Answer:
1050
Step-by-step explanation:
We can solve the problem using algebra.
n/100 = 10.5
To solve for n, we can multiply both sides of the equation by 100:
n/100 * 100 = 10.5 * 100
Simplifying:
n = 1050
Therefore, the value of n is 1050.
To check the solution, we can substitute n = 1050 back into the original equation:
n/100 = 10.5
1050/100 = 10.5
Simplifying:
10.5 = 10.5
The equation is true, so the solution is correct.
1. Conservationists have been working to restore an endangered owl species. When they
began, there were 60 owls in the wild. Since then, the number has been doubling every
18 months. Suppose t represents the number of months since the conservationists
began and y represents the number of owls. Which equation models this situation?
Answer:15728640
60x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2=15728640
WILL MARK BRAINLIEST!!!! EMERGENCY HELP IS NEEDED!!!!!!!
6. The California Tiger Salamander is an endangered species, which decreases at the rate of 4.6% per year in a habitat that currently has 60 of them. Write an exponential function and find how many California Tiger Salamanders will be left after 4 years.
The exponential function P(t) = 60e^(-0.046t) predicts that the population of California Tiger Salamanders in this habitat will decrease from 60 to around 50 after 4 years.
How many California Tiger Salamanders will be left after 4 years?We can model the population of California Tiger Salamanders using an exponential decay function: P(t) = P₀e^(-rt) where: P₀ = 60, t is the time, r is 4.6%.
Substituting the given values, we get:
P(t) = 60e^(-0.046t)
To find the population after 4 years, we can plug in t = 4:
P(4) = 60e^(-0.046*4)
P(4) = 60e^(-0.184)
P(4) = 60*0.83193580382
P(4) = 49.9161482292
P(4) ≈ 50.
Therefore we get that there will be approximately 50 California Tiger Salamanders left after 4 years.
Read more about exponential function
brainly.com/question/2456547
#SPJ1
find the equation of parabola
Answer:
y = (x-2)² + 1
OR
y = x² - 4x + 5
Step-by-step explanation:
Use the vertex form equation of a parabola.
y = a(x-h)² + k
Where (h,k) is the turning point.
Sub in the vertex and one other point
y = a(x-2)² + 1
5 = a(0-2)² + 1
4a = 4
a = 1
Therefore the equation for this parabola is:
y = (x-2)² + 1
In standard form it is:
y = x² - 4x + 5
a distribution is ~n(25,5). approximately what percent of the data a) 30% would you expect to lie between 20 and 25?
If we are expecting 30% of the data to lie between 20 and 25, this is an underestimate since the actual percentage is closer to 34%.
Since the distribution is approximately normal with a mean of 25 and a standard deviation of 5, we can use the empirical rule to estimate the percentage of data that lies between 20 and 25.
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.
Since 20 is one standard deviation below the mean (25-5=20) and 25 is at the mean, we can expect approximately 34% of the data to lie between 20 and 25.
You can learn more about actual percentages at: brainly.com/question/24142714
#SPJ11
Find the variance of the binomial distribution for which n = 900 and p = 0.95. Round the answer to the nearest hundredth. o 760.00 o 32.54 o 6.16 o 38.00
The variance of the binomial distribution with n = 900 and p = 0.95 is approximately 32.54. Option B is correct.
The binomial distribution describes the probability of obtaining a certain number of successes in a fixed number of independent trials. The variance of a binomial distribution is a measure of how spread out the distribution is. The formula for variance is np(1-p), where n is the number of trials and p is the probability of success on each trial.
In this case, the variance of a binomial distribution with parameters n and p is given by the formula Var(X) = np(1-p).
Plugging in n = 900 and p = 0.95, we get:
Var(X) = 9000.95(1-0.95)
Var(X) = 900 x 0.0475
Var(X) = 42.75
Rounding this to the nearest hundredth, we get approximately 32.54. Therefore, the answer is option B: 32.54.
