the area of the rectangle is 80. 1 cm²
What is the area of a rectangle?
From the given information, let's say one side of rectangle = a
The other side = (36 - 2a)/2
= 18 - a cm
The angles between the diagonals of the rectangle is 78°
Then, the angle diagonal has with base will give
= (180° - 78°)/2
= 102/2
= 51°
We have the angle to be 51 degrees, using the tan ratio
Tan θ = opposite/ adjacent
Opposite of angle 51 degrees = a
Adjacent = 18 - a
Thus,
[tex]tan 51 = \frac{a}{18 - a}[/tex]
[tex]1. 2349 = \frac{a}{18-a }[/tex]
cross multiply
[tex]18 -a ( 1. 2349) = a[/tex]
[tex]22. 23 - 1. 2349a = a[/tex]
collect like terms
[tex]a + 1. 2349a = 22. 23[/tex]
[tex]2. 2349 a = 22. 23[/tex]
[tex]a = \frac{22. 23}{2. 2349}[/tex]
a = 9. 95
If a = 9. 95cm
Then, 18 - a = 18 - 9. 95 = 8. 05cm
The formula of area of a rectangle is given as;
Area = width × length
Area = 9.95 x 8.05
Area = 80. 1 cm²
Thus, the area of the rectangle is 80. 1 cm²
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Wat is the word form for 8.008
Answer:
8.008 in Words: eight and eight thousandths in (US) American English, Number Converted (Spelled Out) to Words.
The cost, in dollars, to produce x vats of ice cream is C ( x ) = 4 x + 4 . When selling them to ice cream shops, the price-demand function, in dollars per vat, is p ( x ) = 88 − 3 x. Find the profit function p(x). How many vats of ice cream need to be sold to maximize the profit? Find the maximum profit. Find the price to charge per vat to maximize profit
Answer:
92-7x
Step-by-step explanation:
88-3x-4x+4=92-7x
Components used in a cellular telephone are manufactured with nominal dimension of .3 mm and lower and upper specification limits of .295 mm and .305 mm respectively. the x bar and R control charts for this process are based on subgroups of size 3 and they exhibit statistical control, with the center line on the x bar chart at .3015 mm and the center line of the R chart at .00154 mm.
a) Estimate the mean and standard deviation of this process.
b) Suppose that parts below the LSL can be reworked, but parts above the USL must be scrapped. Estimate the proportion of scrap and rework produced by this process.
c) Suppose that the mean of this process can be reset by fairly simple adjustments. What value of the process mean would you recommend? Estimate the proportion of scrap and rework produced by the process at this new mean.
Answer:
Kindly check explanation
Step-by-step explanation:
Xbar = 0.3015 ; Rbar = 0.00154
USL = 0.295 ; LSL = 0.305
For a subgroup size of 3 ; k = 3 ; d2 = 1.693
The mean = xbar = 0.3015 mm
The standard deviation = Rbar / d2 = 0.00154 / 1.693 = 0.0009096
b) Suppose that parts below the LSL can be reworked, but parts above the USL must be scrapped. Estimate the proportion of scrap and rework produced by this process.
P(X < 0.295)
(x - mean) / standard deviation
(0.295 - 0.3015) / 0.0009096 = 0.00003
0.00003 should be reworked.
P(X > 0.305)
1 - P(X < 0.305)
(x - mean) / standard deviation
(0.305 - 0.3015) / 0.0009096 = 3.847
1 - P(Z < 3.847)
1 - 0.99994
= 0.00006
0.00006 should be reworked.
c) Suppose that the mean of this process can be reset by fairly simple adjustments. What value of the process mean would you recommend? Estimate the proportion of scrap and rework produced by the process at this new mean.
Recommended mean = 0.3000 mm
P(X < 0.295)
(x - mean) / standard deviation
(0.295 - 0.3000) / 0.0009096 = 0.00003
0.00003 should be reworked.
P(X > 0.305)
1 - P(X < 0.305)
(x - mean) / standard deviation
(0.305 - 0.3000) / 0.0009096 = 5.497
1 - P(Z < 5.497)
1 - 0.99997
= 0.00003
0.00003 should be reworked.
X-4y=16
5x+4y=8 Math math math
Answer:
(4,-3)
Step-by-step explanation:
x-4y=16
5x+4y=8
find x for one equation
x=4y+16
Now plug this into the other equation
5(4y+16)+4y=8
20y+80+4y=8
24y=-72
y=-3
x=4
Answer:
y=-3
x=4
Step-by-step explanation:
What type of number is 2?
Choose all answers that apply:
A
Whole number
B
Integer
C
Rational
D
Irrational
Classify each special right triangle in the length ratio of (Side1 : Side2 : hypotenuse)
Answer: i added a pic of the answers
Step-by-step explanation:
Business Maths
1703
The following problems were in your worksheet on direct and inverse proportion. Reformulate the
relationships as algebraic expressions and remember to define the variables you use. You do not
have to solve the expressions.
