Answer:
[tex]h = 3.5[/tex]
[tex]w = 7[/tex]
[tex]l = 7[/tex]
Step-by-step explanation:
Given
[tex]Volume = 171.5ft^3[/tex]
Required
The dimension that requires least material
The volume is:
[tex]Volume = lwh[/tex]
Where:
[tex]l \to length[/tex]
[tex]w \to width[/tex]
[tex]h \to height[/tex]
So, we have:
[tex]171.5 = lwh[/tex]
Make l the subject
[tex]l = \frac{171.5}{wh}[/tex]
The surface area (A) of an open-top rectangular tank is:
[tex]A = lw + 2lh + 2wh[/tex]
Substitute: [tex]l = \frac{171.5}{wh}[/tex]
[tex]A = \frac{171.5}{wh} * w + 2*\frac{171.5}{wh}*h + 2wh[/tex]
[tex]A = \frac{171.5}{h} + 2*\frac{171.5}{w} + 2wh[/tex]
[tex]A = \frac{171.5}{h} + \frac{343}{w} + 2wh[/tex]
Rewrite as:
[tex]A = 171.5h^{-1} + 343w^{-1} + 2wh[/tex]
Differentiate with respect to h and w
[tex]A_h = -171.5h^{-2} +2w[/tex]
[tex]A_w = -343w^{-2} +2h[/tex]
Equate both to 0
[tex]-171.5h^{-2} +2w=0[/tex]
Make w the subject
[tex]2w = 171.5h^{-2}[/tex]
Divide by 2
[tex]w = 85.75h^{-2}[/tex]
[tex]-343w^{-2} +2h = 0[/tex]
Make h the subject
[tex]2h = 343w^{-2}[/tex]
Divide by 2
[tex]h = 171.5w^{-2}[/tex]
[tex]h = \frac{171.5}{w^2}[/tex]
Substitute [tex]w = 85.75h^{-2}[/tex] in [tex]h = \frac{171.5}{w^2}[/tex]
[tex]h = \frac{171.5}{(85.75h^{-2})^2}[/tex]
[tex]h = \frac{171.5}{85.75^2*h^{-4}}[/tex]
[tex]h = \frac{2}{85.75*h^{-4}}[/tex]
Multiply both sides by [tex]h^{-4}[/tex]
[tex]h^{-4} * h = \frac{1}{85.75*h^{-4}} * h^{-4}[/tex]
[tex]h^{-3} = \frac{2}{85.75}[/tex]
Rewrite as:
[tex]\frac{1}{h^3} = \frac{2}{85.75}[/tex]
Inverse both sides
[tex]h^3 = 85.75/2[/tex]
[tex]h^3 = 42.875[/tex]
Take cube roots
[tex]h = 3.5[/tex] ---- height
Recall that: [tex]w = 85.75h^{-2}[/tex]
[tex]w = 85.75 * 3.5^{-2}[/tex]
[tex]w = 7[/tex] --- width
Recall that: [tex]l = \frac{171.5}{wh}[/tex]
[tex]l = \frac{171.5}{3.5 * 7}[/tex]
[tex]l = 7[/tex] --- length
A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation
h =
- 6t2 + 6t where h is the frog's height in meters at any given time, t. Find the maximum height the frog reached
Write an equation. Let x be the unknown number.
10 is the sum of three and twice a number
Answer:
10 = 3 + 2x
Step-by-step explanation:
twice the number is 2x
the sum of 2x and 3 is written as 2x + 3
2x + 3 =10
look at pic 10 pts will mark brainilest
Answer:
111
Step-by-step explanation:
y-18=14
y=14+18
y=32
substitute the vale of y
3(y+5)
3(32+5)
3*37
111
A model train is built at a scale of 1 to 60. If the model train is 10 inches long, how many feet long is the actual train?
Answer:
60 feet
Step-by-step explanation:
how many and what type of solution does 6x^2 -3x+ 5
Step-by-step explanation:
6x² -3x+ 5 =0
Discriminant = b²-4ac
D = 9 - 4(6)(5)
= 9 - 120
= -111
there is not real root solution
Give the answer in its simplest form
Answer:
1/52
Step-by-step explanation:
as there is only one of the three of clubs,
total possible outcomes= 52
favourable outcome= 1
P(getting a three of clubs) = total outcome/ favourable outcome
= 1/52
hope this helps
The table shows how the time it takes a train to travel between two cities depends on its average speed. The table shows how the time it takes a train to travel between two cities depends on its average speed Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour? What does the number 160 represent in the rational function that models the situation? distance, in miles, between the cities amount of fuel, in gallons, used by the train time, in minutes, needed to travel between the cities
Answer:
Step-by-step explanation:
Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour?
✔ y = 160/x
What does the number 160 represent in the rational function that models the situation?
