The dimensions of this rectangular tank that has the minimum surface area are 42 feet and 21 feet.
How to calculate the dimensions of the tank that has the minimum surface area?First of all, we would determine the surface area of this rectangular tank with a square base by using this formula:
h = V/s²
Where:
h represents the height of a rectangular tank.s represents the side of the square base.V represents the volume of a rectangular tank.For the surface area of this rectangular tank with a square base, we have:
Surface area, A = base area + 4(lateral area)
Surface area, A = s² + 4(s × h)
Surface area, A = s² + 4(s × V/s²)
Surface area, A = s² + 4V/s
Next, we would take the first derivative of the surface area as follows:
A' = 2s - 4V/s²
Substituting the given parameters into the formula, we have;
A' = 2s - 4(37044)/s²
For the minimum surface area dimension, the first derivative of the surface area would be equated to zero:
2s - 148,176/s² = 0
148,176/s² = 2s
148,176 = 2s³
s³ = 74,088
s = ∛74,088
s = 42 feet.
For the height, we have:
Height, h = V/s²
Height, h = 37044/42²
Height, h = 37044/1764
Height, h = 21 feet.
Read more on minimum surface area here: https://brainly.com/question/13789217
#SPJ1
Find the exact arc length of f(x)=√2x+1 0≤x≤4
The exact arc length of f(x)=√2x+1 is 4.5.
The arc length is the separation between two points along a curve segment. The arc length of a function f(x) is given by the formula,
[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx[/tex]
Where f'(x) is derivative of function f(x). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.
Finding the arc length of f(x)=√2x+1 0≤x≤4, using the formula,
First finding the derivative of function,
[tex]f'(x)=\frac{d(\sqrt{2x+1})}{dx} \\\\=\frac{2}{2\sqrt{2x+1}} \\\\=\frac{1}{\sqrt{2x+1}}[/tex]
Now, putting the derivative of function f(x) in the formula of arc length L,
[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+(\frac{1}{\sqrt{2x+1}})^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+\frac{1}{2x+1}}}\\\\L=\int\limits^4_0 {\sqrt{\frac{2x+1+1}{2x+1}}}\\L=\int\limits^4_0 {\sqrt{\frac{1}{2x+1}}}\\\approx4.5[/tex]
Therefore, the exact arc length of f(x)=√2x+1 is 4.5.
To learn more about the Length of arc visit here:
https://brainly.com/question/17748353
#SPJ1
Which of the following has a graph that is wider than the graph of y = 5x² - 3?
-
y = 8x² - 10
y = 5x² + 2
y=-6x² + 1
y = 3x² + 4
The equations y = -6x² + 1 and y = 3x² + 4 both have graphs that are wider than the graph of y = 5x² - 3.To determine which equation has a graph wider than the graph of y = 5x² - 3, we need to compare the coefficients of x² in each equation.
A wider graph indicates a smaller coefficient in front of x², which means the parabola will be less steep and have a broader shape.Let's compare the coefficients:y = 8x² - 10: The coefficient is 8, which is larger than 5. Therefore, this equation does not have a wider graph than y = 5x² - 3.
y = 5x² + 2: The coefficient is 5, which is equal to the coefficient in y = 5x² - 3. Therefore, the graphs of these two equations will have the same width.
y = -6x² + 1: The coefficient is -6, which is smaller than 5. Hence, this equation has a wider graph than y = 5x² - 3.
y = 3x² + 4: The coefficient is 3, which is smaller than 5. Hence, this equation also has a wider graph than y = 5x² - 3.
For more such questions on graph
https://brainly.com/question/30287521
#SPJ8
2x+18=4x-14 pls help me - johnny
Answer: x=16
Step-by-step explanation: 18=2x-14
32=2x
x= 16
Question content area top Part 1 What is the constant of proportionality in the equation y=−7.48x?
The constant of proportionality of the equation y =−7.48x is - 7.48.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent
In other words, two variables have a proportional relationship if the ratios of the variables are equivalent.
Therefore, a proportional relationship is one in which two quantities vary directly with each other.
Hence, in mathematical form,
y ∝ x
y = kx
where
k = constant of proportionalityy varies directly as the variable x.
