Step-by-step explanation:
n=5+3p
when p=26,
n=5+3×26=83
a notebook is 8 inches tall and 10 inches wide what is its area?
Answer:
i think 18
Step-by-step explanation:
A fishing pole is leaning against a wall. The base of the pole is 0.5 meters away from the wall, forming a 78 degree angle of elevation. How long is the fishing pole? Equation: (Choose One) A. cos0.5 B. cos0.5 C. cos78 = D. cos78 = x 78 78 x x 0.5 0.5 x
The length of the fishing pole is approximately 2.40 meters.
the equation is
x = 0.5 / cos (78)How to find the angle of elevationThe equation that relates the length of the fishing pole, the distance from the base of the pole to the wall, and the angle of elevation is:
cos (angle of elevation) = adjacent / hypotenuse
In this case, the hypotenuse side is the length of the fishing pole, x, and the adjacent side is the distance from the base of the pole to the wall, 0.5 meters. The angle of elevation is 78 degrees. Therefore:
cos (78) = 0.5 / x
x = 0.5 / cos (78)
x ≈ 2.40 meters
Therefore, the length of the fishing pole is approximately 2.40 meters.
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How to Convert MG to MEQ ?
Answer:
use the formula: mEq = (mg x valence) / atomic or molecular weight
Step-by-step explanation:
What does a 1 standard deviation increase mean?
Answer:
Step-by-step explanation:
A 1 standard deviation increase means that a data point has increased by one unit of standard deviation from the mean of a dataset. In a normal distribution, the standard deviation is a measure of the spread of the data around the mean. Approximately 68% of the data falls within 1 standard deviation of the mean, so a 1 standard deviation increase means that the data point has moved farther away from the mean, but still falls within the range of the typical values.
For example, if the mean of a dataset is 100 and the standard deviation is 10, a data point with a value of 110 would be 1 standard deviation above the mean. This means that it is one standard deviation unit away from the mean, in the direction of higher values. Similarly, a data point with a value of 90 would be 1 standard deviation below the mean, meaning it is one standard deviation unit away from the mean in the direction of lower values.
It's worth noting that standard deviation is a relative measure, so a 1 standard deviation increase or decrease in one dataset may have a different absolute effect than in another dataset with a different mean and standard deviation.
Please answer ASAP (show work)!
The width of a mirror is 2 in. Less than its length. The area of the mirror is 168 in. sq. Find the dimensions of the mirror.
Work Shown:
x = length
x-2 = width
area = length*width
area = x(x-2)
x(x-2) = 168
x^2-2x = 168
x^2-2x-168 = 0
Plug a = 1, b = -2, c = -168 into the quadratic formula.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-168)}}{2(1)}\\\\x = \frac{2\pm\sqrt{676}}{2}\\\\x = \frac{2\pm26}{2}\\\\x = \frac{2+26}{2} \ \text{ or } \ x = \frac{2-26}{2}\\\\x = \frac{28}{2} \ \text{ or } \ x = \frac{-24}{2}\\\\x = 14 \ \text{ or } \ x = -12\\\\[/tex]
Ignore x = -12 since we cannot have a negative length.
The only practical solution is x = 14.
If x = 14, then x-2 = 14-2 = 12
The rectangular mirror is 14 inches by 12 inches
Check: area = length*width = 14*12 = 168
The answers are confirmed.
Cara’s Flower Arrangements
White 3 6 9 12 15
Yellow 5 10 15 20 25
Hector’s Flower Arrangements
White 4 8 12 16 20
Yellow 6 10 14 18 22
Part A
Are the numbers of white and yellow flowers in Cara’s arrangements proportional?
Which equation relates the number of white flowers, w, to the number of yellow flowers, y?
Yes, the numbers of white and yellow flowers in Cara’s arrangements are proportional, the equation relates the number of white flowers, w, to the number of yellow flowers, y is y = 5w/3
What is proportionality?Proportionality are relationships between two variables where their ratios are equivalent.
