a. Constructing the exponential model:
The equation [tex]N(t) = A times Bt[/tex] can be used to depict an exponential functin.
N(t) is the number of flu cases at time t,
A is the number of cases at the beginning, and B is the current number of cases.
b. The exponential model for the number of flu cases is[tex]N(t) = 100 \times 1.8^t.[/tex]
c. Interpretation of part b results:
The exponential model predicts that at t = 5 weeks, there will be roughly 1863 flu cases in the town.
This demonstrates the flu's explosive proliferation during a five-week timeframe.
a. Building the exponential model:
An exponential function can be represented by the equation [tex]N(t) = A \times B^t,[/tex]
where N(t) is the number of flu cases at time t,
A is the initial number of cases,
B is the growth factor, and t is the time in weeks.
We know that N(0) = 100 and N(1) = 180.
First, we need to find the growth factor,
B. Using the data given:
[tex]100 \times B^0 = 100[/tex] (since t=0 is the week with 100 cases)
[tex]100 \times B^1 = 180[/tex] (since t=1 is the week with 180 cases)
From the first equation, we have A = 100.
From the second equation:
100 * B = 180
B = 180/100
B = 1.8
So, the exponential model for the number of flu cases is[tex]N(t) = 100 \times 1.8^t.[/tex]
b. Finding N(5):
Now we need to find the number of flu cases at t = 5 weeks using the model:
[tex]N(5) = 100 \times 1.8^5[/tex].
N(5) ≈ 1863.3
c. Interpretation of the result for part b:
At t = 5 weeks, there will be approximately 1863 flu cases in the town, according to the exponential model.
This shows the rapid growth of flu cases over a period of 5 weeks.
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Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
please help me make a sequence :)
PLEASE DONT DELETE MY QUESTION :(
Rule 1: Multiply by 2 then add 1 starting
( n x 2 +1) => 2n + 1
n is the position of our terms, so I substitute 1 because you're told to start from 1 which becomes our first term
2n + 1
2 x 1 + 1 =3
2 x 2 + 1 = 5
2 x 3 + 1 = 7
2 x 4 + 1 = 9
3,5,7,9....
(you can clearly see the sequence increasing by 2 each time, not following Multiply by 2 then add 1)
However, if we were to do add one each time, you'll add one to your pervious answer. So, this time I'll substitute the pervious answer
2 x 1 + 1 =3
2 x 3 + 1 = 7
2 x 7 + 1 = 15
2 x 15 + 1 = 31
3,7,15,31....
(from 3 to 7, you clearly see its multiplied by 2, then +1 & that's our sequence, this method apply to the second rule too of using previous)
Rule 2: Divide by 2 then add 4
(n ÷ 2 + 4) => n/2 + 4
n/2 + 4
(starting from 40.)
40/2 + 4 = 24
24/2 + 4 = 16
16/2 + 4 = 12
12/2 + 4 = 10
24,16,12,10.....
Answer: (started off with the number it asked of)
R 1 -
1,3,7,15,31....
(1 x 2 +1 does give 3)
R 2 -
40, 24,16,12,10.....
(40÷2 = 20, then + 4, gives 24)
Hope this helps!
Find the mixed number halfway between 6.4 and 6½. Give
your answer in its simplest form.
Answer:
6.45
Step-by-step explanation:
I am not staring at zero. I am starting at 6.4, so I take 6.4 and add that to half way between 6.5 and 6.4.
6.4 + 1/2(6.5-6.4) Combine in the parentheses
6.4 + 1/2(.5) Take half of .5
6.4 + .05 add
6.45
At a sale, dresses were sold for 61% of their original price. If the dresses originally cost $200 each, how much did a dress cost on sale?
The new cost of the dress on sale given the original price is $122
PercentageOriginal cost = $200New cost = 61% of original price
= 61/100 × $200
= 0.61 × 200
New cost = $122
Therefore, the new cost of the dress is $122
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Help please!!! Write an equation that represents the line.
Use exact numbers.
A new toy comes in the shape of a regular hexagonal pyramid. The base has side lengths of 10 inches and the apothem is 5√3 inches. If the surface area is 420 + 150√3 square inches, what is the slant height?
A. 11 inches
B. 14 inches
C. 7 inches
D. 28 inches
The slant height of the hexagonal pyramid is: B. 14 inches.
What is the Area of a Regular Hexagon?Area of a regular hexagon = 3√3/2(s²)
First, find the area of the regular hexagon:
Area = 3√3/2(s²) = 3√3/2(10²) = 150√3 in.².
Surface area is given as 420 + 150√3 in.².
Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150√3 - 150√3
Area of the 6 triangles = 420 in.²
Area of 1 triangle = 420/6 = 70 in.²
Use the area of a triangle to find the slant height (h):
70 = 1/2(10)(h)
2(70) = 10(h)
140/20 = h
h = 14 in.
The answer is B. 14 inches.
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Which equation represents a line that passes through the two points in the
table?
To get 14 liters of antifreeze solution, how much do i need to add to x liters of the solution?
To get 14 liters of antifreeze solution, add 14 - x liters of the solution
Calculating volumeFrom the question, we are to determine how many liters should be added to the solution
From the given information,
We are to get 14 liters of antifreeze solution,
and
we already have x liters of the solution
To get 14 liters of antifreeze solution, we will add 14 - x liters of the solution
Hence, to get 14 liters of antifreeze solution, add 14 - x liters of the solution
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After a robbery, a thief jumps into a taxi and disappears. An eyewitness on the crime scene is telling the police that the cab is yellow. In order to make sure that this testimony is worth something, the assistant district attorney makes a Bayesian analysis of the situation. After some research, he comes up with the following information: (1) In that particular city, 80% of taxis are black and 20% of taxis are yellow; and (2) Eyewitnesses are not always reliable and from past experience, it is expected that an eyewitness is 80% accurate. In other words, he will identify the color of a taxi accurately (yellow or black) eight out of ten times. What is the probability that the cab was really yellow, given that it was reported as being yellow
The probability that the cab was really yellow given that it was reported as being yellow is 0.32.
Given that there are 80% black taxis and 20% yellow taxis, witness is 80% accurate.
Probability is the chance of happening an event among all the events possible. It lies between 0 and 1. The value of probability can be calculated through the following formula:
Probability=Number of items/ total items.
Black taxis=80%
Yellow taxs=20%
Eyewitness is accurate=80%
Probability that the cab was really yellow=
P(X=Yellow)P(Witness is correct)+P(X=Black)P(Witness is incorrect)
Probability that car is black=0.8
Probability that car is yellow=0.2
Probability that witness is correct=0.8
Probability that witness is incorrect=1-0.8
=0.2
We have to just put the values in the formula given above.
Required probability=0.2*0.8+0.8*0.2
=0.16+0.16
=0.32
Hence the probability that the cab is really yellow is 0.32.
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make x the subject! urgent help
Answer:
[tex]x = \frac{n}{b - {t}^{2} } [/tex]
Step-by-step explanation:
I supposed that is a "n".
Steps as below:
[tex] {t}^{2} = b - \frac{n}{x} \\ b - \frac{n}{x} = {t}^{2} \\ - \frac{n}{x} = {t}^{2} - b \\ \frac{n}{x} = - ( {t}^{2} - b) \\ \frac{n}{x} = b - {t}^{2} \\ n = x(b - {t}^{2} ) \\ x(b - {t}^{2} ) = n \\ x = \frac{n}{b - {t}^{2} } [/tex]
Answer:
[tex]x = \frac{h}{b-t^2}[/tex]
Step-by-step explanation:
[tex]t^2 = b - \frac{h}{x}[/tex]
• First add [tex]\frac{h}{x}[/tex] to both sides:
⇒ [tex]\frac{h}{x} + t^2 = b[/tex]
• Now subtract [tex]t^2[/tex] from both sides:
⇒ [tex]\frac{h}{x} = b - t^2[/tex]
• Now multiply both sides by [tex]x[/tex] :
⇒ [tex]h = x(b - t^2)[/tex]
• Next divide both sides by [tex](b - t^2)[/tex] :
⇒ [tex]\frac{h}{b-t^2} = x[/tex]
∴ [tex]\boxed{x = \frac{h}{b-t^2}}[/tex]
What is the probability of rolling a 4, 5, and 6, in that order, on three rolls of a single six-sided die
Answer:
1:216
Step-by-step explanation:
The probability of getting a 4 would be 1/6. The probability of getting a 5 would be 1/6 and the probability of getting a 6 would be 1/6. The bottom number is the total number of outcomes (1,2,3,4,5,6) and the top number is out of that set, how many do I want. In the case of wanting a 4, I want 1 out of those 6 numbers and so on.
Now we multiple these together 1/6 x 1/6 x 1/6 and get 1/216 or another way to write this is 1:216
Read each question carefully and show work. Put your answer in the provided space.
solve for the balloon volume using the equation below
The volume of the balloon is 1441.64cm³.
How to calculate the volume?The radius of the balloon is given as 7cm. Also, the equation to calculate the volume is given as c³/6π²
The circumference c will be:
= 2πr = 2 × 22/7 × 7
= 44
The volume will be:
= c³/6π²
= 44³/(6 × 3.14²)
= 85284/(59.1576)
= 1441.64
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Draw a graph of Lin’s distance as a function of time for this situation:
Lin walked a half-mile to school at a constant rate. Five minutes after arriving at school, Lin realized that she had left her permission slip at home. Lin began sprinting home, but when she was halfway there she got tired and walked the rest of the way.
The graph of Lin's distance as a function of time cannot be a straight line graph because of decrease in speed.
Given that Lin walks half a mile at a constant rate i.e. Lin velocity is constant.
If the speed is low then the time will be high. If speed is high then the time will be low because of the following rule:
Speed=Distance/ time.
For the first five minutes the graph will be upward sloping because he was sprinting and his speed was high so he will cover much more distance.
But after five minutes the graph will be downward sloping as the speed becomes low and he willcover less distance.
Hence the graph of Line's distance will not look like linear curve.
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You can fine the run by subtracting the __ coordinate of the lead point from that of the right point
You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point.
The "slope formula" for a straight line connecting any two locations is another name for the rise over run formula. The rise is the difference between the y-coordinates of the two locations. The run is the difference between the x-coordinates of two locations. Divide the rise by the run to find the slope.
The rise over run formula is also known as the slope formula because the fraction consists of a rise, whether the line is moving up or down, divided by the run, which can be either left or right. The slope of the line dictates the direction of the line as well as its steepness.
Thus, "You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point".
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Can any one help me?
Answer:
64
Step-by-step explanation:
2x-4y=3
x= (3 +4y)/2
substitute into the main equation
y= 0
x= 3/2
16^x /256^y
16^3/2 ÷ 256^0
√16^3 ÷1
= 64
Answer:
64
Step-by-step explanation:
2x - 4y = 3
2x = 4y + 3
x = 2y + 1.5
[tex] \dfrac{16^x}{256^y} = [/tex]
[tex] = \dfrac{16^{2y + 1.5}}{256^y} [/tex]
[tex] = \dfrac{16^{2y + 1.5}}{16^{2y}} [/tex]
[tex] = 16^{2y + 1.5 - 2y} [/tex]
[tex] = 16^\frac{3}{2} [/tex]
[tex] = 4^3 [/tex]
[tex] = 64 [/tex]
There are 52 people in a room. What is the largest value of n such that the statement ""at least n people in this room have birthdays falling in the same month"" is always true?
The largest value of n such that the statement "at least n people in this room have birthdays falling in the same month" is always true is 5
How to determine the value
From the given information, we have 52 people in the room
Note that there are 12 months in a year
Let's divide the number by people by the months of the year
⇒ [tex]\frac{52}{12}[/tex]
⇒ 4 remaining 4
If 48 people are evenly distributed over twelve months, then there will be four people born in each month.
The remaining four people can be placed each in any of the twelve different months.
Hence, if 52 people are evenly distributed as possible, there will be eight months with four people and four months with five people.
Thus, the largest value of n such that the statement "at least n people in this room have birthdays falling in the same month" is always true is 5
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16. If x= y² + 12, what is the value of y in terms of (A)x+12 (B) x-12 (C) √√x+12 (D) √√x-12
Answer:
D. y = √(x - 12)
Step-by-step explanation:
x = y² + 12
y² = x - 12
y = √(x - 12)
During the current year mute corporation expected that sell 24,600 telephone switches. fixed cost of the year were expected to be 12,147,000 the unit sales price was budgeted at 3,500 and unit variable costs are budgeted at 1,680. minutes margin of safety in units is
The corporation's margin of safety is 0.73.
What is the margin of safety?Margin of safety is the amount of sales a company makes in excess of the breakeven point.
Margin of safety = (forecasted sales - break-even sales) / forecasted sales
Break even sales = fixed cost / (price per unit - variable cost)
12,147,000 / (3500 - 1680) = 6,674.18
Margin of safety = (24,600 - 6,674.18) / 24,600 = 0.73
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Select the correct answer.
If vector u = <-3.5, -1.5> and vector v = <-1.25, 2.25>, which graph shows the resulting vector for 2v - u?
The graph that aligns with the information is graph D.
How to illustrate the graph?We know that vector addition is scalar addition.
Given vectors are u = <-3.5, -1.5> and v = <-1.25, 2.25>
2v = < -2.5, 4.5>
2v - u = < -2.5, 4.5> - <-3.5, -1.5> = < -2.5 - (-3.5) , 4.5 -(-1.5) >
2v-u = < 1 , 6 >
This vector is basically i + 6j which is drawn in option D
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. A particular airline offers three free snack options to it's passengers: cookies, chips, and crackers. Along with the snack, passengers are offered two free drink options: soda or water. This is a tree diagram that represents the probability of customers choosing the different snack and drink options. Tree Diagram What is the value of Z
The probability that a particular passenger chooses chips and soda as a snack is 0.25 or 25%.
What is probability?In mathematics, probability is considered as the chances a specific situation or event occurs. For example, you can calculate the probability that it rains tomorrow based on general weather patterns.
How to calculate the probability of two events happenning?Calculate or identify the probability of each event happening.Multiply the probabilities of the events involved.What is the probability of Z event happnening?Probability that a person choses soda: 0.5Probability that a person choses chips: 0.5Now, let's multiply these probabilities:
0.5 x 0.5 = 0.25 or 25% (0.25 x 100)This means the probability of a passenger choosing chips and soda as a snack is 0.25 or 25%.
Note: This question is incomplete; here is the missing section:
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PlllZZZZZZZZ HELPPPPP
Answer:
x = 1.4
Step-by-step explanation:
Visualize the figure as a rectangle with width 4 and height 1 combined with a triangle with base 1 and height 1.
Next, use the Pythagorean Theorem, a^2 + b^2 = c^2. Variables a and b represent the lengths of the legs, in this case 1 and 1, and variable c represents the length of the hypotenuse, in this case x.
1^2 + 1^2 = x^2
2 = x^2
x = 1.41421356237
Step-by-step explanation:
imagine that this shape is the combination of 2 shapes :
1. a rectangle 4×1
it goes from the top down the side of 4 until the tilted line x begins.
2. a right-angled triangle
x being the Hypotenuse (the baseline opposite of the 90° angle). and the legs are the invisible line of 1 (going from the top right of x in parallel to the 1 line all the way to the 5 line) and the part of the 5 line below the 4 line : 5-4 = 1.
so, x can be solved by using Pythagoras
c² = a² + b²
c being the Hypotenuse, a and b are the legs.
x² = 1² + 1² = 2
x = sqrt(2) = 1.414213562... ≈ 1.4
Which function represents a reflection of f(x) = 2(0.35)x over the y-axis?
h(x) = 2(0.35)x
h(x) = –2(0.35)x
h(x) = 2(0.35)–x
h(x) = 2(–0.35)–x
The function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)
How to determine the reflection?The equation is given as:
f(x) = 2(0.35)^x
The reflection of a function over the y-axis is :
f'(x) = f(-x)
So, we have:
f(-x) = 2(0.35)^(-x)
From the list of options, we have
h(x) = 2(0.35)^(-x)
Hence, the function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)
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Can someone help me with this?
Subtract the matrices. What number fills in ?
The missing number for the subtraction of matrices is 4.
How to subtract the matrices?
The subtraction of two matrices of the same size is really direct. You just need to subtract the elements that are in the same position, then:
[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right] \\\\B = \left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]\\\\A - B = \left[\begin{array}{ccc}a_{11} - b_{11}&a_{12}-b_{12}\\a_{21} - b_{21}&a_{22}-b_{22}\end{array}\right][/tex]
Then the missing therm will just be equal to the difference between the last two elements of each matrix:
-2 - (-6) = -2 + 6 = 4
The missing number is 4.
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[please answer quickly] it takes 8 hours to paint a room. how long will it take to paint 2/3 of the room?
Answer:
5 hours 20 minutes.
Step-by-step explanation:
8 * 2/3
= 16/3
= 5 1/3
= 5 hours 20 minutes.
Determine the unknown value in the table using the constant of proportionality.
Time (seconds) 12 18 40
Number of Pencils Produced 42 63
The unknown value in the table using the constant of proportionality is; 96
How to find the constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.
We are given the coordinates;
(12, 42), (18, 63), (40, y)
where x-values represents time in seconds and y-values represents number of pencils that were produced.
To find the constant of proportionality is as good as finding the slope between two consecutive points as;
m = (63 - 18)/(42 - 12)
m = (45/30)
m = 1.5
Thus to find the unknown value y, we will use the formula;
(y - y1)/x - x1) = m
So we will use the coordinates; (18, 63), (40, y)
Plugging them into the formula above will result in;
(y - 63)/(40 - 18) = 1.5
y - 63 = 1.5 * 22
y - 63 = 33
y = 33 + 63
y = 96
Thus, we can conclude that using the constant of proportionality, the number of pencils that were produced after a time of 40 seconds is 96 pencils.
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HALP PLS
what is x?
x =x=x, equals
^\circ
∘
degrees
Answer:
x = 90°
Step-by-step explanation:
The line that contains angle x and the 90° angle is a straight line.
A straight line measures as 180°.
So, subtracting the given 90° from the 180° line that the two angles share, we would get the measure of x.
[tex]180-90 =x[/tex]
Which means, [tex]x=90[/tex].
So the value of x is 90°.
if 4200 men have sufficient food for 32 days at the rate of 12 hectogram per person , how many men may leave so that the same food is sufficient for 42 days at the rate of 16 hectogram per person
Using proportions, it is found that 66 men can leave so there will still be enough food.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the situation described, the rule of three is given as follows:
4200 men - 32 days - 12 hectogram per person.
x men - 42 days - 16 hectogram per person.
Considering that the amount per person and the number of people is inverse proportional, we have that:
[tex]\frac{4200}{x} = \frac{32}{42} \times \frac{16}{12}[/tex]
[tex]\frac{4200}{x} = \frac{512}{504}[/tex]
Applying cross multiplication:
512x = 504 x 4200
x = 504 x 4200/512
x = 4134.
The amount of men that can leave is:
4200 - 4134 = 66.
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simplify: 2y(y2-4y+1)-2(4y²+5y-2) +5y-8
please tell me fast with full solution
Answer:
look the answer is in the picture and don't forget to like and brainlest
Enacting a modeled response depends on your ability to reproduce the response by converting your stored mental images into overt behavior.
Answer:
??
Step-by-step explanation: