The interest rate for the $4000 investment is approximately 2.1% and for the $20000 investment, it is approximately 2.7%.
Explanation:This problem can be solved using the concept of simple interest. Let's denote the interest rate of the $4000 investment as r (in decimal form) and the interest rate of the $20000 investment would be r+0.006. Now, we can set up our equations based on the information given:
1. For $4000 investment: Interest = 4000 * r
2. For $20000 investment: Interest = 20000 * (r + 0.006)
It is also given that the interest earned from the $20000 investment is $1320 more than the $4000 investment. Therefore, we can set up a third equation as:
20000 * (r + 0.006) - 4000 * r = 1320
By solving this equation, we find that r (corresponding to the $4000 investment) is approximately 0.021 or 2.1% and therefore, the interest rate for the $20000 investment is roughly 2.7% (2.1% + 0.6%).
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Is 27/50 closer to 1/2, 1 or 0
Answer:
I think it's closer to [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{27}{50} = 0.54\\[/tex]\\
i do know that 1/2 is < 27/50
Given the functionf ( x ) = x^2 + 7 x + 10/ x^2 + 9 x + 20
Describe where the function has a vertical asymptote and how you found your answer. Remember that an asymptote is represented by an equation of a line and not just a single value.
x = -4 is a vertical asymptote for the function.
Explanation:The graph of [tex]y=f(x)[/tex] is a vertical has an asymptote at [tex]x=a[/tex] if at least one of the following statements is true:
[tex]1) \ \underset{x\rightarrow a^{-}}{lim}f(x)=\infty\\ \\ 2) \ \underset{x\rightarrow a^{-}}{lim}f(x)=-\infty \\ \\ 3) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty \\ \\ 4) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty[/tex]
The function is:
[tex]f(x)=\frac{x^2+7x+10}{x^2+9x+20}[/tex]
First of all, let't factor out:
[tex]f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20} \\ \\ f(x)=\frac{x(x+5)+2(x+5)}{x(x+5)+4(x+5)} \\ \\ f(x)=\frac{(x+5)(x+2)}{(x+5)(x+4)} \\ \\ f(x)=\frac{(x+2)}{(x+4)}, \ x\neq 5[/tex]
From here:
[tex]\bullet \ When \ x \ approaches \ -4 \ on \ the \ right: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(-4^{+}+2)}{(-4^{+}+4)} \\ \\ \\ The \ numerator \ is \ negative \ and \ the \ denominator \\ is \ a \ small \ positive \ number. \ So: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=-\infty[/tex]
[tex]\bullet \ When \ x \ approaches \ -4 \ on \ the \ left: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(-4^{-}+2)}{(-4^{-}+4)} \\ \\ \\ The \ numerator \ is \ a \ negative \ and \ the \ denominator \\ is \ a \ small \ negative \ number \ too. \ So: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=+\infty[/tex]
Accordingly:
[tex]x=-4 \ is \ a \ vertical \ asymptote \ for \\ \\ f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20}[/tex]
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Toby and Marcus both collect stamps. Toby has 10 stamps and collects 4 new stamps every week. Marcus has 60 stamps and collects 2 new stamps every week. After how many weeks will Toby and Marcus have the same number ?
Answer:
25 weeks will Toby and Marcus have the same number of stamps
Explanation:
No of stamps collected by Toby initially= 10
No of stamps Toby collects every week= 4
No of stamps Marcus has initially= 60
No of stamps Marcus collects each week=2
Suppose the no of week when Toby and Marcus have the same number of stamps are x
Hence no of stamps collected by Toby after x weeks
=10+4x
No of stamps collected by Marcus after x weeks
=60+2x
Therefore to calculate the same of stamps collected by Toby and Marcus
No of stamps collected by Toby after x weeks= No of stamps collected by Marcus after x weeks
10+4x =60 +2x
4x-2x= 60-10
2x=50
x=25
Hence after 25 weeks Toby and Marcus will have the same number of stamps
Katie keeps a record of her transactions in a notebook. Looking over her records for the past two weeks, Katie finds that her bank statement does not match her notebook, and she actually has more money than she thought she did. These are the relevant entries in Katie’s notebook:
Transaction
Debit ($)
Credit ($)
Beginning Balance
889.23
Fence repair
75.86
---
Dry cleaning
32.38
---
Paycheck
---
140.91
Gift from cousin
---
35.00
Car payment
178.66
---
Tax refund
---
66.18
New chair
161.55
---
Ending Balance
682.87
However, Katie’s bank statement says that her ending balance is $707.10. Which of the following is a possible explanation for the discrepancy?
a.