5. The students in class usually drink a lot of water to help with their studies. I have found that
with five students in the class at least 30 litres of water is needed. How much water will be
needed when there are 30 students in the class?
Answer:
30/5=6
6*30=180
So 180 litres
A gym teacher placed golf balls into 9
buckets so that each bucket had at least 15
balls. How many total golf balls are there?
Answer:
135
Step-by-step explanation:
9 x 15 = 135
The total number of the golf ball in all buckets is 135 balls using multiply system
Multiply based problem:What information do we have?
Number of buckets = 9
Number of golf ball in each bucket = 15
Total number of golf ball in all buckets = Number of buckets × Number of golf ball in each bucket
Total number of golf ball in all buckets = 9 × 15
Total number of golf ball in all buckets = 135 balls
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15/3 = 5 4_7 + 5 2_3
b=?
Answer:
0 < 5 < 54/7 < 52/3
Step-by-step explanation
0/21 < 105/21 < 162/21 < 364/21
Jefferson’s class was studying sunflowers. They learned that sunflowers are able to make their own food. Which parts of a sunflower collect most of the sunlight needed to make food?
1. Socks are on sale at 10% discount. What is the sale price of a pair of socks originally
marked #125.00?
Answer:
10/100 = x/125
1250 = 100x
1250/100 = 100x/100
12.5 = x
125 - 12.5 = 112.5
the sale price is $112.5
According to the National Center for Education Statistics, there were 13.2 million undergraduate students enrolled in degree-granting postsecondary institutions in Fall 2000. In Fall 2014, the enrollment was 17.3 million students. Assuming this relationship grows linearly, write a linear function that models the undergraduate enrollment in postsecondary institutions
x years after 2000
Answer:
13.2 + 0.292X = Y
Step-by-step explanation:
Given that, according to the National Center for Education Statistics, there were 13.2 million undergraduate students enrolled in degree-granting postsecondary institutions in Fall 2000, while in Fall 2014, the enrollment was 17.3 million students, assuming this relationship grows linearly, a linear function that models the undergraduate enrollment in postsecondary institutions X years after 2000 would be carried out as follows:
2014-2000 = 14
17.3 - 13.2 = 4.1
4.1 / 14 = 0.292
Thus, each year 292,000 new students are enrolled in postsecondary institutions. Therefore, the function that determines what is requested would be the following:
13.2 + 0.292X = Y
Andrew has 1/2 of his assignment left to do. He has three days left to complete it. If he divides up the work evenly over the three days. what fraction of the work should he complete each day to finish on time?
Answer:
the minimum work he can do to complete it in 3 days is 1/3.
So he should do at least 1/3 of the work each day to complete it on time.
Answer = 1/3
Step-by-step explanation:
Place the integers in order from greatest to least ? What the order? I need help
Answer:
9,8,1,0,-10,-15
Step-by-step explanation:
HOPEE HELPSS HEHE
what is 3 1/4 as an improper fraction
Answer: 3.25 = 13/4
Step-by-step explanation:
I got 13/4
A mixed number is an addition of its whole and fractional parts.
3 + 1/4
add 3 and 1/4
To write
3
as a fraction with a common denominator, multiply by 4/4
3 x 4/4 + 1/4
Combine 3 and 4/4
3x4/4+ 1/4
Combine the numerators over the common denominator.
3x4+1/4
Simplify the numerator.
Multiply 3 by 4
12+1/4
Add 12 and 1
And your final answer is
13/4
NEED HELP W GEOMETRY
In △
ABC, ∡A
is 2 more than twice ∡B
, and ∡C
is 7 less than twice ∡B
. What is the measure of each angle in △
ABC and what is its classifications?
Answers:
Angle A = 76Angle B = 37Angle C = 67Triangle ABC is an acute triangle. It's also a scalene triangle.
====================================================
Work Shown:
x = measure of angle B
2x+2 = measure of angle A, since we're told its "2 more than twice angle B"
2x-7 = measure of angle C, for similar reasoning
The three angles add to 180. This is true for any triangle
A+B+C = 180
(2x+2)+(x)+(2x-7) = 180
5x-5 = 180
5x = 180+5
5x = 185
x = 185/5
x = 37
This means angle B is 37 degrees. The other two angles are
A = 2x+2 = 2*37+2 = 74+2 = 76
C = 2x-7 = 2*37-7 = 74-7 = 67
----------------
In summary, we have these three interior angles
A = 76B = 37C = 67As a way to check, note how A+B+C = 76+37+67 = 180. This confirms the answer. All three angles mentioned are smaller than 90 degrees, so this triangle is acute.
Furthermore, because all three angles are different measures, this means all three sides are different lengths. This leads to triangle ABC being scalene.
