Answer:
The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft
Step-by-step explanation:
We were given the volume of the tank as, 2048 cubic feet.
Form minimum weight, the surface area must be minimum.
Let the height be h and the lengths be x
the volume will be: V=x²h then substitute the value of volume, we have
2048=hx²
hence
h=2048/x²
Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.
The surface area of the box described is
A=x²+4xh
Then substitute h into the Area equation we have
A= x² + 4x(2048/x²)
A= x² + 8192/x
We want to minimize
A
dA/dx = -8192/x² + 2 x= 0 for max or min
when dA/dx=0
dA/dx= 2x-8192/x²=0
2x=8192/x²
Hence
2x³=8192
x³=4096
x=₃√(4096)
X=16ft
Then h=2048/x²
h=2048/16²
h=8ft
The box should have base 16ft by 16ft and height 8ft
Hence the dimensions are 16 ft by 16 ft by 8 ft
Timothy stated that the sum of 0.9 + (-9/10) was 18/20.
What mistake(s) did Timothy make?
What is the sum of 0.9 + (-9/10)?
Answer:
18/10
Step-by-step explanation:
Explain whether the function g(x) = x^9 + x^5 is borh an even function and an odd function.
A. The function g is both an odd and even function because it is a polynomial that passed through the origin
B. Although the function g is an odd function, it is not an even function because g(x) does not equal g(-x) for all x in the domain of the function.
C. Although the function g is not an even function, it is not an odd function because g(-x) does not equal -g(x) for all x in the domain of the function
D. The function g is neither an even nor odd function. The value of g(x) does not equal g(-x) for all x in the domain of the function, and g(-x) does not equal -g(x) for all x in the domain of the function.
Answer:
The answer is B
..........
What is the range of the function f(x) = -4|x + 1| − 5?
Answer:
f(x) ≤ -5
Step-by-step explanation:
Answer: hoping the other guy was right lol
Step-by-step explanation:
Write a rational number in fraction form that is equivalent to -1/5
Answer & Step-by-step explanation:
You can find a rational fraction equivalent to [tex]-\frac{1}{5}[/tex] by multiplying the numerator and denominator by the same number. The number can be any:
[tex]-\frac{1}{5} *3\\\\-\frac{1}{5}*\frac{3}{3}=-\frac{3}{15}[/tex]
This works because if you simplify the new number, it will have the same value as the first fraction.
If you simplify both fractions to a decimal value, they both equal -0.2.
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took
7 2/3 hours, what was the speed of the bus?
Answer:
66 miles per hour
Step-by-step explanation:
To find the speed, divide the distance by the amount of time:
506 ÷ 7 2/3
= 66
= 66 miles per hour
Answer:
66
Step-by-step explanation:
Notice that the problem is asking us to find the rate for Sean's trip. Since we are also given the distance he is traveling and the travel time, we should use the distance, rate, and time formula.
d=rt
where d=distance r=rate t=time
We are given
d=506 mi
r=?
t=723=233 hr
Solving for rate and then substituting the given information into the distance, rate, time formula gives
r=dt=506233=5061⋅323=66
So Sean drove at a rate of 66 mph.
Triangle A B C is reflected across line m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated about point A prime to form triangle A prime B double-prime C double-prime What is the composition of transformations mapping △ABC to △A'B''C''? The first transformation is . The second transformation is . △ABC is △A'B'
Answer:
reflection across line mrotation about point A'Step-by-step explanation:
The problem statement tells you exactly what the transformations are.
The first transformation is reflection across line m.
The second transformation is rotation about point A'.
_____
These are both rigid transformations, so ΔABC ≅ A'B''C''.
Answer:
Triangle A B C is reflected across line m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated about point A prime to form triangle A prime B double-prime C double-prime
What is the composition of transformations mapping △ABC to △A'B''C''?
The first transformation is
✔ a reflection across m
.
The second transformation is
✔ a rotation about A'
.
△ABC is
✔ congruent to
△A'B''C''.
Step-by-step explanation:
The instructions for mixing a rose fertilizer call for 3/8 cup of potash and 1 3/4 cups of nitrogen. What is the ratio of nitrogen to potash?
Answer:
7/4 : 3/8
Step-by-step explanation:
nitrogen =1 3/4 =7/4
potash= 3/8
Need helpppppppppp! Show work plz
Answer:
9/169
Step-by-step explanation:
JQK of 4 suits = 12 cards
12/52x12/52=
3/13x3/13=
9/169
solve the simultaneous equation 2p - 3q = 4, 3p + 2q = 9.
b. if 223= 87 find x
Answer:
Step-by-step explanation:
Given the simultaneous equation 2p - 3q = 4 and 3p + 2q = 9, to get the value of p and q we will use elimination method.
