The population of the town be in 2010 will be 121634, and it will take 21 years for the population to get to 50000
The population model is given as:
[tex]P(x) = 3485e^{0.125x}[/tex]
(a) The population in 2010
In 2010, the value of x is 10.
So, we have:
[tex]P(10) = 3485 * e^{(0.125 \times 10)}[/tex]
Evaluate the exponent
[tex]P(10) = 3485 * e^{(1.25)}[/tex]
This gives
[tex]P(10) = 121634[/tex]
(b) Year to reach 50000
This means that P = 50000.
So, we have:
[tex]50000 = 3485e^{0.125x}[/tex]
Divide both sides of the equation by 3485
[tex]14.35 = e^{0.125x}[/tex]
Take natural logarithm of both sides
[tex]\ln(14.35) =0.125x[/tex]
[tex]2.66 =0.125x[/tex]
Divide both sides by 0.125
[tex]21.28 = x[/tex]
Rewrite as:
[tex]x =21.28[/tex]
Approximate
[tex]x =21[/tex]
Hence, the population of the town be in 2010 will be 121634, and it will take 21 years for the population to get to 50000
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Divide using polynomial long division.
2. (x² + 7x +44) = (x +4)
Answer:
the answer is given in the photo below
Question:
Goofy Unlimited Lighting sells a 12 pack of lightbulbs for $8.40. Daisy Luminous Lighting sells a pack of 19 lightbulbs for
$15.35. Which store has the better deal. (3 points - 1 point showing the correct proportional relationship, 1 point
showing the unit rate, 1 point for identifying the store name)
es 0)
balo
Answer:
Goofy unlimited lighting 12 pack of light bulbs
Step-by-step explanation:
12 = 8.40/12 = .70 cents
19 = 15.35 = .81 cents
Put the following equation of a line into slope-intercept form, simplifying all fractions.
9
x
−
3
y
=
9x−3y=12
Answer: 3y = 9x -12
Step-by-step explanation:
PLS HELP GIVING (BRAINLY)
Which statement shows the correct value for the exponential expression 43?
A. 3 x 3 x 3 x 3 = 81
B. 4x3 = 12
C. 4x 4x4 x 4 = 256
D. 4 x 4 x 4 = 64
Answer:
i think D. 4x4x4 = 64 is answer
Step-by-step explanation:
4³ = 4×4×4 = 64
A pair of shoes are on sale for 60% off. The shoes cost $110 before the sale. How much money will you save after the sale?
answer: 60 × 100 = 600
Step-by-step explanation:
Answer:
$66
Step-by-step explanation:
Money saved after sale= 60% of $110
= 60/100 ×$110
= $66
Make x the subject of the formula
t=
[tex] \sqrt{2(x - ut) \div a}[/tex]
[tex]t = \sqrt \frac{ {2(x - ut)} }{a} \\ = > t = \sqrt{ \frac{2x - 2ut}{a} } \\ = > {t}^{2} = \frac{2x - 2ut}{a} \\ = > a {t}^{2} = 2x - 2ut \\ = > \frac{ { - at}^{2} }{2ut} = 2x \\ = > \frac{ - at}{2u} = 2x \\ = > \frac{ - at}{2u \times 2} = x \\ = > \frac{ - at}{4u} = x[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
The slope of a line running through points (6, 2) and (5, 7) is: 5. -5. 1. -1.
Answer:
-5
Step-by-step explanation:
We use the slope formula to find the slope
m = ( y2-y1)/(x2-x1)
= ( 7-2)/(5-6)
= 5/-1
= -5
How many times do 5 go into 32
Answer:
6 times or 6.4
please help me with this math problem please I need help
is 1.25 because you just add them together
What is the perimeter of the rectangle?
Answer:
6x+20 cm
Step-by-step explanation:
-formula : perimeter of rectangle=2(L+W)
L=2x+10 W=x
2(2x+10+x)
=2(3x+10) *distribute 2 on 3x ,10*
=6x+20 cm
A population numbers 18,000 organisms initially and grows by 16% each year.
Answer:
The answer is 20,880
Step-by-step explanation:
This won't be a very long explanation. What I did was add 18,000 plus 16% and I got 20,880.
Hope this helps!
Have a nice day/night/afternoon.
(Can you mark me brainliest?)
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what The Potageriterum
Answer:
Thick soup."coarse, spicy potage"A potage is a category of thick soups, stews, or porridges, in some of which meat and vegetables are boiled together with water until they form into a thick mush.Hope this helps you !!a manufacturer has the following quality control check at the end of a production line. if at least 8 of 10 randomly picked articles meet all specifications, the whole shipment is approved. if in reality, 85% of a particular shipment meets all specifications, what is the probability that the shipment will make it through the control check?
Using the binomial distribution, it is found that there is a 0.8202 = 82.02% probability that the shipment will make it through the control check.
For each article, there are only two possible outcomes, either it meets the specifications, or it does not. The probability of an article meeting the specifications is independent of any other article, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
10 articles are picked, hence [tex]n = 10[/tex].85% of the articles meets all specifications, hence [tex]p = 0.85[/tex]The probability is:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.85)^{8}.(0.15)^{2} = 0.2759[/tex]
[tex]P(X = 9) = C_{10,9}.(0.85)^{9}.(0.15)^{1} = 0.3474[/tex]
[tex]P(X = 10) = C_{10,10}.(0.85)^{10}.(0.15)^{0} = 0.1969[/tex]
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.2759 + 0.3474 + 0.1969 = 0.8202[/tex]
0.8202 = 82.02% probability that the shipment will make it through the control check.
For more on the binomial distribution, you can check https://brainly.com/question/24863377
jjjjjhfvkicdcghgfc ghcvh,glv,kghc ,h..
Answer:
0
Step-by-step explanation:
Is the sum of 5x⁴ + x³ and 2x³ + x² a trinomial expression. If it is true, justify your answer.
Answer:
The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.
Step-by-step explanation:
(5x⁴ + x³) + (2x³ + x²) = 5x⁴ + 3x³ + x²
The sum of 5x⁴ + x³ and 2x³ + x² is a trinomial expression that is 5x⁴ + 3x³ + x²
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.
We are given the expression as;
5x⁴ + x³ and 2x³ + x²
We need to find of the sum of the expression as;
(5x⁴ + x³) + (2x³ + x²)
= 5x⁴ + 3x³ + x²
The sum of 5x⁴ + x³ and 2x³ + x² is 5x⁴ + 3x³ + x²
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Mary has 18 ounces of apple chips she evenly portions the apple chips between four containers how many ounces of apple chips are in one container
Answer:
4.5 ounces
Step-by-step explanation:
18/4=4.5
suppose Amaya wants to bake cookies that require 4.5 cups of flour for a recipe that makes 4 dozen cookies. how much flour would Amaya need to make 126 cookies?
Answer:
11.8125 cups of flour
Step-by-step explanation:
4 dozen = 48 cookies
126/48=2.625 batches of 48 cookies
2.625 x 4.5 = 11.8125 cups of flour
Use the distributive property to write an experssion that is equalent to 10+15x
Answer:
5(2+3x)
Step-by-step explanation:
5 x 2 = 10
5 x 3x = 15x
10+15x
(PEMDAS)
Answer:
Step-by-step explanation:
im a boy
1/2x + 4 = 10
solve the following equation algebratically. Show the work to support the answer.
Answer:
(1/2)x + 4 - 4 = 10 - 4
2(1/2)x = 6 * 2
x = 12
A tree of unknown height casts a shadow that is 18 feet long. If a person that is 5 ft 7 in casts a shadow that is 4 ft long, then how tall is the tree in feet?
Round your answer to the nearest integer. Do not include feet in your answer.
Answer:
25.
Step-by-step explanation:
5 ft 7 in = 5.583 ft.
We have 2 similar triangles here.
If h is the height of the tree, then:
h / 5.583 = 18/4
h = 18*5.583/4
h = 25.12 ft
The height of the tree is approximately 25.12 feet.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The ratio of the shadow lengths is equal to the ratio of the object heights.
In other words, if we let H be the height of the tree in feet and h be the height of the person in feet, we have:
H/h = 18/4
We can find h by converting the person's height to feet. Since 1 inch is equal to 1/12 foot, the person's height in feet is 5 + 7/12 = 5.58 feet.
Substituting this value into the equation above and solving for H, we get:
H = (18/4) x 5.58 feet
= 25.12 feet
Therefore, the tree is around 25.12 feet tall.
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A total of 4.80 consisting of dimes and quarters was collected from a soft drink vending machine. If there is one more quarter than there are dimes find the number of dimes and the number of quarters.