T varies directly as the square of P and inversely as Z and T=12 when P=3 and Z=6
5. Using k as the constant of variation, which of the following is the equation of variation?
A. T=
\frac{kp {}^{2} }{z}
z
kp
2
B. T=
kpz {}^{2}kpz
2
C. T=
\frac{kz}{p {}^{2} }
p
2
kz
D. T=
\frac{pz {}^{2} }{k}
k
pz
2
6. Which of the following is the value of the variation constant:
A. 6
B. 8
C. 10
D. 12
7. Which of the following is twice the value of T when P=9 and Z=6?
A. 108
B. 216
C. 54
D. 36
Answer:
A. [tex] T= \frac{KP^2}{Z}[/tex]
D. K = 8
B. 216
Step-by-step explanation:
Q. T varies directly as the square of P and inversely as Z and T=12 when P=3 and Z=6
Solution:
According to the given information:
T varies directly as the square of P.
[tex] T\alpha P^2..... (1)[/tex]
T varies inversely as Z.
[tex] T\alpha \frac{1}{Z} ..... (2)[/tex]
Combining equations (1) & (2)
[tex] T\alpha \frac{P^2}{Z}[/tex]
[tex] T= \frac{KP^2}{Z}[/tex]
(Where K is proportionality constant)
(This is the equation of variation)
Plug T=12, P=3 and Z=6 in the above equation of variation, we find:
[tex] 12= \frac{K(3)^2}{6}[/tex]
[tex] 12= \frac{K\times 9}{6}[/tex]
[tex] K= \frac{12\times 6}{9}[/tex]
[tex] K= \frac{72}{9}[/tex]
[tex] K= 8[/tex]
So, the value of the variation constant = 8
Next, plug P=9, Z=6 and K = 8 in the above equation of variation, we find:
[tex] T= \frac{8(9)^2}{6}[/tex]
[tex] T= \frac{8\times 81}{6}[/tex]
[tex] T= \frac{648}{6}[/tex]
[tex] T= 108[/tex]
[tex] 2T= 2\times 108[/tex]
[tex] 2T= 216[/tex]
So, 216 is twice the value of T.
#3 Write the fraction in simplest form 5/5
The answer is one.
Its one because when both the numerator and the denominator are the same number they equal 1.
For example, if you needed to fill a bag with 5 candies. The fraction 5/5 would be putting all 5 candies in the bag and them you have one full bag.
Find the measure of an angle such that the difference between the measures of its supplement and three times its complement is 60°
The measure of the angle is
Answer:
X=50
Step-by-step explanation:
x is the angle
180 - x is its suplement
90 - x is its complement
(180 - x) - 3(90 -x) = 10
180 - x -270 +3x = 10
-90 + 2x = 10
2x = 100
X = 50
Which statement is not true about the data shown
by the box-and-whisker plot below?
0 10 20 30 40 50 60 70 80 90 100
Select one:
a. The median of the upper half of the data is
70.
b. The range is 60.
C. Three fourths of the data is less than 58.
d. Half the data lies between 43 and 70.
e. None of the above
Answer:
A
Step-by-step explanation:
Because it's 50 writing it down n scratching it out u will find that 50 is your median not 70
Answer:
for me, the answer was "Three-fourths of the data is less than 58." or C.
Step-by-step explanation:
coz i had the same question and that was the answer for me, but not sure for others.
¿Cómo se dice 80 en números romanos?
Answer:
PLEASE MARK ME BRAINLEST...
Step-by-step explanation:
Para leer y escribir correctamente el número 80 como número romano LXXX, debe leerse y escribirse de izquierda a derecha, y de mayor a menor número.
Answer:
Guessing that Romanos means Roman Numerals = LXXX
Step-by-step explanation:
L=50
X=10
10X3= 30
30+50=80
How many real-number solutions does the equation have? - 7x2 + 6x + 3 = 0
Answer:
How many real-number solutions does the equation have? - 7x2 + 6x + 3 = 0
Step-by-step explanation:
a. B^2-4AC = 36-(-84) = 120.
The discriminant is positive. Therefore, we have 2 real solutions.
b. B^2-4AC = 324-324 = 0. 1 real solution.
Hope this helps!
What is the area of a rectangle
7 inches long and 3 inches wide?
Answer:
21
Step-by-step explanation:
you do 7x3
Evaluate using logarithm table, log (0.65)
Please answer :)
( Will give brainlst)
Answer: 10
Step-by-step explanation:
Step-by-step explanation:
all the processes are shown in the picture hope that helps
what is loss and profit
Answer:
The profit and loss (P&L) statement is a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a fiscal quarter or year. These records provide information about a company's ability or inability to generate profit by increasing revenue, reducing costs, or both.
Step-by-step explanation:
Calculating Profit and Loss. The actual calculation of profit and loss in a position is quite straightforward. To calculate the P&L of a position, what you need is the position size and the number of pips the price has moved. The actual profit or loss will be equal to the position size multiplied by the pip movement.
What does the "s" in the following expression represent: 24 + s
What are three fractions that are equivalent to 1.
Is borrowing money a
Delegated power
Reserved power
Concurrent power
Answer:
C. concurrent power
Step-by-step explanation:
Such powers are called concurrent powers. These include the power to tax, spend, and borrow money. State governments operate their own judicial systems, charter corporations, provide public education, and regulate property rights.
colin did the work to see if 10 is a solution to the equatio