For tax reasons, i need to create a rectangular vegetable patch with an area of exactly 50 square feet. the fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. what are the dimensions of the vegetable patch with the least expensive fence?
Final answer:
The dimensions of the vegetable patch with the least expensive fence are 10 feet by 5 feet.
Explanation:
To find the dimensions of the vegetable patch with the least expensive fence, we can use the formula for the area of a rectangle: length x width = area.
Let's assume the length of the vegetable patch is 'x' and the width is 'y.'
So, xy = 50.
The cost for the east and west sides is $4 per foot, and the cost for the north and south sides is $2 per foot.
Therefore, the cost of fencing the east and west sides would be 4x, and the cost of fencing the north and south sides would be 2y.
For the least expensive fence, we want to minimize the cost, which means minimizing the sum of 4x and 2y.
We can rewrite the equation as:
y = 50/x.
Now substitute the value of y in the cost equation:
cost = 4x + 2(50/x).
To find the minimum cost, we need to find the derivative of the cost equation and set it equal to zero.
Calculating the derivative and solving for x, we find x = √100 = 10.
Therefore, the dimensions of the vegetable patch with the least expensive fence are 10 feet by 5 feet.
A dentist is making identical dental care bags for patients using 56 tubes of toothpaste, 112 packets of floss, and 85 toothbrushes. What is the greatest number of identical dental care bags the dentist can make with the least amount of items leftover
Answer: There would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.
Step-by-step explanation:
Since we have given that
Number of tubes of toothpaste = 56
Number of packets of floss = 112
Number of toothbrushes = 85
We need to find the greatest number of identical dental care bags that dentist can make with the least amount of items leftover.
So, we will find "H.C.F." of 56, 112, 85 which is equal to 1.
So, there would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.
Consider the graph of Cx + Ay = B where A, B, and C are all positive constants. Find the coordinates of the x-intercept.
The coordinates of the x-intercept are (B/C,0)
What is the x-intercept of a graph?The x-intercept of a graph is defined as the places where the graph crosses the x-axis or the locations where the coordinate of the y-axis equals 0, which are known as the x-intercept of a graph.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Consider the graph of Cx + Ay = B
Here A, B, and C are all positive constants.
To determine the coordinates of the x-intercept
⇒ Cx + Ay = B,
Substitute the value of y = 0 and solve for x
⇒ Cx + A(0) = B,
⇒ Cx = B,
Divide both sides by C
⇒ x = B/C
Hence, the coordinates of the x-intercept are (B/C,0).
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Me Ramirez bought 1/4 pounds of cashews. He divided the cashews equally among his 3 children. How much did each child get?
What is 8.675 as a mixed number in simplified formation
There are three more apple trees than pear trees in the yard. Altogether there are 35 trees. How many apple trees and how many pear trees are there?
35-3 =32
32/2 = 16
there are 16 pear trees and 19 apple trees
3942588 to the nearest thousand
four-fifths of a number minus two is greater than three-tenths of twice that number
A garden snail moves 1/6 foot in 1/3 hours. what is the unit rate?
"write the expression in radical form and then evaluate"
M(6, 6) is the midpoint of . The coordinates of S are (8, 9). What are the coordinates of R?
Suppose that there were a strong correlation between the variables g and h. Which of these is a true statement?
a. g must cause h
b. g must not cause h
c. g may cause h
d. h must cause g
Answer: c. g may cause h
Step-by-step explanation:
Correlation: It represents the relation between any two or more than two variable.
Causation: It is a kind of correlation where one variable if affected by the other variable.
Therefore , Causation implies correlation.
But correlation does not imply causation.
Hence, if there were a strong correlation between the variables g and h, then g may cause h.
Sue has $2.10 in dimes and nickels. If she has 12 more dimes than nickels, how many of each coin does she have?
what is the difference? 5/3-1/2
A. 4
B. 7
C. 7/6
D. 7/0 = undefined
A submarine is at the surface of the ocean, preparing to dive. It submerges and dives to −972 feet. Then, it ascends 308 feet to avoid hitting an undersea cliff. What integer represents the submarine's position in feet (depth) after it ascends to avoid the cliff?
Answer:
The integer which represents the submarine's position in feet (depth) after it ascends to avoid the cliff = -664
Step-by-step explanation:
It submerges and dives to −972 feet. Then, it ascends 308 feet.
Initially it goes down by 972 feet and then goes up by 308 ft.
Since depth is more than elevation.
Final position is below sea level.
Final depth = 972 - 308 = 664 ft
The integer which represents the submarine's position in feet (depth) after it ascends to avoid the cliff = -664
F the experimental value for the percentage of o is 37%, the accepted value of the percentage of oxygen is 40%, what is the percentage error in the experiment?
Which expression is equivalent to 10x2y + 25x2? 5x2(2y + 5) 5x2y(5 + 20y) 10xy(x + 15y) 10x2(y + 25)
we have
[tex]10x^{2}y+ 25x^{2}[/tex]
we know that
[tex]10=2*5\\25=5*5[/tex]
substitute
[tex](2*5)x^{2}y+ (5*5)x^{2}[/tex]
Factor [tex]5x^{2}[/tex]
[tex](5x^{2})(2y+ 5)[/tex]
therefore
the answer is
[tex](5x^{2})(2y+ 5)[/tex]
The equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)
What are equivalent expressions?Equivalent expressions are expressions that have equal values
The expression is given as:
10x^2y + 25x^2
Factor out 5x^2 from the expression
5x^2(2y + 5)
Hence, the equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)
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Et f(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 5)j + zk. find the flux of f across s, the part of the paraboloid x2 + y2 + z = 11 that lies above the plane z = 2 and is oriented upward.
The flux of [tex]\vec f(x,y,z)[/tex] across S is given by the surface integral
[tex]\displaystyle \iint_S \vec f(x,y,z) \cdot d\vec s[/tex]
Join to S the disk D of radius 3 in the plane z = 2, for which we have
[tex]x^2+y^2+2=11 \implies x^2+y^2=9=3^2[/tex]
Let S' = S U D (the union of S and D). Since S' is closed, we can use divergence theorem to compute the flux of [tex]\vec f[/tex] through S' :
[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \iiint_R \mathrm{div}\vec f \, dV[/tex]
Compute the divergence of [tex]\vec f[/tex] :
[tex]\mathrm{div}\vec f = \dfrac{\partial\left(z\tan^{-1}(y^2)\right)}{\partial x} + \dfrac{\partial\left(z^3\ln(x^2+5)\right)}{\partial y} + \dfrac{\partial(z)}{\partial z} = 1[/tex]
Compute the volume integral by converting to cylindrical coordinates. Take
[tex]\begin{cases}x=r\cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = r\,dr\,d\theta\,d\zeta\end{cases}[/tex]
Then the flux of [tex]\vec f[/tex] across S' is
[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \int_{-3}^3 \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_2^{11-x^2-y^2} dV = \int_0^{2\pi} \int_0^3 \int_2^{11-r^2} r \, d\zeta \, dr \, d\theta = \frac{81\pi}2[/tex]
To get the flux across S alone, we subtract from this integral the flux of [tex]\vec f[/tex] across D.
Parameterize D by the vector function
[tex]\vec\sigma(\rho,\phi) = \rho \cos(\phi) \, \vec\imath + \rho \sin(\phi) \, \vec\jmath + 2\, \vec k[/tex]
with [tex]0\le\rho\le3[/tex] and [tex]0\le\phi\le2\pi[/tex].
Get the downward-pointing normal vector to D :
[tex]\vec n = \dfrac{\partial\vec\sigma}{\partial\phi} \times \dfrac{\partial\vec\sigma}{\partial \rho} = -\rho\,\vec k[/tex]
Compute the flux across D :
[tex]\displaystyle \iint_D \vec f\cdot d\vec s = \int_0^{2\pi} \int_0^3 \vec f(\vec\sigma) \cdot \vec n \, d\rho\,d\phi = \int_0^{2\pi} \int_0^3 (-2\rho) \, d\rho \, d\phi = -18\pi[/tex]
So the flux of [tex]\vec f[/tex] across S is
[tex]\displaystyle \iint_S \vec f \cdot d \vec s = \frac{81\pi}2 - (-18\pi) = \boxed{\frac{117\pi}2}[/tex]
To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux and evaluate the integral.
