the dimensions of the box that minimize the amount of material used is 4.641cm by 4.641cm by 2.32cm
Let the side of the square base be x
h be the height of the box
Volume V = x²h
50 = x²h
h = 50/x² ..... 1
Surface area = x² + 2xh + 2xh
Surface area S = x² + 4xh ...... 2
Substitute 1 into 2;
From 2; S = x² + 4xh
S = x² + 4x(50/x²)
S = x² + 200/x
To minimize the amount of material used; dS/dx = 0
dS/dx = 2x - 200/x²
0 = 2x - 200/x²
0 = 2x³ - 200
2x³ = 200
x³ = 100
x = ∛100
x = 4.6416cm
Since V = x²h
50 = 4.642²h
h = 50/21.548
h = 2.32cm
Hence the dimensions of the box that minimize the amount of material used is 4.641cm by 4.641cm by 2.32cm
learn more about of volume here
https://brainly.com/question/19494124
#SPJ4
Simple Interest Round answers to the nearest cent. 1. John is going to invest $100 in an account for 3 years. If the account earns 6% simple interest, how much interest can he expect to earn?
Given Data:
The initial investment is: P=$100
The total period of investment is: t=3
The annual interest is: 6%.
For the simple interest, the expression to calculate the interest in t years is,
[tex]I=(P\times\frac{r}{100})\times t[/tex]Here r is in percentage.
Substitute known values in the above expression.
[tex]\begin{gathered} I=(100\times\frac{6}{100})\times3 \\ =(6)\times3 \\ =18 \end{gathered}[/tex]Thus, the total intrest for 3 years will be $18.
Solve for x in the triangle. Round your answer to the nearest tenth.
20
X
52°
X =
Miranda did a survey of what time people
get to their office on Monday morning.
The table shows her results for
150 people.
Time
before 7 am
7am to 7:59 am
8am to 8:59 am
9am to 9:59 am
No of people
15
39
75
21
a) What percentage of the people surveyed arrive at their office before 7 am?
Optional working
+
Answer:
b) What percentage of the people surveyed arrive at their office after 7:59 am?
Optional working
Answer:
%
The percentage of the people surveyed that arrive at their office after 7am is 6.7%.
The percentage of the people surveyed that arrive at their office after 7:59 am is 64%
How to calculate the percentage?From the information, Miranda did a survey of what time people get to their office on Monday morning and the table shows her results.
The number of people that arrived before 7.59am is 15.
The total number of people surveyed will be:
= 15 + 39 + 75 + 21
= 150
The percentage of the people surveyed arrive at their office before 7 am will be:
= 10 / 150
= 6.7%
The percentage of the people surveyed that arrive at their office after 7:59 am will be:
= (75 + 21) / 150.
= 96/150
= 0.64
= 64%
Learn more about percentages on:
brainly.com/question/24877689
#SPJ1
Answer:
the number of people is 15 so you would do 15/150=10percent
b) 66 percent
Step-by-step explanation:
The points (5, r) and (10, -1) lie on a line with slope 5. Find the missing coordinate r
Answer: r=-26
Step-by-step explanation:
[tex]\displaystyle\\(5,r)\ \ \ \ (10,1)\ \ \ \ slope \ m=5\\\\\boxed {m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=5\ \ \ \ \ x_2=10\ \ \ \ \ y_1=r\ \ \ \ y_2=-1\ \ \ \ \ m=5\\\\Hence,\\\\5=\frac{-1-r}{10-5} \\\\5=\frac{-1-r}{5}[/tex]
Multiply both parts of the equation by 5:
[tex]5(5)=-1-r\\\\25=-1-r\\\\25+r=-1-r+r\\\\25+r=-1\\\\25+r-25=-1-25\\\\r=-26[/tex]
Jenn is baking 80 pumpkin spice cookies for a fundraiser. She gets ready to start cutting out cookies at 3:30pm, first rolling out the dough and getting her cookiecutters ready. At 3:38pm she has 12 cookies cut out. By 3:40pm, she has 20 cookies cut out. If she cuts out cookies at a constant rate, when will she be finished cutting out the 80 cookies?
Answer: 4:30
Step-by-step explanation:
Answer:
oh palak cl NC do off is sold em Ms do off do off dlc so off do off sum is sold arrowroot
The concession stand are the football games are 288 customers. Those customers, about 77% bought a hot dog. About how many customers buy a hotdog?
WILL GIVE BRAINLIEST PLS HELP SOLVE
Answer:
The equation is:
y = -3x + 3
Directions: Find the slope between
1. (-8, 18) and (-14, -3)
Answer: The slope of (-8, 18) and (-14, -3) would be 3.5.
Step-by-step explanation: By using a simple calculator, specifically the TI-84 Plus CE, you can put the points you mentioned in stat and it’ll give you an equation based on those points. The equation I got was y = 3.5x + 46. The number attached to the X is your slope.
What number is 40% of 120?
Answer: 48
Step-by-step explanation:
Convert 40% to a decimal = 0.4
Multiply 0.4 x 120 = 48
Answer:
48
Step-by-step explanation:
40\100×120
=48
( fourth divided by one hundred multiplied by one hundred and twenty is equal to 48)
A rancher is filling a trough for her horses. The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. How long will it take for the trough to have 80 gallons of water?
The equation which is useful to find the amount in gallons of water to the number of minutes since filling started is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
The amount of water initially in the trough = 25 gallons.
The rate of adding water = 11 gallons per minute
Therefore, the total amount (A) of water in x minutes will be,
A = 25 + 11x
The number of minutes to have 80 gallons of water is,
80 = 25 + 11x
11x = 55
x = 5 minutes.
Hence "The equation which is useful to find the amount in gallons of water to the number of minutes since filling started is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water".
For more about the equation,
https://brainly.com/question/10413253
#SPJ1
f(x) = 2x - 3
g(x) = 3x - 1
Find (f g)(x).
6x² + 3
6x³-11x² + 3x
6x² - 11x +3
6x² - 7x +3
Answer:
6x^2 - 11x + 3
Step-by-step explanation:
(fg)(x) is just multiplying f(x) and g(x)
This gives: (2x-3)(3x-1) = 6x^2 - 2x -9x - (3*(-1)) = 6x^2 -11x + 3
Write the fraction 622/1000 in its simplest form
Answer:
311/55
Step-by-step explanation:
i devided each by 2 and got this then i looked it up and it said this so id k
hope this helped
A perfect score on a test with 25 questions is 100. Each question is worth 4 points. Fred got a score of 68 on the test to write a division sentence using negative numbers where the quotient represents the number of questions Fred answered incorrectly
The total number of questions that Fred answered incorrectly is 8.
How to express the information?From the information given, a perfect score on a test with 25 questions is 100 and each question is worth 4 points while Fred got a score of 68 on the test.
Therefore, let the number of questions that are got be x.
Based on the information given, this will be:
4 × x = 68
4x = 68
Divide
x = 68 / 4 = 17
The number of questions that he missed will be:
= Total questions - Correct answers.
= 25 - 17.
= 8
Learn more about division on:
brainly.com/question/25289437
#SPJ1
A Curve has the equation y=kx^2 +1 And a line has the equation y=kx where
K is a
non-zero
Constant
1)Find the Set
the value of k
for which the
curve and line have no common point.
(1) state the value for which the line is a
tangent to the Curve and for this case, find the coordinates
of the point where the line
touches the curves
The set of the value for which the curve and line have no common point are is k ∈ (0 , 4).
The value for which the line is a tangent is k = 4.
The coordinates of the point where the line touches the curves is point of tangency = ( 1/2 , 2).
What is tangent?
Tangents in geometry are lines or planes that contact curves or surfaces at points where they are closer to the curve than any other lines or planes drawn through those points.
