Answer: 0.1010052
Step-by-step explanation:
Given : Significance level : [tex]\alpha=0.01[/tex]
Alternative hypothesis : [tex]H_1:\ p\neq\dfrac{3}{4}[/tex]
The test statistic value : [tex]z=-1.64[/tex]
Since , the alternative hypothesis is two-tailed, so the test is a two-tailed test.
Using standard normal distribution table for z, we have
The P-value of two-tailed test will be :-
[tex]2P(z>|-1.64|)=2P(z>1.64)\\\\=2(1-P(z\leq1.64))\\\\=2(1-0.9494974)\\\\=0.1010052[/tex]
Hence, the P-value = 0.1010052
What is the exact distance between point e and point f
Answer:
The answer to your question is: d = √73
Step-by-step explanation:
data
Point E (-3, 4)
Point F (5, 1)
Formula
d = √((x2-x1)² + (y2-y1)²)
d = √(5-(-3))² + (1-4)²) substitution
d= √ (5+3)² + (-3)² simplify
d= √ 8² + -3²
d = √ 64 + 9
d = √73 result
The distance between points E(5,1) and F(-3,4) in coordinate geometry is calculated by using the distance formula derived from the Pythagorean theorem. The computed distance between points E and F comes out to be √73 units.
Explanation:The subject of this question is the distance formula in coordinate geometry, specifically between two points E(5, 1) and F(-3, 4). The formula is derived from the Pythagorean theorem and is represented as: D = √[(x₂ - x₁)² + (y₂ - y₁)²]. It is used to determine the simplest distance or 'path' between two points in a coordinate plane.
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of E and F, we have:
distance = √((-3 - 5)^2 + (4 - 1)^2)
distance = √((-8)^2 + (3)^2)
distance = √(64 + 9)
distance = √73
So, the exact distance between point E and point F is approximately √73 units.
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The complete question is given below:
What is the exact distance between point E and point F. The coordinates are E(5, 1) and F(-3, 4).
Anyone know this Geometry problem?
Answer:
ST = 20
Step-by-step explanation:
RT is the sum of RS and ST
Replacing with length you get:
17 + x + 6 = 3x - 56
17 + 6 + 5 = 3x - x
28 = 2x
14 = x
ST = x + 6 = 14 + 6 = 20
Can someone help me
Answer:
6
Step-by-step explanation:
In a square, all diagonals, vertices, sides, and angles are congruent, and since 36 is its area, take the square root of 36, giving you 6.
* When we are talking about length, we want the NON-NEGATIVE root.
I am joyous to assist you anytime.
Find the following area of the following region, expressing your result in terms of the positive integer n\geq2.
The region bounded by f(x)=x and g(x)= x1/n , for x\geq 0
The area of the region in terms of n is_____???
The two region under whose we have to find area is
f(x)=x
[tex]g(x)=x^{\frac{1}{n}}\\\\x \geq 0\\\\n\geq 2[/tex]
The Point of Intersection of two curves is always , x=0 and x=1.
Area of the Region
=Area under the line - Area Under the curve g(x), when n take different value, that is ≥2.
