The question is asking you to understand that a population which is raised by a common ratio over a certain time period follows an exponential pattern. See:
After 1 hour, the population is 3*10
After 2 hours, the population is 3*3*10
After 3 hours, the population is 3*3*3*10
.....
This can be generalised as a function of t, the time in hours:
f(t) = (3^t) * 10
Since the function determines the population at a given time, it is more prudent to replace f(t) with P, the population after time t:
P = (3^t) * 10
Since 20 minutes is equal to (1/3) hours, t can be substituted for (1/3) in order to calculate the population size after 20 minutes:
P = (3^(1/3)) * 10 = 14.4224957031 ≈ 14
Therefore the population after 20 minutes is 14.
2. A line goes through the points (4, 8) and (-4, 6).
(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form. Show your work
(c) Write the equation of the line in slope-intercept form. Show your work.
Any body can help?
(a) [tex]\frac{6-8}{-4-4}=\frac{-2}{-8}=\boxed{1/4}[/tex]
(b) Using the point (4,8), we get [tex]\boxed{y-8=\frac{1}{4}(x-4)}[/tex]
(c) Rearranging into slope-intercept form,
[tex]y-8=\frac{1}{4}(x-4)\\\\y-8=\frac{1}{4}x-1\\\\\boxed{y=\frac{1}{4}x+7}[/tex]
As an inventory manager, you must decide on the order quantity for an item. Its annual demand is 679 units. Ordering costs are $7 each time an order is placed, and the holding cost is 10% of the unit cost. Your supplier provided the following price schedule. Quantity Price per Unit 1 - 100 $5.65 101 - 350 $4.95 351 or more $4.55 What ordering-quantity policy do you recommend
The ordering-quantity that should be recommended will be 117 units.
How to calculate the order quantity?The following can be deduced from the information given:
Demand = 679
Ordering cost = 7
Holding cost = 10%
Ordering quantity will be:
= ✓(2 × Demand × Ordering cost / Holding cost)
= ✓(2 × 679 × 7/0.1)
= ✓13580
= 116.53
= 117
Learn more about order quantity on:
brainly.com/question/27986709
#SPJ1
Jack has a rectangular piece of land, the area of which is represented by a1 = 9.5l. His brother has a different rectangular piece of land, the area of which is represented by a2 = l(14 − l). Let a represent the area in square meters and l represent the length in meters of the pieces of land. The two equations plotted on a graph meet at a point as shown in the image.
The area of the brothers’ pieces of land will be the same when the length is ______ meters.
Answer:2
Step-by-step explanation:
Answer: 13
Step-by-step explanation:
Which expression shows the sum of the polynomials with like terms grouped together?
The expression of the polynomials with like terms grouped together is (c) [-4x²] + 2xy² + [10x²y + (-4x²y)]
How to group the polynomial by like terms?We have:
10x²y + 2xy² - 4x² - 4x²y
Collect the like terms
- 4x² + 2xy² + 10x²y - 4x²y
Put each group in bracket
- 4x² + 2xy² + [10x²y - 4x²y]
Express as positives
[-4x²] + 2xy² + [10x²y + (-4x²y)]
Hence, the expression of the polynomials with like terms grouped together is (c) [-4x²] + 2xy² + [10x²y + (-4x²y)]
Read more about polynomials at:
https://brainly.com/question/4142886
#SPJ1
Answer:
c
Step-by-step explanation:
please i need this fast
Answer:
the second option
Step-by-step explanation:
UV and AB are at a right Angie to reach other.
and
UV is parallel to ZY
Each team is required to bring 24 baseballs to each game. If there are 3
baseballs in a pack, how many total packs do the teams bring to each game?
The total packs the teams bring to each game is 8 packs.
How many packs do the team bring to each game?
Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷.
Number of packs = 24 ÷ 3 = 8
To learn more about division, please check: https://brainly.com/question/13281206
#SPJ1
Evaluate:
10
Σ¹0 4(1)n-1 = [?]
Round to the nearest hundredth.
Enter
Answer:
Step-by-step explanation:
we are essentially calculating:
4(1/4)^0 + 4(1/4)^1 + 4(1/4)^2 + ... + 4(1/4)^9
Formula: [tex]\frac{a(1-r^n)}{1-r}[/tex]
4(1-(1/4)^10)/ (1-1/4) approximates to 5.33
What is the degree of the monomial?
8x²y³z4
What is the range of the given function?
{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}
O {x|x=-5, -4, -2, 0, 2}
Oy | y=-9, -3, 0, 5, 7}
{x|x = -9, -5, -4, −3,−2, 0, 2, 5, 7}
{y | y=-9, -5, -4, -3, -2, 0, 2, 5, 7}
The range of the function will be (-9, 7). Then the correct option is D.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given in the form of the pair of points.
{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}
Then the range of the function will be (-9, 7).
Then the correct option is D.
More about the domain and range link is given below.
https://brainly.com/question/12208715
#SPJ1
x2y, for x = 3 and y = 6
Answer:
12
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ASSUMING}[/tex]
[tex]\mathsf{x^{2y}}[/tex]
[tex]\huge\textbf{IF SO, FOLLOW THESE STEPS TO}\\\huge\textbf{SOLVE FOR YOUR RESULT}[/tex]
[tex]\mathsf{x^{2y}}\\\mathsf{= 3^{2(6)}}\\\mathsf{= 3^{2\times6}}\\\mathsf{= 3^{12}}\\\mathsf{= 3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3}\\\mathsf{= 9\times9\times9\times9\times9\times9}\\\mathsf{= 81\times81\times81}\\\mathsf{= 6,561\times81}\\\mathsf{= 531,441}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{531,441}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]prove that ABC is a right triangle. Select the correct answer from each drop down menu.
All the blanks have been filled , which proves ultimately that Triangle ABC is a right angled Triangle.
What is Right Angled Triangle ?A triangle in which one angle is 90 degree is called a Right Angled Triangle.
AB is congruent to DB because segment DE was constructed so that DE = AB , BC is congruent to EF , because segment EF was constructed so that EF = BC , Since Triangle DEF is a right angled triangle .
DE² +EF² = DF² by the Pythagoras Theorem .
WE are given that AB² +BC² = AC²
Since DE = AB and EF = BC , DE² +EF² = AC² by the given data
Also DF² = AC² by the above equation .
Taking the square root on both the sides of the equation gives DF = AC .
So AC is congruent to DF by the definition of congruency .
Applying SSS Congruency , Triangle ABC is congruent to DEF .Therefore ABC is a right angled triangle.
To know more about Right Angled Triangle
https://brainly.com/question/3770177
#SPJ1
2 Simplify.
a
e
√72+√162
√50-√8
2√28+√√28
[tex] \sqrt{72} + \sqrt{162} \\ \\ \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{2 \times 3 \times 3 \times 3 \times 3} \\ \\ 2 \times 3 \sqrt{2} + 3 \times 3 \sqrt{2} \\ \\ 6 \sqrt{2} + 9 \sqrt{2} \\ \\ (6 + 9) \sqrt{2} \\ \\ 15\times1.4 \\ \\ 21[/tex]
--------------------------[tex] \sqrt{50} - \sqrt{8} \\ \\ \sqrt{2 \times 5 \times 5} - \sqrt{2 \times 2 \times 2} \\ \\ 5 \sqrt{2} - 2\sqrt{2} \\ \\ (5 - 2) \sqrt{2} \\ \\ 3 \sqrt{2} \\ \\ 1.7 \times 2 \\ \\ 3.4[/tex]
--------------------------[tex]2 \sqrt{28} + \sqrt{28} \\ \\ 2 \sqrt{2 \times 7 \times 7} + \sqrt{2 \times 7 \times 7} \\ \\ 2 \times 7 \sqrt{2} + 7 \sqrt{2} \\ \\ 14 \sqrt{2} + 7 \sqrt{2} \\ \\ (14 + 7) \sqrt{2} \\ \\ 21 \times 1.4 \\ \\ 29.4[/tex]
A culture started with 1,000 bacteria. After 4
hours, it grew to 1,100 bacteria. Predict how
many bacteria will be present after 12 hours.
Round your answer to the nearest whole
number.
Answer:
1331 bacteria
Step-by-step explanation:
Number bact = 1000 e^kt
1100 = 1000 e^k4
shows k = .023827545
Now for 12 hours
x = 1000 e^(.023827545 * 12)
= 1331
i realized my answer is wrong.
4
Jake is the starting quarterback on his school's football team. He has completed 38 of his 79 passes this season. Which of the
following values is closest to his percentage of pass completions this season?
OA. 51%
OB. 48%
OC. 38%
OD. 30%
Reset
Submit
Session Timer: 7:52
Session Score:?
Please help
Answer: A) 51%
Step-by-step explanation:
We can estimate the percentage of pass completions by rounding both values. While estimation does not give an exact answer it will give one that is close.
38 rounds up to 40 and 79 rounds up to 80.
Now it is easier to divide.
40/80=1/2
1/2=50%
The closest answer to 50% is 51% which must be the answer.
Answer:
A)
Step-by-step explanation:
How many full cases and additional items are needed to fulfill the order 80 6
The number of cases is 13 and the additional units are 2 if the 80 units needed 6 units per case.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
80 units needed 6 units per case. What are the number of cases and the number of additional units?
Total number of units = 80 units
6 units per case
Number of case = 80/6 = 13.33 ≈ 13
Total units if the number of cases = 13
= 13×6
= 78
Additional units = 80 - 78 = 2 units
Thus, the number of cases is 13 and the additional units are 2 if the 80 units needed 6 units per case.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ1
PLEASE HELP
True or false
False
Step-by-step explanation:
Answer:
true.
Step-by-step explanation:
[tex]b^t=\frac{n}{a}; \ = > \ t=log_b\frac{n}{a}; \ = > \ t=\frac{log\frac{n}{a}}{logb}.[/tex]
The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the function of A(t)=14(2.71)^-.016*t, where t is the number of years since a government program was began to help clean up the lake. About how long will it take for the amount of pollutant to reach 7 parts per million?
Solving the exponential function, it is found that it will take 43.5 years for the amount of pollutant to reach 7 parts per million.
What is the exponential function for the amount of the substance?It is given by, after t years:
[tex]A(t) = 14(2.71)^{-0.016t}[/tex]
It will reach an amount of 7 parts per million when A(t) = 7, hence:
[tex]A(t) = 14(2.71)^{-0.016t}[/tex]
[tex]7 = 14(2.71)^{-0.016t}[/tex]
[tex](2.71)^{-0.016t} = 0.5[/tex]
[tex]\log{(2.71)^{-0.016t}} = \log{0.5}[/tex]
[tex]-0.016t\log{(2.71)} = \log{0.5}[/tex]
[tex]t = -\frac{\log{0.5}}{0.016\log{2.71}}[/tex]
t = 43.5.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
8. Mrs. Reyes has 4 mangoes, 5 guavas, and 2 bananas in her basket. What is the probability that one can pick a guava?
A. 2 out of 11 or 2/11
B. 5 out of 11 or 5/11
C. 4 out of 11 or 4/11
9. What is the probability of choosing a blue paper if there are 3 red papers and 4 blue papers in the box?
A. 4 out of 7 or 4/7
B. 3 out of 7 or 3/7
C. 0 out of 7 or zero probability
10. In the numbers 2,2,2,5,5,2,3 What is the probability of getting 2?
A. 2/7
B. 3/7
C. 4/7
8) 5 + 4 + 2 = 11
Since there are 5 guavas, the correct answer is B. 5/11
9) 3 + 4 = 7
Since there are 4 blue papers, the correct answer is A. 4/7
10) Count all of the numbers and add them. There are 4 twos, 2 fives, and 1 three:
4 + 2 + 1 = 7
Since there are 4 twos, the correct answer is C. 4/7
Find the sum.
([tex](-54x^{5}+35x^{3}-61)+(5x^{5}-69x^{3}-7)=[/tex]
Answer:
125250
Step-by-step explanation:
I just askeked and it gave me the answere
Answer: [tex]-49x^{5} - 34x^{3} - 68[/tex] or [tex]49x^{5} + 34x^{3} + 68[/tex]
Step-by-step explanation:
Since both groups have the same variables and exponents, just align them and add.
[tex]-54x^{5}+5x^{5} = - 49x^{5}[/tex]
[tex]35x^{3} - 69x^{3} = -34x^{3}[/tex]
- 61 - 7 = - 68
[tex]-49x^{5} - 34x^{3} - 68[/tex]
Hello, I would like help with his question. Please do as quickly as you can, Thank you.
Answer:
Step-by-step explanation:The answer is 45
What is the lowest value of the range of the function
shown on the graph?
O -∞
O -2
0 0
03
The question is incomplete. Below you will find the missing graph.
The lowest value of the range of the function shown on graph is (B) -2.
A graph is the pictorial representation of the function or mathematical relation (Equation or Inequality etc).
The lowest value of the graph is the value of y when y=f(x) gives the least value.
From the given graph we can clearly see that at x=3 the graph of the given function approaches the least value which is -2.
So the lowest value of the range of the function shown on the graph is -2.
Hence the correct option is (B).
Learn more about Graph here -
https://brainly.com/question/4025726
#SPJ10
A sub sandwich shop offers 12 toppings to choose from. How many ways could a person choose a 4-topping sandwich?
HELPPPPPP
Using the combination formula, it is found that there are 495 ways to choose a 4-topping sandwich.
The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
4 toppings are chosen from a set of 12, hence the number of ways is given by:
[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
#SPJ1
f(x)=x2 what is g(x)
Answer:
-x^2-2
Step-by-step explanation:
So by looking at the two curves it appears that g(x) is simply a reflection of f(x) over the x-axis and then shifted 2 units down. So to reflect the parabola you simply make the x^2 negative to get -x^2 and then to go 2 units down you subtract 2 from the -x^2. This gives you the equation
[tex]g(x)=-x^2-2[/tex]
If you receive a 25% MARKUP on an item costing $60.00, how much money do you pay in total?
Answer:
Money Paid in Total = $45
Step-by-step explanation:
Firstly, the term Mark-up refers to the amount added to the cost price to cover the overheads and realize a profit.
A mark-up percentage is a percentage (%) that is used as a basis to determine the mark-up value.
Given
Cost of an Item = 60$
Markup % = 25% on cost
Hence, Mark up in $ = 60$*25%
= 15$
Therefore, Actual cost of an item = Cost of an item - Mark up on Item
= 60$ - 15$
= 45$
Read more on Brainly.com -
https://brainly.in/question/47347085
#SPJ10
Determine if a Poisson experiment is described, and select the best answer:
A paper mill produces paper that comes in 3000-foot rolls. The average number of
defects in the paper is known to be 38.9 per roll. The manager would like to know the
probability that the first 100 feet of paper in the next roll produced will have 0 defects.
The corollary of the statement tends that its not the Poisson experiment.
It is a statistical approach to follow properties that The experiment outcomes that can be opted as successes or failures. That gives a outcome in a specified region is known in average number of successes i.e. (μ).
The probability of a given task is not a Poisson experiment because the mean number of successful outcomes in its domain neither constant nor given.
Learn more about poisson experiment here:
https://brainly.com/question/17280826
#SPJ1
Need help pls..........................................
Answer:
6, -2
Step-by-step explanation:
basically It asks you what's x when y=2, which on the graph is 6, -2, and -5 I think. but there is no point on the -5 so we don't need to talk about that one.
Find the missing side of this right
triangle.
19
X
X =
16
✓[?]
Answer:
x = sqrt(105)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
16^2 + x^2 = 19^2
256 + x^2 = 361
x^2 = 361 -256
x^2 =105
Take the square root of each side
sqrt(x^2) = sqrt(105)
x = sqrt(105)
please help me...!!!???????????????????????????????????????????
Answer: C
Step-by-step explanation:
(rx+t)/s = w [given]rx+t = sw [multiply both sides by s]rx = sw-t [subract t from both sides]x = (sw-t)/r [divide both sides by r]An equation is formed of two equal expressions. The correct option is C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved for x as shown below, Therefore,
[tex]\dfrac{rx+t}{s} = w\\\\[/tex]
Using the multiplication property of equality, multiply s on both the sides of the equation,
rx + t = ws
using the subtraction property of equality, subtract t on both the sides of the equation,
rx = ws - t
[tex]x = \dfrac{sw-t+t}{r}[/tex]
Hence, the correct option is C.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
What is the distance from P to Q?
OA. 1 unit
OB. 7 units
OC. 5 units
D. 25 units
Answer:
C) 5 units
Step-by-step explanation:
In order to find the distance between points P and Q, we will be using the Distance Formula.
[tex]\sf \textsf{\underline{Distance Formula:}}\ \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given:
P (3, -1) Q (-1, -4)where:
⇒ x₁ = 3, y₁ = -1
⇒ x₂ = -1, y₂ = -4
Substitute these values into the formula:
[tex]\sf\\\implies d=\sqrt{(-1-3)^2+(-4-(-1))^2}\\\\\implies d=\sqrt{(-1-3)^2+(-4+1)^2}\\\\\implies d=\sqrt{(-4)^2+(-3)^2}\\\\\implies d=\sqrt{16+9}\\\\\implies d=\sqrt{25}\\\\\implies d=5[/tex]
The distance from P to Q is 5 units.
Learn more here:
brainly.com/question/21095661
Solve for all values of y
in simplest form.
∣y−12∣=16
Answer:
[tex]y=-4; y=28[/tex]
Step-by-step explanation:
The way I like to think about it, with absolute value meaning the distance is
"find which number are 16 apart from 12". Which means 28 (to the right) or -4 (to the left).
More formally, applying the definition of absolute value,
[tex]|y-12|=16 \leftrightarrow y-12=\pm16\\y-12=-16 \rightarrow y=-4\\y-12=+16 \rightarrow y=28[/tex]
