Final answer:
The minimum number of books that must contain colored illustrations is 8100.
Explanation:
To find the minimum number of books that must contain colored illustrations, we can use the concept of conditional probability.
The probability of a book having illustrations is 90%, and the probability of an illustration being in color is also 90%. These two probabilities are independent events.
To find the minimum number of books with colored illustrations, we can multiply the probabilities together.
Therefore, the minimum number of books that must contain colored illustrations is 90% x 90% x 10000 = 8100.
Which expression gives the distance between the points
Apex!!!!
Need help so also comment if you have used apex learning
Answer:
D. √((2 +4)² +(5 -8)²)
Step-by-step explanation:
The distance is found using the formula ...
d = √((x1 -x2)² +(y1 -y2)²)
Selection D has this formula properly filled in with the values ...
(x1, y1) = (2, 5)
(x2, y2) = (-4, 8)
which set of directions correctly describes how to plot the point (6,2) on the coordinate plane?
Start at the origin. Move 6 units to the right, then move 2 units up.
Start at the origin. Move 6 units up, then move 2 units to the right
Start at the origin. Move 6 units to the left, then move 2 units up.
Start at the origin. Move 6 units up then move 2 units to the left
The first one. Start at origin. Move 6 units to the right and up 2 units
Answer:
Option 1 - Start at the origin. Move 6 units to the right, then move 2 units up.
Step-by-step explanation:
To find : Which set of directions correctly describes how to plot the point (6,2) on the coordinate plane?
Solution :
The point (6,2) means the x-coordinate is 6 and y-coordinate is 2.
According to graphing,
As the x-coordinate is positive it moves to right side.
So, From origin there is a shift of 6 units right.
As the y-coordinate is positive it moves to upward side.
So, From origin there is a shift of 2 units up.
Therefore, 'Start at the origin. Move 6 units to the right, then move 2 units up'.
Hence, Option 1 is correct.
Mikey worked 8 hours on Wednesday, 6 hours on Thursday, and 7 hours on Friday. His gross pay for all three days was $187.95
A. $8.95
B. $8.98
C. $28.13
D. 65.63
Answer:
Step-by-step explanation:
Mikey worked 8 hours on Wednesday, 6 hours on Thursday and 7 hours on Friday.
Total Work = 8+6+7 = 21 hours.
Gross Pay = 187.95 dollars.
Hourly Rate = (Gross pay)/(Total work) = (187.95)/21 = 8.95 dollars per hour.
Hence, option A is correct i.e. 8.95 dollars per hour.
a sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. turning the radius-reduction screw on the top of the nozzle lets people the radius by up to 25 percent. to the nearest tenth, what is the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity.
Answer:
1590.4 square ft
Step-by-step explanation:
r=30 so you need to multiply that by 25% (30*.25=7.5)
30-7.5=22.5
A= pi(r)^2
A=pi*(22.5)^2
A=506.25pi
A=1590.43 or 1590.4 (to the nearest tenth)
Answer: 1590.4 square feet
Step-by-step explanation:
Given: The radius of the circular area = 30 feet
Now, 25% of the radius = [tex]0.25\times30=7.5[/tex] feet
If the we reduce the radius by 25%, then the radius of the circular area =
[tex]30-7.5=22.5\text{ feet}[/tex]
Now, the circular area of the spray is given by :-
[tex]\text{Area}=\pi r^2\\\\\Rightarrow\text{ Area}=(3.143.141592653)(22.5)^2\\\\\Rightarrow\text{ Area}=1590.43128088\approx1590.4\text{ ft}^2[/tex]
Therefore, the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity = 1590.4 square feet.
given a=-3 and b=4 and c=-5, evaluate a+b/c
Answer:
1/5 = 0.2
Step-by-step explanation:
First
[a + b] / c is an algebraic expression
Then
[(-3) + (4)] / 5
[1] / 5
1/5
Best regards
Answer:
-3 4/5
Step-by-step explanation:
a+b/c
Substitute the values in
-3 + 4/-5
-3 + -4/5
-3 4/5
If the expression was (a+b)/c
then (-3 +4)/-5
We would do the parentheses first
1/-5
-1/5
Is this right idk but i need work fir it
Answer:
The answer is C 5/4
Step-by-step explanation:
When lines are parallel and you know there is a scalar factor, make the ratio by putting the original over the dilation 15:12 or 15/12 this is the ratio and after you need to reduce by dividing by the greatest common factor. 15 and 12's GCF is 3 so (15/3)/(12/3) = 5/4.
What is the measure of angle x? please help
➷ First find the angle on the opposite side of x.
We can find this using the rule that angles on a straight line equal 180 degrees
180 - (90 + 47) = 43
Vertically opposite angles are equal
Therefore, x would also be 43 degrees.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
x=43
Step-by-step explanation:
The angle between x and 47 is a right angle because it is a vertical angle to the right angle and vertical angles are equal.
Starting with x, we add x + the right angle +47 and we have a straight line. We know straight lines are 180 degrees
x + 90 + 47 = straight line
x+ 137 = 180
Subtract 137 from each side
x+137-137 = 180-137
x = 43
Determine the Domain of the relation
{(x, y): y = x/x-8}
Answer:
Domain: (-∞ , 8) ∪ (8, +∞)
Step-by-step explanation:
Since denominator is x - 8 so x ≠ 8
If x = 8 then y = 8/0 : undefined.
Hence, the domain is all real numbers except 8
So
Domain: (-∞ , 8) ∪ (8, +∞)
Answer:
The correct answer is A) x does not equal 8
Step-by-step explanation:
In order to find gaps in the domain, we look for two things. The first we look for is negatives under square roots (which are not an issue here since there are none) and then we look for 0, denominators. So to find the gap, we set the denominator equal to 0 and see what the x value cannot be.
x - 8 = 0
x = 8
Find the missing length. Round to the nearest tenth, if necessary.
A. 441
B. 22.5
C. 64
D. 19.4
Using the Pythagorean theorem:
21^2 = √(8^2 + x^2)
441 = √( 64 + x)
441 - 64 = √x
377 = √x
x = √377
x = 19.4
The answer is D.
Anyone know how to 1.8
Hope this helps , use SOHCAHTOA
Some
Old
Hag
Cracked
All
Her
Teeth
On
Apples
To remember, hope this helps !
Find x and y for the following problem.
Answer:
x = 5/4
y = 7/4
Step-by-step explanation:
The smaller triangle and the larger one are similar, so the sides are proportional.
(x+5)/5 = 10/8
x/5 + 1 = 1/4 + 1 . . . . . divide it out
x/5 = 1/4 . . . . . . . . . . .subtract 1
x = 5/4 . . . . . . . . . . . . multiply by 5
___
For y, you can do exactly the same computations, replacing every instance of 5 with a 7. Then you get ...
y = 7/4
How to solve:
In(x+3) - In(x-1) = 3
Answer:
x = (e^3 +3)/(e^3 -1) ≈ 1.20958
Step-by-step explanation:
Take the antilog and solve in the usual way.
ln(x+3) -ln(x -1) = 3
ln((x +3)/(x -1)) = 3 . . . . rearrange to a single log
(x +3)/(x -1) = e^3 . . . . take the antilog
x +3 = e^3·(x -1)
3 +e^3 = x(e^3 -1)
x = (e^3 +3)/(e^3 -1) ≈ 1.20958
___
Check
This answer checks OK in the original equation:
ln(4.20958) -ln(0.20958) = 3
The table shows the reduction in costs (in hundreds) after a manager found ways each month to cut back in his store. Identify the best fit mathematical model with its corresponding R^2 value and tell whether it is a good model.
Month: 1. 2. 3. 4. 5
Profit Loss: 86. 82. 72. 45. 15
A: Quadratic model, 0.997
No 0.997 is too high an R^2 value.
B: quadratic model, 0.997
Yes, 0.997 is very close to 1.
C. linear model, 0.902
No, 0.902 is too high an R^2 value.
D. linear model, 0.902
Yes, 0.902 is very close to 1.
Answer:
B: quadratic model, 0.997
Yes, 0.997 is very close to 1.
Step-by-step explanation:
In general, the better the model, the closer the R²-value is to 1. A graph shows the quadratic model to be a good fit.
_____
Comment on "better models"
A 4th-degree polynomial can be written that will fit each of the 5 points exactly and give an R²-value of 1. However, the model does not appear to interpolate or extrapolate well. The quadratic offers a reasonable fit that is better than that of the linear model and seems to have reasonable behavior between and beyond the given data points.
I'll give brainliest if you show your work. Plz answer quickly.
Nolan used the following procedure to find an estimate for the square root of 18.
Step 1: Since 4^2=16 and 5^2= 25 and 16 < 18 < 25, the square root of 18 is between 4 and 5.
4.1^2=16.81
4.2^2=17.64
4.3^2=18.49
4.4^2=19.36
Step 3: Since 18.49 rounds to 18, 4.3 is the best approximation for the square root of 18.
In which step, if any, did Nolan make an error?
A) In step 1, the square root of 18.
is between 4 and 5 because the square root of 18 equals about 20 and 4 times 5= 20.
B) In step 2, he made a calculation error when squaring.
C) In step 3, he should have determined which square is closest to 18.
D) Nolan did not make an error.
Answer:
C) In step 3, he should have determined which square is closest to 18.
Step-by-step explanation:
17.64 also rounds to 18. 17.64 differs from 18 by ...
18 -17.64 = 0.36
whereas 18.49 differs from 18 by ...
18.49 -18 = 0.49
Hence 17.64 is closer to 18 and we might expect 4.2 to be closer to √18 than is 4.3.
___
The actual root of 18 is about 4.243, so 4.2 is a better approximation.
C) In step 3, he should have determined which square is closest to 18.
Which fraction is NOT equivalent to
8/12
?
A)
2/3
B)
24/36
C)
4/6
D)
6/10
PLEASE HELP QUICK!
the answer is D because 6 and 10 aren't multiples of 8 and 12
To find the fraction that is not equivalent to 8/12, simplify each given fraction and check for equivalence.
Explanation:To find which fraction is not equivalent to 8/12, we need to simplify or reduce each of the given fractions. If the simplified form of a fraction is not equal to 8/12, then it is not equivalent. Let's simplify each option:
A) 2/3 - already in simplest form, not equivalent to 8/12
B) 24/36 - can be simplified to 2/3, equivalent to 8/12
C) 4/6 - can be simplified to 2/3, equivalent to 8/12
D) 6/10 - can be simplified to 3/5, not equivalent to 8/12
Therefore, option D is NOT equivalent to 8/12.
Does anyone know #11
Answer:
C. both student 1 and student 2
Step-by-step explanation:
Dilation does not change any angles, so the triangles are similar and the trig functions of corresponding angles will be identical.
The slope of CB is -1/3 and the slope of BA is 3, so they multiply together to give -1. That means the segments are at right angles and the triangle is a right triangle.
Both the premise and the conclusion of each student is correct.
For what values of p is the value of the binomial 1.5p−1 smaller than the value of the binomial 1+1.1p?
Answer:
p < 5
Step-by-step explanation:
We want to find p for ...
1.5p -1 < 1 +1.1p
0.4p < 2 . . . . add 1-1.1p
p < 5 . . . . . . . multiply by 2.5
The desired relationship will be the case for values of p less than 5.
the volume of a cylinder cone and sphere are shown below. The three figures have the same radius. The cylinder and the cone have the same height with h = r.
if the volume of the cone is 36 cubic units, what are the volumes of the cylinder and sphere? Explain your answer.