[tex]\rightarrow[- \int\limits^1_0 {x} \, dx + \int\limits^1_0 {x^{\frac{1}{2}} \, dx]+[ -\int\limits^1_0 {x} \, dx + \int\limits^1_0 {x^{\frac{1}{3}} \, dx]+[ -\int\limits^1_0 {x} \, dx + \int\limits^1_0 {x^{\frac{1}{4}} \, dx]+[ -\int\limits^1_0 {x} \, dx + \int\limits^1_0 {x^{\frac{1}{5}} \, dx]+......[/tex]
[tex]=\int\limits^1_0({x^{\frac{1}{2}}+x^{\frac{1}{3}}+x^{\frac{1}{4}}+x^{\frac{1}{5}}+.......+x^{\frac{1}{200}}}) \, dx -\int\limits^1_0 ({x}+{x}+{x}+{x}...........+200\text{times}) \, dx[/tex]
When, n=200, the first quadrant is completely occupied by the curve
[tex]g(x)=x^{\frac{1}{n}},x\geq 0\\\\2\leq n \leq 200[/tex]
[tex]=\int\limits^1_0{x^{\frac{1}{n}} \, dx=\frac{n\times x^{(\frac{1}{n}+1)}}{n+1}\left \{ {{x=1} \atop {x=0}} \right.}\\\\= \frac{n}{n+1}\\\\\int\limits^1_0{x^{n} \, dx=\frac{x^{n+1}}{n+1}\left \{ {{x=1} \atop {x=0}} \right.}\\\\=\frac{1}{n+1}[/tex]
[tex]=\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+...........+\frac{200}{201}-199 \times \frac{1}{2}\\\\=1-\frac{1}{3}+1-\frac{1}{4}+1-\frac{1}{5}+...........+1-\frac{1}{201}-99.5\\\\=199-99.5+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...........+\frac{1}{201}\\\\=99.5+1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...........+\frac{1}{201}-1-\frac{1}{2}\\\\=98+\frac{1}{d} \times\ln(\frac{2a+(2n-1)d}{2a-d})\\\\=98+\ln(\frac{2 \times 1+(2\times 201-1)\times 1}{2\times 1-1})\\\\=98+\ln 403\\\\=98+6({\text{approx}})\\\\=104 \text{square units}[/tex]
Sum of n terms of Harmonic Progression is
[tex]=\frac{1}{a}+\frac{1}{a+d}+\frac{1}{a+2d}+\frac{1}{a+3d}+\frac{1}{a+4d}.....+\frac{1}{a+(n-1)d}\\\\=\frac{1}{d} \times \ln(\frac{2a+(2n-1)d}{2a-d})[/tex]
Please help me out with this!!!!!!!!!!!!
Answer:
y = - [tex]\frac{3}{4}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (4, 0) ← 2points on the line
m = [tex]\frac{0-3}{4-0}[/tex] = - [tex]\frac{3}{4}[/tex]
Note the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = - [tex]\frac{3}{4}[/tex] x + 3 ← equation of line
What is the simplest form of the expression (5x + 3xy + 4y) + (4x – 2xy – 2y)? A. x + xy + 2y B. x2 + xy + 2y C. 9x + 5xy + 2y D. 9x + 5xy + 6y E. 9x + xy + 2y
2. 5y + 2z + 3x2 – (2y – 2z + 4x) is equivalent to: F. 7y + 4z + 3x2 – 4x G. 3y + 3x2 – 4x H. 3y + 4z + 3x2 – 4x J. 3y + 4z + 7x K. 3y + 4z + 7x2
3. Which of the following polynomials is equivalent to (x – 1)(x + 1)(x – 1)? A. x2 – x + 1 B. x2 – x – 1 C. x3 – x2 – x + 1 D. x3 – x2 – x – 1 E. x3 – 2x2 – 2x + 1
4. What is the product (2a + 6)2? F. 2a2 + 12a + 36 G. 4a2 + 12a + 36 H. 4a2 + 36 J. 4a2 + 24a + 36 K. 4a2 – 36
5. Among the following arithmetic operations, which could the symbol ♣ represent given that the equation (6 ♣ 1)3 – (4 ♣ 1)2 = 200 is true? I. Subtraction II. Multiplication III. Division A. II only B. III only C. II and III only D. I and III only E. I, II, and III
Answer:
1). Option E
2). Option H
3). Option C
4). Option J
5). Option C
Step-by-step explanation:
1). (5x + 3xy + 4y) + (4x - 2xy - 2y)
= (5x + 4x) + (3xy - 2xy) + (4y - 2y)
= 9x + xy + 2y
Option E. is the answer.
2). 5y + 2z + 3x²- (2y - 2z + 4x)
= 5y - 2y - 4x + 2z + 2z + 3x²
= 3y - 4x + 4z + 3x²
Option H is the answer.
3). (x - 1)(x + 1)(x - 1)
= (x² - 1)(x - 1) [Since (a - b)(a + b) = a² - b²]
= x²(x - 1) - 1(x - 1)
= x³ - x² - x + 1
Option C is the answer.
4). (2a + 6)²
= 4a² + 24a + 36
[Since (a + b)² = a² - 2ab + b²]
Option J. is the answer.
5). For subtraction,
(6 - 1)³ - (4 - 1)²
= 5³ - 3²
= 125 - 9
= 116
But the result is 200 so operation subtraction is not the answer.
For Multiplication,
(6 × 1)³ - (4 × 1)²
= 6³ - 4²
= 216 - 16
= 200
For division,
(6 ÷ 1)³ - (4 ÷ 1)²
= 6³ - 4²
= 216 - 16
= 200
Therefore, Option C. is the answer.
A truck can be rented from Company A for $130 a day plus $0.20 per mile. Company B charges $70 a day plus $0.30 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
130+x/5=70+3x/10 x=400
For school photos, 1/5 of the students choose to have a blue background. 2/5 of the students chose to have purple and 1/5 chose to have a gray background. What portions of the students choose to have another background
Answer:
1/5 is the answer
Step-by-step explanation:
1/5 had blue
2/5 had purple
1/5 had gray
add those together you get 4/5
leaving you with 1/5 who chose different backgrounds.
A drawer contains 22 black socks and 22 white socks. If the light is off and Matt reaches into the drawer to get his socks, what is the minimum number of socks he must pull out in order to be sure that he has a matching pair?
Answer: At least 3
Step-by-step explanation:
Lets solve this problem by the pidgeon hole principle. Suppose that Matt pulls out 2 socks, if he gets a matching pair then he is done and that's it. But now suppose that he gets one black sock and one white sock, if he then pulls out a third sock it will be either white or black, in either case he would have gotten with a 100% certainty a matching pair, since he already has a black and a white sock. So the minimum number to ensure he gets a matching pair is 3 socks.
Solve for y.
byl – 19 =-15
If there is more than one solution, separate them with commas,
If there is no solution, click on "No solution".
Answer:
Solution: -4, 4
Step-by-step explanation:
You need to do 2 cases:
Case 1: [tex]y\geq 0[/tex]
[tex]When\ y\geq 0 => | y | = y[/tex]
y - 19 = -15
y = 19 - 15
y = 4
Case 2: [tex]y< 0[/tex]
[tex]When\ y < 0 => |y| = -y[/tex]
-y -19 = -15
-19 + 15 = y
-4 = y
Both are solutions of the equation.
Answer:
-4, 4 would be your answer
Step-by-step explanation:
In a study of factors that might affect memory, research participants were assigned to drink either an alcoholic or a nonalcoholic beverage prior to completing a memory test. Those who drank the nonalcoholic beverage were assigned to the group. A) survey B) control C) experimental D) correlational
Answer:
Answer is B) control group
Step-by-step explanation:
Survey is when you ask questions to a group of people. Has nothing to do in this case. Correlational does not exist but correlation means the association between two groups.
In an experiment, you apply a treatment, or a conditions that differentiates groups and measure an outcome . In this case the treatment is drinking alcohol to measure memory. The group that receives the treatment is the experimental group and the one that not receives the treatment is the control because, we are comparing or controlling alcohol consumption in this group to measure differences in memory with the experimental group.
Don’t Forget the Rules – look them up if you have to. Answer the following with "always", "sometimes", or "never":
• Non-zero digits are ________________ significant.
• Zeros between two significant digits are __________________ significant. (I like to call these "sandwich zeros")
• Leading zeros, (zeros to the left of the first non-zero digit) are ____________________ significant.
• Trailing zeros, (zeros to the right of the last non-zero digit) are ____________________ significant if they are in a number with a decimal point.
Answer:
alwaysalwaysneveralwaysStep-by-step explanation:
As the problem statement suggests, look up the rules if you have to.
In the case of trailing zeros, the decimal point makes them significant.
__
In a number without a decimal point, such as 300, the zeros are sometimes significant. (Different authors may tell you the zeros are never significant in such a number. The problem comes when, for example, you're trying to represent 296 rounded to the nearest 10. That is 30. tens--with 2 significant digits, just as 286 rounded to the nearest 10 would be 290--with 2 significant digits. In some numbers, you cannot tell the difference between a 0 that is a placeholder and a 0 that is present because the value of the number cannot be represented exactly any other way.)