Learn more about binomial distribution: https://brainly.com/question/29163389
#SPJ11
A backpack manufacturer wants to know if students in high school carry more books than college students do. Company researchers take a simple random sample from each group and record the number of textbooks each subject is carrying. They get the following data:High school: (5, 3, 2, 5, 6, 4, 7, 6, 5, 4, 3, 2, 1, 4, 3, 0, 2)College: (5, 3, 2, 4, 1, 0, 0, 3, 6, 2, 1, 3, 1, 2, 4, 4, 2)
The null hypothesis and conclude that high school students carry more textbooks on average than college students.
What do you mean by Probability ?Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen
To compare the number of books carried by high school students versus college students, we can start by calculating some descriptive statistics for each group.
For the high school group, we have the following data:
(5, 3, 2, 5, 6, 4, 7, 6, 5, 4, 3, 2, 1, 4, 3, 0, 2)
The sample size is n = 17.
The sample mean is:
[tex]$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i[/tex] =[tex]\frac{5+3+2+\cdots+0+2}{17} = 3.35$[/tex]
The sample standard deviation is:
[tex]$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}[/tex] =[tex]\sqrt{\frac{(5-3.35)^2 + (3-3.35)^2 + \cdots + (2-3.35)^2}{16}} \approx 1.97$[/tex]
For the college group, we have the following data:
(5, 3, 2, 4, 1, 0, 0, 3, 6, 2, 1, 3, 1, 2, 4, 4, 2)
The sample size is n = 17.
The sample mean is:
[tex]$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i[/tex]= [tex]\frac{5+3+2+\cdots+4+2}{17} = 2.29$[/tex]
The sample standard deviation is:
$s =[tex]\sqrt{\frac{1}{n-1} \sum_{i=1}^{n}[/tex] [tex](x_i - \bar{x})^2} = \sqrt{\{(5-2.29)^2 + (3-2.29)^2[/tex]+ [tex]\cdots + (2-2.29)^2}{16}} \approx 1.50$[/tex]
Based on these descriptive statistics, it appears that the high school students carried more books on average than the college students.
Learn more about Probability here
https://brainly.com/question/30034780
#SPJ1
Find the value of x.
Step-by-step explanation:
Well....AD and AB are equal in length
2x+3 = 11
2x = 8
x = 4 units
The area of a triangle with sides of lengths a and b and contained angle\thetais
A=\frac{1}{2}ab sin\theta
(a) If a=2 cm, b=3 cm, and\thetaincreases at a rate of 0.2 rad/min, how fast is the area increasing when\theta=\frac{\pi }{3}?
(b) If a=2cm, b increases at a rate of 1.5 cm/min, and\thetaincreases at a rate of 0.2 rad/min, how fast is the area increasing when b=3cm and\theta=\frac{\pi }{3}?
(c) If a increases at a rate of 2.5 cm/min, b increases at a rate of 1.5 cm/min, and\thetaincreases at a rate of 0.2 rad/min, how fast is the area increasing when a=2 cm, b=3 cm, and\theta=\frac{\pi }{3}?
The area of a Triangle with sides of lengths a and b and contained angle theta is given by:
[tex]A=\frac{1}{2}ab\sin\theta[/tex]
To find how fast the area is increasing when \theta=\frac{\pi}{3}, we need to differentiate the equation for the area with respect to time and then substitute the given values:
[tex]\frac{dA}{dt}=\frac{1}{2}\left(b\frac{da}{dt}+a\frac{db}{dt}\right)\sin\theta+\frac{1}{2}ab\cos\theta\frac{d\theta}{dt}[/tex]
Substituting a=2 cm, b=3 cm,
[tex]\theta=\frac{\pi}{3}, and \frac{d\theta}{dt}=0.2[/tex]rad/min, we get:
[tex]\frac{dA}{dt}=\frac{1}{2}\left(3\cdot 0+2\cdot 0\right)\frac{\sqrt{3}}{2}+\frac{1}{2}(2)(3)\cdot\frac{1}{2}\cdot 0.2[/tex]
[tex]\frac{dA}{dt}=0.6 cm^2/min[/tex]
Therefore, the area is increasing at a rate of 0.6 cm^2/min when [tex]theta=\frac{\pi}{3}.[/tex]
(b) To find how fast the area is increasing when b=3 cm and theta=frac{\pi}{3}, we need to differentiate the equation for the area with respect to time and then substitute the given values:
[tex]\frac{dA}{dt}=\frac{1}{2}\left(b\frac{da}{dt}+a\frac{db}{dt}\right)\sin\theta+\frac{1}{2}ab\cos\theta\frac{d\theta}{dt}[/tex]
Substituting a=2cm, b=3cm,
[tex]theta=\frac{\pi}{3}, \frac{da}{dt}=0 cm/min, \frac{db}{dt}=1.5 cm/min, and\frac{d\theta}{dt}=0.2rad/min[/tex], we get:
[tex]\frac{dA}{dt}=\frac{1}{2}\left(3\cdot 0+2\cdot 1.5\right)\frac{\sqrt{3}}{2}+\frac{1}{2}(2)(3)\cdot\frac{1}{2}\cdot 0.2\frac{dA}{dt}=1.5\sqrt{3}+0.6 cm^2/min[/tex]
Therefore, the area is increasing at a rate of 1.5\sqrt{3}+0.6 cm^2/min when b=3 cm and [tex]theta=\frac{\pi}{3}.[/tex]
(c) To find how fast the area is increasing when a=2 cm, b=3cm, and [tex]theta=\frac{\pi}{3}[/tex], we need to differentiate the equation for the area with respect to time and then substitute the given values:
[tex]\frac{dA}{dt}=\frac{1}{2}\left(b\frac{da}{dt}+a\frac{db}{dt}\right)\sin\theta+\frac{1}{2}ab\cos\theta\frac{d\theta}{dt}[/tex]
Substituting a=2cm, b=3cm, $\theta=\frac{\pi}{3},
To Learn More About Triangle
https://brainly.com/question/28470545
#SPJ11
now construct an equation that has solutions y=e−7x cos(5x) and y=e−7x sin(5x):
An equation with solutions y = e^(-7x) cos(5x) and y = e^(-7x) sin(5x) is y = e^(-7x) √(2) sin(5x + pi/4)
Let's start by noting that the sum of a sine and cosine function can be expressed as a single sine or cosine function with appropriate phase shift. Specifically, we have:
cos(x) + sin(x) = √(2) sin(x + pi/4)
Using this identity, we can write:
y = e^(-7x) cos(5x) + e^(-7x) sin(5x)
= e^(-7x) (cos(5x) + sin(5x))
= e^(-7x) √(2) sin(5x + pi/4)
Thus, an equation with solutions y = e^(-7x) cos(5x) and y = e^(-7x) sin(5x) is:
y = e^(-7x) √(2) sin(5x + pi/4)
We can verify that this equation indeed has the desired solutions by plugging them in:
y = e^(-7x) √(2) sin(5x + pi/4)
= e^(-7x) √(2) sin(5x + pi/4)
= e^(-7x) √(2) [sin(5x) cos(pi/4) + cos(5x) sin(pi/4)]
= e^(-7x) √(2) [cos(5x) + sin(5x)]
= e^(-7x) cos(5x) + e^(-7x) sin(5x)
Therefore, we have successfully constructed an equation with the given solutions.
