The dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height if the storage shed is to be built in the shape of a box with a square base.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
It is given that:
A storage shed is to be built in the shape of a box with a square base.
It is to have a volume of 729 cubic feet.
Let x be the length of the base
Let y be the height of the box.
V = 729 cubic feet
The base is square:
l = w = x
V = x²y
y = 729/x²
Cost of the base = $8x²
Cost of the roof = 3x²
Cost of the sides = 4(5.50)xy
= 22xy
Total cost
C= 8x² + 3x² + 22xy
C = 11x² + 22x(729/x²)
C = 11x² + 16038/x
Find the first derivative:
dC/dx = 22x - 16038/x²
Equate; dC/dx = 0
22x - 16038/x² = 0
22x = 16038/x²
22x³ =16038
x³ = 729
x = 9
y = 729/(9)² = 9
Length of base = 9 ft
Width of base = 9 ft
Height of box = 9 ft
Thus, the dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height.
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6) Evaluate 4x if x = -1/4
Answer: -1
Step-by-step explanation:
Evaluate 4x if x = -1/4
4(-1/4) = -1
Answer: -1
Step-by-step explanation:
4x and x = -1/4
plug x into the expression
[tex]4(-\frac{1}{4} )[/tex]
simplifies to:
[tex]-\frac{4}{4}[/tex]
4 divided by 4 is just 1, but it is negative so your final answer is
-1
what is 4,928 will rounded to the nearest hundred
Answer:
4900
That is your answer..........
Solve this system of linear equations. Separate the x- and y-values with a comma. 8x + 10y = 10 5x + 4y = -14
Answer
{-10, 9}
Step-by-step explanation:
The above are Simultaneous equations
What are simultaneous equations?These are two or more equations that share same variables.
8X + 10Y = 10--------(1)
5X + 4Y = -14-------(2)
Multiply equation (1) by 5 and equation (2) by 840X + 50Y = 50 ---------(3)
40X + 32Y = - 112--------(4)
Subtract equation (4) from (3)18Y = 162
Divide bothsides by 18[tex] \frac{18y}{18} = \frac{162}{18} \\ y = 9[/tex]
Substitute y = 9 into equation (3)40X + 50Y = 50
40X + 50(9) = 50
40X + 450 = 50
40X = 50 - 450
40X = - 400
[tex]Dividing \: bothsides \: by \: 40 \\ \frac{40x}{40} = \frac{ - 400}{40} \\ \\ x = - 10 \\ therefore \: the \: values \: are \: -10, \: 9[/tex]{-10, 9}
what is 4,928 will rounded to the nearest hundred
Answer:
4,928 rounded to the nearest hundred = 4,900
Step-by-step explanation:
Greetings!
Determine the two consecutive multiples of 100 that bracket 4,928.4,928 is between 4,900 and 5,000.4,950 is the midpoint between 4,900 and 5,000.As illustrated on the number line, 4,928 is less than the midpoint (4,950).Therefore, 4,928 rounded to the nearest hundred = 4,900.Hope it helps!
Answer:
The answer is 4900, because the next number is less than five, due to that we don't have to add a number (+1).
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
Target Costing
Instant Image Inc. manufactures color laser printers. Model J20 presently sells for $460 and has a product cost of $230, as follows:
Direct materials $175
Direct labor 40
Factory overhead 15
Total $230
It is estimated that the competitive selling price for color laser printers of this type will drop to $400 next year. Instant Image has established a target cost to maintain its historical markup percentage on product cost. Engineers have provided the following cost-reduction ideas:
Purchase a plastic printer cover with snap-on assembly, rather than with screws. This will reduce the amount of direct labor by 15 minutes per unit.
Add an inspection step that will add six minutes per unit of direct labor but reduce the materials cost by $20 per unit.
Decrease the cycle time of the injection molding machine from four minutes to three minutes per part. Forty percent of the direct labor and 48% of the factory overhead are related to running injection molding machines.
The direct labor rate is $30 per hour.
a. Determine the target cost for Model J20, assuming that the historical markup on product cost and selling price are maintained.
$fill in the blank 1
per unit
b. Determine the required cost reduction.
$fill in the blank 2
per unit
c. Evaluate the three engineering improvements together to determine if the required cost reduction (drift) can be achieved. Do not round interim calculations but round your final answers to two decimal places.
1. Direct labor reduction $fill in the blank 3
per unit
2. Additional inspection $fill in the blank 4
per unit
3. Injection molding productivity improvement $fill in the blank 5
per unit
Total savings $fill in the blank 6
per unit
The target cost for Model J20 is $2000.
The required cost reduction is $30.
The total saving will be $30.3.
How to compute the cost?The target cost will be:
= Sales price - (100% × Target cost)
= 400 - (100% × Y)
Y + Y = 400
2Y = 400
Y = 400/2 = 200
Target cost = $200
Therefore, the target cost is $200.
The required cost reduction will be:
= $230 - $200
= $30
The required cost reduction is $30.
The three engineering improvements together will be:
Direct labor reduction = 7.5
Additional inspection = 17
Injection molding = 5.8
Total savings = 30.3
The total savings is $30.3.
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Find the length indicated
Find SR (image)
Answer:
SR = 5
Step-by-step explanation:
We know that the two lines are equal to each other and thus TS + SR = 13
So, we can simply set the two equations of the first line equal to 13:
x + 2 + 2x - 7 = 13
3x - 5 = 13
3x = 18
x = 6
Now we plug in 6 for x in the SR equation:
2 * 6 = 12 - 7 = 5
Patrick is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. He uses the following formula to calculate voltage: voltage=(current) × (resistance) The circuit he tests had a current of 4+j2 amps and a resistance of 2-j3 ohms. What is the voltage of the current?
Based on the given current and the given resistance, the voltage of the current is 14 + j8
How to determine the voltage of the current?From the question, we have the following parameters
current of 4+j2 amps and a resistance of 2-j3 ohms.
This can be rewritten as:
Current (I) = 4+j2 amps
Resistance (R) = 2-j3 ohms.
The formula to calculate voltage is given as
Voltage=(current) × (resistance)
Rewrite as:
V = I * R
Substitute the known values in the above equation
V = (4 + j2) * (2 - j3)
Expand the brackets
V = 8 - j4 + j12 + 6
Collect the like ters
V = 8 + 6 - j4 + j12
Evaluate the like term
V = 14 + j8
Based on the given current and the given resistance, the voltage of the current is 14 + j8
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How can you make a 95% confidence interval smaller without changing the confidence level?
Step-by-step explanation:
1. Lower the confidence level.
2. Use a one-sided confidence interval. ...
3. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...
4. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...
PLEASE MARK ME AS BRAINLIST
Answer:
Increase the sample size.
Usually, the more observations that you have, the narrower the interval around the sample statistic is.
The spread of a disease can be modeled as N = 250√ where N is
the number of infected people, and t is time (in days).
How long will it take until the number of infected people reaches
2,500?
The spread of the disease will take a time 100 days to reach 2,500 infected people.
How to find the number of infected people at a certain time
In this problem we have a radical equation that represents the number of infected people as a function of time, we are suppose to find the time when that number will be 2,500 by algebra properties: (N = 2,500)
2,500 = 250 · √t
√t = 2,500 / 250
√t = 10
t = 10²
t = 100
The spread of the disease will take a time 100 days to reach 2,500 infected people.
Remark
The statement is poorly formatted and presents typing mistakes, correct form is shown below:
The spread of a disease can be modeled as N(t) = 250 · √t, where N is the number of infected people, and t is time (in days). How long will it take until the number of infected people reaches 2,500?
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A TV has a listed price of $540.99 before tax. If the sales tax rate is 9.75% , find the total cost of the TV with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
■ Sales tax: $52.75
■ Cost/Price before ST: $540.99
■ Total Cost/Price including ST: $593.74
Step-by-step explanation:
540.99 x 0.0975
= 52.75
Total
= 540.99+52.75
=593.74
Use the counting principle to determine the number of elements in the sample space. Two digits are selected with replacement from the digits 1,2,3, and 4
Answer: 16
Step-by-step explanation:
Someone please help me with this!!!
Answer:
279/1640
Step-by-step explanation:
The relations between the various trig functions can be used to find the necessary function values.
Other trig functionsSolving for cos(θ), we have ...
41 cos(θ) = 9
cos(θ) = 9/41 . . . . . divide by 41
The Pythagorean relation tells you ...
sin²(θ) +cos²(θ) = 1 ⇒ sin(θ) = √(1 -cos²(θ))
sin(θ) = √(1 -(9/41)²) = (√(41² -9²))/41 = 40/41
The tangent relation is ...
tan(θ) = sin(θ)/cos(θ) = (40/41)/(9/41) = 40/9
Expression value
The value of the given expression is ...
(sin(θ) -cos(θ))/tan(θ) = (40/41 -9/41)/(40/9) = (31/41)(9/40) = 279/1640
__
Additional comment
This can also be figured by a suitable calculator or spreadsheet. Output formatted as a fraction is often an option. Here, the result is rational.
ASAP help me with this question <3 number 12
Answer:
False
Step-by-step explanation:
Consider an isoscles trapezoid with angles 75° and 105°.
What is this expression in simplified form 5/2 times 9/6? A.90 B.90/3 C.45/2 D. 45/3
5√2 · 9√6
Simplify.
5 × 9 √ 2 x 6 ⇒ Multiply 2 × 6.
5 × 9 √12
Simplify √12 to 2√3.
5 × 9 × 2√3 ⇔ Multiply
90√3
Therefore, the correct alternative is option "B".
The simplified form of the given expression is 90√3. Therefore, the correct answer is option B.
The given expression is 5√2·9√6.
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Here, 5×9×√2×√6
= 45√12
= 45√4×3
= 90√3
Therefore, the correct answer is option B.
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Calcular el valor del ángulo que falta de dun triangulo rectangulo si uno de sus lados mide 25 grados.
Considerando la definición de triángulo rectángulo y sus propiedades, el valor del ángulo que falta de un triángulo rectángulo es 65°.
Definición de triánguloUn triángulo es un polígono que está determinado por tres segmentos de recta que se denominan lados, o por tres puntos no alineados llamados vértices.
En otras palabras, un triángulo es un polígono conformado por tres lados, así como por tres vértices y tres ángulos interiores.
Una de las propiedades de cualquier triángulo indica que la suma de los ángulos interiores es igual a 180°.
Definición de triángulo rectánguloEl triángulo rectángulo es una figura geométrica que se considera como un polígono formado por tres lados que forman un ángulo recto y dos ángulos agudos.
En otras palabras, el triángulo rectángulo es aquel que tiene un ángulo interior que es recto, es decir, mide 90º.
Valor del ángulo faltante en este casoEn este caso, sabes que:
Al ser un triángulo rectángulo, un ángulo interior mide 90°.Otro ángulo interior mide 25°. La suma de los ángulos interiores es igual a 180°.Entonces, el valor del ángulo faltante se puede calcular mediante:
90° + 25° + ángulo faltante= 180°
Resolviendo:
115° + ángulo faltante= 180°
ángulo faltante= 180° - 115°
ángulo faltante= 65°
Finalmente, el valor del ángulo que falta de un triángulo rectángulo es 65°.
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I'll give you 25 points! I just need help!
Find the surface area of the composite figure.
2 cm
5 cm
4 cm
4 cm
3 cm
3 cm
5 cm
5 cm
If you'd like,
SA = [ ? ] cm2
you can use a
calculator.
Answer:
add sum of all the angle given
Volume oblate spheroid
The volume of the oblate spheroid is approximately equal to 75.398 cubic feet.
What is the volume of an oblate spheroid?
In this problem we have the shape of an ellipse centered at origin, whose vertex form is shown below:
x² / a² + y² / b² = 1 (1)
Where a, b are the lengths of the semiaxes, in feet.
An oblate spheroid is generated by revolving half of the ellipse about the y-axis. Oblate spheroids are a kind of ellipse:
x² / a² + y² / b² + z² / a² = 1 (2)
Where a, b, c are the lengths of the semiaxes, in feet.
And the volume of the oblate spheroid is:
V = (4 / 3) · π · a² · b (3)
If we know that a = 3 ft, b = 2 ft, then the volume of the oblate spheroid is:
V = (4 / 3) · π · (3 ft)² · (2 ft)
V ≈ 75.398 ft³
The volume of the oblate spheroid is approximately equal to 75.398 cubic feet.
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Si la probabilidad de resolver un problema
cualquiera es p, entonces la probabilidad de
resolver un problema de n problemas
propuestos, es:
Utilizando la distribución binomial, la probabilidad de resolver un problema de n problemas propuestos, es p^n.
¿Cuál es la fórmula de distribución binomial?La fórmula es:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
x es el número de éxitos.n es el número de intentos.p es la probabilidad de éxito en un solo intento.La probabilidad de que todos los problemas sean resolvidos es dada por P(X = n), asi:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = n) = C_{n,n}.p^{n}.(1-p)^{n-n}[/tex]
P(X = n) = p^n
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Remy obtains a 30-year mortgage in the amount of $625,000 for a co-op. She secures a 7/1 ARM at an initial interest rate of 3%. Her initial monthly payment is $2,635.03. After 7 years, the interest rate on her loan changes to 4.925%. Calculate her new monthly payment in year 8 of the loan. (Round your answer to the nearest cent.)
$
According to the adjustable-rate mortgage The new monthly payment in year 8 of the loan is $1292.
According o the statement
we have given that the
Remy obtains a 30-year mortgage in the amount of $625,000 And
She secures a 7/1 ARM at an initial interest rate of 3%. Her initial monthly payment is $2,635.03.
And we have to find the new monthly payment when its interest rate increased to the 4.925%.
So, For this purpose we know that the
An adjustable-rate mortgage (ARM) is a loan with an interest rate that changes.
The amount in which she bought mortgage = 625,000
Interest rate = 3%
Initial amount = 2635.03
From this it clear that the
The amount she pays in 7 years = 2635.03*7
The amount she pays in 7 years = 18445.21
The left amount = 625,000 - 18445.21
The left amount = 606554
It means the rate of interest increased on the amount 606554$
So, According to the 4.925% interest the monthly payment will become
amount on interest rate 4.925% = 4.925% *606554/23 years
amount on interest rate 4.925% = $1292.
So, According to the adjustable-rate mortgage The new monthly payment in year 8 of the loan is $1292.
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5. If 15 men can finish a work in 16 days in how many days will 8 men can finish the same work? a. 15 b. 20 c. 30 d. 42
Answer:
C. 30
Step-by-step explanation:
15 men do work in 16 days
This means that 7.5 men (15/2) would do that same work in 32 days (16x2).
If the number of men increase, the amount of days decrease.
8 men would do that work in 30 days
8 men > 7.5 men
30 days < 32 days
Answer:
Option c.
Step-by-step explanation:
It is an inverse proportion, fewer workers more days to finish the job.
15 -----16
8 ----- x
x = (16)(15)/8 = 240/8 = 30 days
Hope this helps
Which of the following is equivalent to (5)7/3
Answer:
11 and 2/3
Step-by-step explanation:
The given expression be [tex]$(5)^{7/3[/tex] then the value exists ³√5⁷.
What is exponential form?The base number exists raised to a power of the exponent numerator and estimated to the root of the exponent denominator.
Given: [tex]$(5)^{7/3[/tex]
The given expression contains an exponent of (7/3)
When we exist transforming from exponential form to radical form you always place the numerator as our constant's exponent in the radical ( [tex]$5^{\frac{7}{3} }$[/tex] exists named the radicand because it exists found in the radical) and the denominator in front of the radical, where it would be named the index.
The formula would be: [tex]$(\sqrt[n]{x})^{q}=x^{\frac{p}{q}}$[/tex]
Therefore, the correct answer is ³√5⁷.
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Find the mode for the scores 3,760, 5,200, 8,750, 4,400, 5,250
what base could be written in the blank to make the exponential function model 15% decay ? y= (___) ^t\12
The base of the exponential function model in order to get 15% decay should be 0.85
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.
The first step would be figuring out the function's base.
The function's form should be, [tex]y=a*b^{t}[/tex]
Here,
'a' denotes the starting value.
'b' denotes the decrease rate.
't' denotes time.
According to the question, the exponential function model is,
[tex]y=b^{\frac{t}{12} }[/tex]
In order to get a 15% decay,
The base of the function should be (100-15)/100 = 0.85
Thus, Base of function(b) = 0.85
The exponential function model is written as:
[tex]y=0.85^{t/12}[/tex]
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PLEASE HELP!!
Select all the correct answers.
Consider the graph of the function f (x) = 2³.
y
-5 -4
Fm.
-~
-5
4
3-
2
-1-
-2-
-3-
-4-
-5-
O
N.