2p - 3q = 4 ...................... 1 * 3
3p + 2q = 9 ..................... 2 * 2
Multiplying equation 1 by 3 and 3 by 2:
6p - 9q = 12
6p + 4q = 18
Subtracting both equation
-9q-4q = 12-18
-13q = -6
q = -6/-13
q = 6/13
Substituting q = 6/13 into equation 2
2p - 3(6/13) = 4
2p - 18/13 = 4
2p = 4+18/13
2p = (52+18)/13
2p = 70/13
p = 70/26
p = 35/13
Hence p = 35/13 and q = 6/13
b) If if 223ₓ = 87 find x
Using the number base system and converting 223ₓ to base 2 will give us;
223ₓ = 2*x² + 2*x¹ + 3*x⁰
223ₓ = 2x²+2x+3
Substituting back into the equation, 2x²+2x+3 = 87
2x²+2x+3-87 = 0
2x²+2x-84 = 0
x²+x-42 = 0
On factorizing:
(x²+6x)-(7x-42) = 0
x(x+6)-7(x+6) = 0
(x+6)(x-7) = 0
x+6 = 0 and x-7 = 0
x = -6 and 7
Hence the value of x is 7 (neglecting the negative value)
I need some help on this question. So, would <FET equal <FDT? or what would it equal...
Hi Hello.....How r u......
the right triangular prism and the square rectangular prism both haven't had a 10 in in the same volume. A plane slices both solid parallel to their bases. The base of the triangular prism is a right triangle with legs 8 and 9 in Long. Find the length of the side of the square prism's cross-section in inches.
Answer: 6 inches
Step-by-step explanation:
Volume (V) = Area of the base (B) × height (h)
Both images have the same volume and the same height, therefore the Area of their bases must be equal to each other.
Area of the triangle
[tex]A=\dfrac{1}{2}\cdot b \cdot h\\\\.\quad=\dfrac{1}{2}\cdot 8 \cdot 9\\\\.\quad= 36[/tex]
Area of a square
A = s²
36 = s²
6 = s
logx - logx-1^2=2log(x-1) what is the value of x
Answer:
Step-by-step explanation:
[tex]logx -log(x-1)^2= 2 log(x-1)[/tex]
[tex]logx-2log(x-1) = 2log(x-1)[/tex]
[tex]logx=log(x-1)^4[/tex]
[tex]x=(x-1)^4[/tex]
[tex]x^4-4x^3+6x^2+1=0[/tex]
solve this equation
A rectangle has a hight of 4x and a with of 3x+1
.Express the area of the entire rectangle. Expression should be expanded.
In 2001, there were 68,490,000 households in the
United States subscribing to cable television ser-
vices. Round this number to the nearest million.
(Source: Nielsen Media Research-NTI)
Answer:
68,000,000
Step-by-step explanation:
Look at the hundred thousands place. If it's a 5 or higher you round up and if it's lower you round down. Since there is 4 in the hundred thousands place you round down. Everything to the right turns into a zero.
a) Is it reasonable to conclude that the weather or mechanical failures caused only about % of recent plane crashes?
A.
Yes, because there is the possibility of overlap between the categories.
B.
No, because there is no possibility for overlap between the categories.
C.
Yes, because there is no possibility for overlap between the categories.
D.
No, because there is the possibility of overlap between the categories.
Answer:
Yes, because there is no possibility for overlap between the categories.
a group of biologists counted the number of birds in migration patterns. The number of birds in each ob observation, but some of the data were lost. Which expression models the number of birds in the nth observation? please help me
Answer:
56 + 6(n - 1)
Step-by-step explanation:
To know which of the equation represent the nth term, we simply test each equation to see the one that will satisfy the table given above.