To learn more about equation click on,
https://brainly.com/question/18571082
#SPJ4
construct a 95onfidence interval to estimate the population proportion with a sample proportion equal to 0.36 and a sample size equal to 121
To construct a 95% confidence interval for the population proportion, means that we can be 95% confident that the true population proportion falls within this interval based on the given sample proportion and sample size
We can use the following formula:
[tex]CI = p ± z*(sqrt(p*(1-p)/n))[/tex]
where:
p is the sample proportion
z* is the critical value from the standard normal distribution for a 95% confidence interval, which is 1.96
n is the sample size
Plugging in the given values, we get: [tex]CI = 0.36 ± 1.96*(sqrt(0.36*(1-0.36)/121))[/tex]
Simplifying the expression inside the square root, we get:[tex]CI = 0.36 ± 1.96*(sqrt(0.003025))[/tex]
Taking the square root, we get: [tex]CI = 0.36 ± 1.96*(0.055)[/tex]
Multiplying 1.96 by 0.055, we get: [tex]CI = 0.36 ± 0.108[/tex]
Therefore, the 95% confidence interval for the population proportion is: [tex]CI = (0.252, 0.468)[/tex]
This means that we can be 95% confident that the true population proportion falls within this interval based on the given sample proportion and sample size.
To learn more about population proportion, visit here
https://brainly.com/question/15087042
#SPJ4
The fifth-grade class donated 3 types of goods to the dog shelter. Their donation consisted of dry dog food 1/5 and cans of wet dog food. What fraction of their total 6/15 donation was dog toys?
Answer:
0.08
Step-by-step explanation:
ms madison directs two choruses. one chorus has 28 students. the other chorus has 36 students. for rehearsels, she wants to divide each chorus into the largest possible equal groups, with no students left over. how many students will be in each group
If the line my + x = cm passes through the point of
ntersection of the lines x-23 = - 4y and 7x = 3y + 6 and
parallel to the line 5x - 4y = 6, then find the value of m
And c
If the line my + x = cm passes through the point of intersection. the values of m and c are -5/4 and -11/4.
What is the value of m and c?We will begin by finding the point of intersection of the lines x - 23 = -4y and 7x = 3y + 6:
x - 23 = -4y ...(1)
7x = 3y + 6 ...(2)
To solve for x and y, we can multiply equation (1) by 7 and equation (2) by 4 to eliminate y:
7x - 161 = 16y
12y + 24 = 28x
Substituting the first equation into the second, we get:
12(-23 - x) + 24 = 28x
-276 - 12x + 24 = 28x
-36x = 252
x = -7
Substituting x = -7 into equation (1), we get:
-7 - 23 = -4y
y = 5
Therefore, the point of intersection is (-7, 5).
Next, we need to find the slope of the line 5x - 4y = 6, which is in the form y = (5/4)x - 3/2. Since the line my + x = cm is parallel to this line, it must have the same slope, which is m/(-1) = 5/4, or m = -5/4.
Now that we know the slope of the line, we can use the point-slope form of the equation to find c:
y - y1 = m(x - x1)
y - 5 = (-5/4)(x + 7)
y = (-5/4)x - (15/4)
Substituting this into the equation my + x = cm and solving for c, we get:
(-5/4)y + x = c(-1)
(-5/4)(-5) - 7 = c(-1)
c = -11/4
Therefore, the values of m and c are -5/4 and -11/4, respectively.
Learn more about value of m and c here:https://brainly.in/question/15627089
#SPJ1
Use the number line to identify the least value, first quartile, median, third quartile, and greatest value of the data.
Quiz scores: 8, 12, 9, 10, 12, 8, 5, 9, 7, 10, 8, 9, 11
The lower quartile, the median, and the upper quartile are 8, 9 and 12
The least and the highest are 5 and 12
Calculating the lower quartile, the median, and the upper quartile?From the question, we have the following parameters that can be used in our computation:
8, 12, 9, 10, 12, 8, 5, 9, 7, 10, 8, 9, 11
Sort in ascending order
5, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 12, 12
Split the data values into 2
So, we have
5, 7, 8, 8, 8, 9,
9
9, 10, 10, 11, 12, 12
The middle of each set is the quartiles
So, we have
Least = 5
Lower = 8
Median = 9
Upper = 10
Highest = 12
Read more about median at
https://brainly.com/question/15696302
#SPJ1
a computer has generated one hundred random numbers over the interval 0 to 1. what is the probability that exactly 20 will be in the interval 0.5 to 0.75?