2
Which statements describe key features of function gif g (z) = f(x + 2)?
horizontal asymptote of y = 2
3 4 5
Oy-intercept at (0,4)
O y-intercept at (0, 1)
O horizontal asymptote of y = 0
O domain of (-∞0 < x < ∞0}
[tex]f(x) = 2 {}^{x} \\ g(x) = f(x + 2) = 2 {}^{x + 2} \\ g(x) = 2 {}^{x + 2} =2 {}^{x} .2 {}^{2} = 4.2 {}^{x} [/tex]
[tex]a.b {}^{x} = > horizontal \: asymp \: y = 0[/tex]
[tex]4.2 {}^{0} = 4 = > vertical \: int \: (0,4)[/tex]
[tex]a.b {}^{x} = > x ∈ \: ] -∞ , ∞ [[/tex]
Answer: Options:2 4 5The horizontal asymptote of the function f ( x ) = 2ˣ is y = 0 and the y-intercept is ( 0 , 4 )
What are Asymptotes?An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required
There are 3 types of asymptotes
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero
Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero
Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b
Given data ,
Let the function be denoted as f ( x )
Now , the value of f ( x ) is
f ( x ) = 2ˣ be equation (1)
The y-intercept of the function is when x = 0
So , when x = 0
f ( 0 ) = 2⁰
f ( 0 ) = 1
So , the y-intercept of the function is at ( 0 , 4 )
And , when the function f ( x ) is tending to zero , the horizontal asymptote is y = 0
Therefore , the horizontal asymptote is y = 0
The domain of the exponential function is { -∞ < x < ∞ }
Hence , the horizontal asymptote of the function f ( x ) = 2ˣ is y = 0
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(04.01, 04.02 HC)
Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he plays volleyball.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Eric plays basketball x) and the number of minutes he
plays volleyball (y) every day. (5 points)
Part B: How much time doos Eric spend playing volleyball every day? Show your work. (3 points)
Part C: Is it possible for Eric to have spent 35 minutes playing basketball if he plays for a total of exactly 95 minutes and plays basketball (or 25 minutes
longer than he plays volleyball? Explain your reasoning. (2 points)
. What are the values a b and c In the following quadratic equation ? -6x^2-8x+12=0
Answer:
a = -6
b = -8
c = 12
Step-by-step explanation:
Quadratic equations follow the general structure:
ax² + bx + c = 0
In this equation, "a" and "b" serve as coefficients which modify the variables and "c" represents the y-intercept. Since the given equation is in the quadratic form, you can easily identify which values match the variables.
-6x² - 8x + 12 = 0
a = -6
b = -8
c = 12
Find the midsegment of the triangle which is parallel to CA.
Answer:
[tex] \pmb{ \pink{QUESTION�}}[/tex]
Find the midsegment of the triangle which is parallel to CA.
[tex] \pmb{ \pink{ANSWER:-}}[/tex]
Tip
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle.This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.If two segments are congruent, then they have the same length or measure.In other words, congruent sides of a triangle have the same length.[tex] \frak{Explanation:-} [/tex]
We have to find the segment which is parallel to CA.
From the given data,
The segment EG is the midsegment of the triangle[tex]\triangle[/tex] ABC.
So we have,
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side.
[tex]\implies\rm{midsegment \: EG \: parallel \: to \: CA}[/tex]
[tex]\frak{RainbowSalt}[/tex]~
Answer:
[tex]\fbox {EG}[/tex]
Step-by-step explanation:
Based on the given diagram, we can clearly see the midsegment (lies in the middle of the figure) that is parallel to AC is EG
I hope it helped you solve the problem.
Good luck on your studies!
4a*(3-2b) for a=1/2 and b=-1
pls hurry
Answer:
2
Step-by-step explanation:
Use pemdas
4a*(3-2b)
4(1/2)*(3-2(-1))
4* 1/2 = 2
2*(3-2(-1)
-2*-1 = 2
2(3-2)
3 -2 = 1
2(1) = 2
The manger of a company planned to distribute a $50 bouns to each employee from the company fund, but the fund contained $5 less than what was needed. Instead, the manger gave each employee a $45 bouns and kept the remaing $95 in the company fund. How much money was in the company fund before any bonuses were paid?
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Let y represent the total company fund and x represent the number of staffs.
From the first statement:
y - 50x = -5 (1)
Also:
y - 45x = 95 (2)
From equation 1 and 2:
x = 20, y = 995
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
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If my savings of $x grows 10% each year. How much will I have in: 5 years
Answer:
See below
Step-by-step explanation:
Assuming the interest is compounded annually
x * (1 + .10)^5 = 1.61051 x
your final amount will be 1.61051 times bigger than the initial deposit
