Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]
[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]
⇒ 198x - 12x² = 0
[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]
By solving for x:
x = 0 or x = [tex]\dfrac{33}{2}[/tex]
Again:
V = 99x² - 4x³
[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]
At x = [tex]\dfrac{33}{2}[/tex]
[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]
[tex]\implies 198 - 12 \times 33[/tex]
= -198
Thus, at maximum value;
[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]
Recall y = 99 - 4x
when at maximum x = [tex]\dfrac{33}{2}[/tex]
[tex]y = 99 - 4(\dfrac{33}{2})[/tex]
y = 33
Finally; the volume V = x² y is;
[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]
[tex]V =272.25 \times 33[/tex]
V = 8984.25 inches³
please answer both thanks
Question 2.1
Solve the following problem. Round to one decimal place if
necessary. If your answer is correct you will see an image
appear on your screen.
Answer:
x = 5.3
Step-by-step explanation:
Reference angle (θ) = 24°
Opposite side to the reference angle = x
Adjacent side = 12
Apply TOA, which is:
Tan θ = Opp/Adj
Plug in the values
Tan 24° = x/12
12*Tan 24° = x
5.34274422 = x
x = 5.3 (approximated to one decimal place)
tv originally cost $400 if the price of the TV increase by 15% what is the new price
Answer:
$460
Step-by-step explanation:
Thus, a product that normally costs $400 with a 15 percent discount will cost you $340.00, and you saved $60.00. You can also calculate how much you save by simply moving the period in 15.00 percent two spaces to the left, and then multiply the result by $400 as follows: $400 x .15 = $60.00 savings.
Need Help ASAP!!!!!!!!
Answer:
The last one the one with (-6,00) and Range (5,00)
Please! Help, Also please show you’re work! will give brainliest to all who gives me the best answer
Answer:
Hope this helps. If it doesn't then I apologize.
please help me i’m begging!!
i need to match them
An angle of depression is measured from the horizon downwards and an angle of elevation is measured from the horizon upwards.
When solving for the sides or angles of a right triangle you can use trigonometry. The sine of an angle is found by the ratio of the opposite side and the hypotenuse. The cosine of an angle is found by the ratio of the adjacent side and the hypotenuse. The tangent of an angle is found by the ratio of the opposite side and the adjacent side.
The opposite side is always the leg opposite the angle that you are using. The adjacent side is the leg that forms one of the sides of the angle you are talking about and the hypotenuse is always across from the right angle.
If you know two lengths you can find the third leg length by using the Pythagorean Theorem.
will give BRAINLEST! See image attached below.
Answer:
See the image below for answer:)
Step-by-step explanation:
Answer:
B. (1 ± sqrt(33)) / 4
Step-by-step explanation:
the 2 solutions for a quadratic equation
ax² + bx + c = 0
are defined as
x = (-b ± sqrt(b² - 4ac)) / 2a
in our example here we have
a = -2
b = 1
c = 4
=>
x = (-1 ± sqrt(1 + 32)) / -4 = (1 ± sqrt(33)) / 4
as we can easily divide top and bottom by -1 to turn the -1 and -4 into positive numbers, and the second top part, the square root, is a ± factor anyway. just withing the sign dues not change the fact that is is still a ± factor (both signs apply).
and now it is clear, it has to be option B.
the others disqualify because they have either no division by any form of 4, or the "1" and the "4" have different signs. but our equation shows they need to have equal signs (either both negative or both positive).
Find the value of x to the nearest tenth.
Step-by-step explanation:
p^2+b^2=h^2
or, 16+9=h^2
or, 25=h^2
or h=5
again, p^2 +b^2=h^2
or, 25+b^2=36
or, b^2=11
or. b=√11 therefore b=x=√11
HELP ME WITH THIS PLSSS!!!
A circle has been divided into three equal angles. is each angle acute obtuse or right?
Answer:
obtuse
Step-by-step explanation:
A circle is 360 degrees
Divide by 3
360/3 =120
This is greater than 90 and less than 180 so it is obtuse
It is reported in USA Today that the average flight cost nationwide is $445.99. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually greater than $445.99. What are the appropriate hypotheses for this test
Answer:
[tex]H_0[/tex] : [tex]\mu \leq 445.99[/tex]
[tex]H_a[/tex] : [tex]\mu > 445.99[/tex]
Step-by-step explanation:
It is given the average cost of the flight nationwide is $ 445.99
I wanted to [tex]\text{perform the hypothesis test}[/tex] to determine that the true average is greater than $ 445.99
Let the hypothesis that the true average is actually greater than $445.99
Therefore,
the [tex]\text{null hypothesis}[/tex] for the test is :
[tex]H_0[/tex] : [tex]\mu \leq 445.99[/tex]
And the alternate hypothesis is :
[tex]H_a[/tex] : [tex]\mu > 445.99[/tex]
Use your graph to find estimates of the solutions to the equation x^2-x-6=-2
Answer:
-2 and 3
Step-by-step explanation:
From the graph, the solution is the points where the curve cuts the x axis. From the graph, you can see that the equation cuts the x axis at two points that is at x=-2 and 3.
Hence the solutions to the equation is -2 and 3
I NEED HELP PLZ THIS JS MY LAST QUESTION WILL MARL YOU
Answer:
-4
Step-by-step explanation:
60 + x + 124 = 180 degree (being linear pair)
x + 184 = 180
x = 180 - 184
x = -4
Answer:
x+124=180(linear pair angle)
x=56
i am confused between -4 and 56
Drag each value to the correct location on the box plot. Not all values will be used.
The heights, in centimeters, of 10 students are given in the table.
160
159
158.5 168
162
164.5
164
169
161
160.5
Sam creates a box plot for this data. Match the values to the correct locations on theplot.
169
161.5
160
159
162
164.5
168
158.5
Answer:
PUT THEM IN ORDER SO I CAN UNDERSTAND oh 56.86
1
5. Monica put $600 in a savings account that pays an interest rate of 3.5%.
She collected $120 in interest
Answer:
pls complete your question. what exactly are we supposed to calculate?
A coffee distributor needs to mix a(n) Mexican Shade Grown coffee blend that normally sells for $8.10 per pound with a Tanzanian coffee blend that normally sells for $14.10 per pound to create 100 pounds of a coffee that can sell for $10.26 per pound. How many pounds of each kind of coffee should they mix?
Answer:
64 pounds of the $8.10 Mexican Shade Grown
36 pounds of the $14.10 Tanzanian
Step-by-step explanation:
8.1x + 14.1(100 - x) = 10.26(100)
Distribute
8.1x + 1410 - 14.1x = 1026
Combine like terms
1410 - 6x = 1026
Subtract 1410 from both sides
-6x = -384
Divide both sides by -6
x = 64 pounds of the $8.10
100 - x = 36 pounds of the $14.10
he monthly sales of furniture stores in Dubai were collected and summarized. The mean and the median of the monthly sales are 130,000 AED and 170,000 AED respectively. The distribution of the monthly sales is
symmetrical.
none of the above.
positively skewed.
negatively skewed.
Given:
The mean and the median of the monthly sales are 130,000 AED and 170,000 AED respectively.
To find:
The distribution of the monthly sales.
Solution:
We know that,
For symmetrical distribution, mean is equal to median.
For positively skewed distribution, mean is greater than median.
For negatively skewed distribution, mean is less than median.
We have,
Mean of the monthly sales = 130,000 AED
Median of the monthly sales = 170,000 AED
Here, Mean is less than the median because 130,000 < 170,000.
Therefore, the distribution is negatively skewed. Hence, the correct option is D.
The sum of two numbers is 90 and their ratio is 1/5.
What is the difference between the largest and the smallest of the two numbers?
a. 15
b. 18
c. 60
d. 75
e. 45
Answer:
C. 60
Step-by-step explanation:
1+5=6
90÷6=15
15 ×5=75
15×1=15
75-15=60
The difference between the largest and the smallest of the two numbers is 60.
We have given that,
The sum of two numbers is 90 and their ratio is 1/5.
What is the difference?
The difference is a key concept of philosophy, denoting the process or set of properties by which one entity is distinguished from another within a relational field or a given conceptual system
[tex]1+5=6\\90\6=15\\15 \times 5=75\\15\times 1=15\\75-15=60[/tex]
Therefore, The difference between the largest and the smallest of the two numbers is 60.
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what are the multiples of 5 between 61 and 69
Answer:
I think it is 65 because we can divide it by 5
Answer:
i think there is only one multiple which is 65
The volume of a cone is 16 n cubic meters. What is the volume of Eylinder having
the same base and same height?
Answer:
it's the threefold (16 pi)
Step-by-step explanation:
if you look at the formula for each, you'll notice that the volume formula of the cone got an '*1/3' extra, so it's one third of the cylinders volume
Kate leans a ladder against her house to get to the roof. The house is 25 feet tall and The ladder is 15 feet away from the side of the house. What is the angle that the latter makes with the ground?
Answer:
this is the correct answer
please mark brainliest
Let g(x) be the transformation of f(x)= 3x - 5 when it is translated 6 units up followed by a horizontal stretch by a factor of 3/2.
g(x) = Blank 1X +Blank 2
Answer:
g(x) = 2x + 1
Step-by-step explanation:
f(x)= 3x - 5 when it is translated 6 units up
Translating a function a units is adding a to the function. So
[tex]3x - 5 + 6 = 3x + 1[/tex]
Horizontal stretch by a factor of 3/2.
This means that [tex]g(x) = f(\frac{2x}{3})[/tex], that is. So
[tex]g(x) = 3(\frac{2x}{3}) + 1 = 2x + 1[/tex]
Then
g(x) = 2x + 1
hi can someone help me w this
Answer:
336 ft³ or 336 cubic feet
Step-by-step explanation:
Volume = Area triangle * height
Area triangle = 1/2(8 x 14)
Area triangle = 1/2(112) = 56 ft²
56 ft² * 6 ft = 336 ft³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
a tree is standing 35 feet high. tom is attempting to align a 40 foot ladder to the tree to get his cat out. find the angle that the ladder will make with the ground.
Answer:
61º
Step-by-step explanation:
sin= opp/hyp
sin∅ = 35/40
∅ = arcsin35/40
use calculator
∅ = 61.044975628140152
∅ ≈ 61º
2x - y - 4 = 0
3x + y - 9 = 0
What is the solution set of the given system?
Answer:
[tex](\frac{13}{5};\frac{6}{5}).[/tex]
Step-by-step explanation:
[tex]1)\left \{ {{5x=13} \atop {y=2x-4}} \right. \ 2)\left \{ {{x=\frac{13}{5} } \atop {y=\frac{6}{5} }} \right.[/tex]
short explanation: 1) to add the 1st equation to the 2d; 2) to calculate the value of 'x', then to substitute x=13/5 into the 2d equation and calculate the value of 'y'.
Mrs Gren baked a cake on her son's birthday and divided it into 12 pieces.
Serah
ate 1/3 of the cake and her son ate 1/4 of the cake.
2. How many pieces of the cake did Serah eat?
- How many pieces of the cake did her son eat?
What fraction of the cake was eaten?
What fraction of the cake was left?
Answer:
2
Step-by-step explanation:
it has 2 in the equation
A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?
a. X1 + X2 + X3 + X4 = 1
b. X1 + X2 + X3 + X4 = 1
c. X1 + X2 + X3 + X4= 1
d. X1 + X2 + X3+ X4= 0
Given:
A company wants to select 1 project from a set of 4 possible projects.
Consider the options are:
a. [tex]X_1+X_2+X_3+X_4=1[/tex]
b. [tex]X_1+X_2+X_3+X_4\leq 1[/tex]
c. [tex]X_1+X_2+X_3+X_4\geq 1[/tex]
d. [tex]X_1+X_2+X_3+X_4\geq 0[/tex]
To find:
The constraints that ensures only 1 will be selected.
Solution:
It is given that the company wants to select 1 project from a set of 4 possible projects. It means the sum of selected projects must be equal to 1.
[tex]X_1+X_2+X_3+X_4=1[/tex]
Therefore, the correct option is (a).
Find two consecutive whole numbers that square root of 63 lies between
Given:
The number [tex]\sqrt{63}[/tex] lies between two whole numbers.
To find:
The two consecutive whole numbers.
Solution:
The perfect squares of natural numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ... .
The number 63 lies between 49 and 64.
[tex]49<63<64[/tex]
Taking square root on each side, we get
[tex]\sqrt{49}<\sqrt{63}<\sqrt{64}[/tex]
[tex]7<\sqrt{63}<8[/tex]
Therefore, the number [tex]\sqrt{63}[/tex] lies between two whole numbers 7 and 8.
Will pick brainliest. How would I do this?
Undefined
Order of matrix Q is 4 by 3
whereas order of R is 4by 4
In order to add two matrices , they should be of same order.
Answer:
DOES NOT EXIST.
Step-by-step explanation:
The sum of two matrices exists only if the matrices are of the same order.
Here Q is 3x3 and R is 4x4, so they do not have the same order, hence the sum DOES NOT EXIST.
I’m so confused plz help
Answer:
[tex]\frac{37}{2}[/tex] ÷ [tex]\frac{17}{4}[/tex]
Step-by-step explanation:
[tex]18\frac{1}{2} =\frac{37}{2}[/tex]
[tex]4\frac{1}{4} =\frac{17}{4}[/tex]
[tex]\frac{37}{2}[/tex] ÷ [tex]\frac{17}{4}[/tex]
Camila sets up a passcode on her tablet, which allows only nine-digit codes. A spy sneaks a look at Camila's tablet and sees her fingerprints on the screen over nine numbers. What is the probability the spy is able to unlock the tablet on his first try
The probability the spy is able to unlock the tablet on his first try is P = 1/362880
Given that,
Camila sets up a passcode on her tablet, which allows only nine-digit codes.
And, A spy sneaks a look at Camila's tablet and sees her fingerprints on the screen over nine numbers.
Hence, the total amount of different sequences that can be built using 9 digits is:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 362,880
Therefore, the probability the spy is able to unlock the tablet on his first try is,
P = 1/362880
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