Answer:
see below
Step-by-step explanation:
f(n) = 10(1.02)^n
Part A
Let f(n) = 11.04
11.04 = 10 * 1.02 ^n
Divide each side by 10
11.04/10 = 1.02^n
1.104 = 1.02^n
Taking the log of each side
log 1.104 = log 1.02^n
We know log a^b = b log a
log 1.104 = n log 1.02
log 1.104 / log 1.02 = n
4.99630=n
Rounding n to 5
The domain should be 0 ≤n≤5
Part B
f(n) = 10(1.02)^n
The function is in the form y =a b^x where a is the y intercept
The y intercept is 10. This is the value when n =0 days.
Part C
To find the average rate of change
f(5) - f(1)
-----------
5-1
f(5) = 11.04
f(1) = 10 *1.02 =10.2
11.04 - 10.2
-----------
5-1
.84
-----
4
.21 cm per day
The average rate of growth over the 4 days is .21 cm per day
Answer:
Part A: A reasonable domain to plot the growth of the function would be: 0 < n < 5.
Part B: The y-intercept of the graph of the function f(n) represents the height of the plant in 0 days when it first began.
Part C: The average rate of change of the function from n = 1 to n = 5 is 0.84 or 0.21cm per day. It represents the amount of growth for the plant over 4 days.
, Hope this helps :)
Have a great day!!
what type of data states that every value in the set is a number
Answer:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Step-by-step explanation:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Answer:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Q. A board that measures feet long is cut into 6 equal pieces. What is the length of each piece?
A. 1} inches
B. 3 inches
C. 3 inches
D. 9 inches
QUESTION :- . A board that measures feet long is cut into 6 equal pieces. What is the length of each piece?
A. 1 inches
B. 3 inches
C. 2 inches
D. 9 inches
ANSWER:- 1 FEET -->12 INCH
ATQ ->
1 FEET IS divided into 6 parts so
1 feet = 12 inches
[tex] \frac{1}{6} feet = \frac{12}{6} inches \\ \frac{1}{6} feet = 2 inches [/tex]
so each part will be equal to 2 inches
1 ft = 12 in
12 inch can be devided into 6 equal parts resulting in 2 inches each.
I guess you mistyped either B or C..
hope it helps
kind regards
Alex
Alec bakes spherical rolls of bread. Each roll is about 8cm
wide. What is the approximate volume of each roll? Use
3.14 to approximate a.
Answer:
Step-by-step explanation:
2143.57
Find the explicit general solution to the following differential equation.
(8+x) dy/dx = 5y
The explicit general solution to the equation is y:_______
Answer:
y = (8+x)^5 + C
Step-by-step explanation:
Given the differential equation
(8+x) dy/dx = 5y
Using the variable separable method
(8+x) dy = 5ydx
dx/8+x = dy/5y
Integrate both sides
[tex]\int\limits^ {} \, \frac{dx}{8+x} = \int\limits^ {} \, \frac{dy}{5y} \\ln(8+x) = \frac{1}{5}lny\\5ln(8+x)= lny\\ln(8+x)^5 = lny\\ (8+x)^5 = y\\Swap\\y = (8+x)^5 + C[/tex]
This gives the required solution
The explicit general solution to the following differential equation[tex](8+x)\dfrac{dy}{dx} = 5y[/tex] is [tex](8+x)^5 +C[/tex], where [tex]C[/tex] is a constant.
The relationship between the unknown function and its derivative is called the differential equation.
The differential equation in which variables are separated from each other is called the variable separable method.
Now, separate the variables using the variable separable method:
[tex](8+x){dy} = 5y \ dx[/tex]
[tex]\dfrac{dx}{8x} = \dfrac{dy}{5y}[/tex]
Integrating both sides,
[tex]\int \dfrac{dx}{x+8} = \int \dfrac{dy}{5y}\\log(x+8) = \dfrac{1}{5} log y\\ 5 log(x+8) = log y\\log(x+8)^{5} = log y \ \ \\y = ( x+8)^{5} +C[/tex]
Thus, the explicit general solution to the equation is [tex](8+x)^5 +C[/tex].
