Answer:
P = 120*([tex]2^{2d-2}[/tex])P(8) = 1, 966, 080Step-by-step explanation:
Since the population quadruples each day, the population for the subsequent day would be 4*(population of the previous day).
Thus, the evolution of the population value takes the form of a geometric progression, with a common ratio, r = 4
The n-th term of a geometric progression is given by:
[tex]a_{n}[/tex] = [tex]ar^{n-1}[/tex] (1)
Where a is the 1st term of the progression.
From (1), our population would generally take the form:
[tex]P_{d}[/tex] = [tex]P_0r^{d-1}[/tex] (2)
In this case, the initial value (1st term) [tex]P_{0}[/tex] = 120.
So putting r and [tex]P_{0}[/tex] into (2):
P(d) = 120*([tex]4^{d-1}[/tex])
Noting that 4 = 2²:
P(d) = 120*([tex]2^{2(d-1)}[/tex])
P(d) = 120*([tex]2^{2d-2}[/tex])FOR d = 8:
P(d) = 120*([tex]2^{2d-2}[/tex])
becomes:
P(8) = 120*([tex]2^{2(8)-2}[/tex])
P(8) = 120*([tex]2^{16-2}[/tex])
P(8) = 120*([tex]2^{14}[/tex])
P(8) = 120*(16,384)
P(8) = 1, 966, 080There are 125 people in a sport centre.
59 people use the gym.
70 people use the swimming pool.
55 people use the track.
25 people use the gym and the pool.
30 people use the pool and the track.
17 people use the gym and the track.
6 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Probability that the person selected at random from the sport centre of 125 people is a fraction of 1/4 or 0.25.
Probability of an eventThe probability of an event is the fraction of the required number of outcome divided by the number of possible outcomes.
We shall determine the answer to the question as follows;
People in the sport centre = 125
People who used the 3 facilities = 6
People who accessed only gym = 59 - (6 + 11 + 19) = 26
People who accessed only track event = 55 - (6 + 11 + 24) = 14
People who accessed only swimming pool event = 70 - (6 + 19 + 24) = 21
People who accessed only gym and swimming pool events = 29 - 6 = 19
People who accessed only gym and track events = 17 - 6 = 11
People who accessed only swimming pool and track events = 30 - 6 = 24
Total number of people who accessed at least any one of the facilities = 121
The number of people who did not access any of the facility = 125 - 121 = 4, which is the number of possible outcomes for our required outcome.
Therefore, the probability that the person selected doesn't use any facility = 1/4
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Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb. How much does each weight now?
Using equations the weight of both Sean and Brad is 156 lbs and 73 lbs.
What do we mean by equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.as in 3x + 5 = 15, for example.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary forms of linear equations are point-slope, standard, and slope-intercept.
So, the weight of Sean and Brad.
Let, Brad, be 'x'.Then Sean be '2x + 10'So, the equation will become:
x + 2x + 10 = 230
Now, solve this equation for 'x' as follows:
x + 2x + 10 = 2303x = 230 - 103x = 220x = 220/3x = 73.33Rounding off: 73 lbs
Then,
Brad weights ⇒ 73 lbsSean weights ⇒ 2(73) + 10 = 156 lbsTherefore, using equations the weight of both Sean and Brad is 156 lbs and 73 lbs.
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Can someone please help answer the attached?
The variables we need to use in the question are defined. We will call the price of a knife as [tex]k[/tex] and the price of a spoon as [tex]s[/tex].
The total price of [tex]12[/tex] spoons and [tex]16[/tex] knives is then given. Let's write knives instead of [tex]4[/tex] spoons.
[tex]12s+16k=105.64[/tex][tex]3k+16k=105.64[/tex][tex]k=5.56[/tex] per knife.===================================================
Explanation:
k = cost of one knife
s = cost of one spoon
costs are in pounds
12s = cost of 12 spoons
16k = cost of 16 knives
12s+16k = 105.64 pounds is the total cost
We can replace k with 4s because of the phrasing "a knife is 4 times the cost of a spoon". Whatever s might be, quadruple it and it leads us to the value of k.
So,
12s+16k = 105.64
12s+16(4s) = 105.64
12s+64s = 105.64
76s = 105.64
s = 105.64/76
s = 1.39 pounds is the cost of one spoon
k = 4s = 4*1.39 = 5.56 pounds is the cost of one knife
----------------------
Check:
1 spoon = 1.39 pounds
12 spoons = 12*1.39 = 16.68 pounds
1 knife = 5.56 pounds
16 knives = 16*5.56 = 88.96 pounds
12 spoons + 16 knives = 16.68+88.96 = 105.64 pounds total
This fully verifies the answer.
what is the doubling timefor this population of alligators ?
3 years
Explanations:The given function representing the population of alligators is:
[tex]P(t)\text{ = (}319)2^{\frac{t}{3}}[/tex]Find the intial population at t = 0
[tex]\begin{gathered} P(0)\text{ = 319 }\times2^0 \\ P(0)\text{ = 319 }\times\text{ 1} \\ P(0)\text{ }=\text{ 319} \end{gathered}[/tex]The population will double when:
P(t) = 319 x 2
P(t) = 638
The doubling time is the value of t at which P(t) = 638
[tex]\begin{gathered} P(t)\text{ = 319 }\times2^{\frac{t}{3}} \\ 638\text{ = 319 }\times2^{\frac{t}{3}} \\ \frac{638}{319}=2^{\frac{t}{3}} \\ 2\text{ }=2^{\frac{t}{3}} \\ 2^1=2^{\frac{t}{3}} \\ 1\text{ = }\frac{t}{3} \\ t\text{ = 3} \end{gathered}[/tex]The population will double after 3 years.
Therefore, the doubling-time for this population of alligators is 3 years
Even though I already got the question right,I need someone to show the work on how to get the answer for this question.
Given
Answer
[tex]\begin{gathered} \sin x=\frac{P}{H} \\ \sin x=\frac{5}{8.3} \\ x=\sin ^{-1}(\frac{5}{8.3}) \end{gathered}[/tex]Which is triangle 2
Find the area of ABC with verticles A(4,-3), B(9,-3) and C(10,-11)
Answer:
Step-by-step explanation:
The area of the triangle when the vertices of the triangle are given can be calculated by the following formula:
Area of triangle = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)| where the vertices are A(Ax, Ay), B(Bx, By), C(Cx, Cy)
Now, we have been given the values of vertices as A(4, -3) B(9,-3) , and C(10, −11)
Therefore,
By applying the formula and substituting the given values, we get
Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|
Area = 0.5 * |44|
Area = 22
Hence, the area of triangle ABC with the given vertices is 22 square units
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NEEED HELP PLSSSS . Find x in triangles Geometry.
Answer:
10) x = 76,12) x = 8, Perimeter = 77 units=========================
Question 10The triangle is isosceles as marked.
The two opposite angles of equal sides are equal, one of them is x and the angle in between them is 28°.
Use angle sum of the triangle:
2x + 28 = 1802x = 152x = 76Question 12Same as previous question, we have an isosceles triangle. Equal sides are:
3x + 5 = 5x - 115x - 3x = 5 + 112x = 16x = 8Find the perimeter by substituting the value of x:
P = 3*8 + 5 + 5*8 - 11 + 2*8 + 3 = 77 unitsVince and Wendy share $2000 in the ratio Vince : Wendy = 19 : 21. Calculate the amount of money that Vince receives
workout:
19+21=40
2000÷40=50
Vince=50×19=950
Wendy=50×21=1050
-u can check by adding 950+1050=2000 (which means the ratio is correct)
Answer:
(vince:wendy)= 950:1050
Answer:
V:W
19:21
19 + 21 = 40
19 over 40 × 200
Vince received $950
in the diagram below , the measure of arc SQ is 160 degrees and the measure of arc PR is 102 degrees . find the value of x .
Given:
The measure of angle of arrc SQ is 160°.
The measure of angle of arc PR is 102°.
The objective is to find the measure of angle x.
Since, the angle x is away from te center of the circle.
Then, the formula to find the value of angle x is,
[tex]x=\frac{PR+SQ}{2}[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} x=\frac{102+160}{2} \\ =\frac{262}{2} \\ =131\degree \end{gathered}[/tex]Hence, the value of x is 131°.
A survey was given to people who own a sertain car. What percent of the people surveyed were completely satisfied with the car
The percent of the people surveyed were completely satisfied with the car is 55%.
How to calculate the percentage?Number of people completely satisfied = 1155
Number of people somewhat satisfied = 755
Number of people not satisfied = 190
Total number of people = 1155 + 755 + 190 = 2100
Therefore, the percent of the people surveyed were completely satisfied with the car will be:
= Number of people completely satisfied / Total number of people × 100
= 1155 / 2100 × 100
= 55%
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Find the inverse of the given function.
5. f= {(1,3), (2,-5), (3,6)}
Check the picture below.
How many cups will stack to the top of the door frame?
Explain why...
Answer:
157 cups
Step-by-step explanation:
First, convert in to cm
83.375 in * 2.54 Cm/in = 211.77 cm
Each cup adds 1.3 cm to the (9.2 - 1.3 cm) base (Base is 7.9)
211.77 = 7.9 + 1.3 x X is the number of cups
X = 156.9 = ~ 157 cups
Please help, i really need help
Answer: m<1 = 146 degrees, m<3 =146 degrees, m<4 = 34 degrees
Step-by-step explanation:
Since m<2 and m<4 are vertical angles, they will be equal to each other.