Nadia is a stockbroker. She earns 12% of commission each week. Last week, she sold 4,500 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answer:
540 last week
52X540.=$28,080 a year
Step-by-step explanation:
Evaluate the expression for m = 45.
m|
54
Submit
[tex]|m| -54\\\\\text{When}~ m=45,\\\\|45| -54 = 45 -54 = -9[/tex]
[tex]\huge\textbf{Hey there!}\\\\\\\\\\\\\\\huge\boxed{\mathbf{|m| - 54 = }}\\\huge\boxed{\rightarrow \mathbf{|45| - 54 = }}\\\huge\boxed{\mathbf{\rightarrow 45 - 54}}\\\\\huge\text{Start at 45 and go back 54 to the left.}\\\huge\text{You should be left on \boxed{\bf -9}}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{-9}}}\checkmark\\\\\\\\\\\\\\\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
How do I add Mixed numbers? Please explain step by step to get brainliest!
The best way to do this is to convert the mixed numbers into improper fractions. Improper fractions are when the numerator is greater than the denominator. An example of an improper fraction would be 5/4. Since 4/4 is one whole that means 5/4 as a mixed number would be 1 1/4. I'll use the expression 3 1/4 + 5 2/9 as an example.
3 1/4 is 3 wholes and 1/4 left over. We know that 4/4 is 1 whole so to find 3 holes we multiply the 1 by 3. 4 x 3 =12 so there are 12/4 in 3 holes. We then add the leftover 1/4 to get 13/4 as our first number.
For the second number, we have 5 2/9. This one is a bit harder. We know that 9/9 is in one whole, but how do we find how many are in 5 wholes? We can use multiplication. 1x 5=5. 5 x 9 =45. That means we have 45/9 in 5 holes. Add the leftover 2/9 to have 47/9 as our 2nd number.
Now that we have these two improper fractions, what do we do with them? The two numbers we are working with are 13/4 and 47/9. We need to find the common denominator. The common denominator is when both fractions have the same bottom number. If two fractions have different denominators we cannot add them.
To make the denominators the same, let's find a common multiple. A common multiple is a number that is a product of all chosen numbers. This is kind of confusing but another way to think of a common multiple is a number that is divisible by all chosen numbers. Take the two denominators and multiply them. 9x4=36. 36 is a common multiple of both 9 and 4 because both of them can go into 36 without being a decimal or a fraction.
To convert the fractions we multiply again. Whatever you do to one side you must always do to the other. In 13/4 we multiplied 4x9 to get 36. So now we multiply the numerator 13x9 to get 117. That means we have 117/36. We multiplied 9x4 to also get 36. So our numerator for our second number is 47x4=188 or 188/36.
Now we have 117/36 and 188/36. We add them together like normal and get 305/36. In some cases you'd need to simplify it, but for the example equation I used this is already the fraction's lowest form. I hope this helped! Comment if you need another example or have any questions! :)
Manny has a garden that is 12 feet long and 9 feet wide. What is the perimeter of
Manny's garden?
Use the formula for perimeter, P =
2 (1 + w).
432 feet
O 33 feet
O 42 feet
216 feet
Answer:
42 ft
Step-by-step explanation:
2(L + W ) = P
2 (12 + 9) = P
2 (21) = P
42 = P
P = 42
Approximately what portion of the box is shaded blue?
Answer:
1/2 approximately 1/2......
Answer: C. (1/2)
Step-by-step explanation: You can see they split the box into 2 halves and one half is shaded so 1/2 is shaded you can also solve by 2/2 - 1/2 = 1/2
Suppose log7(10) = a and log7( 5) = b. Use the change-of-base formula along with properties of
logarithms to rewrite each expression in terms of a and b.
Step-by-step explanation:
log 10/log7=a
log10=alog7
log10=log7^a
10=7^a
log 5/log7=b
log5=blog7
log5=log7^b
5=7^b
Fill in the missing numbers below.
5 feet + 12 inches =
yard(s)
inches = 1 foot + 1 yard
feet = 3 feet + 24 inches
Answer:
2
Step-by-step explanation:
5 feet + 12 inches = 2 yards
Therefore
5 feet + 12 inches = yard(2)
I solving for (s)
hope that helps
how can I simplify of 9/20:3/5 please explain step by step
Answer:
Mark as brainlist
Step-by-step explanation:
Steps for dividing fractions
Find the reciprocal of the divisor. Reciprocal of 35: 53.
So, 920 ÷ 35 = 920 × 53.
= 9 × 520 × 3 = 4560.
After reducing the fraction, the answer is 34.
Answer:
3/4
Step-by-step explanation:
9/20:35=9/20/3/5
=9/20*5/3
=45/60
=simplify both numbers by 15
=3/4
Equivalent ratios
6:3 X:12 18:x