Step-by-step explanation:
to be honest I'm not sure how to do
Comment
Don glover borrowed $14,000 for 250 days and paid $806.20 in simple interest on the loan. what annual simple interest rate did don pay on the loan?
Simple interest formula = I = PRT where I = interest, P = principal, r = interest rate and t = time.
i = 806.20, p = 14,000 t = 250 days.
Change t to be fraction of a full year: t = 250/365
Now solve for r:
806.20 = 14000 x r x 250/365
Simplify :
806.20 = r x 9589.04
Divide both sides by 9589.04:
r = 806.20 / 9589.04
r = 0.08407
Multiply by 100 to get percent:
r = 8.41% (rounded to nearest hundredth)
100
x
x
||
=
8X10
15
||
Answer:
the answer is 6x
Step-by-step explanation:
A poll found that 5% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 11 teenagers sleeping in each tent. Assume that these 11 teenagers are independent of each other. (Round your answers to four decimal places.)
a) Calculate the probability that at least one of them suffers from arachnophobia. - 0.4312
b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666
c) Calculate the probability that at most 1 of them suffers from arachnophobia? What is C?
Answer:
a) Calculate the probability that at least one of them suffers from arachnophobia.
x = number of students suffering from arachnophobia
= P(x ≥ 1)
= 1 - P(x = 0)
= 1 - [0.05⁰ x (1 - 0.05)¹¹⁻⁰ ]
= 1 - (0.95)¹¹
= 0.4311999 = 0.4312
b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666
= P(x = 2)
= (¹¹₂) x (0.05)² x (0.95)⁹
where ¹¹₂ = 11! / (2!9!) = (11 x 10) / (2 x 1) = 55
= 55 x 0.0025 x 0.630249409 = 0.086659293 = 0.0867
c) Calculate the probability that at most 1 of them suffers from arachnophobia?
P(x ≤ 1)
= P(x = 0) + P(x = 1)
= [(¹¹₀) x 0.05⁰ x 0.95¹¹] + [(¹¹₁) x 0.05¹ x 0.95¹⁰]
= (1 x 1 x 0.5688) + (11 x 0.05 x 0.598736939) = 0.5688 + 0.3293 = 0.8981
Please help need to do corrections and can't figure out this homework question??
A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables?
i. The amount of rain, in inches, that will fall next Friday in Dallas, TX.
ii. The major of a randomly drawn student from Arizona State University.
iii. The number of books purchased next year by your local library.
a. i only
b. ii only
c. iii only
d. i and iii
e. ii and iii
f. i, ii, and iii
Answer:
d. i and iii
Step-by-step explanation:
Notice that the definition provided states that the outcome needs to be numerical in order for a variable to be deemed a random variable:
i. The amount of rain is described in inches (i.e. 1.5 in; 2.0 in) and thus may be considered a random variable
ii. The major of a student is not quantitative as it is a descriptive variable (i.e. Arts; Psychology) and thus is not a random variable
iii. The number of books purchased is a numeric quantity (i.e. 15 books) and may be considered a random variable
Therefore, the answer is d. i and iii
Answer:
Step-by-step explanation:
i and iii
Use the definition of Taylor series to find the Taylor series, centered at c for the function. f(x)=ln x, c=1
Answer:
The taylor's series for f(x) = ln x centered at c = 1 is:
[tex]ln (x) = \sum\limits^{\infty}_{n = 1} {\frac{(-1)^{n+1}(x-1)^n}{n} }[/tex]
Step-by-step explanation:
The calculations are handwritten for clarity and easiness of expression.
However, the following steps were taken in arriving at the result:
1) Write the general formula for Taylor series expansion
2) Since the function is centered at c = 1, find f(1)
3) Get up to four derivatives of f(x) (i.e. f'(x), f''(x), f'''(x), [tex]f^{iv}(x)[/tex])
4) Find the values of these derivatives at x =1
5) Substitute all these values into the general Taylor series formula
6) The resulting equation is the Taylor series
[tex]ln (x) = \sum\limits^{\infty}_{n = 1} {\frac{(-1)^{n+1}(x-1)^n}{n} }[/tex]
which one doesn't belong ? please help thx :)
Answer:
THE CURVED ONE
Step-by-step explanation:
THE OTHER ONES R STRAIGHT LINES
THE ONE ON THE TOP RIGHT CORNER IS A PARABOLA
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r=0.767, n=25 A. Critical values: r= +0.396, no significant linear correlation B. Critical values: r= +0.487, no significant linear correlation C. Critical values: r = +0.396, significant linear correlation D. Critical values: r = + 0.487, significant linear correlation
Answer:
C. Critical values: r = +0.396
Step-by-step explanation:
Hello!
A linear correlation for two variables X₁ and X₂ was calculated.
For a sample n= 25 the sample correlation coefficient is r= 0.767.
Be the hypotheses:
H₀: ρ = 0
H₁: ρ ≠ 0
α: 0.05
For this hypothesis test, the rejection region is two-tailed, and the degrees of freedom are Df= n-2= 25-2= 23
So using the Pearson product-moment correlation coefficient table of critical values, under the entry for "two tailed tests" you have to cross the level of significance and the degrees of freedom to find the corresponding critical value:
[tex]r_{n-2;\alpha }= r_{23;0.05}= 0.396[/tex]
Since the calculated correlation coefficient is greater than the critical value, you can reject the null hypothesis, this means that the correlation is significant at level 5%
I hope this helps!
Find the percent of increase. Original Price: $135 Retail Price: $162
20%
Here's a tip: Always start percentage calculating with dividing the current number by 10.
What is the value of this expression when n approaches infinity?
Answer:
C. Approaches 35
Step-by-step explanation:
If we graph the expression, we see that we have an asymptote at y = 35.
An auto parts chain asked customers to complete a survey rating the chain's customer service as below average, average, or above average. The frequency distribution below displays the results for the survey. Calculate the relative frequency.
Response Frequency Relative Frequency
Below Average 7
Average 5
above Average 3
Is this categorical or umerical data?
Answer:
(b)Categorical Data
Step-by-step explanation:
The response, frequency, and calculation of the relative frequency of the data is given in the table below.
[tex]\left|\begin{array}{c|c|c}$Response&$Frequency &$Relative Frequency\\---&----&---\\$Below Average& 7&\dfrac{7}{15} \times 100 \approx 47\% \\&&\\$Average&5&\dfrac{5}{15} \times 100 \approx 33\%\\&&\\$Above Average&3&\dfrac{3}{15} \times 100 =20\%\\---&---&---\\$Total&15&100\end{array}\right|[/tex]
(b)
A quick way to determine if a data is categorical or numerical is to determine if the mean of the data can be found.
In this case, we cannot determine the mean of the data, therefore, it is a categorical data.
When Sam simplified the expression 3.5 - (-4.1), she got -0.6.
What mistake did Sam likely make when she simplified
the expression?
Answer:
She forgot to combine the 2 negative signs and turn it into a positive.
Step-by-step explanation:
When you subtract a negative, you are adding the number. So if we have 3.5 - (-4.1), it would equal 3.5 + 4.1, which is 7.6
Answer:
She subtracted a negative incorrectly by simply subtracting a positive when subtracting a negative means to add a positive.
Step-by-step explanation:
She subtracted 3.5 - 4.1 which is -0.6
The problem is subtracting -4.1 which means to add 4.1
3.5 - (-4.1) = 3.5 + 4.1 = 7.6
She did: 3.5 - (-4.1) = 3.5 - 4.1 = -0.6 which is incorrect.
What is the value of x? The figure contains 2 lines that intersect to form what looks like an x. Two of the 4 angles in the x are labeled. The left angle is labeled open parenthesis 3 x minus 3 close parenthesis degrees. The right angle across from it is labeled open bracket 6 open parenthesis x minus 10 close parenthesis close bracket degrees. Enter your answer in the box. x =
Answer:
[tex]x=38.5^\circ[/tex]
Step-by-step explanation:
Given that the left angle = [tex](3x-3)^\circ[/tex]
The right angle across from it [tex]= 6(x-10)^\circ[/tex]
The other two angles are x and x.
We know that the sum of angles at a point equals 360 degrees.
Therefore,
[tex](3x-3)^\circ+6(x-10)^\circ+x+x=360^\circ\\3x-3+6x-60+2x=360\\11x-63=360\\11x=360+63\\11x=423\\x=38.5^\circ[/tex]
The value of x is approximately 38.5 degrees.
The two triangles are similar. What is the value of x? Enter your answer in the box. x =
Answer:
x=1
Step-by-step explanation:
Since the two triangles are similar you want to look at what two dimensions have x included and if they are similar. Both have the same angles and on the bottom they both have x.
In order to figure out the value you need to compare them:
3x + 1 = 4x
1 = 4x-3x
1 = x
x = 1
A lumber company has just taken delivery on a shipment of 10,000 2 ✕ 4 boards. Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other. Let A = {the first board is green} and B = {the second board is green}.
(a) Compute P(A), P(B), and P(A ∩ B) (a tree diagram might help). (Round your answer for P(A ∩ B) to five decimal places.)
(b) With A and B independent and P(A) = P(B) = 0.1, what is P(A ∩ B)?
Answer:
Step-by-step explanation:
Given That:
Let A = {the first board is green} and B = {the second board is green}.
A lumber company has just taken delivery on a shipment of 10,000 2×4 boards.
Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other.
We are to compute the following probabilities :
P(A)
P(B)
P(A ∩ B)
To start with the probability P(A)
[tex]P(A) = \dfrac{1000}{10000}[/tex]
P(A) = 0.1
[tex]P(B) = P(B|A)*P(A)+P(B|A')*P(A')[/tex]
where;
[tex]P(B|A) = \dfrac{N(B|A)}{N-1}[/tex]
[tex]P(B|A) = \dfrac{999}{9999}[/tex]
[tex]P(B|A) =0.0999[/tex]
[tex]P(B|A') = \dfrac{N(B|A')}{N-1}[/tex]
[tex]P(B|A') = \dfrac{1000}{999}[/tex]
[tex]P(B|A') = 0.10[/tex]
Recall that :
[tex]P(B) = P(B|A)*P(A)+P(B|A')*P(A')[/tex]
[tex]P(B) = 0.0999*0.1+0.10*(1-0.1)[/tex]
[tex]P(B) = 0.00999+0.10*(0.9)[/tex]
[tex]P(B) = 0.00999+0.09[/tex]
[tex]P(B) = 0.0999[/tex]
P(A ∩ B) = P(B|A)B
P(A ∩ B) = 0.0999 × 0.10
P(A ∩ B) = 0.00999
(b)
Given that A and B are independent; Then:
P(A ∩ B) = P(A) × P(B)
0.00999 = 0.1 × 0.09999
0.00999 = 0.00999
As such A and B are independent
However; when P(A ∩ B) = P(A) = P(B) = 0.1
P(A ∩ B) = P(A) × P(B)
P(A ∩ B) = 0.1 × 0.1
P(A ∩ B) = 0.01
if there were only three types of music in the world pop,rock and rap and set A equals all the people in the world who prefer pop music,what is A`?
Answer:
people who prefer rock or rap
Step-by-step explanation:
We assume that "silence" is a type of music that is not in this universe. Hence the complement of set A is ...
people who prefer rock or rap
What multiplication expression is equal to 3/5÷1/4 out of 3/5×1/4 or 5/3×1/4 or 3/5×1/4 or 3/5×4/1
Answer:
it would be 3/5*4/1
Step-by-step explanation:
To divide you multiply the first number by the reciprocal of the second number. Check and you'll see that the answer is the same. Hope this helps!
Answer:
The answer is 3/5 x 4/1
Step-by-step explanation:
What are the y-intercepts for each function? What do these y-intercepts represent?
Answer:
In a function that is represented by Y=mx+b b would be the y-intercept
Definition of y-intercept. : the y-coordinate of a point where a line, curve, or surface intersects the y-axis.
Write the fraction in simplest form. (3/6) x (7/10)
someone help please !
Each line between 0 and 1 is 1/10 ( there are 10 lines)
First arrow is on the 3rd line so would be 3/10
The next arrow is 3 away from that so would be 3/10
The 3rd arrow is 2 away from the 2nd so would be 2/10
3/10 + 3/10 + 2/10 = 8/10
The answer is b
1. A fruitseller bought 200 apples for Rs 300.40 of them were rotten and thrown away.
She sold the rest at Rs 2.25 each. Find its gain or loss percent.
253
A Book of Mathematics-8
Answer:
ok I am tellin6 to you
Step-by-step explanation:
ok I will tell to you
Check that your solutions to part (a) and (b) are consistent by substituting the expression for y into your solution for part (a).
9x^2 - y^2 = 1
Answer:
Step-by-step explanation:
The question is incomplete. Find the complete question in the attached file.
a) Given the expression 9x^2 - y^2 = 1
Differentiating implicitly will give;
[tex]18x-2y\frac{dy}{dx} = 0\\[/tex]
We can then make dy/dx the subject of the formula as shown;
[tex]18x = 2y\frac{dy}{dx}\\\frac{dy}{dx} = \frac{18x}{2y} \\\frac{dy}{dx} = \frac{9x}{y} \\y' = \frac{9x}{y}[/tex]
b) In order to solve the question explicitly, we will first have to make x the subject of the formula before differentiating.
[tex]9x^{2} -y^{2} = 1\\9x^{2} = 1+ y^{2}\\y^{2} =9x^{2}- 1\\y^{2} = 9x^{2} - 1\\y = \sqrt{9x^{2}- 1 } \\[/tex]
Using chain rule to solve the equation;
let;
[tex]u = 9x^{2} -1\\ y = u^{1/2}[/tex]
du/dx = 18x
dy/du = [tex]1/2u^{-1/2}[/tex]
dy/dx = dy/du * du/dx
dy/dx = [tex]1/2u^{-1/2} * 18x[/tex]
[tex]\frac{dy}{dx} = \frac{1}{2}({9x^{2}-1 } )^{-1/2} * 18x\\\frac{dy}{dx} = 9x({9x^{2} -1 } )^{-1/2} \\\frac{dy}{dx} = 9 x(\sqrt{{\frac{1}{9x^{2} -1} } }) \\\frac{dy}{dx} = \frac{9x}{\sqrt{9x^{2}-1 } }[/tex]
c) In order to confrim that solutions to part (a) and (b) are consistent, we will substitute [tex]y = \sqrt{9x^{2} - 1 } \\[/tex] into the answer in (a) as shown;
From (a) [tex]\frac{dy}{dx} = \frac{9x}{y} \\[/tex]
[tex]y' = \frac{9x}{ \sqrt{9x^{2} - 1 } \\} } \\}[/tex]
This shows that they are consistent
Is the area of this shape approximately 57 6 cm ? If not, give the correct area.
O True
O False
Answer: True
Step-by-step explanation: Taking the triangle from the left and moving it to the right creates a rectangle. From there just do 12.8×4.5.
Please answer this correctly
Answer:
The first answer.
Step-by-step explanation:
The first answer.
What was the temperature of the air?
'was 2C warmer than the surface of the ice'
warmer than= +2c
Temp. of ice=-2c
-2c+2c=0
Answer:
Option 1
Step-by-step explanation:
The temp. was -2 degrees celsius.
The temp. got 2 degrees celsius warmer.
-2 + 2 = 0
Question 1
You can ride a taxi and pay a flat rate of $25 to go anywhere in the city, or you can pay a
base rate of $15 and $1 per mile. For which trip would it make more sense to pay the base
rate and 1$ per mile?
15 mile trip
9 mile trip
25 mile trip
O 12 mile trip
Answer:
9 mile trip
Step-by-step explanation:
$15 + $15 = $30
$15 + $9 = $24
$15 + $25 = $40
$15 + $12 = $27
$30 > $25
$24 < $25
$40 > $25
$27 > $25
cos3x-3cosx=cos2x+1 {Domain: 0<=x<=360} The solution is 90deg, 180deg, and 270deg, but what are the simplifying steps in between? I know all trig identities.
Step-by-step explanation:
cos(3x) − 3 cos x = cos(2x) + 1
Use triple and double angle formulas.
(4 cos³x − 3 cos x) − 3 cos x = (2 cos²x − 1) + 1
Simplify.
4 cos³x − 6 cos x = 2 cos²x
4 cos³x − 2 cos²x − 6 cos x = 0
2 cos³x − cos²x − 3 cos x = 0
Factor.
cos x (2 cos²x − cos x − 3) = 0
cos x (cos x + 1) (2 cos x − 3) = 0
Solve.
cos x = 0 → x = 90°, 270°
cos x + 1 = 0 → x = 180°
2 cos x − 3 = 0 → no solution
g A canyon is 1200 meters deep at its deepest point. A rock is dropped from the rim above this point. How long will it take the rock to hit the canyon floor
Answer:
t = 15.6 s
Step-by-step explanation:
According to the kinematic equation:
[tex] y_{f} = y_{0} + v_{0}*t - \frac{1}{2}gt^{2} [/tex] (1)
Where:
[tex]y_{f}[/tex]: is the final position = 1200 m
y₀: is the initial position = 0 m
V₀: is the initial speed = 0 m/s
g: is the gravity = 9.81 m/s²
t: is the time =?
From equation (1) we have:
[tex] -1200 m = 0 + 0*t - \frac{1}{2}*9.81 m/s^{2}*t^{2} [/tex]
[tex] t^{2} = \frac{2*(1200 m)}{9.81 m/s{2}} [/tex]
[tex]t = 15.6 s[/tex]
Therefore, it will take 15.6 seconds to the rock to hit the canyon floor.
I hope it helps you!
what are the multiples of 5,6,8,9?
The scheduled arrival time for a daily flight from Boston to New York is 9:30 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:07 am and a late arrival time of 9:57 am.a. After converting the time data to a minute scale, calculate the mean and the standard deviation for the distribution. (Round your answers to 2 decimal places.)Mean:____________________________ minutes Standard deviation: _________________ minutes b. What is the probability that a flight arrives late (later than 9:30 am)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)Probability:________
Answer:
Step-by-step explanation:
Let x be a random variable representing the flight arrival time from Boston to New York.
For a uniform probability distribution, the notation is
X U(a, b) where a is the lowest value of x and b is the lowest value of x
The probability density function, f(x) = 1/(b - a)
Mean, µ = (a + b)/2
Standard deviation, σ = √(b - a)²/12
From the information given, the time difference in minutes is 9:57 - 9:07 = 50 minutes. Therefore,
a = 0
b = 50
µ = (0 + 50)/2 = 25
σ = √(50 - 0)²/12 = 14.43
b) converting to minutes, it is 9:30 - 9:07 = 23 minutes
the probability that a flight arrives late(later than 9:30 am) is expressed as P(x > 23)
f(x) = 1/(50) = 0.02
P(x > 23) = (50 - 23)0.02 = 0.54
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What is your question?
Answer:
yeah what's your question?