-100,-200,0,-25,30 in order from least to greatest
-200,-100,-25,0,30
Step-by-step explanation:
negatives will always be less than positives with negatives you put greatest to least and then 0 and then positives from least to greatest
In order to get the answer you have to remember that bigger negatives are actually less then smaller negatives so -200 would be less then -25.
[tex]-100, -200, 0, -25, 30[/tex]
[tex]-200 < -100[/tex]
[tex]-100 <-25[/tex]
[tex]-25 < 0[/tex]
[tex]0 <30[/tex]
[tex]= -200,-100,-25,0,30[/tex]
Therefore your answer is "-200,-100,-25,0,30."
Hope this helps.
In a basic sine curve, where can the zeros NOT be found?
Answer:
At the maxium point
Step-by-step explanation:
A maxium point is a point where the function gets the higher value. For example, in the basic sine curve, we can find a maxium point when [tex]x=\frac{\pi }{2}[/tex]. We won't find any maxium point when x=0.
As you can see on the graph I attached, the zeros of a basic sine curve (or, said in other words, the points were x=0), are at the beginning, ath the middle and at the end of the function's graphic.
Which is the definition of a line segment? A) A line segment consists of two points and all points in between. B) A line segment is a set of points that extend infinitely far in one direction. C) A line segment is a set of points that extend infinitely far in both directions. D) A line segment is the set of points in a plane that are equidistant from a given point.
Answer:
A.A line segment consist of two points and all points in between .
Step-by-step explanation:
Definition of a line segment : It is a portion of a line .It has two end points and all point contain between them.It is shortest distance between two points.
A.A line segment consist of two points and all points in between .
By definition of a line is is true.
Hence, option A is true.
B.A line segment is a set of a points that extend infinitely far in one direction.
No, line segment can not be extend infinitely in any direction.
Therefore, option is false.
C.A line segment is a set of points that extend far in both directions.
No, by definition of line segment , it is false.
D.A line segments is the set of points in a plane that are equidistant from a given point.
By definition of line segment , it is false.
Mr.Nolan's code for his ATM card is a four digit number. The digits of the code are the prime factors of 84 listed from least to greatest. What is the code for Mr.Nolan's ATM card?
Answer:
2237
Step-by-step explanation:
84 = 2·2·3·7 . . . . . . prime factorization
Find the value of N such that each expression is a perfect square trinomial for each of the following questions
1) p^2 - 6p + n
2) m^2 - 8m + n
3) v^2 + 24v + n
4) y^2 - 40y + n
5) v^2 - 36w + n
Answer:
The answers are below
Step-by-step explanation:
1) p² - 6p + n = p² - 6p + (3)² = (p-3)² n = 9
2) m² - 8m + n = m² - 8m + (4)² = (m-4)² n= 16
3) v² + 24v + n = v² + 24v + (12)² = (v + 12)² n=144
4) y² - 40y + n = y² - 40y + (20)² = (y - 20)² n= 400
5) v² - 36w + n = v² - 36w + (18)² = (v - 18)² n = 324
Chef Andy needed to adapt his recipes for his European kitchen staff in Paris. He was 1-pound portions of entrecote, 2 ounces of Béarnaise, and 4 ounces of asparagus. What are the metric conversions of each of these items?
Answer:
1 pound = 0.454 kilograms
1 ounce = 0.0296 liters
1 ounce = 0.0283 kilograms
Step-by-step explanation:
You need to convert the quantities to their corresponding unit.
Convert pounds to kilograms (For the entrecote)
1 pound = 0.454 kilograms
Thus, 1 pound of entrecote = 0.454 kilograms
Ounces to liters (for the Béarnaise, since it is a liquid)
1 ounce = 0.0296 liters
2 ounces of Béarnaise = 0.0592 liters
Ounces to kilograms (for the asparagus)
1 ounce = 0.0283 kilograms
4 ounces of asparagus =0.1132 kilograms
By using unit conversion and dimensional analysis, the 1 pound of entrecôte converts to roughly 0.4536 kg, 2 ounces of Béarnaise to around 56.7 grams, and 4 ounces of asparagus to approximately 113.4 grams.