Given that, are two arrangements of flowers done by Cara and Hector,
We need to find whether the Cara’s arrangements proportional or not, and an equation relating the number of flowers,
The numbers of white flowers = 3, 6, 9, 12, 15
The numbers of yellow flowers = 5, 10, 15, 20, 25
A proportional relation given by =
y = kx
Put x = 5, and y = 3
3 = 5x
x = 3/5
Put x = 10, y = 6
6 = 10x
x = 3/5
Therefore, the relation is proportional, and the equation will be y = 5w/3
Hence, the numbers of white and yellow flowers in Cara’s arrangements are proportional, the equation relates the number of white flowers, w, to the number of yellow flowers, y is y = 5w/3
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find the area of a sector with a central angle of 200 and a diameter of 7.5 cm round to the nearest tenth
Answer:
need points srry
Step-by-step explanation:
Members of a soccer team suspect the coin used for the coin toss at the beginning of their games is unfair. They believe it turns up tails less often than it should if it were fair. The coach of the team decides to flip the coin 100 times and count the number of tails. His trial results in 35 tails. He decides to carry out a significance test. What is the p-value he obtains and the general conclusion that can be made at a 99% significance level?.
The p-value he obtains and the general conclusion that can be made at a 99% significance level is 0.01
A p-value is a measure of the evidence against a null hypothesis. In this case, the null hypothesis is that the coin is fair and equally likely to turn up heads or tails.
The coach carries out a significance test to determine if the number of tails in his trial of 100 flips is significantly different from what would be expected if the coin were fair.
The p-value is calculated by comparing the observed number of tails (35) to the expected number of tails (50, if the coin were fair) using a binomial distribution.
This involves finding the probability of observing 35 or fewer tails in 100 flips, assuming the null hypothesis is true. If this probability is low (i.e. if the p-value is small), then it suggests that the coin is not fair and that the observed difference is unlikely to have occurred by chance.
At a 99% significance level, a common threshold used in statistical tests, the p-value needs to be less than 0.01 to reject the null hypothesis and conclude that the coin is not fair.
If the p-value obtained is less than 0.01, then we can conclude with 99% confidence that the coin is biased towards heads. On the other hand, if the p-value is greater than 0.01, then we fail to reject the null hypothesis and conclude that there is not enough evidence to say that the coin is unfair.
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Last year, Terrific Copying had total revenue of $475 000, while operating at 60% of capacity. The total of its variable cost is $150 000. Fixed costs were $180 000. If the current selling price, variable costs, and fixed costs are the same as last year, what net income can be expected from revenue of $500 000 in the current year
If the current selling price, variable costs, and fixed costs are the same as last year, the expected net income in the current year is $162,105.
Net income can be computes as follows:
Net income = total revenue - total cost
Total cost consists of two costs, fixed cost and total variable cost.
Total cost = fixed cost + total variable cost
Fixed cost does not depend on the produced quantity, while total variable cost is a function of produced quantity.
Let q = produced quantity, then:
Total variable cost = variable cost per unit x q.
Let's assume that the sold quantity = produced quantity. Hence,
Total revenue = selling price x q
Information from last year:
Total revenue = $475,000
475,000 = selling price x q
Here, q = the product quantity sold last year.
Let r = the product quantity sold in the current year. Since the selling price is the same, we have:
500,000 = selling price x r
Comparing with last year, we have:
selling price = 475,000/q = 500,000/r
Hence,
r = (500,000/475,000) q
r = (20/19) q
Hence, the quantity sold this year is 20/19 higher than last year.
Total variable cost this year = variable cost per unit x r.
Substitute r = (20/19) q:
Total variable cost this year = variable cost per unit x (20/19) q
Total variable cost this year = (20/19) x variable cost per unit x q
Total variable cost this year = (20/19) x Total variable cost last year
Total variable cost this year = (20/19) x 150,000 = 157,895
Therefore,
Net income this year = total revenue - fixed cost - total variable cost
= 500,000 - 180,000 - 157,895
= 162,105
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Hoover Dam is located on the Colorado River between Nevada and Arizona. Every second, 270,000 cubic feet of water pass through each of the dam’s 2 spillways. Which is the best estimate of the number of cubic feet of water that pass through both spillways in 1 hour?
2 × 10^6
3 × 10^7
3 × 10^8
2 × 10^9
The water spills out from the two spills in 1 hour is [tex]9.72*10^{8}[/tex] cubic feet.
What is volume?Volume is defined as the amount of space occupied by an object within the boundaries in the three dimensional space.
In Hoover Dam, for every second the water is passes through the 2 spills.
Amount of water spills in 1 second in the two spills = 270,000 cubic feet.
We have to estimate the number of cubic feet of water that pass through both spills in 1 hour.
Water spills in one minute = 60*270000
= 1,620,000cubic feet.
Water spills in hour, i.e., 60 minutes = 60*1620000
= 9,72,000,000 cubic feet.
It can be rewrite as [tex]9.72*10^{8}[/tex]
Hence, the water spills out from the two spills in 1 hour is[tex]9.72*10^{8}[/tex] cubic feet.
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What is the approximate volume of the sphere? I need help T>T
Use 3.14 to approximate pi and round the answer to the nearest hundredth if necessary.
A. 48 cm³
48 c, m³
B. 150.72 cm³
150.72 c, m³
C. 288.00 cm³
288.00 c, m³
D. 904.32 cm³
The approximate volume of the sphere is 904.32 cm³
How to find the approximate volume of a sphere?The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant.
From the figure, r = 6cm and we are to use π = 3.14. Thus:
V = (4/3)πr³
V = (4/3) * 3.14 * 6³
V = 904.32 cm³
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The proportional relationship between the number of sweaters a clothing store buys and sells, s, and the profit, in dollars and cents, that it makes off those sweaters, can be represented by the equation
�
=
17
�
p=17s. What is the constant of proportionality from the number of sweaters to the total profit, in dollars and cents?
The constant of proportionality from the number of sweaters to the total profit is 17 dollars and cents.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
It can be seen from the equation p = 17s, where p is the profit and s is the number of sweaters. The constant 17 represents the profit per sweater. So, The constant of proportionality from the number of sweaters to the total profit is 17 dollars and cents.
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A water park offers two types of membership an unlimited use for $70 per month or a monthly $10 fee and $5 per visit which is the better plan?
Two membership options are available at a water park: unlimited use for $70 per month or $10 per month plus $5 per visit. 12 visits are the preferred schedule.
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The cost of a $10 monthly charge plus $5 for each visit can be calculated as follows:
Cost = 10 + 5*v
where v denotes the monthly visits.
If both membership levels have the same price, then:
[tex]10 + 5*v = 70[/tex]
[tex]5*v = 70 - 10[/tex]
[tex]v = 60/5v = 12[/tex]
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1. What is the solution of the equation? (1 point)
•-6
•4
•14
•-8
Answer:
The given equation is:
√(x+10) - 9 = -7
Adding 9 to both sides of the equation, we get:
√(x+10) = 2
Squaring both sides of the equation, we get:
x + 10 = 4
Subtracting 10 from both sides, we get:
x = -6
Therefore, the solution of the equation √(x+10) - 9 = -7 is x = -6.
A rectangular television's length is 3 inches more than twice its width. The
perimeter of the television is 144 inches. What is the width of the television
Answer:
The width of the television is 23 in.
What is rectangle?
A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.
Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches
Perimeter of a rectangle = 2(length+width)
According to question,
l = 3+2w
Therefore,
Perimeter = 2(w + 3+2w) = 144
3w + 3 = 72
3w = 69
w = 23
Hence, The width of the television is 23 in.
Answer:
The width of the television is 23 in.What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inchesPerimeter of a rectangle = 2(length+width)According to question,l = 3+2wTherefore,Perimeter = 2(w + 3+2w) = 1443w + 3 = 723w = 69w = 23
Step-by-step explanation:
What is the measure of asymmetry?
The measure of asymmetry, also known as skewness, is a statistical measure that describes the degree of asymmetry in a distribution of data.
It provides information on the shape of the distribution and the deviation of the data from a normal distribution. In a symmetrical distribution, the mean, median, and mode are all equal, and the distribution is said to have zero skewness. A distribution that is skewed to the right, or positively skewed, has a tail that extends to the right, and the mean is larger than the median. A distribution that is skewed to the left, or negatively skewed, has a tail that extends to the left, and the mean is smaller than the median.
Skewness is calculated by taking the third standardized moment of the distribution, which is the average cubed deviation from the mean, and dividing it by the cube of the standard deviation. This gives a measure of the degree of asymmetry of the distribution.
Skewness is an important measure in many fields, including finance, economics, and biology, as it can indicate whether a distribution is likely to produce extreme values, and can help identify outliers in the data. It is also important in hypothesis testing, as many tests assume that the data are normally distributed, and skewed data can affect the validity of the results.
