Answers
12 in by 22 in by 4 in
the explanation is as shown in the figure
The dimension will be x , 20 - 2x , 30 -2x
the volume= v = x(20-2x)(30-2x) = 4x³ - 100x² + 600x
differentiating with respect to x and equating to zero
dv/dx = 12x² - 200x + 600 = 0
solve for x using calculator
x = 12.7 (unacceptable) or x = 3.92 ≈ 4
∴ The dimension will be 4 , 12 , 22
Solution:The dimension = x , 20 - 2x , 30 -2x
the volume=
v = x(20-2x)(30-2x)
= 4x³ - 100x² + 600x
dv/dx = 12x² - 200x + 600 = 0x = 12.7
x = 3.92
≈ 4
Dimension: 4 , 12 , 22
Related Questions
Please help! What is the simplest form of expression
Answers
First you should reduce the fraction
Subtract the exponent by its common variables;
x^8 - x^2 = x^6
y^9 - y^4 = y^5
Now your equation should be \frac{ \sqrt{6x^{6}y^{5} } }{ \sqrt{5} }
Then you should simplify your radical,
there are 3 groups of 2 in the x variables and 2 groups of 2 in the y variables, as a result, the x and y go outside the square root, and one y variable remains in the root (as there wasn't enough y's to make another group of 2) this should be over 5
Find the area in the first quadrant under the curve y = 1 / (x^2+6x+10)
Answers
[tex]\displaystyle\int_0^\infty\frac{\mathrm dx}{x^2+6x+10}[/tex]
Complete the square in the denominator:
[tex]x^2+6x+10=x^2+6x+9+1=(x+3)^2+1[/tex]
then substitute [tex]x+3=\tan y[/tex], so that [tex]\mathrm dx=\sec^2y\,\mathrm dy[/tex]. Then as [tex]x\to0^+[/tex], we have [tex]y\to\arctan3[/tex]; as [tex]x\to\infty[/tex], we have [tex]y\to\dfrac\pi2[/tex]. So the integral becomes
[tex]\displaystyle\int_{\arctan3}^{\pi/2}\frac{\sec^2y}{\tan^2y+1}\,\mathrm dy=\int_{\arctan3}^{\pi/2}\mathrm dy=\dfrac\pi2-\arctan3[/tex]
Find the dimensions of a rectangle with an area of 100 square feet that has the minimum perimeter.
Answers
The side length of the square with an area of 100 ft² is √(100 ft²) = 10 ft.
The rectangle with the minimum perimeter for an area of 100 ft² is 10 ft by 10 ft.
The rectangle with an area of 100 square feet that has the minimum perimeter is a square with sides of 10 feet each.
Explanation:To find the dimensions of a rectangle with a particular area that has the minimum perimeter, the rectangle should be a square. This is because squares minimize perimeter for a fixed area.
Given the area of the rectangle (square in this case), which is 100 square feet, the sides would be the square root of the area. Therefore, in this case, the length and the width of the rectangle (also known as the dimensions) are both √100 = 10 feet.Hence, the rectangle with an area of 100 square feet and minimum perimeter is a square with side lengths of 10 feet.
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PLEASE HELP ASAP Arrange the expressions in increasing order of their values.
(10⁰x 10¹ x 1¹⁰) (10 x 10¹) (10⁰+10¹+1¹⁰) (10⁰+10¹x 1¹⁰)
Answers
(10⁰x 10¹ x 1¹⁰)
(10 x 10¹)
(10⁰ + 10¹ + 1¹⁰)
(10⁰ + 10¹x 1¹⁰)
Rewrite we have:
(1x 10 x 1) = 10
(10 x 10) = 100
(1 + 10 + 1) = 12
(1 + 10x 1) = 11
Answer:
In increasing order we have:
(10⁰x 10¹ x 1¹⁰)
(10⁰ + 10¹x 1¹⁰)
(10⁰ + 10¹ + 1¹⁰)
(10 x 10¹)
Final answer:
After calculating the values of the expressions, they can be arranged in increasing order of their values as follows:
(10⁰x 10¹ x 1¹⁰), (10⁰ + 10¹x 1¹⁰), (10⁰ + 10¹ + 1¹⁰), (10 x 10¹).
Explanation:
To arrange the expressions in increasing order of their values, we must first calculate the value of each expression.
(10⁰ x 10¹ x 1¹⁰): Here, 10⁰ = 1, 10¹ = 10, and 1¹⁰ = 1 (since any number to the power of zero is 1). Multiplying these together, we get 1 x 10 x 1 = 10.(10 x 10¹): This equals 10 x 10 = 100.(10⁰+10¹+1¹⁰): Adding these values together gives us 1 + 10 + 1 = 12.(10⁰+10¹ x 1¹⁰): Following the rules of operations (multiply before adding), first calculate 10¹ x 1¹⁰ which equals 10 x 1 = 10, then add 10⁰ which is 1. So, this gives 1 + 10 = 11.Now we can arrange the expressions in increasing order:
(10⁰x 10¹ x 1¹⁰) (10⁰ + 10¹x 1¹⁰) (10⁰ + 10¹ + 1¹⁰) (10 x 10¹)During a basketball game a player makes 12 of 18 free throws attempted write the ratio as fraction reduced to the lowest term
Answers
Final answer:
The ratio of free throws made to free throws attempted by the player is 12/18, which can be reduced to its lowest terms by dividing both numbers by their greatest common divisor, 6, resulting in the reduced fraction 2/3.
Explanation:
To find the ratio of free throws made to free throws attempted, we start by looking at the numbers given: 12 made out of 18 attempted. We express this ratio as a fraction 12/18.
To reduce this fraction to its lowest terms, we need to find the greatest common divisor (GCD) that divides both numerator and denominator evenly.
In this case, the number 6 is the GCD of 12 and 18. Dividing both the numerator and the denominator by 6, we get 2/3.
Hence, the ratio of free throws made to free throws attempted, reduced to the lowest term, is 2/3.
the hall family garden is 3/4 of an acre. if they divide their garden into 1/8 acre sections, how many sections will they have?
Answers
The hall family garden is ------------> 3/4 of an acre
if they divide their garden into 1/8 acre sections
so
(3/4)/(1/8)-------> (3/4)*(8)--------> 8*3/4------> 24/4-----> 6 sections
the answer is
6 sections
Answer:
6 sections
Step-by-step explanation:
You backpacked for a distance of 15.75 miles today. If you backpacked at an average speed of 1.26 miles per hour, how many hours did you spend backpacking today?
Answers
Total hour = 15.75 ÷ 1.26 = 12.5 hours
Answer: 12.5 hours
# 14. Q. find the area of rectangle
Answers
You must multiply the height and the width.
8 x 14 = 112
Area = Length x Width
From figure we can see,
Length = 14 ft
Width = 8 ft
So, Area = 14 x 8 = 112 ft²
Thus, the option third gives the correct measure of Area for given rectangle
Hey can you please help me posted picture of question
Answers
Explanation:
All the other options are theoretical probabilities because they were determined using the equation:
probablity = number of positive events / total number of possible events.
While, experimental probabilities are determined from actual results of an experiment (test). That is what the option C. describes. It compares the number of times that she actually got a message (5) with the number of trials (12). It is not determined theoretically.
Find the area for the given shape below
Answers
The base of the triangle is 14m.
The height of the triangle is 10m.
Plug these values into the formula and solve.
A = bh/2
A = 14(10)/2
A = 140/2
A = 70
Answer:
The area of the triangle is 70 m².
Hey can you please help me posted picture of question
Answers
When two probabilities are multiplied together, then the probability represents a compound event. In probability, a compound event refers to two or more events that are happening simultaneously. The calculation goal is usually to find the probability of all those events actually occurring.
Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula [ BLANK ] The value of f(-1) is [BLANK] The value of f(-4) is .[BLANK] The average rate of change of f(x) over the interval [-4, -1] is .[BLANK]
First set of answers: A. [f(-4)-f(-1)]/[-5]
B.[f(-1)-f(-4)]/[-5]
C.[f(-1)-f(-4)]/[3]
D.[f(-4)-f(-1)]/[3]
Second set of answers: A.3 Third set: A.-4 Final set A.-2
B.2 B.-3 B.-1.5
C.-1 C.4 C.2
D.4
Answers
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2
==============================================
Explanation:
For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval
In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ]
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank
-------------------------------------------
To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.
-------------------------------------------
Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4
This is why f(-4) = -3
-------------------------------------------
We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.
From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]
We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3
Doing those replacements and simplifying leads to...
[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2
So the average rate of change is 2
Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.
Sam entered three functions into a graphing calculator, y1 = x + 2, y2 = x2 + 2, and y3 = 2x. A portion of the table created by those functions is shown below.
Answers
y1 = x + 2
y2 = x ^ 2 + 2
y3 = 2 ^ x
For x = 0:
y1 = 0 + 2 = 2
y2 = 0 ^ 2 + 2 = 0 + 2 = 2
y1 = y2
For x = 5
y2 = 5 ^ 2 + 2 = 25 + 2 = 27
y3 = 2 ^ 5 = 32
y3> y2
For x = -1:
y1 = -1 + 2 = 1
y2 = (-1) ^ 2 + 2 = 1 + 2 = 3
y3 = 2 ^ (- 1) = 1/2 = 0.5
y3 <y1 <y2
Answer:
y1 = y2
y3> y2
y3 <y1 <y2
Hey can you please help me posted picture of question
Answers
For example, sample space for tossing a coin will be {H, T} ,where H stands for Head and T stands for Tail
Likewise sample space for throwing a dice will be: {1, 2, 3 ,4, 5 ,6}
Thus, the answer to this question is option A
A. The set of all possible outcomes.
Factor completely a2 - 9a + 20
Answers
You can check, the numbers add up, because -5 - 4 is 9, and 5 * 4 is 20
a^2-9a+20=a(a^2/a-5a/a)+(-4)(-4a/(-4)+20/(-4))
a^2-9a+20=a(a-5)-4(a-5)
a^2-9a+20=(a-5)[a(a-5)/(a-5)-4(a-5)/(a-5)]
a^2-9a+20=(a-5)(a-4)
Find the greatest common factor of 30 and 60
Answers
I hope this helped
NEED HELP ASAP PLEASE
Answers
For example,
(3/28) / (-1/4) = 3/28 * (-4/1) = -12/28 = -3/7
Answer: -3/7
Item 14 You develop an app to help students complete their homework. To earn money, you sell advertising space on the app’s main screen. An advertiser pays you $20 per month and an additional $0.005 each time the app is opened. Graph the linear equation that represents your monthly income y (in dollars) when the app is opened x times.
Answers
x ⇒⇒⇒ number of times app is opened
$20 per month and an additional $0.005 each time the app is opened
∴ y = 0.005 x + 20
The attached figure represents the graph of y
Answer:
See attached diagram
Step-by-step explanation:
Let x be the number of times the app is opened and y be your monthly income (in dollars).
If an advertiser pays you $0.005 each time the app is opened, then he pays you $0.005x for all times the app is opened. Since an advertiser pays you $20 per month, then the total income is
y=20+0.005x.
Plot this line on the coordinate plane (see attached diagram).
The ratio of the number of peas Julia had to the number of peas Vlada had was 3:2. After Julia gave Vlada 15 peas, she still had 10 more peas than Vlada. How many peas did Julia have at first?
Answers
3:2 x 40 = 120:80
J: 120-15 = 105
V: 80+15 = 95
J:V is now 105:95
The original amount of peas that Julia had at first was 120.
Find a negative real number such that the square of the sum of the number and
25 is equal to 36
Answers
[tex](n+25)^2=36[/tex]
Take square root of both sides:
[tex]|n+25|=6\quad\Longrightarrow\quad n+25 = 6\ \text{ or }\ n+25=-6[/tex]
Then subtract both sides by 25:
[tex]n = 6-25\ \text{ or }\ n=-6-25\\\ \\\boxed{n=-19\ \text{or}\ n=-31}[/tex]
Hope this helps.
Mary used a thermometer to measure the temperature of water at different states. What would the Celsius thermometer read when water froze and became a solid ?
A) -32 o
B) 0 o
C) 25 o
D) 32 o
Answers
A transformation of a figure that flips a figure across a line
Answers
2.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $8,900
Finance Charge: $1,030.62
Number of Payments: 24
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Finance Charge: $1,030.62
Number of Payments: 24
(Finance Charge)/(Amount Financed)*100$=($1,030.62)/($8,900)*100$
(Finance Charge)/(Amount Financed)*100$=(0.1158)*100$
(Finance Charge)/(Amount Financed)*100$=$11.58
In the row of number of Payments 24, we look for:
(Finance Charge)/(Amount Financed)*100$=$11.58, and we to which annual porcentage rate it corresponds in the first row
Answer: The annual percentage rate is 10.75%
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Maggie has 7 tiles with pictures of plants and 2 tiles with pictures of animals. Maggie keeps all the tiles on a mat with the pictures hidden and mixes them up. She then turns one tile face up and finds the picture of a plant on it. She removes this tile from the mat and turns over another tile without looking. What is the probability that the second tile that Maggie turns over has a plant on it? 22.2% 28.6% 65.0% 75.0%
@musiclover10045
Answers
15 + (-18) =
Please help quick
Answers
hope this help........................
Solve the problem by applying the fundamental counting principle. an apartment complex offers apartments with four different options, designated by a through
d. aequalsnumber of bedrooms (one through four) bequalsnumber of bathrooms (one through three) cequalsfloor (first through fifth) dequalsoutdoor additions (balcony or no balcony) how many apartment options are available?
Answers
We have been given that an apartment complex offers apartments with four different options, designated by a through d.
From the given directions we have
4 choices are for a3 choices are for b5 choices are for c2 choices are for dTherefore, from the fundamental theorem of counting principle number of available apartments are
[tex]4\times 3\times 5\times 2 =120[/tex]
Hence, 120 apartments options are available.
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Triangle Z' is the image of triangle Z after a series of transformations.
Aliyah and Ivan described the sequence of transformations in different ways.
Which sequence or sequences are correct and why?
GRID AND ANSWERS PROVIDED IN IMAGES!
Answers
Answer:
The third option is correct.
Step-by-step explanation:
at elm elementary school for every 5 students who walk to school there are 7 students who take the bus.if 420 students attend elm elementary school how many of them walk to school? tell me how you got the answer and will mark brainliest
Answers
The students walk to school is 175.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
let the ratio of students who walk to students who take bus = 5: 7
let the common ratio be x.
So, Number of students who walk = 5x
and, Number of students who Bus= 7x
Total students= 420
So, 5x+ 7x = 420
12x= 420
x= 35
Hence, students walk to school =5 x 35 = 175.
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"A magician performing a magic act has asked for 2 volunteers from the audience to help with his routine. If there are 250 people in the audience, which of the following expressions represents the number of possible pairs of volunteers?"
Answers
Number of people in the audience = 250
Number of volunteers required to perform the magic act from the audience =2
As 2 people can be selected from 250 people by using the properties of combination as order of choosing people is not important.
Possible number of ways = [tex]_{2}^{250}\textrm{C}[/tex]
= [tex]\frac{250!}{2!\times 248!}=249 \times 125=[/tex]
= 31125 ways
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.