Danny's belief that doubling all three dimensions would double the volume of the tool box is incorrect.A tool box has the dimensions of 8 in by 5 in by 4 in.
If Danny plans to double all three dimensions to build a larger tool box, he believes he would double the volume of the tool box. Danny is incorrect about doubling all three dimensions to build the larger tool box. If he doubles all three dimensions, the new volume will not be exactly double the volume of the original tool box.
Let's calculate the volume of the original tool box:
Volume = Length x Width x Height
Volume = 8 in x 5 in x 4 in
Volume[tex]= 160 in³[/tex]
Now, if Danny doubles all three dimensions, the new dimensions would be:
Length = 2 * 8 in = 16 in
Width = 2 * 5 in = 10 in
Height = 2 * 4 in = 8 in
The volume of the larger tool box would be:
Volume = Length x Width x Height
Volume = 16 in x 10 in x 8 in
Volume [tex]= 1280 in³[/tex]
Therefore, the volume of the larger tool box is not double the volume of the original tool box[tex](160 in³)[/tex], but rather[tex]1280 in³[/tex]. So, Danny's belief that doubling all three dimensions would double the volume of the tool box is incorrect.
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Which geometric shape could be used to model the building?
cylinder
pyramid
cone
rectangular prism
Answer:
Rectangular Prism
Step-by-step explanation:
We usually see building shaped as a 3D rectangle. If this is the type of building you are talking about, we use a rectangular prism in order to build the building with correct measurements.
Choose the equation that satisfies the data in the table.
Answer:
Option A.
Step-by-step explanation:
Demonstration
[tex]y=\frac{7}{4} x+7[/tex]
for x = -4
[tex]y=\frac{7}{4} (-4)+7=-\frac{28}{4} +7=-7+7=0[/tex]
for x= 0
[tex]y=\frac{7}{4}(0) +7=0+7=7[/tex]
for x= 4
[tex]y=\frac{7}{4} (4)+7=\frac{28}{4} +7=7+7=14[/tex]
Hope this helps
prove that if r is a matrix in echelon form, then a basis for row(R) consists of the nonzero rows of R
Let [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex] be the nonzero rows of [tex]$R$[/tex] starting from the 1st row to the [tex]k[/tex]th row.
Step 1: We want to show that
R(R)= span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]
For any vector [tex]v $$\in \mathcal{R}(R)$$[/tex], We may write
v= [tex]$$c_{1} \boldsymbol{r}_{1}+c_{2} \boldsymbol{r}_{2}+\cdots+c_{k} \boldsymbol{r}_{k}+c_{k+1} \mathbf{0}+\cdots+c_{m} \mathbf{0}$$[/tex]
Then v= [tex]$$c_{1} r_{1}+c_{2} r_{2}+\cdots+c_{k} r_{k}$$[/tex]
So [tex]v[/tex] belongs to span{ [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]}
Thus R(R)[tex]\leq[/tex] Span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]
But trivially,
span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]≤ span{[tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex], 0, . . . , 0} = R(R),
span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]=R(R)
Step 2: We want to show that [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]are linearly independent. Suppose otherwise,
then we can write
[tex]$$c_{1} \boldsymbol{r}_{i_{1}}+\cdots+c_{\ell} \boldsymbol{r}_{i_{\ell}}=\mathbf{0}$$[/tex]
From Steps 1 and 2, we have proven that the nonzero rows of R form a basis for the row space.
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If WX= 82 cm, find the length of YZ. (OV = 9cm and OV is perpendicular to YZ)
The length of the measure of YZ is 80cm
Perpendicular linesPerpendicular lines are lines that are at angle 90 degrees to each other. From the given diagram;
WX = 82cm
Required
Length. of YZ
Using the pythagoras theorem
YV = VZ = √41²-9²
YV = VZ = √1600
YV = VZ = 40
Since YZ = YV + VZ
YZ = 40cm + 40cm
YZ= 80cm
Hence the length of the measure of YZ is 80cm
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please answer both asap!!!
