Answer:
Step-by-step explanation:
There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:
P = 2w + l; solving for l and filling in our length of fencing gives us:
l = 148 - 2w
The area then for this will be:
A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:
[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:
[tex]A=-2w^2+148w[/tex]
The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.
To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:
[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:
[tex]-2(w^2-74w)=0[/tex]
The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:
[tex]-2(w^2-74w+1369)=...[/tex]
But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:
[tex]-2(w^w-74w+1369)=-2738[/tex]
The left side can be simplified down to a perfect square binomial:
[tex]-2(w-37)^2=-2738[/tex]
Now we'll add over the -2738:
[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.
if x = 2 and y = 6 , evaluate the following expression:
100-3(3y-4x)
(Tricky question, so be careful, not as obvious as it seems)
(NO LINKS OR I WILL REPORT)
Please this is due in like 10 minutes please help me
Answer:
628
Step-by-step explanation:
1) Find the circumference of the wheel (the distance it travels in 1 revolution)
[tex]C=\pi d[/tex] where d is the diameter
Plug in 2 ft as the diameter
[tex]C=(3.14) (2)\\C=6.28[/tex]
Therefore, the circumference of the wheel is 6.28 ft.
2) Multiply the circumference by 100
6.28 × 100
= 628 ft
Therefore, Joe would travel 628 feet if his wheel turns exactly 100 complete revolutions in one direction.
I hope this helps!
How can you use 1300 divided by 13 to help you find 1,287 divided 13
Answer:
Step-by-step explanation:
This question is about the benefits of estimation.
1300/13 is easy and results in 100.
1287/13 can be approximated by 1300/13: 1287/13 ≈ 100.
Actually, 1287 = 1300 - 13 = 13(99); just subtract 1 from 100.
So: 1287/13 = 1300 - 13 = 1287. A nice bit of mental math!
Please Help
dont answer unless you really know the answer
The population of a country has been increasing for several decades. In 1990, the population was about 263 million people In 2014, the population was about 307 million people Determine the percent in + The country's population increased by about % during this time period
Answer:
The country's population increased by about 16.73% during this time period.
Step-by-step explanation:
Percent increase:
The percent increase is given by the change multiplied by 100 and divided by the initial value.
In 1990, the population was about 263 million people In 2014, the population was about 307 million people.
Change: 307 - 263 = 44
Initial population: 263
Percentage increase:
44*100/263 = 16.73%
The country's population increased by about 16.73% during this time period.
A family has five children. The probability of having a girl is 1/2. What is the probability of having 3 girls followed by 2 boys?
Answer:
5 1/2
Step-by-step explanation:
Two accounts earn simple interest . The balance y in dollars in account A after x years can be modeled y = 20x + 400
Dooren can type 2 pages of her report in 5 minutes. At this rate, how many pages could she type in half an hour?
Answer:
60 pages
Step-by-step explanation:
2pages = 5min
30 x 2 = 60
Therefore, in half an hour Doreen can type 60 pages
I need help on the problem!! please
Answer:
choice 2) 1/4(n - 64)
Step-by-step explanation:
1/4n - 16 = 1/4(n - 64)
Image not writing all that.
Answer:
imagine
Step-by-step explanation:
Answer:
The answer is 15
Step-by-step explanation:
If the cup is only 15 cm and the pencil is 2 cm over the right amount, it would be 15
Which is larger, a pound or a kilogram?
Answer:
Pounds
Step-by-step explanation:
1 kilogram= about 2.2 pounds
Answer:
kilgoram
Step-by-step explanation:
1 kg= 2.2lb
Does anyone know what the answer?
Answer:
x = 7
Step-by-step explanation:
Hi,
7x - 7 = 4x + 14
3x - 7 = 14
3x = 21
x = 7
I hope this helps :)
The 5 members of the math team at Nielsen Middle School are raising money to go to the
state competition. They need between $55 and $80 per person for each day of the trip. Which
of the following is a reasonable estimate of the total amount of money they will need for the
2-day trip?
Answer:
The answer is $700
Step-by-step explanation:
Brainliest plzz
(OFFERING 50 POINTS!) PLEASE HELP
Can someone plz help me
Answer:
47.5 in²
Step-by-step explanation:
Answer:
47.5 in²
Step-by-step explanation:
A = a+b
/2h = 7+12
/2·5 = 47.5
In Middletown, Main Street and Market Street are parallel to each other. Patrick Street intersects Market Street to form a 76° angle at the northeast corner, as shown in the figure below. What is the measure of the angle formed at the southeast corner of Main Street and Patrick Street? (Note: Each street is straight and has the same uniform width.)
I WILL GIVE OUT BRAINLIEST IF CORRECT!
A. 76°
B. 90°
C. 104°
D. 142°
E. 152° (NOT E)!
Answer:
e
Step-by-step explanation:
Answer
C
Step-by-step explanation:
76+104 is 180
Please help me I can't solve this question I would really appreciate it
Answer:
[tex]\frac{3}{11}[/tex], 28, [tex]\frac{4}{11}[/tex]
Step-by-step explanation:
For the first one, you would subtract [tex]\frac{5}{11}[/tex] from [tex]\frac{8}{11}[/tex], giving you [tex]\frac{3}{11}[/tex].
For the second one, you would subtract 22 from 50, giving you 28.
For the third one, you would subtract [tex]\frac{4}{11}[/tex] from [tex]\frac{8}{11}[/tex], giving you [tex]\frac{4}{11}[/tex].
Hope I helped
PLEASE ANSWER ASAP FOR BRAINLEST, REALLY EASY QUESTION!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The answer is no C . I guess it should be C.Lin says that an octagon has six sides. Chris says that it has eight sides. Whose statement is correct?
Answer:
Chris is correct. All octagons have eight sides and eight angles.
Natalie can type 54 words per minute when transcribing an audio recording. Natalie needs to transcribe an audio recording with 7,938 words.
How many minutes will it take Natalie to transcribe the recording?
Enter your answer in the box.
min
Answer:
147 minutes (2 hours, 27 minutes)
Step-by-step explanation:
United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different
production capacity (in tons per day) for each grade, as follows:
Mill
Aluminum
Grade 1 2
High 6 2
Medium 2 2
Low 4 10
The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of medium-grade aluminum, and 5
tons of low-grade aluminum. It costs United $6,000 per day to operate mill 1 and $7,000 per day to operate mill 2. The company wants to know the
number of days to operate each mill in order to meet the contract at the minimum cost.
Formulate a linear programming model for this problem.
Answer:
uh
Step-by-step explanation:
i need helpppppppp ITSSSSSSSSSSSSSSSSSSSSSSS URGETTTTTTTT HELPPPPPPPPPPPPPPPP
Answer:
what school you do
Step-by-step explanation:
what grade
4m - - - - >4x10=40m^2
6m - - - - >6x10=60m^2
100
100
Students, drow anywhere on this slide!
Answer:
Im sorry what?
Step-by-step explanation:
Please answer the question in the pic and make the answer clear pleaseeeee I'm giving brainliest out as welll
by how much is 68,72,526 less than a crore?
Answer:
10000000 - 6872536 = 3127474
Hence 68,72,536 is 31,27,474 less than 1,00,00,000.
Part D Some of the measurements of the triangular prism with a right triangle base are shown. What is the length of the hypotenuse of the base?
Answer:
Hypotenuse = 5.7 cm
Step-by-step explanation:
Since the base is a right triangle, we would apply pythagorean theorem to find the length of the hypotenuse of the triangular base.
Pythagorean theorem is given as: c² = a² + b²,
Where,
c = hypotenuse
a = 4 cm
b = 4 cm
Substitute
(Hypotenuse)² = 4² + 4²
Hypotenuse = √32
Hypotenuse = 5.65685425
Hypotenuse = 5.7 cm (nearest tenth)
In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan.
a. If they put a big ad in the newspaper asking people to log their opinions on the PTA Web site what kind of bias might they encounter.
1. response bias due to desire to give acceptable answers
2. nonresponse bias
3. bias due to the use of a voluntary response sample
4. bias due to a poor sampling frame resulting in undercoverage
5. no bias
b. If they randomly select one of the elementary schools and contact every parent by phone, what kind of bias is there?
1. bias due to the use of a voluntary response sample
2. response bias due to desire to give acceptable answers
3. undercoverage bias due to a poor sampling frame
4. no bias
5. nonresponse bias
c. Suppose they randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week. What kind of sampling was done?
1. stratified sampling
2. convenience sample
3. simple random sampling
4. voluntary response sample
Find the volume of the prism to the nearest whole number
Answer:
120
Step-by-step explanation:
The prism shown is a rectangular prism with a height of 3 in a length of 5 in and a width of 8 in
The volume of a rectangular prism can easily be calculated by multiplying the height by the length by the width
So V = 3 * 5 * 8
3 * 5 = 15
15 * 8 = 120
V = 120
Therefore your answer is 120
UVT equals what?....
Answer:
m<UVT = 114°
Step-by-step explanation:
½(sum of intercepted arcs) = measure of vertex of an angle inside a circle
Thus:
½(FS + UT) = m<UVT
Substitute
½(53 + 175) = m<UVT
½(228) = m<UVT
114 = m<UVT
m<UVT = 114°
n a study of academic procrastination, it was determined that for a random sample of 18 undergrad students at a mid-size public university, the mean time spent studying for the final exam in an intro statistics course was 7.74 hours with a standard deviation of 3.40 hours. Suppose we wish to compute a 95% confidence interval for the mean time spent studying for the intro statistics final exam by all students. The margin of error for this confidence interval would then be calculated using the critical value (c) determined in the previous question as: (Don't worry if your sample size changed- use the one given here).
Answer:
The 95% confidence interval for the mean time spent studying for the intro statistics final exam by all students is between 6.05 hours and 9.84 hours.
Step-by-step explanation:
We have the standard deviation for the sample, which meas that the t-distribution is used to solve this question
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.11
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.11\frac{3.4}{\sqrt{18}} = 1.69[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 7.74 - 1.69 = 6.05 hours
The upper end of the interval is the sample mean added to M. So it is 7.74 + 1.69 = 9.84 hours.
The 95% confidence interval for the mean time spent studying for the intro statistics final exam by all students is between 6.05 hours and 9.84 hours.