Explanation:To answer your question about Chef Andy and his need to convert his recipes to metric units for his European kitchen staff, we'll need to follow some simple unit conversion steps:
Firstly, to convert 1 pound of entrecote to kilograms, you should know that 1 pound is approximately equivalent to 0.4536 kilograms. So, Chef Andy's 1-pound portion of entrecote is roughly 0.4536 kg in the metric system.As for the 2 ounces of Béarnaise, 1 ounce is about 28.3495 grams. Multiply this by 2 and the result is the conversion for the Béarnaise sauce: around 56.7 grams.For the 4 ounces of asparagus, we do the same as with the Béarnaise. 1 ounce is about 28.3495 grams. Multiplying this by 4, we see that 4 ounces is approximately 113.4 grams.By unit conversion and dimensional analysis, these are the metric conversions for each of those items. It's an essential method in fields like science, math, and of course, international cooking, where one often needs to convert from one type of unit to another.
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Una compañía de telefonía móvil en expansión ha gestionado durante el trimestre que finaliza ochocientas cincuenta mil llamadas al día. En el próximo trimstre espera llegar al millón e ir aumetado trimestralmente en la misma cantidad durante los próximos dos años. ¿Cuántas llamadas diarias espera gestionar dentro de dos años?
Answer:
[tex]2,050,000\ daily\ calls[/tex]
Step-by-step explanation:
The question in English is
An expanding mobile phone company handled eight hundred and fifty thousand calls a day during the quarter. In the next quarter it expects to reach one million and increase quarterly by the same amount over the next two years. How many daily calls do you expect to handle in two years?
Let
x ----> the number of quarter
y ---> number of daily calls
we know that
we have the points
(0,850,000) and (1,1,000,000)
Find the slope m
[tex]m=(1,000,000-850,000)/(1-0)=150,000\ daily\ calls[/tex]
The linear equation that represent this situation is
[tex]y=150,000x+850,000[/tex]
How many daily calls do you expect to handle in two years?
In two years there are 8 quarterly
so
For x=8
substitute
[tex]y=150,000(8)+850,000=2,050,000\ daily\ calls[/tex]
A group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 had been tagged. Using this ratio, how many trout would be estimated to be in the lake?
Answer:
264.
Step-by-step explanation:
Let x represent the number of trout in the lake.
We have been given that a group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 had been tagged.
Using proportions, we will get:
[tex]\frac{\text{Total trouts}}{\text{Tagged trouts}}=\frac{48}{22}[/tex]
[tex]\frac{x}{121}=\frac{48}{22}[/tex]
[tex]\frac{x}{121}*121=\frac{48}{22}*121[/tex]
[tex]x=\frac{24}{11}*121[/tex]
[tex]x=24*11[/tex]
[tex]x=264[/tex]
Therefore, there would be approximately 264 trout in the lake.
264 trouts are estimated to be in the lake.
Using proportion, we write: Tagged trout/Total Trout
This becomes 22/48.
In order to use cross multiplication, we write another fraction using x, the total number of trout in the lake: 121/x.
Now we have 121/x=22/48.
We cross multiply.
121*48=22x.
(121*48)/22 becomes:
264.
Suppose you need to deliver 40 terabytes of data to your co-workers in Atlanta (200 km). You have an available 100 Mbps dedicated link for data transfer. Alternatively, your friend raises homing pigeons and would be willing to let you borrow one. You have a single 1 TB SD card you can strap to the pigeon. Assume pigeons can fly 1000 km per day and that it takes no time to copy to/from the SD card.
Answer: All data will be sent in 89.39 hours
Step-by-step explanation:
Data transfer rate: 100 Mbps=100 [tex]\frac{Mb}{s}[/tex] ×[tex]\frac{1Tb}{1024^{2} Mb}[/tex]×[tex]\frac{3600s}{h}[/tex]=0.3433 [tex]\frac{Tb}{h}[/tex]
The pigeon can fly 1000 km/day and it needs to fly 400 km (round trip).
Pigeon rate: [tex]\frac{1000km}{24h}[/tex]=41.67 [tex]\frac{km}{h}[/tex]
Time of round trip: 400 km÷[tex]\frac{1000km}{24h}[/tex]=9.6 h
So the pigeon can send 1 Tb every 9.6 hours.
If we sum the rates we can get the time for sending all the data:
40 Tb= (0.3433 Tb/h + 1 Tb/9.6h)×t
T= 89.39 hours
He bought a boat for 24000 in the year 2009. The value of the boat depreciated linearly. If the value of the boat in 2010 was 18500,what was the annual rate of change of the boats value?
Answer:
-$5,500
Step-by-step explanation:
The change in the one year from 2009 to 2010 was ...
18,500 -24,000 = -5,500
The annual rate of change in the boat's value was -$5,500.
Thus, the annual rate of change of the boat's value is $5,500 per year.
To find the annual rate of change of the boat's value, we need to determine how much the value decreased from 2009 to 2010 and then calculate the yearly decrease. The boat's value in 2009 was $24,000; in 2010, it was $18,500.
First, calculate the decrease in the boat's value from 2009 to 2010:
Decrease = Initial Value - Final Value
Decrease = $24,000 - $18,500 = $5,500
Since this decrease occurred over one year, the annual rate of change in the boat's value is $5,500 per year.
Therefore, the annual rate of change of the boat's value is $5,500 per year.
A data set includes the entries 2, 4, 5, 7, 7, and 10. Complete the data set with an entry between 1 and 10 so that the median and mode of the set are equal.
Answer:
It can be any digit between 7, 8 and 9.
Step-by-step explanation:
The given data set is: 2, 4, 5, 7, 7, 10
Here mode is 7, So we have to make our median equal to 7.
If one more data point will be included in the data set then we will have an odd number of observations.
For getting a median equal to 7 we have to add a number between 7 and 10 or it can be equal to 7.
Now, if we add any data points between 7, 8 and 9 then our median and mode will equal to 7.
Hence, the any one number between 7, 8 and 9 can be included in given data set to get both median and mean equal.
Further, the Median is the middle observation of the given data. It can be found by following steps:
Arranging data in ascending or descending order.
Taking the average of the middle two values if the total number of observations is even, and this average is our median.
or, if we odd number of observation then the most middle value is our median.
The mode is the observation which has a high number of repetitions (frequency).
The entry that should be added to the data set 2, 4, 5, 7, 7, and 10 to make the median and mode equal is 7. This is because the current mode is 7, and to have the median also equal to 7, a 7 must be added to the data set.
Explanation:The goal is to add an entry between 1 and 10 to your data set (which currently includes 2, 4, 5, 7, 7, and 10) that will make the median and mode equal. To start, let's understand what the median and mode are. The median is the middle value in an ordered data set. If there's an even number of values in the set, the median is the average of the two middle values. The mode, on the other hand, is the most frequent value or values in a data set.
In your original data set, the mode is 7, as it appears twice. Currently, with six numbers in the data set, the median would be the average of the 3rd and 4th numbers when ordered (5 and 7), so the median is 6. To match the mode (7), a 7 needs to be added to the data set. Now the median is (7 + 7) / 2 = 7, which matches the mode of 7. So, the number you need to add to your dataset to make the median and mode both equal 7 is 7.
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A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following exponential function:P(t)=1500/(1+7e^-0.4t)where t is the number of years from the time the species was added to the lake.Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary.
Initial population size is 188 and after 9 years we get 1259 fishes.
We have given that the function
[tex]P(t)=\frac{1500}{1+7e^(-0.04t)}[/tex]
Where t is the number of years from the time the species was added to the lake.
We have to find the initial population size of the species and the population size after 9 years.
where p(0) is the population size of species and p(9) is the population size after 9 years.
Therefore we have the given function is at t=0
[tex]P(0)=\frac{1500}{1+7e^(-0.04(0)))}=\frac{1500}{1+07e^0} \\=\frac{1500}{1+7} \\=\frac{1500}{8} \\=187.5\\=188[/tex]
at t=9 we have
[tex]P(9)=\frac{1500}{1+7ex^{-0.4(9)} }\\=\frac{1500}{1+7e^{-3.6} } \\=\frac{1500}{1.191}\\ =1259.16\\=1259 fishes[/tex]
Therefore after 9 years we get 1259 fishes.
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The initial population size of the species is approximately 188. After 9 years, the population size is approximately 1260.
To find the initial population size of the species, we need to evaluate the population function ( P(t) ) at ( t = 0 ).
Given the population function:
[tex]\[ P(t) = \frac{1500}{1 + 7e^{-0.4t}} \][/tex]
1. **Initial population size (( P(0) )):**
Substitute ( t = 0 ) into the function:
[tex]\[ P(0) = \frac{1500}{1 + 7e^{-0.4 \cdot 0}} \][/tex]
[tex]\[ P(0) = \frac{1500}{1 + 7e^0} \][/tex]
[tex]\[ P(0) = \frac{1500}{1 + 7 \cdot 1} \][/tex]
[tex]\[ P(0) = \frac{1500}{1 + 7} \][/tex]
[tex]\[ P(0) = \frac{1500}{8} \][/tex]
[tex]\[ P(0) = 187.5 \][/tex]
Round to the nearest whole number:
[tex]\[ P(0) \approx 188 \][/tex]
So, the initial population size is[tex]\( \boxed{188} \).[/tex]
2. **Population size after 9 years (( P(9) )):**
Substitute ( t = 9 ) into the function:
[tex]\[ P(9) = \frac{1500}{1 + 7e^{-0.4 \cdot 9}} \][/tex]
[tex]\[ P(9) = \frac{1500}{1 + 7e^{-3.6}} \][/tex]
Calculate [tex]\( e^{-3.6} \):[/tex]
[tex]\[ e^{-3.6} \approx 0.02732 \][/tex]
Substitute this value back into the equation:
[tex]\[ P(9) = \frac{1500}{1 + 7 \cdot 0.02732} \][/tex]
[tex]\[ P(9) = \frac{1500}{1 + 0.19124} \][/tex]
[tex]\[ P(9) = \frac{1500}{1.19124} \][/tex]
[tex]\[ P(9) \approx 1260 \][/tex]
Round to the nearest whole number:
[tex]\[ P(9) \approx \boxed{1260} \][/tex]
So, the population size after 9 years is [tex]\( \boxed{1260} \).[/tex]
Paolo buys a used car for $3,500 and wants to fill it up with gasoline. His gas tank holds 15 gallons and is currently empty. Paolo has $100. One gas station sells gas for $2.50 per gallon. The station across the street sells gas for $2.25 per gallon. What is the cheapest cost to fill up Paolo's tank?
Round your answer to the nearest hundredth. Leave the dollar sign off your answer, so for example if your answer is $10.25, write 10.25.
The cheapest cost to fill the Paolo's tank = $33.75
We have Paolo who bought a used car for $3,500 and wants to fill it up with gasoline. His gas tank holds 15 gallons and is currently empty. Paolo has $100. One gas station sells gas for $2.50 per gallon. The station across the street sells gas for $2.25 per gallon.
We have to determine the cheapest cost to fill up Paolo's tank.
What is mathematics important in Price Estimation ?The price estimation is important in mathematics as it helps us to create mathematical relations among the various factors on which the price depends in order to extract accurate results.
According to question, we have -
Cost of Car = $3500.
Car's gasoline capacity = 15 gallons.
Amount of money with Paolo = $100.
Cost of gas at station A = $2.25.
Cost of gas at station B = $2.50.
Case 1 - If Paolo goes to Station A
Total cost to fill the tank = 2.25 x 15 = $33.75
Case 2 - If Paolo goes to Station B
Total cost to fill the tank = 2.50 x 15 = $37.50
Hence, the cheapest cost to fill the Paolo's tank = $33.75
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Please help!!! step by step
Jane has been growing two bacteria farms. Bacteria farm Rod has a starting population of 2 bacteria, while Bacteria farm Sphere has a starting population of 8 bacteria. However, Jane starts growing Rod five hours before she starts growing Sphere. At 8 p.m., Jane checks her farms and finds that they have the exact same population. If the population of Rod doubles every hour, but the population of Sphere is quadrupled every hour, how many hours ago did she start growing Sphere?
Answer: Jane started growing Sphere 3 hours ago
Step-by-step explanation:
Farm Rod starting population (Rsp) = 2
Farm Sphere starting population (Ssp) = 8
Let´s name "Rh" the quantity of hours since Rod started growing, and
"Sh" the quantity of hours since Sphere started growing.
And, let´s name "R" the population of farm Rod at 8 p.m. and "S" the population of farm Sphere at 8 p.m.
Population of Rod doubles every hour, therefore:
R = [tex]Rsp * 2^{Rh}[/tex]
R = [tex]2(2^{Rh})[/tex]
Population of Sphere is quadrupled every hour, therefore:
S = [tex]Ssp * 4^{Rh}[/tex]
S = [tex]8(4^{Rh})[/tex]
At 8 p.m. Jane found that R = S
Therefore, at 8 p.m:
[tex]2(2^{Rh})[/tex] = [tex]8(4^{Sh})[/tex]
dividing both sides by 2
[tex]2^{Rh} =4(4^{Sh})[/tex]
adding exponents
[tex]2^{Rh} = 4^{Sh+1}[/tex]
[tex]2^{Rh} =2^{2^{Sh+1} }[/tex]
the bases are the same; exponents must be the same
Rh = 2Sh + 2 (equation 1)
And we also know that Jane started growing Rod five hours before Sphere:
Rh = Sh + 5 (equation 2)
Replacing equation 2 into equation 1:
(Sh + 5) = 2Sh + 2
5 - 2 = 2Sh - Sh
3 = Sh, or
Sh = 3
Jane started growing Sphere 3 hours ago.
Jane and Jill want their mom to ride the rollercoaster with them, but she thinks it will be too fast. She asks the girls to find out how fast the rollercoaster will be travelling. They find out that the speed of the rollercoaster, in miles per hour, is modeled by the function g(x) = x4 − 4x2 + 7x − 8, where x is time measured in seconds. How fast is the rollercoaster travelling at 2 seconds?
6 miles per hour
22 miles per hour
26 miles per hour
54 miles per hour
Answer:
6 mph
Step-by-step explanation:
g(x) = x^4 − 4x^2 + 7x − 8
when x = 2,
g(2) = (2)^4 - 4(2^2) + 7 (2) - 8
= 16 - 16 + 14 - 8
= 6 mph
Hey!
-----------------------------------------
Solution:
We know that 2 = x
g(x) = (2)^4 - 4(2)^2 + 7(2) - 8
g(x) = 16 - 16 + 14 - 8
g(x) = 0 + 14 - 8
g(x) = 14 - 8
g(x) = 6
-----------------------------------------
Answer:
6 miles per hour!
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Hope This Helped! Good Luck!
Ted brought a cooler containg 7.5 liters of water to a picnic.If 500 milliters of water milliliters of water are served to each person ,how many people can get water before the cooler is empty?
Answer:
Step-by-step explanation:
15 people can be served because a liter equals to 1000 milliliters and that means that 7 times two equals 14 plus the other 500 milliliters then that's 15.
15 people can get water before the cooler is empty.
In order to find the number of people who would be able to get water before the cooler empties, you need to divide the total quantity of water in the cooler by the quantity given to each person.
To do that, both quantities have to have the same unit. The liters should therefore be converted to milliliters.
1 liter = 1,000 milliliters
7.5 liters = 7.5 x 1,000
= 7,500 milliliters
The number of people that would get a drink is:
= Quantity of water in cooler / quantity of water per person
= 7,500 / 500
= 15 people
Find out more at https://brainly.com/question/17614855.
What is an algebraic expression to find the number of squares in the border of a 75x75 grid?
Answer:
Well, if the grip is 75 x 75, you can rule out that the grid is 75 squares in each border.
Step-by-step explanation:
75 x 75 = a x b
a= horizontal side lengths
b= vertical side lengths
Rule that a= 75 squares and b= 75 squares.