Answer:
a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.
Step-by-step explanation:
a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:
[tex]V = w \cdot h \cdot l[/tex]
Where:
[tex]w[/tex] - Width, measured in meters.
[tex]h[/tex] - Height, measured in meters.
[tex]l[/tex] - Length, measured in meters.
The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:
[tex]\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l[/tex]
Where [tex]\dot w[/tex], [tex]\dot h[/tex] and [tex]\dot l[/tex] are the rates of change related to the width, height and length, measured in meters per second.
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the volume of the box is:
[tex]\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)[/tex]
[tex]\dot V = 54\,\frac{m^{3}}{s}[/tex]
The rate of change associated with the volume of the box is 54 cubic meters per second.
b) The surface area of the parallelepiped, measured in square meters, is represented by this model:
[tex]A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)[/tex]
The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:
[tex]\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h[/tex]
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the surface area of the box is:
[tex]\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)[/tex]
[tex]\dot A_{s} = 18\,\frac{m^{2}}{s}[/tex]
The rate of change associated with the surface area of the box is 18 square meters per second.
c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:
[tex]r^{2} = w^{2}+h^{2}+l^{2}[/tex]
The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:
[tex]2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l[/tex]
[tex]r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l[/tex]
[tex]\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}[/tex]
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the length of the diagonal of the box is:
[tex]\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}[/tex]
[tex]\dot r = -1\,\frac{m}{s}[/tex]
The rate of change of the length of the diagonal is -1 meters per second.
Suppose we want to test the claim that the majority of adults are in favor of raising the vote age to 21. Is the hypothesis test left tailed, right tailed or two tailed
Answer:
The hypothesis test is right-tailed.
Step-by-step explanation:
We are given that we want to test the claim that the majority of adults are in favor of raising the voting age to 21.
Let p = proportion of adults who are in favor of raising the voting age to 21
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%
Alternate Hypothesis, [tex]H_A[/tex] : p > 50%
As we know that the majority is there when we have more 50% chance of happening of that event.
Here, the null hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is less or equal to 50%.
On the other hand, the alternate hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is more than 50%.
This shows that our hypothesis test is right-tailed because in the alternate hypothesis, the greater than sign is included.
Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
u = -4 A = 1 0 3
-5 -2 -1 -4
3 3 -3 0
1 -1 3 6
A) In Col A, not in Nul A
B) Not in Col A, not in Nul A
C) In Col A and in NulA
D) Not in Col in Nul A
Answer: d) Not in Col in Nul A
Step-by-step explanation: The definition of Column Space of an m x n matrix A is the set of all possible combinations of the columns of A. It is denoted by col A. To determine if a vector is a column space, solve the matrix equation:
A.x = b or, in this case, [tex]A.x=u[/tex].
To solve, first write the augmented matrix of the system:
[tex]\left[\begin{array}{cccc}1&0&3&-4\\-2&-1&-4&-5\\3&-3&0&3\\-1&3&6&1\end{array}\right][/tex]
Now, find the row-echelon form of matrix A:
1) Multiply 1st row by 2 and add 2nd row;
2) Multiply 1st row by -3 and add 3rd row;
3) MUltiply 1st row by 1 and add 4th row;
4) MUltiply 2nd row by -1;
5) Multiply 2nd row by 3 and add 3rd row;
6) Multiply 2nd row by -3 and add 4th row;
7) Divide 3rd row by -15;
8) Multiply 3rd row by -15 and add 4th row;
The echelon form matrix will be:
[tex]\left[\begin{array}{cccc}1&0&3&-4\\0&1&-2&13\\0&0&1&-\frac{51}{15}\\0&0&0&-13 \end{array}\right][/tex]
Which gives a system with impossible solutions.
But if [tex]A.x=0[/tex], there would be a solution.
Null Space of an m x n matrix is a set of all solutions to [tex]A.x=0[/tex], so vector u is a null space of A, denoted by null (A)
Help please and thank you
Answer:
1
Cans 4cans 8 cans 12 cans
Cost $2.25 $4.5 $6.75
2
Ice Cream 180 q 360 q 540 q 720q 900q 1080 q
Hours 2 hours 4 hours 6 hours 8 hours 10 hours 12 hours
***q = quarts
3
Distance 650 miles 1300 miles 1950 miles
Hours 3 hours 6 hours 9 hours
Answer:
Question 1 - 8 cans = $4.50, 12 cans = $10.13
Question 2 - 4 hours = 360 quarts, 6 hours = 540 quarts, 8 hours = 720 quarts, 12 hours = 1,170
Question 3 - 1,950 miles in 9 hours
Hope this helps :)
The approximate measurements of the Great Pyramid of Khufu are shown below. A square pyramid. The base is 230 meters by 230 meters. The triangular sides have a base of 230 meters and height of 187 meters. The pyramid has a height of 147 meters. What is the surface area of the pyramid? 86,020 meters squared 138,920 meters squared 224,940 meters squared 2,592,100 meters squared
Answer:
138,920 m²
Step-by-step explanation:
A square pyramid has 1 square base and 4 lateral triangular faces.
Area of square pyramid is given as BASE Area (BA) + ½*Perimeter of Base (P) × Slant height
Area of pyramid = [tex] b^2 + \frac{1}{2}*4(b)*l [/tex]
Where,
b = base length = 230 m
l = slant height = 187 m (height of the triangular sides)
Surface area = [tex] 230^2 + \frac{1}{2}*4(230)*187 [/tex]
[tex] = 52900 + 2(230)*187 [/tex]
[tex] = 52900 + 86020 [/tex]
[tex] = 138920 [/tex]
Surface area of the pyramid = 138,920 m²
Answer:
hope i helped thank you
Step-by-step explanation:
The prices for a loaf of bread and a gallon of milk for two supermarkets are shown below. Sue needs to buy bread and milk for her church picnic. At Supermarket A, she would pay $137.24. At Supermarket B, she would pay $140.04. Which of the following system of equations represents this situation?
Answer:
B. 3.19b + 4.59m = 137.24
3.49b + 4.39m = $140.04
Step-by-step explanation:
A B
Bread $3.19 $3.49
Milk $4.59 $4.39
Sue paid $137.24 in supermarket A
Sue paid $140.04 in supermarket B
Let
Price of bread A=$3.19
Price of bread B=$3.49
Price of milk A=$4.59
Price of milk B=$4.39
Quantity of Bread=b
Quantity of Milk=m
Pb=price of bread
Pm=price of milk
Qb=Quantity of bread
Qm=Quantity of milk
For each supermarket
Supermarket A Equation
PbQb + PmQm =$137.24
3.19b+ 4.59m = 137.24
Supermarket B Equation
PbQb + PmQm=$140.04
3.49b + 4.39m = $140.04
Combining both equations
3.19b + 4.59m = 137.24
3.49b + 4.39m = $140.04
Graph the equation y = 1/2x + 5 on the coordinate plans provided below.
Answer:
Well, of course, i can not graph it in the coordinate plane in the image, but i can try to teach you how to do it.
We have the function y = (1/2)*x + 5
The first step is to generate pairs (x, y)
You can do it by evaluating the function in different values of x.
For example;
if x = 0
y = (1/2)*0 + 5 = 5
then we have the point (0,5)
if x = 2
y = (1/2)*2 + 5 = 6
Then we have the point (1, 6)
Now, with only two points you can graph the line.
First find the points in the coordinate plane, and mark them.
Now, with a ruler, draw a line that connects the two points.
That line is the graph of the function.
An example of the graph is:
N
5. Use AABC to find the value of sin B.
A 7
B
25
B 24
C
24
А
C7
25
D 24
*see the attachment below for the missing figure
Answer:
[tex] sin B = \frac{24}{25} [/tex]
Step-by-step explanation:
Given a right angled triangle, ∆ABC
AB = 25
BC = 7
AC = 24
<ACB = 90°
Required:
Value of Sin B
Solution:
Using trigonometric ratio formula,
[tex] sin B = \frac{opposite}{hypotenuse} [/tex]
Opposite = AC = 24 (the side opposite to <B)
Hypotenuse = AB = 25 (the longest side facing the right angle)
[tex] sin B = \frac{24}{25} [/tex]
Evaluate the expression 23^0-15^1+18^0+(43-12)
Answer:
18
Step-by-step explanation:
23^0 - 15^1 + 18^0 + (43 - 12) =
= 1 - 15 + 1 + 31
= -14 + 1 + 31
= -13 + 31
= 18
Daniels freezer is set to 0degrees Fahrenheit he places a load of bread that was at a temperature of 78 degrees Fahrenheit in the freezer the bread cooled at a rate of 11 degrees Fahrenheit per hour write and graph an equation that models the temperature t of the bread
Answer:
it took 7 hours for the bread to drop at a constent rate
Step-by-step explanation:
Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 66 times and record the outcomes. They conduct a chi-square Goodness-of-Fit hypothesis test at the 5% significance level. (a) The null and alternative hypotheses are: H0: The die has the uniform distribution. Ha: The die does not have the uniform distribution. (b) χ20=15.091. (c) χ20.05=11.070. (d) What conclusions can be made? Select all that apply. Select all that apply: We should reject H0. We should not reject H0. At the 5% significance level, there is sufficient evidence to conclude that the die is not fair. At the 5% significance level, there is not enough evidence to conclude that the die is not fair.
Answer:
We should reject H0
At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The critical value is 15.091 and test statistic is 11.070. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.
Change Y = 3X to the standard form of the equation of a line.
Answer:
-3x+y=0
Step-by-step explanation:
Standard form= Ax+Bx=C
Add -3x both sides, answer -3x+1y=0
pls help me with all 3 questions! correct answer will get brainliest and a kiss...
Answer:
1.union = {20 21 22 23 25 27 29}
2. intersection = {5 14 22}
3.1/3
Step-by-step explanation:
1. union U of sets a nd b ={20 21 22 23 25 27 29}
2. intersection n of sets a nd b = {5 14 22}
3. probability = one item / total
= 1/3
1.
A. {22, 25, 27, 29}
B. {20, 21, 22, 23}
Answer: A∪B = {22, 25, 27, 29, 20, 21, 23}
2.
A. {1, 5, 10, 14, 22}
B. {5, 14, 20, 22, 27}
Answer: A∩B = {5, 14, 22}
3.
A. {1, 5, 10, 14, 22}
B. {5, 14, 20, 22, 27}
Answer: The three items that are intersecting each have a 1/3 chance of being chosen.
Rewrite2(4)(6) in a different way, using the Commutative Law of Multiplication.
Answer:
2(6)(4)
Step-by-step explanation:
The commutative law of multiplication states that the order of the numbers does not affect the answer. To rewrite 2(4)(6) using the commutative law of multiplication, rearrange the order of the numbers.
A baseball is hit into the air, and its height h in feet after t seconds is given by h(t)= -16t^2+128t+2. The height of the baseball when it is hit is ? The baseball reaches its maximum height after ? The maximum height of the baseball is ?
Answer:
[tex]\large \boxed{\sf \ \text{2 feet, 4 seconds, 258 feet } \ }[/tex]
Step-by-step explanation:
Hello,
To know the height of the baseball when it is hit we have to compute h(0), as t = 0 is when the baseball is hit into the air.
[tex]h(0)=-16\cdot 0^2+128 \cdot 0+2=2[/tex]
So, the answer is 2 feet.
h(x) is a parabola which can be written as [tex]ax^2+bx+c[/tex], it means that the vertex is the point (-b/2a,h(-b/2a)).
The baseball reached its maximum height after
[tex]\dfrac{-b}{2a}=\dfrac{-128}{-2*16}=\boxed{4 \text{ seconds}}[/tex]
And the maximum height of the baseball is h(4).
[tex]h(0)=-16\cdot 4^2+128 \cdot 4+2=-256+512+2=\boxed{258 \ \text{feet}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
HELP PLZZZ will give branliesstttttt Triangle congruence with sss asa aas sas
Answer:
1) Not congruent
2) AAS
3) Not congruent
4) SAS
5) SSS
6) ASA
Step-by-step explanation:
In SSS, ASA, AAS, and SAS, S stands for side and A stands for angle. If the sides and angles are congruent in any of those patterns, the triangles are congruent.
Hope it helps <3
Answer:
1. Not congruent
2. AAS, Congruent
3. Not congruent
4. SAS, congruent
5. SSS, congruent
6. ASA, Congruent
Step-by-step explanation:
1. Not congruent
It only shows that there are 3 similar angles. There were no sides described.
2. AAS, Congruent
They are congruent, just rotated in an angle (see proof 2)
3. Not congruent
It only shows 2 sides next to each other and an angle next to one side.
4. SAS, congruent
It shows 2 sides that are congruent and congruent angles between them (see proof 4)
5. SSS, congruent
All 3 sides are congruent (see proof 5,6)
6. ASA, Congruent
2 angles and an adjacent side are congruent(see proof 5,6)
A submarine is moving parallel to the surface of the ocean at a depth of 626 m. It begins a
constant ascent so that it will reach the surface after travelling a distance of 4420 m.
a) What angle of ascent, to the nearest tenth of a degree, did the submarine make? (3
marks)
b) How far did the submarine travel horizontally, to the nearest metre, during its ascent to
the surface? (3 marks)
Answer:
a) the angle of ascent is 8.2°
b) the horizontal distance traveled is 4375 m
Step-by-step explanation:
depth of ocean = 626 m
distance traveled in the ascent = 4420 m
This is an angle of elevation problem with
opposite side to the angle = 626 m
hypotenuse side = 4420 m
a) angle of ascent ∅ is gotten from
sin ∅ = opp/hyp = 626/4420
sin ∅ = 0.142
∅ = [tex]sin^{-1}[/tex] 0.142
∅ = 8.2° this is the angle of ascent of the submarine.
b) The horizontal distance traveled will be gotten from Pythagoras theorem
[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]
The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances
[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]
adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]
adj = 4375 m this is the horizontal distance traveled.
A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured.
Fertilizer Amount (ounces) Tomato Plant Height (inches)
1.9 20.4
5.0 49.2
4.2 56.1
1.3 24.3
4.9 29.2
5.4 60.8
3.1 24.6
0.0 25.3
2.3 26.2
2.5 25.7
0.9 26.5
1.0 28.6
4.5 62.9
3.8 30.8
5.3 43.2
2.3 33.4
4.0 35.1
1.4 22.1
3.9 40.6
Required:
a. Estimate the model: Height = β0 + β1Fertilizer + ε.
b. Does the y-intercept make practical sense?
c. Use the estimated model to predict, after four months, the height of a tomato plant which received 3.0 ounces of fertilizer.
Answer: hello your table is incomplete here is the complete table
Fertilizer Amount (ounces) Tomato Plant Height (inches)
1.9 20.4
5.0 49.2
4.2 56.1
1.3 24.3
4.9 29.2
5.4 60.8
3.1 24.6
0.0 25.3
2.3 26.2
2.5 25.7
0.9 26.5
1.0 28.6
4.5 62.9
3.8 30.8
5.3 43.2
2.3 33.4
4.0 35.1
1.4 22.1
3.9 40.6
4.0 44.5
3.6 29.7
0.6 21.1
1.6 25.4
2.5 29.6
4.5 27.6
3.6 32.6
2.0 33.5
0.0 22.5
2.5 27.6
3.1 46.4
Answer : a)Height = 18.639 + 5.208 * fertilizer
b) The Y intercept make practical sense because without fertilizer there will still be an increase in plant height ( y intercept )
c) 34.263
Step-by-step explanation:
A) Estimating the model
Height = β0 + β1 FERTILIZER + ∈
β0 = 18.639
β1 = 5.208
hence
Height = 18.639 + 5.208 * fertilizer ( using excel )
B) The y- intercept
The Y intercept make practical sense because without fertilizer there will still be an increase in plant height ( y intercept )
C ) using the estimated model to predict after four months
the model = 18.639 + 5.208 * fertilizer
fertilizer ounce given = 3
therefore height of tomato plant after 4 months that received 3 ounces of fertilizer = 18.639 + 5.208 * 3 = 34.263
What is the value of x?
Answer:
13=x
Step-by-step explanation:
Since BE is a bisector
ABE = EBC
2x+20 = 4x-6
Subtract 2x from each side
2x+20-2x =4x-6-2x
20 = 2x-6
Add 6 from each side
20+6 = 2x-6+6
26 = 2x
Divide each side by 2
26/2 = 2x/2
13=x
Answer:
x = 13
Step-by-step explanation:
The angle bisector theorem means that m<ABE = m<EBC. Now that we know they are equal, we can set the equations to each other and solve for x.
2x + 20 = 4x - 6
26 = 2x
13 = x
So the value of x is 13.
Cheers.
A bag of 20 tulip bulbs purchased from a nursery contains 10 red tulip bulbs, 7 yellow tulip bulbs, and 3 purple tulip bulbs. What is the probability of randomly selecting a purple tulip bulb from the bag
Answer:
3/20
Step-by-step explanation:
since there is a total of 20 tulips that would be your denominator then your numerator would be the number of purple tulips which would be 3 so you probability of randomly selecting a purple tulip would be 3/20
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C
Maricopa's Success scholarship fund receives a gift of $ 230000. The money is invested in stocks, bonds, and CDs. CDs pay 2.5 % interest, bonds pay 2.2 % interest, and stocks pay 11.3 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 12095 , how much was invested in each account?
Maricopa's Success scholarship fund receives a gift of $ 170000. The money is invested in stocks, bonds, and CDs. CDs pay 3.25 % interest, bonds pay 4.4 % interest, and stocks pay 11.4 % interest. Maricopa Success invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 10055 , how much was invested in each account?
--------------------------
Equations:
s + b + C = 170000
11.4s + 4.4b + 3.25C = 1005500
b = C + 25000
-----------------------
Rearrange::
s + b + C = 170000
1140s + 440b + 325C = 100550000
0 + b - C = 25000
--------------------------
Use any method you know to solve the system to get:
stocks = 45000
bonds = 75000
CD's = 50000
----------------
Cheers,
Stan H.
--------------
Maricopa Success invested $
in stocks.
Maricopa Success invested $
in bonds.
Maricopa Success invested $
--------------
Hope this helps!
Brainliest would be great!
--------------
With all care,
07x12!
Which of the following situations may be modeled by the equation y = 2x +20
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day.
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week.
C. Martin has saved $2. He plans to save $20 per month.
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month
Answer:
D.
m = 2 = figures/month
b = 20 = # of action figures
The floor of a rectangular room is to be covered with square floor tiles with
1
-foot sides. The floor of the room is
18
feet long and
12
feet wide. If the square tiles cost
$
4
each, how much would it cost to completely cover the floor with these tiles?
Answer:
Total cost = $864
Step-by-step explanation:
The area of the rectangular room
= 18*12
= 216 ft²
The sides of the square is 1ft
The area of the square= 1ft²
To know how many square tiles it will take= 216/1 = 216 square tiles.
The total cost to completely cover the room with tiles if each tiles cost $4
= 216*4
= $864
Total cost=$864
Help all mathematicians!
Answer: Choice D
Maximums = (0,1) and (2pi, 1)
minimum = (pi, -3)
======================================================
Explanation:
Cosine is a periodic function that bounces up and down forever. The highest y = cos(x) gets is y = 1 and that happens when x = 0, 2pi, etc. Basically anything in the form x = 2pi*n for any integer n will have y = cos(x) maxed out. Consequently, this means y = 2cos(x)-1 maxes out at the same mentioned x values.
Plug in those x values to find that y = 1 is the max y value for y = 2cos(x)-1
A similar situation happens for the mins as well. We have y = cos(x) be the smallest when x = pi+2pi*n for any integer n.
If the sampled population is finite and at least _____ times larger than the sample size, we treat the population as infinite.
Answer:
The answer is "20".
Step-by-step explanation:
It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.
Its sampling distribution of the "x bar" should also be naturally independent of the random sample, that is usually distributed. We consider the population as endless if the sampling size is at least 20 times greater than the sample size.PLEASE HELP!!! The side lengths of a square are each 5q. By adding 3 to the length and subtracting 3 from the width, a rectangle is made. What is the area of the rectangle? a. 10q^2-6 b. 9q^2+25 c. 25q^2-9 d. 25q^2-30q-9
The area of the rectangle is [tex]25q^2-9[/tex].
Area of the rectangleThe area of the rectangle is the product of length and width.
How to determine the area of the rectangle?The length of the sides of the square is 5q.
3 is added and 3 is subtracted to the length and the width of the square so, the dimensions of the new quadrilateral is (5q+3) and (5q-3).
So, the area of the rectangle is-
[tex]A=(5q+3)\times (5q-3)\\=25q^2-9[/tex]
Thus, the area of the rectangle is [tex]25q^2-9[/tex].
Learn more about the area of the rectangle here- https://brainly.com/question/20693059
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Answer:25q^2-9
Step-by-step explanation:
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Find the length of BC
Answer:
The answer is option AStep-by-step explanation:
To find the length of BC we use tan
tan ∅ = opposite / adjacent
From the question
AC is the opposite
BC is the adjacent
So we have
tan 61 = AC / BC
tan 61 = 47/BC
BC = 47/tan 61
BC = 26.05Hope this helps you
.19 OF JOE'S SALARY GOES FOR TAXES. WHAT PERCENT OF HIS SALARY DOES THIS REPRESENT?
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▹ Answer
19%
▹ Step-by-Step Explanation
0.19 → hundreth's place.
19/100 (since the denominator is 100, that represents 100% while 19 represents 19%)
Final Answer - 19%
Hope this helps!
CloutAnswers ❁
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This represent 19% of his salary.
Given, Joe's salary goes for tax is 0.19.
We have to represent the value in percent.
Here 0.19 can be written in fraction form as,
[tex]\dfrac{19}{100}[/tex]
It means 19 part from 100 part goes for taxes, means 19% of the Joe's salary goes for taxes.
Hence this represent 19% of his salary.
For more details follow the link:
https://brainly.com/question/8011401
In the given diagram, find the values of x, y, and z.
a. x = 36°, y = 36°, z = 34°
b. x = 44º, y = 44°, z = 44°
c. x = 34º, y = 34°, z = 34°
d. x = 36°, y = 34°, z = 34°
Answer:
a. x = 36°, y = 36°, z = 34°
Step-by-step explanation:
X = 36° because x and 144° are supplementary angles and the sum of supplementary angles = 180°
The sum of interior angles in a triangle is equal to 180° since one of the angle is given as 110° the sum of z and y must be equal to 70° the option that fits these qualities is a. x = 36°, y = 36°, z = 34°
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5 36 − x2 , y = 0, x = 2, x = 4; about the x-axis
Answer: V = 193.25π
Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:
V = [tex]\pi\int\limits^a_b {[f(x)]^{2}} \, dx[/tex]
f(x) is the area is the function that rotated forms the solid.
For f(x)=y= [tex]\frac{5}{36}-x^{2}[/tex] and solid delimited by x = 2 and x = 4:
V = [tex]\pi\int\limits^4_2 {(\frac{5}{36}-x^{2} )^{2}} \, dx[/tex]
V = [tex]\pi\int\limits^4_2 {(\frac{25}{1296}-\frac{10x^{2}}{36}+x^{4}) } \, dx[/tex]
V = [tex]\pi(\frac{25.4}{1296}-\frac{10.4^{3}}{108}+\frac{4^{5}}{5}-\frac{25.2}{1296}+\frac{10.2^{3}}{108}-\frac{2^{5}}{5} )[/tex]
V = [tex]\pi(\frac{50}{1296}-\frac{560}{1296}+\frac{992}{1296} )[/tex]
V = 193.25π
The volume of a solid formed by y = [tex]\frac{5}{36} - x^{2}[/tex] and delimited by x = 2 and x = 4
is 193.25π cubic units.