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[tex]\bf \begin{cases} x=3\implies &x-3=0\\ x=2\implies &\begin{cases} x-2=0\\ x-2=0\\ x-2=0 \end{cases} \end{cases} \\\\\\ (x-3)(x-2)~~(x-2)(x-2)=\textit{original polynomial} \\\\\\ (x^2-5x+6)~~(x^2-4x+4)=y \\\\\\ x^4-4x^3+4x^2-5x^3+20x^2-20x+6x^2-24x+24=y \\\\\\ 1x^4-9x^3+30x^2-44x+24=y[/tex]
Related Questions
Help please!! A bacteria culture is started with 300 bacteria. After 4 hours, the population had grown to 500 bacteria. If the population grows exponentially. a: write a recursive formula for the number of bacteria. b: write an explicit formula for the number of bacteria. c: if this trend continues, how many bacteria will there be in 1 day?
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Answer:
a).[tex]P_{t}=\frac{5}{3}P_{t-1}[/tex]
b).[tex]A_{t}=300e^{0.1277\times t}[/tex]
c). 6429 bacteria
Step-by-step explanation:
Population of the bacteria grows exponentially.
Therefore, growth of the bacteria will be represented by the formula
[tex]P_{t}=P_{0}e^{kt}[/tex]
Where [tex]P_{t}[/tex] = Population of the bacteria after time t
[tex]P_{0}[/tex] = Initial population of the bacteria
k = growth constant
t = time taken for growth
Now we plug in the values in the formula
[tex]P_{t}[/tex] = 500
[tex]P_{0}[/tex] = 300
Time t = 4 hours
[tex]500=300e^{4k}[/tex]
[tex]e^{4k}=\frac{500}{300}[/tex]
Now we take the natural log (ln) on both the sides
[tex]ln(e^{4k})=ln(\frac{500}{300})[/tex]
4k(lne) = ln(500) - ln(300)
4k = 6.2146 - 5.7038
4k = 0.5108
k = [tex]k=\frac{0.5108}{4}=0.1277[/tex]
a). Recursive formula for the sequence formed by the bacterial growth
Since [tex]P_{t}=(1+r)P_{t-1}[/tex]
500 = (1 + r)300
[tex](1+r)=\frac{5}{3}[/tex]
r = [tex]\frac{5}{3}-1=\frac{2}{3}[/tex]
Therefore, the recursive formula will be
[tex]P_{t}=\frac{5}{3}P_{t-1}[/tex]
b). Explicit formula for the number of the bacteria will be
[tex]A_{t}=300e^{0.1277\times t}[/tex]
c). We have to calculate the number of bacteria after 24 hours
[tex]A_{t}=300e^{0.1277\times 24}[/tex]
[tex]A_{t}=300e^{3.0648}[/tex]
[tex]A_{t}=300\times 21.43[/tex]
[tex]A_{t}=6429[/tex] bacteria
Add. Write your answer as a mixed number in simplest form.
2 3/4+ 1 9/10=
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[tex] 2\frac{3}{4} = 2 \frac{30}{40} =====\ \textgreater \ 1 \frac{9}{10} = 1\frac{36}{40} Add[/tex]
[tex]2 \frac{30}{40} + 1 \frac{36}{40} = 3 \frac{66}{40} = 4 \frac{22}{40} = 4 \frac{11}{20} [/tex]
[tex]Answer: 4 \frac{11}{20} ________ You're welcome. [/tex]
Evaluate −f(a)
f(x)=−5x²+2x−1
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The quotient of two numbers subtracted from 20
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1.5x+0.5y=12
solve for y
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Hope this helps :)
A new born baby has about 26,000,000,000 cells. An adult has about 4.94 × 10^13 cells. How many times as many cells does an adult have than a newborn? Write your answer in scientific notation
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3,10,24,52 what is the pattern
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3 x 2 = 6 + 4 = 10
10 x 2 = 20 + 4 = 24
24 x 2 = 48 + 4 = 52
hope this helps
"a dealer in a casino has rolled a 6 on a single die four times in a row. what is the probability of his rolling another 6 on the next roll, assuming it is a fair die?"
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is 30 x 10 to the 4th power equal 3,000,000
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The answer would then be...
30×10^5
Hope this helps!
Marcus works for 8 hours a day for 2 days at the bank and earned $165.12 how much did he earn per hour
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165.12/16
16= hours worked
$165.12= pay for those 16 hours worked
Answer is $10.32 per hour
82.56/8=10.32
I believe Marcus earns $10.32 Per hour
From the time of my beginning, my part was made of fibrous material called collagen, which is secreted by
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Collagen is a major structural protein in connective tissue, made of fibrous materials predominantly secreted by fibroblasts. It provides strength and flexibility to tissues like tendons, ligaments, and skin. This protein is crucial for maintaining the body's structural integrity.
Collagen is a key structural protein found in various connective tissues in animal bodies. It is made up of fibrous material, predominantly formed from collagen fibers secreted by fibroblasts. Collagen fibers provide tensile strength and flexibility to tissues such as tendons, ligaments, skin, and bones. This matrix not only holds connective tissues together but also enables the body to maintain its structural integrity even under movement.A formula that helps you calculate how long it will take for your savings to double is the Rule of 72.
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For example, if your annual rate of return is 12%, then it will take approximately 6 years to double your savings.
---> 72/12 = 6
If your return is 18%, Then it will take about 4 years.
---> 72/18 = 4
It works best for lower growth rates, less than 30%.
Answer:
True I hoped this helped!
Step-by-step explanation
Got it right on my quiz
Larry received 1/3 pound of candy from his grandmother and 2/5 pound of candy from his best friend. Larry's sister ate 1/2 pound of candy. How many pounds of candy does Larry have?
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10/30 + 12/30 - 15/30 =
22/30 - 15/30 =
7/30 lbs (or 0.233 lbs) <==
Answer:
Larry received 1/3 pound of candy from his grandmother and 2/5 pound of candy from his best friend. Larry's sister ate 1/2 pound of candy. How many pounds of candy does Larry have?
the answer is 7/30
Step-by-step explanation:
Five sixths of Forty two
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Five sixths of forty two is = 35.
What is the value of x in diagram
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At Shaw's Market apples cost $10 per case and bananas cost $6 per case. If an order comes in for a total of 300 cases for $2,000, what was the specific number of cases of apples?
Answers
10a + 6b = 2000
10a + 6(300 - a) = 2000
10a + 1800 - 6a = 2000
10a - 6a = 2000 - 1800
4a = 200
a = 200/4
a = 50 <=== 50 cases of apples
b = 300 - a
b = 300 - 50
b = 250....250 cases of bananas
Mr. Khans is buying staplers for his office. Each stapler costs $16.99. Write a function to represent the situation.
Answers
X stands for per stapler you buy and you times that but 16.99 and you get your answer
Answer:
[tex]C(x)=16.99x[/tex]
Step-by-step explanation:
Let x be the number of staplers and C(x) be total cost in dollars of x stapler.
Cost of each stapler = $16.99
So, the formula for total cost is
Total cost = Cost of each units × Number of units
Substitute 16.99 for Cost of each units and x for number of units in the above formula.
Total cost = [tex]16.99\times x[/tex]
Total cost = [tex]16.99x[/tex]
C(x) be total cost in dollars of x stapler. So, the cost function is
[tex]C(x)=16.99x[/tex]
Therefore, the function C(x)=16.99x represents the given situation.
0.27 repeating in simplest form
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The standard notation for a repeating decimal is to put a bar over the repeating digits, that is, 0.27272727...=0.27 repeating
** if u have 1 number repeating, like 0.222, then u put that 1 number over 9...2/9
if u have 2 numbers repeating, like 0.1414, then u put those 2 numbers over 99....14/99
if u have 3 numbers repeating, like 0.234234, then u put those 3 numbers over 999.....234/999
what is the slope intercept of 2y=14-4x
Answers
At a school, 174 students play at least one sport. This is 75% of the students at the school. How many students are at the school?
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174/3=58
Multiply by 4:
58·4=232.
There are 232 students at the school :)
Six sandwiches are being divided evenly among 4 friends.
How many sandwiches will each friend receive?
A. 2
B. 3/2
C. 2/3
D. 3/4
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Steve purchases a new car with a down payment and a loan at a 4.9% interest rate. His loan contract is for 60 months and has no prepayment penalties. Steve makes all his payments on time. What should he do if he wants to pay his loan off before 60 months has passed?
make more than the minimum payments
use the down payment to pay down the loan
increase his auto insurance premiums to decrease the amount owed
pay the principal and interest due each month
Answers
Answer:
Pay more than the required premiums
Step-by-step explanation:
The loan contract is of for 60 months. If Steve wants to repay the loan before 60 months , he need to pay more than the promised premiums.
In this way , the Steve will have more payment and as there is no prepayment charges, he will not be paying any penalties also. So the extra payment will help him to reduce the borrowed principle and thus thereby reducing the interest charged.
Hence out answer is option one , which says make more than the minimum payments
What is the difference between the mean and the median of the data set? {22, 8, 10 ,18 ,12, 20} 0 2 4 6
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Answer: The correct option is (A) 0.
Step-by-step explanation: We are given to find the difference between the mean and median of the following data set:
{22, 8, 10 ,18 ,12, 20}.
MEAN: It is the sum of all the values together divided by the number of values in the set.
So, the MEAN of the given data set is
[tex]m=\dfrac{22+8+10+18+12+20}{6}\\\\\\\Rightarrow m=\dfrac{90}{6}\\\\\Rightarrow m=15.[/tex]
MEDIAN: The median of a data set is given by the middle-most value in the data.
If there is an even number of items in the data set, then the median is found by taking the mean of the two middlemost numbers.
Arranging the given data in ascending order, we have
8, 10, 12, 18, 20, 22.
Since there are 6 values, that is even number of values. so the MEDIAN is given by
[tex]M=\dfrac{12+18}{2}\\\\\Rightarrow M=\dfrac{30}{2}\\\\\Rightarrow M=15.[/tex]
Therefore, m = M.
That is, mean and median of the given data are equal.
Hence, the difference is
m - M = 15 - 15 = 0.
Thus, option (A) is CORRECT.
Answer:
Option A - 0
Step-by-step explanation:
Given : Data set {22, 8, 10 ,18 ,12, 20}
To find : What is the difference between the mean and the median of the data set?
Solution :
Data set in increasing order {8, 10 ,12,18, 20,22}
Mean is defined as the division of sum of set values by total number of values.
[tex]M=\frac{\sum x}{n}[/tex]
Substitute the values we get,
[tex]M=\frac{8+10+12+18+20+22}{6}[/tex]
[tex]M=\frac{90}{6}[/tex]
[tex]M=15[/tex]
So, The mean of the set is 15.
Median of even numbers is the average of two middle terms.
[tex]m=\frac{3rd+4th}{2}[/tex]
[tex]m=\frac{12+18}{2}[/tex]
[tex]m=\frac{30}{2}[/tex]
[tex]m=15[/tex]
So, The median of the set is 15.
Now, The difference of the mean and the median of the set is
[tex]d=M-m[/tex]
[tex]d=15-15[/tex]
[tex]d=0[/tex]
Therefore,Option A is correct.
The difference of the mean and the median of the set is 0.
What is the simplified form of the expression 3 + 8x − 2y − x + 1 + 4y?
Answers
that is your answer
8x-x= 7x 7x is positive
You still have 3 and - 2y +4y and +1. Now combine -2y and +4y
-2y + 4y = 2y
you still have 2 like terms, 3 and 1.
3+ 1 is 4
so its 4+2y+7x
a function is defined by f(x)=x/4, what is f(-8)
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so
f(-8) = -8/4 = -2
answer
f(-8) = -2
Answer: -2
Step-by-step explanation:
the product of a number and 9 increased by 4 is 58 find the number
Answers
9x+4=58
9x=54
X=6
CHECKING
9(6)+4=58
54+4=58
58=58
Rafael wants to buy a car he needs it down payment of $3000 if he saves $340 each month about how many months will it take him to save the down payment
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It will take Rafael 10 months to save the down payment.
