Answer:
a) The population in 2020 will be of 7.14 million people.
b) It will take 9.23 years for the population to drop below 7 million people
Step-by-step explanation:
Exponential equation for population decay:
The equation that models a population in exponential decay, after t years, is given by:
[tex]P(t) = P(0)(1-r)^t[/tex]
In which P(0) is the initial population and r is the decay rate, as a decimal.
The total population of a European country is decreasing at a rate of 0.6% per year.
This means that [tex]r = 0.006[/tex]
In 2014, the population of the country was 7.4 million people.
This means that [tex]P(0) = 7.4[/tex]. Then
[tex]P(t) = P(0)(1-r)^t[/tex]
[tex]P(t) = 7.4(1-0.006)^t[/tex]
[tex]P(t) = 7.4(0.994)^t[/tex]
a) What is the population likely to be in 2020 if it decreases at the same rate?
2020 - 2014 = 6, so this is P(6).
[tex]P(6) = 7.4(0.994)^6 = 7.14[/tex]
The population in 2020 will be of 7.14 million people.
b) How long will it take for the population to drop below 7 million people?
t when P(t) = 7. So
[tex]P(t) = 7.4(0.994)^t[/tex]
[tex]7 = 7.4(0.994)^t[/tex]
[tex](0.994)^t = \frac{7}{7.4}[/tex]
[tex]\log{(0.994)^t} = \log{\frac{7}{7.4}}[/tex]
[tex]t\log{0.994} = \log{\frac{7}{7.4}}[/tex]
[tex]t = \frac{\log{\frac{7}{7.4}}}{\log{0.994}}[/tex]
[tex]t = 9.23[/tex]
It will take 9.23 years for the population to drop below 7 million people
At what values of x, does f(x) = 0?
(-1,0) (2,0) (4,0)
Answer:
-1, 2, 4
Step-by-step explanation:
As one can see in the given values,
(-1, 0), (2, 0), (4, 0)
When one substitutes these values for (x), the outputs, also known as the results or what (f(x)) equals or the (y) values are equal to (0). Therefore, (f(x)) equals zero at these given values.
Someone please help I have 40 mins for this test !
Answer:
It would be Linear
Step-by-step explanation:
Answer:
i think its quadratic because the graph isnt straight and has different slopes between the x,y.
Step-by-step explanation:
Please help me with this ive been struggling on it for a while
in a random sample of 28 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.3 minutes. assume the population is normally distributed and use a t-distribution to construct a 99% confidence interval for the population mean u. What is the margin of error of u
Answer:
The margin of error of u is of 3.8.
The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 28 - 1 = 27
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.7707
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.7707\frac{7.3}{\sqrt{28}} = 3.8[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error of u is of 3.8.
The lower end of the interval is the sample mean subtracted by M. So it is 31.2 - 3.8 = 27.4 minutes
The upper end of the interval is the sample mean added to M. So it is 31.2 + 3.8 = 35 minutes
The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.
What is the MAXIMUM of the data set: 24, 25, 29, 30, 31, 31, 32, 34, 34?
The graphs below show measurements from cubes
with different side lengths.
Which pairs of variables have a linear relationship?
Select two options.
24
side length and perimeter of 1 face
20
perimeter of 1 face and area of 1 face
16
Perimeter of 1 Face
surface area and volume
A
area of 1 face and surface area
side length and volume
1
2
3
4
5
6
Side Length
40
36
32
Answer:
the first one and the third one
Step-by-step explanation:
Answer:
Side length and perimeter of 1 face
Area of 1 face and surface area
Step-by-step explanation:
If there is an 10+ lax
on a $25 pair of pants
what is the tax
amount?
Answer:
A 6% sales tax.
Step-by-step explanation:
Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.43cm and a standard deviation of 0.35cm. Using the empirical rule, what percentage of the apples have diameters that are between 7.08cm and 7.78cm
Answer:
Approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.
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 7.43cm, standard deviation of 0.35cm.
What percentage of the apples have diameters that are between 7.08cm and 7.78cm?
7.43 - 0.35 = 7.08 cm.
7.43 + 0.35 = 7.778 cm.
Within 1 standard deviation of the mean, so approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.
A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?
Answer:
3
Step-by-step explanation: 6 11 10 48
spent $504
hair dryers cost $8 each
6 floors with the same number of rooms on each floor.
Money spent / hair dry cost = number of hair dryers bought
number of hair dryers = number of floors = hair dryers per floor Plus any remainder
504 / 8 = 63 hair dryers
63 / 6 = 10.5 so 10 rooms per floor = 60 hairs dryers with 3 left over
Answer:
well IMA just copy the other guy and say 3
Step-by-step explanation:
just cause it is.
Find the volume in cm³ of a length of pipe which has these measurements.
Volume of a cylinder = πr²h
π = 3.14
Which number line shows the solutions to 1/2 x -2 > 0
Answer:
The top choice
Step-by-step explanation:
1/2 x -2 > 0
Add 2 to each side
1/2 x -2+2 > 0+2
1/2 x > 2
Multiply each side by 2
1/2 x *2 > 2*2
x > 4
There is an open circle at 4 and the line goes to the right
Answer:
It is the first option everything to the right of 4.
Step-by-step explanation:
help me fast plsssdsssssss
A random sample of items is selected from a population of size . What is the probability that the sample mean will exceed if the population mean is and the population standard deviation eq
Answer:
The probability is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which X is the value we want to find the probability of the sample mean exceeding, [tex]\mu[/tex] is the population mean, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
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.
Central Limit Theorem for the sample mean:
Sample of size n, and thus:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]Z = \frac{X - \mu}{s} = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Probability of the sample mean exceeding a value:
The probability is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which X is the value we want to find the probability of the sample mean exceeding, [tex]\mu[/tex] is the population mean, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
i don’t understand the whole thing i need help How many plants are shorter than 9 inches?
Answer:
9 plants
Step-by-step explanation:
Since we are trying to find the number of plants that are shorter than 9 inches, we will look at the plants that are 2, 3, 4, 5, 6, 7, and 8 inches tall.
Each x counts as a plant
# of 2 inch plants: 1
# of 3 inch plants: 1
# of 4 inch plants: 4
# of 5 inch plants: 1
# of 6 inch plants: 1
# of 7 inch plants: 1
# of 8 inch plants: 0
Add up the number of plants:
1 + 1 + 4 + 1 + 1 + 1 + 0 = 9
Answer:
9 plants
Hope this helps!
How much water must be added to 12 quarts of a 10% solution of salt and water to reduce to a 6% solution?
Answer:
Let x = quarts of water to be added
so then
12* 10% + x * 0% = (12+x) * 6% (this says 12 quarts of 10% solution + x quarts of 0%(water) equals the new total (12+x) of a 6% solution
1.2 = .72 + .06x
.48 = .06x
x = 8 (quarts of water to be added)
Step-by-step explanation:
Hope this helps
in a company ther are bell ring after interval of 3,5 and 15 minutes if they ring together at 8:00 AM when they ring together next
Answer:
8:15 AM
Step-by-step explanation:
This is an interval question so we use LCM to solve such kind of questions
LCM of 3,5,15=15
So after 15 minutes it will ring again
So at 8:15 AM it will ring
A hot air balloon is cruising at an altitude of 120 meters above the ground when it begins its descent. The balloon descends at a rate of 4.5 meters per minute. Explain how you would set up an equation to model when the balloon will reach an altitude of 75 meters above the ground. Then solve the equation and check your solution.
PLEASE HELP ASAP
Answer:
y = - 4.5x + 120
75 = - 4.5x + 120
x = 10 minutes
Step-by-step explanation:
To model the scenario described above, we use the linear equation model ;
Where ;
y = bx + c ; c = intercept ; b = slope ; y = altitude at time x
The initial altitude of the hot air Ballon here is the intercept = 120 meters
The descent rate = 4.5 m per minute is the slope ; since it is descent, then the slope will be negative as the altitude will reduce.
Hence, we have ;
y = - 4.5x + 120
Hence, the time altitude will be 75 cabnbe modeled as :
y = 75
75 = - 4.5x + 120
75 - 120 = - 4.5x
- 45 = - 4.5x
x = 10 minutes
What is the end behavior of the polynomial function?
Answer:
As x→∞, y→-∞
Step-by-step explanation:
Notice how as the x values increase, the y values get closer to negative infinity. As the x values decrease into the negatives, the y values get closer to positive infinity.
I need the answer to #3
Answer:
I think its b but im not sure
Step-by-step explanation:
If h (x) = 1 - 2/3, find h (x) when x is -6.
Answer:
h = 19/3
Step-by-step explanation:
Simplify 6-(-14)+(-2)
Answer:
18
Step-by-step explanation:
when there is a - in front of an expression in parentheses, change the sign of each term in the expression
6+14+(-2)
then calculate the sum or difference
6+14-2= 18
pls pls pls pls help :( im really bad at math and im trying so hard not to fail... i will mark brainliest!
Answer:
142
Step-by-step explanation:
5. What is the volume of a cube with a side that is 7 ft. long
[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
[tex]\huge\underline{\sf{\red{Problem:}}}[/tex]
5.) What is the volume of a cube with a side that is 7 ft. long.[tex]\huge\underline{\sf{\red{Given:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{v = volume}[/tex]
[tex]\quad\quad\quad\quad\sf{s = side}[/tex]
[tex]\quad\quad\quad\quad\sf{s = 7ft}[/tex]
[tex]\huge\underline{\sf{\red{Fomula:}}}[/tex]
[tex]\quad\quad\quad\quad \boxed{\sf{v = {s}^{3} }}[/tex]
[tex]\huge\underline{\sf{\red{Solution:}}}[/tex]
[tex]\quad\quad\quad\quad {\sf{⟶v = {s}^{3} }}[/tex]
[tex]\quad\quad\quad\quad {\sf{⟶v = {(7)}^{3} }}[/tex]
[tex]\quad\quad\quad\quad {\sf{⟶v = 7×7×7 }}[/tex]
[tex]\quad\quad\quad\quad {\sf{⟶v = 343 }}[/tex]
[tex]\quad\quad\quad\quad ⟶\boxed {\sf{v = 343 \: {ft}^{3} }}[/tex]
[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]
[tex] \huge\quad\quad \underline{\boxed {\sf{ \red{v = 343 \: {ft}^{3} }}}}[/tex]
[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
#CarryOnLearning
[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]
mainly an addition to the terrific reply above, which is absolutely correct
Check the picture below.
A segment has endpoints A and C. What are two names for the segment?
Answer:
Ac CA is your answer
Step-by-step explanation:
MARK ME AS BRAINLIEST
AC and CA
Step-by-step explanation:
[tex]line \: which \: has \: endpoint \: \\ \\ A \: and \: C \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ it \: shows \: that \: line \: starts \: from \: \\ \\ A \: \: and \: ends \: with \: C \\ \\ so \: \: its \: name \: is \: \: \: \: AC \\ \\ hope \: it \: is \: helpful \: to \: you....[/tex]
A box has dimensions of 4.0 cm by 8.5 cm by 2.0 cm. The volume of the box in mL is:
SOMEONE HELP ME PLEASE
Answer:
The missing value is 5/2
Step-by-step explanation:
If y=13 and x=y/2, solve
(5y) + (6x)
Answer:
104
Step-by-step explanation:
(5y) + (6x)
Let y = 13
x = y/2 = 13/2
(5*13) + (6*13/2)
65+39
104
Answer:
104
Step-by-step explanation:
See image below:)
Based on the cumulative frequency histogram, determine the number of swimmers who swam between 200 and 249 yards. Determine the number of swimmers who swam between 150 and 199 yards. Determine the number of swimmers who took the swim test.
Answer:
[tex](a)\ 200 \to 249 =3[/tex]
[tex](b)\ 150 \to 199 = 0[/tex]
[tex](c)\ Total = 20[/tex]
Step-by-step explanation:
Given
See attachment for cumulative frequency histogram
Solving (a): Swimmers between 200yd and 249yd
To do this, we simply read the data from the 0 mark
From the histogram, we have:
[tex]0 \to 249 = 15[/tex]
and
[tex]0 \to 199 = 12[/tex]
So:
[tex]200 \to 249 = 0 \to 249 - 0 \to 199[/tex]
This gives:
[tex]200 \to 249 = 15-12[/tex]
[tex]200 \to 249 =3[/tex]
Solving (b): Swimmers between 150yd and 199yd
To do this, we simply read the data from the 0 mark
From the histogram, we have:
[tex]0 \to 149 = 12[/tex]
and
[tex]0 \to 199 = 12[/tex]
So:
[tex]150 \to 199 = 0 \to 199 - 0 \to 149[/tex]
This gives:
[tex]150 \to 199 = 12-12[/tex]
[tex]150 \to 199 = 0[/tex]
Solving (c): Total swimmers
To do this, we simply read the longest bar of the histogram
[tex]Longest = 20[/tex]
Hence:
[tex]Total = 20[/tex]
Help with this Geometry question please
Answer:
Angle A = [tex]77^{o}[/tex]
Step-by-step explanation:
cos A = adjacent / hypotenuse
cos A = 18/82
cos A = 0.22
A = [tex]cos ^{-1}[/tex]0.22
A = [tex]77^{o}[/tex]
Please help me with this question
9514 1404 393
Answer:
D(1, 2)
Step-by-step explanation:
The ordered pair is always (x-coordinate, y-coordinate).
The x-coordinate is the distance to the right of the y-axis. (It is negative for points left of the y-axis.) Here, point D lies 1 unit right of the y-axis, so its x-coordinate is 1.
The y-coordinate is the distance above the x-axis. (It is negative for points below the x-axis). Here, point D lies 2 units above the x-axis, so its y-coordinate is 2.
The ordered pair describing the location of D is ...
(x-coordinate, y-coordinate) = (1, 2)