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Each of 8 students reported the number of movies they saw in the past year. Here is what they reported. 4, 17, 17, 20, 13, 4, 16, 18 Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.
Answer:
13.6
Step-by-step explanation:
To find the mean number of movies that the students saw, we add up all the reported numbers of movies and then divide by the total number of students (which is 8 in this case).
Adding up the reported numbers of movies:
4 + 17 + 17 + 20 + 13 + 4 + 16 + 18 = 109
Dividing by the number of students:
109/8 = 13.625
Rounding to the nearest tenth:
Mean number of movies seen = 13.6
Therefore, the mean number of movies that the students saw, rounded to the nearest tenth, is 13.6.
Answer: 13.6
Step-by-step explanation:
Your basically finding the average:
(4+17+17+20+13+4+16+18)/8 = 13.6
What could you multiply the top equation by to be able to add the equations and eliminate the x-values in this system?
You should multiply the top equation by 3 to be able to add the equations and eliminate the x-values in this system.
How to solve these system of linear equations?In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
2x + 5y = 5 .........equation 1.
-6x + 7y = -37 .........equation 2.
By multiplying equation 1 by 3, we have:
3(2x + 5y = 5) = 6x + 15y = 15 ......equation 3
By adding equation 2 to equation 3, we have:
6x + 15y = 15
-6x + 7y = -37
22y = -22
y = -22/22
y = -1.
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Elizabeth records the number of minutes she walks each day for 5 days. Her results are shown in this table.
Day
x Minutes
y
1 18
2 27
3 38
4 45
5 60
Using the best-fit linear model, what is the approximate predicted number of minutes she walks on day 8?
A.
92 minutes
B.
70 minutes
C.
82 minutes
D.
89 minutes
Answer:
Step-by-step explanation:
Objective: Solve distance problems by creating and solving a linear
equation.
An application of linear equations can be found in distance problems. When
solving distance problems we will use the relationship rt = d or rate (speed) times
time equals distance. For example, if a person were to travel 30 mph for 4 hours.
To find the total distance we would multiply rate times time or (30)(4) = 120.
This person travel a distance of 120 miles. The problems we will be solving here
will be a few more steps than described above. So to keep the information in the
problem organized we will use a table. An example of the basic structure of the
table is blow:
Rate Time Distance
Person 1
Person 2
Table 1. Structure of Distance Problem
The third column, distance, will always be filled in by multiplying the rate and
time columns together. If we are given a total distance of both persons or trips we
will put this information below the distance column. We will now use this table to
set up and solve the following example
1
Example 1.
Two joggers start from opposite ends of an 8 mile course running towards each
other. One jogger is running at a rate of 4 mph, and the other is running at a
rate of 6 mph. After how long will the joggers meet?
Rate Time Distance
Jogger 1
Jogger 2
The basic table for the joggers, one and two
Rate Time Distance
Jogger 1 4
Jogger 2 6
We are given the rates for each jogger.
These are added to the table
Rate Time Distance
Jogger 1 4 t
Jogger 2 6 t
We only know they both start and end at the
same time. We use the variable tfor both times
Rate Time Distance
Jogger 1 4 t 4t
Jogger 2 6 t 6t
The distance column is filled in by multiplying
rate by time
8 We have total distance, 8 miles, under distance
4t + 6t = 8 The distance column gives equation by adding
10t = 8 Combine like terms, 4t + 6t
10 10 Divide both sides by 10
t =
4
5
Our solution fort, 4
5
hour(48 minutes)
As the example illustrates, once the table is filled in, the equation to solve is very
easy to find. This same process can be seen in the following example
Example 2.
Bob and Fred start from the same point and walk in opposite directions. Bob
walks 2 miles per hour faster than Fred. After 3 hours they are 30 miles apart.
How fast did each walk?
Rate Time Distance
Bob 3
Fred 3
The basic table with given times filled in
Both traveled 3 hours
2
Rate Time Distance
Bob r + 2 3
Fred r 3
Bob walks 2 mph faster than Fred
We know nothing about Fred,so use r for his rate
Bob is r + 2,showing 2 mph faster
Rate Time Distance
Bob r + 2 3 3r + 6
Fred r 3 3r
Distance column is filled in by multiplying rate by
Time.Be sure to distribute the 3(r +2)for Bob.