Explanation:To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux: flux = ∫∫(f•n)dA. Here, f(x,y,z) = z tan⁻¹(y²)i + z³ ln(x² + 5)j + zk.
The equation of the paraboloid is x² + y² + z = 11. Using these equations, we can set up the double integral and solve for the flux.
After evaluating the integral, we can find the flux of f across the given surface.
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Find the values of a, b, and c for which the quadratic equation ax^2 + bx + c = 0 has the solutions 8i and −8i.
One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $139,700 to invest would like to have an income of $18,930 per year from her investments. How much should she invest at each rate?
To achieve an annual income of $18,930, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate.
To determine how much a woman should invest at each rate to achieve an income of $18,930 per year, we can set up a system of linear equations. Assuming she invests x dollars at the 10% rate and y dollars at the 18% rate, we can use the following equations:
x + y = $139,700: This equation represents the total amount of money she has to invest.
0.10x + 0.18y = $18,930: This equation represents the annual income from the investments.
To solve:
Multiply the first equation by 0.10:
0.10x + 0.10y = $13,970
Subtract this from the second equation:
0.18y - 0.10y = $18,930 - $13,970
0.08y = $4,960
Divide by 0.08 to find y:
y = $62,000
Substitute y back into the first equation to find x:
x + $62,000 = $139,700
x = $77,700
Therefore, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate to achieve her desired income.
Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans. Plan A: Raise the price by $0.05 each week until the price reaches $8.00. Plan B: Raise the price by 10 percent each week until the price reaches $8.00. Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00. Plan D: Raise the price by $0.25 each week until the price reaches $8.00. Which plan will result in the price of the bagels reaching $8.00 fastest? plan A plan B plan C plan D
Answer:
Plan B
Step-by-step explanation:
Plan B and plan C start out at the same increase: 10% ($0.50) for the first week. The increase under plan C stays at 10% of the original value, but the increase under plan B increases according to the value the week before, which keeps getting larger.
Hence, plan B gets to $8.00 the fastest — after about 5 weeks.
Find the area of a circle with radius 7cm
What is the price of $1000 face-value one year zero coupon discount bond that offers 1.5% yield?
a.$992.3
b.$1001.5
c.$998.5
d.$985.2?
mulch to cover a rectangular garden costs 48. mulch is needed to cover a larger, similar garden. the ratio of dimensions is 2:3. how much would it cost to cover the larger
Answer: $108
Step-by-step explanation:
It would cost $288 to cover the larger rectangular garden.
What is ratio?"It is relationship between two numbers that describe how many times one value can contain another. "
What is proportion?"It is an equation in which two ratios are equal."
What is area of rectangle?[tex]A=l\times w[/tex], where 'l' is length of the rectangle and 'w' is width of the rectangle
For given question,
Let 'l' be the length of the rectangle and the 'w' be the width of the rectangle.
The ratio of dimensions of a rectangular garden would be w:l.
mulch is needed to cover a larger, similar garden.
The ratio of dimensions is 2:3
As both the gardens are similar, their dimensions must be in proportion.
[tex]\Rightarrow \frac{w}{2}= \frac{l}{3}[/tex]
[tex]\Rightarrow \frac{w}{l}= \frac{2}{3}[/tex]
So, the length of the larger rectangular garden would be [tex]3l[/tex]
and the length of the larger rectangular garden would be 2w
A mulch to cover the first rectangular garden costs $48.
This means, for the area of [tex]A_1=l\times w[/tex] it costs $48.