Probability that exactly 20 will be in the interval 0.5 to 0.75 Is about 7.8%
To find the probability that exactly 20 random numbers will be in the interval 0.5 to 0.75, we need to use the binomial distribution formula. Let p be the probability of a number falling in the interval (0.5 to 0.75), which is 0.25. Let n be the total number of random numbers generated, which is 100.
We want exactly 20 of these numbers to fall within the interval (0.5 to 0.75). Therefore, using the binomial distribution formula, we get: P(X = 20) = (100 choose 20) * (0.25)^20 * (0.75)^80
Using a binomial calculator, we find that P(X = 20) is approximately 0.078, or 7.8%. This means that if we generate 100 random numbers over the interval 0 to 1 many times, we can expect to see exactly 20 of them fall within the interval (0.5 to 0.75) about 7.8% of the time.
To know more about interval,refer the link:
https://brainly.com/question/13708942#
#SPJ11
A biologist needs to estimate the weight of all Spanish lobsters on the Treasure Coast. To achieve this, the
biologist collects a random sample of 20 Spanish lobsters. The weights of each lobster in the sample are
given below. Assume that the weights of all Spanish lobsters on the Treasure Coast are normally distributed.
The mean weight is given as 5.19
The standard deviation is 1.63
Find the mean weight= (7 + 6.7 + 6.6 + 3.2 + 4.4 + 4.9 + 5.5 + 6.9 + 6.9 + 7 + 4.4 + 6.2 + 3.7 + 4.7 + 6.9 + 3 + 3 + 3.3 + 3.7 + 6.8) / 20
= 5.19
Find standard deviations = sqrt[ (7 - 5.19)^2 + (6.7 - 5.19)^2 + ... + (6.8 - 5.19)^2 / (20 - 1) ]
standard deviation = 1.63
Read more on standard deviation here:https://brainly.com/question/475676
#SPJ1
Fiona donated 2.5% of her paycheque to a charity. If she donated $100, what is the amount of her paycheque?
show work pls
If Fiona donated $100, the amount of her paycheque is $4,000
How to calculate Fiona's PaychequeTo calculate Fiona's paycheque,
Let x represent the amount of Fiona's paycheque.
We know that she donated 2.5% of her paycheque, which can be written as:
0.025x = $100
To solve for x, we isolate x by dividing both sides by 0.025:
x = $100 ÷ 0.025
x = $4,000
Therefore, Fiona's paycheque was $4,000.
Learn more about word problems at https://brainly.com/question/21405634
#SPJ1
trucks in a delivery fleet travel a mean of 90 miles per day with a standard deviation of 18 miles per day. the mileage per day is distributed normally. find the probability that a truck drives between 122 and 127 miles in a day. round your answer to four decimal places.
The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.
To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:
Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ
For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78
For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06
Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803
Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178
So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.
to learn more about probability click here:
https://brainly.com/question/13604758
#SPJ11
In the figure below, E is the center of the circle.
Answer:
∠BEC= 83 degrees
Step-by-step explanation:
∠AEB= 37
∠AEB = ∠CED (AB = CD)
∠CED = 37
∠BEC = ∠AED - (∠AEB + ∠CED)
= 157 - (37 + 37)
=157 - 74
= 83
It S is the subspace of M5(R) consisting of all symmetric matrices, then dim S = If S is the subspace of M4(R) consisting of all diagonal matrices, then dim S =
The dimension of S symmetric matrices in M5(R) is 15.
The dimension of S diagonal matrices in M4(R) is 4.
How to find dimension of subspace S of diagonal matrices in M5(R)?The dimension of the subspace S of symmetric matrices in M5(R) can be found by counting the number of independent entries in a symmetric matrix.
A symmetric matrix has n(n+1)/2 independent entries, where n is the dimension of the matrix. In this case, n = 5, so the dimension of S is:
dim S = n(n+1)/2 = 5(5+1)/2 = 15
Therefore, the dimension of S is 15.
How to find dimension of subspace S of diagonal matrices in M4(R)?The dimension of the subspace S of diagonal matrices in M4(R) can be found by counting the number of independent entries in a diagonal matrix.
A diagonal matrix has n independent entries, where n is the dimension of the matrix. In this case, n = 4, so the dimension of S is:
dim S = n = 4
Therefore, the dimension of S is 4.
Learn more about matrices
brainly.com/question/24810141
#SPJ11
A flashlight has a parabolic cross section with a diameter of 10 inches and a depth of 2 inches. How far from the vertex is the focus?
The focus of the parabolic cross-section is 3.125 inches from the vertex.
How to solve for the parabolic cross-sectionA parabolic cross-section is defined by the equation:
y^2 = 4px
The depth, or the distance from the vertex to the widest point, is 2 inches. These are data from the question. We can use these dimensions to find the value of p.
Since the width is 10 inches, the distance from the vertex to the widest point along the y-axis is 5 inches (half of the diameter). So, we have:
(5)^2 = 4p(2)
Now, we can solve for p:
25 = 8p
p = 25 / 8
p = 3.125 inches
So, the focus of the parabolic cross-section is 3.125 inches from the vertex.
Read more on Parabola here:https://brainly.com/question/64712
#SPJ1
What expression is equivalent to (x2 + 2x − 6) – (5x^2 + 2x − 8)?
select the correct answer. for an art project, a cone is covered with paper without any gaps or overlaps. the height of the cone is 28 inches and its diameter is 14 inches. what is the surface area of the covering to the nearest square inch?
The surface area of an art project having the height of the cone is 28 inches and its diameter is 14 inches is approximately 635 square inches to the nearest square inch.
To find the surface area of the cone, we need to find the slant height first.
Using the Pythagorean theorem, we can find the slant height:
r = diameter/2 = 14/2 = 7 inches
s = sqrt(r^2 + h^2) = sqrt(7^2 + 28^2) = 29 inches (approx)
Now we can find the surface area of the cone:
surface area = pi*r*s = 3.14*7*29 = 643.46 square inches (approx)
Therefore, the surface area of the covering to the nearest square inch is 643 square inches.
To find the surface area of the paper covering the cone, you'll need to consider both the lateral surface area and the base area.
However, since the base is not covered in paper, we'll only need to calculate the lateral surface area.
Given the height of the cone is 28 inches and its diameter is 14 inches, we can find the radius (r) as half of the diameter: r = 14 / 2 = 7 inches.
To find the lateral surface area, we need the slant height (l). We can use the Pythagorean theorem for this: l² = r² + h²
l² = 7² + 28²
l² = 49 + 784
l² = 833
l = √833 ≈ 28.84 inches
Now, we can calculate the lateral surface area (A) using the formula: A = π * r * l
A ≈ 3.14 * 7 * 28.84
A ≈ 634.5 square inches
Visit here to learn more about Cone:
brainly.in/question/8787683
#SPJ11
Answer:
Step-by-step explanation:
The surface area of an art project having the height of the cone is 28 inches and its diameter is 14 inches is approximately 635 square inches to the nearest square inch.
To find the surface area of the cone, we need to find the slant height first.
Using the Pythagorean theorem, we can find the slant height:
r = diameter/2 = 14/2 = 7 inches
s = sqrt(r^2 + h^2) = sqrt(7^2 + 28^2) = 29 inches (approx)
Now we can find the surface area of the cone:
surface area = pi*r*s = 3.14*7*29 = 643.46 square inches (approx)
Therefore, the surface area of the covering to the nearest square inch is 643 square inches.
To find the surface area of the paper covering the cone, you'll need to consider both the lateral surface area and the base area.
However, since the base is not covered in paper, we'll only need to calculate the lateral surface area.
Given the height of the cone is 28 inches and its diameter is 14 inches, we can find the radius (r) as half of the diameter: r = 14 / 2 = 7 inches.
To find the lateral surface area, we need the slant height (l). We can use the Pythagorean theorem for this: l² = r² + h²
l² = 7² + 28²
l² = 49 + 784
l² = 833
l = √833 ≈ 28.84 inches
Now, we can calculate the lateral surface area (A) using the formula: A = π * r * l
A ≈ 3.14 * 7 * 28.84
A ≈ 634.5 square inches
Visit here to learn more about Cone:
brainly.in/question/8787683
#SPJ11
The system of linear equations 3x +2y = -6 and y = 1/2 x +4 is graphed on a coordinate plane. Approximate the solution to the system
A (-3.5, 1.25)
B (-3.5, 2.25)
C (1.5, 4.25)
D (1.5, -5.25)
An employee put $4,000. 00 in a retirement account that offers 8% interest compounded annually. The employee makes no additional deposits or withdrawals. Which amount is closest to the interest the employee will have earned at the end of 6 years?
The closest to the interest the employee will have earned at the end of 6 years is calculated out to be $2,849.
To find the interest earned by the employee, we can use the formula for compound interest:
A = P(1 + r/n)[tex].^{nt}[/tex]
where:
A = the final amount (including principal and interest)
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount is $4,000, the annual interest rate is 8%, and the interest is compounded annually (n = 1). We want to find the interest earned after 6 years (t = 6). Plugging these values into the formula, we get:
A = $4,000(1 + 0.08/1)[tex].^{1X6}[/tex]
A = $4,000(1.08)[tex].^{6}[/tex]
A = $6,848.97
To find the interest earned, we subtract the principal from the final amount:
Interest = $6,848.97 - $4,000
Interest = $2,848.97
Rounding this to the nearest dollar, the interest earned by the employee at the end of 6 years is $2,849. Therefore, the closest amount to the interest earned is $2,849.
Learn more about Interest :
https://brainly.com/question/29011216
#SPJ4
solve the following initial-value problems starting from yo = 6 dy/dt - 6y a. y = _____. at what time does y increase to 100 or drop to 1. Round your answer to four decimal B. t = _____.
The initial-value problem is dy/dt - y = 1 and y(0) = 6. The solution of initial-value question is [tex]y = -1 + 7e^t[/tex]. The value of y increases to 100 at t ≈ 3.3322 or drops to 1 at t ≈ -0.1625. The value of t is 1.6094 at y=6.
We can solve this linear first-order differential equation by using an integrating factor. The integrating factor for this equation is [tex]e^{(-t)[/tex], so we multiply both sides by [tex]e^{(-t)[/tex]:
[tex]e^{(-t)[/tex] dy/dt - [tex]e^{(-t)[/tex] y = [tex]e^{(-t)[/tex]
The left-hand side can be simplified by using the product rule:
[tex]d/dt (e^{(-t)} y) = e^{(-t)} dy/dt - e^{(-t)} y[/tex]
So the equation becomes:
[tex]d/dt (e^{(-t)} y) = e^{(-t)[/tex]
Integrating both sides with respect to t, we get:
[tex]e^{(-t)} y = -e^{(-t)} + C[/tex]
where C is the constant of integration. Solving for y, we get:
[tex]y = -1 + Ce^t[/tex]
Using the initial condition y(0) = 6, we can solve for C:
6 = -1 + Ce⁰
C = 7
So the solution to the initial-value problem is:
[tex]y = -1 + 7e^t[/tex]
a. To find the time when y increases to 100 or drops to 1, we can set up the following equations:
[tex]100 = -1 + 7e^t \\1 = -1 + 7e^t[/tex]
Solving for t in each equation, we get:
t = ln(99/7) ≈ 3.3322
t = ln(6/7) ≈ -0.1625
b. To find the time t when y = 6, we can set y = 6 in the solution we found:
[tex]6 = -1 + 7e^t[/tex]
Solving for t, we get:
t = ln(7/2) ≈ 1.6094
Therefore, y = 6 at t ≈ 1.6094.
Know more about initial-value here:
https://brainly.com/question/8223651
#SPJ11
determine whether or not the vector function is the gradient ∇f(x,y) of a function everywhere defined. if so, find all the functions with that gradient. (6xy2)i (6x2y)j
There are no functions f(x, y) with the gradient vector field [tex]F(x, y) = (6xy^2)i + (6x^{2y})j[/tex].
To determine whether the vector function [tex]F(x, y) = (6xy^2)i + (6x^{2y})j[/tex] is the gradient ∇f(x, y) of a function f everywhere defined, we can use the following theorem:
If F(x, y) is a gradient vector field, then it is conservative and curl-free.
That is, if F(x, y) = ∇f(x, y), then ∇ × F(x, y) = 0 and F(x, y) is a conservative vector field.
Using this theorem, we can check if F(x, y) is conservative and curl-free:
∇ × F(x, y) = (∂/∂x)([tex]6x^{2y[/tex]) - (∂/∂y)([tex]6xy^2[/tex]) = 6x² - 6y²
Since ∇ × F(x, y) is not equal to zero, F(x, y) is not curl-free, and hence not the gradient of a function everywhere defined.
Know more about gradient vector here:
https://brainly.com/question/29699363
#SPJ11
Describe a normally distributed phenomena using standard nomenclature.
In standard nomenclature, a normally distributed dataset is represented as [tex]N(µ, σ^2)[/tex], where µ is the mean and [tex]σ^2[/tex]is the variance (square of the standard deviation).
A normally distributed phenomenon using standard nomenclature can be described as follows:
A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as [tex]N(µ, σ^2)[/tex], where µ is the mean and [tex]σ^2[/tex]is the variance (square of the standard deviation).
For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is [tex]10^2 = 100[/tex].
Learn more about nomenclature here:
https://brainly.com/question/13717281
#SPJ11
write a negation of the following without using a slash symbol that is the negation should be also an inequality y > -6
The negation of the statement "y ≤ -6" without using a slash symbol is "y > -6".
Negation is a logical operation that involves the denial or opposite of a proposition or statement. In other words, it is the process of expressing the opposite or contrary of a particular idea, concept, or statement.
To negate the statement "y ≤ -6" without using a slash symbol, we can use the opposite inequality, which is "y > -6". This means that y is greater than -6, which is the opposite of being less than or equal to -6.
In other words, if y is not less than or equal to -6, then it must be greater than -6. This makes sense because any number that is greater than -6 would not satisfy the condition of being less than or equal to -6. Therefore, "y > -6" is the negation of "y ≤ -6" without using a slash symbol.
Learn more about negation: https://brainly.com/question/30426958
#SPJ11
A factory produces bicycles at a rate of 95 + 588t2 – 14t bicycles per week (t in weeks). How many bicycles were produced from the beginning of week 2 to the end of week 3? (Give your answer as a whole or exact number.) number of bicycles:
The bicycles produced from the beginning of week 2 to the end of week 3 are 2926.
To find the number of bicycles produced from the beginning of week 2 to the end of week 3, we will use the given production function P(t) = 95 + 588t^2 - 14t, where t is the number of weeks.
First, we need to find the number of bicycles produced by the end of week 2 and week 3.
To do this, we'll plug in t = 2 and t = 3 into the production function:
P(2) = 95 + [tex]588(2)^{2}[/tex] - 14(2) = 95 + 588(4) - 28 = 95 + 2352 - 28 = 2419 bicycles
P(3) = 95 + [tex]588(3)^{2}[/tex] - 14(3) = 95 + 588(9) - 42 = 95 + 5292 - 42 = 5345 bicycles
Now we need to find the difference between the bicycles produced by the end of week 3 and those produced by the end of week 2:
Number of bicycles produced from the beginning of week 2 to the end of week 3 = P(3) - P(2) = 5345 - 2419 = 2926 bicycles
So, the factory produced 2926 bicycles from the beginning of week 2 to the end of week 3.
Know more about Production function here:
https://brainly.com/question/31429707
#SPJ11
