Answer:
This means that the correct initial value problem for the population p(t) as a function of time is is [tex]P(0) = 1000[/tex]
Step-by-step explanation:
The population of a town increases at a rate proportional to its population:
This means that this situation is modeled by the following differential equation:
[tex]\frac{dP}{dt} = kP[/tex]
In which k is the growth rate.
By separation of variables, the solution is given by:
[tex]P(t) = P(0)e^{kt}[/tex]
In which P(0) is the initial population.
Initial population of 1000.
This means that the correct initial value problem for the population p(t) as a function of time is is [tex]P(0) = 1000[/tex]
what percentage is the following 3 upon 4 of 3 upon 8
Step-by-step explanation:
the answer is in the image above
Step-by-step explanation:
3/4×3/8
9/32
9/32×100
~28%
in which quadrant or axis will the poit lie if...
Step-by-step explanation:
a.fourth quadrent
b.third quadrent.
Rafael ate one-fourth of a pizza and Rocco ate one-third of it. What fraction of the pizza did they eat?
They ate
Answer:
7/12
Step-by-step explanation:
They ate 1/4 and 1/3
1/4 +1/3
Get a common denominator
1/4 *3/3 + 1/3 *4/4
3/12 + 4/12
7/12
What is cos(A)? please explain
Answer:
cos(A) = adjacent side / hypotenuse
= 4/5
Answer:
[tex] \small \sf \: cos ( A ) = \green{ \frac{ 4}{ 5}} \\ [/tex]
Step-by-step explanation:
[tex] \small \sf \: cos ( A ) = \frac{ adjacent \: side }{ Hypotenuse} \\ [/tex]
Where, we have given
adjacent side is 4 Hypotenuse is 5substitute the values that are given
[tex] \small \sf \: cos ( A ) = \green{ \frac{ 4}{ 5}} \\ [/tex]
Use the digits 0 - 9 to fill in the blank.
[tex]243 \frac{1}{5} = blank[/tex]
Answer:
use 0-9 to fill in blanks
Step-by-step explanation:
Write as many observations as you can for 5k + 23 - 4
Answer:
5k+19
Step-by-step explanation:
Subtract 4 from 23
please help me look at the photo!
A jet travels 5192 miles against a jetstream in 8 hours and 6072 miles with the jetstream in the same amount of time. What
is the rate of the jet in still air and what is the rate of the jetstream?
the answer is in the picture
write 145,567 in expanded notation
Answer:
100000+45000+500+60+7
21(2-y)+12y=44 find y
Answer:
[tex]\textbf{HELLO!!}[/tex]
[tex]21\left(2-y\right)+12y=44[/tex]
[tex]42-21y+12y=44[/tex]
[tex]~add ~similar\:elements[/tex]
[tex]42-9y=44[/tex]
[tex]Subtract~42~from~both~sides[/tex]
[tex]42-9y-42=44-42[/tex]
[tex]-9y=2[/tex]
[tex]Divide\:both\:sides\:by\:}-9[/tex]
[tex]\frac{-9y}{-9}=\frac{2}{-9}[/tex]
[tex]y=-\frac{2}{9}[/tex]
----------------------
hope it helps...
have a great day!
Nikki grows 20 tomato plants.
She measures their heights to the nearest centimeter and writes them down.
15 14 12 17 18
11 16 14 21 19
10 16 16 13 17
9 15 20 19 9
Complete the frequency table.
Answer:
I found answer
Step-by-step explanation:
1) 9
2) 12
3)15
4)20
If f(x) = 3x⁴ - 13x, find f(-2)
Answer:
answer is
74....................
Find all solutions to the equation.
cos^2 x +2cosx+1=0
[tex]x= \pi[/tex]
Step-by-step explanation:
[tex]\cos^2x+\cos x+1=0[/tex]
Let [tex]u= \cos x[/tex]
Then [tex]u^2+2u+1=(u+1)^2=0[/tex]
or
[tex]\cos x = -1[/tex]
This gives us [tex]x= \pi[/tex] or all integer multiples of [tex]\pi (n \pi)[/tex]
according to a salad recipe each serving requires 4 teaspoons of vegetable oil and 12 teaspoons of vinegar. if 14 teaspoons of vegetable oil were used how many teaspoons of vinegar should be used
Answer:
42 teaspoons of vinegar
Step-by-step explanation:
Given
[tex]x \to vegertable[/tex]
[tex]y \to vinegar[/tex]
[tex]x : y = 4 :12[/tex]
Required
Find y when [tex]x = 14[/tex]
[tex]x : y = 4 :12[/tex] implies that:
[tex]14 : y = 4 : 12[/tex]
Express as fraction
[tex]\frac{y}{14} = \frac{12}{4}[/tex]
[tex]\frac{y}{14} = 3[/tex]
Multiply by 3
[tex]y = 14* 3[/tex]
[tex]y = 42[/tex]
PLEASE HELP! I'm lost. :(
In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean
µ = 520 and population standard deviation = 115.
What math SAT score is 1.5 standard deviations above the mean? Round answer to a whole number.
Answer:
A math SAT score of 693 is 1.5 standard deviations above the mean
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 µ = 520 and population standard deviation = 115.
This means that [tex]\mu = 520, \sigma = 115[/tex]
What math SAT score is 1.5 standard deviations above the mean?
This is X when [tex]Z = 1.5[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.5 = \frac{X - 520}{115}[/tex]
[tex]X - 520 = 1.5*115[/tex]
[tex]X = 693[/tex]
A math SAT score of 693 is 1.5 standard deviations above the mean
A pile of 15 boxes is 3 metres high. What is the depth of each box?
5 m
0.002 km
200 cm
200 mm
pls help
Which best explains whether or not ABC = LMN?
Answer:
If I've done it right the answer should be A, the figures are congruent because a 270 rotation about the origin a d a reflection of the x-axis
PLEASE HELP ME WITH THIS ONE QUESTION
If Linda is at the store and can buy any two fruits (the store sells apples, oranges, pears, bananas, and kiwis), how many combinations of fruit can she choose?
A) 25
B) 3
C) 10
D) 15
Answer:
option C
Step-by-step explanation:
Total number of items = 5
Number of items to choose = 2
Therefore, the number of combinations is
[tex]5C_2 = \frac{5 \times 4}{1 \times 2} = 10[/tex]
For the following right triangle find the side length x
Step-by-step explanation:
everything can be found in the picture
Answer:
x=15
Step-by-step explanation:
Hi there!
We're given a right triangle with the measures of the 2 legs (sides that make up the right angle). We're also given the measure of the hypotenuse (the side opposite to the right angle) as x
We need to find x
The Pythagorean Theorem states that if a and b are the legs and c is the hypotenuse, then a²+b²=c²
Let's label the values of a, b, and c to avoid any confusion first
a=12
b=9
c=x
now substitute into the theorem
12²+9²=x²
raise everything to the second power
144+81=x²
add 144 and 81 together
225=x²
take the square root of 225
15=x (note: -15=x is technically also an answer, but since lengths cannot be negative, it's an extraneous solution in this case)
Therefore, the side length of x is 15
Hope this helps! :)
A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.
Calculate the cyclist's average speed in mph.
Answer:
v = 15 mph
Step-by-step explanation:
Given that,
A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.
Total distance, d = 3 + 7 = 10 miles
Total time, t = 15 + 25 = 40 minutes = 0.6667 hours
Average speed,
[tex]v=\dfrac{d}{t}[/tex]
Put all the value,
[tex]v=\dfrac{10}{0.6667}\\\\= $$14.99\ mph[/tex]
or
v = 15 mph
So, the required average speed is equal to 15 mph.
pls help! show your work!
(3sqrt4)/(3sqrt5)
Answer:
3sqaure root 100/5
Step-by-step explanation:
It would look like this picture Below
d= (r+c)t
how do i solve for t?
Answer:
[tex] { \tt{d = (r + c)t}}[/tex]
Divide ( r+c ) on both sides:
[tex]{ \tt{t = { \frac{d}{(r + c)} }}}[/tex]
Answer:
d / ( r + c) = t
Step-by-step explanation:
d = ( r + c ) t
Divide each side by ( r + c)
d / (r + c ) = ( r + c ) t / ( r + c)
d / ( r + c) = t
Please answer the following.
Answer:
[tex] \sqrt{4 \times 5 + \sqrt{4 \times 9} } [/tex]
Mass of a proton: 1.007825 units
Mass of a neutron: 1.008665 units
Calculate the mass Defect of 214 N has actual mass of 14.0031 u.
Given:-
mass of proton = 1.007825 umass of neuron = 2.008625 u .Actual mass = 14.0031 uTo find:-
The mass defect.Answer:-
Mass defect arises when the mass of the atom differs from the sum of masses of nucleons . As we know that the nucleus of an atom is made up of neutrons(n) and protons (p) , and the total mass of a atom is the mass of nucleons ( protons and neutrons ) as electrons have mass very low as compared to that of n or p .
If we denote mass number by [tex]\green{A}[/tex] , then ;
[tex]\implies A = n_{\rm neutrons} + n_{\rm protons} [/tex]
Let [tex] Z[/tex] be the atomic number, then ;
[tex]\implies n_p = Z [/tex]
So, the number of neutrons will be;
[tex]\implies n_n = (A-Z) [/tex]
Therefore total mass would be ;
[tex]\implies M = m_pZ +m_n (A-Z) [/tex]
Then the mass defect would be ,
[tex]\implies\underline{\underline{\green{ \Delta M = [Zm_p + (A-Z)m_n - M ] }}} [/tex]
where ,
[tex]Z [/tex] = atomic number[tex] A[/tex] = mass number[tex] m_p [/tex] = mass of a proton[tex] m_n [/tex] = mass of a neutron_______________________________________
Now we know that the Atomic number of Nitrogen is 7(Z) and its mass number is 14(A) .
Now substitute the respective values,
[tex]\implies \Delta M = 7(1.007825) + (14-7)1.008665 - 14.0031 \\ [/tex]
[tex]\implies \Delta M = 7.054775 + 7(1.008665) - 14.00 31 [/tex]
[tex]\implies \Delta M = 7.054775 + 7.060655 - 14.0031 [/tex]
[tex]\implies \Delta M = 14.11543 - 14.0031 [/tex]
[tex]\implies \underline{\underline{\green{ \Delta M = 0.11233 \ u }}}[/tex]
Hence the mass defect is 0.11233 u .
Also this mass defect appears as energy which is responsible for the binding of nucleons together.
and we are done!
A trailer is 22 feet long. 9 feet wide,
and 7 feet high. What is the volume of
the trailer?
Answer:
1386
Step-by-step explanation:
22 × 9 × 7 = 1386 cubic feet
On a coordinate plane, a line goes through (negative 3, negative 3) and (negative 1, 5). What is the equation of the line parallel to the given line with an x-intercept of 4?
Answer:
4, -16
Step-by-step explanation:
A cube with side lengths of 4 cm has a density of 3 grams/cubic centimeters. The mass of the cube is _____ grams?
9514 1404 393
Answer:
21 1/3 grams
Step-by-step explanation:
The mass is the product of the volume and the density. The volume of a cube is the cube of its edge dimension.
M = Vρ
M = (4 cm)³×(3 g/cm³) = 64/3 g
The mass of the cube is 64/3 = 21 1/3 grams.
According to records, the amount of precipitation in a certain city on a November day has a mean of inches, with a standard deviation of inches. What is the probability that the mean daily precipitation will be inches or less for a random sample of November days (taken over many years)
Answer:
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is mean amount of inches of rain and [tex]\sigma[/tex] is the standard deviation.
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.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
n days:
This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Applying the Central Limit Theorem to the z-score formula.
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is mean amount of inches of rain and [tex]\sigma[/tex] is the standard deviation.
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When traveling to work, Cherise averages 60 miles per hour.Because of heavy traffic in the evening, she averages only 40 miles per hour. If the distance from home to work is 80 miles, how much longer does it take Cherise to make the drive home?
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Explanation:
The distance traveled is d = 80 miles.
When going to work, her speed is r = 60 mph. She takes t = d/r = 80/60 = 4/3 hours which converts to 80 minutes. Multiply by 60 to go from hours to minutes.
Notice how the '80' shows up twice (in "80 miles" and "80 minutes"). This is because traveling 60 mph is the same as traveling 1 mile per minute.
-----------------
Now as she's coming home, her speed becomes r = 40 and she takes t = d/r = 80/40 = 2 hours = 120 minutes.
The difference in time values is 120 - 80 = 40 minutes.
Her commute back home takes 40 more minutes compared to the morning drive to work.