Missing information :
The model was omitted from the question ; the possible model relating to the question was browsed online and could possibly be :
N(t) = 1.07t^2.3 for 0 ≤ t ≤ 10 months
Answer:
30.9 cases per month
Step-by-step explanation:
Given the model to determine the number of rats that have developed cancer after initial exposure ; N(t) = 1.07t^2.3
N(t) = 1.07t^2.3
Take the first derivative of N with respect to t to obtain the rate of change ;
N'(t) = (1.07)(2.3)t^2.3-1
N'(t) = (1.07)(2.3)t^1.3
The rate of growth of cancer cases at the 7th month can be calculated thus :
t = 7
N'(7) = (1.07)(2.3)t^1.3
N'(7) = 1.07 * 2.3 * 7^1.3
N'(7) = 1.07 * 2.3 * 12.549529
N'(7) = 30.884
The rate of growth of cancer at the 7th month is 30.9 cases per month.
On the unit circle, an arc of length 2 subtends an angle, β. What is the radian measure of β?
Answer:
[tex](d)\ \beta = 2\ rad[/tex]
Step-by-step explanation:
Given
[tex]L =2[/tex] -- length of the arc
[tex]r = 1[/tex] --- radius of a unit circle
[tex]\beta =[/tex] the subtended angle
Required
Find [tex]\beta[/tex]
The length of an arc is:
[tex]L = r * \beta[/tex]
This gives:
[tex]2 = 1 * \beta[/tex]
[tex]2 = \beta[/tex]
Make [tex]\bets[/tex][tex]\beta[/tex] the subject
[tex]\beta = 2[/tex]
Hence:
[tex]\beta = 2\ rad[/tex]
Answer:
2rad
Step-by-step explanation:
GUYS HELP PLEASE ASAP You are deciding between two jobs. Offer 1 is $40,000 and a raise of
$4,000 per year. Offer 2 is $52,000 and a raise of $2,000 per year. In how
many years will both jobs pay you the same salary? What would the salary
be? Which offer should you choose if you plan on working for 10 years?
Answer:
offer 1= you get 80k for the first offer for 10 years.
offer 2= you get 72k for the second offer for 10 years.
Result:
offer one would be better as you would get more money.
The question is on the ss btw
Answer:
The shop
Step-by-step explanation:
Given
Shop
[tex]Cost = E9[/tex]
[tex]Bag = 12.5kg[/tex]
Supermarket
[tex]Cost=E1.83[/tex]
[tex]Bag = 2.5kg[/tex]
Required
The better value
To do this, we simply calculate the unit price.
This is calculated as:
[tex]Unit = \frac{Price}{Bag}[/tex]
So, we have:
Shop
[tex]Unit = \frac{9}{12.5}[/tex]
[tex]Unit = 0.72[/tex]
Supermarket
[tex]Unit = \frac{1.83}{2.5}[/tex]
[tex]Unit = 0.732[/tex]
At the shop, the unit price is £0.72 per bag while at the supermarket, the unit price is £0.732
The best value is at the shop, because it is cheaper
i.e.
[tex]0.72 < 0.732[/tex]
14/7 = n/21 what is the value of n
Answer:
n=42
Step-by-step explanation:
14/7=n/21
2=n/21
42=n
n=42
Answer:
n = 42
Step-by-step explanation:
14/7 = 2
42/21 = 2
Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 72.3 inches. Round to four decimal places.
Answer:
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
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 estabilishes 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.
Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches.
This means that [tex]\mu = 71.3, \sigma = 2.1[/tex]
Sample of 36:
This means that [tex]n = 36, s = \frac{2.1}{\sqrt{36}} = 0.35[/tex]
Find the probability that they have a mean height greater than 72.3 inches.
This is 1 subtracted by the pvalue of Z when X = 72.3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{72.3 - 71.3}{0.35}[/tex]
[tex]Z = 2.86[/tex]
[tex]Z = 2.86[/tex] has a pvalue of 0.9979
1 - 0.9979 = 0.0021
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
A plane is traveling at a constant rate described by d = 525t where d is the distance and t is the time. What is the constant of proportionality?
Answer:
50 points
Step-by-step explanation:
Answer:
525 is the constant of proportionality
Step-by-step explanation:
What is the mean for the data shown in the dot plot? 4 5 6 10
Answer:
Mean = 6.25
Step-by-step explanation:
Data values: 4, 5, 6, 10
Mean = (Sum of all values)/(Number of values)
Mean = (4 + 5 + 6 + 10)/4
Mean = 25/4
Mean = 6.25
The mean for the data shown in the dot plot is 6.25.
The given data is 4, 5, 6 and 10.
We need to find the mean for the data shown in the dot plot.
What is the dot plot?A dot plot is used to encode data in a dot or small circle. The dot plot is shown on a number line that displays the distribution of numerical variables where a value is defined by each dot.
Now, mean = Sum of all the observations / Total number of observations
=(4+5+6+10)/4
=25/4
=6.25
Therefore, the mean for the data shown in the dot plot is 6.25.
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PLSSS HELP (4x - 1)
(3x)
Answer:
x = 13
Step-by-step explanation:
3x + 4x-1 +90 = 180
7x = 91
x = 13
10,045 rounded to the tens place
Answer:
10045 rounded to nearest tens is10050
According to some sources, the African continent has about 170 million Internet users. According to the bar graph, which statement is true?
Africa has fewer users than the Middle East.
Africa has more users than Asia.
Africa has more users than Europe but fewer than Asia.
Africa has more users than the Middle East but fewer users than North America.
Answer:
The last answer choice
Step-by-step explanation:
Interpretation of internet users
Middle East - about 100 million
North America - about 250 million
Europe - about 500 million
Asia - over 1 billion
Now lets look back at the question.
If Africa has 170 million internet users, according to the graphs, which statement is true.
"Africa has fewer users than the middle east"
This is false as Africa has 170 million users whereas The middle east has about 100 million users
170 mil > 100 mil therefore the statement is false
"Africa has more users then Asia"
This is also false as Asia has the most internet users at 1 billion
Africa has no where near as many users at 170 million users therefore the statement is false
"Africa has more users than Europe but fewer than Asia."
We have already identified that Africa has fewer users than Europe so this one could be it if the other part is true.
"Africa has more users than Europe" This is false as Europe has 500 million internet users while Africa only has 170 million users
Therefore this statement is false
"Africa has more users than the Middle East but fewer users than North America."
Africa has more internet users than the Middle East ( 170 mil > 100 mil ) and fewer users than North America ( 250 mil > 170 mil )
therefore this is the correct statement
Find the missing side of a right triangle a b c
Answer:
Use Pythagorean Theorem.
Step-by-step explanation:
To find any side of a right angled triangle, we use Pythagorean Theorem. It states that the square of hypotenuse is equal to the sum of squares of it's sides.
Let hypotenuse is a
Perpendicular is b
and base is c
According to the theorem:
a²= b² + c²
Add values and solve for the unknown variable / side.
If you had added the problem, I would have elaborated more but still this will help you out.
If the Math Olympiad Club consists of 13 students, how many different teams of 5 students can be formed for competitions?
Answer:
2 teams
Step-by-step explanation:
13 divided by 5 is 2.6, but you cannot split a person in half, so it would be two teams with a remainder of three people.
There are 1287 different teams of 5 students can be formed for competitions.
What is Combination?A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
The Math Olympiad Club consists of 13 students.
And, To form different teams of 5 students can be formed for competition.
Hence, We get;
Number of different teams of 5 students can be formed for competitions is,
⇒ ¹³ C ₅
⇒ 13! / 5! 8!
⇒ 1287
Thus, There are 1287 different teams of 5 students can be formed for competitions.
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The distance from Detroit, MI to Paris, France is approximately 3930 mi. Flying from Detroit to Paris takes 8 hr with the jet stream. The return flight takes 8.3 hr since the plane is flying against the jet stream.
a. The speed of the plane in still air, rounded to the nearest whole number, is
b. The speed of the jet stream, rounded to the nearest whole number, is
Answer:
a. 482
b. 9.0
Step-by-step explanation:
The speed of the plane in still air is approx 482 miles per hour(mph). The speed of the jet stream, rounded to the nearest whole number, is 9 mph
How does air stream affects speed of flight?Flight speed in air stream = Flight speed in still air + effect of air stream
If the flight is going opposit, then:
Flight speed in air stream = Flight speed in still air - speed of air streamIf the flight is going along with flight, then:
Flight speed in air stream = Flight speed in still air + speed of air streamFor this case, we're specified that:
Distance from Detroid to Paris is approx 3930 milesTime it takes by flight along the air stream = 8 hoursTime it takes by flight against the air stream = 8.3 hoursSpeed of flight along the stream is:
[tex]S = \dfrac{\delta D}{\delta T} = \dfrac{3930}{8} = 491.25 \: \rm mph[/tex]
Speed of flight against the stream is:
[tex]S = \dfrac{\delta D}{\delta T} = \dfrac{3930}{8.3} \approx 473.49 \: \rm mph[/tex]
Let the speed of air stream be y, and that of the flight in still air be x miles per hour, then we get:
Along air stream:
[tex]x + y =491.25\\[/tex] (in miles per hour)
and Against the stream:
[tex]x - y =473.49\\[/tex] (in miles per hour)
Adding both the equations side by side, we get:
[tex]2x + y - y = 491.25 + 473.49\\\\x = \dfrac{964.74}{2} =482.37 \: \rm mph[/tex]
Using this value, we get the value of y as:
[tex]x + y =491.25\\y = 491.25 - x = 491.25 - 482.37 = 8.88 \: \rm mph[/tex]
Rounding to the nearest whole numbers, we get:
x = 482 mph, and y = 9 mph
Thus, the speed of the plane in still air is approx 482 miles per hour(mph). The speed of the jet stream, rounded to the nearest whole number, is 9 mph
Learn more about motion in stream here:
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In which step does a mistake first occur?
8 + 2 + (3 X 3 -2)
Step 1: 8 +2 + (3 x 1)
Step 2: 8 +2 + 3
Step 3: 4 + 3
Step 4: 7
Answer:
Step 3 because they didn't add correctly
WILL GIVE BRAINLIEST!!!
In a test of hypothesis for a mean, which statement is CORRECT?
The population must be normal because that is the only case when the sample mean is Normally distributed.
As long as the population distribution consists only of positive values, sample size does not matter.
The population distribution can be any distribution because the sample mean is always Normally distributed.
The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
Answer:
As long as the population distribution consists only of positive values, sample size does not matter.
Step-by-step explanation:
As long as the population distribution consists only of positive values, sample size does not matter.
This is a hypothesis because a hypothesis is basically a prediction of what's gonna happen; the other choices are mostly facts that can be backed up, this can only be confirmed after it happens since it can end in different ways. This is a prediction where it says that if the population distribution continues to go on to positive value, then the sample size won't matter; this can come out in different ways, the sample size could matter or it would have to be negative values, e.t.c. This has different ways it could end up.
The starting numbers for x and y are already entered in a table below the blanks in the table represent the next two terms for each of the patterns the pattern for the X-Files is added to pattern for the y values it at 4 which graph represents the order pairs of first three terms of the pattern from the table?
Answer:
it is this one
Step-by-step explanation:
because since x is 4 and y is 8 that one matches up better than any other one
guys please i need help in this question, whoever gets it right will get a brainliest
Answer:
4/20 or 1/5 if you want it simplified
Room's volume is 600 m^3. There is 800 ppm (parts per million) of CO2 in the room.
Fresh air, with the CO2 concentration of 400 ppm starts flowing into the room at the rate of 40 m^3/min. The pressure in the room is constant, so an equal amount of stale air flows out as fresh air flows in, and the CO2 is evenly distributed.
a) Form the differential equation for the amount of CO2 in the room.
b) Solve this differential equation
c) What is the CO2 concentration of the room after fresh air has been flowing in for 30 minutes?
Answer: C
Step-by-step explanation: Hope this help :D
What fraction of the whole are the blue piece, the orange piece, the red piece, and the purple piece. How do you know?
Answer:
blue piece is 1/2 because it takes up half of the square, the purple is only 1/4 because it would take 4 purple to fill the big square and the orange is half of the purple so it takes double of pieces so 8 pieces which is 1/8
The sequence below shows the
number of cells in a sample at
the end of the four hours. 6, 12,
24, 48, which recursive formula
models the sequence?
Answer:
Step-by-step explanation:
Option B 2. Now is the correct answer because when we multiply 6 by 2 we get 12 then we multiply 12 by 2 we get 24
find x with the formulaaa
Which expressions simplify to 4? Select all that apply.
Answer:
B and D
Step-by-step explanation:
Find the answer
5/8 + (2/3 - 1/4) =
Answer:
25/24
Step-by-step explanation:
simplify: 2/3-1/4 to 5/12
5/8+5/12
=25/24
A mountain climber started at 150 feet below sea level. What would he need to climb to so that his starting spot and his ending spot were opposites?
Answer:
Your answer is 24.333.
Step-by-step explanation:
..If you round this, it would be 24 or 24.3. you get this answer by doing 3650 divided by 150.
What is the value of 1 − ( 2 − ( 3 − ( 4 − 5 ) ) ) 1 − ( 2 − ( 3 − ( 4 − 5 ) ) )
Answer:
51
1−2+3−4+5−.....+101
=(1+3+5+.....+101)−(2+4+6+.....+100)
=(1+3+5+.....+101)−2(1+2+3+.....+50)
=(51)
2
−2(
2
50(50+1)
)
=2601−2×1275
=2601−2550
=51
What is the equation of a line with a y-intercept at (0, 2) and a slope of 3?
a. y = 2x + 3
C. y = 3x + 2
b. y = 3x - 2
d. y = -2x + 3
Answer:
answer is C
the slope is 3 and the intercept is (0,2) which is 2
Answer please and explain
Answer:
18.84956, 18.84 if rounded to the nearest hundredth, and 18 if rounded to nearest whole number.
Answer:
Step-by-step explanation:
Please please i need help i will mark u brill
Answer:
Step-by-step explanation:
8d + 54 = 150
Putting value of D = 12 in the equation
8(12) + 54 = 150
96 + 54 = 150
150 = 150
Bringing like terms on one side
150 - 150 = 0
Answer:
Correct.
Step-by-step explanation:
8d+54=150
Putting d=12 we get
8(12)+54=150
96+54=150
150=150
What is the median of the data set?
73, 20, 63, 23, 20, 40, 67
Answer:
40
Step-by-step explanation:
if you line the numbers up like so you will see the number in the middle is 40
aka the median
20,20,23,40,63,67,73
Look at the image below, please! (I mark brainliest!)
Answer:
C, D, E
Step-by-step explanation:
10% of 33 is the same as the following, 0.1 * 33, 1/10 * 33, and 10/100 * 33, because they are all multiplying 33 by 0.1
