Answer:
a) [tex]V(t) = 24 - 2t[/tex]
b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Step-by-step explanation:
The volume of the tank in terms of the time can be described by the following equation:
[tex]V(t) = V(0) - at[/tex]
In which V(0) is the initial volume and a is the hourly decrease rate.
a. Write a formula that expresses v in terms of t.
The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]
Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]
Then
[tex]V(t) = V(0) - at[/tex]
[tex]V(t) = 24 - 2t[/tex]
b. As t increases from 3 to 6, v varies from _________ to _________
[tex]V(t) = 24 - 2t[/tex]
[tex]V(3) = 24 - 2*3 = 18[/tex]
[tex]V(6) = 24 - 2*6 = 12[/tex]
So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
As part of an insurance company’s training program, participants learn how to conduct an analysis of clients’ insurability. The goal is to have participants achieve a time in the range of 30 to 47 minutes. Test results for three participants were: Armand, a mean of 37.0 minutes and a standard deviation of 3.0 minutes; Jerry, a mean of 38.0 minutes and a standard deviation of 2.0 minutes; and Melissa, a mean of 38.5 minutes and a standard deviation of 2.9 minutes.
a.Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Participants :
Armand: Cpk _____ Cp Capable ? No/Yes
Jerry: Cpk _____ Capable ? Yes/No
Melissa Cp ________ No/Yes
b.Can the value of the Cpk exceed the value of Cp for a given participant?
yes or no
Answer:
1) cpk < 1.33, therefore it is not capable
b) cpk = 1.33, therefore it is capable
c) cpk < 1.33, therefore it is not capable
2) Cpk can never be greater than the Cp, but can be equal to it
Step-by-step explanation:
Upper limit (USL) = 47 minutes and Lower limit (LSL) = 30 minutes
1)
a) mean (μ) = 37 minutes, standard deviation (σ) = 3 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-37}{3*3},\frac{37-30}{3*3} )=min(1.11,0.78)=0.78[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*3}=0.94[/tex]
cpk < 1.33, therefore it is not capable
b) mean (μ) = 38 minutes, standard deviation (σ) = 2 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-38}{3*2},\frac{38-30}{3*2} )=min(1.5,1.33)=1.33[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*2}=1.42[/tex]
cpk = 1.33, therefore it is capable
c) a) mean (μ) = 38.5 minutes, standard deviation (σ) = 2.9 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-38.5}{3*2.9},\frac{38.5-30}{3*2.9} )=min(0.98,0.98)=0.98[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*2.9}=0.98[/tex]
cpk < 1.33, therefore it is not capable
2) Cpk can never be greater than the Cp, but can be equal to it
Simplify -|-5 + 2|. this is all of the question
Answer:
-3
Step-by-step explanation:
-(absolute value of -3)
-(3)
-3
Please answer this correctly
Answer:
174
Step-by-step explanation:
l x w
5x20
8x4
6x7
174
1. Two people have $10 to divide between themselves. Each person names a number (nonnegative integer) no more than 10. If the sum of the two numbers is at most 10, each person gets the named amount of dollars, and the rest of the money is destroyed. If the sum exceeds 10, and the numbers are different, the person who has named the smaller number, receives the corresponding number of dollars, and the second person receives the rest. If the sum exceeds 10, and the numbers are equal, each person receives $5. Determine the be
Answer:
Step-by-step explanation:
Determine the best response of each player to each of the other player’s actions; plot them in a diagram and thus find the Nash equilibria of the game.
The best response for player 2 can be stated as:
(where X1 equals the dollar that a person names and Y2(X1) being the amount the person receives)
X1 Y2(X1)
0 10
1 9,10
2 8,9,10
3 7,8,9,10
4 6,7,8,9,10
5 5,6,7,8,9,10
6 5,6
7 6
8 7
9 8
10 9
Th best responses for player 1 would be the same.
Nash equilibria is the set of strategies that every person forms given no person has any incentive to change. Hence, we can say that there are 4 Nash equilibria: (5,5) , (5,6) , (6,5) , (6,6)
one car takes half a minute to complete a circuit.
the other car takes 1 minute and 10 seconds to complete a circuit.
if they start side by side, how long will it be before they are next side by side on the start line? state the units in your answer!
please help me I just need the answer
Answer:
7 laps
Step-by-step explanation:
Nathan spins 2 different spinners at the same time.There are a total of 10 possible outcomes.which pair of spinners did Nathan spin?
Answer:
The one divided into five part and the one divided into two parts
Step-by-step explanation:
find the option with one that has five parts and one with two parts :3
hope this helps!!
It is the graph with 5 numbers and 5 letters
I ready diagnostic
what expression are equivalent to 4(4x + 9)
Answer:
16x+36
Step-by-step explanation:
4(4x + 9)
16x+36
____________________________________
Solution,
4(4x+9)
=4*4x+4*9
=16x+36
So the answer is 16x+36
Hope it helps
Good luck on your assignment
___________________________________
Find the area of the trapezoid to the nearest tenth.
Answer:
2.2 metres squared
Step-by-step explanation:
We need to find the area of this trapezoid.
The area of a trapezoid is denoted by:
[tex]A=\frac{(b_1+b_2)h}{2}[/tex], where [tex]b_1[/tex] and [tex]b_2[/tex] are the parallel bases and h is the height
Here, we already know the lengths of the two bases; they are 0.9 metres and 2.3 metres. However, we need to find the length of the height.
Notice that one of the angles is marked 45 degrees. Let's draw a perpendicular line from top endpoint of the segment labelled 0.9 to the side labelled 2.3. We now have a 45-45-90 triangle with hypotenuse 2.0 metres. As one of such a triangle's properties, we can divide 2.0 by √2 to get the length of both legs:
2.0 ÷ √2 = √2 ≈ 1.414 ≈ 1.4
Thus, the height is h = 1.4 metres. Now plug all these values we know into the equation to find the area:
[tex]A=\frac{(b_1+b_2)h}{2}[/tex]
[tex]A=\frac{(0.9+2.3)*1.4}{2}=2.2[/tex]
The answer is thus 2.2 metres squared.
~ an aesthetics lover
What is equivalent to
16x-12-24x+4
Answer:
-8x - 8
Step-by-step explanation:
You have to combine like term.
So you add 16x + -24x = -8x
And you add -12 + 4 = -8
Your answer would be -8x - 8
I hope this helps!
Translate the following into algebraic expressions:
Mike is c years old. He is half as old as Steve. How old was Steve two years ago?
Answer:
2c -2 = Steve's age 2 years ago
Step-by-step explanation:
in a survey of more than 3000 people 93% of the respondents claimed to prefer Isaac's immaculate ice cream over any other brand of ice cream. which of the folloling groups were surveyed.
Answer:
The answer is 2,790.
Step-by-step explanation:
Here's a handy tool.
93% of 1 = 0.93 93% of 131 = 121.83 93% of 261 = 242.73 93% of 391 = 363.63
93% of 2 = 1.86 93% of 132 = 122.76 93% of 262 = 243.66 93% of 392 = 364.56
93% of 3 = 2.79 93% of 133 = 123.69 93% of 263 = 244.59 93% of 393 = 365.49
93% of 4 = 3.72 93% of 134 = 124.62 93% of 264 = 245.52 93% of 394 = 366.42
93% of 5 = 4.65 93% of 135 = 125.55 93% of 265 = 246.45 93% of 395 = 367.35
93% of 6 = 5.58 93% of 136 = 126.48 93% of 266 = 247.38 93% of 396 = 368.28
93% of 7 = 6.51 93% of 137 = 127.41 93% of 267 = 248.31 93% of 397 = 369.21
93% of 8 = 7.44 93% of 138 = 128.34 93% of 268 = 249.24 93% of 398 = 370.14
93% of 9 = 8.37 93% of 139 = 129.27 93% of 269 = 250.17 93% of 399 = 371.07
93% of 10 = 9.30 93% of 140 = 130.20 93% of 270 = 251.10 93% of 400 = 372.00
A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought in to the time repairs are completed. A random sample of 12 repair records showed the following repair times (in days): 5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.
H0: \mu \leq 5 days versus H1: \mu > 5 days. At \alpha = .05, choose the right option.
a) Reject H0 if tcalc < 1.7960
b) Reject H0 if tcalc >1.7960
Answer:
The degrees of freedom first given by:
[tex]df=n-1=12-1=11[/tex]
Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:
[tex] t_{\alpha}= 1.796[/tex]
And for this case the rejection region would be:
b) Reject H0 if tcalc >1.7960
Step-by-step explanation:
Information given
5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.
System of hypothesis
We want to test if the true mean is higher than 5, the system of hypothesis are :
Null hypothesis:[tex]\mu \leq 5[/tex]
Alternative hypothesis:[tex]\mu > 5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
The degrees of freedom first given by:
[tex]df=n-1=12-1=11[/tex]
Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:
[tex] t_{\alpha}= 1.796[/tex]
And for this case the rejection region would be:
b) Reject H0 if tcalc >1.7960
please help! ill give 24 points just tryna finish before the last day
Answer:
(1,3)
Step-by-step explanation:
Note that the solution for a graphed system of equations is just the point where the two lines intersect.
A point is (x coordinate, y coordinate).
This said, we can find the point where it intersects then see which value it is above for the x axis.
It is directly above 1.
So the x coordinate is 1.
Now, let's look at what coordinate it is next to on the y axis.
It would be 3.
So the y coordinate is 3.
Therefore, the solution to the system of equations graphed below is (1,3)
Solve Systems of Algebraic Equations in Two Variables
Hello I need some help on setting up 2 equations of this problem. The answers are cheeseburger costs $1.55 and the milkshake $0.85
Four cheeseburgers and two chocolate milkshakes cost a total of $ 7.90. Two
Shakes cost 15 cents more than a hamburger with
cheese so What is the price of a cheeseburger?
And the price of a shake?
Answer:
4c+ 2m = 7.90
2m -.15 = c
Step-by-step explanation:
Let c = cheese burger
m = milkshake
4c+ 2m = 7.90
2m -.15 = c
Substitute into the first equation
4( 2m -.15) +2m = 7.90
Distribute
8m -.6 +2m = 7.90
Combine like terms
10m - .6 = 7.90
Add .6 to each side
10m = 7.90+.6
10m = 8.50
Divide by m
10m = 8.50/10
m = .85
Now find c
2m -.15 = c
2(.85) - .15=c
1.70-.15 = c
1.55 =c
A study published in 2010 showed that city dwellers have a higher risk of developing anxiety disorders and a higher risk of developing mood disorders than those who live in the country. A follow-up study published in 2011 used brain scans of city dwellers and country dwellers as they took a difficult math test.1 To increase the stress of the participants, those conducting the study tried to humiliate the participants by telling them how poorly they were doing on the test. The brain scans showed very different levels of activity in stress centers of the brain, with the urban dwellers having greater brain activity than rural dwellers in areas that react to stress.
Required:
a. Is the 2010 study an experiment or an observational study?
i. Experiment
ii. Observational study
b. Can we conclude from the 2010 study that living in a city increases a person's likelihood of developing an anxiety disorder or mood disorder?
i. Yes
ii. No
c. Is the 2011 study an experiment or an observational study?
i. Experiment
ii. Observational study
d. Can we conclude from the 2011 study that living in a city increases activity in stress centers of the brain when a person is under stress?
i. Yes
ii. No
Step-by-step explanation:
a.It is a controlled experiment because it is clearly seen that an established hypothesis or study is being verified through an experiment, now in this case the hypothesis is tested through an experiment where excessive stress is placed on the Participants during their math exam to effectively verify that people in urban or city areas live with more stress than people in rural areas.
2..As now that the previously established hypothesis has been verified, it is concluded that people who live in the city live with more anxiety and stress than people who live in rural areas.
Which of the following describes the function x^3-8
Answer:
Is there any options if so just repost with the options and i will answer it
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
3724 in^3
Step-by-step explanation:
19 times 14 times 14 = 3724
Answer:
3724 inches ³
Step-by-step explanation:
Volume of cooler = whl
Where w is width, h is height and l is length
V = (19)(14)(14)
V = 3724 inches³
Use the mathematical induction to prove that 7^n -1 is divisible by 6 whenever n is a positive integer
Answer:
Step-by-step explanation:
1) first of all, let s check for n = 1
[tex]7^1 -1=7-1=6[/tex]
that s true
2) We assume that this is true for n
[tex]7^n-1[/tex] is divisible by 6
what about [tex]7^{n+1}-1[/tex] ?
we know that there is a k natural so that [tex]7^n-1=6k[/tex]
so [tex]7^n = 1+6k[/tex]
then [tex]7^{n+1} = 7*7^n = 7(1+6k)\\[/tex]
so [tex]7^{n+1}-1 = 7(1+6k)-1 = 6+7*6k = 6(1+7k)[/tex]
so it means that [tex]7^{n+1}-1[/tex] is divisible by 6
3) finally as this is true for n=1 and if this is true for n then it is true for n+1 we can conclude that [tex]7^n-1[/tex] is divisible by 6 for n positive integer
A box is with a square base and open top is to be constructed and a total volume of 720 cubic inches is required. The cost of material for the base is 8 dollars per square inch and the cost of material for the sides is 6 dollars per square inch. Express the total cost of the box as a function of the length of the base.
Answer:
total cost = 8x^2 +17280/x
Step-by-step explanation:
Let x represent the base length. Then the area of the base is x^2, and the height is h = 720/x^2.
The area of the four sides is ...
(4x)(h) = (4x)(720/x^2) = 2880/x
The cost of the base is ...
base cost = 8x^2
And the cost of the sides is ...
side cost = 6(2880)/x = 17280/x
The total cost of the box is ...
total cost = base cost + side cost
total cost = 8x^2 +17280/x
_____
Comment on the cost function
You will find this function has a minimum at x=∛1080 ≈ 10.260 in. The total cost is about $2526.35, and the box is 2/3 times as tall as wide. That aspect ratio makes any pair of opposite sides cost the same as the base, the generic solution to a cost optimization problem of this sort.
Given that (- 2, 7) is on the graph of f(x) , find the corresponding point for the function f(x + 4).
Answer:
[tex]\boxed{\ the \ corresponding\ point\ is \ (-6,7)\ }[/tex]
Step-by-step explanation:
We know that f(-2)=7
x+4 = -2 <=> x = -6
so f(-6+4) = f(-2)=7
then the corresponding point is (-6,7)
Create an explicit formula for the following sequence 1/3,-1,3,-9
Answer:
multiply by -3
Step-by-step explanation:
1/3 gives -3/3=-1
-1*-3=3
3*-3=-9
it defines the function f so that f(x)=-3x
The radius of a circle is 5 cm. Find its area to the nearest tenth.
Answer:
78.5 cm^2
Step-by-step explanation:
The area of a circle is found by
A = pi r^2
A = pi (5)^2
A = 25pi
Letting pi = 3.14
A = 25(3.14)
A =78.5 cm^2
Letting pi be the pi button
A =78.53981634
Rounding to the nearest tenth
78.5
Answer:
78.5 cm²
Step-by-step explanation:
The area of a circle can be found using the following formula.
a=πr²
We know the radius of the circle is 5 centimeters.
r=5
Substitute 5 in for r.
a=π(5²)
Evaluate the exponent. 5² is equal to 5*5, which equals 25.
a=π(25)
Multiply 25 and pi
a=78.5398163397
Round to the nearest tenth. The 3 in the hundredth place tells use to leave the 5 in the tenths place as is.
a≈78.5
Add appropriate units. Area always uses units², and the units in this case are centimeters.
a≈78.5 centimeters²
The area of the circle is about 78.5 square centimeters.
What’s the correct answer for this question?
Answer:
A: 97π/18 m
Step-by-step explanation:
Central Angle = 97°
In radians:
97° = 97π/180
Now
S = r∅
S = (10)(97π/180)
S = 97π/18 m
Answer:
The answer is option 1.
Step-by-step explanation:
Given that the formula for length of Arc is Arc = θ/360×2×π×r when r represents the radius of circle. Then, you have to substitute the following values into the formula :
[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]
Let θ = ∠VCW = 97°,
Let r = 10m,
[tex]arc = \frac{97}{360} \times 2 \times \pi \times 10[/tex]
[tex]arc = \frac{97}{360} \times 20 \times \pi[/tex]
[tex]arc = \frac{97}{18} \pi \: m[/tex]
determine the slope of a line with the equation 6x+2y-4=0
Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled for the flowers to last the longest. Her cylinder vase has a radius of 2 in and a height of 9 in. How much water should Mary pour into the vase?
please help
Answer:
113.09 hope this helps
Step-by-step explanation:
Can someone help me with this
Answer:
Yes
sum of angle = 180°
First diagram
R+D+E=180°
110°+28°+E=180°
138°+E=180°
E=180°-138°
E=42°
Second diagram
T+V+A=180°
T+28°+42°=180°
T+70°=180°
T=180°-70°
T=110°
Suppose that the functions u and w are defined as follows.
Answer:
- 3 and 3
Step-by-step explanation:
To evaluate (u ￮ w)(- 1), evaluate w(- 1) then use this value to evaluate u(x)
w(- 1) = (- 1)² + 2 = 1 + 2 = 3, then
u(3) = - 3
---------------------------------------------------
To evaluate (w ￮ u)(- 1), evaluate u(- 1) then use this value to evaluate w(x)
u( - 1) = - (- 1) = 1, then
w(1) = 1² + 2 = 1 + 2 = 3
Which of the following is the solution to 4 | X+32 8 ?
A. XS-5 or x 2-1
B. X25 or x 2-1
C. $-5 and x-1
D. -1
SUBMIT
Answer:
A
Step-by-step explanation:
x + 3 must be 2 or greater, or -2 or less
So x must be ≥ -1 or ≤ -5
WRITING BOOK
Personal Writing
AD 1
NUMBERS
Which of the following cannot be an integer?
A. 0.8
B. -3
C. 4
D. 25
Answer:
A
Step-by-step explanation:
Integers are negative and positive whole numbers
Answer: A. 0.8
Step-by-step explanation:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14
Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below.
TIME REMAINING
54:06
3x
x
If Kyle uses 10 feet of wood to make the frame, what is the length of the frame? Write the answer in decimal form,
0.75
4.60
0.00
Answer:
3.75 feet
Step-by-step explanation:
The length of the frame is 3 times the width.
Let the width be x.
The length will be 3x.
Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.
The perimeter of a rectangle is:
P = 2(L + W)
=> 10 = 2(3x + x)
=> 10/2 = 4x
5 = 4x
=> x = 5/4 = 1.25 feet
The width is 1.25 feet. The length is therefore:
1.25 * 3 = 3.75 feet