1}{3} + 6 = 11\frac{2}{3} + 6 = 17\frac{2}{3} \][/tex]
- For the second component:
[tex]\[ -9 + (-4) + 0 = -9 - 4 = -13 \][/tex]
- For the third component:
[tex]\[ 15 + \frac{2}{3} + 8 = 15 + \frac{2}{3} + 8 = 23\frac{2}{3} \][/tex]
The ordered triple for vector u is then [tex]\( u = (17\frac{2}{3}, -13, 23\frac{2}{3}) \)[/tex].
However, to express this as a proper ordered triple, we usually write the components as fractions or decimals. So, let's convert the fractions into decimals:
[tex]\[ 17\frac{2}{3} = 17 + \frac{2}{3} = 17 + 0.666\ldots \approx 17.67 \\\\\[ 23\frac{2}{3} = 23 + \frac{2}{3} = 23 + 0.666\ldots \approx 23.67 \][/tex]
So the ordered triple for vector u in decimal form is approximately u = (17.67, -13, 23.67).
Please note that the approximation is to two decimal places. If exact values are desired, it is best to leave the answer in fraction form as [tex]\( u = (17\frac{2}{3}, -13, 23\frac{2}{3}) \)[/tex].
Consider the function represented by the equation y – x – 4 = 0. What is the equation written in function notation, with x as the independent variable?
Writing an equation in function notation, with x as the independent variable is the same as solving the equation for y.
So, we start with
[tex]y-x-4=0[/tex]
and we move [tex]-x-4[/tex] to the right hand side, i.e. we add [tex]x+4[/tex] to both sides:
[tex]y-x-4+(x+4)=0+(x+4) \iff y=x+4[/tex]
Which function is the inverse of f(x) = –5x – 4?
The answer is C. f(X)=-1/5x-4/5
Hope this helps !!
Answer:
[tex]f^{-1}(x)=-\frac{1}{5} x-\frac{4}{5}[/tex]
Step-by-step explanation:
It is called an inverse or reciprocal function of [tex]f[/tex] to another function [tex]f^{-1}[/tex] that fulfills that:
If [tex]f(a)=b[/tex], then [tex]f^{-1} (b)=a[/tex]
The inverse of [tex]f(x)=-5x-4[/tex] is:
We change the x for the y
[tex]x=-5y-4[/tex]
Now, let's clear y
[tex]y=\frac{x+4}{-5}[/tex]
Ordering
[tex]y = -\frac{1}{5} x-\frac{4}{5}[/tex]
So, the inverse of the function [tex]f(x)=-5x-4[/tex] is:
[tex]f^{-1}(x)=-\frac{1}{5} x-\frac{4}{5}[/tex]
.
Which of the following is the best estimate of the direction of the given vector?
Answer:
The direction of the given vector is 45° N of W
Step-by-step explanation:
* Lets revise the four directions with the four quadrants
- The four directions are:
# North which represented by the positive part of y-axis
# South which represented by the negative part of y-axis
# East which represented by the positive part of x-axis
# West which represented by the negative part of y-axis
∴ The first quadrant is between the East and the North
∴ The second quadrant is between the West and the North
∴ The third quadrant is between the West and the South
∴ The fourth quadrant is between the East and the South
* The direction of any vector is tan Ф, where Ф is the angle between
the vector and the x-axis, then:
- The direction of North of East is 45° ⇒ first quadrant
- The direction of North of West is 45° ⇒ second quadrant
- The direction of South of West is 45° ⇒ third quadrant
- The direction of South of East is 45° ⇒ fourth quadrant
* Now lets solve the problem
∵ The direction of the vector is between the North and the West
(its vertex in the second quadrant)
∴ Its direction is 45° North of West
* The direction of the given vector is 45° N of W
Tayler has $320 $ 320 to pay for dining room chairs. She expects to pay about $80 $ 80 per chair. Her friend told her that she has 3 3 that Taylor can have for free. Complete the equation below to find the total number of chairs that Taylor can get for her dining room. Use c to represent the total chairs.
Answer:
7
Step-by-step explanation:
The formula would be c=(320/x)+3
C is the total chairs and x is the price per chair and we add 3 since she is getting 3 for free
Following PEMDAS, we should do 320/80 first which is 4
Then the equation becomes 4+3=7
Please help with this don’t understand please help with answers!
Answer:
see attachment
Step-by-step explanation:
The directions tell you what you need to know. It is a matter of adding up the values shown and finding the missing number to make the total be -20. Of course, it works best to start with a row, column, or diagonal that has 4 numbers already.Then, you're only finding the 5th number.
You can start with either diagonal, column 1 or 4, and row 4 or 5. Filling the missing numbers in those spots (red) will let you find the remaining missing numbers (green, then blue).
The square at row 2, column 2 can be filled on the first round using the down-right diagonal. I have shown it as filled on the second round after row 5 column 2 is filled.
Using a spreadsheet can make this easier, because you can write formulas for the sums in each row, column, and diagonal. Then you're just making those sums be -20.
___
For example, consider the up-right diagonal. The sum of the given values, -6, 0, -4, -2, is -12. Then the spot at row 1, column 5 must be filled with -8 to make the sum be -20.
What is the similarity ratio of a cube with volume 216 m³ to a cube with volume 2744 m³
A. 3:7
B. 7:3
C. 36:196
D. 196:36
Answer:
A. 3:7
Step-by-step explanation:
The volume of the smaller cube is 216 m³.
The volume of the larger cube is 2744 m³
Let the similarity ratio be [tex]l:L[/tex]
The volume of these two cubes are in the ratio:
[tex]l^3:L^3=216:2744[/tex]
This implies that:
[tex](\frac{l}{L})^3 =\frac{216}{2744}[/tex]
We take the cube root of both sides to obtain:
[tex]\frac{l}{L} =\sqrt[3]{\frac{216}{2744}}[/tex]
[tex]\frac{l}{L} =\frac{6}{14}[/tex]
This simplifies to:
[tex]\frac{l}{L} =\frac{3}{7}[/tex]
Therefore the ratio is 3:7
William is planning to create a rectangular mosaic which measures 120 cm by 144 cm. The mosaic will be covered completely with square pieces of colored glass. William has decided that he will purchase only one size of glass squares, and he does not plan to cut any of the pieces. If the art supply store only sells the glass squares in whole-number side lengths (measured in centimeters), find the smallest number of squares which William could use for his mosaic.
Answer:
30
Step-by-step explanation:
We need to find the greatest common factor of 120 and 144.
First, write the prime factorization of both:
120 = 2³×3×5
144 = 2⁴×3²
Both have 2³ and 3 in common, so the GCF is:
GCF = 2³×3
GCF = 24
So the side length is 24 cm. The number of squares along the width is:
120 / 24 = 5
And the number of squares along the length:
144 / 24 = 6
So the number of squares need to fill the entire area is 5×6 = 30. This is the least number of squares with whole-number side lengths that he can use.