Answer:
0.4207149;0.7271136; 0.3063987; 0.04979 ; 0.01832
Step-by-step explanation:
For an exponential distribution:
IF Mean time until failure = 23100
λ = 1/ 23100 = 0.0000432900
What is the probability that a randomly selected fan will last at least 20,000 hours
x ≥ 20000
P(X ≥ 20000) = 1 - P(X ≤ 20000)
1 - P(X ≤ 20000) = [1 - (1 - e^(-λx))]
1 - P(X ≤ 20000) = [1 - (1 - e^(-0.0000432900*20000)
1 - P(X ≤ 20000) = [1 - (1 - 0.4207148)]
1 - P(X ≤ 20000) = 1 - 0.5792851
1 - P(X ≤ 20000) = 0.4207149
11) What is the probability that a randomly selected fan will last at most 30,000 hours?
x ≤ 30000
P(X ≤ 30000) = 1 - e^(-λx)
P(X ≤ 20000) = 1 - e^(-0.0000432900*30000)
= 1 - e^(−1.2987)
= 1 - 0.2728863
= 0.7271136
111) What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?
0.7271136 - 0.4207149 = 0.3063987
B) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?
More than two standard deviation
X = 23100 + 2(23100) = 23100 + 46200 = 69300
Using the online exponential probability calculator :
P(X > 69300) = 0.04979
C) What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?
X = 23100 + 3(23100) = 23100 + 69300 = 92400
P(X > 92400) = 0.01832
Solve for x: 7 > x/4
Answer: x < 28
Step-by-step explanation:
What is the area of polygon EFGH?
Answer:
C. 42 square units
Step-by-step explanation:
This is a rectangle and to calculate the area of a rectangle we multiply length and width
The length of this rectangle is 7 units and the width is 6 units
6 × 7 = 42 square units
Find the product of all solutions of the equation (10x + 33) · (11x + 60) = 0
Answer:
18
Step-by-step explanation:
Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:
10x + 33 = 0 or 11x + 60 = 0
10x = -33 or 11x = -60
x = -33/10 or x = -60/11
Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.
A researcher is interested in determining whether various stimulant drugs improve maze leaming performance in rats. To find out, the researcher recruits 16 rats and assigns 4 rats to one of 4 research conditions: caffeine, nicotine, cocaine, placebo. Each rat completes the maze once and in only one research condition and is timed; time to complete the maze is the researcher's measure of performance. Answer the following questions considering the data below (alpha)
Caffeine Nicotine Cocaine Placebo
30.00 45.00 30.00 60.00
45.00 75.00 30.00 75.00
45.00 60.00 60,00 60.00
45.00 45.00 30.00
What is the dependent variable in this study?
a. Drug condition
b. Time to complete maze
c. Number of rats
d. Research conditions
16. What analysis should be used to answer the researcher's question?
a. One-way between-subjects (a.ka. independent-samples) ANOVA
b. One-way within-subjects (a.k.a. dependent-samples, repeated-measures) ANOVA
c. Factorial ANOVA
d. T-test 17.
What is the Null hypothesis for this analysis?
a. There will be no difference between any group means
b. Maze performance will get worse with stimulants
c. Maze performance of at least one group will differ from typing of at least one other group
d. Maze performance on placebo will be worse than on all drugs
What are the degrees of freedom for the numerator of the F-ratio?
2
3
8
11
What are the degrees of freedom for the denominator of the F-ratio?
2
3
8
11
What is the critical F value for this analysis?
a. 3.49
b. 4.07
c. 6.04
d. 19.00
What is the SSbetween-groups value?
a. 425.00
b. 1181.25
c. 2517.19
d. 3698.44
What is the SSwithin value?
Answer:
1) The dependent variable is : time to complete the maze
2) The analysis used should be : One -way within-subjects ANOVA ( B )
3) Null hypothesis is ; There will be no difference between any group means
4) Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3
5) degree of freedom for the denominator = 11
6) critical F value = 3.49
Step-by-step explanation:
The dependent variable is the time to complete the maze this is because the time depends on the effects of the stimulant drugs on the rats in the maze .
The analysis used should be : One -way within-subjects ANOVA ( B )
Null hypothesis is ; There will be no difference between any group means
Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3
degree of freedom for the denominator = N - k = 16 - 4 = 12. the closest answer from the options is 11
The critical value is 3.49 ,because at degree of freedom = 12 , ∝ = 0.05, and Dfn = 3, from the F - table the critical value would be 3.49
The state of Georgia is divided up into 159 counties. Consider a population of Georgia residents with mutually independent and equally likely home locations. If you have a group of n such residents, what is the probability that two or more people in the group have a home in the same county
Answer:
[tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]
Step-by-step explanation:
number of counties = 159
n number of people are mutually independent and equally likely home locations
considering the details given in the question
n ≤ 159
The number of ways for people ( n ) will live in the different counties (159) can be determined as [tex](\left \{ {{159} \atop {n}} \right} )[/tex]
since the residents are mutually independent and equally likely home locations hence there are : [tex]159^{n}[/tex] ways for the residents to live in
therefore the probability = [tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]
Given the exponential growth function f(x)=87(1.02)^x
What is the initial value of the function? _____
What is the growth factor, or growth rate of the function (as a percent)? _____%
Answer:
87; 2%
Step-by-step explanation:
An exponential growth model is defined as :
F(x) = A( 1 + r)^x
Where;
A = Initial amount,
r = rate of increase
x = time
Comparing the exponential growth function with the exponential growth model given;
f(x)=87(1.02)^x
A = 87 = Initial amount
The growth rate of the model expressed as a percentage :
Taking :
(1 + r) = 1.02
1 + r = 1.02
r = 1.02 - 1
r = 0.02
Expressing r as a percentage :
0.02 * 100% = 2%
Use the definition of continuity and the properties of limits to show that the function f(x)=x sqrtx/(x-6)^2 is continuous at x = 36.
Answer:
The function is continuous at x = 36
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = x * \sqrt{ \frac{x}{ (x-6) ^2 } }[/tex]
The point at which continuity is tested is x = 1
Now from the definition of continuity ,
At function is continuous at k if only
[tex]\lim_{x \to k}f(x) = f(k)[/tex]
So
[tex]\lim_{x \to 36}f(x) = \lim_{n \to 36}[x * \sqrt{ \frac{x}{ (x-6) ^2 } }][/tex]
[tex]= 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]
[tex]= 7.2[/tex]
Now
[tex]f(36) = 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]
[tex]f(36) = 7.2[/tex]
So the given function is continuous at x = 36
because
[tex]\lim_{x \to 36}f(x) = f(36)[/tex]
7. Over the past 50 years, the number of hurricanes that have been reported are as follows: 9 times there were 6 hurricanes, 13 times there were 8 hurricanes, 16 times there were 12 hurricanes, and in the remaining years there were 14 hurricanes. What is the mean number of hurricanes is a year
Answer:
Step-by-step explanation:
Let us first generate the frequency table from the information given:
Hurricane number(X) Frequency(f) f(X)
6 9 54
8 13 104
12 16 192
14 12 168
Total ∑(f) = 50 ∑f(x) =518
In order to determine the last frequency (the remaining years), we will add the other frequencies and subtract the answer from 50, which is the total frequency (50 years). This is done as follows:
Let the last frequency be f
9 + 3 + 16 + f = 50
38 + f = 50
f = 50 - 38 = 12
Now, calculating mean:
[tex]\bar {X} = \frac{\sum f(x)}{\sum(f)} \\\\\bar {X} = \frac{518}{50} \\\\\bar {X} = 10.36[/tex]
Therefore mean number of hurricanes = 10.4 (to one decimal place)
Jessica just bought a refrigerator for $799. She paid $79.80 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
$179.80
Step-by-step explanation:
799-79.80=719. That's the down payment subtracted from the total price of the refrigerator. 719/4, since there's four equal installments, gives you 179.8. Since cents go in 10s, you make it 179.80 and slap a dollar sign in front of that.
The sum of two numbers is 15. One number is 101 less than the other. Find the numbers.
Answer:
The numbers:
-43 and 58
Step-by-step explanation:
a + b = 15
a = b - 101
then:
(b-101) + b = 15
2b = 15+101
2b = 116
b = 116/2
b = 58
a = b - 101
a = 58 - 101
a = -43
Check:
a + b = 15
-43 + 58 = 15
The manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2. The manufacturer also has fixed costs each month of $8,000.
Answer:
C(x)=1.2x+8,000.
Step-by-step explanation:
C(x)=cost per unit⋅x+fixed costs.
The manufacturer has fixed costs of $8000 no matter how many drinks it produces. In addition to the fixed costs, the manufacturer also spends $1.20 to produce each drink. If we substitute these values into the general cost function, we find that the cost function when x drinks are manufactured is given by
In order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2.
Suppose that you have to sell [x] number of bars to make profits. So, we can write -
{2x} - {1.20x} > {8000}
0.8x > 8000
8x > 80000
x > 10000
Therefore, in order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands. The probability is 90% that the sample percentage is contained within what symmetrical limits of the population percentage
Answer:
the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.
Step-by-step explanation:
From the given information:
Sample size n = 200
The standard deviation for a sampling distribution for two brands are equally likely because the individual has no ability to discriminate between the two soft drinks.
∴
The population proportion [tex]p_o[/tex] = 1/2 = 0.5
NOW;
[tex]\sigma _p = \sqrt{\dfrac{p_o(1-p_o)}{n}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.5(1-0.5)}{200}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.5(0.5)}{200}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.25}{200}}[/tex]
[tex]\sigma _p = \sqrt{0.00125}[/tex]
[tex]\sigma _p = 0.035355[/tex]
However, in order to determine the symmetrical limits of the population percentage given that the z probability is 90%.
we use the Excel function as computed as follows in order to determine the z probability = NORMSINV (0.9)
z value = 1.281552
Now the symmetrical limits of the population percentage can be determined as: ( 1.28, -1.28)
[tex]1.28 = \dfrac{X - 0.5}{0.035355}[/tex]
1.28 × 0.035355 = X - 0.5
0.0452544= X - 0.5
0.0452544 + 0.5 = X
0.5452544 = X
X [tex]\approx[/tex] 0.545
X = 54.5%
[tex]-1.28 = \dfrac{X - 0.5}{0.035355}[/tex]
- 1.28 × 0.035355 = X - 0.5
- 0.0452544= X - 0.5
- 0.0452544 + 0.5 = X
0.4547456 = X
X [tex]\approx[/tex] 0.455
X = 45.5%
Therefore , we can conclude that the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.
Please help answer the following questions!!! :D I will do anything in return!
Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)
Answer:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 1 to 3.
= -196.5
Step-by-step explanation:
Given
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to infinity
The expression that includes all terms up to order 3 is:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to 3.
= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)
= -125/2 + 100000/6 - 759375/5040
= -62.5 + 16.67 - 150.67
= - 196.5
Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 350 spins, 163 landed with the heads side up. Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5?
Complete question is;
Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 350 spins, 163 landed with the heads side up. Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5?
Test the relevant hypotheses using α = 0.01
Answer:
The Test result doesn't support the claim that proportion of the time the coin would land heads is not 0.5. Rather it supports the the probability to be 0.5. So the students shouldn't interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5
Step-by-step explanation:
The hypotheses would be;
Null hypothesis; H0: p = 0.5
Alternative hypothesis; Ha: p ≠ 0.5
We are given, X = 163 and n = 350
Thus; p^ = X/n = 163/350 = 0.4657
Since we are not given standard deviation, we will use test statistic formula;
Z = (p^ - p)/(√(p(1 - p)/n)
Z = (0.4657 - 0.5)/(√(0.5(1 - 0.5)/350)
Z = -1.28
From online P-value from T-score calculator as attached, we have;
p-value = 0.201395.
Since the p-value is > 0.01, it's not significant and so we will fail to reject the null hypothesis H0.
We will conclude that the Test result supports the conclusion that p = 0.5
If the sides of a square measure 9.3 units the.find the length of the diagonal
Answer:
Approximately 13.1521 units.
Step-by-step explanation:
To find the diagonal, we can use the Pythagorean Theorem.
Since the figure is a square, all four sides are equivalent. A square also has four right angles. Therefore, we can use the Pythagorean Theorem to find the diagonal d. Therefore:
[tex]a^2+b^2=c^2[/tex]
Substitute 9.3 for a and b, and let c equal d:
[tex](9.3)^2+(9.3)^2=d^2[/tex]
Instead of squaring, add the like-terms:
[tex]2(9.3)^2=d^2[/tex]
Take the square root of both sides:
[tex]d=\sqrt{2(9.3)^2}[/tex]
Expand:
[tex]d=\sqrt{2}\cdot\sqrt{(9.3)^2}[/tex]
The right cancels:
[tex]d=\sqrt2\cdot(9.3)\\d=9.3\sqrt2\\d\approx13.1521\text{ units}[/tex]
what is 90.125 written in expanded from?
Answer:
The answer is 90+0+0.1+0.02+0.005.
Step-by-step explanation:
The reason for my answer is because 90 is in the tens place. 90+0 is equal to 90 so that's why it is a +0 after the 90. Now, we have a decimal. After the decimal, we have 125. It is +0.1 because the 1 in 90.125 is in the tenths place. Next, it is +0.02 because the 2 in 90.125 is in the hundredths place. Last but not least, it is +0.005 because the 5 in 90.125 is in the thousandths place.
Kevin's total payroll deductions are 30% of his earnings. If his deductions add up to $369 for a two week period, how much were his earnings for the period?
Answer:
His earnings for the period= $123
Step-by-step explanation:
Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.
If 30% of his earnings = $369
His earnings = x
30/100 * x= 369
X= 369*100/30
X= 123*10
X=$ 1230
His earnings for the period= $123
Hi I need help with 800×200= 8 × ______ hundreds=_____ Hundreds = _______ plz help me
Answer:
800×200= 8 × 200 hundreds= 1600 Hundreds = 160000
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose is
Answer:
8
Step-by-step explanation:
Ham with or without cheese-2 choices
Bologna with or without cheese-2 choices
Bologna with cheese with water or juice-2 choices
Bologna without cheese with juice or water-2 choices
Ham with cheese with juice or water -2 choices
Ham without cheese with juice or water -2 choices
2+2+2+2=8
Kile has 8 choices for lunch
Adrianna has a court to play basketball with her friends.
The it is 600 square feet. It is 30 feet long. How many feet across is
court?
Answer:
Hey there!
The area of a rectangle is the length times width.
Thus, we can write the equation, 600=30w.
Solving for the width, we get that the width is equal to 20 ft.
Let me know if this helps :)
Answer:
20 feet across.
Step-by-step explanation:
You will have to do a simple equation solve.
x is how many feet across the court is.
* could be our multiplying sign
600 = 30*x
Now divide 30 on both sides. 30 will cross out (since 30/30 is 1 and anything times 1 is the same number as it was before) on the right side and 600/30 is 20 so we change the 600 to 20.
That leaves 20 = x.
So it is 20 feet across.
Which of the following relations is a function? A. (1, 4), (-4, 2), (8, 1), (-8, 2) B. (1, 4), (-4, 6), (1, 3), (-8, 2) C. (1, 0), (-4, 3), (8, 1), (-4, 5) D. (8, 1), (-4, 4), (1, 1), (8, 2)
Answer:
A. (1, 4), (-4, 2), (8, 1), (-8, 2)
Step-by-step explanation:
Each x goes to only 1 y to be a function
A. (1, 4), (-4, 2), (8, 1), (-8, 2)
function
B. (1, 4), (-4, 6), (1, 3), (-8, 2)
1 goes to 4 and 3 so not a function
C. (1, 0), (-4, 3), (8, 1), (-4, 5)
-4 goes to 3 and 5 so not a function
D. (8, 1), (-4, 4), (1, 1), (8, 2)
8 goes to 1 and 2 so not a function
Answer:
[tex]\Large \boxed{\mathrm{A. \ (1, 4), (-4, 2), (8, 1), (-8, 2)}}[/tex]
Step-by-step explanation:
[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]
[tex](1, 4), (-4, 2), (8, 1), (-8, 2) \ \sf represents \ a \ function.[/tex]
[tex](1, 4), (-4, 6), (1, 3), (-8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]
[tex](1, 0), (-4, 3), (8, 1), (-4, 5) \ \sf does \ not \ represent \ a \ function.[/tex]
[tex](8, 1), (-4, 4), (1, 1), (8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]
In the adjoining figure, in ΔABC, D is the midpoint of the side BC.Hence a) AD is ___________ A b) AM is ____________ c) Is BD = DC please help!!!!!!!!!!!!!!
Answer:
a) AD is Median
b) AM is Perpendicular Bisector
Step-by-step explanation:
c) Yes because the Median divides the line into two equal parts
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
3/4=x/20,find the value of 'x'
Answer:
[tex]\boxed{x=15}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4} =\frac{x}{20}[/tex]
[tex]\sf Cross \ multiply.[/tex]
[tex]4 \cdot x = 20 \cdot 3[/tex]
[tex]4x=60[/tex]
[tex]\sf Divide \ both \ sides \ by \ 4.[/tex]
[tex]\frac{4x}{4} =\frac{60}{4}[/tex]
[tex]x=15[/tex]
. line containing ( −3, 4 ) ( −2, 0)
Answer:
The equation is y= -4x -8
Step-by-step explanation:
The -4 is the slope and the -8 is the y intercept
Answer:
Slope: -4
Line type: Straight and diagonal from left to right going down.
Rate of change: a decrease by 4 for every x vaule
y-intercept is: (0,-8)
x-intercept is: (-2,0)
Step-by-step explanation:
Slope calculations:
y2 - y1 over x2 - x1
0 - 4
-2 - ( -3) or -2 + 3
=
-4/1 =
-4
More slope info on my answer here: https://brainly.com/question/17148844
Hope this helps, and have a good day.
A bag contains 12 blue marbles, 5 red marbles, and 3 green marbles. Jonas selects a marble and then returns it to the bag before selecting a marble again. If Jonas selects a blue marble 4 out of 20 times, what is the experimental probability that the next marble he selects will be blue? A. .02% B. 2% C. 20% D. 200% Please show ALL work! <3
Answer:
20 %
Step-by-step explanation:
The experimental probability is 4/20 = 1/5 = .2 = 20 %
f(x)=−5x^3−4x^2+8x and g(x)=−4x^2+8, find (f−g)(x) and (f−g)(−2).
Answer:
see explanation
Step-by-step explanation:
(f - g)(x) = f(x) - g(x) , that is
f(x) - g(x)
= - 5x³ - 4x² + 8x - (- 4x² + 8) ← distribute parenthesis by - 1
= - 5x³ - 4x² + 8x + 4x² - 8 ← collect like terms
= - 5x³ + 8x - 8
Substitute x = - 2 into this expression, thus
(f - g)(- 2)
= - 5(- 2)³ + 8(- 2) - 8
= - 5(- 8) - 16 - 8
= 40 - 16 - 8
= 16
if 280 is to be shared between iyene and nokob in the ratio 2:3. in how many equal part will thE money be shared
Answer:
5
Step-by-step explanation:
There will be five equal part because Iyene takes 2 parts and nokob takes 3 parts
Thus, the total parts which have been shared is 2+3=5
Further more, every part is
[tex] \frac{280}{5} = 56[/tex]
Hence, there is 5 parts have been shared and every part is 56 dollars
Answer:
5 equal parts
Because one of the dudes will get 2 and the other one will get 3 parts
3+2 is 5
280/5=56 (1 part)
so iyene will get 56*2=112 and nokob will get 56*3=168
1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river. Each monkey had 1 tortoise in each hand.
How many animals were going to the river?
Answer:
91 animals
Step-by-step explanation:
Because every elephant saw 3 monkeys, there were 9 * 3 = 27 monkeys and because every monkey had 1 tortoise in each hand and we know that monkeys have 2 hands, there were 27 * 2 = 54 tortoises. To find the total number of animals that were going to the river, we can calculate 1 + 9 + 27 + 54 = 91 animals.
Answer:
10
Step-by-step explanation:
Only the rabbit and the 3 monkeys are described as going to the river. The tortoises seem to be going to the river by virtue of being taken there by the monkeys. Those on the path to the river were ...
1 rabbit
3 monkeys
6 tortoises
A total of 10 animals.