Katie’s neighbor paid for half of the fence repair, which Katie forgot to record.
b.
Katie transposed the digits in the cost of the dry cleaning, which actually cost $23.38.
c.
Katie’s new chair was on sale for 15% off, making it cost $137.32, but Katie wrote down the before-sale price.
d.
Katie’s tax refund came in two equal-sized checks, but Katie only recorded one of them.
Answer: C
Step-by-step explanation:707.10-682.87= 24.23. Similar difference can also be found in only chair which is. 161.55-137.32=24.23
Answer:
The correct answer is C on edge :) i just did the test
Step-by-step explanation:
A large insurance company wanted to estimate u, the mean claim size (in 5) on an auto insurance policy. A random sample of 225 claims was chosen and it was found that the average claim size was $2875. From past experience the population standard deviation is assumed to be $1350.
Which of the following is the point estimate for u?
A. $225
B. $2875
C. $1350
D. None of the above.
Answer: B. $2875
Step-by-step explanation:
We know that best point estimate of population mean[tex](\mu)[/tex] is the sample mean[tex](\overline{x})[/tex] .
Given : A large insurance company wanted to estimate [tex]\mu[/tex], the mean claim size (in 5) on an auto insurance policy.
A random sample of 225 claims was chosen and it was found that the average claim size was $2875.
i.e. Sample mean [tex]\overline{x}=\$2875[/tex]
That means , the point estimate for [tex]\mu=\$2875[/tex]
Hence , the correct answer is option B . $2875.
The point estimate of u, the mean claim size, is $2875 as determined by the average claim size of a random sample of 225 claims.
Explanation:In statistics, a point estimate is often the best guess that one can make for an unknown parameter. In this case, we are looking for the mean claim size, denoted as u. When the question states that a random sample of 225 claims showed an average claim size of $2875, they are giving you the point estimate of u, because the calculated average is our best estimate of the population mean in this context. Therefore, the point estimate of u is $2875.
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An object is in simple harmonic motion with amplitude a and period 2π/ω. Find an equation that models the displacement y at time t under the given condition. y = 0 at time t = 0
Answer:
y(t) = a sin(ωt).
Step-by-step explanation:
The graph of the motion starts at y-0 t = 0 so we use sine in the equation
y(t) = A sin (2π t / T) where A = the amplitude and T = the period so here we can write:
Displacement at t = y(t) = a sin(2π/ 2π/ω)t
y(t) = a sin(ωt)
This is about graph of simple harmonic motion.
y(t) = a sin (ωt)
We are told the condition of the simple harmonic motion we want to model is at y = 0 and t = 0. This condition means the motion starts at the origin. Therefore, we will make use of the solution;y(t) = A sin ωt
Where;
A is amplitude
ω is angular frequency
y(t) is the displacement at time(t)
Now, we know that;ω can also be expressed as;
ω = 2π/T
Where T is period.
Thus;
y(t) = A sin (2π/T)t
We are given that;Period; T = 2π/ω
Thus
y(t) = A sin (2π/(2π/ω))t
2π will cancel out to give;
y(t) = A sin (ωt)
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Supppose A is an invertible n\times n matrix and v is an eigenvector of A with associated eigenvalue -3. Convince yourself that v is an eigenvalue of the following matrices, and find the associated eigenvalues:
1. \ A^6, \ eigenvalue = ,
2. \ A^{-1}, \ eigenvalue = ,
3. \ A + 5 I_n, \ eigenvalue = ,
4. \ 6 A, \ eigenvalue = .
Answer:you will an app go to =567
Marco is making Mosaic garden tools using red yellow and blue tiles. He has 45 red tiles, 90 blue tiles, and 75 yellow tiles. Each Stone must have the same number of each color tile. How many of each color tile will Marco use in each stone if the greatest number of stones he can make is 45?
Answer:
Marco will use [tex]1[/tex] red tile, [tex]2[/tex] blue tiles and [tex]1\frac{2}{3}[/tex] yellow tiles in each stone.
Step-by-step explanation:
Given:
Number of red tiles = 45
Number of blue tiles = 90
Number of yellow tiles = 75
Greatest number of stones that Marco can make = 45
To determine how many each color tile Marco will use in each stone.
Solution:
In order to determine the number of each color tile in each stone we need to divide total number of a particular tile by total number of stones. By doing this we can get the exact number of that color tile used in each stone.