Given equations in the question:
y = kx² + 1
y = kx
Equating y
kx² + 1 = kx
kx² -kx + 1 = 0
This is Quadratic equation is of the form ax²+bx+c=0 where a , b and c are real also a≠0.
D = b²-4ac is called discriminant.
and we know that,
D >0 roots are real and distinct
D =0 roots are real and equal
D < 0 roots are imaginary ( not real ) and different
For no common solution D < 0
For tangent D = 0
so,
kx² -kx + 1 = 0
D = (-k)² - 4k = k² - 4k = k(k - 4)
k(k - 4) < 0
if 0 < k < 4
Hence values of k for which the curve and the line have no common points is k ∈ (0 , 4).
for tangent
k(k - 4) = 0
k is non zero
Hence k = 4
After putting the value of k, given equations are:
y = 4x² + 1
y = 4x
solving these equations to get value of x and y:
4x² + 1 = 4x
4x² - 4x + 1 = 0
(2x - 1)² = 0
x = 1/2
y = 2
Point of tangency = ( 1/2 , 2)
To know more about tangent, go to link
https://brainly.com/question/4470346
#SPJ9
Three sisters each bought 3 pairs of shoes and a dress the dress cost 45.50 if the total cost of the bill was 352.50 how much did a pair of shoes cost
A pair of shoes cost 102.23
Arithmetic: Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. The basic operations of math are addition, subtraction, multiplication and division. Also called higher arithmetic, theoretical arithmetic.
Cost of 3 pairs of shoes and a dress = 352.50
Cost of dress = 45.50
Cost of 3 pairs of shoes = Cost of 3 pairs of shoes and a dress - the cost of dress = 352.20 - 45.50
= 306.7
So, the cost of each pair of shoes will be = Cost of 3 pairs of shoes/Number of pairs bought
= 306.7/3
= 102.23
Learn more about arithmetic:
#SPJ1
need someone to answer as soon as possible!
Please please with proof too
The solutions to the system of equations are x=5, z=1,y=-3
What is system of equations?
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where each of these equations crosses, are the solutions of systems of equations.A system of equations in algebra consists of two maybe more equations and looks for common answers to the equations.Given equations:
x+y+z=3
3x+(y/3)-2z=12
-5x-6y+3z=-4
Solving by using the substitution method:
[tex]\begin{bmatrix}x+y+z=3\\ 3x+\left(\frac{y}{3}\right)-2z=12\\ -5x-6y+3z=-4\end{bmatrix}[/tex]
Substitute x=3-y-z
[tex]\begin{bmatrix}3\left(3-y-z\right)+\frac{y}{3}-2z=12\\ -5\left(3-y-z\right)-6y+3z=-4\end{bmatrix}[/tex]
Substitute z={8y+9}/{15}
[tex]\begin{bmatrix}-y+8\left(-\frac{8y+9}{15}\right)-15=-4\end{bmatrix}[/tex]
simplify
[tex]\begin{bmatrix}\frac{-79y-72}{15}-15=-4\end{bmatrix}[/tex]
Substitute y=-3
[tex]z=-\frac{8\left(-3\right)+9}{15}[/tex]
z=1
For x=3-y-z
Substitute z=1,y=-3
x=3-(-3)-1
x=5
The solutions to the system of equations are:
x=5, z=1,y=-3
Learn more about the system of equations here;
https://brainly.com/question/25869125
#SPJ1
Solve for s.
19.1 = s − –7.3
s =
A figure is rotated 270 degrees counterclockwise about the origin. Then the image is rotated 90 degrees counterclockwise about the origin. Complete the coordinate notation that represents the series of rotations. What can you conclude about the position of the figure after the series of rotations?
If you don't mind, I need the answer ASAP
The series of rotations are : (x, y) -----> (y, -x) → (y, -x) ----> (x, y).
The total rotation is 360 degrees. So the figure is the original figure itself.
First a figure is rotated 270 degrees counterclockwise about the origin.
A 270 degree counterclockwise rotation is given by the co-ordinate transformation, (x, y) -----> (y, -x)
Then the figure is again rotated 90 degrees counterclockwise about the origin. A 90 degree counterclockwise rotation is given by, (x, y) -----> (-y, x)
So combining with the above transformation, the 90 degree counterclockwise rotation gives, (y, -x) ----> (x, y).
Thus the total rotation transformation is in turn, (x, y) ----> (x, y).
Thus the total rotation in counterclockwise direction about the origin is 360 degrees. So the final figure is the original figure itself.
Learn more about rotation at https://brainly.com/question/26249005
#SPJ1
HELP ASAP! brainliest for the best answer.
Answer:
[tex]\textsf{C.} \quad r=\dfrac{27-P}{3P}[/tex]
Step-by-step explanation:
Given formula:
[tex]A=P(1+rt)[/tex]
Given values:
A = 27t = 3Substitute the given values into the given formula and solve for r:
[tex]\begin{aligned}A&=P(1+rt)\\\\\implies 27&=P(1+3r)\\\\\dfrac{27}{P}&=\dfrac{P(1+3r)}{P}\\\\\dfrac{27}{P}&=1+3r\\\\\dfrac{27}{P}-1&=1+3r-1\\\\\dfrac{27}{P}-1&=3r\\\\3r&=\dfrac{27}{P}-\dfrac{P}{P}\\\\3r&=\dfrac{27-P}{P}\\\\\dfrac{3r}{3}&=\dfrac{\dfrac{27-P}{P}}{3}\\\\r&=\dfrac{27-P}{3P}\end{aligned}[/tex]
Solution
[tex]\boxed{r=\dfrac{27-P}{3P}}[/tex]
How is 9.746 x 10 ^13 written in standard form?
0000000000009746
97,460,000,000,000
9.746000000000000
9,746,000,000,000,000
The measure of an angle is 78.3°. What is the measure of its complementary angle?
The complementary angle of the angle is 11.7 degrees
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the complementary angle?The measure of the angle is given as
Angle = 78.3 degrees
Complementary angles add up to 90 degrees
So, we have the other angle to be
Other angle = 90 - 78.3
Evaluate the difference
Other angle = 11.7
Hence, the other angle is 11.7
Read more about angles at
https://brainly.com/question/7620723
#SPJ1
12
Find the horizontal asymptote of f of x equals quantity negative 2 x squared plus 3x plus 5 end quantity over quantity x squared plus 1. (5 points)
y = −2
y = −1
y = 1
y = 2
The horizontal asymptote is y = -2
The horizontal asymptote is an equation of the form y = k, for some constant k, is a straight line parallel to x-axis.
Horizontal asymptotes are found for rational functions of polynomials when x becomes extremely large, or, as x → ∞.
The function given is, f(x) = (-2x²+3x+5)/(x²+1)
Horizontal asymptote is given by,
y = [tex]\lim_{x \to \infty} \frac{-2x^2+3x+5}{x^2+1}[/tex]
= [tex]\lim_{x \to \infty} \frac{x^2(-2+\frac{3}{x} +\frac{5}{x^2}) }{x^2(1+\frac{1}{x^2}) }[/tex]
= [tex]\lim_{x \to \infty} \frac{(-2+\frac{3}{x} +\frac{5}{x^2}) }{(1+\frac{1}{x^2}) }[/tex]
= -2
So the horizontal asymptote of f(x) is, y = -2
Learn more about horizontal asymptotes at https://brainly.com/question/1851758
#SPJ1
Answer:
A) y = -2
Step-by-step explanation:
The rules to find the horizontal asymptote (HA) is shown below
Y = A if the numerator and denominator have same highest exponent for example
A^3
B^3
Y = 0 if the numerator have lower exponent and denominator have higher exponent for example
A^1
B^2
None HA if the numerator have higher exponent and denominator have lower exponent for example
A^2
B^1
And the equation shown in the question have same exponent so the answer is -2
PS: please give me brainiest
-7/8u = -21 solve for u and simplify your answer as much as possible
Answer:
u= 18.37
Step-by-step explanation:
-7/8 u= -21
We have to isolate the variable. Since the -7 is being divided, you would take it to the other side and multiply.
8u= -21 * -7
8u= 147
u= 147/8
u= 18.37
I need help................
Answer:
D
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (1, 7) ← 2 points on the line
m = [tex]\frac{7-1}{1-(-2)}[/tex] = [tex]\frac{6}{1+2}[/tex] = [tex]\frac{6}{3}[/tex] = 2
use either of the 2 points on the line
using (- 2, 1 ) , then
y - 1 = 2(x - (- 2) ) , that is
y - 1 = 2(x + 2) ← equation in point- slope form
-3x+7=-x-1
Simplify and solve for the variable
Is a number closer to 0 greater or less than a number more away from 0? (negatives and positives)
Answer:
A number closer to 0 is generally less than a number more away from 0. When it comes to negative numbers the closer the number to 0, the greater it is.
Step-by-step explanation:
If you need further help please let me know.
Please mark brainliest!
Brian deposited $2,419 into a savings account for which interest is compoundedquarterly at a rate of 2.54%. How much interest will he earn after 7 years? Roundanswer to the hundredths place. If answer does not have a hundredths place theninclude zeros so it does. Do not include units in the answer.
Given
Principal = $2419
rate = 2.54%
time = 7 years
compounds quarterly
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2419(1+\frac{0.0254}{4})^{4(7)} \\ A=2419(1.00635)^{28} \\ A=2888.08 \end{gathered}[/tex]After 7 years, the amount deposit is now $2888.08, subtract by the principal amount to get the interest.
[tex]\begin{gathered} I=A-P \\ I=2888.08-2419 \\ I=469.08 \end{gathered}[/tex]Therefore, the interest that he will earn after 7 years us $469.08.
Elsie is a project manager
in 2016 she earned £2100
in 2017 she was awarded a 3% increase on her monthly salary
given that in 2017 worked 42 hours a week for 45 weeks.
week out her average pay-per-hour of the year
The average pay-per-hour of the year for Elise will be 13.73 pounds.
How to calculate the average pay?From the information, in 2016 she earned £2100 and in 2017 she was awarded a 3% increase on her monthly salary.
Therefore, the new salary will be:
= 2100 + 3%(2100)
= 2100 + 63
= 2163
Now she worked for 42 hours per week for 45 weeks. This will be:
= 42 × 45
= 1890 hours
Therefore, the total earnings for the year will be:
= 2163 × 12 months
= 25956
The average pay-per-hour of the year will be:
= Total amount / Number of hours
= £25956 / 1890
= £13.73
Learn more about average per hour on:
brainly.com/question/9447238
#SPJ1
Can I have some help with the question in the attachment. I've done (a) but I think I'm doing (b) wrong
Answer:
8.33
Step-by-step explanation:
He has to be at work by 10:30, but it takes 20 mins to walk
So, 10:30-20 minutes=10:10
We then look at the arrival time closest to this, which would mean he would arrive at 10.06.
trace this back the bus would gett him at 8:38, but its a 5min walk.
8:38-5 minutes+8.33
hope this helps :)
An item costs y dollars and then a 20% discount is applied. Create an expression that could represent the price of the item after the discount. Explain your reasonin
The percentage 20% of the costs y is given as 0.20y thus the expression which represents the price of the item after the discount is P = y - 0.20y.
What is the percentage?The percentage is just like the amount of that value but between 1 to 100 and it is very useful to predict for example if you say 678 then we have to know about the full number also but if you say 80% then it becomes clear.
It is known that x% of something y is given as,
x% of y = (x/100)y
Given that discount of 20% of y
20% of y = (20/100)y
20% of y = 0.20y
Now the final price = initial price - discount
Final price (P) = y - 0.20y
Hence"The percentage 20% of the costs y is given as 0.20y thus the expression which represents the price of the item after the discount is P = y - 0.20y".
For more about the percentage,
brainly.com/question/13450942
#SPJ1