This can be obtained as follow:
For 56 + 6(n - 1)
1. n = 2
56 + 6(n - 1) = 56 + 6(2 - 1)
= 56 + 6(1)
= 56 + 6
= 62
2. n = 5
56 + 6(n - 1) = 56 + 6(5 - 1)
= 56 + 6(4)
= 56 + 24
= 80
For 56 + 12(n - 1)
1. n = 2
56 + 12(n - 1) = 56 + 12(2 - 1)
= 56 + 12(1)
= 56 + 12
= 68
2. n = 5
56 + 12(n - 1) = 56 + 12(5 - 1)
= 56 + 12(4)
= 56 + 48
= 56 + 24
= 104
For 62 + 6(n - 1)
1. n = 2
62 + 6(n - 1) = 62 + 6(2 - 1)
= 62 + 6(1)
= 62 + 6
= 68
2. n = 5
62 + 6(n - 1) = 62 + 6(5 - 1)
= 62 + 6(4)
= 62 + 24
= 86
For 62 + 12(n - 1)
1. n = 2
62 + 12(n - 1) = 62 + 12(2 - 1)
= 62 + 12(1)
= 62 + 12
= 74
2. n = 5
62 + 12(n - 1) = 62 + 12(5 - 1)
= 62 + 12(4)
= 62 + 48
= 110
From the illustrations made above,
Only equation 56 + 6(n - 1) satisfied the table.
Therefore, the expression 56 + 6(n - 1) can be used to obtain the nth term.
NEED HELP PLZ!! Use the definition, identities, and properties of imaginary numbers to simplify each of the following expressions. Match each item with its correct simplest form. 1. (i 3)5 2. -i 6 · i 3 · i -5 3. -(i 4) (i 0) (i 7) 4. (i 5 · i -2 · i 8)0 Choices: 1 -1 i -i
Answer:
-i, -1, i, 1
I think the previous answer is arranged in the order of correct answers, if that make sense. For example, next to -i, you would put 1.
Also, are you a member of Calvert? Because this layout looks familiar.
The required expressions with their correct simplest form, follow as:
1. (i³)⁵ = - i
2. - i⁶·i³·i⁵ = - 1
3. - (i)⁴·i⁰·i⁷ = 1
4. (i⁵·i²·i⁸)⁰= 1
What is a complex number?A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,
where a, and b are real numbers and i is an imaginary number.
The expressions are given in the question, as follows:
1. (i³)⁵
= (i)¹⁵
= (i²)⁷ × i
As we know that i² = -1, where i is an imaginary number.
= (-1)⁷ × i
= (-1 ) × i
= - i
Similarly, further expressions are solved below.
2. - i⁶·i³·i⁵
= i⁶·i³·i⁵
= (i)¹⁴
= (i²)⁷
= (-1)⁷
= (-1)
= - 1
3. - (i)⁴·i⁰·i⁷
= - (i)¹¹
= - (i²)⁵ × i
= - (-1)⁵ × i
= - (-1 ) × i
= - (- i)
= 1
4. (i⁵·i²·i⁸)⁰
= ((i)¹⁵)⁰
= 1
Thus, the required expressions with their correct simplest form in the above solution part.
Learn more about the complex numbers here:
brainly.com/question/19007885
#SPJ5
y is directly proportional with x. Write an equation that shows the relationship if x=2 and y=6. A. y=3x B. 6y=2x C. y=13x D. 3y=x
Answer:
Hey there!
The relationship can be y=3x.
Let me know if this helps :)
When Mount Saint Helens erupted in 1980, the top of the mountain was blown off. A surveyor determined the height of the new summit by measuring the angle of elevation to the top to be 37°46'. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40°30'. Find in ft the new height of Mount Saint Helens.
Answer:
Height= 8341.6 feet
Step-by-step explanation:
A surveyor determined the height of the new summit by measuring the angle of elevation to the top to be 37°46'. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40°30'.
40°30'= 40.5°
37°46'= 37.767°
b = 180-40.5
b= 139.5°
a= 180-139.5-37.767
a= 2.733°
Using sine method
1000/Sina= y/sinB
1000/sin 2.733= y/sin 139.5
(1000*sin 139.5)/sin 2.733= y
(1000*0.6494)/0.04768= y
13619.96= y
Y= 13620 feet
Height/sin 37.767= 13620
Height=13620*sin37.767
Height= 8341.59
Height= 8341.6 feet
1. How many percent of 50 is 10? 2. 20 Is 60% of what number?
Answer:
1. 20%
2. [tex]33.\overline{33}[/tex]
Step-by-step explanation:
We can use percentage proportions to find out these answers.
For number one, 10 is what percent of 50, we already know our two values so we can make the equation:
[tex]\frac{10}{50} = \frac{x}{100}[/tex]
Using the cross products property, we know that x is [tex](100\cdot10)\div50[/tex] which is 20.
So 10 is 20% of 50.