Number of red tile in each stone
⇒ [tex]\frac{\textrm{Total number of red tiles}}{\textrm{Total number of stones}}[/tex]
⇒ [tex]\frac{45}{45}=1[/tex]
Number of blue tiles in each stone
⇒ [tex]\frac{\textrm{Total number of blue tiles}}{\textrm{Total number of stones}}[/tex]
⇒ [tex]\frac{90}{45}=2[/tex]
Number of yellow tile in each stone
⇒ [tex]\frac{\textrm{Total number of yellow tiles}}{\textrm{Total number of stones}}[/tex]
⇒ [tex]\frac{75}{45}[/tex]
⇒ [tex]\frac{5}{3}[/tex] [Reducing to simpler fraction by dividing both numbers by their GCF=15]
⇒ [tex]1\frac{2}{3}[/tex] [Converting improper fraction to mixed number]
∴ Marco will use [tex]1[/tex] red tile, [tex]2[/tex] blue tiles and [tex]1\frac{2}{3}[/tex] yellow tiles in each stone.
Answer:
Marco will use 3 red, 6 blue and 5 yellow tiles on each stones
Explanation:
Given, each stone must have same number of each colour tile
Then, calculating the highest common factors of the number HCF (45, 90, 75)
Factors of 45 = 3 × 3 × 5
Factors of 90 = 2 × 3 × 3 × 5
Factors of 75 = 3 × 5 × 5
Highest Common Factors (HCF) = 3 × 5 = 15
Dividing all three numbers by 15, we get
Red Tiles =[tex]\frac{45}{15}[/tex] = 3
Blue Tiles = [tex]\frac{90}{15}[/tex] = 6
Yellow Tiles = [tex]\frac{75}{15}[/tex] = 5
Therefore, Marco will use 3 red, 6 blue and 5 yellow tiles on each stones
I plan on opening a savings account with $800 and leaving it in the account for 4 years. If the bank is going to pay me an interest rate of 5%, how much money will I have in the account at the end of 4 years? A. $2,400 B. $1,600 C. $960 D. $160
Answer:
i would think that its c
let me know if its wrong
Answer:
c
Step-by-step explanation:
i know
You can travel to New York San Francisco, or Miami during June July or August. How many possible outcomes are illustrated in the tree diagram?
a. 3
b. 6
c. 9
d. 18
Answer:9
Step-by-step explanation:
You would count the possible outcomes on the right side of the diagram
The number of possible outcomes is 9.
Given that,
You can travel to New York San Francisco, or Miami during June July or August.Based on the above information, the calculation is as follows:
From NewYork = 3
From San Francisco = 3
From Miami = 3
Total = 9
Therefore we can conclude that the number of possible outcomes is 9.
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Jera and Bipu are friends. Jera’s age 5 years ago was 20 less than Bipu’s age in 8 years. Bipu’s age 5 years ago was 34 years less than twice Jera’s age in 8 years. How old are they at present?
Answer:
Jera is 20Bipu is 27Step-by-step explanation:
Let j and b represent Jera's and Bipu's current ages.
j-5 = (b +8) -20 . . . . . Jera's age 5 years ago was 20 less than Bipu's age in 8 years
b-5 = 2(j+8) -34 . . . . .Bipu's age 5 years ago was 34 less than Jera's age in 8 years
__
Solving the first equation for j gives ...
j = b + 8 -20 + 5
j = b -7
Using that in the second equation, we get ...
b -5 = 2((b -7)+8) -34
0 = b -27 . . . . . . . subtract (b-5) and simplify
b = 27
j = 27 -7 = 20
Jera is 20; Bipu is 27.
Assume a circle of radius r has the same area as a square with side length s. Express the radius of the circle in terms of the length of a side of the square (i.e. write r as a function of s)
Final answer:
To express the radius of a circle in terms of the length of a side of a square, use the formula: r = s/√π.
Explanation:
A circle of radius r has the same area as a square with side length s. We can express the radius of the circle in terms of the length of a side of the square using the formula for the area of a circle: A = πr², where π is approximately 3.14159. Similarly, for the square, the area is given by A = s². Equating these two areas gives us the equation:
s² = πr²
Now, we can solve for r by rearranging the equation:
r = s/√π
Final answer:
To express the radius of a circle in terms of the side length of an equal-area square, use the formula r = s / √π.
Explanation:
To express the radius r of a circle in terms of the length of a side of the square s, where the circle and square have the same area, we start by setting the area formulas for both shapes equal to each other. The area of the circle is πr^2 and the area of the square is s^2. By equating the two areas, we have πr^2 = s^2. To solve for r, we need to take the square root of both sides of the equation divided by π, which gives us r = s / √π.
Scenario: The market for used cell phones is very popular in Barylia. However, several phones available in this market are of inferior quality and it is often impossible to differentiate between a good-quality phone and a poor-quality phone. Refer to the scenario above. Based on the given information, we can conclude that the market for used cell phones in Barylia: is perfectly competitive. has only one seller. is monopolistically competitive. has asymmetric information.
Answer:
D: has asymmetric information.
Step-by-step explanation:
Several phones available in Barylia market are of inferior quality and it is often impossible to differentiate between a good-quality phone and a poor-quality phone.
So, we can conclude that the market for used cell phones in Barylia: has asymmetric information.
Asymmetric information or often called information failure shows the decision in transactions where one market or party has got better information than the others.
A 35-ft long solid steel rod is subjected to a load of 8,000 lb. This load causes the rod to stretch 0.266 in. The modulus of elasticity of the steel is 30,000,000 psi. Determine the diameter of the rod (precision of 0.00).
Step-by-step explanation:
We have the equation for elongation
[tex]\Delta L=\frac{PL}{AE}\\\\A=\frac{\pi d^2}{4}[/tex]
Here we have
Elongation, ΔL = 0.266 in = 0.00676 m
Length , L = 35 ft = 10.668 m
Load, P = 8000 lb = 35585.77 N
Modulus of elasticity, E = 30,000,000 psi = 2.07 x 10¹¹ N/m²
Substituting
[tex]\Delta L=\frac{PL}{AE}\\\\A=\frac{\pi d^2}{4}\\\\\Delta L=\frac{4PL}{\pi d^2E}\\\\d^2=\frac{4PL}{\pi \Delta LE}\\\\d=\sqrt{\frac{4PL}{\pi \Delta LE}}\\\\d=\sqrt{\frac{4\times 35585.77\times 10.668}{\pi \times 0.00676 \times 2.07\times 10^{11}}}=0.019m\\\\d=19mm[/tex]
Diameter of rod = 19 mm
Samantha is the best middle manager the company has. She constantly puts countless hours into her job and is one of the best and brightest around. Samantha has not received a raise or promotion for many years and believes it is because she is a woman experiencing unseen discrimination. It is clear that Samantha is feeling the effects of a_____.
Answer:Glass ceiling
Step-by-step explanation:
Samantha is feeling the effect of glass ceiling .A glass ceiling is a term used to describe an unseen barrier that prevents a particular demographic (usually applied to minorities) from increasing in a hierarchy beyond a certain level.
Here The phrase “glass ceiling” is used to describe the difficulties faced by women when trying to move to higher roles in a male-dominated hierarchy.
A builder wishes to construct a ramp 21 feet long that rises to a height of 5 feet above level ground. What angle should the ramp make with the horizontal? Decimal approximations will be marked incorrect. Symbolic trigonometric expressions such as arctan(5) are accepted. 1/ 5 21 α cos radians
Answer:
α = 13.39249775
Step-by-step explanation:
Length of the vamp = 21 ft long
Height of the vamp= 5 ft
using SOHCAHTOA
tanα = opposite /adjacent
Tan α = 5/21
α = arctan(5/21)
α = 13.39249775
find the value(s) of the missing variables
Answer: x = 9
y = 13
Step-by-step explanation:
what does x and oe equal?
Answer:
œ=50
Step-by-step explanation:
Solve the equation: 120+œ+60+15+20 = 130+35+2œ
Simplifies as follows: œ+215 = 2œ+165
œ = 215 - 165 = 50
Alex was biking along a 48 mile trail. First half of the time he was biking twice as fast as the second half of the time. If he spent 4 hours on the road, how fast was he biking at first?
Answer:
The speed in the first part is 16 mph.
Step-by-step explanation:
The total distance is 48 miles. The total time is 4 hours.
In the second part of the trip, he was traveling at speed s for distance d for 2 hours.
In the first part of the trip he was traveling at twice the speed, or 2s, for distance 48 - d, for 2 hours.
speed = distance/time
distance = speed * time
First part of trip:
48 - d = 2s * 2
d + 4s = 48 Equation 1
Second part of the trip:
d = s * 2
d = 2s Equation 2
Equations 1 and 2 form a system of equations in two unknowns, d and s.
d + 4s = 48
d = 2s
Substitute 2s for d in equation 1.
