An experiment involves placing the males and females of a laboratory animal species in two separate controlled environments. there is a limited time available in these environments, and the experimenter wants to maximise the number of animals subject to the constraints described. how many males and how many females will maximise the total number of animals? males females time available environment a 20 min 25 min 800 min environment b 20 min 15 min 600 min
Answers
15 males and 20 females would maximize the total number of animals
How to determine the number of males and females?The table is given as:
Males Females Time available
Environment a 20 min 25 min 800 min
Environment b 20 min 15 min 600 min
Represent the male with x and the female with y.
The time available is limited i.e. ≤
So, the constraints are:
20x + 25y ≤ 800
20x + 15y ≤ 600
Solve the above system of inequalities graphically (see attachment)
(x, y) = (15,20)
Hence, 15 males and 20 females would maximize the total number of animals
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Related Questions
if [tex]v=v_{1} +v_{2}[/tex], where [tex]v_{1}[/tex] and [tex]v_{2}[/tex] are not both 0 and [tex]u=-3v[/tex], find the measure of the angle between [tex]u[/tex] and [tex]v[/tex].
Given:
[tex]\frac{u*v}{||u|| ||v||}[/tex]
Answers
If θ is the angle between u and v, then
u • v = ||u|| ||v|| cos(θ)
Since u = -3v, we have
u • v = (-3v) • v = -3 ||v||²
and
||u|| = ||-3v|| = 3 ||v||
If v₁ and v₂ are both not zero, then ||v| ≠ 0.
Then
cos(θ) = (-3 ||v||²) / (3 ||v|| ||v||) = 1
which means θ = π rad = 180°.
It the perimeter of an isosceles triangle is 56 units and the base is 8 units, how long are the other sides?
Answers
4. Lou ran 72 more miles than Lee. Lou ran 128 miles. How many miles did Lee run?
60 Miles
56 Miles
144 Miles
200 Miles
Answers
If Lou ran 72 more miles than lee. Just subtract 72 from 128 (128-72) and you get 56.
how me solve this problem please
Answers
Answer:
3 3/4
Step-by-step explanation:
The area of rectangle patio=5 5/8
Length=1 1/2
5 5/8 divided by 1 1/2= 3 3/4
80% of what number is 52
Answers
Because 80% goes in 50, 40 times
the height of a cuboid is 12cm,the volume is 1200cm3 find the side of the of a cuboid
Answers
Answer:
area=volume/height
area=1200cm cubed/12cm
area=100cm squared
Juan borrowed $10 from his cousin. He borrowed another $30 from his uncle. Juan bought a $10 lottery ticket and won $100. How much money will Juan have after he pays his cousin and uncle back?
Answers
Answer:
$90
Step-by-step explanation:
Since Juan pays back the $10 and $30 he borrowed from his cousin and uncle they do not affect the total outcome ($10+$30-$10-$30=0)
Subtract the price of the ticket from the total amount he won.
$100-$10=$90
Elmo decided to take two classes
during summer school. For first period,
he can choose either math or English.
For second period, he can choose
either art, music, drama, or cooking.
How many different schedules of two
classes are possible?
Answers
Answer:
There are a total of 8 different schedules.
Step-by-step explanation:
In situations like these, it's best to write down all possible combinations on a tree diagram. However, I use a different way to solve problems like these. For the equation multiply the choices of the first period with the choices of the second period. 2×4=8
You can do this other problems that can include 3 choices, 4 choices, and so on.
[tex]2\sqrt{3} *3\sqrt{8}[/tex]
Answers
Explanation
2 over 3 times 3 over 8, simplify it
Then calculate 2 over 3 times 3
The graph shows the prices of different numbers of bushels of corn at a store in the current year. The table shows the prices of different numbers of bushels of corn at the same store in the previous year. A graph shows Number of Bushels on x-axis and Price of Corn in dollars on y-axis. The x-axis scale is shown from 0 to 14 at increments of 2, and the y-axis scale is shown from 0 to 98 at increments of 14. A straight line joins the ordered pairs 2, 14 and 4, 28 and 6, 42 and 8, 56 and 10, 70 and 12, 84. Previous Year Number of Bushels Price of Corn (dollars) 2 10 4 20 6 30 8 40 Part A: Describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. (5 points) Part B: How many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? Show your work. (5 points)
Answers
Answer:
Part A: Rate of change of a bushel of corn is 7
Part B: 2 dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year
Step-by-step explanation:
Let me know if you have any questions !
the solution set of |R-3| = 10 is
Answers
[tex]~~~~~~|R-3| = 10\\\\\implies R -3 = 10~~~~~~ \text{or}~~~~~~~R -3 = -10\\\\\implies R = 10+3~~~~~~\text{or}~~~~~~~R = -10+3\\\\\implies R = 13~~~~~~~~~~~ \text{or}~~~~~~~R = -7\\\\\text{Solution set:} ~\{-7,13\}[/tex]
Find the mean, median, and mode(s) of the data. Do not round.
Please show work!
48, 12, 11, 45, 48, 48, 43, 32
The mean is
.
The median is
.
The mode is
Please show work!
Answers
The mean , median and mode of the data are 35.875, 44 and 48
How to find mean , median and mode?The mean, median and mode can be found as follows:
mean = sum of terms / number of terms
mean = 48 + 12 + 11 + 45 + 48 + 48 + 43 + 32 / 8
mean = 287 / 8 = 35.875
11, 12, 32, 43, 45, 48, 48, 48
The median is the centre number.
Hence,
median = 43 + 45 / 2 = 88 / 2 = 44
The mode is the number that appears most which is 48.
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The Mean, Median and Mode of the given set of data ( 11, 12, 32, 43, 45, 48, 48, 48 ) are 35.875, 44 and 48 respectively.
What is Arithmetic mean?Arithmetic mean is simply the average of a given set numbers. It is determined by dividing the sum of a given set number by their number of appearance.
Mean = Sum total of the number ÷ n
Where n is number of numbers
Given the sets;
48, 12, 11, 45, 48, 48, 43, 32n = 8First, we arrange in ascending order.
11, 12, 32, 43, 45, 48, 48, 48
Mode
Mode is the number with the highest appearance
Number with highest appearance or frequency is 48 ( 3 appearance )
Mode = 48
Median
Middle numbers fall between 43 and 45
Median = ( 43 + 48 ) / 2
Median = 88 / 2
Median = 44
Mean
We add the numbers
11 + 12 + 32 + 43 + 45 + 48 + 48 + 48 = 287
Mean = Sum total of the number ÷ n
Mean = 287 / 8
Mean = 35.875
Therefore, the Mean, Median and Mode of the given set of data ( 11, 12, 32, 43, 45, 48, 48, 48 ) are 35.875, 44 and 48 respectively.
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Find the total surface area of the following square pyramid
Answers
Answer:
160 cm^2.
Step-by-step explanation:
Surface area = area of base + 4 * area of triangular side.
= 8^2 + 4 * 1/2 * 8 * 6
= 64 + 96
= 160 cm^2.
Answer:
179.38cm²
Step-by-step explanation:
By using the formula, it is 179.38cm.
there are 1800 pupils in a school of witch 2/5 are girls. 540 of the pupils do not play sports. Of these pupils who do not play sports, 5/9 are girls. How many boys play sports?
Answers
========================================================
Explanation:
There are 1800 students total.
Take 2/5 of this to find the number of girls
(2/5)*1800 = 720 students are girls
Subtract that result from the total to get the number of boys
1800-720 = 1080 students are boys
We'll use this value later, so let A = 1080.
-------------
540 students do not play sports
(5/9)*540 = 300 girls do not play sports.
540-300 = 240 boys do not play sports
Let B = 240
------------
We found that
A = 1080 boys totalB = 240 boys do not play sportsTherefore,
A-B = 1080 - 240 = 840 boys play sports
23. Tyrese is making a map of his neighborhood using
a coordinate plane. He plots the following
locations
• His home is at the origin
• The school is at (4,5)
• The zoo is at (-3,2).
. The park is at (-4,-4). /
• The grocery store is at (4.-1)./
Plot the locations on the coordinate plane. If each unit
of the coordinate plane represents 750 feet, what is the
distance from the school to the grocery store?
The distance from the school to the grocery store is
feet.
Answers
The distance between the school and the grocery store is 3,000ft.
What is the distance from the school to the grocery store?First, we need to find the distance between the two locations, we know that:
School is at (4, 5)Grocery store is at (4, -1)The distance between these two points is:
[tex]d = \sqrt{(4 - 4)^2 + (5 - 1)^2} = 4[/tex]
And we know that each unit represents 750ft, then we can see that the total distance is:
d = 4*750ft = 3,000ft
And the graph of the 4 points can be seen below.
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The distance between the school to the grocery store is 4500 feet.
What is a coordinate plane?A coordinate plane is a two-dimensional plane produced by the intersection of the x-axis and the y-axis on the graph.
We are to represent the given data on the graph which can be seen in the image below.
His home is at the originThe school is at (4,5)The zoo is at (-3,2).The park is at (-4,-4).The grocery store is at (4.-1)From the image attached below, there are 6 unit differences showing the distance from the school to the grocery store. If each unit in the coordinate plane represents 750 feet.
Thus, 6 units will be = 6 × 750 = 4500 feets
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A teacher had 111 pens. he shared equally among 30 learners . how many pens did each learners get? how many pens remained?
Answers
Answer:
Everyone got 3 pens, 21 remained
Step-by-step explanation:
111:30=3 21/30
Suppose y varies directly with x. If y is 8 when x is 12, find y when x is 18.
Answers
[tex]\large\textsf{\textbf{Answer\::}}[/tex]
Please consult the "calculations" section of this ans .
[tex]\large\textsf{\textbf{Calculations\::}}[/tex]
If y varies directly with x , the equation looks like this :
y=kx , where k is the constant of proportionality
Plug in the values :
8=k/12
Multiply times 12 on both sides :
96=k
So the constant of proportionality is 96 .
Now solve for y when x is 18 as follows :
y=96/18
y≈5.33
[tex]\footnotesize\texttt{hope\:helpful~}[/tex]
Use an identity to find the value of
Answers
Answer:
[tex] \bigodot\: - \sin\theta.[/tex]
Step-by-step explanation:
We know that:cos (A + B) = cos A . cos B - sin A . sin B[tex] \implies \cos (\theta +90\degree) =\cos\theta.\cos 90\degree - \sin\theta.\sin 90\degree[/tex][tex] \implies \cos (\theta +90\degree) =\cos\theta.0 - \sin\theta.1[/tex] [tex] \implies \cos (\theta +90\degree) =0 - \sin\theta.[/tex] [tex] \implies \cos (\theta +90\degree) = - \sin\theta.[/tex]help meee :))) GIVING BRAINEST
Answers
Answer: 462 cm^3
Step-by-step explanation:
formula for triangular prisms:
0.5*b*h = V
b or base = 6*6 cm
h or height = 7 cm
7 * 6 * 6 * 0.5 = 126
V or Volume of triangular prism is 126 cm^3.
formula for rectangular prisms:
b * h = V
b or base = 8*6 cm
h or height = 7 cm
8 * 6 * 7 = 336
V or Volume for rectangular prism is 336 cm^3.
Total Volume of Composite Figure = sum of both Volumes
336 + 126 = 462 cm^3.
[tex]v = a \times b \times h \times \frac{1}{2} [/tex]
[tex]v = 6 \times 6 \times 7 \times \frac{1}{2} [/tex]
[tex]v = 126 \: {cm}^{3} [/tex]
Volume of the rectangular prism:[tex]v = whl[/tex]
[tex]v = 7 \times 8 \times 6[/tex]
[tex]v = 336 \: {cm}^{3} [/tex]
Total volume:[tex]v = 126 + 336[/tex]
[tex]v = 462 \: {cm}^{3} [/tex]
Which statements describe the figure on the grid if each square has side lengths of 1 cm? Check all that apply. On a coordinate plane, a figure covers 12 full squares and 12 partial squares. The bottom of the figure is diagonal and crosses 6 squares. The perimeter of the figure is 18 cm. The length of the top of the figure is less than 6 cm. The area of the figure is the sum of 12 full squares and 12 partial squares. The area of the figure is greater than 24 square centimeters. The length of the bottom of the figure is greater than 6 cm. The area of the figure is the sum of 6 full squares and 12 partial squares.
Answers
The figure on the grid is an illustration of areas and perimeters of a shape
How to determine the true statements?The question is incomplete, as the figure is not given.
So, I will provide a general explanation on how to determine the area and the perimeter of a shape.
The area of a shape is the amount of space on that shape.
Take for instance a square that has a side length 5 units.
The area of the square would be:
Area = 5 * 5 = 25 square units
On the other hand, the perimeter is the sum of the side lengths of the shape.
Using the same square that has a side length 5 units.
The perimeter of the square would be:
Perimeter = 4 * 5 = 20 units
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Answer: its 3, 5
Step-by-step explanation: im honestly not too sure if this is the answer
8 m
6 m
10 m
6 m
20 m
Answers
Step-by-step explanation:
6 m is the answer of given question
A basketball hoop is purchased for use outside. It is on a moveable
base which needs to be filled with sand before you can start to play.
The base is a rectangular prismit
measures 49 in long by 32 in wide
by 9 in tall
Solve for the amount of sand that
wif the base Show your eous-
tion and work below
Answers
Answer:
49 + 32 = 81 81 divided by 9 is 9 in
Step-by-step explanation:
HELP PLEASEE!!!!!!!!!! ASAP!!!!!!!!!!!!!!!!
Answers
Answer:
the answer is C
Step-by-step explanation:
i know because I did this
Answer:
(2,3)
Step-by-step explanation:
if the square rotated 90 degrees clockwise, it would go to the otherside of the y-axis and B' would end up on 2,3
I will give you a CROWN!!! Also, there are 42 points!!! Can somebody please help?
Answers
By the angle sum property of a triangle, the value of x would be equal to 9.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
The sum of the triangle of angles is 180.
6x + 56 + 38 + t = 180
t = 180 - 94 - 6x
t = 86 - 6x
By linear pair
10x + 58 + t = 180
10x + 58 + 86 - 6x = 180
4x + 144 = 180
4x = 180 - 144
4x = 36
x = 9
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what are the zeros of the function represented by the quadratic expression 2x^2 + x - 3?
A: x= -3/2 and x= 1
B: x= -2/3 and x= 1
C: x= -1 and x= 2/3
D: -1 and x= -3/2
Answers
do yall know what the answer is (2x)(10x)
Answers
Answer:
20x^2
Step-by-step explanation:
2*x*10*x
20*x^2
20x^2
Answer:
[tex]20x^2[/tex]
Step-by-step explanation:
Step 1: Multiply
[tex](2x)(10x)[/tex]
[tex]2x * 10x[/tex]
[tex](2*10)*(x*x)[/tex]
[tex](20)*(x^2)[/tex]
[tex]20x^2[/tex]
Answer: [tex]20x^2[/tex]
Multiplication Equations
Solve the equation. Check your
solution.
1) 6n = 42
2) 3y = 192
3) 8x= 72
4) 4 = 2a
5) 7n = 112
6) 8x = 272
7) 7n = 49
8) 33y = 66
9) 6b = 96
10) 5n = 280
11) 6n = 72
Answers
Answer:
use calculator on chrome it will help u :)
Step-by-step explanation:
because then u do'nt have to wait for the answer
Answer:
Step-by-step explanation:
1) n=7
2)y=64
3)x=9
4)a=2
5)n=16
6)x=34
7)n=7
8)y=2
9)b=16
10)n=56
11)n=12
Find the value of x to the nearest tenth!!
Answers
Hypotenuse of triangle on the right is 3sqrt(5) so if you plug that in for b on the triangle on the left you get sqrt(55) for your answer
f(x)=−7x 2 +8x+2f, left parenthesis, x, right parenthesis, equals, minus, 7, x, squared, plus, 8, x, plus, 2 What is the value of the discriminant of fff? How many xxx-intercepts does the graph of fff have?
Answers
The discriminant of the function is 120, and the function has 2 different x-intercepts
How to determine the discriminant?
The function is given as:
f(x) = -7x^2 + 8x + 2
The discriminant (d) is calculated using:
D =b^2 - 4ac
So, we have:
D = 8^2 - 4 * (-7) * 2
Evaluate
D = 120
Because the value of D is greater than 0, then the function has 2 different x-intercepts
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7 students have 8 books each. Which helps you find the total number of
books?
78
7 + 8
с
7-8
D
7.8
Answers
Answer:
7x8
Step-by-step explanation:
none of those seem right
Explanation
None of those seem right