Using the formula for area of rectangle the area of the larger garden would be,
[tex]A_2=3l\times 2w\\A_2=6(l\times w)\\A_2=6\times A_1[/tex]
For the second garden it would costs,
6 × 48 = 288
Therefore, it would cost $288 to cover the larger rectangular garden.
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Marcus recorded the high temperature each day for a week. the daily high temperatures in degrees Fahrenheit were: 68,74,66,78,72,80, and 74 which best describes what 74 represents in this data set?
A. median only
B. mean and mode
C. median and mode
D. mode only
Answer:
The answer is C. median and mode.
Step-by-step explanation:
First, we have to ensure that the list of the set of data is from least to greatest: 66, 68, 72, 74, 74, 78, 80 .
The mean = (66 + 68 + 72 + 74 + 74 + 78 + 80) ÷ 7 = 512 ÷ 7 = 73.14 . (Note that the mean is not equal to 74.)
The median = middle number when the set of data is listed in order from least to greatest = the fourth number = 74.
The mode = the temperature that occurred the most = 74 .
These results prove that the median and mode best describe what 74 represents in the data set, because they are the same value.
Answer: C
I think its right. Was it for the I ready diagnostic?
The number of customers for a new online business can be modeled by y = 6x2 + 75x + 200, where x represents the number of months since the business started. Which is the best prediction for the number of customers in month 25?
A. 5825
B. 3791
C. 2936
D. 4754
Answer:
A. 5825
Step-by-step explanation:
Given: The number of customers for a new online business can be modeled by y = 6x^2 + 75x + 200, where "x" represents the number of months.
We are asked to find number of customers in month 25.
To find the number of customers in 25th month, we need to plug x = 25 in the given function.
y = 6([tex]25)^2[/tex] + 75(25) + 200
y = 6(625) + 1875 + 200
y = 3750 + 1875 + 200
y = 5825
Therefore, the answer is A. 5825
Find the price of a $35 basketball that is on sale for 50% off the regular price.
The price of the basketball on sale is $17.50.
To calculate this:
1. Calculate 50% of $35:
$35 x 0.50 = $17.50
2. Subtract the discount from the original price:
$35 - $17.50 = $17.50
When an item is on sale for a percentage off, you first find what that percentage represents of the original price. In this case, 50% of $35 is $17.50. Then, you subtract that amount from the original price to find the sale price. So, the basketball, originally priced at $35, would be $17.50 when it's on sale for 50% off.
Complete question:
Find the price of a $35 basketball that is on sale for 50% off the regular price.
Which would take up more space, a pound of granite or a pound of basalt?
Answer:
1 pound of granite
Step-by-step explanation:
The density of granite is 168.6 lb/ft³. The volume occupied by 1 pound of granite is:
1 lb × (1 ft³/168.6 lb) = 0.00593 ft³
The density of basalt is 188 lb/ft³. The volume occupied by 1 pound of basalt is:
1 lb × (1 ft³/188 lb) = 0.00532 ft³
As we can see, 1 pound of granite takes up more space than 1 pound of basalt.
An international company has 26,900 employees in one country. If this represents 16.9% of the company's employees, how many employees does it have in total?
Answer:
89,349
Step-by-step explanation:
i just did this problem on aleks and this is the answer they gave me how it helps other in the future
How many years would it take Jim to earn interest equal to half of his original principal at 10% simple interest?
A. 6 months
B. 12 months
C. 5 years
D. 10 Years
Jim would need 5 years to earn interest equal to half of his original principal at a 10% simple interest rate.
To find out how many years it would take for Jim to earn interest equal to half of his original principal at a 10% simple interest rate, we use the formula for simple interest: I = PRT, where I is the interest, P is the principal, R is the rate of interest per year, and T is the time in years.
In this case, Jim wants the interest I to be half of the principal P. So the equation becomes :
[tex]\frac{P}{2} = P \times 0.10 \times T[/tex] or T
= [tex]\frac{P}{2 \times P \times 0.10}[/tex], which simplifies to T =[tex]\frac{1}{2 \times 0.10}[/tex]or T = 5 years. Therefore, the correct answer is C. 5 years.