2s + 4s = 48
6s = 48
s = 8
The speed in the second part is 8 mph.
The speed in the first part is 2s = 2(8) = 16.
The speed in the first part is 16 mph.
Check:
d = 2s = 2(8) = 16
48 - d = 48 - 16 = 32
The second part is 16 miles. The first part is 32 miles.
16 miles at 8 mph takes 2 hours.
32 miles at 16 mph takes 2 hours.
2 hours + 2 hours = 4 hours.
Our answer is correct.
Answer: The speed in the first part is 16 mph.
Answer:
The speed in the first part is 16 mph.
Step-by-step explanation:
The total distance is 48 miles. The total time is 4 hours.
In the second part of the trip, he was traveling at speed s for distance d for 2 hours.
In the first part of the trip he was traveling at twice the speed, or 2s, for distance 48 - d, for 2 hours.
speed = distance/time
distance = speed * time
First part of trip:
48 - d = 2s * 2
d + 4s = 48 Equation 1
Second part of the trip:
d = s * 2
d = 2s Equation 2
Equations 1 and 2 form a system of equations in two unknowns, d and s.
d + 4s = 48
d = 2s
Substitute 2s for d in equation 1.
2s + 4s = 48
6s = 48
s = 8
The speed in the second part is 8 mph.
The speed in the first part is 2s = 2(8) = 16.
The speed in the first part is 16 mph.
Check:
d = 2s = 2(8) = 16
48 - d = 48 - 16 = 32
The second part is 16 miles. The first part is 32 miles.
16 miles at 8 mph takes 2 hours.
32 miles at 16 mph takes 2 hours.
2 hours + 2 hours = 4 hours.
Our answer is correct.
Answer: The speed in the first part is 16 mph
Which domain restrictions apply to the rational expression? 14–2x / x^2–7x
Answer:
3. [tex]\displaystyle 1\frac{1}{3} = x[/tex]
2C. [tex]\displaystyle III.[/tex]
2B. [tex]\displaystyle I.[/tex]
2A. [tex]\displaystyle II.[/tex]
1. [tex]\displaystyle Set-Builder\:Notation: {x|7, 0 ≠ x} \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]
Step-by-step explanation:
3. See above.
2C. The keyword is ratio, which signifies division, so you would choose "III.".
2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".
2A. The keyword is total, which signifies addition, so you would choose "II.".
1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:
[tex]\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: {x|7, 0 ≠ x} \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]
I am joyous to assist you anytime.
Answer:
\[(-\infty ,0)\cup (0,7)\cup (7,\infty )\]
Step-by-step explanation:
Given expression is \[14 - 2x / x^{2} - 7x\]
For this rational expression to be valid it must satisfy the constraint that the denominator is not equal to 0.
This implies that \[x^{2} - 7x = 0\] should be false.
In order words \[x*(x-7) = 0\] should be false.
Or, x=0, x=7 must be false.
Hence the domain restriction that applies is as follows :
\[(-\infty ,0)\cup (0,7)\cup (7,\infty )\]
explain with words how you find the area of the figure. then find the area.
image attached
Answer:
The answer to your question is 13x² - 14x
Step-by-step explanation:
Process
1.- Divide the figure in to sections to get to rectangles (see the picture below)
2.- Get the area of each rectangle
3.- Add the areas
2.- Area of a rectangle = base x height
Rectangle 1
Area 1 = (3x - 7) (x)
= 3x² - 7x
Rectangle 2
Area 2 = (5x + 2)(2x)
= 10x² + 4x
3.- Total area
Area = (3x² - 7x) + (10x² - 7x)
= 13x² - 14x
A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 36 cm3. If nickel plating costs $1 per cm2 and silver plating costs $2 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length _______ cm and a height of________ cm
Answer:
The box which minimizes the cost of materials has a square base of side length 4.16 cm and a height of 2.08 cm
Step-by-step explanation:
The cost is minimized when the cost of each pair of opposite sides is the same as the cost of the top and bottom. Since the top and bottom are half the cost of the sides (per unit area), the area of the square top and bottom will be double that of the sides. That is, the box is half as tall as wide, so is half of a cube of volume 72 cm³.
Each side of the square base is ∛72 = 2∛9 ≈ 4.16 cm. The height is half that, or 2.08 cm.
_____
If you want to see this analytically, you can write the equation for cost, using ...
h = 36/s²
cost = 2(1)(s²) + (2)(4s)(36/s²) = 2s² +288/s
The derivative is set to zero to minimize cost:
d(cost)/ds = 4s -288/s² = 0
s³ = 72 . . . . . multiply by s²/4
s = ∛72 = 2∛9 ≈ 4.16 . . . . . cm
h = 36/(2∛9)² = ∛9
The box is 2∛9 cm square and ∛9 cm high, about 4.16 cm square by 2.08 cm.
To minimize the cost of materials, the dimensions of the box that minimize the cost of materials are approximately: Square base side length: 4.18 cm, Height: 2.05 cm.
Explanation:To minimize the cost of materials, we need to consider the areas that need to be plated with silver and nickel. Let's assume the side length of the square base is x cm, and the height of the box is h cm. The cost of silver plating the sides is $2 per cm², and the cost of nickel plating the bottom and top is $1 per cm².
The area of each silver-plated side is 4xh cm², and the area of each nickel-plated bottom and top is x² cm². The total cost of materials can be calculated using the formula:
Total cost = 4xh * $2 + 2x² * $1 = 8xh + 2x²
To minimize the cost, we need to find the values of x and h that will minimize this expression.
Since the volume of the box is given as 36 cm³, we have the equation x²h = 36.
Using the equation for the volume, we can solve for h in terms of x:
h = 36 / x².
Substituting this into the expression for the total cost:
Total cost = 8x(36 / x²) + 2x² = 288 / x + 2x²
To find the values of x and h that minimize the cost, we need to find the critical points of the expression. Taking the derivative of the total cost with respect to x, and setting it to zero:
d(Total cost) / dx = -288 / x² + 4x = 0
Simplifying this equation:
288 = 4x³
x³ = 72
x = ∛72 ≈ 4.18 cm
Substituting this value of x back into the equation for h:
h = 36 / (4.18)² ≈ 2.05 cm.
Therefore, the dimensions of the box that minimize the cost of materials are approximately:
Square base side length: 4.18 cm
Height: 2.05 cm
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Suppose that one person in 10,000 people has a rare genetic disease. There is an excellent test for the disease; 98.8% of the people with the disease test positive and only 0.4% of the people who don't have it test positive.
A) What is the probability that someone who tests positive has the disease?
B) What is the probability that someone who tests negative does not have the disease?
Answer:
A)The probability that someone who tests positive has the disease is 0.9995
B)The probability that someone who tests negative does not have the disease is 0.99999
Step-by-step explanation:
Let D be the event that a person has a disease
Let [tex]D^c[/tex] be the event that a person don't have a disease
Let A be the event that a person is tested positive for that disease.
P(D|A) = Probability that someone has a disease given that he tests positive.
We are given that There is an excellent test for the disease; 98.8% of the people with the disease test positive
So, P(A|D)=probability that a person is tested positive given he has a disease = 0.988
We are also given that one person in 10,000 people has a rare genetic disease.
So,[tex]P(D)=\frac{1}{10000}[/tex]
Only 0.4% of the people who don't have it test positive.
[tex]P(A|D^c)[/tex] = probability that a person is tested positive given he don't have a disease = 0.004
[tex]P(D^c)=1-\frac{1}{10000}[/tex]
Formula:[tex]P(D|A)=\frac{P(A|D)P(D)}{P(A|D)P(D^c)+P(A|D^c)P(D^c)}[/tex]
[tex]P(D|A)=\frac{0.988 \times \frac{1}{10000}}{0.988 \times (1-\frac{1}{10000}))+0.004 \times (1-\frac{1}{10000})}[/tex]
P(D|A)=[tex]\frac{2470}{2471}[/tex]=0.9995
P(D|A)=[tex]0.9995[/tex]
A)The probability that someone who tests positive has the disease is 0.9995
(B)
[tex]P(D^c|A^c)[/tex]=probability that someone does not have disease given that he tests negative
[tex]P(A^c|D^c)[/tex]=probability that a person tests negative given that he does not have disease =1-0.004
=0.996
[tex]P(A^c|D)[/tex]=probability that a person tests negative given that he has a disease =1-0.988=0.012
Formula: [tex]P(D^c|A^c)=\frac{P(A^c|D^c)P(D^c)}{P(A^c|D^c)P(D^c)+P(A^c|D)P(D)}[/tex]
[tex]P(D^c|A^c)=\frac{0.996 \times (1-\frac{1}{10000})}{0.996 \times (1-\frac{1}{10000})+0.012 \times \frac{1}{1000}}[/tex]
[tex]P(D^c|A^c)=0.99999[/tex]
B)The probability that someone who tests negative does not have the disease is 0.99999
Jack went out for dinner at Red Lobster, his meal was $45, jack wants to leave an 18% tip, list three different calculations jack can use to determine his bill including the tip
Answer:
Step-by-step explanation:
Jack went out for dinner at Red Lobster and his meal was $45, This is the amount that he needs to pay if there was no tax or tip.
jack wants to leave an 18% tip, The amount of tip that jack wants to leave is 18/100 × 45 = 0.18×45 = $8.1
To determine how much jack needs to pay including the tip,
Amount that jack would pay is bill + tip = 45 + 8.1 = $53.1
Another way of calculating it is,
Since the tip is 18% and his bill was 100%, we will add the percentages and multiply by the bill. It becomes
118/100 × 45 = $53.1
33% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. If convenient, use technology to find the probabilities.
Answer:
3.3 in other words between 2-5
Step-by-step explanation:
33% of 100 is 33 so
33% of 10 is 3.3
Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = x + 1 intersect the circle with radius 6 and center (0, 1)?
Answer:
(3√2, 1+3√2) ≈ (4.243, 5.243)
Step-by-step explanation:
The line has a slope of 1 and goes through the center of the circle, so will intersect the circle at the point ...
(6, 6)/√2 +(0, 1) = (3√2, 1+3√2) ≈ (4.243, 5.243)
A wire is to be cut into two pieces. One piece will be bent into a square, and the other piece will be bent into a circle. If the total area enclosed by the two pieces is to be 64 cm2,
what is the minimum length of wire that can be used?
What is the maximum length of wire that can be used?
Answer:
minimum: 28.36 cmmaximum: 42.76 cmStep-by-step explanation:
The relationships between the radius of a circle and its circumference and area are ...
C = 2πr
A = πr²
The relationships between the side length of a square and its perimeter and area are ...
P = 4s
A = s²
So, the length of wire will be ...
w = C + P
w = 2πr + 4s
subject to the constraint that the sum of areas is 64 cm²:
πr² + s² = 64
___
Using the method of Lagrange multipliers to find the extremes of wire length, we want to set the partial derivatives of the Lagrangian (L) to zero.
L = 2πr + 4s + λ(πr² +s² -64)
∂L/∂r = 0 = 2π +2πλr . . . . . . [eq1]
∂L/∂s = 0 = 4 +2λs . . . . . . . . [eq2]
∂L/∂λ = 0 = πr² +s² -64 . . . . [eq3]
__
Solving for λ, we find ...
0 = 1 +λr . . . . divide [eq1 by 2π
λ = -1/r . . . . . . subtract 1, divide by r
Substituting into [eq2], we get ...
0 = 4 + 2(-1/r)s
s/r = 2 . . . . . . . . . .add 2s/r and divide by 2
This tells us the maximum wire length is that which makes the circle diameter equal to the side of the square.
Substituting the relation s=2r into the area constraint, we find ...
πr² +(2r)² = 64
r = √(64/(π+4)) = 8/√(π+4) ≈ 2.99359 . . . . cm
and the maximum wire length is ...
2πr +4(2r) = 2r(4+π) = 16√(4+π) ≈ 42.758 . . . cm
_____
The minimum wire length will be required when the entire area is enclosed by the circle. In that case, ...
πr² = 64
r = √(64/π)
C = 2πr = 2π√(64/π) = 16√π ≈ 28.359 . . . cm
_____
Comment on the solution method
The method of Lagrange multipliers is not needed to solve this problem. The alternative is to write the length expression in terms of one of the figure dimensions, then differentiate with respect to that:
w = 2πr + 4√(64-πr²)
dw/dr = 2π -4πr/√(64-πr²) = 0
64 -πr² = 4r²
r = √(64/(π+4)) . . . . same as above
_____
Comment on the graph
The attached graph shows the relationship between perimeter and circumference for a constant area. The green curve shows the sum of perimeter and circumference, the wire length. The points marked are the ones at the minimum and maximum wire length.
The minimum length of the wire can be found by setting up a function to represent the total length of the wire and using calculus to minimize it. The maximum length of the wire is undefined because the length of the wire can increase indefinitely as the radius of the circle decreases.
Explanation:To solve this problem, we use the formulas for the perimeters of a square and a circle, and the fact that the sum of their areas should equal 64 cm2. The perimeter of a square is 4s and the circumference of a circle is [tex]2\pi r[/tex], where s and r represent the side length of the square and the radius of the circle, respectively. The area of a square is s2 and the area of a circle is πr2.
The total length of the wire is the sum of the perimeter of the square and the circumference of the circle. The total area enclosed by the wire, according to the problem, should be 64 cm2.
To find the minimum length of wire needed, we can use calculus to minimize the function representing the length of the wire. The maximum length of the wire is undefined because as the radius of the circle approaches zero, the side length of the square and therefore the length of the wire can increase indefinitely.
Learn more about Minimum Wire Length here:https://brainly.com/question/31786854
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Mars Inc. claims that they produce M&Ms with the following distributions:
Brown 30% Red 20% Yellow 20%
Orange 10% Green 10% Blue 10%
How many M&Ms must be sampled to construct the 97% confidence interval for the proportion of red M&Ms in that bag if we want a margin of error of ± .15?
a) 33
b) 36
c) 34
d) 26
e) 25
f) None of the above
Answer:
C) 34
Step-by-step explanation:
1) Some definitions
By definition the margin of error (ME) is the error that tell to us how many percentage points your results will differ from the real population value, on this case our parameter of interest is pr = proportion of red M&M's
ME = Critical value x Standard error of the sample =0.15.
The proportion of red M&M's follows a normal distribution, and our critical value would be from the normal standard distribution on this case
2) Calculate the critical value
a) Compute alpha (α): α = 1 - (confidence level / 100) = 1- 0.97 = 0.03
b) Calculate the critical probability (p*): p* = 1 - α/2 = 1 - (0.03/2) = 0.985
c) Find the z-score using the cumulative probability obtained at step b)
On this case P(Z<z) = 0.985 , the value of z = 2.17 using the normal standard table
3) Calculate n from the formula of ME
The margin of error for a proportion is given by this formula
ME = z sqrt{{pr(1-pr)/n}}
Squaring both sides :
(ME/z) ^2 = (pr(1-pr))/n
And solving for n we got
n = (pr(1-pr))/(ME/z)^2 = (0.2x0.8)/ (0.15/2.17)^2 = 33.488
We need to round up the sample in order to ensure that the confidence level of 97% is meeted, and on this case the answer would be 34.
The number of M&Ms needed to construct a confidence interval for the proportion of red M&Ms with a margin of error of ± .15 is n = 36.
To construct a confidence interval for the proportion of red M&Ms with a margin of error of ± .15, we can use the formula for the sample size needed:
n = (Z² × p × (1-p)) / E²
Substitute Z = 2.17 (for 97% confidence), p = 0.20 (given proportion of red M&Ms), and E = 0.15 into the formula:
n = (2.17²× 0.20 × 0.80) / 0.15²
= 36
Therefore, the number of M&Ms that must be sampled to construct the 97% confidence interval for the proportion of red M&Ms with a margin of error of ± .15 is 36.
A five-digit number is represented by ABCDE. If we add the number 1 in front of ABCDE, then the product of 1ABCDE and 3 will be the six-digit number ABCDE1. What is the original five-digit number ABCDE?
Answer:
ABCDE = 42857
Step-by-step explanation:
First, we will use logic. The only number that when it's multiplied by 3, gives 1 at the end is 7, so E should be 7, so:
1ABCD7 * 3 = ABCD71
If 3 times 7 is 21, we carry two, so, the next number by logic, cannot be 1, because 3*1 = 3 + 2 = 5, it's not 7, so, it should be another number, like 5.
5*3 = 15 + 2 = 17 and we carry one. So this number fix in the digit, and D = 5.
We have now: 1ABC57 * 3 = ABC571
Letter C, we have to get a number that when it's multiplied by 3 and carry one, gives 5. In this case 8, because: 3 * 8 = 24 + 1 = 25 and carry two. D = 8.
So far: 1AB857 * 3 = AB8571
Now, the same thing with B. If we multiply 3 by 2, and carry two we will have 8 so: 3 * 2 = 6 + 2 = 8. B = 2
1A2857 * 3 = A28571
Finally for the last number, a number multiplied by 3 that hold the 1 as decene, In this case, the only possibility is 4, 3 * 4 = 12 so:
142857 * 3 = 428571
Determine the amplitude of the function y = -2 sin x from the graph shown below:
Answer:
2
Step-by-step explanation:
y=a sin x
amplitude=|a|
a=-2
amplitude=2