Answer:
The right answer is "605 persons".
Step-by-step explanation:
Given that,
⇒ [tex]\frac{dP}{dt} \alpha P[/tex]
or,
⇒ [tex]\frac{dP}{dt} =RP[/tex]
⇒ [tex]\frac{1}{R} \int\limits^{PT}_{500} {\frac{dP}{P} } = \int\limits^{t}_{0} dt[/tex]
⇒ [tex]\frac{1}{R} [log PT-log500]=t[/tex]
⇒ [tex]log[\frac{PT}{500} ]=Rt[/tex]
At t = 10 years,
⇒ [tex]PT=\frac{110}{100}\times 500[/tex]
[tex]=550[/tex]
∴ [tex]log[\frac{550}{500} ]=R\times 10[/tex]
[tex]R=\frac{log(1.1)}{10}[/tex]
At t = 20,
⇒ [tex]log{\frac{PT}{500} }=\frac{log \ 1.1}{10}\times 20[/tex]
[tex]PT=500\times (1.1)^2[/tex]
[tex]=605 \ persons[/tex]
NEED HELP FAST!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. f(x) = -0.5(x+3) (x-5)
y=6x/5 +27 find y-intercept and slope
Answer:
General equation of a line is given by y = mx +c, where m is the gradient /slope, c is the intercept. To find for the intercept on y- axis, put x = 0.[tex]y = \frac{6(0)}{5 } + 27 \\ y = \frac{0}{5} + 27 \\ y = 27 \\ therefore \: the \: intercept \: on \: y \: is \: 27 \\ [/tex]By comparison, [tex]y = mx + \: c \\ y = \frac{6}{5} x \: +27 \\ m = \frac{6}{5 \: } \: \\ hence \: slope \: is \: \frac{6}{5} [/tex]calculate to the nearest million m³.the current amount of water in the berg river dam
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the dimension of the dam is not given.
However, a general way of calculating volume is to calculate the base area and the multiply by height.
Take for instance,the dam has a rectangular base of 20m by 30m.
The base area will be
Area = 20m * 30m = 600m²
If the height of the water in the dam is 40m, then the volume is:
Volume = 600m² * 40m
Volume = 24000m³
The following function represents exponential growth or decay.
P= 2.9(1.05)^t
a. The initial quantity is :_______________
b. The initial quantity is :__________
c. Is the quantity growing or decaying?
Answer:
a) The initial quantity is 2.9.
b) The initial quantity is 2.9.
c) The multiplier is 1.05 > 1, and thus, the quantity is growing.
Step-by-step explanation:
Exponential equations:
Have the following format:
[tex]A(t) = A(0)(k)^t[/tex]
In which A(0) is the initial amount and k is the multiplier.
If k > 0, the quantity is growing.
If k < 0, the quintity is decaying.
In this question:
[tex]P(t) = 2.9(1.05)^t[/tex]
a, b. The initial quantity is
P(0). So
[tex]P(0) = 2.9(1.05)^0 = 2.9*1 = 2.9[/tex]
The initial quantity is 2.9.
c. Is the quantity growing or decaying?
The multiplier is 1.05 > 1, and thus, the quantity is growing.
y'+y=y^2; y(0)=-1/3
Giải phương trình trên
Step-by-step explanation:
[tex]y' + y = y^2[/tex]
We can rewrite the differential equation above as
[tex]\dfrac{dy}{dx} + y = y^2[/tex]
[tex]dy = (y^2 - y)dx[/tex]
or
[tex]\dfrac{dy}{y^2 -y} = dx[/tex]
We can rewrite the left side of the equation above as
[tex]\dfrac{dy}{y^2-y}=\dfrac{dy}{y(y-1)}= \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy[/tex]
We can the easily integrate this as
[tex]\displaystyle \int \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy = \int dx[/tex]
or
[tex]\displaystyle \int \dfrac{dy}{y-1} - \int \dfrac{dy}{y} = \int dx[/tex]
This will then give us
[tex]\ln |y-1| - \ln |y| + \ln |k| = x[/tex]
where k is the constant of integration. Combining the terms on the left hand side, we get
[tex]\ln \left|\dfrac{k(y-1)}{y} \right| = x[/tex]
or
[tex]\dfrac{y-1}{y} = \frac{1}{k}e^x[/tex]
Solving for y, we get
[tex]y= \dfrac{1}{1- \frac{1}{k} e^x}=\dfrac{k}{k-e^x}[/tex]
We know that [tex]y(0)= \frac{1}{3}[/tex], so when we substitute [tex]x=0[/tex], we find that [tex]k = -\frac{1}{2}[/tex].
Therefore, the final form of the solution to the differential equation above is
[tex]y = \dfrac{1}{1+2e^x}[/tex]
A rectangular area is to be enclosed using an existing
wall as one side 100m of fencing are available for the
three side. It is desire to make the areas as large as
possible. Find the necessary dimension of the
enclosure and the maximum area.
Answer:
[tex]\text{Dimensions: 25 x 50},\\\text{Area: }1,250\:\mathrm{m^2}[/tex]
Step-by-step explanation:
Let the one of the side lengths of the rectangle be [tex]x[/tex] and the other be [tex]y[/tex].
We can write the following equations, where [tex]x[/tex] will be the side opposite to the wall:
[tex]x+2y=100,\\xy=\text{Area}[/tex]
From the first equation, we can isolate [tex]x=100-2y[/tex] and substitute into the second equation:
[tex](100-2y)y=\text{Area},\\-2y^2+100=\text{Area}[/tex]
Therefore, the parabola [tex]-2y^2+100y[/tex] denotes the area of this rectangular enclosure. The maximum area possible will occur at the vertex of this parabola.
The x-coordinate of the vertex of a parabola in standard form [tex]ax^2+bx+c[/tex] is given by [tex]\frac{-b}{2a}[/tex].
Therefore, the vertex is:
[tex]\frac{-100}{2(-2)}=\frac{100}{4}=25[/tex]
Plug in [tex]x=25[/tex] to the equation to get the y-coordinate:
[tex]-2(25^2)+100(25)=\boxed{1,250}[/tex]
Thus the vertex of the parabola is at [tex](25, 1250)[/tex]. This tells us the following:
The maximum area occurs when one side (y) of the rectangle is equal to 25The maximum area of the enclosure is 1,250 square meters The other dimension, from [tex]x+2y=100[/tex], must be [tex]50[/tex]And therefore, the desired answers are:
[tex]\text{Dimensions: 25 x 50},\\\text{Area: }1,250\:\mathrm{m^2}[/tex]
Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)
Answer: Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational.
Step-by-step explanation:
Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth
Answer ASAP! Please answer! please answer (NOT HARD)
Answer:
221
Step-by-step explanation:
5(3)2-4
Answer:
221
Step-by-step explanation:
Identify the restrictions on the domain.
x+1x+9÷xx−4
x≠−1,4
x≠−9,4
x≠−1,0
x≠−9,0
[tex]Identify the restrictions on the domain. x+1x+9÷xx−4x≠−1,4x≠−9,4x≠−1,0x≠−9,0[/tex]
Which expression has the same value as the one below?
38 + (-18)
O A. 38
O B. 38 - 18
O C. 38 + 18
O D. 56
Answer:
answer is B 38-18
Step-by-step explanation:
38 + (-18)
38-18
A national survey of 1516 respondents reached on land lines and cell phones found that the percentage of adults who favor legalized abortion has dropped from 55% a year ago to 45%. The study claimed that the error
atributable to sampling is 4 percentage points. Would you claim that a majority of people are not in favor of legalized abortion?
Answer:
The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion
Step-by-step explanation:
Confidence interval:
Sample proportion plus/minus margin of error.
In this question:
Sample proportion of 0.45, margin of error of 0.04. So
0.45 - 0.04 = 0.41
0.45 + 0.04 = 0.49
The confidence interval is of (0.41,0.49). The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion
CNNBC recently reported that the mean annual cost of auto insurance is 1049 dollars. Assume the standard deviation is 275 dollars. You take a simple random sample of 72 auto insurance policies.
