The area of the living room is approximately 238 square feet.
To find the area of the living room, we need to multiply its length by its width.
First, let's convert the dimensions from feet and inches to feet. We have:
Length: 12 feet + 4 inches = 12 + 4/12 = 12.33 feet
Width: 19 feet + 4 inches = 19 + 4/12 = 19.33 feet
Now, we can multiply the length and width to find the area:
Area = length × width = 12.33 feet × 19.33 feet = 238.1289 square feet
Rounding to the nearest whole square foot, the area of the living room is approximately 238 square feet.
Please help me with this problem.
The diagram shows the floor plan of a one-bedroom apartment. Find the area of the living room in square feet. Round to nearest square foot.
The dimensions of living room are 12' 4" x 19' 4"
On rounding off to nearest feet we get the area of the living room as 238 ft²
In the figure it is given that the dimensions of the living room are 12' 4" x 19' 4". This means that the dimensions are:
12 ft 4 in x 19 ft 4 in
To get the area in feet, we need to convert the dimensions into feet. This can be done by using the conversion factor that 1 foot = 12 inch
So, 12 ft 4 in can be converted into feet as follows:
[tex]12\ \text{ft}\ 4\ \text{in} = 12\ \text{ft}\ + \frac{4}{12}\ \text{ft} = 12.333\ \text{ft}[/tex]
19 ft 4 in can be converted into feet as follows:
[tex]19\ \text{ft}\ 4\ \text{in} = 19\ \text{ft}\ + \frac{4}{12}\ \text{ft} = 19.333\ \text{ft}[/tex]
Now to calculate the area we multiply the dimensions of the living room (as the living room is a rectangle and area of rectangle is product of its length and breadth):
[tex]area = 12.333 \times 19.333 =238.433889[/tex] ft²
On rounding of to nearest feet we get the area as 238 ft². So, the area of the living room is 238 ft²
HELP QUICK!!! 3. There is a special sale at the pet store. You can buy a fish bowl and get 6 free goldfish. Carlos and Olivia each buy a bowl and get 6 fish. They want to keep track of their fishes’ growth, so they carefully measure each fish and record these lengths:
1 ¼ in
1 7/8in.
1 1/4in.
1 3/4in.
1 3/8 in.
1 7/8 in.
1 3/8 in.
1 1/4in.
1 4/8in.
1 6/8in.
1 7/8in.
1 3/4in.
(a) Plot the lengths of each of the 12 goldfish on the line plot.
(b) Which is greater: the amount of fish that measure less than 1 1/2 inches in length or the amount of fish with a length greater than 1 1/2 inches?
for a, make a dot on the line plot at each of the given lengths
b) there are more fishes greater than 1 1/2
How many 1/2 cups servings of r ice are in 3/8 cups of rice? Explain your answer
What is the inverse of the statement? A number that has exactly two distinct factors is prime.
Answer:
The inverse statement is
"A number that does not has exactly two distinct factors is not prime"
Step-by-step explanation:
Given a statement we have to tell the inverse of that statement.
The given statement is
"A number that has exactly two distinct factors is prime".
We have to write the inverse of the above statement.
The inverse of the statement is
"A number that does not has exactly two distinct factors is not prime"
Which inequality models this problem?
Esin started a T-shirt-printing business. She spent $2500 to purchase supplies to get started and she uses about $4.50 worth of supplies per T-shirt printed. Esin charges $25 for each T-shirt. Let s represent the number of T-shirts.
What is the minimum number of T-shirts Esin will need to sell to make a profit?
25s<2500+4.5s
Rearrange the formula A = \pi r ^ ( 2) for r
A rectangular table is 4 times as long as it is wide. If the area is 100ft^2, find the width and length of the table.
A swimming pool is being filled ata rate of 15 pints per minute. How many gallons per hour is this
1 gallon = 8 pints
15/8 = 1.875 gallons per minute
60 minutes per hour
1.875 * 60 = 112.5 gallons per hour
Plz help it’s du in like 1 hour
Jeremy Spent 1/4hours on homework after school another 1/2 after she got home and a final 1/3 hour after dinner. Did she spend more or less than one hour on homework and all? Explain.
Line segment CD is shown on a coordinate grid:
A coordinate plane is shown. Line segment CD has endpoints 1 comma 2 and 1 comma negative 1.
The line segment is rotated 90 degrees counterclockwise about the origin to form C'D'. Which statement describes C'D'?
A) C'D' and CD are equal in length.
B) C'D' is parallel to CD.
C) C'D' is half the length of CD.
D) C'D' is greater than twice the length of CD.
Which expression is modeled by this arrangement of tiles?
A.-40/10
B.40/(-10)
C.40/10
D.40/40
ASAP
Is the symbol μμ used for the population mean or sample mean?
choices are.....
population mean
sample mean
The symbol μ is used for population mean, while x is used for sample mean in statistics.
Explanation:The symbol μ (pronounced "mew") is used to represent the population mean.
The population mean is a parameter that represents the average value of a variable in the entire population.
On the other hand, the symbol x is used to represent the sample mean, which is the average value calculated from a subset of the population called a sample.
The symbol μ (pronounced "mew") is used to represent the population mean.
It denotes the mean of all values within an entire population, which is a parameter of that population.
To illustrate why μ represents the population mean, consider a dataset: 1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 4.
If this were to represent an entire population, we would calculate the mean and then denote it with μ.
Put a check by all the factors of 15
answers : 1, 2, 3, 4, 5, 10, 15.
please answer ASAP
Pascal wants to find the sum of the measures of the interior angles of a polygon that has n sides. How could he do this?
Answer with explanation:
Smallest Polygon = Triangle , which has 3 sides
Sum of angles of triangle = 180°→→, Using the angle sum property of triangle.
We can find the Sum of angles of triangle, using the formula
= (n-2)×180°
= (3-2)×180°
= 1 × 180°
= 180°
A Quadrilateral has four sides.
Sum of angles of Quadrilateral = 360°
Or , using the formula
=(4-2)×180°
=2 × 180°
=360°
For, n sided Polygon
Sum of it's Interior angles = (n-2) × 180°
To prove this, we should divide that polygon into triangles, and multiply number of triangles by angle of 180°.
For, example, Quadrilateral can be divided into two triangles , sum of interior angles of Quadrilateral =2 × 180°=360°
On a recent business trip, a salesman traveled 52 miles the first hour, 64 miles the second hour and 49 miles the third hour.
How many miles did he average per hour?
Answer: He traveled 54.28 miles per hour as an average.
Step-by-step explanation:
Since we have given that
Number of miles traveled in first hour = 52 miles
Number of miles traveled in second hour = 64 miles
Number of miles traveled in third hour = 49 miles
Average per hour is given by
[tex]=\dfrac{3}{\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}}\\\\\\=\dfrac{3}{\dfrac{1}{52}+\dfrac{1}{64}+\dfrac{1}{49}}\\\\\\=\dfrac{3}{\dfrac{784+637+832}{40768}}\\\\\\=\dfrac{3}{\dfrac{2253}{40768}}\\\\\\=\dfrac{40768\times 3}{2253}\\\\\\=\dfrac{122304}{2253}\\\\\=54.28\ miles/hr[/tex]
Hence, he traveled 54.28 miles per hour as an average.
Bob has a dog who weighs 12 pounds. His cat weighs 2/3 as much as the dog. How many pounds does his cat weigh?
Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of drinks she needs to sell to earn $100.
1.25x + 1.49 = 100
What error did Barbara make in writing the equation?
Which expression shows the result of applying the distributive property to 12(5y+4) ?
A. 17y + 16
B. 5y + 48
C. 60y + 48
D. 60y + 4
Select all statements below which are true for all invertible n×nn×n matrices aa and bb
a. (ab)−1=a−1b−1(ab)−1=a−1b−1
b. aba−1=baba−1=b
c. (in+a)(in+a−1)=2in+a+a−1(in+a)(in+a−1)=2in+a+a−1
d. a2b7a2b7 is invertible
e. a+ba+b is invertible f. (a+b)(a−b)=a2−b2(a+b)(a−b)=a2−b2
Answer:
The statements that are correct are:
c) [tex](in+a)(in+a^{-1})=2in+a+a^{-1}[/tex]
d) [tex]a^2b^7[/tex] is invertible.
e) [tex]a+b[/tex] is invertible.
Step-by-step explanation:
We are given that:
a and b are invertible n×n matrices.
We have to tell which of the following statements are true.
a)
[tex](ab)^{-1}=a^{-1}b^{-1}[/tex]
This statement is false.
Since:
[tex](ab)^{-1}=b^{-1}a^{-1}[/tex] and it may not be equal to the term [tex]a^{-1}b^{-1}[/tex]
b)
[tex]aba{-1}=b[/tex]
This expression could also be written as:
[tex]ab=ba[/tex]
Since on Post multiplying by a on both the sides.
But here we don't know whether the matrices are commutative or not.