Learn more about differential equations here:
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If a franchise company wanted to determine why sales were higher at some locations rather than others, what statistical process would be most appropriate? Group of answer choices Regression with sales as an independent variable Regression with sales as the dependent variable Use a confidence interval with the posted speed as the mean Hypothesis testing with a null hypothesis that the sales are less than or equal to the highest sales Hypothesis testing with a null hypothesis that the sales are more than the highest sales
Answer: Regression with sales as the dependent variable
Step-by-step explanation:
Since the franchise company wanted to determine why sales were higher at some locations rather than others, the statistical process that would be most appropriate is regression with sales as the dependent variable.
Regression will be used in determining the strength of the relationship that exist between one dependent variable and the independent variables. In this case, the dependent variable is sales.
You put $600 in a savings account. The account earns 6% simple interest per year.
a. What is the interest earned after 10 years?
b. What is the balance after 10 years?
Consider the given statements below.
• A central angle in a circle measures 70°.
An inscribed angle in the same circle also measures 70°.
Which statement best describes the relationship between the arcs
intersected by these angles?
.
1 of 4 QUESTIONS
The inscribed angle intersects an arc that is twice the measure of the arc
intersected by the central angle. The inscribed angle's arc measures 70°,
and the central angle's arc measures 35º.
The inscribed angle intersects an arc that is half the measure of the arc
intersected by the central angle. The inscribed angle's arc measures 35º,
and the central angle's arc measures 70°.
The inscribed angle intersects an arc that is half the measure of the arc
O intersected by the central angle. The inscribed angle's arc measures 70°
and the central angle's arc measures 140°.
The inscribed angle intersects an arc that is twice the measure of the arc
O intersected by the central angle. The inscribed angle's arc measures 140°,
and the central angle's arc measures 70°.
Answer:
1-90
2-80
3-033
Step-by-step explanation:
Kaleigh wants to buy a car that costs $17360. She deposits $14,000 in a savings account that earns 8% simple interest. How long was Kaylee leave the money in the savings account to be able to buy the car?
Answer:
Kaylee must leave the money in the savings account for 3 years.
Step-by-step explanation:
Given that Kaylee wants to buy a car that costs $ 17,360, and she deposits $ 14,000 in a savings account that earns 8% simple interest, to determine how long was Kaylee leave the money in the savings account to be able to buy the car must be made the following calculation:
14,000 + (14,000 x 0.08 x X) = 17360
1,120X = 17,360 - 14,000
X = 3,360 / 1,120
X = 3
Therefore, Kaylee must leave the money in the savings account for 3 years.
HELP ASAP I WILL GIVE BRAINLIST
A = {1, 3, 4, 5, 7, 9}
B = {1, 2, 4, 6, 8, 10}
List the outcomes of A ∪ B? What does this represent?
List the outcomes of A ∪ B? What does this represent?
Answer:
A U B={1,2,3,4,5,6,7,8,9,10} represents A union B
(includes all the members of set Sand the members of set Bout together, do not repeat anyone that comes twice)
A n B={1,4} represents A interception B( this refers to the members that sets A and B have in common)
Answer:
A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
Step-by-step explanation:
A = { 1 , 3 , 4 , 5 , 7 , 9 }
B = { 1 , 2 , 4 , 6 , 8 , 10 }
A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
It represents the whole numbers between 0 and 11
[ A ∪ B is the elements of both A and B , without any repetition ]
A ∩ B = { 1 , 4 }
It represents the common numbers in both A and B
What value of y makes the sentence true?
y + 3 = 30
Type your answer in the box below.
I
y =

Hey there!
y + 3 = 30
SUBTRACT 3 to BOTH SIDES
y + 3 - 3 = 30 - 3
CANCEL out: 3 - 3 because that gives you 0
KEEP: 30 - 3 because that gives you the value of y
y = 30 - 3
30 - 3 = y
y = 27
Answer: y = 27
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Can someone tell me if its A,B, or C? Thanks besties.
