Answer:
30 by 30. Area=900
Step-by-step explanation:
The dimensions of the garden to maximize the area are length + width = 60 and the maximum area is 900 ft².
A rectangular garden will be fenced on all four sides.
120 ft. of fencing is available, what should be the dimensions of the garden to maximize the area and What is the maximum area to be determined.
The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
The perimeter of the rectangle = 120
Perimeter = 2 (length + width)
120 =2(length + width)
length + width = 120/6
length + width = 60 - - - -(1)
So, the sum of the sides of the rectangle should not increase by 120.
Now, the Maximum area of a rectangle,
Let Length = width
Equation 1
Length + Length = 60
length = 60/2
length = 30 = width
Area of the rectangle = length * width
= 30 * 30
= 900 ft²
So the maximum area of the rectangle is 900ft²
Thus, the dimensions of the garden to maximize the area is length + width = 60 and maximum area is 900 ft².
Learn more about rectangles here:
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In 2007, Bob Jones University ended its fall semester a week early because of a whooping cough outbreak; 158 students were isolated with suspected infection and another 1200 given antibiotics as a precaution.14 Authorities react strongly to whooping cough outbreaks because the disease is so contagious. Because the effect of childhood vaccination often wears off by late adolescence, treat the Bob Jones students as if they were unvaccinated. It appears that approximately 1400 students were exposed. What is the probability that at least 75% of these students would develop infections if not treated
Answer:
If not treated, the probability of at least 75 percent of 1400 students being infected is approximately equal to 1.
Step-by-step explanation:
Let Y be the no. of infections
The number of students who have been exposed to whooping cough is as follows:
n = 1400
n = 1400 and p = 0.8
nm = 1400 x 0.8
nm = 1120
n(1-m) = 1400 x (1-0.8)
n(1-m) = 280
Here,
Both nm and n(1-m) are greater than or equal to 10. So, we use normal distribution.
The mean and standard deviation of number of new infections is:
u = np
u =1400 x 0.8
u = 1120 = mean
SD = Standard Deviation
SD = [tex]\sqrt{1120(1-0.8)}[/tex]
SD = 14.966
The number of infections is distributed in an approximately normal way
N(1120,14.966)
75% of 1400 means 0.75 x 1400 = 1050
So,
Probability required.
P (Y[tex]\geq[/tex] 1050) = P (Y [tex]\geq[/tex] 1050 - 0.5) (Continuity Correction)
P (Y[tex]\geq[/tex] 1050) = P([tex]\frac{Y - u}{SD} \geq \frac{1049.5 - 1120}{14.966}[/tex])
P (Y[tex]\geq[/tex] 1050) = P(Z [tex]\geq[/tex] -4.71)
P (Y[tex]\geq[/tex] 1050) = P(Z [tex]\leq[/tex] 4.71)
Using the z table:
P (Y[tex]\geq[/tex] 1050) ≈ 1
Hence,
If not treated, the probability of at least 75 percent of 1400 students being infected is approximately equal to 1.
PLEASE HELP!!! K Is the midpoint of JL Find JK,LK and JL
Answer:
6x+1 = 8x - 7
8 = 2x
x = 4
JK = 6*4+1 = 25
KL = 8*4 - 7 = 25
3x3 grid using 24cm wire. How much wire for 20x20 grid?
Answer:
840cm
Let Me Know If This Is Correct I Always Want To Improve!
Thanks :)
Solve the equation in two different ways. Choose one method of solving in detail 5x+7(x+1) = 5x - 21
Answer:
METHOD 1:
5x+7(x+1)=5x-21
5x+7x+7=5x-21
12x+7=5x-21
12x-5x=-21-7
7x=-28
x=28/7
x=4
METHOD 2:
5x+7(x+1)=5x-21
5x+7(x+1)=5x-21-5x
7(x+1)=-21
7x+7=-21
7x=-28
x=4
Step-by-step explanation:
METHOD 1:
5x+7(x+1)=5x-21
5x+7x+7=5x-21
12x+7=5x-21
12x-5x=-21-7
7x=-28
x=28/7
x=4
METHOD 2:
5x+7(x+1)=5x-21
5x+7(x+1)=5x-21-5x
7(x+1)=-21
7x+7=-21
7x=-28
x=4
1O POINTS PLS ANSWER ASAP THANKS
Answer:
Step-by-step explanation:
The angle measuring 152 is split up, per se, into 2 angles. One of them is a 90 degree angle, as demonstrated by the little square that is above the 152. That 90 degree angle is on a straight line with the 28 degree angle and the angle measured as x. A straight line has a measure of 180. Therefore, 180 - 28 - 90 = x, so x = 62
please help me i really need help please
Answer:
7: 100
8: 40
9: 74
Step-by-step explanation:
Answer:
7. x= 100 8. x= 40 and 9. x= 74
Step-by-step explanation:
x + 45 +35=180(sum of angle of triangle )
or, x+ 80=180
or, x=180-80
or, x=100
same process as above for all
Fill the blanks using Product formula.
Answer: (-4s-1)*(-8) + (-4)*(-8s+7)
You have the right idea, but you swapped the items in the wrong order. Meaning that you applied the derivative to the wrong pieces as shown in the order above. It seems you have to follow this specific order for the computer to accept the answer.
A lunch menu consists of 8 different sandwiches, 5 different soups, and 5 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink?
A) 291
B) 18
C) 200
D) 296
Find the average of the following numbers. -100 and 102.
The average is the sum of the numbers divided by the quantity of numbers.
-100 + 102 =2
2/2 = 1
The average is 1
Answer:
1
Step-by-step explanation:
To find average, add up all of the numbers and divide it by how many numbers there are.
[tex]\frac{-100+102}{2} = \frac{2}{2} =1[/tex]
A mouse is moving through a maze and must make four turns where it can go either left or
right. The mouse will escape the maze if it makes three lefts and one right, in any order.
(a) To the right, draw a tree diagram
of all possible routes the mouse
could take.
(b) Using your tree diagram, create
an organized list of the routes. For
example, a route of right, left, left,
right could be listed as RLLR.
(C) What is the probability the mouse
escapes the maze if all turns are
randomly made?
giving brainliest ! *easy*
Answer:
170
Step-by-step explanation:
17π/18 * 180/π
17*180/18
=170
PLS HELP AND HURRY
After how many hours is the price the same in both companies? Explain how you found the answer.
Step-by-step explanation: 5
Answer:
Step-by-step explanation:
Raging River costs
y=9x
Paddlers costs
y=x+40
So they cost the same when y=y
9x=x+40
8x=40
x=5
So they cost the same for 5 hours.
Which two numbers are exactly 10 units away from 5?
Answer:
-5 and 15
Step-by-step explanation:
10±5 = -5, 15
Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment. An experiment is conducted to compare peach-tree seedling growth when the soil and weeds are treated with one of two herbicides. In a field containing 20 seedlings, 10 are randomly selected throughout the field and assigned to receive herbicide A. The remainder of the seedlings is assigned to receive herbicide B. Soil and weeds for each seedling are treated with the appropriate herbicide, and at the end of the study period, the height in centimeters is recorded for each seedling. The following results are obtained: Herbicide A = 94.5 cm s1 = 10 cm Herbicide B = 109.1 cm s2 = 9 cmWhat is a 90% confidence interval (use the conservative value for the degrees of freedom) for μ2 – μ1?
a. 14.6 ± 7.00
b. 14.6 ± 7.38
c. 14.6 ± 7.80
d. 14.6 ± 9.62
Answer:
A. 14.6 ± 7.00
Step-by-step explanation:
Formula for the confidence interval between the two mean is;
CI = (μ2 - μ1) ± z√[((s1)²/n1) + ((s2)²/n2)]
We are given;
μ1 = 94.5
μ2 = 109.1
s1 = 10
s2 = 9
n1 = 10
n2 = 10
The z-value at confidence interval of 90% is 1.645
Thus;
CI = (109.1 - 94.5) ± 1.645√[(10²/10) + (9²/10)]
CI = 14.6 ± 7.00
Rohan bought an almirah for Rs 15,600 and spent Rs 400 on its transportation. The total C.P is __________
From the question,
Rohan bought an almirah for =Rs.13600= cost price
Transportation cost =Rs.400
The total cost price of almirah =Rs.(13600+400)
The total cost price of almirah =Rs.(13600+400)=Rs.14000
He sold it for =Rs.16800= selling price
By comparing SP and CP=SP>CP, so there is a gain
Gain=SP−CP
=16800−14000
=Rs.2800
Gain %={(gain/CP)×100}
={(2800/14000)×100}
={2800/140}
=20%
Given that n is an integer, prove that 6 is a factor ofn3+ 5n
Answer:
n3+5n=6
taking common as n
n(5+3)=6
n8=6
Sarah has 30 pencils. She wants to give her 5 friends the same amount of pencils. How many pencils does Sarah give each friend? (Write an equation and then solve.)
Answer:
6 pencils
Step-by-step explanation:
30/5=6
Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1,3).
A)
y = -x +
16
5
B)
y = -5x - 5
16
y = 5x + 10
D)
y=-x-2
I need help!!!! I’m stuck!!!
Answer:
66.3
Step-by-step explanation:
what is the absolute value of -5+9
In 2008, the world record for swimming the 50 meter freestyle event was 21.34 seconds. Supposing the athlete swam at a constant rate what was his speed? Round your answer to the nearest hundredth m/s.
Answer:
Speed of swimmer = 2.34 m/s (Approx.,)
Step-by-step explanation:
Given:
Distance covered in world record swimming = 50 meters
Time taken by free style swimmer = 21.34 seconds
Find:
Speed of swimmer
Computation:
Speed = Distance / Time taken
So,
Speed of swimmer = Distance covered in world record swimming / Time taken by free style swimmer
Speed of swimmer = 50 / 21.34
Speed of swimmer = 2.34 m/s (Approx.,)
Please help and give brainliest answer
A car dealership allows you to customize your new car. You can choose between blue, red, black, or silver paint. The interior comes in leather or cloth. You can also choose between a manual or automatic transmission. How many different new cars can you create?
a 32
b 16
c 8
d 10
Answer:
I think the answer is 16 option b
pretty pls help with this questionn pls i need helpp
g A test was conducted to determine if there is a difference between Canadian and American average heart rates. A group of 36 Canadians and 34 Americans were randomly selected and their heart rates measured in beats per minute (bpm). The mean heart rate for Canadians was 68.5 and 70 for Americans. The pooled standard deviation of 2.0 beats/minute was calculated. Estimate a plausible range of differences between the mean heart rate of Canadians and Americans. What statistical procedure should be used to answer this research question
Answer:
The test statistic | t | =4.45
Step-by-step explanation:
Step(i):-
Given that the first sample size n₁ = 36
Given that the second sample size n₂ = 34
Mean of the first sample x₁⁻ = 68.5
Mean of the second sample x₂⁻ = 70
Step(ii):-
Test statistic
[tex]t = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } } )}[/tex]
[tex]t = \frac{68.5-70}{\sqrt{2(\frac{1}{36}+\frac{1}{34} ) } }[/tex]
[tex]t = \frac{-1.5}{0.337} = -4.45[/tex]
The test statistic | t | = |-4.45| =4.45
The test statistic is given by t and t is calculated with the help of the test statistic formula. The value of t is 4.45.
What is test statistics?The test statistic summarises the observation data into a unique number using central tendency, the variation, sample, and size in your statistical model.
The given information will be shown below.
The first sample size n₁ = 36
The second sample size n₂ = 34
The mean of the first sample x₁ = 68.5
The mean of second sample x₂ = 70
Then the test statistic will be given as
[tex]\rm t = \dfrac{x_1 - x_2}{\sqrt{S^2 (\dfrac{1}{n_1}+\dfrac{1}{n_1})}} \\\\\\\t = \dfrac{68.5 - 70}{\sqrt{2 (\dfrac{1}{36} + \dfrac{1}{34})}} \\\\\\t = \dfrac{-1.5}{0.337}\\\\\\t = -4.45[/tex]
The test statistic | t | = |–4.45| = 4.45
More about the test statistic link is given below.
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(Need help) (ASAP)
Point: 18
Answer:
10
Step-by-step explanation:
need help with this one
Answer:
Step-by-step explanation:
B + 87 +78 +66 = 360
B = 129 °
the angle next to B then is
180 = 129 + b '
51 ° = b '
A + 61 + b ' = 180
A = 68 °
Distribute: -8(3f - 9)
Step-by-step explanation:
[tex] - 8(3f - 9) = [/tex]
[tex] - 24f + 72[/tex]
Zak buys 6 gallons of fruit punch. He has
coupons for $0.55 off the regular price of
each gallon of fruit punch. After using the
coupons, the total cost of the fruit punch is
$8.70. Determine the regular price of a
gallon of fruit punch.
David can type a 50-page paper in 8 hours. Last month, David and Andy together typed a
50-page paper in 6 hours. How long would Andy take to type a 50-page paper by himself?
Answer:
12.5pages
Step-by-step explanation:
50pages ×6hours=300 and then we divide by 8 to get 37.5(the number of pages printed by david in 6 hours)
subtract 37.5 from 50 to find the number of pages printed by andy