Find the probability that a single randomly selected value is less than 962 dollars.
P(X < 962) =
Find the probability that a sample of size
n
=
72
is randomly selected with a mean less than 962 dollars.
P(M < 962) =
Enter your answers as numbers accurate to 4 decimal places.
Answer:
0.3745 = 37.45% probability that a single randomly selected value is less than 962 dollars.
0.0037 = 0.37% probability that a sample of size 72 is randomly selected with a mean less than 962 dollars.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
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.
CNNBC recently reported that the mean annual cost of auto insurance is 1049 dollars. Assume the standard deviation is 275 dollars.
This means that [tex]\mu = 1049, \sigma = 275[/tex]
Find the probability that a single randomly selected value is less than 962 dollars.
This is the p-value of Z when X = 962. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{962 - 1049}{275}[/tex]
[tex]Z = -0.32[/tex]
[tex]Z = -0.32[/tex] has a p-value of 0.3745
0.3745 = 37.45% probability that a single randomly selected value is less than 962 dollars.
Sample of 72
This means that [tex]n = 72, s = \frac{275}{\sqrt{72}}[/tex]
Probability that the sample mean is les than 962.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{962 - 1049}{\frac{275}{\sqrt{72}}}[/tex]
[tex]Z = -2.68[/tex]
[tex]Z = -2.68[/tex] has a p-value of 0.0037
0.0037 = 0.37% probability that a sample of size 72 is randomly selected with a mean less than 962 dollars.
A basket contains five apples, five peaches, and three pears. You randomly select a piece of fruit. what is the chance you pick an apple or a peach?
Answer:
10/13
Step-by-step explanation:
The chance that you pick an apple is 5/13 and the chance it's a peach is 5/13 because in total there's 13 fruits.
Since it says what's the chance it's either an apple OR peach you add these two fractions: 5/13+5/13 = 10/13
If the question said what's the probability you pick an apple AND a peach then you'd mutiply not add.
HELP!!! Please simplify: 4^(x+1)*2^(2x)
Answer:
24x+2
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST.Write the log equation as an exponential equation. You do not need to solve for x.
In (5) = 2x
Answer:
10x ÷ 5x=2x
10x ÷ 5x = 2x
10x÷ 5x = 2x
Answer:
[tex]e^{2x}=5[/tex]
Step-by-step explanation:
Recall that [tex]\log_b a=c\implies b^c=a[/tex].
In this case, we need to find the base of the logarithm. The logarithm [tex]\ln[/tex] denotes natural [tex]\log[/tex] with a base of [tex]e[/tex], a mathematical constant.
Therefore, we can re-write the equation as:
[tex]\log_e5=2x[/tex]
To write the equation as an exponential equation, recall the definition of log (first sentence of explanation):
[tex]\boxed{e^{2x}=5}[/tex]
Statins are used to keep cholesterol in check and are a top-selling drug in the U.S. The equation:
S
−
1.3
x
=
6
gives the amount of sales (
S
) of statin in billions of dollars
x
years after 1998. According to this equation, how much will/did people in the U.S. spend on statins in the year 2008?
Answer:
19 billion dollars
Step-by-step explanation:
Given the equation :
S - 1.3x = 6
Where, S = amount of sale of statin in billions of dollars ; x = number of years after 1998
Amount spend in 2008
x = 2008 - 1998 = 10
Put x = 10 in the equation ;
S - 1.3x = 6
S - 1.3(10) = 6
S - 13 = 6
S = 6 + 13
S = 19
People will spend about 19 billion dollars on statin in 2008
When Riley goes bowling, her scores are normally distributed with a mean of 160 and
a standard deviation of 13. Using the empirical rule, determine the interval that
would represent the middle 68% of the scores of all the games that Riley bowls.
Answer:
The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 160, standard deviation of 13.
Middle 68% of the scores of all the games that Riley bowls.
Within 1 standard deviation of the mean, so:
160 - 13 = 147.
160 + 13 = 173.
The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).
Solve for d.
d + 67 = 87
р
Submit
Answer:
[tex]d=20[/tex]
Step-by-step explanation:
[tex]d+67=87[/tex]
Subtract 67 from both sides
[tex]d=20[/tex]
Hope this is helpful
Answer:
d = 20
Step-by-step explanation:
-4n(2n-7)=0
Simplif your answer
Answer:
n=3.5, n=0
Step-by-step explanation:
Open the parenthesis
2n(-4n)-7(-4n)=0
-8n^2+28n=0
Factor:
n(-8n+28)=0
Solve:
n=0, or -8n+28=0
-8n=-28
8n=28
n=28/8
n=3.5
n can be either 3.5 or 0
Answer:
0, 7/2
Step-by-step explanation:
See image below:)
can you help me?
(4n+13)+(6+7n)
i will mark brailest first to answer correct if you tell how to do it??
Answer:
11n + 19
Step-by-step explanation:
The parentheses can be removed immediately without affecting the clarity of this expression:
4n + 13 + 6 + 7n
Next we combine like terms, obtaining:
11n + 19
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{(4n + 13) + (6 + 7n)}\\\\\large\textsf{ = 4n + 13 + 6 + 7n}\\\\\large\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{(4n + 7n) + (13 + 6)}\\\\\large\textsf{4n + 7n = \boxed{\large\textsf{\bf 11n}}}\\\\\large\textsf{13 + 6 = \boxed{\large\textsf{\bf 19}}}\\\\\\\boxed{\huge\textsf{= 11n + 19}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 11n + 19}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Solve for x. See the image below!
Answer:
x = 17
Step-by-step explanation:
in such a constellation (two beams from the same point of origin cut through the same circle) the relative relation between the segments of these beams to the overall length of the beam have to be the same :
7 × (7+x) = 8 × (8+13)
49 + 7x = 8 × 21 = 168
7x = 119
x = 17
need an answer show work please thank you
Answer:
[tex]\text{C. }1[/tex]
Step-by-step explanation:
In the question, we're given that the notation [tex]\#\#(a,b,c)[/tex] produces a number [tex]a[/tex] less than the product of [tex]b[/tex] and [tex]c[/tex] raised to the [tex]a[/tex] power. Let the number produced be [tex]n[/tex]. As a mathematical equation, we can write this production as [tex]n=(bc)^a-a[/tex]
For [tex]\#\#(2, 5, x)[/tex], we can assign:
[tex]a\implies 2[/tex] [tex]b\implies 5[/tex] [tex]c\implies x[/tex]Substituting these values into [tex]n=(bc)^a-a[/tex], we get:
[tex]23=(5x)^2-2[/tex]
Add 2 to both sides:
[tex]25=(5x)^2[/tex]
Take the square root of both sides:
[tex]5=|5x|[/tex]
For [tex]y=|z|[/tex], there are two cases:
[tex]\begin{cases}y=z,\\y=-z\end{cases}[/tex]
Therefore, we have:
[tex]\begin{cases}5=5x, x=\boxed{1}\\5=-(5x), 5=-5x, x=\boxed{-1}}\end{cases}[/tex]
The only answer choice applicable is [tex]\boxed{\text{C. }1}[/tex].
Two cars are parked at the points (4, 5) and (8, 7). Find the midpoint between the two cars. O (12, 12) O (-6, -6) O (6,6) O (-2,-1) < Previous 00:00 / 00:00
Answer:
(6,6)
You can use the midpoint formula.
The diameter of the stem of a wheat plant is an important trait because of its relationship to breakage of the stem. An agronomist measured stem diameter in eight plants of a particular type of wheat. The mean of these data is 2.275 and the standard deviation is 0.238. Construct a 80% confidence interval for the population mean.
Answer:
7.79771≤x≤8.20229
Step-by-step explanation:
Given the following
sample size n = 8
standard deviation s = 0.238
Sample mean = 2.275
z-score at 980% = 1.282
Confidence Interval = x ± z×s/√n
Confidence Interval = 8 ± 1.282×0.238/1.5083)
Confidence Interval = 8 ± (1.282×0.15779)
Confidence Interval = 8 ±0.20229
CI = {8-0.20229, 8+0.20229}
CI = {7.79771, 8.20229}
Hence the required confidence interval is 7.79771≤x≤8.20229
What is the radius of a circular swimming pool with a diameter of 20 feet?
Answer:
10 feet
Step-by-step explanation:
The half of 20 is 10. So, hence it is 10 feet.
The radius of a circular swimming pool with a diameter of 20 feet will be 10 feet.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Assume 'r' is the radius of the circle and 'd' is the diameter of the circle.
The radius of the circle is half of the diameter of the circle. Then the equation is given as,
r = d / 2
The diameter of the swimming pool is 20 feet. Then the radius of the swimming pool is given as,
r = 20 / 2
r = 10 feet
The radius of a roundabout pool with a measurement of 20 feet will be 10 feet.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
If ⃗ = + + is perpendicular to both ⃗ = 5 + − 2 and = 3 − 3 + 6 , find and .
Answer:
The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.
Step-by-step explanation:
If [tex]\vec {c} = m\,\hat{i} + n\,\hat{j} + \hat{k}[/tex] is perpendicular to [tex]\vec {a} = 5\,\hat{i} + \hat{j} -2\,\hat{k}[/tex] and [tex]\vec {b} = 3\,\hat{i} - 3\,\hat{j} + 6\,\hat{k}[/tex], then the following relationships must be observed:
[tex]\vec {c}\,\bullet\,\vec {a} = 0[/tex] (1)
[tex]\vec{c}\,\bullet \,\vec{a} = 0[/tex] (2)
Then, we expand the previous expressions:
[tex](m, n, 1)\,\bullet\,(5, 1, -2) = 0[/tex]
[tex]5\cdot m + n = 2[/tex] (1b)
[tex](m, n, 1)\,\bullet\,(3, -3, 6) = 0[/tex]
[tex]3\cdot m - 3\cdot n = -6[/tex] (2b)
Then, we solve for [tex]m[/tex] and [tex]n[/tex]:
[tex]m = 0, n = 2[/tex]
The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.
Get brainiest if right!!
Answer:
4 1/8 units
Step-by-step explanation:
I believe this to be so if these points were on a number line. You would add the two points together to get the distance between the two points.
Which of the following relations represents a function? (0, 3), (0.-3). (-3,0). (3.0)) (-2. 4). (-1.0), (2.0), (2.6) -1.-1), (0.0), (2, 2), (5, 5]] None of these
Answer:
(-1.0) (2.0) is the answer
A shoreline observation post is located on a cliff such that the observer is 280 feet above sea level. The observer spots a ship approaching the shore and the ship is traveling at a constant speed.
Requried:
a. When the observer initially spots the ship, the angle of depression for the observer's vision is 6 degrees. At this point in time, how far is the ship from the shore?
b. After watching the ship for 43 seconds, the angle of depression for the observer's vision is 16 degrees. At this point in time, how far is the ship from the shore?
Using the slope concept, it is found that the distances from the shore at each moment are given by:
a) 2664 feet.
b) 976 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
Item a:
The vertical distance is of 280 feet, with an angle of 6º. The distance from the shore is the horizontal distance of x. Hence:
[tex]\tan{6^\circ} = \frac{280}{x}[/tex]
[tex]x = \frac{280}{\tan{6^\circ}}[/tex]
x = 2664.
Item b:
The vertical distance is of 280 feet, with an angle of 16º. The distance from the shore is the horizontal distance of x. Hence:
[tex]\tan{16^\circ} = \frac{280}{x}[/tex]
[tex]x = \frac{280}{\tan{16^\circ}}[/tex]
x = 976.
More can be learned about the slope concept at https://brainly.com/question/18090623
In triangle ABC, AC = 4, BC = 5, and 1 < AB < 9. Let D, E and F be the
midpoints of BC, CA, and AB, respectively. If AD and BE intersect at G
and point G is on CF, how long is AB?
A. 2
B. 3
C. 4
D. 5