30 Total distance is put under distance
3r + 6+ 3r = 30 The distance columns is our equation, by adding
6r +6 = 30 Combine like terms 3r + 3r
− 6 − 6 Subtract 6 from both sides
6r = 24 The variable is multiplied by 6
6 6 Divide both sides by 6
r =4 Our solution for r
Rate
Bob 4+2 =6
Fred 4
To answer the question completely we plug 4 in for
r in the table.Bob traveled 6 miles per hour and
Fred traveled 4 mph
Some problems will require us to do a bit of work before we can just fill in the
cells. One example of this is if we are given a total time, rather than the individual times like we had in the previous example. If we are given total time we
will write this above the time column, use t for the first person’s time, and make
a subtraction problem, Total − t, for the second person’s time. This is shown in
the next example
Example 3.
Two campers left their campsite by canoe and paddled downstream at an average
speed of 12 mph. They turned around and paddled back upstream at an average
rate of 4 mph. The total trip took 1 hour. After how much time did the campers
turn around downstream?
Rate Time Distance
Down 12
Up 4
Basic table for down and upstream
Given rates are filled in
1 Total time is put above time column
Rate Time Distance
Down 12 t
Up 4 1 − t
As we have the total time, in the first time we have
t,the second time becomes the subtraction,
total − t
3
Rate Time Distance
Down 12 t 12t
Up 4 1 − t 4 − 4t
=
Distance column is found by multiplying rate
by time.Be sure to distribute 4(1 − t)for
upstream. As they cover the same distance,
= is put after the down distance
12t = 4 − 4t With equal sign, distance colum is equation
+ 4t + 4t Add4tto both sides so variableis onlyon one side
16t =4 Variable is multiplied by 16
16 16 Divide both sides by 16
t =
1
4
Our solution,turn around after 1
4
hr(15 min )
Another type of a distance problem where we do some work is when one person
catches up with another. Here a slower person has a head start and the faster
person is trying to catch up with him or her and we want to know how long it
will take the fast person to do this. Our startegy for this problem will be to use t
for the faster person’s time, and add amount of time the head start was to get the
slower person’s time. This is shown in the next example.
A cruise ship traveled at a constant rate of 16 mph for 3 hours. Then it traveled for 2 hours at a constant rate of 15 mph. How many miles did the cruise ship traveled in all?
The cruise ship traveled 78 miles.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
A cruise ship traveled at a constant rate of 16 mph for 3 hours.
Then it traveled for 2 hours at a constant rate of 15 mph.
The total traveled distance,
= distance at the rate of 16 mph for 3 hours + distance of 15 mph for 2 hours.
= 16 x 3 + 15 x 2
= 48 + 30
= 78 miles.
Therefore, the total distance is 78 miles.
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How many cc are in 1 ounces?
Answer:
29.5735296 cc = 1 oz
HELPPPPP PLEASEEEE QUICKKKKKKK
A school photographer just bought a new memory card for her camera. She took 2 pictures to check that everything is working properly. Now that it's picture day, she expects to take 1 picture of each student.
Write an equation that shows the relationship between the number of students photographed, x, and the total number of pictures on the memory card, y.
y=
yº
20
b
20
16
zoom in
Solve the triangle by finding the missing sides
and angles. Round to 2 decimal points.
10.
11.
b=
12
Type a response
* REQUIRED
1
U
*REQUIRED 1
The measure of the missing side b is 12 unit.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
The triangle is right angled so we have;
opposite = side opposite the angle 42° = 20
adjacent = b
hypotenuse = 20
b^2 + 16^2 = 20^2
b^2 = 400 - 256
b^2 = 144
b = 12 unit
Approximately to the nearest whole number, b = 12
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What is the first step in solving a system by GRAPHING?
Answer:
Write both linear equations in slope intercept form.
Solve the equation AB=BC for A, assuming that AB and C are square matrices and Bis invertible.?
[tex]A = B^-1 * BC[/tex]
Since B is invertible, it can be used to solve the equation.
1. Calculate the inverse of B, [tex]B^-1[/tex].
2. Multiply[tex]B^-1[/tex] with BC, to obtain A.
Assuming that AB and C are square matrices and B is invertible, the equation AB=BC can be solved for A. To do this, we first need to calculate the inverse of B, [tex]B^-1[/tex]. The inverse of a matrix is defined as the matrix which when multiplied to the original matrix, yields the identity matrix. Once we have the inverse of B, we can use it to solve the equation by multiplying [tex]B^-1[/tex] with BC, which will give us A. This works because when we multiply a matrix by its inverse, the result is always the identity matrix. Hence, by multiplying the inverse of B with BC, we can obtain A.
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Simplifying algebra radicals
Please help!!
The solution is, √27xy × √3xy² = 9xy√y
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
here, we have,
here, we have,
√27xy × √3xy²
=√27×3× xy × xy²
=√9×3×3×xy × xy²
=9xy√y
Hence, The solution is, √27xy × √3xy² = 9xy√y
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Buddy invests $600 in a savings account that pays 3% interest. How much interest will he make after 7 years
The amount of interest in 7 years will be $126.
How to calculate the interest?To calculate the interest earned by Buddy after 7 years, we can use the formula for simple interest, which is given by:
I = Prt
Where I is the interest earned, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the time period in years.
We are given that Buddy invests $600 in a savings account that pays 3% interest, which means that the annual interest rate r is 0.03. Therefore, we can plug these values into the formula and solve for I:
I = 600 x 0.03 x 7
I = $126
Therefore, Buddy will earn $126 in interest after 7 years.
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What would be the 50th term than?
The 50th term is 290.
What is an arithmetic sequence?It is a sequence where there is a common difference between each consecutive term.
Example:
12, 14, 16, 18, 20 is an arithmetic sequence.
We have,
-4, 2, 8, 14,
This is an arithmetic sequence.
First term = a = - 4
Common difference.
d = 2 - (-4) = 6
d = 8 - 2 = 6
Now,
The nth term = a + (n -1)d
So,
n = 50
a = -4
d = 6
50th term.
= -4 + (50 - 1) 6
= - 4 + 49 x 6
= - 4 + 294
= 290
Thus,
The 50th term is 290.
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The complete question:
What is the 50th term of the sequence that begins −4, 2, 8, 14, ...?
Blueprint
3 in
Deck
3 in
1 in
1 in
1 In
The area of the scale drawing is
square inches.
If the scale is 1 inch = 4 feet, the area of the actual deck would be
Numerically, the value of the area of the actual deck would be
Based on these results, if the scale is 1 inch = k feet, the area of the actual deck would be "
square feet.
times the value of the area of the scale drawing.
square feet
Area of the scale drawing is 10 square inches. Area of the actual deck would be 160 square feet.
Area of the actual deck would be 16 times the area of the scale drawing.
What is Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Given scale drawing can be made into two squares.
One with a side length of 1 inch and other with side length of 3 inches.
Area of a square with side length 'a' = a²
Area of the given scale drawing = (1 inch)² + (3 inches)²
= 1 inch² + 9 inches²
= 10 inches²
If the scale is 1 inch = 4 feet,
Area of the actual deck = (1 × 4 feet)² + (3 × 4 feet)²
= 4² [(1 feet)² + (3 feet)²]
= 4² (10)
= 160 feet²
Area of the actual deck = 160 feet²
= 16 (Area of the scale drawing)
If the scale is 1 inch = k feet,
Area of the actual deck = k² ( Area of scale drawing)
= 10 k² square feet
Hence the area of the actual deck would be 10k² if the scale is 1 inch = k feet.
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A product of permutation matrices is again a permutation matrix. The inverse of a permutation matrix is again a permutation matrix.True or False
True
A square matrix called a permutation matrix is one in which every row and column has exactly one element equal to 1 and every other element is equal to 0. A matrix's rows or columns can be permuted by using permutation matrices.
The resultant matrix will also include exactly one 1 in each row and column and all other elements will be 0. This is because two permutation matrices are multiplied together. This is thus because a permutation matrix created by multiplying two other matrices represents the composition of the permutations represented by the individual matrices.
Similarly, By switching the rows and columns in a permutation matrix, it is possible to create the inverse of that matrix. For example, to get the inverse of a permutation matrix P, swap its rows and columns so that the 1s now occupy the locations where the row and column indices were original. Because each row and column still contain exactly one element that is equal to 1 and all other elements are equal to 0, this matrix is also a permutation matrix.
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