Rafael needs down payment of $3000 If he saves $340 each month, to determine how many months it will take him to save the down payment: Further ExplanationMethod:
To solve this question, round out one of the factors to estimate the product
We have:
340 ≈ 300 (we rounded 340 to the nearest hundred)
Let x represent the number of months, then we have:
300 x X = 3000
3 x 100 x X = 3 x 100 times 10 (for better understanding)
X = [tex]\frac{3000}{300}[/tex]
X = 10
so, it will take him about 10 months to save the down payment.
Notably, we rounded 340 to 300 so that it can be easier to use when calculating.
Some examples of numbers rounded to the nearest hundreds 7671 ≈ 7700 534 ≈ 500 2221 ≈ 2200 195 ≈ 200 8671 ≈ 8700 424 ≈ 400 348 ≈ 300LEARN MORE:
Raphael wants to buy a new car He needs a down payment of 3000 if he saves 340 each month about how many months will it take him to save the down payment https://brainly.com/question/11540707Raphael wants to buy a new car https://brainly.com/question/2442284KEYWORDS:
$3000$340 each monthrafaeldown paymentcarestimate the productrounded to the nearest hundredMichael Ross earned $44 on Monday, $36 on Tuesday, $58 on Wednesday, took Thursday off, and earned $51 on Friday. His total earnings for the week
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The difference between two numbers is 30. The
ratio of the bigger number to the smaller number is
7:2. What is the smaller number?
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The smaller number of the two numbers that have a difference of 30 and a ratio of 7:2 is 12.
How to find the smaller number?The difference between the two numbers is 30.
The ratio of the bigger number to the smaller number is 7:2.
The smaller number can be calculated as follows;
let
x = bigger number
y = smaller number
Hence, the difference in the numbers is as follows:
x - y = 30
Also, the ratio of the bigger number to the smaller number is 7:2.
The bigger number can be found using the ratio. Recall x + y is the total sum of the numbers.
x = 7 / 9(x + y)
x = 7 / 9x + 7 / 9y
x - 7 / 9x = 7 / 9 y
2 / 9 x = 7 / 9 y
multiply both sides by 9
2x = 7y
The bigger number is 7 / 2 of the smaller number.
x = 7 / 2 y
Therefore, let's substitute the value of x in equation(i).
Recall x - y = 30
7 / 2 y - y = 30
5 / 2 y = 30
cross multiply
5y = 60
y = 60 / 5
y = 12
Hence,
x = 30 + 12
x = 42
Therefore,
smaller number = 12
learn more on differences and number: https://brainly.com/question/28476518
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Ricardo is treating his employees and makes the following purchases at the store: 2 packages of bagels at $3.49 each 2 containers of cream cheese at $2.89 each 3 dozen doughnuts at $5.39 each 4 bottles of juice at $3.49 each Ricardo has a business account which saves him 5% on all purchases at this store. The discount is applied before tax. He is charged sales tax of 7%. If Ricardo paid $45.89, then he _____ for his purchase. a. did not pay enough b. paid the correct amount c. paid $2.29 too much d. paid $5.14 too much
Answers
Answer:
Ricardo paid $2.29 too much
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
To begin answering this question we need to calculate the total before applying anything. We calculate this by adding up all the amounts of each item purchased. Like so,
[tex](2*3.49)+(2*2.89)+(3*5.39)+(4*3.49) = Total[/tex]
[tex]6.98+5.78+16.17+13.96 = Total[/tex]
[tex] 42.89= Total[/tex]
Now that we have the total we can apply the 5% discount to this total.
[tex]42.89 * (1-0.05) = 40.75[/tex] ... rounded up
Finally we can apply the 7% sales tax to this purchase to calculate the final price that Ricardo should have paid.
[tex]40.75*(1+0.07) = 43.58[/tex] ... rounded up
As we can see Ricardo paid $2.29 too much
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.