By using straight lines, we can easily find out that m<1 = 180-34 = 146
Since m<1 and m<3 are vertical angles, they are equal to each other.
Hope this helped :))
Solve the following equation: 5(n + 2) = 3(1 + 2n)
Answer: n=7
Step-by-step explanation:
First distribute the numbers to get 5n+10=3+6n
Next Subtract 6n from both sides to get -n=10=3
Finally divide both sides my -1 to get rid of the -n to get n=7
Hope this helps :)
The midpoint of AB is M(0, -7). If the coordinates of A are (-2,-6), what arethe coordinates of B?Answer:Submit AnswerPASSA
Explanation:
The coordinates are given below are
[tex]\begin{gathered} A(-2,-6) \\ M(0,-7) \\ B=(x,y) \end{gathered}[/tex]The image is given below as
To calculate the coordinate of A,we will use the formula below
[tex]M=\frac{(x_1+x_2}{2},\frac{y_1+y_1}{2})[/tex]By substituting the values, we will have
[tex]\begin{gathered} M=\frac{x_1+x_2}{2},\frac{y_{1}+y_{1}}{2} \\ (0,-7)=\frac{-2+x)}{2},(\frac{-6+y}{2}) \\ \frac{-2+x}{2}=0,\frac{6+y}{2}=-7 \\ -2+x=0,6+y=-14 \\ x=2,y=-14+6 \\ x=2,y=-8 \end{gathered}[/tex]Hence,
The coordinate of B will be
[tex]B=(2,-8)[/tex]I'm in a rush and need help on this one
4.
The volume of a cube equals its side cubed. Since the side of the cube is 12ft long, then its volume is given by:
[tex]V=(12ft)^3=1728ft^3[/tex]Then, the volume of the cube, is:
[tex]1728ft^3[/tex]5.
The volume of the prism equals the product of each of its dimensions. Then:
[tex]V=(7m)(2m)(3m)=42m^3[/tex]Then, the volume of the rectangular prism, is:
[tex]42m^3[/tex]Please help!! Math is not my cup of tea and I’m really struggling!! ASAP
Given the function:
f(x)=x²-3x - 4
Find the following values.
a) f(2)
f(2)=
b) f(4)
ƒ(4)=
c) f(-3)
ƒ(-3) =
The values of f(2), f(4) and f(-3) for the function, f(x) = [tex]x^{2} -3x-4[/tex], are -6, 0 and 14 respectively.
According to the question,
We have the following information:
f(x) = [tex]x^{2} -3x-4[/tex]
Now, to find the values of each function we will put the values in place of x.
We will find the value of f(2) by putting 2 in place of x.
f(2) = [tex](2)^{2} -3(2)-4[/tex]
f(2) = 4-6-4
f(2) = -2-4
f(2) = -6
(We know that the numbers with negative sign are added but the result always remains in negative.)
We will find the value of f(4) by putting 4 in place of x:
f(4) = [tex](4)^{2} -3(4)-4[/tex]
f(4) = 16-12-4
f(4) = 4-4
f(4) = 0
Now, we will find the value of f(-3) by putting -3 in place of x:
f(-3) = [tex](-3)^{2} -3(-3)-4[/tex]
f(-3) = 9+9-4
f(-3) = 18-4
f(-3) = 14
Hence, the values of f(2), f(4) and f(-3) are -6, 0 and 14 respectively.
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Write two hundred thousand and
Seventeen in figures
Answer:
200,017
Step-by-step explanation:
2 at the front for 200,000 , and then you have 17 which are the last 2 digits
Your mom Paid $8 for 10 Granny Smithapples and bought 15 Golden Delicious at60 cents an apple. What is her average costper apple?
First, let's find the total cost of all the apples:
[tex]8+(0.6\cdot15)=17[/tex]Now, we divide this by the total amount of apples bought. In our case, we know that there were 10 Granny Smith apples and 15 Golden Delicious, for a total of 25 apples.
[tex]\frac{17}{25}\rightarrow0.68[/tex]Therfore, we can conclude that the average cost per apple was $0.68
what is the formula to find the circumference of a circle?
Answer:
C = 2 \pi r
Step-by-step explanation:
Alysa buys 23 boxes of toothpicks. There are 255 toothpicks in each box. Which equation and solution show the number toothpicks, t, in all the boxes?
Answer:
255 ^t because the amount if toothpicks depend on the number of boxes she/he gets.
In the figure shown below, all the corners form right angles. What is the area of the figure?
15 ft
B.
44 ft²
17 ft
215 ft2
5 ft
7 ft
Based on the dimensions of the shape, the area of the figure can be found to be 215 ft².
How to find the area of the figure?To find the area of the figure, you can divide the shape into two different shapes and then find the area of those shapes, and then sum them up to find the area of the entire figure.
As shown in the attached photo, you can divide the figure into two rectangles with the dimensions:
15 ft and 12 ft (17 - 5)7 ft and 5 ftThe areas are:
= 15 x 12
= 180 ft²
Second rectangle:
= 7 x 5
= 35ft²
The area of the figure is:
= 35 + 180
= 215 ft²
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Which of the following statements is true about the graph shown?
The equation y = 4.5x is correctly represented by the graph.
The graph is incorrect and the line should go through the point (3, 13.5).
The graph is incorrect and the line should go through the point (4.5, 4.5).
The graph does not show a proportional relationship
Answer: A
Step-by-step explanation:
Let f(x) = 2x + 8, 9(x) = x2 + 2x – 8, and h(x) = 3x - 6. Perform the indicated operation. (Simplify as far as possible.) (h. f)(3) = =
x=3
[tex]\begin{gathered} 6\cdot3^2+12\cdot3-48 \\ 6\cdot9+36-48 \\ 54+36-48=42 \end{gathered}[/tex]A function is a fifth-degree polynomial. how many turning points can it have? exactly four exactly five four or less five or less
A fifth-degree polynomial function can have five turning points in its graph.
What is a quintic function?In other terms, a polynomial of degree 5 defines a quintic function. When graphed, normal quintic functions resemble normal cubic functions since they have an odd degree, with the possible exception that they might contain an extra local maximum and/or local minimum. 9x5– 2x + 3x4– 2 – A leading term to the fifth degree and a term to the fourth degree are both included in this four-term polynomial. It is known as a polynomial of fifth degree.The given polynomial must be factored as much as feasible in order to solve a polynomial equation of degree 5. We can solve for the variable after factoring by equating factors to zero.Examples of polynomials with degrees include the following: The degree of the polynomial 5x5+4x2-4x+3 is 5To learn more about quintic functions, refer
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Answer:
The correct is answer is option C: "four or less"
The answers to the next part of the question on Edge are options A and C :)
Step-by-step explanation:
Hope this helped!
Brainliest would be greatly appreciated - Have a great day :3
what do you divide by 15 to get to 9
Answer:
aproamitly 1.66666666667
Step-by-step explanation: 15/9=1.66666666667 thus
15/1.66666666667=9
Answer: it's 135 the other dude used a calculator probs
someone please help me!!!
Im going to answer for the first one.So angles 1 and 2 are corresponding angles and so they are equal because line k and line p and parellel
The function g(x) is defined as g(x) = -2x^2 - 4x + 2 The value of g(-3)
a ladder 10 feet long rests against a vertical wall. let be the angle between the top of the ladder and the wall, and let be the distance from the bottom of the ladder to the wall. if the bottom of the ladder slides away from the wall, how fast does change with respect to when ?
Rate of change of x with respect to [tex]\alpha[/tex] when [tex]\alpha =\frac{\pi }{3}[/tex] is 5ft/s.
Since the ladder is 10ft long resting against a vertical wall.
Let the angle between the top of the ladder and the wall is [tex]\alpha[/tex] .
And let the distance from the bottom of the ladder to the wall is x.
Thus we need to find the rate of change of x with respect to [tex]\alpha[/tex] when [tex]\alpha =\frac{\pi }{3}[/tex]
Consider L to be the length of the ladder.
Then, L = 10ft
Thus, we get the relation between the angle and distance x i.e.
x = L [tex]\sin \alpha[/tex]
On differentiating the above equation,
[tex]\frac{dx}{dt} =L \cos \alpha[/tex]
Now after putting the values [tex]\alpha =\frac{\pi }{3}[/tex] in above equation, we get,
[tex]=(10)\cos(\frac{\pi }{3} )=(10)(\frac{1}{2} )=5[/tex]
Therefore, [tex]\frac{dx}{dt} =5[/tex] ft/s
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what is - 8x-6y= -8 in slope- intercept form
Answer:
y = [tex]\frac{-4}{3}[/tex] x + [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
-8x - 6y = -8 Add 8x to both sides
-6y = 8x - 8 Divide all the way through by -6
y = [tex]\frac{-8}{6}[/tex] c + [tex]\frac{8}{6}[/tex] Simplify
y = [tex]\frac{-4}{3}[/tex] x + [tex]\frac{4}{3}[/tex]
A negative times a negative is a positive.
A negative times a positive is a negative.