Hence, the statement is false.
c)
[tex](in+a)(in+a^{-1})=2in+a+a^{-1}[/tex]
This statement is true.
since,
[tex](in+a)(in+a^{-1})=in(in+a^{-1})+a(in+a^{-1})\\\\=in^2+in.a^{-1}+a.in+aa^{-1}\\\\=in+a^{-1}+a+in\\\\=in+a^{-1}+a[/tex]
where in denote the identity matrix.
and we know that:
[tex]in^2=in[/tex]
d)
[tex]a^2b^7[/tex] is invertible.
This statement is true.
Since we know that prodct of invertible matrices is also invertible.
As [tex]a[/tex] is invertible so is [tex]a^2[/tex].
Also [tex]b[/tex] is invertible so is [tex]b^7[/tex].
Hence Product of [tex]a^2[/tex] and [tex]b^7[/tex] is also invertible.
i.e. [tex]a^2b^7[/tex] is invertible.
e)
[tex]a+b[/tex] is invertible.
This statement is true as sum of two invertible matrices is invertible.
f)
[tex](a+b).(a-b)=a^2-b^2[/tex]
This statement is false.
Since,
[tex](a+b).(a-b)=a(a-b)+b(a-b)\\\\=a.a-a.b+b.a-b.b\\\\=a^2-ab+ba-b^2[/tex]
Now as we are not given that:
[tex]ab=ba[/tex]
Hence, we could not say that:
[tex](a+b).(a-b)=a^2-b^2[/tex]
The correct statements which are true for all invertible [tex]\left({n\times n}\right)\cdot\left({n\times n}\right)[/tex] are:
(c). [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex]
(d). [tex]{a^2}{b^7}[/tex] is invertible.
(e). [tex]a+b[/tex] is invertible.
Further Explanation:
Given:
The matrix [tex]a[/tex] and [tex]b[/tex] are invertible [tex]\left({n\times n}\right)[/tex] matrices.
Calculation:
(a)
The statement is [tex]{\left({ab}\right)^{-1}}={a^{-1}}{b^{-1}}[/tex] false.
[tex]\begin{aligned}{\left({ab}\right)^{-1}}&={a^{-1}}{b^{-1}}\\\left({ab}\right){\left({ab}\right)^{-1}}&=\left({ab}\right){a^{-1}}{b^{-1}}\\I&\ne ab{a^{-1}}{b^{-1}}\\\end{aligned}[/tex]
The statement is [tex]{\left({ab}\right)^{-1}}={a^{-1}}{b^{-1}}[/tex] false.
(b)
The statement is [tex]ab{a^{-1}}=b[/tex].
Now multiply by a both the side.
[tex]\begin{aligned}ab{a^{-1}}a&=ba\\ab&\ne ba\\\end{aligned}[/tex]
The statement is [tex]ab{a^{-1}}=b[/tex] is false.
(c)
The statement is [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex].
Solve the above equation to check whether it is invertible.
[tex]\begin{aligned}\left({in+a}\right)\left({in+{a^{-1}}}\right)&=in\left({in+{a^{-1}}}\right)+a\left({in+{a^{-1}}}\right)\\&=i{n^2}+in\cdot{a^{-1}}+a\cdot in+a{a^{-1}}\\&=in+{a^{-1}}+a+in\\&=in+{a^{-1}}+a\\\end{aligned}[/tex]
The statement is true.
(d)
The statement is [tex]{a^2}{b^7}[/tex].
The product of invertible matrices is always invertible.
As [tex]a[/tex] is invertible so [tex]{a^2}[/tex] is also invertible.
As [tex]b[/tex] is invertible so [tex]{b^7}[/tex] is also invertible.
Hence, the product of [tex]{a^2}[/tex] and [tex]{b^7}[/tex] is also invertible.
The statement is true.
(e)
The statement [tex]a+b[/tex] is true as [tex]a+b[/tex] is always invertible.
(f)
The statement is [tex]\left({a+b}\right)\cdot\left({a-b}\right)={a^2}-{b^2}[/tex].
Solve the equation to check the inevitability.
[tex]\left({a+b}\right)\times\left({a-b}\right)={a^2}-ab+ba-{b^2}[/tex]
The statement is not true as [tex]ab=ba[/tex].
Hence, the correct statements which are true for all invertible [tex]\left({n\times n}\right)\cdot\left({n\times n}\right)[/tex] are:
(c). [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex]
(d). [tex]{a^2}{b^7}[/tex] is invertible.
(e). [tex]a+b[/tex] is invertible.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: Invertible, matrices, matrix, statement, function, true, determinants, elements, inverse.
Please help! (Picture included)
At one basketball game there were 1207 people. At the next game they were 958 people how many people were at two games?
how many 5/16 are in 1 7/8
To determine how many 5/16 are in 1 7/8, you convert 1 7/8 to an improper fraction, 15/8, and then divide it by 5/16, which yields 6.
Explanation:To find out how many 5/16 are in 1 7/8, you first need to convert 1 7/8 to a improper fraction. Since 1 is equal to 8/8, adding 7/8 gives us 15/8. Now, to find how many 5/16 are in 15/8, you can divide 15/8 by 5/16. To do this, you multiply 15/8 by the reciprocal of 5/16, which is 16/5.
15/8 × 16/5 = (15×16)/(8×5) = 240/40. This simplifies to 6, meaning there are 6 segments of 5/16 in 1 7/8.
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A bag contains 450 blue and yellow marbles. The probability of drawing a yellow marble is 46%. How many blue marbles are in the bag?
In 1943 the temperature in rapid city South Dakota fell about 45 degrees in 5 minutes what was the average drop in temperature per minute
Answer:-9 degrees
Step-by-step explanation:The average drop in temperature per minute is 9 degrees.
how do you write 2.22 in expanded form
Answer:
[tex]2 + \frac{2}{10}+\frac{2}{100}[/tex]
Step-by-step explanation:
In the expanded form we write a number as the sum of all place value of its digits from left to right,
Here, the given number,
2.22
By the place value chart,
Place value of first digit = 2 ( ones )
Place value of the first digit after decimal = [tex]\frac{2}{10}[/tex] ( tenth )
Place value of the second digit after decimal = [tex]\frac{2}{100}[/tex] ( hundredth )
[tex]\implies 2.22 = 2 + \frac{2}{10}+\frac{2}{100}[/tex]
Describe the graph of the basic rational function, f(x)=1/x. Talk about its domain and range and compare the function to other ones, i.e. linear or quadratic or exponential.
Final answer:
The graph of f(x) = 1/x is a hyperbola with vertical and horizontal asymptotes at x = 0 and y = 0, respectively. The domain is all real numbers except 0, and the range is the same. Unlike linear, quadratic, or exponential functions, the hyperbolic shape of 1/x presents its unique characteristics needing careful domain consideration.
Explanation:
The graph of the basic rational function f(x) = 1/x is characterized by two distinct branches, one in the first quadrant (where x and y are both positive) and the other in the third quadrant (where x and y are both negative). This function is a hyperbola, and as the value of x approaches zero from either the positive or negative side, the value of f(x) increases without bound, referred to as a vertical asymptote at x = 0. Additionally, as the value of x becomes very large or very small (approaching positive or negative infinity), the value of f(x) approaches zero, creating a horizontal asymptote at y = 0. Importantly, this function is undefined at x = 0, so the domain is all real numbers except 0, (domain: ℝ \ {0}). The function takes on all real number values for the output, so the range is also all real numbers except 0 (range: ℝ \ {0}).
Comparing to other types of functions, unlike linear functions like f(x) = 7x which produces a straight line or quadratic functions such as f(x) = 2x² which graphs as a parabola, the rational function f(x) = 1/x leads to a non-linear graph with two separate branches. Exponential functions like f(x) = eⁿ¹, however, grow or decline at an increasing rate, which is a different behavior compared to the hyperbolic decline or rise of a rational function. It's vital to note that as with the function |√x|, there are points along the graph of 1/x where the function is not defined, highlighting the importance of considering the domain in function analysis.
The function 1/x² also represents a rational function but with a different characteristic as it exhibits positive blowup on both sides. This means that as x approaches zero, whether from the positive or negative side, the function tends to positive infinity, a behavior different from the reciprocal function 1/x.
Find the perimeter of 6 regular octagons linked together side by side,if one side is 4.5 inches.
the sum of two consecutive numbers is 73. what are the numbers?
A game of chance involves rolling a 14-sided die once. If a number from 1 to 3 comes up, you win 2 dollars. If the number 4 or 5 comes up, you win 9 dollars. If any other number comes up, you lose. If it costs 5 dollars to play, what is your expected net winnings?
The expected net winnings are -$36. That is you lose $36 according to chance.
We have given
A game of chance involves rolling a 14-sided die once. If a number from 1 to 3 comes up, you win 2 dollars.
We have to determine expected net winnings
What is the expected net winnings?The expected value is what the player can expect to win or lose if they were to play many times with the same game.
let's say that you have a 3/13 chance of winning $3 and a 2/13 chance of winning $10 and an 8/13 chance of winning $0.
Therefore if the dice is rolled 13 times then the expected to win 3X$3 + 2X$10 = $29
But you pay $5 per roll so 13 rolls would cost me 13X$5 = $65
Therefore the expected net winnings are $29-$65 = -$36
Therefore the expected net winnings are -$36.
So you lose $36 according to chance.
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need help with this plz help me