Answer:
true
Step-by-step explanation:
The owner of an orange grove estimates that if 24 trees are planted per acre, then each mature tree will yield 600 oranges per year. For each additional tree planted per acre, the number of oranges produced by each tree decreases by 12 per year. How many trees should be planted per acre to obtain the most oranges per year
Answer:
16428 oranges
Explanation:
Total yield = number of trees × number of oranges in each tree
Initial yield = 600×24= 14400 oranges
To find the equation needed, let x = additional trees and y= total yield
Number of trees = 24 +x
Number of oranges in each tree = 600-12x
Equation of total yield y= (24+x)(600-12x)
y= 14400-288x+600x-12x²
y= -12x²+312x+14400
Using a graphing calculator, from the graph drawn for this quadratic equation, we notice that it is a parabola. Therefore to find the maximum value, we should find the maximum point which is at the vertex of the parabola, we use the formula x= -b/2a
A quadratic equation is such: ax²+bx+c
Therefore x =-312/2×-12
x= -312/-24
x= 13
So we can conclude that in order to maximise oranges from the trees, the person needs to plant an additional 13 trees. Substituting from the above:
24+x=24+13= 37 trees in total
y= -12x²+312x+14400= -12×13²+312×13+14400= -2028+4056+14400
=16428 oranges in total yield
The number of trees that gives the most yield is 37
The given parameters are:
Trees per acre = 24Yield = 600Represent the additional number of trees with x.
So, we have:
Trees per acre = 24 + xYield = 600 - 12xThe equation that represents the total yield (y) becomes
[tex]y = (24 + x) \times (600 - 12x)[/tex]
Expand
[tex]y= 14400-288x+600x-12x\²[/tex]
Evaluate the like terms
[tex]y= 14400+312x-12x\²[/tex]
Rewrite as:
[tex]y= -12x\²+312x+14400[/tex]
Differentiate
[tex]y'= -24x+312[/tex]
Set to 0
[tex]-24x+312 = 0[/tex]
Solve for x
[tex]-24x=-312[/tex]
[tex]x=13[/tex]
Recall that:
Trees per acre = 24 + x
This gives
[tex]Trees = 24 + 13[/tex]
[tex]Trees = 37[/tex]
Hence, the number of trees that gives the most yield is 37
Read more about quadratic functions at:
https://brainly.com/question/11631534
Suppose that scores on a particular test are normally distributed with a mean of 110 and a standard deviation of 20. What is the minimum score needed to be in the top 2% of the scores on the test
Answer:
The minimum score needed to be in the top 2% of the scores on the test
is n = 10,00,000
Step-by-step explanation:
Step(i):-
Mean of the Population = 110
Standard deviation of the Population = 20
The estimated error = 2% = 0.02
Step(ii):-
The estimated error is determined by
[tex]E = \frac{S.D}{\sqrt{n} }[/tex]
[tex]0.02 = \frac{20}{\sqrt{n} }[/tex]
⇒ [tex]\sqrt{n} = \frac{20}{0.02} = 1000[/tex]
Squaring on both sides, we get
n = 10,00,000
The minimum score needed to be in the top 2% of the scores on the test
is n = 10,00,000
32/8 = 28/x
Please select the best answer from the choices provided
A: x = 4
B: x = 28
C: x = 8
D: x = 7
32/8=28/x
we multiply by x
x*32/8=28
we multiply by 8/32
x=28*8/32
8 divides by 32
x=28/4=7
D: x = 7
Answer:
D
Step-by-step explanation:
Given
[tex]\frac{32}{8}[/tex] = [tex]\frac{28}{x}[/tex] ( cross- multiply )
32x = 224 ( divide both sides by 32 )
x = 7 → D
1. Let U the set of students of the university of Cambridge. Let the subsets of U:
A: over 20 years, B: women, C: with social stratum of 1, 2 and 3.
Describe in words the next sets:
a)A
0
∩ C b)A ∪ B c)B
0
∪ C
0
d)(A ∩ C)
0
e)A
0
∪ C
0
f)(A ∪ C)
0
g)A
0
∩ C
0
h)A ∩ B ∩ C
i)A − B j)(A − B) ∩ C k)B 4 C l)A 4 B.
Compare the given description in c) and d) and the given in f) and g), can you conclude something?.
Answer:
A) A ∩ C means in both sets, in this case A and C, and in this question all students both over 20 years and with social stratum of 1, 2 and 3.
B) A ∪ B means in either set or both, both will do, in this case meaning all students in A or B or any in between, and in this question all students over 20 years and/or are women.