In the equation,
k = - 7.48
Therefore, the constant of proportionality is - 7.48.
learn more on proportional relationships here: https://brainly.com/question/28861337
#SPJ1
The blood types of 200 people are collected at a doctor’s office. The table shows the breakdown of patients by blood type.
If a person from this group is selected at random, what is the probability that this person has type AB blood? Express your answer as a fraction in lowest terms or as a decimal rounded to the nearest millionth (if necessary).
Blood Type Survey Results
Blood Type Number of Patients
A 45
B 65
O 75
AB 15
Answer:
[tex]\frac{3}{40}=0.075[/tex]
Step-by-step explanation:
The probability of a person selected at random from this group having type AB blood is 15 out of 200 total people. Therefore:
[tex]\frac{15}{200}=\frac{3}{40}=0.075=7.5\%[/tex]
NEED HELP ASAP WILL GIVE BRAINLIEST!
3Fill blanks
1. _ 2. _<6ab+3b/3a+1<_
Answer:
Step-by-step explanation:
Josh loves to visit his aunt's house. When there, his two favorite activities are walking the dog and playing darts. Let A represent the event that he walks his dog at his aunt's house and B represent the event that he plays darts at his aunt's house. If A and B are independent events with P(A)=0.9 and P(B)=0.4, find P(A AND B).
The probability of P(A AND B) when Josh visit his aunt's house is 0.36.
What is probability?Probability is the likelihood that an event will occur or take place.
Let A = the event that he walks his dog at his aunt's house
Let B = the event that he plays darts at his aunt's house.
When A and B are independent events with P(A)=0.9 and P(B)=0.4, the probability of P(A AND B) will be:
= P(A) × P(B)
= 0.9 × 0.4
= 0.36
The probability is 0.36.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
If f(x) = 2x + 1, find f(1). Just write the answer no equals or variable!!!
Answer:
3
Step-by-step explanation:
f(1)=2(1)+1
f(1)=3
What 1+2
Apparently that wasn’t enough info…
Answer:
3???
Step-by-step explanation:
A study of bone density on 5 random women at a hospital produced the following results.
Age 41, 53, 57, 61, 65.
Bone density: 360, 355, 340, 325, 310
Calculate the correlation coefficient, r. Round your answer to three decimal places.
The correlation coefficient when there is a study of bone density on 5 random women is -0.909.
What is the correlation coefficient?It is the statistical measure of the strength of the linear relationship that's between two variables. The correlation coefficient is calculated by calculating the covariance of the variables and dividing that number by the product of the standard deviations of those variables.
The steps for calculating the correlation coefficient are as follows:
Choose your data sets.Determine the standardized value for your x variables.Determine the standardized value for your y variables.Find the sum by multiplying.Determine the correlation coefficient by dividing the total.The statistical software was used and the values include
Dependent variable = y
Independent variable = x
It should be noted that linear regression has an equation that is in the form of Y = a + bx. The equation is y = 451.674 - 2.051. This was gotten through the statistical software used.
Sample size = 5
Correlation coefficient = -9.09
In conclusion, the coefficient is -9.09.
Learn more about correlation coefficient on:
brainly.com/question/4219149
#SPJ1
Urgent .. Suppose that a national testing service gives a test in which the results are
normally distributed with a mean of 550 and standard deviation of 85. If you score a
625 on the test, what fraction of the students taking the test exceeded your score?
The fraction of the students taking the test exceeded your score will be 47 / 250.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
Assume that a public testing administration gives a test in which the outcomes are regularly dispersed with a mean of 550 and a standard deviation of 85. On the off chance that you score a 625 on the test.
Then the fraction of the students taking the test exceeded your score will be given as,
z = (625 - 550) / 85
z = 75 / 85
z = 0.8824
Then the fraction is given as,
P(x > 625) = P(z > 0.8824)
P(x > 625) = 0.188
P(x > 625) = 47 / 250
The fraction of the students taking the test exceeded your score will be 47 / 250.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
#SPJ1
Two mechanics worked on a car. The first mechanic charged $85 per hour, and the second mechanic charged $45 per hour. The
mechanics worked for a combined total of 15 hours, and together they charged a total of $1075. How long did each mechanic work?
The first mechanic worked for 10 hours and second mechanic worked for 5 hours.
Given,
Price of first mechanic service =$85/hr
Price of second mechanic service=$45/hr
Total time they worked together=15 hours
Total combined price charged=$1075
Let
Time spend by first mechanic on work =x
Time spend by second mechanic on work =y
Price charged by first mechanic on total work =85x
Price charged by second mechanic on total work=45y
Equation for total time spend by them together on work can be written as,
[tex]x+y=15.....i\\\\y=15-x[/tex]
Equation for total price charged by them can be written as,
[tex]85x+45y=1075\\[/tex]
Substituting y,
[tex]85x+45(15-x)=1075\\\\85x+675-45x=1075\\\\40x+675=1075\\\\40x=1075-675\\\\40x=400\\\\x=10\\[/tex]
Substituting x in eq.[tex]i[/tex],
[tex]10+y=15\\\\y=15-10\\\\y=5[/tex]
Hence, the first mechanic worked for 10 hours and second mechanic worked for 5 hours.
To learn more about work and time refer here
https://brainly.com/question/3578188
#SPJ9
the graph of f(x)=x^3+3x^2-4 is shown. what is the value of f^-1(-4)
Since the function is not one-to-one, the inverse function of f(x) = x³ + 3x² - 4 is not defined at x = -4.
How to obtain the numeric value of the inverse function?An original function is composed by a set of points in the following format:
(x,y).
On the graph of the function, we have that:
The x-coordinate represents the input of the function, being the horizontal axis of the graph.The y-coordinate represents the output of the function, being the vertical axis of the graph.On the inverse function, the input and the output are exchanged, hence the format of the point is:
(y,x).
To find the numeric value of the inverse function at x = -4, we need to identify the value of x on the original function where y = -4.
However, looking at the graph of the function given at the end of the answer, the function is not one-to-one at y = -4, since f(-3) = f(0) = 4, thus the inverse function is not defined at x = -4.
More can be learned about inverse functions at brainly.com/question/11735394
#SPJ1
Line b passes through the point (4, 2) and is
perpendicular
to the x-axis. What is the slope of line b?
Answer:
The slope would be undefined
Step-by-step explanation:
If the slope is perpendicular to the x-axis that means it is vertical, all vertical lines have undefined slopes therefore the slope is undefined.
What is 3 inches above average written as an integer
The integer +3 describes the statement, 3 inches above average.
What is an average?
A single number chosen to represent a group of numbers is called an average, and it is typically calculated by dividing the total number of numbers in the group by the number of numbers in the group. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.
One point in the average refers to the amount of 1 inch.
If the average is above 3 inches, it means that the value of the average is above 3 inches. It further implies that the total value has gained 3 inches on that average.
Inches mainly describe the gains and losses in short-time investments. A positive sign (+) shows the above average, and a negative sign (-) represents the below average.
Therefore, the integer +3 describes the statement, 3 inches above average.
To learn more about the average visit,
https://brainly.com/question/20118982
#SPJ9
A denim shirt at a certain factory requires 2 1/5 yards of material. How many shirts can be made from 70 2/5 yards of material?
Answer: 32
Step-by-step explanation:
If you multiply 2 1/5 by 35 you would get 70.4, .4 is equivalent to 2/5, so 70.4 = 70 2/5.
How many solutions does the equation have?
12x + 6 = 14(2x – 24) because when simplified we get?
a) 6=-6
a) infinitely many solutions
b) x=-6
b) one solution
c) 6=6
c) no solution
Answer:
One solution: x =21.6
Step-by-step explanation:
Equation
12x + 6 = 14(2x – 24) Remove the brackets
Solution
12x + 6 = 28x - 336 Add 336 to both sides.
12x + 6+336 = 28x - 336 Combine
12x + 342 = 28x -336+336
12x + 342 = 28x Subtract 12x from both sides.
12x-12x + 342 = 28x - 12x Combine
342 = 16x Divide by 16
342/16 = 16x/16
21.6=x
Please Help 25 points
stu took a test. There were 60 questions. He answered 35 correctly. What grade did Stu make
Answer:
58%
Step-by-step explanation:
35/60=0.58333=58/100=58%
a.) find the test statistic
b.) what is the p-value
c.)what is the conclusion about the null hypothesis
d.) what is the final conclusion?
Regarding the hypothesis tested in this problem, it is found that:
a) The test statistic is: t = 0.49.
b) The p-value is: 0.6297..
c) The null hypothesis is not rejected, as the p-value is greater than the significance level.
d) It appears that the students are legitimately good at estimating one minute, as the sample does not give enough evidence to reject the null hypothesis.
What is the test statistic?The test statistic of the t-distribution is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the variables of the equation are given as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the hypotheses.s is the standard deviation of the sample.n is the sample size.The value tested at the hypothesis is:
[tex]\mu = 60[/tex]
From the sample, using a calculator, the other parameters are given as follows:
[tex]\overline{x} = 62.47, s = 19.2, n = 15[/tex]
Hence the test statistic is obtained as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{62.47 - 60}{\frac{19.2}{\sqrt{15}}}[/tex]
t = 0.49.
What are the p-value and the conclusion?The p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, in this case 60, with:
15 - 1 = 14 df, as the number of degrees of freedom is one less than the sample size.t = 0.49, as obtained above.Hence the p-value is of 0.6297.
Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected, attesting to the ability of the students to estimate one minute.
More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
#SPJ1
For all real values of x if f((x)=(x-3)^2 and g(x)=(x+3)^2 what is f(x)-g(x)?
The composition f(x) - g(x) has its value to be 12x
How to evaluate the composite function?The definitions of the functions are given as
f(x) = (x - 3)²
Also, we have the definition of another functions to be given as
g(x) = (x + 3)²
To find the composition f(x) - g(x), we make use of the following equation
f(x) - g(x) = f(x) - g(x)
So, we have the following equation
f(x) - g(x) = f(x) - g(x)
Substitute the known values in the above equation
So, we have the following equation
f(x) - g(x) = (x + 3)² - (x - 3)²
Apply the differece of two squares rules
So, we have
f(x) - g(x) = (x + 3 + x - 3)(x + 3 - x + 3)
So, we have
f(x) - g(x) = (2x)(6)
This gives
f(x) - g(x) = 12x
Hence, the value of the composition is f(x) - g(x) = 12x
Read more about composite functions at
brainly.com/question/10687170
#SPJ1
I know this is easy for some, but I have no idea what happened here. Can someone explain to me? These are congruent triangles.
8x -13 = 5x + 17
3x = 30
x = 10
The x value we get is 10 when the sides are 8x-13 and 5x+17 in a congruent triangle.
Given that,
The sides as 8x-13 and 5x+17
We have to find the x value.
If two or more triangles are congruent, it depends on how big their sides and angles are. The three sides and three angles of a triangle determine its size and shape, accordingly. Two triangles are said to be congruent if the pairings of respective sides and corresponding angles are equal.
We say now,
8x-13 = 5x+17
8x-5x=17+13
3x=30
x=30/3
x=10
Therefore, The x value we get is 10 when the sides are 8x-13 and 5x+17 in a congruent triangle.
To learn more about triangles visit: https://brainly.com/question/2773823
#SPJ9
Drag the tiles to the correct boxes to complete the pairs.
Determine whether each pair of lines is perpendicular, parallel, or neither.
2y = 4x + 4
y=-2x-2
4y= 2x - 4
y=-2x+9
Perpendicular
Parallel
y = 2x+4
2y = 4x - 7
Neither
Answer:
neitherperpendicularparallelStep-by-step explanation:
You want to know whether the pairs of equations describe lines that are parallel, perpendicular, or neither.
ParallelParallel lines have the same slope. When the equations are written in slope-intercept form, the coefficients of x are identical.
PerpendicularPerpendicular lines have opposite reciprocal slopes. When the equations are written in slope-intercept form, the product of the x-coefficients is -1.
Application1. 2y = 4x +4; y = -2x -2Solving the first equation for y gives ...
y = 2x +2
The x-coefficients are 2 and -2, so the lines are neither parallel nor perpendicular.
2. 4y = 2x -4; y = -2x +9Solving the first equation for y gives ...
y = 2/4x -1 = 1/2x -1
The x-coefficients are 1/2 and -2, which have a product of -1. These lines are perpendicular.
3. y = 2x +4; 2y = 4x -7Solving the second equation for y gives ...
y = 2x -7/2
The x-coefficients are 2 and 2, which are identical. These lines are parallel.
2x + 4y = 4
number of solution
Given equation 2x + 4y = 4 has infinitely many solutions.
We have been given an equation 2x + 4y = 4
We need to find the number of solutions.
Above equation is a linear equation with two variables.
We know that, a linear equation in two variables has infinitely many solutions.
For any value real value of x we can find corresponding value of y.
Since x can takes infinitely many inputs the output would be infinitely many.
Therefore, given equation 2x + 4y = 4 has infinitely many solutions.
Learn more about an equation here:
https://brainly.com/question/649785
#SPJ9
Write a coordinate rule for the composition 
Answer:
so basically u do that and then u do that and then
Step-by-step explanation:
8
In a raffle, 100 tickets are sold. George buys 10 tickets Julia by 5 tickets. There is one winning ticket. Find a probability that
a. George will win
b. jullia will win
Probability of (a) George winning is 0.1
(b) Julia winning is 0.05
Given in question,
Total ticket sold = 100
George bought tickets = 10
Julia bought tickets = 5
Winning ticket = 1
Selecting 1 ticket from 100 = [tex]\left[\begin{array}{ccc}100\\1\\\end{array}\right][/tex]
= 100
Selecting 1 ticket from 10 = [tex]\left[\begin{array}{ccc}10\\1\\\end{array}\right][/tex]
= 10
Selecting 1 ticket from 5 = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
= 5
Probability = favorable outcome/total outcome
Probability of George winning = [tex]\frac{10}{100}[/tex]
= 0.1
Probability of Julia winning = [tex]\frac{5}{100}[/tex]
= 0.05
Hence, probabilities are 0.1 and 0.05 respectively.
To learn more about Probability here:
https://brainly.com/question/11234923
#SPJ1
What is 804082 written in expanded form
Answer:
Step-by-step explanation:
(8 x 100000) + (0 x 10000) + (4 x 1000) + (0 x 100) + (8 x 10) + (2 x 1) = 804082
At 2 hours before sunset, the temperature is 0°F. At 2 hours after sunset, the temperature is −4°F. Identify the equation representing the temperature y, in degrees Fahrenheit, at x hours after sunset
The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;
⇒ y = - 4°x + 0°
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
At 2 hours before sunset, the temperature is 0°F.
And, At 2 hours after sunset, the temperature is −4°F.
Now,
Let the temperature in degrees Fahrenheit = y
So, We can formulate;
⇒ y = - 4°x + 0°
Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;
⇒ y = - 4°x + 0°
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
This is a statistics/applications question
Using percentages, the answer to all the subparts are shown:
(A) % who scored between 46 and 106: 67% approx(B) % who scored less than 46: 17% approx(C) % who scored between 61 and 91: 33% approx(D) % who scored between 76 and 121: 50%What are percentages?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, calculate the percentages as follows:
(A) % who scored between 46 and 106:
Total marks: 121 - 30 = 90Students between 46 and 106: 106 - 46 = 60Then,
60/90 × 1002/3 × 10066.66Rounding off: 67% approx
(B) % who scored less than 46:
Total marks: 121 - 30 = 90Students who scored less than 46: 46 - 31 = 15Then,
15/90 × 10016.66Rounding off: 17% approx
(C) % who scored between 61 and 91:
Total marks: 121 - 30 = 90Students between 61 and 91: 91 - 61 = 30Then,
30/90 × 1001/3 × 10066.6633.33Rounding off: 33% approx
(D) % who scored between 76 and 121:
Total marks: 121 - 30 = 90Students between 76 and 121: 121 - 76 = 45Then,
45/90 × 10050%
Therefore, using percentages, the answer to all the subparts are shown:
Know more about percentages here:
https://brainly.com/question/9553743
#SPJ13
use the distributive property to solve the equation 2x - 4(x - 2) = - 8 + 4x + 4