✔distance, in miles, between the cities
amount of fuel, in gallons, used by the train
time, in minutes, needed to travel between the cities
Answer: NOTE Pictures Are not in order! Make sure you check page number.
Step-by-step explanation:
On page 6 the answers are ”C” and ”5lbs”
On page 7 the answers are “C”, “$ 418”, “ The cat”, and then “ $960”.
On page 8 the answers are : < Just copy paste this below.>
“Based on the calculation, they should purchase the second television as the cost is cheaper.
Based on the information given in the question, the cost of the first television will be:
= $330 + ($14 × 8)
= $330 + $102
= $442
The cost of the second television will be:
= $369 + ($9 × 8)
= $369 + $72
= $441
Therefore, the second television is cheaper.”
^
<Just copy paste this. > [Then check. “A,B,C,”.]
On page 9 the answer is “ D “.
5. In A ABC, mZ A = 100%, m B = 30°, and m2 C = 50°. Which lists the sides from largest to
smallest?
Answer:
BC>AB>AC
Step-by-step explanation:
The side length that sees the largest angle measure has the longest length
BC>AB>AC
A company hopes to improve customer satisfaction, setting a goal of less than 5% negative comments. A random survey of 850 customers found only 34 with complaints. Does this provide evidence at the 10% significance level that the company has reached its goal of decreasing the percentage of complaints
Answer:
The p-value of the test is 0.0901 < 0.1, which means that this provides evidence at the 10% significance level that the company has reached its goal of decreasing the percentage of complaints.
Step-by-step explanation:
A company hopes to improve customer satisfaction, setting a goal of less than 5% negative comments.
At the null hypothesis, we test if the proportion of negative comments is of at least 5%, that is:
[tex]H_0: p \geq 0.05[/tex]
At the alternative hypothesis, we test if this proportion is less than 0.05, that is:
[tex]H_1: p < 0.05[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.05 is tested at the null hypothesis:
This means that [tex]\mu = 0.05, \sigma = \sqrt{0.05*0.95}[/tex]
A random survey of 850 customers found only 34 with complaints.
This means that [tex]n = 850, X = \frac{34}{850} = 0.04[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.04 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{850}}}[/tex]
[tex]z = -1.34[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.04, which is the p-value of z = -1.34.
Looking at the z-table, z = -1.34 has a p-value of 0.0901.
The p-value of the test is 0.0901 < 0.1, which means that this provides evidence at the 10% significance level that the company has reached its goal of decreasing the percentage of complaints.
A ladder is 74 inches tall. How tall is it in feet and inches?
Answer:1 inch = 0.0833333 feet so 74 x 0.0833333 = 6.16667
Step-by-step explanation:
Factor the expression. x2 + 7x+ 10
Answer:
Make me a Brainlist plsStep-by-step explanation:
x²+7x+10=0
ur answer is there in image
In how many ways can the letters in the word 'Oklahoma' be arranged?
Answer:
720
Hope that this helps!
please help! (listing BRAINLIST and giving points) :)
Answer:
[tex]x=7.8[/tex]
Step-by-step explanation:
In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse.
The angle marked 33 degrees has its opposite side labelled with [tex]x[/tex] and the hypotenuse of the triangle labelled with 12.
Thus, we can set up the following equation to solve for [tex]x[/tex]:
[tex]\tan 33^{\circ}=\frac{x}{12},\\x=12\tan 33^{\circ}=7.79289111837\approx \boxed{7.8}[/tex]
Answer:
Step-by-step explanation:
tan(33°) = x/12
x = 12tan(33°) ≈ 7.79
Olivia randomly samples 50 students attending a basketball game and asks what grade they are in. Of the studets surveyed, 19 were in the seventh grade. I
there are 200 students attending the basketball game, based on the sample, how many of them are in seventh grade?
Answer:
76
Step-by-step explanation:
19 out of 50 are in 7th grade.
200/50 = 4
Multiply both numbers in the ratio by 4.
19 out of 50 = 76 out of 200
Answer: 76
I need help pls and thank you
Answer:
unbounded region
A feasible region that cannot be enclosed in a closed figure is known as an unbounded region. A feasible region is a set of all possible points of an optimization problem that satisfy the problem's constraints; feasible sets may be bounded or unbounded.
Step-by-step explanation:
Two and three fifths plus one and three fifths
Answer:
2 3 + 1 3 = 3/5 + 3/5 = 1 1/5 + 2+1 = 3 + 1 !/5 = 4 1/5
5 5
Step-by-step explanation: The Slashes mean The number bellow
Please make this answer Brainlist...
UB needs to need to create a team of 4 players for the competition out of 10 volunteers. How many
different teams are possible?