For number two, we know a different pair of two numbers now: we know the percent of x, and the percent it is, so the equation can become:
[tex]\frac{20}{x} = \frac{60}{100}[/tex]
Again, cross products property tells us that x is [tex](100\cdot20)\div60[/tex], which is [tex]33.\overline{33}[/tex].
Hope this helped!
NEED HELP ASAP!! Angles of Elevation and Despression! Need to find x!
Answer:
80.385
Step-by-step explanation:
It requires you to use trigonometry. First, ask yourself, which of the angle relationship (between sin, cos, tan) that includes the triangle's "x" and "300", from the angle 15°.
It's tan, because in this case, tan 15° = x / 300.
You then set x = 300 tan 15°, type it on calculator, and voila you get the answer.
Answer:
Hey there!
Tangent 15=x/300
Tangent 15(300)=x
x=80.4
Let me know if this helps :)
Ben can type 25 words in half a minute. At this rate, how many words can he type in 5 minutes?
A student found the unit rate and solved the problem. The student’s work is shown below. Has the student answered the question completely?
StartFraction 25 words over One-half minute EndFraction = StartFraction 50 words over 1 minute EndFraction
No, the student should have divided the unit rate by 5.
No, the student should have multiplied the unit rate by 10.
No, the student should have multiplied the unit rate by 5.
Yes, the student found how many words he can type in 5 minutes.
Answer:
CCCC!!!!!
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Find the distance that (5, 1) is from the origin. Round to three decimal places.
Answer: Distance = 2.449
Step-by-step explanation:
Given that the distance that (5, 1) is from the origin. That is (0,0) to (5,1)
where
X1 = 0
X2 = 5
Y1 = 0
Y2 = 1
The distance from the origin to the point (5, 1) can be calculated by using the formulae
Substitute all the parameters into the formular
D = [tex]\sqrt{(X2-X1) + (Y2-Y1)}[/tex]
D = [tex]\sqrt{(5-0) + (1-0)}[/tex]
D = [tex]\sqrt{5 + 1}[/tex]
D = [tex]\sqrt{6}[/tex]
D = 2.44948
D = 2.449 ( Three decimal places)
Help me please thank you
===========================================
Explanation:
The angles 4x and 3x+10 are corresponding angles. They are on the same side of the transversal cut (above the transversal) and to the right of each parallel line.
If the corresponding angles are congruent, then line A is parallel to line B.
4x = 3x+10
4x-3x = 10
x = 10
Write "six times 3 minus 3" as an expression.
Answer:
6(3)-3
Step-by-step explanation:
Answer:
Step-by-step explanation:
6x(−3)
Money received by an employee after deductions is called
Answer:
disposal earnings I think
Step-by-step explanation:
it is the legal deduction of money by the government I think
How many pennies could you have if: When you break the pennies into groups of 2, you have 1 penny left over, AND when you break the pennies into groups of 3, you have 1 penny left over, AND when you break the pennies into groups of 5, you have 1 penny left over, AND when you break the pennies into groups of 7, you have NO pennies left over?
Answer:
91
Step-by-step explanation:
"When you break the pennies into groups of 2, you have 1 penny left over"
You have an odd number of pennies.
"when you break the pennies into groups of 3, you have 1 penny left over"
The number of pennies is one more than a multiple of 3.
"when you break the pennies into groups of 5, you have 1 penny left over"
A number that is divisible by 5 ends in 0 or 5. You have one more penny than that, so the number will end in 1 or 6. We already know the number is odd, so it cannot end in 6. The number of pennies must end in 1.
"when you break the pennies into groups of 7, you have NO pennies left over"
The number is a multiple of 7.
We need a multiple of 7 that ends in 1.
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, ...
You could have 91.
Help! Please! Geometry Question 9.
Answer:
see below
Step-by-step explanation:
|AB| = | 2 - 5.25| = 3.25
The lines starts at 2 not at 1
Confidence Interval: What is the 95% confidence interval to estimate the population mean?
Answer: The 95% confidence interval to estimate the population mean describes a range of values that a person can be 95% sure that it contains the population mean.
Step-by-step explanation:
A 95% confidence interval for population mean ([tex]\mu[/tex]) is an interval on which a person can be 95% confident that the true population mean lies in it.
i.e. The probability that it contains the true population mean is 95%.
i.e. P( Sample mean- margin of error < [tex]\mu[/tex] < Sample mean + margin of error) = 0.95.
Estimate and then solve the equation x-17 4/5=13 1/5
Answer:
x=31
Step-by-step explanation: