The exponential function that represents the number of cells present at x hours is y = 100(2)ˣ
What is an exponential function?An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Let y represent the number of cells after x hours.
From the table, at point (0, 100):
100 = ab⁰
a = 100
At point (1, 200):
200 = 100b
b = 2
The exponential function is y = 100(2)ˣ
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Answer:
100(2)^h=6,400
Step-by-step explanation:
Explanation:
For an equation in the form A(b)^x=y, A represents the initial amount, and b represents the growth rate. At 0 hours, there were 100 cells, so A=100.
Between 0 hours and 1 hour, the number of cells doubled from 100 to 200, or 100(2). Between 1 and 2 hours, the number of cells again doubled from 200 to 400, or 100(2)^2. So the growth rate, or b, is 2.
The table shows that at h hours, there were 6,400 cells. Therefore, the equation that represents the number of cells at h hours is .100(2)^h=6,400
A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions.
Session A: $50
Session B: $50
Session C: $100
Session D: $150
Session E: $200
Here is a graph of the cost of all 5 sessions.
A dotplot titled Graph A. A number line labeled session cost (dollars) goes from 40 to 200. 50, 2; 100, 1; 150, 1; 200, 1.
A participant plans to attend 3 sessions. Here is a list of all possible samples of size 3 sessions from this population of 5 sessions: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, and CDE.
Here is a graph displaying the minimum session cost for each possible sample of 3 sessions.
A dotplot titled Graph B. A number line labeled sample minimum session cost (dollars) goes from 50 to 100. 50, 9; 100, 1.
The participant chooses 3 sessions at random from the list of all 5 sessions. The result of the random selection is sessions B, D, and E.
Here is a graph displaying the distribution of session cost for this sample.
A dotplot titled Graph C. A number line labeled session cost (dollars) goes from 40 to 200. 50, 1; 140, 1; 200, 1.
Which of the following gives the correct order of the graphs of the population distribution, distribution of a single sample, and sampling distribution, respectively?
C, A, B
B, C, A
A, B, C
A, C, B
Answer:
A, C, B
Step-by-step explanation:
Took the test on EDG
Answer:
The answer is D
Step-by-step explanation:
what is the weight of a 55 kg person on earth where the acceleration due to gravity is 9.8m/s²
Answer:
The weight of an object is the force of gravity exerted on that object. The mass of an object is the amount of matter it has, and it stays the same wherever you are, regardless of gravity.[1] That's why an object that has 20 kilograms of mass on earth also has 20 kilograms of mass while on the moon, even though it would only weigh 1/6 as much. It weighs 1/6 as much on the moon because the force of gravity on the moon is 1/6 of what it is on Earth.
Step-by-step explanation:
Answer:
your mother
Step-by-step explanation:
The logical answer would be your mother because 9.8m/s^2 x 55 would equal your mother weight, 539 squared pounds.
Find the value of k so that the quadratic inequality x² + 14x + k < 0 only for x is an element of [-11,–3]
Answer:
x²+14x+33<0.
Step-by-step explanation:
1) according to the condition x=-11 and x=-3 are zeros of the function y=ax²+bx+c;
2) if -3;-11 are zeros, then (-3)*(-11)=c ( already a=1; b=14). Then
3) x²+14x+33<0.
In January 2011 the rate of VAT increased from 17.5% to 20%.
Work out the difference in price of a car worth £17000 + VAT
due to the increase in VAT.
Answer: Attributed to the increase in VAT, the change in cost of a car worth RS 15000+VAT is Rs 375.
Step-by-step explanation:
Emily wants to put trim around a square window and measures 3 ft on each side. How many feet of t r i m does she need?
Answer:
12 feet
Step-by-step explanation:
3 times 4 is 12
you would multiply by 4 because of the 4 sides of the window
simplify 3(r + 4) - 5r
Answer: 12-2r
Step-by-step explanation:
3r+12-5r
= -2r+12 or 12-2r
Answer:
-2r + 12
Step-by-step explanation:
simplify 3(r + 4) - 5r
3(r + 4) - 5r <== distribute first
3(r) + 3(4) - 5r
3r + 12 - 5r <== combine like terms
-2r + 12 <== final answer
Hope this helps!
Using proportions to solve for missing sides.
RST~YSZ, find YZ.
Answer:
YZ = 28
Step-by-step explanation:
A proportion involving the known and unknown sides is ...
TR/ST = ZY/SZ
__
This proportion uses SZ, which is not shown on the diagram. The length of SZ can be found from ...
SZ +ZT = ST . . . . . . . segment sum theorem
SZ + 5 = 40 . . . . with given values
SZ = 35 . . . . . subtract 5
__
So, the proportion with values filled in is ...
(3x -7)/40 = (2x +2)/35
7(3x -7) = 8(2x +2) . . . . . . . multiply by 280
21x -49 = 16x +16 . . . . . . . eliminate parentheses
5x = 65 . . . . . . . . . . add 49 -16x
x = 13 . . . . . . . . divide by 5
YZ = 2x +2 = 2(13) +2
YZ = 28
_____
Additional comment
RT = 3x -7 = 3(13) -7 = 32
What is the mean of the data set? 66, 71, 75, 83, 88, 89, 90, 91
A. 88
B. 85.5
C. 80
D. 81.625
Answer: D
Answer:
D
Step-by-step explanation:
the 3 sides of triangle are n, 4n + 1 , 5n- 8. if the perimeter of the triangle is 93 cm, what is the length of each side?
Answer:
10, 41, 42
Step-by-step explanation:
(n)+(4n+1)+(5n-8)=93 because triangle perimeter
10n-7=93
10n=100
n=10
Answer: 10 cm, 41 cm, and 42 cm
Step-by-step explanation:
We can set up an equation knowing the perimeter to solve for the lengths of each side. Then, we will plug the value of n into the different expressions that represent each side.
Perimeter of a triangle:
P = side a + side b + side c
Plug in our known values:
93 cm = (n) + (4n + 1) + (5n - 8)
Simplify and combine like terms:
93 cm = n + 4n + 1 + 5n - 8
93 cm = n + 4n + 5n + 1 - 8
93 cm = 10n -7
Add 7 to both sides of the equation:
100 cm = 10n
Divide both sides of the equation by 10:
10 cm = n
n = 10 cm
-
Solve for the lengths of each side:
n = 10 cm
4n + 1 = 4(10) + 1 = 40 + 1 = 41 cm
5n - 8 = 5(10) - 8 = 50 - 8 = 42 cm
The clients who get haircuts at Cameron's salon have a variety of hair colors.
brown 7
black 7
blond 4
4
What is the experimental probability that the next client to get a haircut Cameron's salon will
have blond hair?
Write your answer as a fraction or whole number.
P(blond)
Using it's concept, it is found that there is a [tex]\frac{2}{9}[/tex] experimental probability that the next client to get a haircut Cameron's salon will have blond hair.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these number of outcomes are taken from previous trials.
In this problem, 4 out of 18 clients had blond hair, hence the probability is given by:
P(blond) = 4/18 = 2/9
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#SPJ1
Trevor, Lucy, and james want to make a total of 50 paper airplanes. the table shows how many they have made so far. how many more paper airplanes do they need to make
you didn't show the pic
hope you understood...!!!
What is the area, in square feet, of the rectangle shown below
Answer:
Step-by-step explanation I can answer if you pin in the pic below
Sam is climbing 9000 m every 30 minutes. How many meters will he climb in 1 hour
Answer:
18000 m
Step-by-step explanation:
Hey there!
In order to solve this problem, we need to first know how many minutes are in an hour
As you know, there are 60 minutes in an hour so this means in 1 hour, he will climb 9000 meters two times
So 9000 two times is 18000,
Meaning, in 1 hour, Sam will climb 18000 m
Answer:
18,000m in an hour
Step-by-step explanation:
We know this because if its 9000 m in 30 minutes, we can do 9000 x 2 and get 18,000m for an hour.
Find the inner diameter of the washer.
The inner diameter of the washer is 7/10 inch, this value is gotten by multiplying the path by 2 and subtracting the result from the outer diameter
Mensuration of ShapesGiven Data
Outer Diameter = 1 inchPath Distance = 3/20 inchThe inner diameter
= Outer Diameter - 2*Path Distance
= 1 - 2*3/20
= 1- 6/20
= 1- 3/10
= 1/1 - 3/10
Find the LCM we have 10
= 10-3/10
= 7/10 inch
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Review the table on page 3 comparing in-network and out-of-network costs under the Standard Plan. Which statement is TRUE? Insurance plans encourage the use of out-of-network doctors by offering lower costs on most services they perform. Insurance plans encourage the use of out-of-network doctors by offering lower costs on most services they perform. Insurance plans encourage the use of in-network doctors by offering lower costs on most services they perform. Insurance plans encourage the use of in-network doctors by offering lower costs on most services they perform. The costs for in-network and out-of-network doctors are the same for ALL services they offer. The costs for in-network and out-of-network doctors are the same for ALL services they offer. Office visits, immunizations and annual physicals have the same costs for both in-network and out-of-network doctors.
The true statement is that most insurance plans encourage the use of In-Network doctors by offering lower costs on most services they perform.
What is the meaning of Health Maintenance Organization?An HMO is regarded as an acronym that is used for “Health Maintenance Organization”. It is know to be companies that has been given the power to solely to manage the provision of health care services to the people.
The use of the in-network option is one that tends to save money. The Providers in your network are known to have a form of agreements with your insurance company that tends to make one to save money.
Lean more about insurance plans from
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Answer: B-Insurance plans encourage the use of in-network doctors by offering lower costs on most services they perform.
De 17 estudiantes 4 hablan frances, si se seleccionan 3, ¿cuál es la probabilidad de que ninguna habla frances?
Esta es una cuestión de probabilidad condicional, y la resolución podría ser la siguiente:
Estudiantes seleccionados ÷ ninguno habla francés3 / (17 - 4) = 3/13¿Qué es la probabilidad condicional?Corresponde a un concepto matemático que involucra la probabilidad de que ocurran dos eventos, es decir, la probabilidad de que ocurra el evento A, sabiendo que el evento B ya ocurrió.
Por lo tanto, la probabilidad de que ningún estudiante hable francés es 3/13 o 23%.
Encuentre más información sobre la probabilidad condicional aquí:
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Freemont Run Club surveyed a random sample of
30
3030 of their members about their running habits. Of the members surveyed,
9
99 said that they run more than
5
55 days a week. There are
84
8484 Freemont Run Club members.
Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than
5
55 days a week?
Answer:
24 for estimate, the accurate is 25.2
Step-by-step explanation:
surveyed total = 30
9 = run 5> days a week
84 = total members
9/30 = percent of members who run 5> days a week
9/30 => 3/10
percent of members who run 5> days a week * total members = number of members who run 5> days a week
3/10 x 84 = 25.2 members
84 = 80
3/10 x 80 = 24
24, a reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week.
5, 5, 9, 11, 13
Mean:
Median:
Range:
Answer:
The median is 9
The Range is 13-5=8
The mean is 5+5+9+11+13/5=43/5=8 3/5=8.6
Out-of-pocket spending in a country for health care increased between 2003 and 2008. The function f(x) = 2573e^0.0359x models average annual expenditures per household, in dollars. In this model, x represents the year, where x = 0 corresponds to 2003 .
(a) Estimate out-of-pocket household spending on health care in 2008 .
(b) Determine the year when spending reached $2783 per household.
Answer:
(a) The total expenditures per household in the year 2008 were approximately $3,080.
(b) The spending reached $2875 per household in 2006.
Step-by-step explanation:
Note: This question is not complete, and the part c is not another question but the same question as part a. The complete question is therefore provided before answering the question as follows:
Out of-pocket spending in a country for health care increased between 2003 and 2008. The function f(x) = 2574e^(0.0359x) models average annual expenditures per household, in dollars. In this model, x represents the year, where x = 0 corresponds to 2003.
(a) Estimate out-of-pocket household spending on health care in 2008.
(b) Determine the year when spending reached $2875 per household
The explanation to the answer is now given as follows:
(a) Estimate out-of-pocket household spending on health care in 2008.
Given;
f(x) = 2574e^(0.0359x) ........................ (1)
Since x = 0 corresponds to 2003; by counting from 2003 to 2008, it implies that x = 5 corresponds to 2008.
Substituting x = 5 into equation (1) to estimate out-of-pocket household spending on health care in 2008, we have:
f(6) = 2574e^(0.0359 * 5)
f(6) = 2574 * 1.19661890406748
f(6) = 3,080.09705906969
Rounding to the nearest dollar as needed, we have:
f(6) = $3,080
Therefore, the total expenditures per household in the year 2008 were approximately $3,080.
(b) Determine the year when spending reached $2875 per household
This can be determined using equation (1) in part a by equating f(x) to $2875 solve for x as follows:
2875 = 2574e^(0.0359x)
2875 /2574 = e^(0.0359x)
1.11693861693862 = e^(0.0359x)
Taking the natural log of both sides, we have:
ln(1.11693861693862) = ln(e^(0.0359x))
0.110591565075382 = 0.0359x
x = 0.110591565075382 / 0.0359
x = 3.0805449881722
Approximating to a whole number, we have:
x = 3
Since x = 0 corresponds to 2003; by counting from 2003, x = 3 corresponds to 2006.
Therefore, the spending reached $2875 per household in 2006.
Which correctly compares the numbers?
518,317 > 518,246 > 518,197
678,200 > 678,194 > 678,227
290,061 > 289,937 > 290,324
158,364 > 158,379 > 158,397
Answer:
518,317 > 518,246 > 518,197
Given the functions f(x) = –4x + 5 and g(x) = x3 + x2 – 4x + 5, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
The f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.
The key features that they have in common are the y-intercept, domain, and range
Linear and quadratic equationsLinear equations are equations that has a degree of 1 while polynomial equations are equations that has a degree of 2 and above.
Given the following functions
f(x) = –4x + 5 and;
g(x) = x^3 + x^2 – 4x + 5
Since the f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.
The key features that they have in common are the y-intercept, domain and range
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Help with all questions in pictures please
Just put the answers please (ex: 1A 2C 3B. etc)
For question number 7 where it says (Which of the following images represents the polar graph of r = 4cos 2θ?) only two of the graphs are shown please if you can include a graph of the correct answer *70Points*
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Convert point Q to polar coordinates (accounting for correct direction):
[tex]\displaystyle r=\sqrt{x^2+y^2}=\sqrt{(-5)^2+(-5\sqrt{3})^2}=\sqrt{25+75}=\sqrt{100}=10\\\\\theta=\tan^{-1}\biggr(\frac{-5\sqrt{3}}{-5}\biggr)=\tan^{-1}\bigr(\sqrt{3}\bigr)=\frac{4\pi}{3}[/tex]
Thus, the answer is [tex]\displaystyle \biggr(10,\frac{4\pi}{3}\biggr)[/tex], or A
Problem 2
Make polar substitutions:
[tex]x^2+y^2-2x+8y=0\\\\r^2-2r\cos\theta+8r\sin\theta=0\\\\r^2=2r\cos\theta-8r\sin\theta\\\\r=2\cos\theta-8\sin\theta\\\\r=-8\sin\theta+2\cos\theta[/tex]
Hence, the answer is C
Problem 3
Eliminate the parameter:
[tex]x=t+3\\x-3=t\\\\y=t^2+2t\\y=(x-3)^2+2(x-3)\\y=x^2-6x+9+2x-6\\y=x^2-4x+3[/tex]
Hence, the answer is C
Problem 4
Identify [tex]z_1[/tex] and [tex]z_2[/tex] and add the complex numbers:
[tex]z_1+z_2=(-3+5i)+(-5-2i)=-3+5i-5-2i=-8+3i[/tex]
Thus, the correct answer is S
Problem 5
Use the formula for multiplying complex numbers in polar form:
[tex]z_1z_2=r_1r_2(\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2))\\z_1z_2=(5)(15)(\cos(240^\circ+135^\circ)+i\sin(240^\circ+135^\circ))\\z_1z_2=75(\cos375^\circ+i\sin375^\circ)\\z_1z_2=75(\cos15^\circ+i\sin15^\circ)[/tex]
Hence, the answer is A
Problem 6
Determine when the ball first hits the ground:
[tex]y=-\frac{1}{2}gt^2+(v\sin\theta)t+y_0\\0=-\frac{1}{2}(32)t^2+(58\sin19^\circ)t+1.9\\0=-16t^2+(58\sin19^\circ)t+1.9\\t\approx1.273[/tex]
Determine the horizontal distance covered by the ball:
[tex]x=(v\cos\theta)t\\x=(58\cos19^\circ)(1.273)\\x\approx69.811[/tex]
Hence, the best answer is C
Problem 7
The equation is in the form of [tex]r=a\cos(n\theta)[/tex] where [tex]a[/tex] is the length of each petal and the curve has a horizontal pole. If [tex]n[/tex] is odd, then there are [tex]n[/tex] petals, but if [tex]n[/tex] is even, then there are [tex]2n[/tex] petals.
From our given equation, there are clearly 4 petals since [tex]n[/tex] is even, and each petal length is 4 units. Hence, the first graph is correct.
(n-1 +7) simplify plssss helppp
Answer: n+6
-1 + 7 = 6
So therefore, the answer is n+6
Hope this helped
Answer:
[tex]\boxed{\sf{n+6}}[/tex]Step-by-step explanation:
To solve this problem, first, you have to do is isolate it on one side of the equation.
(n-1+7)First, remove parentheses.
→ n-1+7
Add the numbers from left to right.
→ -1+7=6
→ n+6
Therefore, the final answer is n+6.I hope this helps you! Let me know if my answer is wrong or not.
Help! Surface area!!!
Answer:
6656 cm²
Step-by-step explanation:
6656 cm² is the required answer
Find the sum of the integers between 23 and 47.
Answer:
70
Step-by-step explanation:
23+47
10)A shirt normally costs £42. If you receive a 15% discount, how much change will you get from £50? o £35.70 o £23.00 o £8.00 o £14.30
Answer:
35.70
Step-by-step explanation:
because 15% of 42 is 6.3 and 6.3 - 42 = 35.70
8. Identify the point corresponding to P.
Answer:
So I might not be understanding, but P is at (-4,0) and Q is at (-1,-3)
The expression below is a sum of cubes.
64x^3 + 125
A. True
B. False
Answer:
A True
Step-by-step explanation:
[tex]4^{3} x ^{3} + 5^{3} [/tex]
the values in a data set r 15,7,11,12,6,3,10, and 6. where would u draw the box in a
Answer:
8.5
put numbers least to greatest and find the median by crossing numbers out front from back.
Subtract the sum of -1000 and 848 from 590
Answer:
742
Step-by-step explanation:
the sum of -1000 and 848
= -1000+848
= -152
Subtract the sum of -1000 and 848 from 590
= 590-(-152)
= 590+152
= 742