Answer:
Length of the sides of the base (x) = 7.606 ft
Height (h) = 3.802 ft
The minimum surface area is 173.55 ft²
Step-by-step explanation:
Surface area is given by:
[tex]S(x) = x^2+\frac{880}{x}[/tex]
The value of x for which the derivate of the surface area function is zero, is the length of the sides of the base that minimizes surface area:
[tex]S(x) = x^2+\frac{880}{x} \\\frac{dS(x)}{dx}=0=2x-\frac{880}{x^2}\\x^3=440\\x=7.606\ ft[/tex]
The height of the box is given by:
[tex]V=hx^2\\220 =h*7.606^2\\h=3.802\ ft[/tex]
The dimensions of the box with minimum surface area are:
Length of the sides of the base (x) = 7.606 ft
Height (h) = 3.802 ft
The absolute minimum is:
[tex]S(x) = 7.606^2+\frac{880}{7.606}\\S_{min}=173.55\ ft^2[/tex]
The minimum surface area is 173.55 ft²
Answer:
The absolute minimum of the surface area[tex]=173.55$ ft^2[/tex]
At the minimum surface area,
Base length=7.61 feetHeight of 3.8 feet.Step-by-step explanation:
Volume of the box =220 cubic feet.
[tex]\text{Surface Area, } S(x)=x^2+\dfrac{880}{x}[/tex]
To find the absolute minimum of the surface area function on the interval [tex](0,\infty)[/tex], we take the derivative of S(x) and solve for its critical points.
[tex]S(x)=\dfrac{x^3+880}{x}\\S'(x)=\dfrac{2x^3-880}{x^2}\\$Setting the derivative equal to 0\\S'(x)=\dfrac{2x^3-880}{x^2}=0\\2x^3-880=0\\2x^3=880\\$Divide both sides by 2\\x^3=440[/tex]
Take the cube root of both sides
[tex]x=\sqrt[3]{440}\\ x=7.61$ ft[/tex]
Therefore, the absolute minimum of the surface area function on the interval [tex](0,\infty)[/tex], is:
[tex]S(x)=\dfrac{7.61^3+880}{7.61}\\\\=173.55$ ft^2[/tex]
Since the volume of the box =220 cubic feet
[tex]V=x^2h\\220=7.61^2 \times h\\h=220 \div 7.61^2\\h=3.80 ft[/tex]
The dimensions of the box with the minimum surface area are base length of 7.61 feet and height of 3.8 feet.
The given equation has been solved in the table. In which step was the subtraction property of equality applied?
Answer:
Option (D)
Step-by-step explanation:
Subtraction property of equality tells that whatever subtracted from one side of the equation must be subtracted from the other side.
If x + 2 = 2,
By the property of subtraction of equality,
x + 2 - 2 = 2 - 2
x = 0
But in the given question,
[tex]\frac{x}{2}-7=-7[/tex]
[tex]\frac{x}{2}-7+7=-7+7[/tex]
shows the addition property of equality in step (2)
Therefore, subtraction property of equality was not applied.
Option (D) will be the answer.
Please help me and my daughter.
Answer:
you can either factorise or use tge formula method
Step-by-step explanation:
3x2−7x−20=03x2-7x-20=0
Use the quadratic formula to find the solutions.
−b±√b2−4(ac)2a-b±b2-4(ac)2a
Substitute the values a=3a=3, b=−7b=-7, and c=−20c=-20 into the quadratic formula and solve for xx.
7±√(−7)2−4⋅(3⋅−20)2⋅37±(-7)2-4⋅(3⋅-20)2⋅3
Simplify.
Tap for more steps...
x=7±176x=7±176
The final answer is the combination of both solutions.
x=4,−53
what is the y-intersept of y=4x-6
━━━━━━━☆☆━━━━━━━
▹ Answer
y-intercept = -6
▹ Step-by-Step Explanation
The format of slope is:
y = mx + b
The b represents the y-intercept which is, -6.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer: -6
Step-by-step explanation: This equation is written in slope-intercept form which is more commonly known as y = mx + b form where the multiplier or the coefficient of the x term represents the slope of the line and the b or the constant term represents the y-intercept.
So this line has a y-intercept of -6.
This means it crosses the y-axis 6 units up from origin.
A Japanese garden has a circular koi pond in the middle that has a radius of 3 feet. A rectangle with length of 16 feet and width of 14 feet. A circle with radius 3 feet is cut out of the rectangle. What is the area of the Japanese garden around the koi pond? Use 3.14 for Pi. 195.74 feet squared 224.00 feet squared 252.26 feet squared 337.04 feet squared
Answer:
first, find the area of the circle cut.
r= 3 feet
π=3.14
area of a circle= πr²= 3.14×3×3= 28.26 sq.feet
Now, find the area of the rectangle and subtract it by the area of the circle.
area of rectangle = l×b
length of the rectangle= 16 feet
breadth/width of the rectangular garden= 14 feet
area= 16×14= 224 sq. feet
now, area of the garden surrounding the koi pond= 224-28.26
=195.74 sq. feet
Answer:
A. 195.74
Step-by-step explanation:
Edge2020
xpress 8/(1 - 2x)2 as a power series by differentiating the equation below. What is the radius of convergence? 4 (1 - 2x) = 4(1 + 2x + 4x2 + 8x3 + ...) = 4 [infinity] Σ n=0 (2x)n SOLUTION Differentiating each side of the equation, we get 8 (1 - 2x)2 = 4(2 + Correct: Your answer is correct. + 24x2 + ...) = 4 [infinity] Σ n=1 Incorrect: Your answer is incorrect. If we wish, we can replace
Recall that for |x| < 1, we have
[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
Replace x with 2x, multiply 4, and call this function f :
[tex]f(x)=\dfrac4{1-2x}=\displaystyle4\sum_{n=0}^\infty(2x)^n[/tex]
Take the derivative:
[tex]f'(x)=\dfrac8{(1-2x)^2}=\displaystyle8\sum_{n=0}^\infty n(2x)^{n-1}=\boxed{8\sum_{n=0}^\infty (n+1)(2x)^n}[/tex]
By the ratio test, the series converges for
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)(2x)^{n+1}}{(n+1)(2x)^n}\right|=|2x|\lim_{n\to\infty}\frac{n+2}{n+1}=|2x|<1[/tex]
or |x| < 1/2, so the radius of convergence is 1/2.
Copy the diagram and calculate the sizes of x°, yº and zº. What is the sum of the angles of the
triangle?
Answer:
180
Step-by-step explanation:
to find angle :
x =180 - 150=30
y =180-80=100
z = 180-130=50
so, 30+50+100=180
Hurrryy plzzz!!
Which linear inequality is represented by the graph?
y<1/2x+2
y>1/2x+2
y<1/3x+2
y>1/3x+2
In math list the angles in order from smallest to the largest
Answer:
A) S,T,R
Step-by-step explanation:
Write an equation:
For every 2 apples there
are 6 bananas
Answer:
[tex]2a=6b\\a=3b[/tex]
Step-by-step explanation:
Let [tex]a[/tex] equal the amount of apples and [tex]b[/tex] equal the amount of bananas.
[tex]2a=6b\\a=3b[/tex]
Answer:
every 2 apples there
are 6 bananas
Step-by-step explanation:
2a=6b
What is the measure of
Answer:
C. 35
55 degrees + 35 degrees= 90 degrees
Which of the following is equal to 7 1/3
You add 7 to 1/3 and that gives 22/3
Herschel uses an app on his smartphone to keep track of his daily calories from meals. One day his calories from breakfast were more than his calories from lunch, and his calories from dinner were less than twice his calories from lunch. If his total caloric intake from meals was , determine his calories for each meal.
Answer:
let the number of calories from lunch be called L. As such, breakfast is then L + 128, and dinner is 2L - 400. We can then sum the three meals and equate it to the total caloric intake, the known value of 1932.
So: 1932 = L + L + 128 + 2L - 400 = 4L - 272.
Lunch = 551
Breakfast = 551 + 128 = 679
Dinner = 2*551 - 400 = 702
Hello, can someone help me with this problem?
Answer:
Area of Rectangle A
[tex]Area = 4x^2[/tex]
Area of Rectangle B
[tex]Area = 2x^2[/tex]
Fraction
[tex]Fraction =\frac{2}{3}[/tex]
Step-by-step explanation:
From the attached, we understand that:
The dimension of rectangle A is 2x by 2x
The dimension of rectangle B is x by 2x
Area of rectangle is calculated as thus;
[tex]Area = Length * Breadth[/tex]
Area of Rectangle A
[tex]Area = 2x * 2x[/tex]
[tex]Area = 4x^2[/tex]
Area of Rectangle B
[tex]Area = x * 2x[/tex]
[tex]Area = 2x^2[/tex]
Area of Big Rectangle
The largest rectangle is formed by merging the two rectangles together;
The dimension are 3x by 2x
The Area is as follows
[tex]Area = 2x * 3x[/tex]
[tex]Area = 6x^2[/tex]
The fraction of rectangle A in relation to the largest rectangle is calculated by dividing area of rectangle A by area of the largest rectangle;
[tex]Fraction = \frac{Rectangle\ A}{Biggest}[/tex]
[tex]Fraction =\frac{4x^2}{6x^2}[/tex]
Simplify
[tex]Fraction =\frac{2x^2 * 2}{2x^2 * 3}[/tex]
[tex]Fraction =\frac{2}{3}[/tex]
12
12
Francis Bacon and his wife purchased a condominium on the beach for $235,000.
They made a $40,000 down payment. Their annual expenses were mortgage
interest of $11,700, depreciation of 3% of the purchase price of the house, and
taxes, repairs, and insurance of $15,430. They rented the condo for $3,000 per
month. What is the annual yield?
(A) 1.52%
(C) 3.62%
(B) 2.55%
(D) 4.55%
Answer:
D) 4.55%
Step-by-step explanation:
Given:
Rented Income = $3000 per month
= $3000 * 12 = $36,000 annually
Less : - Annual expenses = $11700
Depreciation(3% OF 235000) = $7050
Tax, repairs and Insurance = 15430
Annual net income = $36,000 - ($11,700+$7,050+$15,430)
= $36,000 - $34,180
Annual net income = $1,820
To find annual yield, use the formula below:
Annual yield = (annual net income/down payment) * 100
Therefore, annual yield will be:
Annual yield [tex] = \frac{1,820}{40,000} * 100 [/tex]
= 0.0455 * 100
= 4.55%
Annual yield = 4.55%
What is the equation of BD, simplified?
Third option is the correct answer.
Answer:
[tex] y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg][/tex]
Step-by-step explanation:
[tex]y - y_1 = m(x - x_1) \\ \\ y - 0 = \bigg[ \frac{2b}{(2a - c)} \bigg] (x - c) \\ \\ y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2b}{(2a - c)} \bigg]c \\ \\ \purple { \boxed{ \bold{y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg]}}} \\ [/tex]
Basic factoring. Please help!
Answer:
-1(3 - y)
Step-by-step explanation:
If you factor out a negative 1, you will get the opposite signs you already have, so -1(3 - y). To check, we can simply distribute again:
-3 + y
So our answer is 2nd Choice.
1. Write down a pair of integers
(a) sum is -7
Answer:
-10, 3
Step-by-step explanation:
-10, 3 work since
-10 + 3 = -7
Which of the following is the equation of the quadratic function below?
A. y = x2 - 2x+2
B. y = x +2x-2
C. y = x2 - 8x+12
D. y = x2 +8x-12
help asap!! will get branliest.
Answer:
C
Step-by-step explanation:
A reflection is when the original diagram or picture is fliped exactly over the x axis.
HEYA!!
Answer:
Your Answer of the Question is C
if you want to prove it you can do the same thing in real life by drawing a 'W' on a paper and see its reflection on the mirror
HOPE IT MATCHES!!
Suppose that the number of square feet per house are normally distributed with an unknown mean and standard deviation. A random sample of 22 houses is taken and gives a sample mean of 1500 square feet and a sample standard deviation of 151 square feet. 1. The EBM, margin of error, for a 95% confidence interval estimate for the population mean using the Student's t. distribution is 66.96.2. Find a 95% confidence interval estimate for the population mean using the Student's t-distribution.
Answer:
1. The margin of error is of 66.96 square feet.
2. The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet
Step-by-step explanation:
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 = 22 - 1 = 21
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.08
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.08*\frac{151}{\sqrt{22}} = 66.96[/tex]
In which s is the standard deviation of the sample.
The margin of error is of 66.96 square feet.
The lower end of the interval is the sample mean subtracted by M. So it is 1500 - 66.96 = 1433.04 square feet
The upper end of the interval is the sample mean added to M. So it is 1500 + 314 = 1566.96 square feet
The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet
which of these is a ratio table?
Answer:
The last graph.
Step-by-step explanation:
The last graph is the only one that has a constant pattern that can have a rule, which is every number is multiplied by two.
Hope this helped ! good luck :)
Determine the function which corresponds to the given graph. (3 points) a natural logarithmic function crossing the x axis at negative two and y axis at one.
The asymptote is x = -3.
Answer:
[tex]y =log_e(x+3)[/tex]
Step-by-step explanation:
It is given that the graph corresponds to a natural logarithmic function.
That means, the function [tex]y[/tex] has a natural log (Log with base [tex]e[/tex]) of some terms of x.
It is given that asymptote of given curve is at [tex]x= -3[/tex]. i.e. when we put value
[tex]x= -3[/tex], the function will have a value [tex]y \rightarrow \infty[/tex].
We know that natural log of 0 is not defined.
So, we can say the following:
[tex]log_e(x+a)[/tex] is not defined at [tex]x= -3[/tex]
[tex]\Rightarrow x+a =0\\\Rightarrow x = -a[/tex]
i.e. [tex]x =-a[/tex] is the point where [tex]y \rightarrow \infty[/tex]
a = 3
Hence, the function becomes:
[tex]y =log_e(x+3)[/tex]
Also, given that the graph crosses x axis at x = -2
When we put x = -2 in the function:
[tex]y =log_e(-2+3) = log_e(1) = 0[/tex]
And y axis at 1.
Put x = 0, we should get y = 1
[tex]y =log_e(0+3) = log_e(3) \approx 1[/tex]
So, the function is: [tex]y =log_e(x+3)[/tex]
The inclination (tilt) of an amusement park ride is accelerating at a rate of 2160 degreesmin22160\,\dfrac{\text{degrees}}{\text{min}^2} 2160 min 2 degrees 2160, start fraction, start text, d, e, g, r, e, e, s, end text, divided by, start text, m, i, n, end text, squared, end fraction . What is the ride's acceleration rate in degreess2\dfrac{\text{degrees}}{\text{s}^2} s 2 degrees start fraction, start text, d, e, g, r, e, e, s, end text, divided by, start text, s, end text, squared, end fraction ? degreess2\dfrac{\text{degrees}}{\text{s}^2} s 2 degrees
Answer:
um
Step-by-step explanation:
not sure sorry
In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,075 and a standard deviation of $300. The distribution of the monthly rent does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 55 one-bedroom apartments and finding the mean to be at least $1,985 per month
Answer:
Probability is 1
Step-by-step explanation:
We are given;
mean;μ = $2,075
Standard deviation;σ = $300
n = 55
x' = $1,985
Now, we want to find x' to be at least $1,985 which is P(x' > $1,985).
The z-value is calculated from;
z = (x' - μ)/(√σ/n)
Plugging in the relevant values;
z = (1985 - 2075)/(√300/55)
z = -38.536
So, P(x' > $1,985) = P(z > -38.536)
This transforms to;
P(z < 38.536)
Probability from z distribution table is 1
Population of town was 21000 in 1980 and it was 20000 in 1990. Assuming the population is decreasing continuously at a rate proportion to the existing population, estimate the population in 2010.
Answer:
19,000
Step-by-step explanation:
Here, we are to estimate the population in the year 2010
From the question, we can see that within a period of a decade which is 10 years, 1000 was lost
So within the period of another decade, it is possible that another 1000 be lost
The estimated population in the year 2010 is thus 20,000 - 1,000 =
19,000
Find the lateral area of the prism. Use the 10 by 6 rectangle as the base.
5 ft
6 ft
9 ft
Answer:
lateral area =150 square feet
Step-by-step explanation:
lateral area =(perimieter of prism base) times the height of the prism
so, the perimeter of the base is 9 ft*2 + 6 ft*2 which equals 30 ft
then you multiply the perimeter of the base by the height of the prism
so, height of prism =5 ft, so 5 ft times 30 ft =150 feet
therefor, the lateral area of the prism = 150 feet squared
13 lb 14oz + 30 lb 12 oz = lb. oz
Answer:
33 lbs 10 ounces
Step-by-step explanation:
13 lb 14oz
+ 30 lb 12 oz
================
32 lbs 26 oz
But we know that 16 ounces 1 1 lb
Subtract 16 ounces and add 1 lb
32 lbs 26 oz
+1 lb - 16 ounces
==================
33 lbs 10 ounces
If bis the unknown number of blankets, which equation best represents the
situation described below?
Ling gave some of her blankets to charity, decreasing her
total number of blankets by 9. After she gave the blankets
away, she had 11 left.
A. 6-9 = 11
B. 6+9 = 11
C.
= 11
D. b +11 = 9
Answer:
A. b-9=11
Step-by-step explanation:
I‘m assuming the equation should say b, not 6. She had b blankets, subtracted 9, and was left with 11. b-9=11.
find the common ratio of the geometric sequence: 16/3,4,3,…
Answer:
3/4
Step-by-step explanation:
r= a3/a2=3/4
or
r= a2/a1= 4÷16/3= 4×3/16= 3/4
Please answer this correctly
Answer:
100%
Step-by-step explanation:
The numbers odd or greater than 1 are 1, 2, 3, 4, 5, and 6.
6 numbers out of 6.
6/6 = 1.
P(odd or greater than 1) = 100%
Answer:
100%
Step-by-step explanation:
So the original fraction is 6/6 because is is odd and 3 and 5 also 2,4,6 are all more than 1.