answers: Cylinder:_______cubic units
sphere:________cubic units
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Answer:
Part 1) The volume of the cylinder is [tex]V=108\ units^{3}[/tex]
part 2) The volume of the sphere is [tex]V=144\ units^{3}[/tex]
Step-by-step explanation:
step 1
Find the radius of the cone
we know that
the volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]V=36\ units^{3}[/tex]
[tex]h=r\ units[/tex]
substitute and solve for r
[tex]36=\frac{1}{3}\pi r^{2} (r)[/tex]
[tex]108=\pi r^{3}[/tex]
[tex]r^{3}=108/ \pi[/tex] ------> equation A
step 2
Find the volume of the cylinder
we know that
the volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=r\ units[/tex]
substitute
[tex]V=\pi r^{2} (r)[/tex]
[tex]V=\pi r^{3}\ units^{3}[/tex]
substitute the equation A in the formula above
[tex]r^{3}=108/ \pi[/tex] ----> equation A
[tex]V=\pi (108/ \pi)\ units^{3}[/tex]
[tex]V=108\ units^{3}[/tex]
step 3
Find the volume of the sphere
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}\ units^{3}[/tex]
substitute the equation A in the formula above
[tex]r^{3}=108/ \pi[/tex] ----> equation A
[tex]V=\frac{4}{3}\pi (108/ \pi)[/tex]
[tex]V=144\ units^{3}[/tex]
Put this into Y=Mx+B form please
I need someone’s help please
Answer: 90 pounds.
Step-by-step explanation:
Let's call:
A: pounds of type A coffee.
B: pounds of type B coffee.
Based on the information given in the problem you can set up the following system of equations:
[tex]\left \{ {{A+B=153} \atop {4.25A+5.45B=758.25}} \right.[/tex]
You can use the Elimination method:
- Multiply the first equation by -4.25.
- Add both equations.
- Solve for B.
Then, you obtain:
[tex]\left \{ {{-4.25A-4.25B=-650.25} \atop {4.25A+5.45B=758.25}} \right.\\----------\\1.2B=108\\B=90[/tex]
He used 90 pounds of type B coffee.
Answer:
B = 90 pounds
Step-by-step explanation:
We know that Han's Coffee shop uses coffee A at $4225 per pound and coffee B at $5.45 per pound and this month it made 153 pounds of blend for a total cost of $758.25.
We are find the number of pounds for coffee B used.
[tex]A+B=153[/tex]
[tex]A=153-B[/tex] --- (1)
[tex]4.25A+5.45B =758.25[/tex] --- (2)
Substituting equation (1) in (2) to get:
[tex]4.25(153-B)+5.45B=758.25[/tex]
[tex]650.25-4.25B+5.45B=758.25[/tex]
[tex]1.2B=758.25-650.25[/tex]
[tex]1.2B=108[/tex]
B = 90 pounds
Finnegan shot 2 rolls of film film with 36 exposures on each roll. It costs $39.60 to develope all the pictures. How much did it cost for each person.
Answer:
$0.55
Step-by-step explanation:
2x36= 72
39.60/ 72
find the missing measure for the cone. round your answer to the nearest tenth.
diameter = 6 cm
height = _____ cm
volume = 84.78 cm3
Final answer:
To find the missing height of a cone with a given diameter of 6 cm and volume of 84.78 cm³, the volume formula for a cone is used, and after plugging in the known values, solving for the height gives an approximate value of 3.0 cm when rounded to the nearest tenth.
Explanation:
The student is asking for the missing height of a cone given the diameter and the volume. The formula to calculate the volume of a cone is V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone. Since the diameter is given as 6 cm, the radius is half of that, which is 3 cm. The known volume of the cone is 84.78 cm³. Plugging these values into the formula gives:
84.78 cm³ = (1/3)π(3 cm)²h
After solving for h, we get:
h = ³ × 84.78 cm³ / (π × (3 cm)²)
h = 84.78 cm³ / (9π cm²)
h = 84.78 / (9 × 3.14159)
Now calculating h and rounding to the nearest tenth:
h = 84.78 / 28.27431
h ≈ 3.0 cm
Therefore, the height of the cone is approximately 3.0 cm.
A small island in the middle of a river is eroding away. Each year, the island has 85% of the area from the previous year. After one year the island has an area of 10.2 thousand square yards. Graph the sequence and describe the pattern. How much of the island is left after 6 years?
Answer:
see the attachment for a graph
4.53 thousand square yards remain after 6 years
Step-by-step explanation:
The area can be described by an exponential equation that multiplies the area by 0.85 when the time variable increases by 1 year. Such an equation might be ...
a(t) = 10.2·0.85^(t-1)
The graph of this is attached.
After 6 years, the equation predicts
a(6) = 10.2·0.85^(6-1) ≈ 4.53 thousand square yards
of island will remain.
An incoming airplane is x miles due north from the control tower at an airport. A second incoming airplane is y miles due east of the same control tower. The shortest distance between the two airplanes is z miles.
Which of the following functions would best model the situation above?
A.
cube root
B.
square root
C.
piecewise
D.
step
Answer:
B. Square root
Step-by-step explanation:
using distance formula:
x = √z^2 - y^2
y = √z^2 - x^2
=> z = √x^2 + y^2
Answer:
Option B. square root
Step-by-step explanation:
An incoming airplane is x miles due North at A from the control tower and a second airplane is y miles East at B of the same control tower.
The shortest distance between the two airplanes is z miles.
By Pythagoras Theorem
z² = x² + y²
z = √(x² + y²)
So function which models the situation best is "square root".
Therefore, option B. square root is the answer.
i need help on 2, 3 and 4 plz thank u ( :
Answer:
2. x = √3
3. y = 3√2
4. a = (2/3)√2
Step-by-step explanation:
In an isosceles right triangle, the length of the hypotenuse is √2 times the length of one side. Said another way, the length of the side is 1/√2 times the length of the hypotenuse.
___
2. x = √6/√2 = √(6/2) = √3 . . . . . divide the hypotenuse by √2 to find x
___
3. (12 -√2y) = √2y . . . . . equate the hypotenuse to √2 times the leg and solve
12 = 2√2y
12/(2√2) = y = 6/√2 = 3√2
___
4. 3a = 2√2 . . . . . . equate the hypotenuse to √2 times the leg and solve
a = 2√2/3 = (2/3)√2
_____
Comment on "rationalizing the denominator"
"Simplest radical form" usually means the radical is in the numerator. To eliminate it from the denominator, multiply by the radical:
1/√n = (√n)/(√n) · 1/√n = (√n)/(√n)^2 = (√n)/n
That is, ...
1/√2 = (√2)/2 . . . . for example.
Isosceles △ABC (AC=BC) is inscribed in the circle k(O). Prove that the tangent to the circle at point C is parallel to AB .
Explanation:
Let M be the midpoint of AB. Then CM is the perpendicular bisector of AB. As such, center O is on CM, and OC is a radius (and CM). The tangent is perpendicular to that radius (and CM), so is parallel to AB, which is also perpendicular to CM.
If you need to go any further, you can show that triangles CMA and CMB are congruent, so (linear) angles CMA and CMB are congruent, hence both 90°.
A farm supply store sells a variety of treat balls for small and large animals. Martha wants to purchase a ball that can hold 1437 cubic centimeters of treats. What is the diameter of the ball she should purchase? Round to the nearest whole number.
The volume of a sphere is v=4/3 x 3.14 r to the the third power
Answer: 14 centimeters.
Step-by-step explanation:
You need to use the formula for calculate the volume of a sphere:
[tex]V=\frac{4}{3}(3.14r^3)[/tex]
Where the radius of the sphere is "r".
As you know the volume of the ball, you can susbtitute it into the formula [tex]V=\frac{4}{3}(3.14r^3)[/tex], and solve for the radius "r":
[tex]1437=\frac{4}{3}(3.14r^3)\\\\3( 1437)=4(3.14r^3)\\\\4311=12.56r^3\\\\r=\sqrt[3]{\frac{4311}{12.56}}\\\\r=7.0cm[/tex]
The diameter of the ball can be calculated with:
[tex]D=2r[/tex]
Where r is the radius of the ball.
Substituting the radius of the ball into [tex]D=2r[/tex], you get that the diameter of the ball that she should purchase, rounded to the nearest whole number, is:
[tex]D=2(7.0cm)\\D=14.0cm\\D=14cm[/tex]
Final answer:
To solve for the diameter of the ball, the volume of a sphere formula is used. The calculated diameter is rounded to the nearest whole number, and Martha should purchase a treat ball with a diameter of approximately 14 centimeters.
Explanation:
To find the diameter of the ball that can hold 1437 cubic centimeters of treats, we need to use the formula for the volume of a sphere: V = (4/3) π r^3, where V is the volume and r is the radius. We will solve for r and then multiply by 2 to find the diameter. Given that the volume, V, is 1437 cubic centimeters, the formula becomes:
1437 = (4/3) × 3.14 × r^3
To isolate r, we first divide both sides of the equation by (4/3) × 3.14:
r^3 = 1437 / ((4/3) × 3.14)
Calculating the right side gives us the approximate value of r^3. Then, we take the cube root of both sides to solve for r:
r = ∛(1437 / ((4/3) × 3.14))
Once we find r, we can calculate the diameter, D, by:
D = 2 × r
Calculating the above with the given volume, we find:
r ≈ ∛(1437 / ((4/3) × 3.14)) ≈ 6.83 cm
D ≈ 2 × 6.83 cm ≈ 13.66 cm
So, rounding the diameter to the nearest whole number, Martha should purchase a treat ball with a diameter of approximately 14 centimeters.
Remove the parentheses from the following expression: (+6) – (+2)
A. –6 – 2
B. 6 – 2
C. –6 + 3
D. 6 + 2
The correct answer:
B. 6 - 2
Answer:
B. 6-2
Step-by-step explanation:
We have been given expression : [tex]\left(+6\right)-\left(+2\right)[/tex]
Now we need to rewrite that expression [tex]\left(+6\right)-\left(+2\right)[/tex], without parenthesis then select which of the given choices are correct.
[tex]\left(+6\right)-\left(+2\right)[/tex]
We know that product of opposite sign is always negative sign.
Then product of - and +2 gives -2
So we can rewrite the problem as:
[tex]=6-2[/tex]
Hence choice B. 6-2 is the final answer.
1. Write an equation in point slope form for the line through the given point with the given slope.
(8,3);m=6
A. Y+3=6(x-8)
B. Y-3=6(x-8)
C. Y-3=6(x+8)
D. Y+3=6x +8
2. Write an equation in point slope form for the line through the given point with the given slope.
(-3,-5);m= -2/5
A. Y+5= -2/5(x+3)
B. Y+5= (-2/5) x+3)
C. Y-5= -2/5 (x+3)
D. Y-5= -2/5 (x-3)
To write an equation in point slope form, we use the formula: y - y1 = m(x - x1). The correct equations are: Y + 3 = 6(x - 8) and Y + 5 = -2/5(x + 3).
Explanation:To write an equation in point slope form, we use the formula: y - y1 = m(x - x1). Where (x1, y1) is the given point and m is the given slope.
Question 1:
Given point: (8, 3) and slope: 6
Substituting the values into the formula, we have: y - 3 = 6(x - 8)
Therefore, the correct answer is option A: Y + 3 = 6(x - 8).
Question 2:
Given point: (-3, -5) and slope: -2/5
Substituting the values into the formula, we have: y + 5 = -2/5(x + 3)
Therefore, the correct answer is option A: Y + 5 = -2/5(x + 3).
Final answer:
The point-slope form equations for the given points and slopes are y - 3 = 6(x - 8) for the first set and y + 5 = (-2/5)(x + 3) for the second set.
Explanation:
The equation of a line in point-slope form is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a given point on the line.
1. With the given point (8,3) and slope m = 6, the equation in point-slope form will be y - 3 = 6(x - 8). This corresponds to option B. Y-3=6(x-8).
2. For the given point (-3,-5) and slope m = -2/5, the point-slope form of the equation is y + 5 = (-2/5)(x + 3), which matches option A. Y+5= -2/5(x+3).
assuming that the pentagon is regular, what is the area of the shaded region below? PLEASE HELP ASAP
Answer:
46.20 square units
Step-by-step explanation:
The area of a regular polygon can be found from the side length and apothem as ...
A = (1/2)ap . . . . . where a = apothem, p = perimeter (# of sides times side length)
The total area of the pentagon is then ...
A = (1/2)(5.51)(5·8) = 110.20 . . . . . square units
__
The shaded area is the difference between the area of the pentagon and the area of a square with side length 8. The square's area is ...
A = s^2 = 8^2 = 64 . . . . . . square units
__
Then the shaded area is ...
A = (pentagon area) - (square area) = 110.20 -64.00 = 46.20 . . . . . square units