Answer:
604,800
Step-by-step explanation:
10*9*8*7*6*5*4
What percent of 50 is 44
Answer:
here u go
Step-by-step explanation:
88%
Answer:
88% of 50 is 44
Step-by-step explanation:
50x=44
x=44/50
x=0.88
Therefore, 88% of 50 is 44
The temperature in Alaska was -12 degrees Fahrenheit.It then dropped 5 degrees overnight.what is the new temperature.
Answer:
-17 degrees Fahrenheit.
Step-by-step explanation:
-12 minus 5 is -17
A company operates three machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.
Machine
Shift A B C
1 Observed 46 11 13
Expected 40.27933 14.07821 15.64246
2 Observed 37 10 11
Expected 33.3743 11.6648 12.96089
3 Observed 20 15 16
Expected 29.34637 10.25698 11.39665
a. Yes, you can reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.0423
b. Yes, you can reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.9577
c. No, you cannot reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.0423
d. No, you cannot reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.9577
Which ordered pairs are solutions to the equation x+6y=4?
Answer:
(10 , -1)
Step-by-step explanation:
(10)+6(-1)=4
10-6=4
Find the nth term of the geometric sequence whose initial term is a1
= 0.5 and common ratio is 10
(Your answer must be a function of n.)
Answer:
Step-by-step explanation:
geometric progresion formula:
[tex]a_n=a_1*r^{n-1}\\a_1=0.5\\r=10\\a_n=0.5*10^{n-1}[/tex]
1. Determine the length of JG using
circle D.
Show your work and write out your
justification.
Be prepared to answer questions
about additional angles, arcs and
segments from circle D.
Given:
In circle D, [tex]\angle EDH\cong \angle EDG[/tex].
To find:
The length of JG.
Solution:
We know that, if two central angles are congruent then the corresponding chords are congruent and their measures are equal.
We have,
[tex]\angle EDH\cong \angle EDG[/tex]
It means chords EH and EG are congruent and their measures are equal.
[tex]EH=EG[/tex]
[tex]9=EG[/tex]
Using segment addition property, we get
[tex]EJ+JG=EG[/tex]
[tex]4+JG=9[/tex]
[tex]JG=9-4[/tex]
[tex]JG=5[/tex]
Therefore, the length of JG is 5 units.
Answer:
5
Step-by-step explanation:
Si compraste 0.5 mts. de alambre grueso con un costo de $ 4.00 pesos por metro y 0.4 mts. de alambre delgado con un costo de $5.00 pesos por metro,
¿Cuánto fue el costo total en la compra de los metros de alambre?
Answer:
El costo total en la compra es $4.00 pesos.
Step-by-step explanation:
El costo total en la compra de los metros de alambre viene dado por la suma de los costos de los metros individuales de los alambres gruesos y delgados:
[tex] C_{t} = C_{g} + C_{d} [/tex]
En donde:
[tex] C_{t} [/tex]: es el costo total
[tex] C_{g} [/tex]: es el costo del alambre grueso
[tex] C_{d} [/tex]: es el costo del alambre delgado
Podemos encontrar el costo de cada alambre multiplicando el valor por la cantidad de metros:
[tex]C_{g} = 0.5 m*\frac{\$ 4.00}{m} = \$2.00[/tex]
[tex]C_{d} = 0.4 m*\frac{\$ 5.00}{m} = \$2.00[/tex]
Entonces, el costo total es:
[tex]C_{t} = 2.00 + 2.00 = \$4.00[/tex]
Por lo tanto, el costo total en la compra es $4.00 pesos.
Espero que te sea de utilidad!
How much is 142,560 inches in miles
Answer:
11880 ft
Step-by-step explanation:
12 in = 1 ft
142560/12 = 11880
what number is exactly halfway between 2.5 and 3.5
Answer:
3 is exactly halfway between 2.5 and 3.5.
Step-by-step explanation:
The first number is 2.5
The second number is 3.5
We need to find the number that is exactly halfway between 2.5 and 3.5. It can be calculated as follows :
[tex]n=\dfrac{2.5+3.5}{2}\\\\n=\dfrac{6}{2}\\\\n=3[/tex]
Hence, 3 is exactly halfway between 2.5 and 3.5.
Somebody Please Help!!!
Step-by-step explanation:
11. shape 1 => A = ½×17×10=85m²
shape 2=> A = 17×9 =153 m²
total area = 238 m²
12. shape 1 => A = 7×3= 21 m²
shape 2=> A = 3×2 = 6 m²
total area = 27 m²
o
63°
Please helppppp
Answer:
27
Step-by-step explanation:
180 - 90 - 63 = 27
all angles in a triangle add up to 180 degrees
i need help on this one please help! (listing BRAINLIST and giving points) :D
Answer:
tan C is 90
tan B is 60
tan A is 60
What is the value of x?
Answer:12
Step-by-step explanation: