Answer:
t = 13.56915448 hrs.
Step-by-step explanation:
500 = 300 [tex]e^{2k}[/tex]
5/3 = [tex]e^{2k}[/tex]
ln(5/3) = 2k ln(e)
k = ln(5/3)/2
k= 0.255412812
~~~~~~~~~~~~
9600 = 300 [tex]e^{0.255412812 t}[/tex]
32= [tex]e^{0.255412812 t}[/tex]
ln(32) = [tex]0.255412812 t[/tex] ln(e)
t = ln(32)/0.255412812
t = 13.56915448 hrs.
One number is eight less than a second number. Five times the first is 6 more than 6 times the second. Find the numbers.
The value of the first number is -
Answer:
-42/11
Step-by-step explanation:
x = y - 8
5x = 6 - 6y
So now solve the system of equations, divide everything in the second equation by 5 to get it to x = 6/5 - 6y/5
Now...
x = y - 8
x = 6/5 - 6y/5
Now substitute first equation into the second and x is gonna be -42/11 or the first number
Differentiate 4x^2+y^2=36 with respect to x. Hence find the turning points of the curve.
If y = y(x), then the derivative with respect to x is dy/dx. Differentiating both sides of the given equation gives
d/dx [4x ² + y ²] = d/dx [36]
8x + 2y dy/dx = 0
2y dy/dx = -8x
dy/dx = -4x/y
The turning points of the curve, taken as a function of x, are those points where the derivative vanishes.
-4x/y = 0 ===> x = 0
This value of x corresponds to two points on the curve,
4×0² + y ² = 36 ===> y ² = 36 ===> y = ±6
So there are two turning points, (0, -6) and (0, 6).
At what point on the curve x = 6t2 + 6, y = t3 − 2 does the tangent line have slope 1 /2 ?
Answer:
Hello,
P=(30,6)
Step-by-step explanation:
[tex]x=6t^2+6\\y=t^3-2\\\\\dfrac{dx}{dt}= 12t\\\dfrac{dy}{dt}= 3t^2\\\\\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } =\dfrac{3t^2}{12t} =\dfrac{t}{4} \\\\\dfrac{t}{4} =\dfrac{1}{2} \Longrightarrow t=2\\\\\\x=6t^2+6=6*2^2+6=30\\\\y=t^3-2=2^2-2=8-2=6\\\\\\Tangence\ point=(30,6)\\[/tex]
The point on the curve x = 6t² + 6, y = t³ - 2 where the tangent line have slope 1/2 is (30, 6).
How to depict the point on the curve?From the information given, x = 6t² + 6, y = t³ - 2. We'll find the first order derivative of x and y which will be:
dx/dt = 12t
dy/dt = 3t²
Therefore, 3t²/12t = t/4, t = 2.
We'll put the value of t back into the equations.
x = 6t² + 6,
x = 6(2)² + 6
x = 24 + 6 = 30
y = t³ - 2.
y = (2)³ - 2
y = 8 - 2 = 6
In conclusion, the correct options is (30, 6).
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A geometric sequence is a sequence of numbers where the next term equals to
the previous term multiplied by a common factor (for example, (3, 6, 12, 24, ...)
is a geometric sequence with the first term ”3” and the common factor ”2”). If
the 5th term of a geometric sequence is 24 and the 7th term is 144, what is the
first term of the sequence?
(A) 2
(B) 3/2
(C) 2/3
(D) 1/3
(E) 1/4
Answer:
C
Step-by-step explanation:
Let the first term be a and the common ratio be r.
ATQ, ar^4=24 and ar^6=144, r=sqrt(6) and a=24/(sqrt(6))^2=24/36=2/3
You take out a 60-day loan for $5000. At the end of the loan, you owe $73.97 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.
The PERCENTAGE ANNUAL RATE is 9.0% to the nearest tenth using the SIMPLE INTEREST FORMULA
The question is related to a SIMPLE INTEREST problem:
Loan period = 60 days
using 365 days a year ;
converting to years , 60 days = (60 / 365) years
interest on loan = 73.97
principal = 5000
Using the formula:
interest = (principal * rate * time)
73.79 = (5000 * rate * (60/365)
Rate = 73.79/(5000 * (60/365)) =8.977%
rate = 9%
Therefore, PERCENTAGE ANNUAL RATE is 9.0%
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i will give brainliest help please
Answer:
SA = 52 square meters
Step-by-step explanation:
First, the equation I'll be using for this problem is SA=2(wl+hl+hw)! Our width is 4m, our length is 3m, and our height is 2m. To begin to solve this problem we are going to input these values in to the equation above.
SA = 2(4 × 3 + 2 × 3 + 2 × 4)
Next, we are going to multiply our values inside the parenthesis based on the PEMDAS strategy (if you have any questions about this, feel free to ask below :).
SA = 2(12 + 6 + 8)
Now, we can add our values inside the parenthesis.
SA = 2(26)
Finally, all we have to do is distribute the 2 outside of the parenthesis to inside the parenthesis.
SA = 52 square meters
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
define ascending and descending order by your and give one example
Answer:
ascending order} an order of numbers from least to greatest like 1 2 3 4
descending order} an order of numbers from greatest to least like 4 3 2 1
find the quadratic equations whose roots are 3 and -4
Answer:
Hello,
Step-by-step explanation:
(x-3)*(x+4)=0 or x²+x-12=0
Answer:
Step-by-step explanation:
[tex]\displyastyle \Large \boldsymbol{} (x-x_1)(x-x_2) \ \ x_1 \ ; \ x_2 -roots \\\\(x-3)(x-(-4))=(x-3)(x+4)=\boxed{x^2+x-12}[/tex]
What is the equation of a line that passes through the point (8,-2) and is parallel to the line whose equation is 3x+4y=15?
Answer:
y = -3x/4 + 4
Step-by-step explanation:
slope m = -3/4
-2=(-3/4)×8+b
or, b = 4
y = mx + b
y = -3x/4 + 4
Answered by GAUTHMATH
Consider the following. fourteen less than the total of a number and three Translate into a variable expression. (Use x for your variable. Do not simplify.)
9514 1404 393
Answer:
(x +3) -14
Step-by-step explanation:
The total of a number and 3 will be represented by (x +3). Fourteen less than that is ...
(x +3) -14 or -14 +(x +3)
The area between z=.34 and z=1.93
Answer:
34.013%
0.36693 - 0.0268 = 0.34013
Step-by-step explanation:
z=.34 and z=1.93
0.34 0.36693
1.93 0.0268
What lines are parallel?
Solve for x.
5x - 3 = 12
A) X = 3
B) X = -3
C) X = -9/5
D) X = 9/5
Answer:
A. x = 3
Step-by-step explanation:
5x - 3 = 12
5x = 12 + 3
5x = 15
x = 15/5
= 3
Which phrase describes the linear relationship between the x and y values shown in the table?
x l y
8 l 2
9 l 3
10 l 4
A. y is 6 times x
B. x is 6 times y
C. y is 6 less than x
D. y is 6 more than x
9514 1404 393
Answer:
C. y is 6 less than x
Step-by-step explanation:
It is not hard to check.
A. 6 times x is 6×8 = 48, not 2
B. 6 times y is 6×2 = 12, not 8
C. 6 less than 8 is 2; 6 less than 9 is 3
D. 6 more than 8 is 14, not 2
__
The relation described in C matches the table.
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x represent the length of each of the equal pieces of yarn that julie decides to cut. what is the equation that can be used to determine the total length of all the yarn that she ends up cutting, y? is the graph of the equation continuous or discrete?
Answer:
The answer is below
Step-by-step explanation:
Let x represent the length of each of the equal piece of yarn. Since they are 4 equal pieces of yarn, then the total length of the equal pieces of yarn = 4x.
Also, besides cutting the 4 equal pieces of yarn Julie further cuts a yarn 7.75 inches long, therefore if y represent the total length of all the yarn that she ends up cutting, hence:
y = 4x + 7.75
Since the graph produced by this equation have all points connected to each other, hence this is a continuous graph.
Problem 2 find m<GEF
Answer:
m<GEF = 66°
Step-by-step explanation:
(72+60)/2
= 132/2
= 66
Answered by GAUTHMATH
*20 points*
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1: 4
Sample 2: 1
Sample 3: 9
How do the sample statistics compare to the population mean and standard deviation?
There will be about 6.25 sheep on each acre.
250/40 = 6.25
Describe what is contained in a credit report
Answer:
Your credit report contains personal information, credit account history, credit inquiries and public records. This information is reported by your lenders and creditors to the credit bureaus. Much of it is used to calculate your FICO® Scores to inform future lenders about your creditworthiness.
The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. Which of the following correctly labels the population?
1–1020
01–1020
001–1020
0001–1020
I think its (B), 01-1020.
Answer:
Should be (B)
01-1020
ED2021
The correct label for the population is 1 - 1020,
Option A is the correct answer.
What is random sampling?It is the way of choosing a number of required items from a number of population given.
Each items has an equal probability of being chosen.
We have,
The population in this case refers to the entire group of interest, which is the entire student body of the school.
The total number of students is 1,020.
The population is usually labeled with a range or interval that includes all the possible values of the variable of interest.
In this case, the variable of interest is whether or not a student has an opinion on parking.
The correct label for the population is 1-1020, as this range includes all possible student identification numbers at the school.
The other options (01-1020, 001-1020, and 0001-1020) are not correct because they suggest that there are leading zeros in the student identification numbers, which is not usually the case.
Thus,
The correct label for the population is 1-1020,
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An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 127 brakes using Compound 1 yields an average brake life of 42,814 miles. A sample of 163 brakes using Compound 2 yields an average brake life of 37,197 miles. Assume that the population standard deviation for Compound 1 is 1819 miles, while the population standard deviation for Compound 2 is 1401 miles. Determine the 98% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
Step 1 of 3 is Point estimate so 42,814 - 37,197 = 5,617
Step 2 of 3 :
Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Step 3 of 3:
Construct the 98% confidence interval. Round your answers to the nearest whole number. (lower and upper endpoint)
Answer:
The point estimate is 5,617.
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
The 98% confidence interval for the difference between the two population means is (5163, 6071).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Compound 1:
127 brakes, average brake life of 42,814 miles, population standard deviation of 1819 miles. This means that:
[tex]\mu_1 = 42814[/tex]
[tex]s_1 = \frac{1819}{\sqrt{127}} = 161.41[/tex]
Compound 2:
163 brakes, average brake life of 37,197 miles, population standard deviation of 1401 miles. This means that:
[tex]\mu_2 = 37197[/tex]
[tex]s_2 = \frac{1401}{\sqrt{163}} = 109.73[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 42814 - 37197 = 5617[/tex]
The point estimate is 5,617.
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{161.41^2 + 109.73^2} = 195.18[/tex]
Confidence interval
The confidence interval is:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = zs[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Margin of error:
[tex]M = zs = 195.18*2.327 = 454.18386 [/tex]
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
For the confidence interval, as we round to the nearest whole number, we round it 454. So
The lower bound of the interval is:
[tex]\mu - zs = \mu - M = 5617 - 454 = 5163[/tex]
The upper bound of the interval is:
[tex]\mu + zs = \mu + M = 5617 + 454 = 6071[/tex]
The 98% confidence interval for the difference between the two population means is (5163, 6071).
solve the inequality y-6>/2y-4
Answer:
Step-by-step explanation:
Let's solve your inequality step-by-step.
y - 6 > 2y - 4
y - 2y > -4 + 6
-y > 2
now divide by -1 and inequality sign changes
-y/-1 < 2/-1
y < -2
For a normal distribution with mean 47 and standard deviation 6, find the probability of obtaining a value less than 45 or greater than 49.
Answer:
0.7392 = 73.92% probability of obtaining a value less than 45 or greater than 49.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 47 and standard deviation 6
This means that [tex]\mu = 47, \sigma = 6[/tex]
Less than 45:
p-value of Z when X = 45, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 47}{6}[/tex]
[tex]Z = -0.3333[/tex]
[tex]Z = -0.3333[/tex] has a p-value of 0.3696.
More than 49:
1 subtracted by the p-value of Z when X = 49. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 47}{6}[/tex]
[tex]Z = 0.3333[/tex]
[tex]Z = 0.3333[/tex] has a p-value of 0.6304.
1 - 0.6304 = 0.3996
Less than 45 or greater than 49:
2*0.3696 = 0.7392
0.7392 = 73.92% probability of obtaining a value less than 45 or greater than 49.
Please help! Thank you!!!!!
9514 1404 393
Answer:
f(x) = x² -3g(x) = 6x +7h(x) = 3^xStep-by-step explanation:
f(x) is copied from the problem statement.
g(x) is a symbolic representation of the English wording, using x to represent "a number."
h(x) is the exponential function that corresponds to the geometric sequence in the table. It has a common ratio of 3, and a multiplier of 1 at x=0.
The doubling time for an investment is 7.5 yeas. Find an exponential model for the growth of your money. Then find how long will take your investment to grow by factor of 5(Assume that you make an investment P)
Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
Given:
Doubling time,
= 7.5 years
As we know,
[tex]P(t) = P_oe^{rt}[/tex]
now,
⇒ [tex]2P_o=P_o e^{r\times 7.5}[/tex]
[tex]2 = e^{r\times 7.5}[/tex]
[tex]r = \frac{ln2}{7.5}[/tex]
[tex]=0.092[/tex]
[tex]=9.2[/tex]%
then,
⇒ [tex]P(t) = P_o e^{0.092 t}[/tex]
here,
[tex]P(t) = 5P_o[/tex]
hence,
⇒ [tex]5P_o = P_o e^{0.092 t}[/tex]
[tex]e^{0.092t}=5[/tex]
[tex]t = \frac{ln5}{0.092}[/tex]
[tex]=17.414 \ years[/tex]
Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
If p is true and ~ q is false, then p ~ q is _____ false.
a. sometimes
b. always
c. never
What is the length of the arc of a circle with a radius of 4 by a central angle of 7pi/4?
9514 1404 393
Answer:
(b) 7π
Step-by-step explanation:
The arc length is the product of the radius and the central angle in radians.
s = rθ
s = (4)(7π/4) = 7π . . . units
A square steel bar has a length of 5.1 ft and a 2.7 in by 2.7 in cross section and is subjected to axial tension. The final length is 5.10295 ft . The final side length is 2.69953 in . What is Poisson's ratio for the material
Answer:
The Poisson's ratio for the material is 0.0134.
Step-by-step explanation:
The Poisson's ratio ([tex]\nu[/tex]), no unit, is the ratio of transversal strain ([tex]\epsilon_{t}[/tex]), in inches, to axial strain ([tex]\epsilon_{a}[/tex]), in inches:
[tex]\nu = -\frac{\epsilon_{t}}{\epsilon_{a}}[/tex] (1)
[tex]\epsilon_{a} = l_{a,f}-l_{a,o}[/tex] (2)
[tex]\epsilon_{t} = l_{t,f}-l_{t,o}[/tex] (3)
Where:
[tex]l_{a,o}[/tex] - Initial axial length, in inches.
[tex]l_{a,f}[/tex] - Final axial length, in inches.
[tex]l_{t,o}[/tex] - Initial transversal length, in inches.
[tex]l_{t,f}[/tex] - Final transversal length, in inches.
If we know that [tex]l_{a,o} = 61.2\,in[/tex], [tex]l_{a,f} = 61.235\,in[/tex], [tex]l_{t,o} = 2.7\,in[/tex] and [tex]l_{t,f} = 2.69953\,in[/tex], then the Poisson's ratio is:
[tex]\epsilon_{a} = 61.235\,in - 61.2\,in[/tex]
[tex]\epsilon_{a} = 0.035\,in[/tex]
[tex]\epsilon_{t} = 2.69953\,in - 2.7\,in[/tex]
[tex]\epsilon_{t} = -4.7\times 10^{-4}\,in[/tex]
[tex]\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}[/tex]
[tex]\nu = 0.0134[/tex]
The Poisson's ratio for the material is 0.0134.
6. 5x = -25
a. X= 5
b. X=-5
c. x=2
Answer:
x = -5
Step-by-step explanation:
5x = -25
Divide each side by 5
5x/5 = -25/5
x = -5
Answer:
[tex]Option\ B,\ x = -5[/tex]
Step-by-step explanation:
Step 1: Divide both sides by 5
[tex]5x = -25[/tex]
[tex]5x / 5 = -25 / 5[/tex]
[tex]x = -25/5[/tex]
[tex]x = -5[/tex]
Answer: [tex]Option\ B,\ x = -5[/tex]
I need help ASAP please help me solve this math question
Answer:
b appears to be correct
Step-by-step explanation:
What is the range of the function?
{(1.2, 11.6), (3.6, 11.5), (1.9, 11.4), (2.7, 11.5)}
Answer:
Range: 10.4
Step-by-step explanation:
Range = maximum(xi) - minimum(xi), where xi represents the set of values
= 11.6 - 1.2
= 10.4
Answer:
Range-
{
11.6
,
11.5
,
11.4
}
Step-by-step explanation:
