A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 8 tables is $87. The total cost to rent 5 chairs and 2 tables is $26.
What is the cost to rent each chair and each tabl
Answer:
(Chairs):C=29−8t/3
(Tables):T=87/8−3c/8
Step-by-step explanation:
For C: Move all terms that don't contain c to the right side and solve.
For T: Move all terms that don't contain t to the right side and solve.
(Do the same thing with the other numbers as well)
(CHeck your work for each one)
2. A more efficient packing of the discs is obtained by dividing the metal sheet into hexagons and cutting the circular lids and bases from the hexagons (see the last figure). Show that if this strategy is adopted, then
[tex] \frac{h}{r}=\frac{4 \sqrt{3}}{\pi} \approx 2.21 [/tex]
This exercise is about optimization and seeks to prove that if the new strategy of packing the discs is adopted, then h/r = [tex]\sqrt[4]{3}[/tex]/n ≈2.21.
What is the proof for the above strategy?We must determine the amount of metal consumed by each end, or the area of each hexagon.
The hexagon is divided into six congruent triangles, each of which has one side (s in the diagram) in common with the hexagon.
Step I
Next, let's derive the length of s = 2r tan π/6 = (2/([tex]\sqrt{3}[/tex])r². From this we can state that the area of each of the triangles are 1/2(sr) = (1/[tex]\sqrt{3}[/tex])r²
while the total area of the hexagon is 6 * (1/[tex]\sqrt{3}[/tex])r² = (2/[tex]\sqrt{3}[/tex])r².
From the above, we can state that the quantity we want to minimize is given as:
A = 2πrh + 2* (2/[tex]\sqrt{3}[/tex])r²
Step 2
Next, we substitute for h and differentiate. This gives us:
da/dr = - (2V/r²) + [tex]\sqrt[8]{3r}[/tex].
Let us equate the above to zero.
[tex]\sqrt[8]{3r} ^{3}[/tex] = 2V = 2πr²h ⇒ h/r =[tex]\sqrt[4]{3}[/tex]/n
The above is approximately 2.21
Because d²A/dr²=[tex]\sqrt[8]{3}[/tex] + 4V/r[tex]^{3}[/tex] > 0 the above minimizes A.
Learn more about Optimization at:
https://brainly.com/question/17083176
#SPJ1
61-63 Sketch the region bounded by the given curves and find the area of the region.
61. [tex]y=1 / x, \quad y=1 / x^{2}, \quad x=2[/tex]
The area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
To find the area of the bounded region by the curves(refer to attached picture):
[tex]\rm A= \int\limits^2_1 {(\frac{1}{x}-\frac{1}{x^2}) } \, dx[/tex]
After solving:
A = 0.193 square units
Thus, the area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.
Learn more about integration here:
brainly.com/question/18125359
#SPJ1
two coins are flipped then a card is drawn. there are how many total outcomes? deck is 52 and coins are fair.
Answer:
208
Step-by-step explanation:
A coin can have 2 total outcomes
A card deck can have 52 total outcomes
Im flipping 2 coins and then drawing a card
2 x 2 x 52 = 208
find the area of the figure
and how to find the answer
Answer:
The area of figure is 29.
Step-by-step explanation:
By counting the square box.
Answer:
28.5 square units
Step-by-step explanation:
Spit it into a triangle and a rectangle.
The Triangle is
(3 * 3) / 2
= 9 / 2
= 4.5
The Rectangle is
3 * 8
=24
The total is 4.5 + 24 = 28.5
Pleas I really need help with this
Answer:
4r ^2 +9r + 12
Step-by-step explanation:
Hope this helps! :)
Somebody help me to solve this problem.please help me.
Answer:
Tama po
Yan
Step-by-step explanation:
Enjoy po
Godbless
Find the area of a regular nonagon with a radius of 4
If it's a regular nonagon, each exterior angle has measure 360°/9 = 40°, so the supplementary interior angles each have measure 180° - 40° = 140°.
We can split up the nonagon into 9 congruent isosceles triangles whose longer side coincides with the radius of the circle. (The language in the question is a bit ambiguous; I think it's clearler to say the nonagon is itself circumscribed by the circle, so that each of its vertices lie on the circle. See attached image - not mine, but it's in public domain.)
