Answer:
y=-2
Step-by-step explanation:
5 (y-1)+6= -9
Subtract 6 from each side
5 (y-1)+6-6= -9-6
5 ( y-1) = -15
Divide by 5
5(y-1)/5 = -15/5
y-1 = -3
Add 1 to each side
y-1+1 = -3+1
y = -2
1. There are a total of 230 mint and chocolate sweets in a jar. 60% of the total number of sweets were mint sweets. After more chocolate sweets were added into the jar, the percentage of the mint sweets in the jar decreased to 40% How many chocolate sweets were added into the jar?
2. In August, 36% of the people who visited the zoo were locals and the rest were foreigners. In September, the percentage of local visitors decreased by 25% while the percentage of foreign participants increased by 50%. In the end, there were 161 fewer visitors in August than in September. How many visitors were there in September?
Answer:
1. 115 chocolates were added
2. 861 visitors in September
Step-by-step explanation:
1.
Initially:
m=number of mints
60% of 230 sweets were mints =>
m = 230*0.6 = 138 mints
initial number of chocolates, c1 = 230 - 138 = 92
Now chocolates were added
138 mints represented 40% of the total number of sweets, so
total number of sweets = 138 / 0.4 = 345
Number of chocolates added = 345 - 230 = 115
2.
In August 36% were locals, 64% were from elsewhere.
In suptember,
locals decreassed by 25% to 36*0.75=27% (of August total)
foreigner increased by 50% to 64*1.5=96% (of August total)
Total Inrease = 96+27-100 = 23% of August total = 161 visitors
August total = 161/0.23 = 700 visitors
September total = 700 + 161 = 861 visitors
ANSWER FAST PLEASE HELP
Answer:
see below
Step-by-step explanation:
Because two sides are congruent, the triangle in the diagram is isosceles which means that angle c = angle e because of the Base Angles Theorem. We know that angle c = 63 degrees because we see that it's vertical to a 63 degree angle, and vertical angles. Since angle c = angle e, angle e = 63 degrees. Since angles e and b form a linear pair, they are supplementary, meaning that they add up to 180 degrees which means that angle b = 180 - 63 = 117 degrees. To find angle d, we notice that d and c are alternate interior angles, and since these angles are congruent in parallel lines, angle d = 63 degrees as well. To find angle a, we know that the sum of angles in a triangle is 180 degrees so angle a = 180 - 63 - 63 = 54 degrees.
See in the attachment.
Question 6 of 10
Which equation matches the graph of the greatest integer function given
below?
Write the following exponential expression in expanded form 28 to the 6th power. Enter your answer in the following format a • a• a
Answer:
28 • 28 • 28 • 28 • 28 • 28
Step-by-step explanation:
The exponent signifies the number of times the base appears as a factor in the product. Here, the base 28 is a factor 6 times:
28×28×28×28×28×28
Does anyone know the answers to these?
Step-by-step explanation:
a. The point estimate is the mean, 47 days.
b. The margin of error is the critical value times the standard error.
At 31 degrees of freedom and 98% confidence, t = 2.453.
The margin of error is therefore:
MoE = 2.453 × 10.2 / √32
MoE = 4.42
c. The confidence interval is:
CI = 47 ± 4.42
CI = (42.58, 51.42)
d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.
e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.
helpppp with this will give bralienst but need hurry
Answer:
20.25is how much each friend gets.Step-by-step explanation:
40.50/2 = 20.25
You have to divide by 2. This way both of the people will get the same amount of money.
Answer:
each friend will get
Step-by-step explanation:
20 .25
as 40 .50 ÷ 2 = 20 .25
hope this helps
pls can u heart and like and give my answer brainliest pls i beg u thx !!! : )
What is the length of in the right triangle below?
A.
120
B.
C.
D.
218
Answer:
b. sqrt(120)
Step-by-step explanation:
a^2+b^2=c^2
a^2+7^2=13^2
13^2-7^2=a^2
120=a^2
sqrt(120)=a
This is using Pythagorean theorem
On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 4 days for several months. As of July 27, 2009, the number of new cases was 15,784. Determine the instantaneous growth rate for the virus (rounded to the nearest ten-thousandths).
Answer:
growth rate = 0.1733 per day, or 17.33% per day
Step-by-step explanation:
Since the doubling time is 4 days, the growth factor over a period of t days is ...
2^(t/4)
Then the growth factor for 1 day is
2^(1/4) ≈ 1.189207
The instantaneous growth rate is the natural log of this:
ln(1.189207) ≈ 0.1733 . . . per day
There are three points on a line, A, B, and C, so that AB = 12 cm, BC = 13.5 cm. Find the length of the segment AC . Give all possible answers.
Answer:
AC = 25.5 or 1.5
Step-by-step explanation:
If they are on a line and they are in the order ABC
AB + BC = AC
12+13.5 = AC
25.5 = AC
If they are on a line and they are in the order CAB
CA + AB = BC
AC + 12 =13.5
AC = 13.5 -12
AC = 1.5
If they are on a line and they are in the order ACB
That would mean that AB is greater than BC and that is not the case
Simplify.
Remove all perfect squares from inside the square roots.
Assume a and b are positive.
Answer:
9a^2sqrt(ab)
Step-by-step explanation:
The first noticable thing is that 81 has a perfect square of 9.
So it is now 9sqrt(a^5b)
you can split the a^5, to a^4 × a.
you can now take the sqrt of a^4, which is a^2, and pull it out from the sqrt
You are now left with 9a^2sqrt(ab)
Answer:
9a^2sqrt(ab)
Step-by-step explanation:
In an isolated environment, a disease spreads at a rate proportional to the product of the infected and non-infected populations. Let I(t) denote the number of infected individuals. Suppose that the total population is 2000, the proportionality constant is 0.0001, and that 1% of the population is infected at time t-0, write down the intial value problem and the solution I(t).
dI/dt =
1(0) =
I(t) =
symbolic formatting help
Answer:
dI/dt = 0.0001(2000 - I)I
I(0) = 20
[tex]I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]
Step-by-step explanation:
It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.
Also given I(t) is the number of the infected individual at a time t.
[tex]\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}[/tex]
Given total population is 2000. So the non infected population = 2000 - I.
[tex]\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I[/tex]
Now, I(0) is the number of infected persons at time t = 0.
So, I(0) = 1% of 2000
= 20
Now, we have dI/dt = 0.0001(2000 - I)I and I(0) = 20
[tex]\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k[/tex]
[tex]\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]
The required expressions are presented below:
Differential equation[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]
Initial value[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]
Solution of the differential equation[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]
Analysis of an ordinary differential equation for the spread of a disease in an isolated population
After reading the statement, we obtain the following differential equation:
[tex]\frac{dI}{dt} = k\cdot I\cdot (n-I)[/tex] (1)
Where:
[tex]k[/tex] - Proportionality constant[tex]I[/tex] - Number of infected individuals[tex]n[/tex] - Total population[tex]\frac{dI}{dt}[/tex] - Rate of change of the infected population.Then, we solve the expression by variable separation and partial fraction integration:
[tex]\frac{1}{k} \int {\frac{dI}{I\cdot (n-I)} } = \int {dt}[/tex]
[tex]\frac{1}{k\cdot n} \int {\frac{dl}{l} } + \frac{1}{kn}\int {\frac{dI}{n-I} } = \int {dt}[/tex]
[tex]\frac{1}{k\cdot n} \cdot \ln |I| -\frac{1}{k\cdot n}\cdot \ln|n-I| = t + C[/tex]
[tex]\frac{1}{k\cdot n}\cdot \ln \left|\frac{I}{n-I} \right| = C\cdot e^{k\cdot n \cdot t}[/tex]
[tex]I(t) = \frac{n\cdot C\cdot e^{k\cdot n\cdot t}}{1+C\cdot e^{k\cdot n \cdot t}}[/tex], where [tex]C = \frac{I_{o}}{n}[/tex] (2, 3)
Note - Please notice that [tex]I_{o}[/tex] is the initial infected population.
If we know that [tex]n = 2000[/tex], [tex]k = 0.0001[/tex] and [tex]I_{o} = 20[/tex], then we have the following set of expressions:
Differential equation[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]
Initial value[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]
Solution of the differential equation[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]
To learn more on differential equations, we kindly invite to check this verified question: https://brainly.com/question/1164377
A ball is thrown from a height of 20 meters with an initial downward velocity of 5 m/s. The ball's height h (in meters) after t seconds is given
by the following.
h=20-5t-5t²
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answer:
1.56 seconds
Step-by-step explanation:
When the ball hits the ground, h = 0.
0 = 20 − 5t − 5t²
Divide both sides by -5.
0 = t² + t − 4
Solve with quadratic formula.
t = [ -1 ± √(1² − 4(1)(-4)) ] / 2(1)
t = (-1 ± √17) / 2
The time must be positive, so:
t = (-1 + √17) / 2
t ≈ 1.56
Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by compounding continuously? Round to the nearest cent.
Answer:
$7200
Step-by-step explanation:
The interest rate on $5,000 accumulated by Edgar is 20%.
He does not make any payment for 2 years and the interests are compounded continuously.
The amount of money he owes after 2 years is the original $5000 and the interest that would have accumulated after 2 years.
The formula for compound amount is:
[tex]A = P(1 + R)^T[/tex]
where P = amount borrowed = $5000
R = interest rate = 20%
T = amount of time = 2 years
Therefore, the amount he will owe on his debt is:
[tex]A = 5000 (1 + 20/100)^2\\\\A = 5000(1 + 0.2)^2\\\\A = 5000(1.2)^2\\[/tex]
A = $7200
After 2 years, he will owe $7200
Answer:7,434.57
Explanation: A= 5000(1+0.2/12)^12•2
What will happen to the median height of the outlier is removed?
{75, 63, 58, 59, 63, 62, 56, 59)
Answer:
The meadian decreases by 1.5 when the outlier is removed.
Step-by-step explanation:
Well first we need to find the median of the following data set,
(75, 63, 58, 59, 63, 62, 56, 59)
So we order the set from least to greatest,
56, 58, 59, 59, 62, 63, 63, 75
Then we cross all the side numbers,
Which gets us 59 and 62.
59 + 62 = 121.
121 / 2 = 60.5
So 65 is the median before the outlier is removed.
Now when we remove the outlier which is 75.
Then we order it again,
56, 58, 59, 59, 62, 63, 63
Which gets us 59 as the median.
Thus,
the median height decreases by 1.5 units when the outlier is removed.
Hope this helps :)
4
Consider the following equation.
-)* + 12 = 25 – 3
Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.
12
X
12
A I=
33
Edmentum. All rights reserved.
The solution to the equation above using three iterations of successive approximation is x = 25/16
What is an equation solution?The solution of an equation is the true values of the equation
The equation is given as:
[tex]5^{-x} + 7 =2x + 4[/tex]
Equate to 0
[tex]5^{-x} + 7 -2x - 4 = 0[/tex]
Write the equation as a function
[tex]f(x) = 5^{-x} + 7 -2x - 4[/tex]
The equation has a solution only when the function f(x) equals 0.
From the graph, we have:
x = 1.5
So, we have:
[tex]f(1.5) = 5^{-1.5} + 7 -2*1.5 - 4[/tex]
Evaluate
f(1.5) = 0.089
Set x to 1.52 to determine a closer value of f(x) to 0.
[tex]f(1.52) = 5^{-1.52} + 7 -2*1.52 - 4[/tex]
Evaluate
f(1.52) = 0.047
Set x to 1.54 to determine a closer value of f(x) to 0.
[tex]f(1.54) = 5^{-1.54} + 7 -2*1.54 - 4[/tex]
Evaluate
f(1.54) = 0.004
Notice that 0.004 is closer to 0 than 0.047 and 0.089
The closest value to 1.54 is 25/16 in the given options
Hence, the solution to the equation above using three iterations of successive approximation is x = 25/16
Read more about equation solutions at:
https://brainly.com/question/14174902
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the domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values excpet 2. what are the restrictions on the domain of (u•v)(x)?
Answer:
[tex](-\infty, 0) \cup (0,2) \cup (2,\infty)[/tex]
Step-by-step explanation:
Remember that the domain of the product of functions is the intersection of domains, therefore when you intercept them you get the following interval.
[tex](-\infty, 0) \cup (0,2) \cup (2,\infty)[/tex]
James runs on the school track team he runs 4 2/3 miles and 3/4 of an hour. What is James' speed in miles per hour?
Answer:
6 2/9 miles per hour
Step-by-step explanation:
Take the miles and divide by the hours
4 2/3 ÷ 3/4
Change to an improper fraction
( 3*4+2)/3 ÷3/4
14/3 ÷3/4
Copy dot flip
14/3 * 4/3
56/9
Change back to a mixed number
9 goes into 56 6 times with 2 left over
6 2/9 miles per hour
Answer:
6 2/9 miles per hour
Step-by-step explanation:
Divide the miles by the hour.
4 2/3 ÷ 3/4
Reciprocal
4 2/3 × 4/3
Convert to improper fraction.
14/3 × 4/3
56/9
Convert to mixed fraction.
9 × 6 + 2
6 2/9
What is the output of the function f(x) = x + 21 if the input is 4?
When the input is 4, the output of f(x) = x + 21.
Work Shown:
Replace every x with 4. Use the order of operations PEMDAS to simplify
f(x) = x + 21
f(4) = 4 + 21
f(4) = 25
The input 4 leads to the output 25.
Am I right or wrong?
You are absolutely right.
as a sales person at Trending Card Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sells $400 worth of merchandise in one month, he is paid $500. If he sells $700 worth of merchandise in one month, he is paid $575. Find justin's salary if he sells $2500 worth of merchandise
Answer:
$1025
Step-by-step explanation:
We can use the 2-point form of the equation of a line to write a function that gives Justin's salary as a function of his sales.
We start with (sales, salary) = (400, 500) and (700, 575)
__
The 2-point form of the equation of a line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
salary = (575 -500)/(700 -400)(sales -400) +500
salary = 75/300(sales -400) +500
For sales of 2500, this will be ...
salary = (1/4)(2500 -400) +500 = (2100/4) +500 = 1025
Justin's salary after selling $2500 in merchandise is $1025.
A shoes store sells three categories of shoes, Athletics, Boots and Dress shoes. The categories are stocked in the ratio of 5 to 2 to 3. If the store has 70 pairs of boots, how many shoes do they have in total?
Answer:
350 pairs
Step-by-step explanation:
If the ratio of Athletics, Boots, and Dress shoes is 5 to 2 to 3, it means that for every 2 pairs of Boots they have 5 pairs of Athletics shoes and 3 pairs of dress shoes.
So, if they have 70 pairs of boots, we can calculate the number of Athletics as:
[tex]\frac{5*70}{2} =175[/tex]
And if they have 70 pairs of boots, the number of dress shoes are:
[tex]\frac{3*70}{2}=105[/tex]
Finally, they have 70 pairs of boots, 175 pairs of athletics, and 105 pairs of dress shoes. It means that they have 350 pairs in total.
70 + 175 + 105 = 350
Solve for x −ax + 2b > 8
Answer:
x < -( 8-2b) /a a > 0
Step-by-step explanation:
−ax + 2b > 8
Subtract 2b from each side
−ax + 2b-2b > 8-2b
-ax > 8 -2b
Divide each side by -a, remembering to flip the inequality ( assuming a>0)
-ax/-a < ( 8-2b) /-a
x < -( 8-2b) /a a > 0
Answer: [tex]x<\frac{-8+2b}{a}[/tex]
[tex]a>0[/tex]
Step-by-step explanation:
[tex]-ax+2b>8[/tex]
[tex]\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}[/tex]
[tex]-ax>8-2b[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)[/tex]
[tex]ax<-8+2b[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}a[/tex]
[tex]\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0[/tex]
[tex]x<\frac{-8+2b}{a};\quad \:a>0[/tex]
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
x+y>0
x + y +5<0
Answer:
Step-by-step explanation:
x+y>0, x>0, when y=0
x+y<-5 x<-5 when y=0
since the sign is only< then it is dotted line, and since one is greater and is less than they actually do not intersect
Answer:
No solution with slanted lines
Step-by-step explanation:
One positive integer is 6 less than twice another. The sum of their squares is 801. Find the integers
Answer:
[tex]\large \boxed{\sf 15 \ \ and \ \ 24 \ \ }[/tex]
Step-by-step explanation:
Hello,
We can write the following, x being the second number.
[tex](2x-6)^2+x^2=801\\\\6^2-2\cdot 6 \cdot 2x + (2x)^2+x^2=801\\\\36-24x+4x^2+x^2=801\\\\5x^2-24x+36-801=0\\\\5x^2-24x-765=0\\\\[/tex]
Let's use the discriminant.
[tex]\Delta=b^4-4ac=24^2+4*5*765=15876=126^2[/tex]
There are two solutions and the positive one is
[tex]\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{24+126}{10}=\dfrac{150}{10}=15[/tex]
So the solutions are 15 and 15*2-6 = 30-6 = 24
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Help me!!! please!!!
Answer:
a) The five ordered pairs are:-
(1,60) , (2,120) , (3,180) , (4,240) , (5,300)
b)When You divide the y value by x value for each ordered pair u find the slope.
c)The graph shows a proportional relationship.Because as x-value increases so does y-value.
d)Y=mx+b--> Y=60x (No y-intercept because it starts from 0)
e)If a person hiked for 9 hours then the distance would be 540. Because If u plug in the number of hours in the x value of the equatione then u will get 540. Here's the work:-
Y=60(9)
Y=540
Step-by-step explanation:
Hope it helps u. And if u get it right pls give me brainliest.
A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09 *Note: An increase in film speed would lower the value of the observation in microjoules per square inch. We may also assume the speeds of the film follow a normal distribution. Use this information to construct a 98% interval estimate for the difference in mean speed of the films. Does decreasing the thickness of the film increase the speed of the film?
Answer:
A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Step-by-step explanation:
We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.
For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.
Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;
P.Q. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15
[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06
[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11
[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09
[tex]n_1[/tex] = sample of 25-mil film = 8
[tex]n_2[/tex] = sample of 20-mil film = 8
[tex]\mu_1[/tex] = population mean speed for the 25-mil film
[tex]\mu_2[/tex] = population mean speed for the 20-mil film
Also, [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005
Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.
So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;
P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98 {As the critical value of t at 14 degrees of
freedom are -2.624 & 2.624 with P = 1%}
P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98
P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ) = 0.98
P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98
98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]
= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]
= [-0.042, 0.222]
Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.
The current particulate standard for diesel car emission is .6g/mi. It is hoped that a new engine design has reduced the emissions to a level below this standard. Set up the appropriate null and alternative hypotheses for confirming that the new engine has a mean emission level below the current standard. Discuss the practical consequences of making a Type I and a Type II error. (continue #5) A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4. Find the p-value of the test. Do you think that H0 should be rejected? Explain. To what type of error are you now subject?
Answer:
Step-by-step explanation:
From the summary of the given statistics;
The null and the alternative hypothesis for confirming that the new engine has a mean emission level below the current standard can be computed as follows:
Null hypothesis:
[tex]H_0: \mu = 0.60[/tex]
Alternative hypothesis:
[tex]H_a: \mu < 0.60[/tex]
Type I error: Here, the null hypothesis which is the new engine has a mean level equal to .6g/ml is rejected when it is true.
Type II error: Here, the alternative hypothesis which is the new engine has a mean level less than.6g/ml is rejected when it is true.
Similarly;
From , A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4.
Sample size n = 64
sample mean [tex]\overline x[/tex] = .5 g/ml
standard deviation σ = .4
From above, the normal standard test statistics can be determined by using the formula:
[tex]z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{0.5- 0.6}{\dfrac{0.4}{\sqrt{64}}}[/tex]
[tex]z = \dfrac{-0.1}{\dfrac{0.4}{8}}[/tex]
z = -2.00
The p-value = P(Z ≤ -2.00)
From the normal z distribution table
P -value = 0.0228
Decision Rule: At level of significance ∝ = 0.05, If P value is less than or equal to level of significance ∝ , we reject the null hypothesis.
Conclusion: SInce the p-value is less than the level of significance , we reject the null hypothesis. Therefore, we can conclude that there is enough evidence that a new engine design has reduced the emissions to a level below this standard.
The amount of carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.00012 t Baseline . The paint contains 27% of its carbon-14. How old are the paintings?
Answer:
The painting is [tex]t = 10911.1 \ years \ old[/tex]
Step-by-step explanation:
From the question we are told that
The amount of carbon present after t year is
[tex]y(t) = y_o * e ^{-0.00012t}[/tex] {Note ; This is the function }
Here [tex]y(t)[/tex] is the amount of carbon-14 after time t
[tex]y_o[/tex] the original amount of carbon-14
Now given that the paint as at now contain 27% of the original carbon-14
Then it mean that
[tex]y(t) = 0.27 y_o[/tex]
So the equation is represented as
[tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]
=> [tex]0.27 = * e ^{-0.00012t}[/tex]
=> [tex]ln(0.27) = -0.00012t[/tex]
=> [tex]- 1.30933 = -0.00012t[/tex]
=> [tex]t = \frac{-1.30933}{-0.00012}[/tex]
=> [tex]t = 10911.1 \ years[/tex]
The bar graph below shows trends in several economic indicators over the period . Over the six-year period, about what was the highest consumer price index, and when did it occur? Need help with both questions!
in science class savannah measures the temperature of a liquid to be 34 celsius. her teacher wants her to convert the temperature to degrees fahrenheit. what is the temperature of savannah's liquid to the nearest degress fahrenheit