Answer:
A = 66×6 cm²
Step-by-step explanation:
Given that,
The width of a rectangular garden, w = (6x2) cm
The length of a rectangular garden, l = (11x2) cm
We need to find the area of Ms. Alberta’s garden. The area of a rectangular garden is given by :
A = LW
Put all the values,
A = (6x2) × (11x3)
= (11×6)(2×3)
= 66×6 cm²
Hence, the area of the Ms. Alberta’s garden is 66×6 cm².
Asap plzz,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below:
Student type
Region undergraduate graduate
East $10 $15
Central $12 $18
West $15 $21
The requirements for the survey are as follows:
The survey must have at least 1500 students.
At least 400 graduate students.
At least 100 graduate students should be from the West
No more than 500 undergraduate students should be from the East
At least 75 graduate students should be from the Central region
At least 300 students should be from the West
The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region.
Required:
Clearly state the problem (objective function, constraints)
Answer:
Objective Minimize 10x1 +15x2 + 12x3+18x4+15x5+ 21x6
The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.
The total minimum cost would $ 17586 +$260+ $300= $ 18146
Step-by-step explanation:
Let
X1 = # of undergraduate students from the East region,
X2 = # of graduate students from the East region,
X3 = # of undergraduate students from the Central region,
X4 = # of graduate students from the Central region,
X5 = # of undergraduate students from the West region, and
X6 = # of graduate students from the West region.
Then the cost functions are
y1= 10x1 +15x2
y2= 12x3+18x4
y3= 15x5+ 21x6
According to the given conditions
The constraints are
x1 +x2 + x3+x4+ x5+ x6 ≥ 1500------- A
15X2 +18X4+21X6 ≥ 400---------B
21X6 ≥ 100
X6 ≥ 100/21
X6 ≥ 4.76
Taking
X6= 5
10X1 ≤ 500
X1 ≤ 500/10
X1≤ 5
18X4 ≥ 75
X4 ≥ 75/18
X4 ≥ 4.167
Taking
X4= 5
Putting the values
15X5+ 21X6 ≥ 300
15X5+ 21(5) ≥ 300
15X5+ 105 ≥ 300
15X5 ≥ 300-105
15X5 ≥ 195
X5 ≥ 195/15
X5 ≥ 13
Putting value of X6 and X4 in B
15X2 +18X4+21X6 ≥ 400
15X2 +18(5)+21(5) ≥ 400
15X2 +195 ≥ 400
15X2 ≥ 400-195
15X2 ≥ 205
X2 ≥ 205/15
X2 ≥ 13.67
Taking X2= 14
Now putting the values in the cost equations to check whether the conditions are satisfied.
y1= 10x1 +15x2
y1= 10 (5) + 15(14)= 50 + 210= $ 260
y3= 15x5+ 21x6
y3= 15 (13) + 21(5)
y3= 195+105= $ 300
x1 +x2 + x3+x4+ x5+ x6 ≥ 1500
5+14+x3+5+13+5≥ 1500
x3≥ 1500-42
x3≥ 1458
y2= 12x3+18x4
y2= 12 (1458) + 18 (5)
y2= 17496 +90
y2= $ 17586
The cost can be minimized if the number of students from
Undergraduate Graduate
East Region X1≤ 5 X2 ≥ 13.67
Central X3≥ 1458 X4 ≥ 4.167
West X5 ≥ 13 X6 ≥ 4.76
This will result in the required number of students that is 1500
Constraints:
East Undergraduate must not be greater than 5
East Graduate must not be less than 13
Central Undergraduate must be greater than 1458
Central Graduate must be greater than 4
West Undergraduate must be greater than 13
West Graduate must be greater than 4
The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.
The east region has a least cost of $260 and west region has a cost of $300.
The total minimum cost would $ 17586 +$260+ $300= $ 18146
please help me someone
Base = 5 * 12 = 60 in^2
Height = 4 in
Perimeter is the sum of all straight
Perimeter = 20 + 16 + 48
Perimeter = 84 in
Perimeter of base = 12 * 2 + 5 * 2 = 34
Harrison goes to a thrift shop and is going to buy a sports coat, a dress shirt, or a tie. Harrison tends to like everything but decides to stick to a power tie, which would be a tie with red or yellow in it. The thrift shop has 6 sports coats that fit him and 8 dress shirts that fit him. The thrift shop has 4 red ties and 5 yellow ties. How many choices does Harrison have
Answer:
Harrison has 432 choices.
Step-by-step explanation:
Harrison will choose:
One sports coat from a set of 6.
One dress shirt from a set of 8.
One power tie from a set of 4 + 5 = 9.
How many choices does Harrison have?
6*8*9 = 432
Harrison has 432 choices.
Which equation shows 3/4 x+1/2y=1/8 converted to slope intercept form?
A. Y=3/2x-1/4
B.Y=-3/8x+1/16
C. Y=3/8x-1/16
D.Y=-3/2x+1/4
Answer:
D
Step-by-step explanation:
A number is equal to half the sum of the same number and ten. Set up and equation and find that number.
9514 1404 393
Answer:
n = n/2 + 1020Step-by-step explanation:
Let n represent the number. Then half the number is n/2. We are told that ...
n = n/2 +10 . . . . the number equals half the number plus 10
n/2 = 10 . . . . . . .subtract n/2
n = 20 . . . . . . . . multiply by 2
The number is 20.
A school has a 20% sale on all headphones. With this discount, the price of headphones is $47. What was the original price of the pair of headphones?
Answer:
$56.40
Step-by-step explanation:
If you take the $47.00 and add 20% you will get 56.4
In basketball each basket scored from inside the 3 point line is worth 2 points. Each basket scored from outside the 3 point line is worth 3 points. Part B
x^2-64=0 solve for all real values of x
Hi there! Use the difference of two squares formula to solve the problem below:
[tex] \large \boxed{ {x}^{2} - {y}^{2} = (x + y)(x - y)}[/tex]
From the equation, 64 comes from 8². Thus,
[tex] \large{ {x}^{2} - 64 = 0} \\ \large{(x + 8)(x - 8) = 0}[/tex]
The question also asks you to solve for all real values. Thus,
[tex] \large{x = 8, - 8}[/tex]
Answer
x = 8,-8 are the real solutions to x²-64 = 0.
What is the area of a rectangle that measures 4 1/2 by 2 1/2 inches
Answer:
11.25
Step-by-step explanation:
the equation to find the area of a rectangle is A=w*l
A=2.5*4.5
A=11.25
PLEASE HELP
Which equation is the slope-intercept form of this equation?
y−10=−2(x+6)
a) y−10=−2x−12
b) 2x+y=−2
c) y=−2x−2
d) x=−12y−1
Answer:
C.
Step-by-step explanation:
The slope intercept form is:
y= mx +b
so you first want to start off by looking for the equation with y being the sum. In this case, there is only one, so you don't have to do anymore work.
A point at (4.6) is reflected across the x-axis. What is the
y-coordinate of the reflected point?
(4,-6)
OR -6
GOODLUCK :)
Consider strings of four decimal digits. Which rule must be used to find the number of strings of four decimal digits that have exactly three digits that are 9s? multiple choice the sum rule the subtraction rule the product rule the division rule How many strings of four decimal digits have exactly three digits that are 9s?
Answer:
36 possible ways
Step-by-step explanation:
Range of digit : 0 up to 9
To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the multiplication rule :
In other to have exactly 3 digits from 4 that are 9s :
Say:
We have 3 9s and the last number could be any of the 10 possible digits except 9
First 9 = 1 possible way (since we have only one 9 between (0 to 9)
Second 9 = 1 possible way
Third 9 = 1 possible way
4th digit = 9 ways (could be any digit between 0 and 9, except 9)
Also, we consider the 4th digit's position ; as it could take up any of different positions in between the 9s = 4 ways
Using the product rule :
1 * 1 * 1 * 9 * 4 = 36 possible ways
i need some help if you could
Step-by-step explanation:
35A) arc AC = 360-(100+110+80)=
360-290 = 70°
35B) L D = ½× 70 = 35°
35C) L AEC = ½(100+70)=½×170= 85°
35D) L P = ½(100-70) = ½×30 = 15°
What is the slope-intercept equation of the line below?
(2,3)
(0,-5)
Answer:
y = 4x - 5
Step-by-step explanation:
plug the coordinates into the equation: y = mx + b
3 = 2m + b
-) -5 = 0m + b
___________
8 = 2m => m = 4
substitute 4 into either of the equation 3 = 2m + b or -5 = 0m + b to solve for b
=> 3 = 2(4) + b
=> b = -5
plug m = 4 & b = -5 into the slope-intercept equation: y = mx + b
=> y = 4x - 5
7(x+4)-6(x+3)=x+5
What is x?
Answer:
Equation has no solutions.
Step-by-step explanation:
7x + 28 - 6x - 18 = x + 5
7x + 10 - 6x = x + 5
x + 10 = x + 5
x + 10 - 10 = x + 5 - 10
x = x - 5
x - x = x - x - 5
0 ≠ - 5
Integration of ∫(cos3x+3sinx)dx integration
Answer:
[tex] I = \dfrac{1}{3}sin(3x) - 3cos(x) + C[/tex]
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]
Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx .Rewrite using du and u .[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]
Answer:
[tex]\displaystyle \large{\frac{\sin 3x}{3} - 3\cos x + C}[/tex]
Step-by-step explanation:
We are given the indefinite integral:—
[tex]\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx}[/tex]
Important Formulas
[tex]\displaystyle \large{\int f(ax+b) \ dx = \frac{1}{a} F(ax+b) + C}\\\displaystyle \large{\int \cos(ax) \ dx = \frac{1}{a} \sin (ax) + C \ \ \tt{(a \ \ is \ \ a \ \ constant.)}}\\\displaystyle \large{\int \sin x \ dx = - \cos x + C}\\\displaystyle \large{\int [f(x) \pm g(x)] \ dx = \int f(x) \ dx \pm \int g(x) \ dx}\\\displaystyle \large{\int kf(x) \ dx = k \int f(x) \ dx \ \ (\tt{k \ \ is \ \ a \ \ constant.})}[/tex]
Therefore, from the integral, apply the properties above:—
[tex]\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \int \cos 3x \ dx + \int 3 \sin x \ dx}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \int \cos 3x \ dx + 3 \int \sin x \ dx}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \frac{1}{3} \sin 3x + 3\cdot -\cos x + C}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \frac{\sin 3x}{3} - 3\cos x + C}[/tex]
Hence, the solution is:—
[tex]\displaystyle \large \boxed{\frac{\sin 3x}{3} - 3\cos x + C}[/tex]
Determine the length of the missing side of the right triangle? ? inches 15 inches 8 inches
Answer:
the missing angle would be 17 inches. I am not exactly sure but if the leg a and leg b were calculated with those 2 numbers then the other side(known as hypotenuse) should be 17 inches
A bakery makes a $5 profit for each cake it sells. It makes
a $6 profit for each pie it sells. The expression 5c+6p
represents the profit for selling c cakes and p pies. How
much profit is made if the bakery sells 10 cakes and 7 pies?
Answer:
$92
Step-by-step explanation:
Find the profit by plugging in 10 as c and 7 as p into the expression:
5c + 6p
5(10) + 6(7)
50 + 42
= 92
So, the bakery will make $92
2. If an older television with an aspect ratio of 4:3 has a screen area of 1550 square inches, but the image displayed has an aspect ratio of 16:9, how much area does the image actually occupy? First determine what percent of the screen does the image occupy?
a. 825.5 sq. in.
b. 1162.5 sq. in.
c. 1181.5 sq. in.
d. 1375.5 sq.in.
Speedometer readings for a vehicle (in motion) at 10-second intervals are given in the table.
t (sec) 0 10 20 30 40 50 60
v (ft/s) 0 9 33 59 75 72 53
Estimate the distance traveled by the vehicle during this 60-second period using the Riemann sums
L6:
R6:
M3:
Of the sundaes recently sold at Ice Cream Haven, 4 had nuts and 20 did not. Considering this
data, how many of the next 84 sundaes sold would you expect to have nuts?
The expectation of having nuts in the 84 sundaes if 4 had nuts and 20 did not is 14.
What is division?It is a fundamental operation in mathematics where you divide a number into smaller parts.
Given:
The sundaes had nuts = 4,
Total sundaes = 24,
So from this the possibility of having nuts in sundae = 4/24 = 1 / 6,
Hence, in 84 sundaes the possibility of having nuts is = 1 / 6 × 84 = 14,
Therefore, the expectation of having nuts in the 84 sundaes is 14.
To know more about division:
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Find the volume of this solid figure. Use π = 3.14.
WITH SOLUTION PLEASE AND NO LINKS!
Step-by-step explanation:
you can get simply V= ABh πr^2 h π3.14^2 x 17.9 then you get the answer Ihope I can help you
Can anyone help? ................
answer:
x = 64
step-by-step explanation:
in order to solve this, we have to add up all the angles given and subtract from 360° in order to find xwe subtract from 360° because a circle adds up to 360°since there is a square shown as an angle, it is 90°so we know that, 180 + 26 + x + 90 = 360°
now, we solve for x180 + 26 + x + 90 = 360°
296 + x = 360
x = 64°
This is a regular octagon.
What is the measure of x?
IX
x = [? ]°
Enter
Answer:
x=360/8
=45 degrees,,,,
The measure of x = 45°.
What is exterior angles of a regular polygon?Exterior angles of a polygon are formed when by one of its side and extending the other side. The sum of all the exterior angles in a polygon is equal to 360 degrees. You are already aware of the term polygon. A polygon is a flat figure that is made up of three or more line segments and is enclosed. The line segments are called the sides and the point where two sides meet is called the vertex of the polygon.
According to question,
There is a regular octagon.
Number of sides in regular octagon, n = 8
Since, measure of each exterior angle = 360°÷8
= 45°
Hence, the measure of each exterior angle of a regular octagon is 45°
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(1/4)^3+(3/4)^3+3(1/4)(3/4)(1/4+3/4)
Answer:
[tex]\frac{43}{16}[/tex]
Step-by-step explanation:
[tex](\frac{1}{4})^{3}+(\frac{3}{4})^{3}+3(\frac{1}{4})(\frac{3}{4})(\frac{1}{4}+\frac{3}{4}) = \\\\\frac{1}{64}+\frac{27}{64}+3(\frac{3}{4})(\frac{4}{4}) = \\\\\frac{28}{64}+3(\frac{3}{4}) = \\\\\frac{28}{64}+\frac{9}{4} =\\\\\frac{28}{64}+\frac{144}{64} = \frac{172}{64} = \frac{43}{16}[/tex]
Find the volume of the cylinder. Find the volume of a cylinder with the same radius and double
the height.
The volume of the cylinder is __ in.³.
The volume of a cylinder with the same radius and double the height is __ in.³.
about 78.54
V=π·5^2·1 = 78.54
Answer:
Find the volume of the cylinder.
[tex]\star \: \: \purple{Volume_{(cylinder)} = \pi {r}^{2} h}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times ( {5)}^{2} \times 1 }[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} =3.14 \times 25 \times 1 }[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} =78.50 \: in {}^{3} }[/tex]
Find the volume of a cylinder with the same radius and double the height.
[tex]\star \: \: \purple{Volume_{(cylinder)} = \pi {r}^{2} h}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times {(5)}^{2} \times 2}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times 25 \times 2}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 157 \: in {}^{3} }[/tex]
i need 33 and 35!!!!!
Please help me solve this
Answer:
x=2√41
Step-by-step explanation:
According to Pythagorean theorem:
14²=(4√2)²+x²
x²=14²-32=164
x=√164=2√41
HELP ASAP!!!!!!
Colin saved $30 in July, $21.50 in August, and $50 in September. He spent $18 on video games and $26.83 on books. How much money does Colin have left?