As the image suggests, each triangle will have interior angles measuring 70°, 70°, and 40°.
We can use trigonometry to find the side length of the nonagon, i.e. the length of the shortest side of each triangle - I'll call it x. For example, using the law of cosines,
x² = 4² + 4² - 2 • 4 • 4 cos(40°) ⇒ x = 4√2 √(1 - cos(40°))
Then the perimeter of the nonagon is
9x = 36√2 √(1 - cos(40°)) in ≈ 24.623 in
The area of a triangle is 1/2 the product of its base and height. The base will be b = x, but to get the height we cut the isosceles triangle in half to produce a right triangle. We use trig again to determine its height h:
tan(70°) = h/(b/2) ⇒ h = 1/2 x tan(70°)
so each triangle contributes an area of
a = 1/2 bh = 1/4 x² tan(70°) ≈ 5.142 in²
and so the area of the nonagon is
9a = 9x²/8 tan(70°) ≈ 46.281 in²
Calculate the volume of the figure.
5 ft
7 ft
A 48 cubic feet
B 63 cubic feet
99 cubic feet
D) 140 cubic feet
4 ft
Answer:
Step-by-step explanation:
Formula
Volume = L * w * h
Givens
L = 7 feet
w = 4 feet
h = 5 feet
Solution
V = L * w * h Substitute values into the formula
V = 7 * 4 * 5
V = 140 cubic feet.
Answer
140 ft^3
Answer:
D) 140 cubic feet
Step-by-step explanation:
The given information is,
→ Length (l) = 7 ft
→ Breadth (b) = 4 ft
→ Height (h) = 5 ft
Formula we use,
→ Volume of cuboid = l × b × h
Let's solve the problem,
→ l × b × h
→ 7 × 4 × 5
→ [ 140 ft³ ]
Hence, the volume is 140 ft³.
Use the number line. How many 2-yard
long pieces of pipe can be cut from two
1-yard long pieces of pipe?
Answer:
Answer:
16 inches
Step-by-step explanation:
2 1/4 = 9/4 inches
Number of pieces = 36 / 9/4
= 36 + 4/9
= 16 inches
BRAINLIEST!!!
A website requires users to set up an account that is password protected. If the password
format is four letters (A-Z) followed by a single digit number (0-9), and letters can be repeated, how
many different passwords are possible?
Answer:
4,569,760 different passwords
Step-by-step explanation:
[tex]26 \times 26 \times 26 \times 26 \times 10 = 4569760[/tex]
Digits can be repeated means repeatation is allowed
So
Total letters=26Total nos=10Total ways
26⁴×10456976×104569760For which values of the parameter "p" the equation
"8x^2 - 4x + 1 - p = 0" (with unknown x) has two different real roots less than 1?
Can you please explain in detail how this problem is solved?
Answer:
[tex]\dfrac12 < p < 5[/tex]
Step-by-step explanation:
To solve this, we need to use the discriminant.
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
If the given equation has 2 real roots, then we need to use:
[tex]b^2-4ac > 0[/tex]
Given equation: [tex]8x^2-4x+1-p=0[/tex]
[tex]\implies a=8, \quad b=-4, \quad c=(1-p)[/tex]
Substituting these values into [tex]b^2-4ac > 0[/tex] and solve for p:
[tex]\implies (-4)^2-4(8)(1-p) > 0[/tex]
[tex]\implies 16-32(1-p) > 0[/tex]
[tex]\implies 16-32+32p > 0[/tex]
[tex]\implies -16+32p > 0[/tex]
[tex]\implies 32p > 16[/tex]
[tex]\implies p > \dfrac{16}{32}[/tex]
[tex]\implies p > \dfrac12[/tex]
For the roots to be less than 1, first find the value of p when the root is 1.
If the root is 1, then [tex](x-1)[/tex] will be a factor, so [tex]f(1)=0[/tex]
Substitute [tex]x=1[/tex] into the given equation and solve for p:
[tex]\implies 8(1)^2-4(1)+1-p=0[/tex]
[tex]\implies 5-p=0[/tex]
[tex]\implies p=5[/tex]
Therefore, the values of p for which the given equation has two different real roots less than 1 are:
[tex]\dfrac12 < p < 5[/tex]
simplify (2x-3)^3-(x-4)^3
please help urgently
Answer:
7x^3 -24x^2 +6x +37
Step-by-step explanation:
Step 1:
Expand (2x-3)^3
(2x)^3 - 3(2x)^2 * 3+3 * 2x * 3^2 -3
(8x^3 -36x^2 +54x -27)
Step 2:
Expand (x-4)^3
x^3 -3x^2 *4 +3x *4^2 -4^3
(x^3 -12x^2 +48x -64)
Step 3: Subtract and add like terms
(8x^3 -36x^2 +54x -27) - (x^3 -12x^2 +48x -64)
7x^3 -24x^2 +6x +37
Ans: 7x^3 -24x^2 +6x +37
Unit Test
Active
12
13
14
15
16
17
18
balan
Max and Tara are each designing a playground for a school project. In Max’s design, x square feet of the playground will be covered in wood chips. In Tara’s design, the area to be covered is 40 square feet less than 1.5 times the area covered in wood chips in Max’s design. Which expression represents the area, in square feet, to be covered in wood chips in Tara’s design? 1.5x-40
use ABC to find the value of cos A
40/9
9/41
40/41
9/40
Answer:
Yes the one you clicked on is the right answer.
Samantha's age is 3 years more than half her uncle's age. If her uncle's age is z years, which of the following expressions best shows Samantha's age?
Answer:
See below
Step-by-step explanation:
z = uncle's age
1/2z +3 = Sam's age
What is 10 to the 3 power
[tex]10^3 = 10 \times 10 \times 10 = 1000[/tex]
Represent absolute value, not brackets. Calculate the value of this expression: |-7|×|5|+18÷|-6|. -38, -35, 32, 38.
Answer:
38
Step-by-step explanation:
|-7|×|5|+18÷|-6|
First take the absolute value of each number, which means take the positive value
7×5+18÷6
Multiply and divide from left to right
35 + 3
Then add
38
If 1/(a + b + c) = 1/a + 1/b + 1/c, show that 1/(a + b + c)^3 = 1/a^3 + 1/b^3 + 1/c^3
Expanding the cube, we have
[tex]\dfrac1{(a+b+c)^3} = \left(\dfrac1{a+b+c}\right)^3 \\\\ = \dfrac1{a^3} + \dfrac1{b^3} + \dfrac1{c^3} + 3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc}[/tex]
so it remains to be shown that
[tex]3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc} = 0[/tex]
Factorize the grouped sum on the left as
[tex]\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2} = \dfrac1{abc} \left(\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac\right)[/tex]
so that with simplification, it remains to be shown that
[tex]\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac + 2 = 0[/tex]
With a little more manipulation, we have
[tex]\dfrac ba + \dfrac ca = \dfrac{a+b+c}a - 1[/tex]
[tex]\dfrac cb + \dfrac ab = \dfrac{a+b+c}b - 1[/tex]
[tex]\dfrac bc + \dfrac ac = \dfrac{a+b+c}c - 1[/tex]
so that our equation simplifies to
[tex]\dfrac{a+b+c}a + \dfrac{a+b+c}b + \dfrac{a+b+c}c - 1 = 0[/tex]
which we can factorize as
[tex](a+b+c)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]
Finish up by using the hypothesis:
[tex]\left(\dfrac1{\frac1{a+b+c}}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]
[tex]\underbrace{\left(\dfrac1{\frac1a+\frac1b+\frac1c}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right)}_{=1} - 1 = 0[/tex]
and the conclusion follows.
Find the length of the indicated side.
Answer:
Step-by-step explanation:
Suppose you deposit $2500 in a savings account that pays you 5% interest per year. (Calculator)
(a) How many years will it take for you to double your money?
Answer:
14.20669 years
Roughly 14 years and 2.5 months.
Step-by-step explanation:
Assuming this is compound interest.
The formula is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=[/tex] Final Amount
[tex]P=[/tex] Principal Amount
[tex]r=[/tex] Interest Rate
[tex]n=[/tex] # of times interest is compounded per year
[tex]t=[/tex] Time in years
We are looking for the times in years to double the money so
[tex]2500*2=5000[/tex]
[tex]A=5000[/tex]
[tex]P=2500[/tex]
[tex]r=0.05[/tex]
[tex]n=1[/tex]
[tex]t=?[/tex]
Lets solve for [tex]t[/tex] .
Step 1.
Plug in our numbers into the compound interest formula.
[tex]5000=2500(1+\frac{0.05}{1}) ^{1*t}[/tex]
Step 2.
Simplify the equation.
Evaluate [tex]1+\frac{0.05}{1}=1.05[/tex]
Evaluate [tex]1*t=t[/tex]
[tex]5000=2500(1.05) ^{t}[/tex]
Step 3.
Divide both sides of the equation by [tex]2500[/tex]
[tex]\frac{5000}{2500}=1.05 ^{t}[/tex]
Evaluate [tex]\frac{5000}{2500}=2[/tex]
[tex]2=1.05 ^{t}[/tex]
Step 4.
Take the natural log of both sides of the equation and rewrite the right side of the eqaution using properties of exponents/logarithms.
[tex]ln(2)=t*ln(1.05)[/tex]
Step 5.
Divide both sides of the equation by [tex]ln(1.05)[/tex]
[tex]\frac{ln(2)}{ln(1.05)}=t[/tex]
Step 6.
Evaluate
[tex]t=14.20669[/tex]
Roughly 14 years and 2.5 months.
A bag contains 10 red marbles, 7 white marbles, and 9 blue marbles. You draw 5 marbles out at random, without replacement. For the questions below, enter your answers in fraction form. What is the probability that all the marbles are red? The probability that all the marbles are red is . What is the probability that exactly two of the marbles are red? The probability that exactly two of the marbles are red is . What is the probability that none of the marbles are red? The probability of picking no red marbles is .
Answer:
ALL RED = 19/5000
Two Red = 3831/10000
No red marbles = 16/26
Step-by-step explanation:
1. Find the total number of marbles
7+10+9= 26
2. There are 10 red marbles so the probability that the first marble is red 10/26
3. When the second marble there are 25 marbles so the probability that it is red is 9/25
4. Third Marble probability
8/24
5. Fourth Marble probablity
7/23
6. Fifth marble probability
6/22
7. Now to find that ALL the marbles are red you multiply all the fractions above
10/26 * 9/25 * 8/24 * 7/23 * 6/22 = 0.0038
8. Convert to fraction form
19/5000
9. Two marbles are red
5!/(3!*2!) * 10/26 * 9/25 * 16/24 * 15/23 * 14/22 = 0.3831
10. Convert to fraction
3831/10000
A metal strip is being installed around a workbench that is 8 feet long and 2 feet wide. If the stripping costs $3 per foot, find the total cost of the stripping.
Length x width x price
8x2 = 16
16x$3 = $48
the total cost is $48
Question 2 help meeee pleaseee
Thank you
3 cm/h easy peasy
Step-by-step explanation:
12 cm in 4 hrsFor 1 cm : 12/4 = 3 cmTeresa is maintaining a campfire.She has kept the fire steadily burning for 4 hours using 6 logs. The number of logs needed to keep the fire burning is proportional to the number of hours it burns. She wants to know how many logs she needs to keep the fire burning for 18 hours.
Select the equationis Teresa can use to determine the number of logs she needs, x, to maintain the fire for 18 hours.
A. x/6 = 4/18
B. x/6 = 18/4
C. x/18 = 6/4
D. x/4 = 18/6
E. 4/6 = 18/x
Answer:
E. 4/6 = 18/x
Step-by-step explanation:
4 hour using 6 logs
18 hours using x logs
Austin finished his English assignment ib 1/3 hours.then he completed his math assignment in 2/5 hours. What wS the total time hw sentence this two assignments
Answer:
11/15
Step-by-step explanation:
sum the two 1/3+2/5=11/15
41 is 82% of what number?
Enter your answer in the box.
Answer:
The answer is 50.
Step-by-step explanation:
Set up a proportion: [tex]\frac{41}{y} =\frac{82}{100}[/tex]
Step 2- Multiply 41 by 100 to get 4100
Step 3. Divide 4100 by 82 to get 50.
Hope this helps! :)
9) work out 6 - 3x-2--10
On any given day, the number of users, u, that access a certain website can be represented by the inequality | 125-u | -<30. Which of the following represents the range of users that access the website each day?
Answer: D
Step-by-step explanation:
Answer:
D. 95 ≤ u ≤ 155
Step-by-step explanation: