The complete sentence is shown below:
Reason: Given
Reason: Angles forming a linear pair sum to 180° (Given)
Reason: Substitution from Statement 1.
To complete the proof that HJ GI, we can use the given statements and reasons:
Statement 1: <HKI = <GKH
Reason: Given
Statement 2: m<GKH + m<HKI = 180°
Reason: Angles forming a linear pair sum to 180° (Given)
Statement 3: m,GKH + m<GKH = 180°
Reason: Substitution from Statement 1
Statement 4: m<GKH = 90°
Reason: From Statement 2 and Statement 3, we can subtract m<GKH from both sides, which results in m<GKH = 180° - m<GKH.
Since the angles forming a linear pair sum to 180°, m<GKH + m<GKH = 180° implies that m<GKH = 90°.
Therefore, based on the given statements and reasons, we can conclude that HJ and GI are congruent (m<GKH = 90°)
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When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 40 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 4000 batteries, and 3% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
The probability of accepting the whole shipment is 0.9093. Therefore, almost all such shipments will be accepted.
What is the probability that this whole shipment will be accepted?The probability that the whole shipment will be accepted is calculated as follows;
First, we calculate the probability of having at most 3 batteries that do not meet specifications out of the 40 randomly tested batteries.
Assuming:
p = probability that a single battery does not meet specifications = 0.03q = probability that a single battery meets specifications = 1 - p = 0.97n = number of batteries tested = 40k = number of batteries that do not meet specifications (at most) = 3We can use the binomial probability formula to calculate the probability:
[tex]P(X \leq k) = \sum (from\: i = 0 \:to\: k) [(nCi) * p^{i} * q^{(n-i)}][/tex]
P(X ≤ 3) = [(⁴⁰C₀) * (0.03⁰) * (0.97⁴⁰] + [(⁴⁰C₁) * (0.03¹) * (0.97³⁹)] + [(⁴⁰C₂) * (0.03²) * (0.97³⁸)] + [(⁴⁰C₃) * (0.03³) * (0.97³)]
P(X ≤ 3) = 0.9093.
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Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.
8 divided by the sum of a number and 4
Answer:
Step-by-step explanation: you are sped that is the answer black n
Lorri had a gross income of $3256.15 during each pay period in 2010. If she got paid monthly, how much of her pay was deducted for FICA in 2010?
Erica bought a road bike using the store’s payment plan. She made a $320 down payment and makes monthly payments of $91. If the total cost is $1,867, how many months will Erica be paying for the bike?
Answer: 17 months
Step-by-step explanation:
Total cost of the bike = $1,867
Down payment = $320
so $1,867 - $320 = $1,547
$91 * 17 = 1,547
(17 = months) so $91 * 17 months = 1,547
Trapezoid TUVW is shown on the coordinate plane below:
Trapezoid TUVW on the coordinate plane with ordered pairs at T negative 5, 5, at U negative 2, 5, at V negative 2, 2, at W negative 7, 2.
If trapezoid T'U'V'W' represents trapezoid TUVW reflected over the y-axis, the ordered pair of W' is ___________.
The ordered pair of W' in trapezoid T'U'V'W' is (7, 2).To reflect a point over the y-axis, we need to change the sign of its x-coordinate while keeping the y-coordinate the same.
In trapezoid TUVW, the ordered pair of W is (-7, 2).
To find the ordered pair of W' in trapezoid T'U'V'W', we need to reflect the x-coordinate of W over the y-axis. Therefore, the x-coordinate of W' will be the opposite of the x-coordinate of W, while the y-coordinate remains the same.
Given that the coordinates of point W are (-7, 2), reflecting it over the y-axis means changing the sign of the x-coordinate, while keeping the y-coordinate the same.
So, when we reflect point W(-7, 2) over the y-axis, the x-coordinate becomes positive and the y-coordinate remains the same. Therefore, the ordered pair of W' is (7, 2).
The x-coordinate of W' will be -(-7) = 7, and the y-coordinate remains 2.
So, the ordered pair of W' is (7, 2).
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The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers. The data are normally distributed and s=9.904 weeks. Construct and interpret a 90% confidence interval for the population standard deviation of the age (in weeks) at which babies first crawl. 31 39 36 38 51 48 55 Click the icon to view the table of critical values of the chi-square distribution. choice.
Select the correct choice below and fill in the answer boxes to complete your
(Use ascending order. Round to three decimal places as needed.) O
A. If repeated samples are taken, 90% of them will have the sample standard deviation between ___ and___
B. There is a 90% probability that the true population standard deviation is between ___ and ___
C. There is 90% confidence that the population standard deviation is between and___ and ___
There is 90% confidence that the population standard deviation is between 5.094 weeks and 19.803 weeks.
The correct option is C.
What is the confidence interval or the population standard deviation?To construct a confidence interval for the population standard deviation, we can use the chi-square distribution.
Given data:
Sample size (n) = 12
Sample standard deviation (s) = 9.904 weeks
The chi-square distribution is right-tailed and at 90% confidence level, the significance level is 0.1 on each tail.
Degrees of freedom (df) = n - 1
Degrees of freedom (df) = 12 - 1
Degrees of freedom (df) = 11
From the chi-square distribution table, the critical values for a 90% confidence level with 11 degrees of freedom are 3.816 and 22.362.
Therefore, the 90% confidence interval for the population standard deviation is:
Lower bound = √(n-1) * s² / χ² upper)
Lower bound = √(11 * 9.904²) / 22.362)
Lower bound = 5.094
Upper bound = √(n-1) * s² / χ² lower)
Upper bound = √(11 * 9.904²) / 3.816)
Upper bound = 19.803
Therefore, there is 90% confidence that the population standard deviation of the age at which babies first crawl is between approximately 5.094 weeks and 19.803 weeks.
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Hello, someone help me with this integral, it gets complicated when they are like this, please help, I need it to pass: c
.....dx
∫ --------
...1−25x²
Answer:
∫(1 - 25x²) dx
Step-by-step explanation:
Aubree owns a small business selling clothing. She knows that in the last week 69 customers paid cash, 2 customers used a debit card, and 7 customers used a credit card. Based on these results, express the probability that the next customer will pay with something other than cash as a percent to the nearest whole number.
The probability that the next customer will pay with something other than cash, rounded to the nearest Whole number, is approximately 12%.
The probability that the next customer will pay with something other than cash, we need to consider the total number of customers who paid with something other than cash and divide it by the total number of customers in the last week.
In the given information, it is stated that 69 customers paid with cash, 2 customers used a debit card, and 7 customers used a credit card. To find the total number of customers who paid with something other than cash, we add the number of customers who used a debit card and the number of customers who used a credit card:
Total number of customers who paid with something other than cash = Number of customers who used a debit card + Number of customers who used a credit card
= 2 + 7
= 9
Now, to calculate the probability, we divide the number of customers who paid with something other than cash by the total number of customers:
Probability = Number of customers who paid with something other than cash / Total number of customers
= 9 / (69 + 2 + 7)
= 9 / 78
= 0.1154 (rounded to four decimal places)
To express the probability as a percentage, we multiply the probability by 100:
Probability as a percent = 0.1154 * 100
≈ 11.54
Therefore, the probability that the next customer will pay with something other than cash, rounded to the nearest whole number, is approximately 12%.
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given the function f(x)=logbase2(X), find the y-intercept of g(x) = f(x+4)+8
The y-intercept of f(x + 4) + 8 is given as follows:
10.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]f(x) = \log_2{x}[/tex]
The translated function is then given as follows:
[tex]g(x) = \log_2{x + 4} + 8[/tex]
The y-intercept of the function is the numeric value at x = 0, hence:
[tex]g(0) = \log_2{0 + 4} + 8[/tex]
g(0) = 2 + 8 = 10.
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A population data set produced the following information N-250 Σx=9880, Σy=1456. Σxy-85080 Σx²=485870, Σy² = 135675 Find the value of oe and p²
The value of p² is approximately 0.999999528.
To find the value of oe (the standard error of estimate) and p² (the coefficient of determination), we can use the given population data set information.
The formula for the standard error of estimate (oe) is:
oe = √((Σy² - (Σy)² / N) / (N - 2))
Substituting the given values, we have:
oe = √((135675 - (1456)² / 250) / (250 - 2))
oe = √((135675 - 2124736 / 250) / 248)
oe = √(541.96)
oe ≈ 23.27
Therefore, the value of oe is approximately 23.27.
The coefficient of determination (p²) can be calculated using the formula:
p² = 1 - (Σxy - (Σx × Σy) / N) / ((Σx² - (Σx)² / N) × (Σy² - (Σy)² / N))
Substituting the given values:
p² = 1 - (85080 - (9880 × 1456) / 250) / ((485870 - (9880)² / 250) × (135675 - (1456)² / 250))
p² = 1 - (85080 - 14358080 / 250) / ((485870 - 968144 / 250) × (135675 - 2124736 / 250))
p² = 1 - (85080 - 57432.32) / (478352.56 × 123346.74)
p² = 1 - (27647.68) / (59022875580.02)
p² ≈ 0.999999528
Therefore, the value of p² is approximately 0.999999528.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Based on the information given about the geometry, the value of CF will b A. 6cm.
How to calculate the valueSince OE and OF are both 4 cm, then OEF is an equilateral triangle. This means that EOF is 60 degrees.
Since AB is 12 cm, then AB is twice the length of OE. This means that ABE is a 30-60-90 triangle.
In a 30-60-90 triangle, the hypotenuse is twice the length of the side opposite the 30 degree angle. This means that CF is 6 cm.
In conclusion, the correct option is A.
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Simplify the following expression.
(6m5g5) 2
The simplified exponential expression in the context of this problem is given as follows:
[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]
How to simplify the exponential expression?The exponential expression in the context of the problem is defined as follows:
[tex](6m^5g^5)^2[/tex]
The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.
Applying the exponent of 2, we have that:
6² = 36.5 x 2 = 10.Hence the simplified exponential expression in the context of this problem is given as follows:
[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]
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The circle has center O. Its radius is 4 ft, and the central angle a measures 110°. What is the area of the shaded region?
Give the exact answer in terms of it, and be sure to include the correct unit in your answer.
The area of the shaded region is (133π/9) square feet.
Given that the radius (r) is 4 ft, the area of the entire circle is:
A = π(4)² = 16π ft²
To find the area of the sector, we need to calculate the fraction of the circle that the central angle represents.
The fraction is determined by dividing the measure of the central angle (110°) by the total angle in a circle (360°).
Fraction of the circle represented by the sector = 110° / 360° = 11/36
To find the area of the sector, we multiply the fraction by the area of the entire circle:
Area of the sector = (11/36) × (16π)
= (11π/9) ft²
Finally, to find the area of the shaded region, we subtract the area of the sector from the area of the entire circle:
Area of shaded region = Area of entire circle - Area of sector
Area of shaded region = 16π - (11π/9)
= (144π - 11π)/9
= (133π/9) ft²
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What is the measure of angle T and angle V?
The measures of angle T and angle V are T = 90 and V = 90
How to determine the measure of angle T and angle V?From the question, we have the following parameters that can be used in our computation:
The circle
The point T and V are at the tangent of the circle
By definition, the tangent is perpendicular to the radius of the circle, with which it intersects.
This means that the angle T and angle V are right angled
Using the above as a guide, we have the following:
T = 90 and V = 90
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Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 113.8°.
Answer:
m<A = 66.2°
Step-by-step explanation:
m<A + m<B = 180°
m<B = 113.8°
m<A + 113.8° = 180°
m<A = 180° - 113.8°
m<A = 66.2°
Use the hundredths grid to answer the question. A 10 by 10 grid is shown. 4 columns and 7 squares are shaded. 2 columns and 5 squares are shaded. Which equation is shown by the shaded area of the model? A. 0 . 29 + 0 . 43 = 0 . 72 B. 0 . 43 + 0 . 22 = 0 . 65 C. 0 . 47 + 0 . 25 = 0 . 72 D. 0 . 23 + 0 . 42 = 0 . 65
Answer:
What the other guy said
Step-by-step explanation:
Which statements are true regarding the expression below? Choose three answers. 8 ^-1. 8 ^-3. 8
The statements that are true regarding the expression with the exponents -1, -3, and 1 are;
An equivalent expression is 8⁷·8⁻¹⁰The sum of the exponent is -3The value of the expression is 1/512What is an exponent?An exponent is a quantity or power to which a value, expression or number is to be raised.
The specified expression can be presented as follows;
8⁻¹ × 8⁻³ × 8
Therefore; 8⁻¹ × 8⁻³ × 8 = 8⁽⁻¹ ⁺ ⁻³ ⁺ ¹⁾ = 8⁻³ = 1/8³
The sum of the exponent is; -1 + (-3) + 1 = -31/8³ = 1/512
Therefore, the value of the expression is; 1/512Similarly, we get; 8⁷ × 8⁻¹⁰ = 8⁽⁷ ⁻ ¹⁰⁾ = 8⁻³ = 1/8³
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100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
The missing angles are m ∠1 = 53° and m ∠k = 12°.
Given that are two circles we need to find the missing measures,
Using the concept of intersecting chords angles,
When two chords intersect inside a circle, the angle between the chords is half the sum of the intercepted arcs.
And,
When two chords intersect outside a circle, the angle between the chords is half the difference of the intercepted arcs.
So,
a) m ∠1 = 1/2 [arc LP + arc RQ]
m ∠1 = 1/2 [50°+56°]
m ∠1 = 1/2 × 106°
m ∠1 = 53°
b) m ∠k = 1/2 [arc MJ - arc LR]
arc LR = 360° - [72° + 100° + 140°]
arc LR = 48°
So,
m ∠k = 1/2 [72° - 48°]
m ∠k = 12°
Hence the missing angles are m ∠1 = 53° and m ∠k = 12°.
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What is the correct order of the functions from least to greatest according to the average rate of
change on the interval from x=-1 to x-3? (2 points)
The correct option is the second one, the order is:
g(x), f(x), h(x).
How to find the rates of change?To find the rate of change for a function f(x) on an interval [a, b] we need to get:
R = (f(b) - f(a))/(b - a)
Here the interval is [-1, 3]
The first function is:
f(x)= (x + 3)² - 2
Evaluating we get:
f(-1) = (-1 + 3)² - 2
f(-1) = 2² - 2 = 4 -2 = 2
and f(3) = (3 + 3)² - 2 = 34
Then the rate is:
R = (34 - 2)/(3 + 1) = 8
For g(x) we can use the graph, we have:
R = (0 + 2)/4 = 1/2
For the last function we need to use the table, then we will get:
R = (62 - 14)/(3 + 1) = 12
Then the order, from least to greatest is:
g(x), f(x), h(x).
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100 Points! Geometry question. Photo attached. Find x and y in the right triangle. Please show as much work as possible. Thank you!
Answer:
x = 10.5
y =5.25
Step-by-step explanation:
sin60° = 21√3/x
√3/2 = 21√3/x
=> x = 21√3/√3/2 = 10.5
cos60° = y/x
1/2 = y/10.5
y = 10.5/2 = 5.25
In the figure below, S is the center of the circle. Suppose that JK = 19, LK = 3x+ 1, SN = 12, and SP= 12. Find the
for
In the figure, applying perpendicular bisector theorem for chords in a circle, the value of JN = 9 1/2
How to find JN in the figureThe perpendicular bisector theorem for chords in a circle states that if a radius of a circle is perpendicular to a chord, then it bisects the chord.
In other words, the radius divides the chord into two equal segments.
This theorem is a direct consequence of the properties of perpendicular lines and congruent triangles.
applying this to the figure
JN = JK/2
JN = 19/2
JN = 9 1/2
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Appling the tangent of circle properties, the length of RS is solved to be
C. 13 in
How to find the length of the tangentTo find the length of the tangent named RS, we applied the tangent of a circle property which says that the length of tangents to a particular point are equal
This leads to the mathematical equation represented below
SR = 7 in + 6 in
SR = 13 in
thus we can say that length of the tangent SR = 13 in
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Identify the axis of symmetry, vertex, and range for the quadratic function.
pls, I need help fast !!! here are questions 5 and 6
5. The minimum value of g(x) is -8.
The maximum value of g(x) is 17.
6. The average rate of change of the function g(x) over the interval [-2, 3] is 5.
How to determine the maximum and minimum value?By critically observing the table representing the function g(x), we can logically deduce the following minimum value and maximum value over the interval [-2, 3];
When x = -2, the minimum value of g(x) is equal to -8.
When x = 0, the maximum value of g(x) is equal to 17.
Question 6.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function g(x) over the interval [-2, 3]:
a = -2; f(a) = -8
b = 3; f(b) = 17
Average rate of change = (17 + 8)/(3 + 2)
Average rate of change = 25/5
Average rate of change = 5
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Here is your answer!
Answer:
[tex](x - 5)^2 + (y + 2)^2 = 5[/tex]
Step-by-step explanation:
The equation of a circle with a center at (h, k) and radius r is given by:
[tex]\bold{(x - h)^2 + (y - k)^2 = r^2}[/tex]
In this case, the center is at (5, -2) and the point that the circle passes through is (4, 0).
The distance between the center and the point is:
[tex]\sqrt{(5 - 4)^2 + ((-2) - 0)^2} = \sqrt{1 + 4} = \sqrt{5}[/tex]
Therefore, the equation of the circle is:
[tex](x - 5)^2 + (y + 2)^2 = \sqrt{5}^2[/tex]
Simplifying the equation, we get:
[tex]\bold{(x - 5)^2 + (y + 2)^2 = 5}[/tex] is a required equation
A wagon is pulled with a force of 80 pounds by a handle that
makes an angle of 20° with the horizontal.
A
What is the horizontal component of the force correct to the
nearest tenth?
27.4
B
75.2
80
20°
C
76.2
D 76.4
Explanation:
The horizontal component is found using cos fxn
80 x cos 20 = 75.2 pounds
50 points, pls answer
Is it possible for a satellite to see
of the Earth’s equator? Why or why not?
11-94.
a. The image is attached below.
b. Length of the equator is 24,000 miles.
c. The image is attached below.
d. No, it is not possible for a satellite to see 50% of the Earth's equator.
Satellite B will see more of the Earth's equator than Satellite A. This is because the viewing angle of Satellite B is larger than the viewing angle of Satellite A. The viewing angle of Satellite B is 60 degrees, while the viewing angle of Satellite A is 45 degrees.
The length of the equator in view of Satellite B is 24,000 miles. This can be calculated using the following formula:
length of the equator = 2 * [tex]\Pi[/tex] * radius * sin(m/2)
Use a third color to draw the viewing angle from Satellite C. Label the points of tangency J and K. If m/C=45", find the mJK and mJZK
This is because the Earth is a sphere, and a sphere has no flat surfaces. A satellite can only see a portion of the Earth's surface, and the portion that it sees will always be less than 50% of the total surface area.
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Ayuda operaciones y respuesta es para ahora
The perimeter of the given window is 48 centimeter.
From the given figure,
Perimeter of window = 2(Length+Breadth)
= 2(10+14)
= 2×24
= 48 centimeter
Perimeter of house = 2(Length+Breadth)
= 2(37+35)
= 2×72
= 144 centimeter
Perimeter of roof = 2(Length+Breadth)
= 2(37+5)
= 2×42
= 84 centimeter
Therefore, the perimeter of the given window is 48 centimeter.
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Need assistance with #8, #9, #10, and #11
Any help will be graetly apprciated. Studying for final exam
Below are the right probabilities for each scenario;
8. P(red, then green) [tex]\frac{1}{32}[/tex]; P(yellow, then blue) = [tex]\frac{1}{16}[/tex] and P(blue both times) [tex]\frac{1}{4}[/tex]
9. The probability of choosing a boy then rolling a number that is at most 4 is [tex]\frac{5}{14}[/tex]
10. The probability that both flights will be delayed is [tex]\frac{2}{7}[/tex].
11. P(nickel, then quarter) [tex]\frac{1}{20}[/tex]; P(penny, then not a dime) [tex]\frac{1}{10}[/tex]; P(both dimes)[tex]\frac{3}{20}[/tex]; P(both nickels) [tex]\frac{1}{20}[/tex]
How do we solve the probability questions?For the compounded probability, we can solve them the following way;
8. a) P(red, then green) = P(red) × P(green) = (2/8) × (1/8) = 1/32
b) P(yellow, then blue) = P(yellow) × P(blue) = (1/8) ×(4/8) = 1/16
c) P(blue both times) = P(blue) × P(blue) = (4/8) ×(4/8) = 1/4
9. There are 28 total students and 6 total outcomes on a standard die.
P(boy, then a number at most 4) = (15/28) × (4/6) = 5/14
10. The probability of the first flight being delayed is 6/14, and the probability of the second flight being delayed is 8/12.
P(both flights delayed) = 6/14 × 8/12 = 2/7
11. There are 25 total coins: 4 pennies, 6 nickels, 10 dimes, and 5 quarters.
a) P(nickel, then quarter) = (6/25) × (5/24) = 1/20
b) P(penny, then not a dime) = (4/25) × (15/24) = 1/10
c) P(both dimes) = (10/25) × (9/24) = 3/20
d) P(both nickels) = (6/25) × (5/24) = 1/20
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An office 8.5m long and 6.3m wide is to be carpeted to leave a surrounding 60 cm wide around the carpet, what is (a) the area of the office (b) the area of the carpet (c) the area of the surrounding
(a) The area of the office is 53.55 meters square.
(b) The area of the Carpet would be 52.6656 meters square.
(c) The area of the surrounding is 0.8844 meters square.
Area of the office floor= Length × Breadth
= 8.5 meters × 6.3 meters
= 53.55 meters square
Area of the Carpet = Length × Breadth
= (8.5-0.06) meters × (6.3-0.06) meters
Since, 60 cm = 0.06 meters
Because 1 meter = 100 cm
= 52.6656 meters square
Area of surrounding = Area of Office floor - Area of Carpet
= 53.55 meters square - 52.6656 meters square
= 0.8844 meters square
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