Answer:
The dimensions are four by two by two meters.
Step-by-step explanation:
The volume for a rectangular prism is given by:
[tex]V=\ell wh[/tex]
Where l is the length (or depth), w is the width, and h is the height.
Since the height and width are both two meters less than the depth, we can write that:
[tex]h=\ell -2\text{ and } w = \ell -2[/tex]
We are also given that the total volume is 16 cubic meters. Substitute:
[tex]16=\ell(\ell -2)(\ell -2)[/tex]
Expand:
[tex]16=\ell(\ell^2 -4\ell +4)[/tex]
Distribute:
[tex]16=\ell ^3-4\ell ^2+4\ell[/tex]
Isolate the equation. So:
[tex]\ell ^3-4\ell ^2+4\ell -16=0[/tex]
We can factor by grouping. From the first two terms, factor out a l² and from the last two terms, factor out a 4:
[tex]\ell ^2(\ell -4)+4(\ell -4)=0[/tex]
Factor:
[tex](\ell ^2+4)(\ell -4)=0[/tex]
Zero Product Property:
[tex]\ell ^2+4=0\text{ or } \ell - 4=0[/tex]
Solve for each case:
[tex]\ell^2=-4\text{ or } \ell =4[/tex]
Since we cannot take the square root of a negative number, we can ignore the first case.
Therefore, the length (or depth) of the storage space is four meters.
Thus, the dimensions are four by two by two meters.
Kern Shipping Inc. has a requirement that all packages must be such that the combined length plus the girth (the perimeter of the cross section) cannot exceed 99 inches. Your goal is to find the package of maximum volume that can be sent by Kern Shipping. Assume that the base is a square.
a. Write the restriction and objective formulas in terms of x and y. Clearly label each.
b. Use the two formulas from part (a) to write volume as a function of x, V(x). Show all steps.
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
Identify the relationship between sampling error and sample size.
Answer:
as the sample size increases, the margin of error decreases
Find the distance between a point (–7, –19) and a horizontal line at y = 3.
4. Temperature graphs from two cities on July 1 are shown below. Which statement is true?
O A. City A experienced a bigger temperature change than City B.
O B. City B experienced a bigger temperature change than City A.
O C. The low temperature in City B was lower than the low temperature in City A.
O D. Both B and C are true.
Answer:
City B experienced a bigger temperature change than City A.
Step-by-step explanation:
From the graph of the temperature given, using visual inspection, we can see how the graph of both cuties change, for city A, the change in temperature, very low as the highest temperature is about 80 and the lowest temperature value is about 76 ;
However. For city B, the highest temperature value is about 100 and the lowest is about 76
Hence, City B experienced a bigger temperature change than A.
For low temperature, the low temperature in city A and B are the same with a value of about 76°
PLEASE ANSWER!! Find EF using Pythagorean theorem. Express answer to one decimal place.
Answer:
115.5 cm
Step-by-step explanation:
A^2 + B^2 = C^2
41^2 + 108^2 = C^2
C^2 = 13345
C = 115.5 cm
Question 14 of 14
Which expression gives the distance between the points
(1,-2) and (2, 4)?
O A. (1+23° +(2-47
O B. (1-2)*+(-2-4)
O c. 111-23 +4:32-47
O D. Hit+2y +(2-479
Answer:
c
Step-by-step explanation:
A ramp is in the shape of a triangle
Answer:
Step-by-step explanation:
Which inequality has the solution shown below?
-18 -17 -16 -15 -14 -13 -12
Answer:
0.2x+5>2
Step-by-step explanation:
0.2 is the same as 2/10;
(2/10)x>2-5
(2/10)x>-3
2x>-30
X>-15( since -15 is lesser than -14,-13,-12 and so on. the sign should be >
In a sample of 400 students, 60% of them prefer eBooks.
A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.
b. Find the margin of erro
Answer:
a) The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).
b) The margin of error is of 0.05.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In a sample of 400 students, 60% of them prefer eBooks.
This means that [tex]n = 400, \pi = 0.6[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.054[/tex].
Margin of error -> Question b:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 2.054\sqrt{0.6*0.4}{400}}[/tex]
[tex]M = 0.05[/tex]
The margin of error is of 0.05.
A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.
Sample proportion plus/minus the margin of error.
0.6 - 0.05 = 0.55
0.6 + 0.05 = 0.65
The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).
The retail cost of a TV is 50 % more than its wholesale cost. Therefore, the retail cost is ____ times the wholesale cost.
Answer:
Let the retail cost be x and the wholesale cost be y
Step-by-step explanation:
x = y + 0.50y
x = 1.50y
Therefore the retail cost is 1.50 times the wholesale cost.
Please help a girl out, math is not my forte
Answer:
80 ft²
Step-by-step explanation:
You are given the formula
a = (1/2)bh
Just plug in the base and height, then multiply
a = (1/2) * 8 *20
a = (1/2) * 160
a = 80 ft²
Answer:
80 [tex]ft^{2}[/tex]
Step-by-step explanation:
Area = [tex]\frac{1}{2} bh[/tex]
Area = [tex]\frac{1}{2}[/tex] 8 · 20
Area = [tex]\frac{1}{2}[/tex] 160
Area = 80 [tex]ft^{2}[/tex]
The company has only two division division eight and division be last year division a made 60% of the companies total revenue and division be made 40% of the total revenue this year division as revenue has decreased by 35% and division bees revenue has decreased by 5% which division had higher revenue this year?
9514 1404 393
Answer:
Division A
Step-by-step explanation:
Suppose last year's revenue for the company was 100 units.
Last year's Division A revenue was 0.60×100 = 60. This year's revenue is 1-35% = 65% of last year's, so is ...
60 × 0.65 = 39 . . . . units
__
Last year's Division B revenue was 0.40×100 = 40. This year's revenue is 1-5% = 95% of last year's, so is ...
40 × 0.95 = 38 . . . . units
__
At 39 units this year, Division A still has the higher revenue than Division B at 38 units.
Is this the correct answer?
Answer:
Correct.
Step-by-step explanation:
It looks good to me.
Good job!
PLEASE HELP ME!!! I need to simplify these equations, not answer them.
Answer:
Step-by-step explanation:
a= 2qr^3 quotent 6p^2
[tex] {x}^{2} + \sqrt{x} + \sqrt[5]{x} [/tex]
what is f'(3) of this equation?
Answer:
[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
Step-by-step explanation:
Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex] This way we could more easily use the power rule of derivatives.
So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.
f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]
to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
Write the simplified expression that represents the perimeter of the triangle below.
X - 3
4x + 4
2x + 1
Show Work
Answer:
Just plus everything together
X-3+4X+4+2X+1
Step-by-step explanation:
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was $2,033.00, and the tax rate in the area is 7%, what was the pre-tax subtotal?
Answer:
i believe the pre-tax subtotal would be 1890.69
Step-by-step explanation:
the 2,033 represents 100%. to remove that 7% you would do
.93 • 2,033 which gives you 1890.69
33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
7) Point P is located at (4,8) on a coordinate plane. Point P will be relfected over y = x. What will bee
the coordiantes of the image of point P?
A. (28,4)
B. 24,8)
C. (4,28)
D. (8,4)
Which of the following points lies on the graph of the function y = 3 Superscript x?
a. (1, 0)
c. (3, 1)
b. (2, 9)
d. (0, 3)
Please select the best answer from the choices provided
A
B
C
D
Answer:
(2,9)
Step-by-step explanation:
I am assuming that you mean: [tex]y= 3^x[/tex]
I have graphed the function given along the points given. When they are graphed, only the point (2,9) lie on the line.
This means that Option B is the correct answer.
See graph below.
Hope this helps.
The radius of a circle is 10 cm. Find its circumference in terms of \piπ.
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle "[tex]r[/tex]" = 10 cm.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The circumference of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:20\:π\:cm.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]
[tex] = 2 \: \pi \times 10 \: cm \\ \\ = 20 \: \pi \: cm[/tex]
Therefore, the circumference of the circle is 20 π cm.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
The Centers for Disease Control and Prevention Office on Smoking and Health (OSH) is the lead federal agency responsible for comprehensive tobacco prevention and control. OSH was established in 1965 to reduce the death and disease caused by tobacco use and exposure to secondhand smoke. One of the many responsibilities of the OSH is to collect data on tobacco use. The following data show the percentage of U.S. adults who were users of tobacco for a recent 11-year period
Year Percentage of Adults Who Smoke
1 22.9
2 21.7
3 21
4 20.3
5 20.3
6 19.9
7 19.4
8 20.7
9 20.7
10 19
11 18.8
What type of pattern exists in the data?
Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to three decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)
y-intercept, b0 =
Slope, b1 =
MSE =
One of OSH’s goals is to cut the percentage of U.S. adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does your regression model from part (b) suggest that OSH is on target to meet this goal?
Use your model from part (b) to estimate the number of years that must pass after these data have been collected before OSH will achieve this goal. Round your answer to the nearest whole number.
years.
Answer:
1.) A negative linear pattern
2.) Y = - 0.298X1 + 22.241
3.) slope = - 0.298 ; intercept = 22.241
Kindly check explanation
Step-by-step explanation:
Fitting the time series data using technology, the regression equation obtained is :
Y = - 0.298X+ 22.241
Where ; y = percentage of adults who smoke
x = year
Comparing with the linear equation model :
y = b1x + b0
y = - 0.298x + 22.41
-0.298 = slope
22.41 = intercept
The mean squared error, MSE = 0.512
To achieve, percentage users of 12% or less :
y = 12
Y = - 0.298X+ 22.241
12 = - 0.298X + 22.241
12 - 22.241 = - 0.298X1
-10.241 = - 0.298X
X = 10.241 / 0.298
X = 34.365
X = 35 years
From the model OSHA is not on target to meet it's goal as it will take 35 - 11 = 24 years from the last year of the data to achieve a smoker percentage less Than 12%
Let f(x)=x2+10x+37 .
What is the vertex form off(x)?
What is the minimum value off(x)?
Enter your answers in the boxes.
Vertex form: f(x)=
Minimum value of f(x):
Answer:
f(x) = (x+5)^2 +12
The minimum value is 12
Step-by-step explanation:
f(x)=x^2+10x+37
The vertex will be the minimum value since this is an upwards opening parabola
Completing the square by taking the coefficient of x and squaring it adding it and subtracting it
f(x) = x^2+10x + (10/2) ^2 - (10/2) ^2+37
f(x) = ( x^2 +10x +25) -25+37
= ( x+5) ^2+12
Th is in vertex form y = ( x-h)^2 +k where (h,k) is the vertex
The vertex is (-5,12)
The minimum is the y value or 12
Xavier shoots a basketball in which the height, in feet, is modeled by the equation,h(t) = -4t2 + 10 + 18, where t is time, in
seconds. What is the maximum height of the basketball?
Answer:
The maximum height of the basketball is of 24.25 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Height of the basketball:
Given by the following function:
[tex]h(t) = -4t^2 + 10t + 18[/tex]
Which is a quadratic function with [tex]a = -4, b = 10, c = 18[/tex]
What is the maximum height of the basketball?
y(in this case h) of the vertex. So
[tex]\Delta = b^2-4ac = 10^2 - 4(-4)(18) = 388[/tex]
[tex]y_{v} = -\frac{388}{4(-4)} = 24.25[/tex]
The maximum height of the basketball is of 24.25 feet.
Answer to the question?
Answer:
35
Step-by-step explanation:
AEC and AEB form a straight angle(180°)
180-40=140
AEV and AED are equal
140 divided by 4 = 35
Sand is being dumped from a conveyor belt and forms a conical pile. Assuming that the height of this cone is always exactly 3 times the size of the radius of its base, and that thesand is added at the rate of 10 m^3/min, how fast is the height increasing when the pile is15 m high?
Answer:
dh/dt = 0.4 m/min
Step-by-step explanation:
The volume of the cone is:
V(c) = (1/3)*r² *h if always h = 3r then r = h/3
The volume of the cone as a function of h will be:
V(h) = (1/3)* (h/3)²*h
V(h) = (1/27)*h³
The increasing rate of the volume is equal to the rate of sand added the:
D(V)/dt = (1/27)*3*h²*dh/dt
D(v) / dt = 10 m³/min
h = 15 m and dh/dt is the rate of increasing of the height
By substitution
10 m³/min = ( 1/9)* 225 * dh/dt (m²)
dh/dt = 90 / 225 m/min
dh/dt = 0.4 m/min
a Dhruv sold one second-hand car for 1,10,500 and two second-hand scooters for 7,500 each.
Answer:i actually dunno
Step-by-step explanation:
wat
question : Suppose you have VND 100 million to save orspend. If you lend, you will receive 112 million after a year. Inflation is 14% / year.
a. What is the nominal interest rate you get?
b. What is the real interest rate?
c. Should you save or spend that money?
d. Question (c) how will be answered if inflation is 10% / year, nominal interest rates do not change?
Answer:
Step-by-step explanation:
Based on the information below, which statement provides a logical
conclusion?
On Monday, Suzanne got up at 6:00 a.m. and was on time for first period.
On Wednesday, Suzanne got up at 6:15 a.m. and was late to first period.
Answer:
It's A because on b it says is she gets up after 6:00 she will not be late and that's wrong cause she will be
Which of the following is the simplified form of? Jx/
xVx?
ox
x21
O 21 /
Points eamed on this question: 0
Use the following property below:
[tex] \large \boxed{ \sqrt[n]{a} \times \sqrt[n]{a} \times \sqrt[n]{a} = { (\sqrt[n]{a}) }^{3} }[/tex]
Therefore,
[tex] \large{ \sqrt[7]{x} \times \sqrt[7]{x} \times \sqrt[7]{x} = { (\sqrt[7]{x}) }^{3} }[/tex]
Then we use next property.
[tex] \large{ \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } }[/tex]
Hence,
[tex] \large{ \sqrt[7]{ {x}^{3} } = {x}^{ \frac{3}{7} } }[/tex]
Answer
x^(3/7)