Answer:
The prediction for the population in 2012 will be of 324.9 million.
Step-by-step explanation:
Exponential equation for population growth:
Considering that the population growth varies directly with time, it's value after t years is given by:
[tex]P(t) = P(0)e^{kt}[/tex]
In which P(0) is the initial value and k is the growth rate.
The population of the United States in 1990 was approximately 249 million
This means that [tex]P(0) = 249[/tex], so:
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]P(t) = 249e^{kt}[/tex]
In 2000, 281 million.
2000 - 1990 = 10, so [tex]P(10) = 281[/tex]. We use this to find k.
[tex]P(t) = 249e^{kt}[/tex]
[tex]281 = 249e^{10k}[/tex]
[tex]e^{10k} = \frac{281}{249}[/tex]
[tex]\ln{e^{10k}} = \ln{\frac{281}{249}}[/tex]
[tex]10k = \ln{\frac{281}{249}}[/tex]
[tex]k = \frac{\ln{\frac{281}{249}}}{10}[/tex]
[tex]k = 0.0121[/tex]
So
[tex]P(t) = 249e^{0.0121t}[/tex]
Use this information to predict the population for 2012.
2012 - 1990 = 22, so this is P(22).
[tex]P(22) = 249e^{0.0121*22} = 324.9[/tex]
The prediction for the population in 2012 will be of 324.9 million.
find the value of x (in this picture)
Answer:
x = 76°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityGeometry
All angles in a triangle add up to 180°Step-by-step explanation:
Step 1: Define
Identify and set up
30° + 74° + x = 180°
Step 2: Solve for x
Add: 104° + x = 180°[Subtraction Property of Equality] Subtract 104° on both sides: x = 76°Answer:
x° = 76 °
Step-by-step explanation:
We know that sum of interior angles of triangle is 180 °.
74 ° + 30 ° + x° = 180 °
combine like terms
104 ° + x° = 180 °
subtract each side by 104°
x° + 104 ° - 104 ° = 180 ° - 104 °
x° = 76 °
How many quarts are in 150 cups?
Answer:
37.5 quarts
Step-by-step explanation:
4 cups = 1 quart
150/4=37.5
Answer:
there are 37.499999997608 quarts in 150 cups
Refer To The Equation 2x-6y=12
Please Help :)
I'm sorry I can't answer that but I know something so you can answer that. search in browser 'quickmath' all your problems, equations and more can be solved
Step-by-step explanation:
I hope it helps trust me
Change fraction ( 11/4) from an improper fraction to a mixed number.
Answer:
Have a nice day :)
Step-by-step explanation:
To convert 11/4 into a mixed number, we need to divide 11 by 4 and get the values of quotient and remainder after performing division. When we divide 11/4, we get 2 as the quotient and 3 as the remainder. Now use the calculator to convert the following improper fractions to mixed fractions: 45/6
need answer quick !!! please
Answer:
f(-10) = 186
Step-by-step explanation:
Sub in -10 to the x - values:
f(x) = 2[tex]x^{2}[/tex] + [tex]x[/tex] - 4
f(-10) = 2(-10)^2 - 10 - 4
f(-10) = 200 - 10 - 4
f(-10) = 186
double the difference of 25 and 10 is
Answer:
30
Step-by-step explanation:
25-10 = 15
15 x 2 = 30
------------------
First we must get the difference between 25 and 10.
[tex]25 - 10 = \green{15}[/tex]
Next, we must double the answer.
[tex]15 \times 2 = \bold \blue{30} \\ \tt or \\ {15}^{2} = \purple {\sf{30}}[/tex]
Therefore, the answer is 30.Stay safe!
Question: Simplify (3 1/7)^7
Answer:
3
Step-by-step explanation:
see image below:)
Answer:
[tex]\frac{22^7}{823543}[/tex] B. 3
Step-by-step explanation:
help asap !!!!!!!!!!
Answer:
Diagram 2= 5
Diagram 3=10
Diagram 4= 15
Diagram 8 would be 35
Step-by-step explanation:
4x-1divide by 2=x+7
what is x
convert 15 to gray code
Step-by-step explanation:
15 = 1000
its done .
may it helped u
Think about the following relation: {(2,4),(-2,1),(2,2),(-3,1)}
What is the domain of the relation? {
}
What is the range of the relation? {
}
9514 1404 393
Answer:
D: {-3, -2, 2}
R: {1, 2, 4}
Step-by-step explanation:
The domain is the list of first-values of the ordered pairs:
D: {-3, -2, 2}
The range is the list of second-values of the ordered pairs:
R: {1, 2, 4}
Randy's gross salary is $760 per week. his salary is taxed at 16% what is his net salary
Answer:
$638.4
Step-by-step explanation:
Randy's gross salary (salary without any deduction) = $760
taxed rate =16%
Amount tax paid =tax% of gross income
=16/100 * $760
=$16*760/100
=$12160/100
=$121.6
net salary = gross salary - tax paid
=$760 - $ 121.6
=$638.4
Randy's net salary is $638.40
Randy's gross salary = $760 per week.
Tax paid on his salary = 16%
Net salary is the difference between the salary earned and the amount paid as tax. This will be:
= Salary - Tax
= $760 - (16% × $760)
= $760 - (0.16 × $760)
= $760 - $121.60
= $638.40
Read related link on:
https://brainly.com/question/23421215
Liam bought pizza and wings for $27.58. How much change should Liam receive if he gave the clerk three $10 bills?
Use coins and bills to help solve.
A. $1.52
B. $2.42
C. $2.52
D. $12.42
Answer:
B. $2.42
Step-by-step explanation:
If Liam gave the clerk three $10 bills, that means he gave the clerk $30. This is because 3 times 10 equals 30.
Find how much change he will receive by subtracting $27.58 from the $30 that Liam gave to the clerk:
30 - 27.58
= 2.42
So, Liam will receive $2.42 in change.
The correct answer is B. $2.42
Answer:
2.42
Step-by-step explanation:
3 ten dollar bills = 3*10 = 30 dollars
Subtract the cost of pizza and wings
30 - 27.58
Line up the decimals
30.00
- 27.58
----------------
2.42
If the exercise ball has been filled with Nitrogen which has a density of 0.2 grams per cubic inches. Find the mass in grams.
Options
11,581.2 grams
12,370.6 grams
13,891.5 grams
15,156.3 grams
Answer:
m = 11581.2 grams
Step-by-step explanation:
Given that,
The density of the ball, d = 0.2 g/in³
The radius of the ball, r = 24 inches
We need to find the mass of the ball in grams.
The density of an object is hiven by :
[tex]d=\dfrac{m}{V}\\\\d=\dfrac{m}{\dfrac{4}{3}\pi r^3}\\\\m=\dfrac{4}{3}\pi r^3\times d[/tex]
Put all the values,
[tex]m=\dfrac{4}{3}\pi \times 24^3\times 0.2\\\\m=11581.16\ g[/tex]
or
m = 11581.2 grams
Hence, the mass of the ball is 11581.2 grams.
Which describes the shape of the distribution of total points in Mr. Price's science class? Please help
Answer:
The distribution is negatively (left) skewed
Step-by-step explanation:
Notice how most of the data is clustered on the right side of the distribution and there's more spread in the left side of the data, meaning the left tail is longer. This creates a negative skew in the data. Review the attached diagram to learn more.
While at her family reunion, Anaya surveys the people there and makes a list of everyone's ages. She wants to make a data display that shows the youngest age, the mean age, and the oldest age, along with the way the other ages are distributed. What kind of display is her best choice?
A. Box-and-whisker plot
B. Histogram
C. Scatterplot
D. Ogive
Answer:a box and whisker plot
Step-by-step explanation:
Just took the quiz
The Math Team is hosting a raffle, and only 100 people will be allowed to enter. A ticket costs $2 and the prize is a $50 gift card. Only one
person will win.
What is the probability that you will win?
What is the probability that you will not win?
Find the expected value.
Answer:
given the information all your chances will be out of a 100% you don't have to convert these numbers because there is already only 100 people allowed to enter meaning you are 1 out of 100 people entered and have a 1/100 (1%) chance of winning and a 99/100 (99%) chance someone else winning
which statement describes the vector plotted below
I need help with this
Base: 3 units
Height: 5 units
Area: 15 square units
([tex]A=b*h=3*5=15[/tex])
hope this helps :)
A sheriff is interested in the average speed that people drive on Highway 50. Match the vocabulary word with its corresponding example.
A- The average speed that all drivers go on Highway 50
B- All people who drive on Highway 50
C- The average speed that the 250 randomly selected drivers drove on Highway 50
D- The speed that a driver drives on Highway 50
E- The 250 randomly selected drivers who were on Highway 50
F- The list of the 250 speeds that the drivers studied drove
a. Statistic
b. Population
c. Sample
d. Parameter
e. Data
f. Variable
Answer:
A: Parameter
B: Population
C: Statistic
D: Variable
E: Sample
F: Data
Step-by-step explanation:
A- The average speed that all drivers go on Highway 50: This is the parameter because it is the mean of the population.
B- All people who drive on Highway 50: This is the Population because it is from here that the sample was taken.
C- The average speed that the 250 randomly selected drivers drove on Highway 50: This is the statistic because it represents the mean of the sample.
D- The speed that a driver drives on Highway 50: This is the Variable because it varies with each driver.
E- The 250 randomly selected drivers who were on Highway 50: This is the sample because it is taken from a part of the population.
F- The list of the 250 speeds that the drivers studied drove: This is the data because it gives us information on the different speeds for this specific research.
An individual has $40,000 to invest: $28,000 will be put into a low-risk mutual fund averaging 6.9% interest compounded monthly, and the remainder will be invested in a high-yield bound fund averaging 9.8% interest compounded continuously.
Required:
a. Write an equation for the total amount in the two investments.
b. Write the rate-of-change equation for the combined amount.
c. How rapidly is the combined amount of the investments growing after 6 months? after 15 months?
Answer:
a) F(x) = 28,000( 1.00575 )^12x + 12,000e^0.098x
b) F'(x ) = 28,000 ( In 1.071224 ) ( 1.071224 )^x + 1176 e^0.098x dollar per year
c) 3228.94 dollar/year, 3428.73 dollar/year
Step-by-step explanation:
Capital = $40,000
$28,000 = low-risk mutual fund
6.9% monthly compounded interest for the low risk mutual fund
$12,000 = high-risk yield bound fund
9.8% continuously compounded interest
A) Equation for total amount in two investments
F(x) = F1(x) + F2(x) ----- ( 1 )
where :
F1(x) ( future value for monthly compounded interest)
= 28,000( 1 + 0.069/12 )^12x = 28,000 ( 1.00575 )^12x
F2(x) ( future value for continuously compounded interest )
= ( 40,000 - 28,000 )e^0.098x = 12,000 e^0.098x
back to equation 1
F(x) = 28,000( 1.00575 )^12x + 12,000e^0.098x
B Rate of change equation
f'(x) = d/dx (28,000( 1.00575 )^12x) + d/dx ( 12,000e^0.098x )
∴ f'(x) = 28,000 d/dx (1.00575^12)^x + 12,000 d/dx(b^x)
= 28,000 ( In 1.071224 ) ( 1.071224 )^x + 12,000 ( In b ) ( b^x )
f'(x ) = 28,000 ( In 1.071224 ) ( 1.071224 )^x + 1176 e^0.098x dollar per year
C) Determine how rapidly the combined amount will grow after 6 months and after 15 months
i.e. x = 0.5 , x = 1.25 years
after 6 months
28,000 ( In 1.071224 ) ( 1.071224 )^(0.5) + 1176*e^((0.098(0.50))
= 1993.88 + 1235.06 = 3228.94 dollar/year
after 15 months
28,000 ( In 1.071224 ) ( 1.071224 )^(1.25) + 1176*e^((0.098(1.25 ))
= 2099.47 + 1329.26 = 3428.73 dollar/year
2,10,18,26 find the 61st term
Answer:
482
Step-by-step explanation:
We can see that the numbers shown resemble an arithmetic sequence because they have a common difference. The formula for the nth term of an arithmetic sequence is:
[tex]a_{n} =a_{1} +(n-1)d[/tex]
Where [tex]a_{1}[/tex] is the first term, [tex]a_{n}[/tex] is the nth term, and [tex]d[/tex] is the common difference. To find the 61st term, all we need is the first term and the common difference. By looking at what given, we can say the first term is 2. Now, to find the common difference, we find the difference of a term from the term before it. In this case we can do [tex]10-2[/tex], which is [tex]8[/tex] , or the common difference. Since we have everything we need, it can be plugged into the equation:
[tex]a_{61} =2 + (61 - 1)*8\\a_{61} = 2 + 60*8\\a_{61} = 2 + 480\\a_{61} = 482[/tex]
So, the 61st term is 482.
E gawain sa pagktuto bilang 1 basahin at unawain ang bawat suliranin lutasin ang suliranin gamit ang polyas 4 step process.
Answer:
CHerry emoji
Step-by-step explanation:
MULTIPLE CHOICE
Select all that apply.
There are 3 red marbles, 2 green marbles, and 5 blue marbles in a bag. Which of the following are true?
The probability of randomly drawing a red marble and then a green marble is .
The probability of drawing a blue marble is the same as drawing either a red or a green marble.
The probability of randomly drawing either a red marble or a green marble is .
The probability of not drawing a blue marble is 50%.
Answer:
The probability of drawing a blue marble is the same as drawing either a red or a green marble. and the probability of not drawing a blue marble is 50%.
Step-by-step explanation:
Look at the image below help me
Answer:
y=12, x=6
Step-by-step explanation:
y+3=15
3x-6=12
What is the value 3/4 to the power of 3
Answer:
2/8
Step-by-step explanation:
Answer:
27/64
Step-by-step explanation:
3/4 to the second power is 9/16. 3/4 to the third power is 27/64
The work of a student to find the dimensions of a rectangle of area 8 + 12x and width 4 is shown below:
Step 1: 8 + 12x
Step 2: 4(4) + 4(8x)
Step 3: 4(4 + 8x)
Step 4: Dimensions of the rectangle are 4 and 4 + 8x
In which step did the student first make an error and what is the correct step? (1 point)
Select one:
a. Step 2; 4(2) + 4x(2)
b. Step 2; 4(2) + 4(3x)
c. Step 3; 4 + (4 + 8x)
d. Step 3; 4 + (4 ⋅ 8x)
Answer:
step c
Step-by-step explanation:
The number of cans the soup kitchen has is represented by the equation, y = -63x + 825, where x represents the number of days and y represents the number of cans. How many cans will the soup kitchen have after 10 days?
Answer:
this equation means that if your multiple the amount of days by -63 and add 825 you'll get the amount of cans
can substitute 10 in as x so
-63(10)+825
-630+825
195
so the soup kitchen will have 195 cans after 10 days
I'll like a math genius to solve this.
8÷2 (2+2)
Answer:
16
Step-by-step explanation:
8÷2(2+2)
From PEMDAS, we do the equation in the parenthesis first.
8÷2(4)
Since this is division and multiplication we go left to right.
4(4)
16
Hey there!
[tex]\large\textsf{Do PEMDAS:}\\\\\\\large\textsf{Parentheses}\\\\\large\textsf{Exponents} \\\\\large\textsf{Multiplication}\\\\\large\textsf{Division}\\\\\large\textsf{Addition}\\\\\textsf{Subtraction}[/tex]
[tex]\large\textsf{8 }\mathsf{\div}\large\textsf{ 2 (2 + 2)}\\\\\large\textsf{2 + 2}\\\large\text{= \bf 4}}\\\\\large\textsf{8 }\mathsf{\div }\large\textsf{ 2(4)}\\\\\large\textsf{8 }\mathsf{\div}\large\textsf{ 2}\\\large\textsf{= \bf 4}\\\\\large\textsf{4(4)}\\\large\textsf{= \bf 16}\\\\\\\\\\\\\boxed{\boxed{\huge\textsf{Answer: \bf 16}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
PLEASE HELP WILL MARK YOU!!!
Answer:
hear is your required answer
Answer:
please see the image given above. hope this helps
