Answer:
16ft by 16ft by 8ft.
Step-by-step explanation:
Let the total surface area of the rectangular tank be S = 2LW+2LH+2WH where;
L is the length of the box
W is the width of the box
H is the height of the box.
Since the box is openend at the top, S = lw + 2lh+ 2wh
If the base is a square base then, l = w
S = l(l) + 2wh+2wh
S = l²+4wh ............... 1
If volume = lwh
lwh = 2028 ft³
wh = 2048/l ................ 2
Substitute equation 2 into 1;
S = l²+4(2048/l)
S = l²+8192/l
dS/dl = 2l - 8192/l²
If dS/dl = 0 (since we are looking for dimensions of the tank with minimum weight.)
2l - 8192/l² = 0
2l = 8192/l²
2l³ = 8192
l³ = 8192/2
l³ = 4096
l =∛4096
l = 16 ft
Since the length is equal to the width, hence the width = 16ft (square based tank)
Given the volume V = lwh = 2048
lwh = 2048
16*16*h = 2048
256h = 2048
divide both sides by 256
256h/256 = 2048/256
h = 8ft
Hence, the dimensions of the tank with minimum weight is 16ft by 16ft by 8ft.
The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. A paper described a study in which the left atrial size was measured for a large number of children ages 5 to 15 years. Based on this data, the authors conclude that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.5 mm and a standard deviation of 4.8 mm.
Required:
a. Approximately what proportion of healthy children has left atrial diameters less than 24 mm?
b. Approximately what proportion of healthy children has left atrial diameters greater than 32 mm?
c. Approximately what proportion of healthy children has left atrial diameters between 25 and 30 mm?
d. For healthy children, what is the value for which only about 20% have a larger left atrial diameter?
Answer:
a) P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b) P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) z(s) = 0,84
Step-by-step explanation:
Normal Distribution N ( μ₀ ; σ ) is N ( 26,5 ; 4,8 )
a) P [ X < 24 mm ] = ( X - μ₀ ) / σ
P [ X < 24 mm ] = (24 - 26,5)/ 4,8 = - 0,5208 ≈ - 0,52
P [ X < 24 mm ] = - 0,52
And from z-table we find area for z score
P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b)P [ X > 32 mm ] = 1 - P [ X < 32 mm ]
P [ X < 32 mm ] = ( 32 - 26,5 ) / 4,8
P [ X < 32 mm ] = 5,5/4,8 = 1,1458 ≈ 1,15
P [ X < 32 mm ] = 1,15
And from z-table we get
P [ X < 32 mm ] = 0,8749
Then:
P [ X > 32 mm ] = 1 - 0,8749
P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = P [ X < 30 ] - P [ X < 25 ]
P [ X < 30 ] = 30 - 26,5 / 4,8 = 0,73
From z-table P [ X < 30 ] = 0,7673
P [ X < 25 ] = 25 - 26,5 / 4,8 = - 0,3125 ≈ - 0,31
From z-table P [ X < 25 ] = 0,2709
Then
P [ 25 < X < 30 ] = 0,7673 - 0,2709
P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) If 20 %
z- score for 20% is from z-table
z(s) = 0,84
y varies directly as z, y=180, z=10 , find ywhen z=14
Step-by-step explanation:
To find the value of y when z = 14 we must first find the relationship between them
The statement
y varies directly as z is written as
y = kz
where k is the constant of proportionality
when y = 180
z = 10
180 = 10k
Divide both sides by 10
k = 18
The formula for the variation is
y = 18z
When z = 14
y = 18(14)
y = 252Hope this helps you
Erik drew the diagram below of his irregularly shaped garden.
What is the area of Erik's garden? Show all work.
answer:
238 ft
explanation:
area of rhombus base×hight (14×12) = 168
find area of triangle 1/2(10)(14)=70
total area 168+70=238 ft.
look at the image below
Answer:
4.2 mi²
Step-by-step explanation:
Volume of a cone = (1/3)πr²h, where r = radius and h = height
(1/3)πr²h
= (1/3)×π×1²×4
= 4π/3
= 4.2 mi² (rounded to the nearest tenth)
look at the image below
Answer:
16
Step-by-step explanation:
volume= Length x width x height
Answer:
Volume: [tex]1/3\times Area\; of\; base\;\times height[/tex]
[tex]= 1/3\times2\times 2\times 4[/tex]
[tex]=16/3\; ft^{3}[/tex]
[tex]=5.3\; ft^{3}[/tex]
OAmalOHopeO
solve for y then find the slope and y intercept and graph
y=4x+3
y=
b=
m=
Answer:
y = 4x+3
m =4
b =3
Step-by-step explanation:
y=4x+3
This is already solved for y
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x+3
m =4
b =3
Which represents a measure of volume?
O 5 cm
O 5 square cm
05 cm
05 cm
Answer:
5 cm³
Step-by-step explanation:
The correct options to the given question will be:
5 cm³ 5 square cm 5 cm 5 cm²The volume of a solid is referred to as the space that the figure occupies. The three dimensions are covered and recorded to measure the volume. It is measured by multiplying the length, breadth, and the height of the solid. Since three units are multiplies, therefore the unit of the volume becomes a cubic unit. Usually, the volume is measured in cubic meter or cubic centimetre.
twice the square of the number
Answer:
this is easy
Step-by-step explanation:
The number to find square X 2= ?
For eg. 12X2=24
Step-by-step explanation:
The answer of twice the square number
6×6=36
An opinion poll asked a random sample of adults whether they believe flu shots are ineffective in the United States. A commentator believes less than 35% of all adults believe they are ineffective. Which null and alternative hypotheses should be used to test this claim? H0: p ≠ 0.35, Ha: p 0.35
Complete Question
The complete question is shown on the first uploaded image
Answer:
The second option is the correct option
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.35[/tex]
The Null Hypothesis is [tex]H_o : \r p = 0.35[/tex]
The reason for this is that the this original claim when represented mathematically does not contain an equality sign ([tex]i.e \ it \ is \ mathematically \ represented \ as \ \r p < 0.35[/tex]) so the null hypothesis is the compliment of it ( i.e [tex]\r p = 0.35[/tex])
The Alternative hypothesis is [tex]H_a : \r p < 0.35[/tex]
Identify the vertex of the graph. Tell whether it is a minimum or maximum.
(-2,-2); maximum
(-2,-2); minimum
(-2, -1); minimum
(-2, -1); maximum
Answer:
(-2,-2); minimum
Step-by-step explanation:
From the graph, the vertex is (-2, -2) and since there are no y values that go less than the y value of the vertex, it is a minimum.
0.25÷3=x÷1 1/2 That fraction is one and a half.
Answer:
x = 1/8Step-by-step explanation:
Given the expression 0.25÷3=x÷1 1/2, we are to look for the value of x from the given equation. Rewriting the equation we will have;
[tex]\dfrac{0.25}{3} = \dfrac{x}{1\frac{1}{2} }[/tex]
On simplification;
[tex]0.25 * \frac{1}{3} = x * \frac{2}{3} \\ \\ \frac{25}{100}*\frac{1}{3} =\frac{2x}{3}\\\\ \frac{1}{4} * \frac{1}{3} = \frac{2x}{3}\\\\ \frac{1}{12} = \frac{2x}{3}\\\\cross \ multiply\\\\2x * 12 = 3\\\\24x = 3\\\\Divide \ both \ sides \ by \ 24\\\\24x/24 = 3/24\\\\x = 1/8[/tex]
Hence the value of x in the expression is 1/8
A population of bacteria P is changing at a rate of dP/dt = 3000/1+0.25t where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t. Then find the population when t = 3 days.
Answer:
- At any time t, the population is:
P = 375t² + 3000t + 1000
- At time t = 3 days, the population is:
P = 13,375
Step-by-step explanation:
Given the rate of change of the population of bacteria as:
dP/dt = 3000/(1 + 0.25t)
we need to rewrite the given differential equation, and solve.
Rewriting, we have:
dP/3000 = (1 + 0.25t)dt
Integrating both sides, we have
P/3000 = t + (0.25/2)t² + C
P/3000 = t + 0.125t² + C
When t = 0, P = 1000
So,
1000/3000 = C
C = 1/3
Therefore, at any time t, the population is:
P/3000 = 0.125t² + t + 1/3
P = 375t² + 3000t + 1000
At time t = 3 days, the population is :
P = 375(3²) + 3000(3) + 1000
= 3375 + 9000 + 1000
P = 13,375
Three guests check into a hotel room. The manager says the bill is $30, so each guest pays $10. Later the manager realizes the bill should only have been $25. To rectify this, he gives the bellhop $5 as five one-dollar bills to return to the guests.
On the way to the guests' room to refund the money, the bellhop realizes that he cannot equally divide the five one-dollar bills among the three guests. As the guests aren't aware of the total of the revised bill, the bellhop decides to just give each guest $1 back and keep $2 as a tip for himself, and proceeds to do so.
As each guest got $1 back, each guest only paid $9, bringing the total paid to $27. The bellhop kept $2, which when added to the $27, comes to $29. So if the guests originally handed over $30, what happened to the remaining $1?
Answer:
the manager has it
Step-by-step explanation:
this sounds more like a riddle than a math question
Answer:
This was so confusing and I had to use like 3 sheets of paper
Step-by-step explanation:
$25 + $2 + $1 + $1 + $1 = $30.
So the manager has it, the point is to change the numbers so your brain gets confused.
Graph the following set of parametric equations on your calculator and select the matching graph.
Answer:
Graph 2
Step-by-step explanation:
As you can see the first equation is present with a negative slope, and none of the graphs have a line plotted with a negative slope, besides the second graph. That is your solution.
9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d overbar and s Subscript d. In general, what does mu Subscript d represent? Temperature (degrees Upper F )at 8 AM 98.1 98.8 97.3 97.5 97.9 Temperature (degrees Upper F )at 12 AM 98.7 99.4 97.7 97.1 98.0 Let the temperature at 8 AM be the first sample, and the temperature at 12 AM be the second sample. Find the values of d overbar and s Subscript d.
Answer:
[tex]\frac{}{d}[/tex] = −0.26
[tex]s_{d}[/tex] = 0.4219
Step-by-step explanation:
Given:
Sample1: 98.1 98.8 97.3 97.5 97.9
Sample2: 98.7 99.4 97.7 97.1 98.0
Sample 1 Sample 2 Difference d
98.1 98.7 -0.6
98.8 99.4 -0.6
97.3 97.7 -0.4
97.5 97.1 0.4
97.9 98.0 -0.1
To find:
Find the values of [tex]\frac{}{d}[/tex] and [tex]s_{d}[/tex]
d overbar ( [tex]\frac{}{d}[/tex]) is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5
[tex]\frac{}{d}[/tex] = ∑d/n
= (−0.6 −0.6 −0.4 +0.4 −0.1) / 5
= −1.3 / 5
[tex]\frac{}{d}[/tex] = −0.26
s Subscript d is the sample standard deviation of the difference which is calculated as following:
[tex]s_{d}[/tex] = √∑([tex]d_{i}[/tex] - [tex]\frac{}{d}[/tex])²/ n-1
[tex]s_{d}[/tex] =
√ [tex](-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1[/tex]
= √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −
(−0.26))² + (−0.1 − (−0.26))² / 5−1
= [tex]\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }[/tex]
= [tex]\sqrt{\frac{0.712}{4} }[/tex]
= [tex]\sqrt{0.178}[/tex]
= 0.4219
[tex]s_{d}[/tex] = 0.4219
Subscript d represent
μ[tex]_{d}[/tex] represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.
the area of an equilateral triangle of side 8cm is
pls i need answer ASAP
I'll mark brainliest for anyone who can help me
[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}a^2[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}(8)^2[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{64\sqrt{3}}{4}[/tex]
[tex]\\ \sf\longmapsto Area=16\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto Area=16\times 1.732[/tex]
[tex]\\ \sf\longmapsto Area=27.7cm^2[/tex]
5 pencils for 15 dollers how much for each pencil
5 pencils = 15 dollors
1 pencil = 15/5 dollors
therefore 1 pencil = 3 dollors...
Answer:
Each pencil would cost $3.00
Step-by-step explanation:
If 5 costs $15, to find the cost of one you divide 15 by 5
15 ÷ 5 = 3
Need help with this problem ASAP, don’t need an explanation, just an answer
Answer:
x^3-10x^2+1/9
Step-by-step explanation:
For standard form you need to put the exponents in order. So x^3 is first, followed by -10x^2, and finally 1/9. Hope this helps!
Find the function h(x) = f(x) - g(x) if f(x) = 3^x and g(x) = 3^2x - 3^x. A.h( x) = 0 B.h( x)=-3^2x C.h( x) = 3^x (2 - 3^x) D.h( x) = 2(3^2x)
Answer:
3^x( 2-3^x)
Step-by-step explanation:
f(x) = 3^x and g(x) = 3^2x - 3^x
h(x) = f(x) - g(x)
3^x - ( 3^2x - 3^x)
Distribute the minus sign
3^x - 3^2x + 3^x
2 * 3^x - 3 ^ 2x
Rewriting
We know that 3^2x = 3^x * 3^x
2 * 3^x - 3^x* 3^x
Factoring out 3^x
3^x( 2-3^x)
Find the particular solution of the differential equation that satisfies the initial condition. f '(x) = −8x, f(1) = −3
Step-by-step explanation:
f(x) = integral (-8x) dx = -4x^2 + C
f(1) = -3 = -4 + C
C = 1
f(x) = -4x^2 + 1
The particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is: f(x) = -4x² + 1.
Here, we have,
To find the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3,
we can integrate the equation and use the initial condition to determine the constant of integration.
First, integrate both sides of the equation with respect to x:
∫ f'(x) dx = ∫ -8x dx
Integrating, we get:
f(x) = -4x² + C
Now, we can use the initial condition f(1) = -3 to find the value of the constant C.
Substituting x = 1 and f(x) = -3 into the equation, we have:
-3 = -4(1)² + C
-3 = -4 + C
C = -3 + 4
C = 1
Therefore, the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is:
f(x) = -4x² + 1
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Black Diamond Ski Resort charges $50 for ski rental and $15 an hour to ski. Bunny Hill Ski Resort charges $75 for ski rental and $10 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same. 15x − 75 = 10x − 50 15x − 50 = 10x − 75 15x + 50 = 10x + 75 15x + 75 = 10x + 50
Answer:
The cost of 5 hours of skiing would be the same ($125) after 5 hours.
Step-by-step explanation:
Black Diamond: ChargeBD(h) = $50 + ($15/hr)h, where h is the number of hours spent skiing.
Bunny Hill: ChargeBH(h) = $75 + ($10/hr)h
We equate these two formulas to determine when the cost of using the ski slopes is the same:
ChargeBD(h) = $50 + ($15/hr)h = ChargeBH(h) = $75 + ($10/hr)h
We must now solve for h, the number of hours spent skiing:
50 + 15h = 75 + 10h
Grouping like terms, we obtain:
5h = 25, and so h = 5 hours.
The cost of 5 hours of skiing would be the same ($125) after 5 hours.
Write the degree of the following polynomials.
a⁴+a³b²+a²b²+b⁵
Answer:
downloadable content of the year and I have a nice day ahead of
Answer:
5Step-by-step explanation:
The highest cumulative degree of variables is the degree of the polynomial.
a⁴+a³b²+a²b²+b⁵4, 5, 4, 5As we see the highest degree is 5
The values of 9’s in 9905482
Answer:
9,905,482=
Million place
9,905,482=
one hundred thousandth
Which formula used in probability to find Independence question
Answer:
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
Answer:
Events are independent if the outcome of one effect does not effect the outcome
Step-by-step explanation:
Question 7
2 pts
Find the value of x and the length of segment AC if point B is between A and C.
AB = 5x, BC = 9x-2, AC = 11x + 7.6
Value of x=
Length of AC is
Answer: x=3.2 AC= 42.8
Step-by-step explanation:
As point B lies at segment AC AC=AB+BC
Otherwise we can write the equation
5x+9x-2=11x+7.6
14x-2=11x+7.6
14x-2+2=11x+7.6+2
14x=11x+9.6
14x-11x=11x-11x+9.6
3x=9.6
x=9.6:3
x=3.2
AC= 11*x+7.6= 11*3.2+7.6=35.2+7.6=42.8
Find the axis of symmetry of the graph of
y = x2 + 2x + 2
A- x= 1
B- y=1
C- x= -1
D- y=-1
Answer:
x = -1
Step-by-step explanation:
The graph's turning point is at ( -1 , 1 ), therefore the line of symmetry is at x = -1.
Answer: x = -1
Step-by-step explanation:
The formula to find the axis of symmetry in a function y = ax² + bx + c is:
[tex]x=\frac{-b}{2a}[/tex]
For y = x² + 2x + 2, where:
a = 1b = 2c = 2The axis of symmetry would be:
[tex]x=\frac{-b}{2a} =\frac{-2}{2(1)} =\frac{-2}{2} =-1[/tex]
3. Convert 10% into fraction.
1/10 to get your answer
10÷100=
0.1=1/10
what is the answer of
445+584-85
Answer:
944 is the correct answer
Answer:
the answer it's 944
445+558=1,029
1,029-85=. [944]✓
Which of the following is the correct factorization of 64x³ + 8? (2x + 4)(4x² - 8x + 16) (4x + 2)(16x² - 8x + 4) (4x - 2)(16x² + 8x + 4) (2x - 4)(4x² + 8x + 16)
Answer:
work is pictured and shown
Find the area of the following figure. Explain how you found your answer.
HELP ASAP WILL GIVE BRIANLYEST
Answer:
Below
Step-by-step explanation:
Let's say that each square on the grid represents 1 cm
First find the area of the two triangles
For the larger one: A = bh/2
A = 3 x 3 / 2
= 4.5 cm^2
For the smaller one : A = bh/2
A = 2 x 2 / 2
= 2 cm^2
For the rectangle : A = lw
A = 4 x 5
= 20 cm^2
Add them all up to get the area
4.5 + 2 + 20 = 26.5 cm^2
Hope this helps!
Answer:
26 1/2 units
Step-by-step explanation:
First find the area of the rectangle at the bottom
A = l*w
A = 5 *4 = 20
Then find the area of the left triangle
A =1/2 bh = 1/2 (3 * 3) = 9/2
Then find the area of the right triangle
A = 1/2 bh = 1/2 ( 2*2) = 4/2 =2
Add the areas together
20 + 9/2+2 = 22 +9/2 = 22+4 1/2= 26 1/2