C) As is already explained above, B ∪ C means in this question all students that are women and/or have social stratum of 1, 2, and 3.
D) This is the same as A). Refer to A).
E) A ∪ C is already explained above, and in this question means all students over 20 years and/or have social stratum of 1, 2, and 3.
F) Same as E). Refer to E).
G) Same as A). Refer to A).
H) A ∩ B ∩ C means in students in all three sets simultaneously, and in this question all students that are over 20 years, women, and with social stratum of 1, 2 and 3.
I) A - B, in set theory would mean all students in A but not in B, in other words the difference. In this question, it would mean all students over 20 years that are not women.
J) (A - B) ∩ C would mean, as already explained above, all students over 20 years that are not women and with social stratum of 1, 2 and 3. Usually, it's easier to treat all unions or intersections or whatnot inside brackets as one whole thing, kind of like how you do algebra.
K) B 4 C is nonsensical, there is nothing in set theory like this.
L) Same as K).
The given description between C) and D) would be that they are the same, and comparing F) and G), it seems that the question is trying to make the point that they are almost the same but defined differently.
Step-by-step explanation:
Hope this helped!
The ordered pair (2, 5) is a solution to the system of linear equations.
x + y = 7
2x - 3y = -11
True
False
A scientist studies the development of brain size in mice, believing that exposure to statistics videos is related to brain development.. After having mice intensively watch statistics videos, the scientist discovers that mice have doubled the size of their brains. After running a statistical test on the difference, the scientist obtained a p-value of .04. What should the scientist conclude, assuming an a
Answer:
The conclusion of the scientist should be that the results are statistically significant and that there is a high probability that the mice brains doubled in sizes after watching the videos
Step-by-step explanation:
The complete question is as follows;
A scientist studies the development of brain size in mice, believing that exposure to statistics videos is related to brain development.. After having mice intensively watch statistics videos, the scientist discovers that mice have doubled the size of their brains. After running a statistical test on the difference, the scientist obtained a p-value of .04. What should the scientist conclude, assuming an a=.05?
Solution;
We start by forming the null hypothesis
The null hypothesis H0 here is that;
The mice have not doubled the sizes of their brains after watching the the videos
While the alternative hypothesis H1 is that the mice have double their brain sizes after watching the videos
To know what to conclude, we will need to look at the p-value obtained
The p-value we have here is 0.04 which is less than 0.05 and thus , shows the existence of a strong evidence against the null hypothesis which means we will have to accept the alternative
Hence, the conclusion of the scientist should be that the results are statistically significant and that there is a high probability that the mice brains doubled in sizes after watching the videos
wirte the fractional coefficient for 1 1/4
TAKE A PIC OF PAPER WITH THE WORK AND AWNSERS I need help ASAP!!! Only 5 questions
1.
4x-5x+3-8
-x-5
2.
3x^2+8x^2-2x+7x
11x^2-5x
3.
4x+9x+2y+3y^2
3y^2+5y+13x
4.
-5x-7x-2
-5x+-7x-2
-12x-2
5.
6(3x-5)-9x
6(3(4)-5)-9(4)
6(12-5)-36
6(7)-36
6
Answer:
m
Step-by-step explanation:
Shelby is shopping for fruit to pack in her lunch each day this week. She's sees that grapes are on sale for $1.49/lb and pears are on sale for $1.29/lb. She decides to purchase some of each. She spends a total of $8.44 on all fruit she purchased and brought home a total of 6lbs of fruit.
Answer:
What am i supposed to be solving please give more description
Step-by-step explanation:
Find the value
of
(3x + 3y)^2
If xy = =-2 and x^2+y^2=5
Step-by-step explanation:
9x^2 + 9y^2 + 18xy
9(5)+18(-2)
45-36
9
Which of the number lines is the correct graph for the inequality x ≥ 9?
Answer:
graph D.
Step-by-step explanation:
The inequality that is being shown in the question means that the value of x is equal to or greater than 9. Greater values are represented as all of the values to the right of a certain number. On a number line "equal to" is represented by a closed circle. Therefore, with this knowledge we can see that out of all of the provided options the only one that follows these set of rules would be graph D.
In the figure, angle K measures 45°. What is the measurement of angle C? A. 38° B. 45° C. 90° D. 98°
Answer:
B. 45°Step-by-step explanation:
C = 90° - J as CGJ is right triangleJ = 90° - K = 90° - 45° = 45° as AKJ is right triangleC = 90° - 45° = 45°Option B is correct
Answer:
45°
Step-by-step explanation:
Can someone please help me
Answer: B the second answer
Step-by-step explanation:
7+2x/4=5 i ll mark the brailliest
Your expression is a little unclear, but I am assuming your expression as:
[tex]7+\frac{2x}{4}=5[/tex]
The solution would still clear your concept in anyway.
Answer:
The value of x = -4
Step-by-step explanation:
Given the expression
[tex]7+\frac{2x}{4}=5[/tex]
solving the expression
[tex]7+\frac{2x}{4}=5[/tex]
as 2x/4 = x/2, so
[tex]7+\frac{x}{2}=5[/tex]
subtract 7 from both sides
[tex]7+\frac{x}{2}-7=5-7[/tex]
simplify
[tex]\frac{x}{2}=-2[/tex]
Multiply both sides by 2
[tex]\frac{2x}{2}=2\left(-2\right)[/tex]
simplify
[tex]x=-4[/tex]
Thus, the value of x = -4
Which are 60% as a fraction?
Answer:
3/5
Step-by-step explanation:
PLS HELP will give brainliest answer both
Answer:
8 3/5
false
Step-by-step explanation:
Shareen walked a total of 9.52 miles in a walk-a thon. If her average speed was 2.8 miles per hour, how long did it take Shareen to complete the walk?
Answer:
t = 3.4 hour
Step-by-step explanation:
Distance to be covered by Shareen, d = 9.52 miles
The average speed of Shareen, v = 2.8 mph
We need to find the time taken by Shareen to complete the walk.
The formula for average speed,
v = distance/time
[tex]t=\dfrac{d}{v}\\\\t=\dfrac{9.52}{2.8}\\\\t=3.4\ \text{hour}[/tex]
Hence, it will take 3.4 hour to complete the walk.
What’s 4/5 of 3 And what’s 2/9 of 20
Answer:
4/5 of 3 = 12/5
2/9 of 20 = 40/9
Step-by-step explanation:
Answer:
1. 2.4
2. 4.444
Step-by-step explanation:
First, let's look at 4/5 of 3. We can set it up like this:
[tex]3 * \frac{4}{5}[/tex]Next, multiply the 3 by the 4 to get this:
[tex]\frac{12}{5}[/tex]Then, if a calculator is permitted, we get the answer of 2.4.
The next thing to do would be to repeat the steps for 2/9 of 20.
[tex]20 * \frac{2}{9}[/tex]
[tex]\frac{40}{9} = 4.444[/tex]
Hope this helps!!
- Kay :)
which ordered pair lies on the graph of the function y= -2x +1
Note: You did not mention the ordered pair choices. So, I am letting you clear your concept about taking some sample ordered pairs which anyways would clear your concept.
Answer:
The ordered pairs (1/2, 0) and (0, 1) are on the graph.
The graph is also attached.
Step-by-step explanation:
Given the function
[tex]y= -2x +1[/tex]
Any ordered pair which may satisfy the equation would lie on the graph.
Let us determine the x and y-intercepts.
Determining the x-intercept
We know that the x-intercept can be determined by setting y=0, and the solving for x. so
[tex]y= -2x +1[/tex]
0 = -2x+1
-2x = -1
Divide both sides by -2
x = 1/2
Thus, the x-intercept is (1/2, 0)
Determining the y-intercept
We know that the y-intercept can be determined by setting x=0, and the solving for y. so
[tex]y= -2x +1[/tex]
y = -2(0)+1
y = 1
Thus, the x-intercept is (0, 1)
Thus, the ordered pairs (1/2, 0) and (0, 1) are on the graph.
The graph is also attached.
The ordered pairs (1/2, 0) and (0, 1) are on the graph.
Let us plug x = 0.
So,
[tex]y=-2x+1\\y=-2(0)+1\\y=1[/tex]
So the point is (0, 1).
Let us plug x = 1/2.
So,
[tex]y=-2x+1\\y=-2\left(\frac{1}{2}\right)+1\\y=-1+1\\y=0[/tex]
So the point is (1/2, 0).
Learn more about ordered pairs: https://brainly.com/question/1528681
Helppp mee quickkkkk pleasee Im struggling!
Answer:
y= -3/1 plus 5
Step-by-step explanation:
correct me if im wrong u can just write -3 instead of -3/1
I have the answers i just need to know the solution on how you do 10 and 11.
Find the H.C.F. of 40 and 60
Answer:
it's answer is 20
Step-by-step explanation:
hope it helps you
PLEASE HELP i’ll mark brainliest it’s MULTIPLE CHOICE i also added extra points
Answer:
(-2,2)
Step-by-step explanation:
Factor out the coefficient of the variable.
3.4c+10.2
Answer:
1.7(2c+6)
Step-by-step explanation:
!!!! PLEASEEE HELP ME, IDK WHAT TO DO PLEASE !!!!
Express cos in terms of sin.
A. ±√(1 - sin²θ)
B. 1 + sin²θ
C. sin²θ - 1
-----------------
Simplify 1/2 (-sin^2 x - cos^2 x).
A. -1 1/2
B. -1/2
C. 1/2
-----------------
Simplify tan^2 x + 1/cot^2 x + 1
A. 1/sinx
B. tanx
C. cotx
Answer:
The first question is A.
The second question is C.
The thid question is B., I think i'm not quit sure sorry
4 gallons= ________________ quarts *
Answer:
4 gallons=16 quarts
Step-by-step explanation:
Brainliest me pls
Have a nice day!
Answer:
16 Quarts
Step-by-step explanation:
First I figured out how many quarts are in a gallon which is 4.
Then I multiplied 4 by 4 which gives you 16.
Hope This helps! ^w^
Jess has 2 3/4 books to read for school. Jess read 1 1/4 books on Tuesday. How many more books does jess have to read
Answer:
1 1/2(simplified)
Step-by-step explanation:
subtracting 1 from 2 is one and then 1/4 from 3/4 which is 2/4 simplifying makes it 1/2
Answer:
23/4+11/4=23+11/4=34/4 more books.Step-by-step explanation:
Please mark my answer as a brainliest. Please follow me. ❤❤❤❤can you help me please
Answer:
The answers are:
2u = <10,2>-3u = <-18,-6>u+v = <11,3>3u-4v = <-9,-5>Step-by-step explanation:
Given vectors are:
u = <5,1>
v = <6,2>
The vectors are given in the form of ordered pairs, the operations can be applied on the coordinates of ordered pairs
Now,
[tex]2u = 2(5,1) = (10,2)[/tex]
[tex]-3v = -3(6,2) = (-18,-6)[/tex]
Now we have to add two vectors
In order to add two vectors, their respective coordinates are added:
So,
[tex]u+v = (5,1) + (6,2)\\= (5+6, 1+2)\\=(11,3)[/tex]
And
[tex]3u-4v = 3(5,1) - 4(6,2)\\= (15,3) - (24,8)\\= (15-24, 3-8)\\=(-9, -5)[/tex]
Hence,
The answers are:
2u = <10,2>-3u = <-18,-6>u+v = <11,3>3u-4v = <-9,-5>A random sample of 12 recent college graduates reported an average starting salary of $54,000 with a standard deviation of $6,000.
a. Construct a 95% confidence interval for the mean starting salary of college graduates.
a. 50188 to 57812$
b. 45,0000 to 50,000$
c. 48,000 to 60,000$
d. 50,000 to 54000$
b. The National Association of Colleges and Employers reports that the mean starting salary for 2017 college graduates is $50,516. Does your confidence interval (part a) indicate that starting salaries have significantly changed since 2017? Why or why not?
Answer: a.) $50188 to $57812
Step-by-step explanation: Confidence Interval (CI) is an interval of values in which we are confident the true mean is in.
The interval is calculated as
x ± [tex]z\frac{s}{\sqrt{n} }[/tex]
a. For a 95% CI, z-value is 1.96.
Solving:
54,000 ± [tex]1.96.\frac{6000}{\sqrt{12} }[/tex]
54,000 ± [tex]1.96\frac{6000}{3.464}[/tex]
54,000 ± 1.96*1732.102
54,000 ± 3395
This means the interval is
50605 < μ < 57395
With a 95% confidence interval, the mean starting salary of college graduates is between 50605 and 57395 or from 50188 to 57812$.
b. The mean starting salary for college students in 2017 is $50,516, which is in the confidence interval. Therefore, since we 95% sure the real mean is between 50188 and 57812, there was no significant change since 2017.
answer this question plzzzzz
Answer:
This is my best solution for your question
Step-by-step explanation:
radius=10cm
<A0B=90°
Length of arc AB,
[tex] 10 \times \frac{\pi}{2 } = 5 \times 3.14 = 15.4cm[/tex]
[tex]perimeter \: of \: quadrant = \: 10 + 10 + 15.4 = 35.4cm[/tex]
Area of quadrant=
[tex] \frac{90}{360 } \times 3.14 \times {10 }^{2} = 78.5cm ^{2} [/tex]