The following two-way table describes student's
after school activities. find the probability that a
randomly selected student either does sports or
works.
grade
sports
music/drama
work
20
7
sophomore
3
junior
20
13
2
25
5
senior
5
p(sports u work) = [?]
round to the nearest hundredth.
lol
P ( work/ senior ) = 0.14
The attached table
required
P ( work/ senior )
This is calculated using:
P ( work/ senior ) = n ( work/ senior )/ n ( senior ).
n ( work/ senior ) = 5
n ( senior ) = 25 + 5 + = 35
So:
P ( work/ senior ) = 5/35
P ( work/ senior ) = 0.14
Add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).
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How do I put the pairs for the values in the domain
Answer:
Step-by-step explanation: use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.
Help please!!!
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The parameters of the sinusoidal function graphs can be found from the coordinates of the given locations.
First graph;
a. Amplitude = 0.5
b. The period = 2•π
c. The horizontal shift = 1
d. The vertical shift = π/4
Second graph;
a. Amplitude = 2
b. The period = π
c. The horizontal shift = -π/4
d. The vertical shift = -2
Which method can be used to find the graph parameters?First graph;
a. The amplitude is half the distance between the y-value peak point and the y-value of a throw (lowest point) on the graph.
The coordinate of a peak point in the first graph is (0, -1.5)
The coordinate of a throw point is (π/2, -2.5)
Therefore;
Amplitude = (-1.5 - (-2.5)) ÷ 2 = 0.5
b. The period is the number of cycles per second, we have;
Period = 1/ff = FrequencyFrom the graph, we have;
f = 1 cycle per πTherefore;
The frequency = 1/π cycle per unit length
Period = 1/(1/π) = πc. The horizontal shift is the distance from the closet intersection of the midline and the rising region of the graph and the y-axis.
Therefore;
The horizontal shift = (-π/2)/2 = -π/4
d. The vertical shift is the distance from the horizontal axis to the midline of the graph.
By observation, the midline is y = -2
Therefore;
The vertical shift = -2Second Graph;
For the second graph, we have;
a. Amplitude = (3 - (-1))/2 = 2
b. Frequency = 1/(2×(5•π/4 - π/4)) = 1/(2•π)
Therefore;
Period = 1/(1/(2•π)) = 2•πc. Horizontal shift = Distance between x-coordinate of the intersection of the midline and the graph and the x-coordinate of the closest peak.
Therefore;
Horizontal shift = π/4 - 0 = π/4d. Vertical shift = (3 + (-1))/2 = 1
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I can't figure out the equivalent fraction. Whoever gets it first gets brainliest, and please do explaination
Factorize the numerator and denominator. You'll see that they both have a factor of 4 that can be canceled. The introduce a factor of 3 to change the denominator to 36.
[tex]\dfrac{28}{48} = \dfrac{4\times7}{4\times12} = \dfrac7{12} = \dfrac{3\times7}{3\times12} = \boxed{\dfrac{21}{36}}[/tex]
Use the box-and-whisker plots to determine which statements are true.
The true statements are :
the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.
The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.
What are the true options?
A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers. The whiskers represents the minimum and maximum scores.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Range for New Orleans = 85 - 50 = 35
Range for Indianapolis = 75 - 25 = 50
Median for New Orleans = 70
Upper quartile for Indianapolis = 70
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Matthew is flying with his jet pack at 100m/min. A strong wind has blown him 10m east of his intended flight path in 2 minutes. By how many degrees is Matthew off his flight path? Include a diagram.
Mathew's speed of 100 m/min, and the distance of 10 m. east to which he is blown by the wind gives the angle in degrees Mathew is blown off his path as approximately 2.86°.
How can the angle of deflection be found from the given speeds?The given parameters are;
Speed at which Mathew is flying = 100 m/min
Distance and direction in which the strong wind blows him = 10 m. east
Time it takes the wind to deflect Mathew by 10 m. = 2 minutes
Therefore;
Speed and direction of the wind = 10/2 m/min east
Speed and direction of the wind = 5 m/min east
Mathew's flight path can be represented using a vector diagram (please see attached drawing)
Distance Mathew travels in 2 minutes = 100 m/min × 2 minutes = 200 m.
Tangent of the angle by which Mathew is off his flight path, A, can be found as follows;
tan(A) = 10/200 = 1/20
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two hundred twenty five students play a team sport at lincoln high school these students represent 3/8 of the total
The total number of students in the school is calculated as; 600 students
How to find fraction of a total?Usually, some figures are expressed as a fraction of a whole as depicted in this case. Thus, when we are given a fraction of a whole to be equal to a particular figure, we will just cross multiply to get the total number.
We are told that;
Number of students that play a team sport at Lincoln high school = 225
Now, we are told that the number above represents a fraction of 3/8 of the total students in that school.
Thus, if the total number of students in the school is x, then we can say that;
(3/8)x = 225
Multiply both sides by 8 to get;
3x = 1800
x = 1800/3
x = 600 students
Thus, we can conclude that if two hundred and twenty five students play a team sport at Lincoln high school and these students represent 3/8 of the total, then we can say that the total number of students in the school is 600 students.
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find the slope of the line on the graph write your answer as a fraction or a whole number
Answer:
-3/2
Step-by-step explanation:
Slope=rise/run
Pick any 2 points and you can see that for every increase in 2 increases for x, there are 3 decreases for y.
Which of the following expressions has a product of 36?
A. (-3)(12)
B. (-6)(-6)
C. 2(-18)
D. 4 · 8
Answer:
B. (-6)(-6)
Step-by-step explanation:
- X - = +
and 6 x 6 = 36.
Suppose that events E and F are independent, P(E)=0.6, and P(F)=0.7.
What is the P(E and F)?
The probability P(E and F) is
(Type an integer or a decimal.)
Answer:
Step-by-step explanation:
hello :
P(E and F)=0.7×0.6 =0.42
You work on a surgical unit that receives 87 new patients per week. In your spare time, you are trying to improve pain control across the unit. As you prepare to collect your baseline data before testing your change, you consider your plan to gather this information. Which of the following would be the best data collection plan for this project, and why
Collect data on a representative selection of patients for two weeks.
is the best data collection plan for this project.
According to the statement
we have a given that the surgical unit that receives 87 new patients per week.
and we have to tell the data plan to collect the baseline data before testing your change to control the pain across the unit.
And We know that the Data collection is A representative sample is one technique that can be used for obtaining insights and observations about a targeted population group
So,
Collecting data on a representative portion of your population — that is, sampling — allows you to collect baseline data and start making improvements faster, using fewer resources, than would be possible if you tried to look at every patient. Baseline data is important so that you can see if the changes you are testing are leading to improvement. Collecting data about a non representative sample of your population, such as by looking only at patients with the most severe pain, won't show the broad impact of your project on your unit.
So, Collect data on a representative selection of patients for two weeks.
is the best data collection plan for this project.
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Disclaimer: This question is incomplete. Please read the full content below.
Question:
You work on a surgical unit that receives 87 new patients per week. In your spare time, you are trying to improve pain control across the unit. As you prepare to collect your baseline data before testing your change, you consider your plan to gather this information. Which of the following would be the best data collection plan for this project, and why?
(A) Collect data on the pain level of every patient for at least a year.
(B) Collect data for at least a year, focusing only on patients who have undergone especially painful surgeries.
(C) Collect data on a representative selection of patients for two weeks.
(D) There is no reason to collect baseline data.
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Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x + y = 6 x - y = 0
The solution of the system of equations contains one point
How to determine the number of solutions?The system is given as:
x + y = 6
x - y = 0
Add both equations
2x = 6
Divide by 2
x = 3
Substitute x = 3 in x - y = 0
3 - y = 0
Solve for y
y = 3
So, we have x =3 and y = 3
Hence, the solution of the system of equations contains one point
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Stronger evidence against the null hypothesis is indicated by: Group of answer choices lower levels of significance. smaller p-values. lower probabilities for the power of the test. smaller critical values.
Stronger evidence against the null hypothesis is indicated by: smaller p-values.
What is null hypothesis?A statistical conjecture known as a null hypothesis asserts that certain features of a population or data-generating process are not different from one another.
A mechanism to reject the null hypothesis with a predetermined level of confidence is provided by hypothesis testing.
The alternative hypothesis is supported if the null hypothesis can be rejected.
The foundation of the scientific falsification principle is null hypothesis testing. The null hypothesis presupposes that any variation in the selected characteristics you observe in a set of data is the result of chance.
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Select the correct answer. Find the solution(s) for x in the equation below. x^2 -25 =0
Answer:
Step-by-step explanation:
Find the roots of x^2-25=0 by solving for x.
Add 25 to both sides
x^2=25
Square root both sides
x=-5
x=5
Answer:
x=5;x=-5
Step-by-step explanation:
It was right for me
Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job. Casey correctly wrote and solved a system of linear equations by substitution. In his work, he substituted an expression for one variable and solved for the other. This resulted in the equation 5
One landscaper's hourly rate is $15 lower than the other landscaper's. Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.
What is system of linear equations?
A set of two linear equations with two variables is a system of linear equations. Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly rate. A set of linear equations was appropriately written and solved by Casey using substitution. He solved for the other variable and substituted an expression for one in his work. The intersection of the lines that represent the linear equations is where a system of linear equations finds its solution. Each landscaper bills a fee for each job in addition to an hourly cost. Casey produced a system of linear equations that was correctly written and solved. The hourly rates for both landscapers are the same, however their rates for individual jobs vary.
Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly cost. By using substitution, Casey created and properly figured out a set of linear equations. He solved for the other variable and replaced an expression for one in his work, producing the equation 5 = 20.
equation 5=20
20-5 = 15
Therefore, One landscaper's hourly rate is $15 lower than the other landscaper's.
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Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle of elevation of 61°. Dan is standing on the ground at a point directly west of the base of the tower and must look up at an angle of elevation of 72° in order to see the top. If the CN Tower is 553.3 m tall,how far apart are Vic and Dan to the nearest meter? Include a well-labeled diagram as part of your solution.
The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.
How can the distance between Vic and Dan be calculated?Location of Vic relative to the tower = South
Vic's sight angle of elevation to the top of the tower = 61°
Dan's location with respect to the tower = West
Dan's angle of elevation in order to see the top of the tower = 72°
Height of the tower = 553.3m
[tex]tan( \theta) = \frac{opposite}{adjacent} [/tex]
[tex]tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower} [/tex]
[tex]distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7[/tex]
Vic's distance from the tower ≈ 306.7 mSimilarly, we have;
[tex] Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8[/tex]
Dan's distance from the tower ≈ 179.8 mGiven that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan d is found as follows;
d = √(306.7² + 179.8²) ≈ 356Therefore;
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Jagrit is looking at two computer repair stores.
Store 1: Data-Fix
The total cost charged by Data-Fix is represented by the graph
as shown.
a) Write an equation to model the relation of total cost, C, and
number of hours, n as shown in the graph.
b) One of the points on the graph is (3, 60). Explain the
meaning of this point, in the context of this scenario.
Store 2: Comput-Repair
It charges a fixed cost of $10 plus $15 per hour for repair
services.
c) Write an equation to model the relation of total cost, C, and
number of hours, n, in Comput-Repair.
d) On the grid provided, graph the line that describes the fee structure for Compu-Repair.
e) What are the coordinates of the point of intersection?
f) What does it mean in this scenario?
g) Based on the point of intersection, how would you advise Jagrit when trying to choose between the two
computer repair stores? Fully explain your answer supported by the information from the graph.
PLEASE I DON'T HAVE TIME
See below for the solution of each question
The equation of the modelThe points are given as:
(3,60) and (5, 80)
The equation is calculated as:
[tex]C(n) = \frac{C_2 -C_1}{n_2 -n_1} * (n - n_1) + C_1[/tex]
This gives
[tex]C(n) = \frac{80- 60}{5-3} * (n - 3) + 60[/tex]
Evaluate the quotient
C(n) = 10 * (n - 3) + 60
Expand
C(n) = 10n - 30 + 60
Evaluate
C(n) = 10n + 30
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10n + 30
Explain the points on (3, 60)The point (3, 60) means he paid $60 for 3 hours
The equation of the model for Comput-RepairHere, we have:
Fixed = $10
Hourly rate = $15
The equation is calculated as:
C(n) = Fixed + Rate * Number of hours
This gives
C(n) = 10 + 15n
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10 + 15n
The graph of the fee structure for Compu-RepairThe equation is represented as:
C(n) = 10 + 15n
See attachment for the graph
The coordinates of the point of intersectionThis is the point where the two lines intersect.
From the graph, we have the point of intersection to be:
(n, C(n)) = (4, 70)
The meaning in this scenarioThis means that the charges for Comput-Repair and Data-Fix are the same after 4 hours
Advice JargitBased on the point of intersection, it is best that Jargit uses Compu-Repair because they have a lesser hourly rate
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a total of $7000 is invested: part at 6% and the remainder at 10%. How much is invested at each rate if the annual interest is $470?
Answer:
680
Step-by-step explanation:
Please HELP!!!!
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Answer:
Original equation:
y = a sin(b(θ -c)) + d
a = vertical dilation (stretch) of the amplitude
b = horizontal compression (shrink) of the period
c = horizontal shift (left/right)
d = vertical shift (up/down)
Your function is:
y = 3 sin(3θ + π) - 2
First, put it into the general from by factoring out the three in the argument of the sine:
y = 3 sin(3(θ + π/3)) - 2
a = vertical (amplitude) dilation = 3
b = horizontal (period) compression = 2π/period = 3
c = horizontal shift = π/3 to the left
d = vertical shift = -2
The line plot (shown in the attached image) shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Please help!! show all work
a. The median is 70, the mode is 60, and the mean is 70.8.
b. Mean best captures the data.
c. When there are outliers, the mean might be a deceptive center measure.
Calculating the Mean, Median, and Mode
Mean: Total number of sunglasses / total quantity of pries
Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25
Mean = 70.8
Median is equal to the (n/2 + 1)th term.
The number of sunglasses in this case is n.
(25/2 + 1)th term as the median
Median = 13th term
Median is 70
Mode is the most frequent data
Therefore, mode = 70
Why is mean the most appropriate central measure ?
The mean is often the ideal measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data are normally distributed. So, mean here denotes the typical cost of the sunglasses.
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Answer:
Step-by-step explanation:
Suppose a random samples of ticket prices for concerts by the Rolling Stones was obtained. For comparison purposes another random sample of Coldplay ticket prices was obtained. True or False: The two groups of data are independent samples.
A random samples of ticket prices for concerts and the random samples of Coldplay ticket prices are independent . The answer is True.
According to the questions,
A random samples of ticket prices for concerts by the Rolling Stones was obtained. For comparison purposes another random samples of Coldplay ticket prices was obtained.
The two groups of data are independent samples.
Hence, a random samples of ticket prices for concerts and the random samples of Coldplay ticket prices are independent . The answer is True.
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A compound inequality is shown below.
x ≤ 3 and x ≥ 0
Which graph represents the solution of the inequality?
Answer:
It is the first graph
Step-by-step explanation:
The line under the > and < sign means that it must include the 3 and the 0. The closed circle is showing that the 3 and 0 or included.
solve these linear equation
x + 4y = 16
3x + 5y = 27
Use elimination
x+4y=16--(1)3x+5y=27--(2)(1)×5 and (2)×4
5x+20y=80--(3)12x+20y=108--(4)(3)-(4)
-7x=-28x=4Putting in eq(1)
4y=16-44y=12y=3x + 4y = 16 __(1)
3x + 5y = 27 __(2)
Multiply the 1st equation by 3
3x + 12y = 48 __(3)
Solving (2) and (3)
3x + 12y = 48
3x + 5y = 27
__________
(-) (-) (-)
7y = 21
So, y = 3
By, putting the value of y = 3 in equation 1
x + 4(3) = 16
x + 12 = 16
x = 16 - 12
x = 4
We got -The value of x = 4 and y = 3
Hope it helps you any confusions you may ask!
For the real-valued functions f(x)=2x+3 and g(x)=√x-5, find the composition fog and specify its domain using interval notation.
(fog)(x) =
Domain of fog:
Find fog
fog(x)f(g(x))f(√x-5)2√(x-5)+3For real range the domain
x-5≥0x≥5Domain is [5,oo)
Bens barbershop has a rectangular logo for their business that measures 7 1/5 feet long with an area that is exactly the maximum area allowed by the building owner. create an equation that could be used to determine m, the unknown side length of the logo.
A = 7M is the equation that might be used to find the unknown side length, M, of the rectangular logo.
Expression steps of the equationWe can determine the following details from the query:
Logo= rectangle with a
Length ,L= 7-foot
'A' stands for the logo's area, and 'M' for the side that isn't recognized.
The rectangle's area (A) is computed using:
A = L*W
⇒A = 7*M
(As per query, length, L=7 & W= M)
Consequently, the formula 'A = 7M' might be used to calculate the logo's undetermined side length, M.
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