Answer:
... ..... C is the answer
50 + x + 10 + 8x + 2x =650
what is the value of x?
Answer:
x = 590/11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
50 + x + 10 + 8x + 2x = 650
Step 2: Solve for x
[Addition] Combine like terms: 11x + 60 = 650[Subtraction Property of Equality] Subtract 60 on both sides: 11x = 590[Division Property of Equality] Divide both sides by 11: x = 590/11Answer:
x= 590/11
Step-by-step explanation:
Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
A small town experienced explosive population increase. Originally the town had population 170. Within 3 years, the town's population increased by 400%. What's the town's current population
Answer:
850
Step-by-step explanation:
Given that :
Initial population = 170
Percentage rise in population within 3 years = 400%
Hence, the current population of the town will be ;
Current population = Initial population * (1 + rate)
Current population = 170(1 + 400%)
Current population = 170(1 + 4)
Current population = 170(5)
Current population = 850
Find the value for the side marked below.
Round your answer to the nearest tenth.
50°
122
y
y = [?
Enter
Answer:
y = 189.8
Step-by-step explanation:
Apply trigonometric function to find y.
Reference angle (θ) = 50°
Adjacent side = 122
Hypotenuse = y
Apply CAH, since the Hypotenuse and the Adjacent are involved.
Thus:
Cos θ = Adj/Hypo
Plug in the values
Cos 50° = 122/y
y*Cos 50° = 122
y = 122/cos 50°
y = 189.8 (beater tenth)
Solve the following system of equations and show all work. y = 2x2-3 y = 7x + 1 (10 points)
Answer:
x = -1/2 , y = -5/2
x = 4, y = 29
Step-by-step explanation:
y = 2x² - 3
y = 7x + 1
------------------
set equal
2x² - 3 = 7x + 1
Subtract 7x + 1 from both sides
2x² - 7x - 4 = 0
Factor
(2x + 1)(x - 4) = 0
x = {-1/2, 4}
For x = -1/2
y = 7(-1/2) + 1
y = -5/2
(-1/2 , -5/2)
For x = 4
y = 7(4) + 1
y = 29
(4, 29)
3.42x16.5 show your work plz
Answer:
= 56.43
Step-by-step explanation:
= 3.42 × 16.5
multiply the numbers= 56.43
Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 At 95% confidence, the null hypothesis _____. a. should not be rejected b. should be revised c. should be rejected d. None of these answers are correct
Answer:
Option C
Step-by-step explanation:
n = 81
s2 = 625
H0: σ2 = 500
Ha: σ2 ≠ 500
Test Statistics X^2 = (n-1)s^2/ σ2 = (81-1)*625/500
X^2 = 100
P value = 0.0646 for degree of freedom = 81-1 = 80
And X^2 = 100
At 95% confidence interval
Alpha = 0.05 , p value = 0.0646
p < alpha, we will reject the null hypothesis
At 95% confidence, the null hypothesis
What is the system of equations represented by the tables?
O A. y=2x-1
y = -x + 3
B. y = x + 2
y = x-1
O c. y=-3x-1
y = 3x + 2
O D. y = 2x-3
y = -x + 2
Answer:
C.
y = -3x - 1
y = 3x + 2
Step-by-step explanation:
Find the slope (m) and y-intercept (b) of each table to write an equation for each.
✔️First table:
Find the slope (m) = change in y/change in x
Using any two pair of values, say (0, -1) and (1, -4),
Slope (m) = (-4 - (-1))/(1 - 0) = -3/1
m = -3
Find the y-intercept:
y-intercept is the value of y when x = 0
From the table, y = -1 when x = 0. Therefore,
y-intercept (b) = -1
To write an equation for table 1, substitute m = -3 and b = -1 into y = mx + b
Equation for table 1:
y = -3x - 1
✔️ Second table:
Find the slope (m) = change in y/change in x
Using any two pair of values, say (0, 2) and (1, 5),
Slope (m) = (5 - 2)/(1 - 0) = 3/1
m = 3
Find the y-intercept:
y-intercept is the value of y when x = 0
From the table, y = 2 when x = 0. Therefore,
y-intercept (b) = 2
To write an equation for table 1, substitute m = 3 and b = 2 into y = mx + b
Equation for table 1:
y = 3x + 2
brainliest answer po yung tama
nk tym for nega NEED HELP PK TALAG
A
A
B
C
A
D
B
C
May choices po yan saamen
Step-by-step explanation:
Love you
I need a math genius please
!!WILL MARK BRAINLIEST!! PLEASE SOMEONE HELP!! IM TRYING TO PREPARE FOR MATH CAMP AND THEY GAVE US THIS PROBLEM AND I CANT FIND ANYTHING LIKE IT!!
Answer:
How long is the [shirt] in the air? 3 seconds
How many seconds after launching is the t-shirt at 17 feet? 0.25 seconds
Step-by-step explanation:
Formula to represent the shirt's flight path (given): [tex]h=-16t^2+vt+c[/tex], where [tex]h[/tex] is the height of the shirt, [tex]v[/tex] is the initial velocity of the shirt, [tex]c[/tex] is the shirt's starting height, and [tex]t[/tex] is elapsed time since launch.
The function forms a parabola concave down. Since the shirt is caught at 17 feet, we want to second x-coordinate of a point with a y-coordinate of 17 that the function passes through. This is because the shirt was caught going down, not up.
Therefore, let [tex]h=17[/tex]:
[tex]17=-16t^2+52t+5,\\\\-16t^2+52t-12=0,\\\\ y= \frac{-52\pm\sqrt{52^2-4(-16)(-12)}}{2(-16)},\\\\y=\frac{1}{4},\boxed{y=3}[/tex].
The second x-coordinate is the larger of the two and therefore the shirt was in the air for 3 seconds.
However, the first time the shirt reaches a height of 17 feet is on its way up, which occurs at 1/4 or 0.25 seconds (the first x-coordinate). Therefore, the t-shirt reached a height of 17 feet 0.25 seconds after launching.
Please help me I am confused and i will give you anything you want just help me. SOS
Answer:
hope it helps you..........
please help meeeee!!
Step-by-step explanation:
[tex]\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}[/tex]
In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?
m∠X + m∠Z < 90°
m∠Y > 90°
∠X and∠Y are complementary
m∠X + m∠Y < 90°
Answer:
M < X + M < Y < 90
Step-by-step explanation:
Suppose that each student at a university has one of 4 expected graduation years and one of 21 majors. How many students must be enrolled to guarantee 2 graduations in the same year and major?
Answer:
The correct answer is "168 students".
Step-by-step explanation:
According to the question,
Graduation probability,
[tex]P_g=\frac{1}{4}[/tex]
Major probability,
[tex]P_m=\frac{1}{21}[/tex]
Now,
The probability of having both graduation as well as major will be:
= [tex]\frac{1}{4}\times \frac{1}{21}[/tex]
= [tex]\frac{1}{84}[/tex]
hence,
The number of students having guarantee two graduations throughout the same year and major will be:
⇒ [tex]\frac{x}{84}=2[/tex]
By applying cross-multiplication, we get
⇒ [tex]x = 84\times 2[/tex]
⇒ [tex]=168[/tex]
Two angles are complementary. One angle measures 60 degrees. What is the measure of the other angle?
I'm not sure if its A.
Answer:
30
Step-by-step explanation:
Complementary angles add to 90
x+60 = 90
x+60-60 = 90-60
x = 30
Answer: A
Step-by-step explanation:
Complementary angles sum up to 90 degrees. Thus, we can write that:
90=angle1+angle2
90-angle1=angle2
90-60=angle2
angle2=30
A professor has been teaching introductory statistics for many years and the final exam performance has been very consistent from class to class and the scores have been normally distributed. Overall, the whole data base (i.e. population) of final scores has a mean (μ) of 24 points (out of a maximum of 30 points) and a standard deviation (Ï) of 5 points. The professor would like to revise the course design to see if student performance on the final could be improved.
The new course design was implemented in the most recent academic year. There were 100 students and the average final exam score was 24.7. The professor would like to run a hypothesis test to see if this sample of students in the recent academic year performed significantly better than the past population. In other words, the hypothesis was a comparison between the population taking the course with the new design (represented by the sample of 100 students) with the population taking the course with the old design. The professor is predicting an increase of final score with the new design, so the hypotheses should be directional, and the test should be one-tailed. The significance level is set at α = .1.
Required:
a. Identify the dependent variable for this study.
b. State the null hypothesis and alternative hypothesis using both words and symbol notation
Answer:
a) Independent variable - Design of the course
Dependent variable - Final score of the students
b) H0 - Final score >24.7
Alternate hypothesis - Final score is less than or equal to 24.7
Step-by-step explanation:
a) Independent variable - Design of the course
Dependent variable - Final score of the students
b) Null Hypothesis : Performance of student taking course with the new design is better as compared to the population of student taking the course with the old design.
H0 - Final score >24.7
Alternate hypothesis - Final score is less than or equal to 24.7
Differentiate the function. y = (3x - 1)^5(4-x^4)^5
Answer:
[tex]\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (3x - 1)⁵(4 - x⁴)⁵
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(3x - 1)^5](4 - x^4)^5 + (3x - 1)^5\frac{d}{dx}[(4 - x^4)^5][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' =[5(3x - 1)^{5-1} \cdot \frac{d}{dx}[3x - 1]](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^{5-1} \cdot \frac{d}{dx}[(4 - x^4)]][/tex]Simplify: [tex]\displaystyle y' =[5(3x - 1)^4 \cdot \frac{d}{dx}[3x - 1]](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot \frac{d}{dx}[(4 - x^4)]][/tex]Basic Power Rule: [tex]\displaystyle y' =[5(3x - 1)^4 \cdot 3x^{1 - 1}](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot -4x^{4-1}][/tex]Simplify: [tex]\displaystyle y' =[5(3x - 1)^4 \cdot 3](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot -4x^3][/tex]Multiply: [tex]\displaystyle y' = 15(3x - 1)^4(4 - x^4)^5 - 20x^3(3x - 1)^5(4 - x^4)^4[/tex]Factor: [tex]\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 3(4 - x^4) - 4x^3(3x - 1) \bigg][/tex][Distributive Property] Distribute 3: [tex]\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 12 - 3x^4 - 4x^3(3x - 1) \bigg][/tex][Distributive Property] Distribute -4x³: [tex]\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 12 - 3x^4 - 12x^4 + 4x^3 \bigg][/tex][Brackets] Combine like terms: [tex]\displaystyle y' = 5(3x-1)^4(4 - x^4)^4(-15x^4 + 4x^3 + 12)[/tex]Factor: [tex]\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
The perimeter of a rectangle is 12cm the area is 5cm square what is the length of the sides?
Answer:
l=5, w=1
Step-by-step explanation:
5*1=5 for area
5+1+5+1=12 for perimeter
PLEASE HELP ASAP!!! What is the range of the function shown on the graph?
(The graph is below)
Answer:
-6 < y < ∞
Step-by-step explanation:
The range is the values that y can take
y goes from almost -6 to infinity ( there is an asymptote at -6)
-6 < y < ∞
PLEASE HELP ASAP
Add the complex numbers: (4 + 8i) + (–2 – i)
Answer:
2 + 7i
Step-by-step explanation:
(4 + 8i) + (-2 - i)
open the brackets
4 + 8i - 2 - i
add or subtract like terms
2 + 7i
Answer:
2+7i
Step-by-step explanation:
Open the brackets.
4+8i-2-i
You will get…
2+7i