Problem 1
If 0 < b < 1, then we have exponential decay. The curve will decrease downhill as you move from left to right.
If b > 1, then we have exponential growth and the curve goes uphill as we move from left to right.
Examples: y = 2(0.5)^x is exponential decay while y = 2(1.2)^x represents exponential growth.
Note that the base b cannot be negative.
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Problem 2
Plug x = 0 into the general template given
y = a(b)^x
y = a(b)^0
y = a(1)
y = a
Plugging x = 0 leads to the output y = a
Therefore, the point (0,a) is on the curve. This is the y intercept. It's where the curve crosses the y axis. If you change the value of 'a', then you change the y intercept.
Examples:
y = 2(5)^x has y intercept 2y = 3(0.8)^x has y intercept 3The track team has 12 more boys than girls. There are a total of 142 team members. How many boys and girls are on the team?
Answer:
77 boys, 65 girls
Step-by-step explanation:
x as the variable to represent amount of girls, and there are 12 more boys than girls (x+12). So the equation would be:
x + x + 12 = 142
2x + 12 = 142
x = 65
65 girls
then 65+ 12 = 77 boys
Find the area of this triangle. Round to the nearest tenth.
Area = 1/2 × 24 × 11 × Sin(76)
Area = 12 × 11 × 0.9703
Area = 132 × 0.9703
Area = 128.0796
Area = 128.1 in^2
find the largest prime factor of 6108
Answer:
509
Step-by-step explanation:
There are 4 prime factors of 6108
6108 ÷ 2 = 3054
3054 ÷ 2 = 1527
1527 ÷ 3 = 509
509 ÷ 509 = 1
Task 4: gasoline cost
you have $40 to spend on n gallons of gas that costs $3.25 per gallon. determine whether each of the following is an expression or an equation. using the structure, give an interpretation of the practical meaning of each. that is, what do they represent in the real world?
1. 3.25n
2.3.25n=26
3.40-3.25n
4. 40-3.25n=1.00
1) 3.25n
Overall cost of n gallons of gas
2)3.25n = 26
we are spending 26 dollars on 8 gallons of gas
3)40-3.25n
Ammount we have remaining after spending on n gallons of gas out of 40 dollars
4) 40-3.25n = 1.00
The maximum number of gallons of gas we can buy from 40 dollar is 13 gallons and 1 dollar is still remaining to us.
The given representations could be classified thus :
3.25n (Expression)
3.25n=26 (Equation)
40-3.25n (Expression)
40-3.25n=1.00 (Equation)
Total amount to spend = $40
Cost per gallon = $3.25
Number of gallons = n
An expression could be a variable, constant or a combination of both which is related by an operation symbol.
An equation on the other hand maybe defined as a relationship between two expressions linked by an equal to symbol.
Evaluating the representations given :
3.25n : This is an expression as it lacks an equal to sign connecting the expression. The expression means the cost of n gallons of gas.
3.25n = 26 : This is an equation as it contains two Seperate expressions connected by the equal to sign. The equation means that number of gallons of gas, n that can be purchased with $26.
40 - 3.25n : This is an expression. The amount left after purchasing n gallons from $40.
40 - 3.25n = 1.00 : This is an equation. The number of gallons of gas that can be purchased from $40 and still have $1 left.
Learn more : https://brainly.com/question/18109354
Plz help me!!(ᗒᗣᗕ)՞
Plz!
Answer:
A) 64 cm²
Step-by-step explanation:
Trapezoid area formula:
[tex]A=\frac{a+b}{2} h[/tex]
Given:
a = 6
b = 10
h = 8
Work:
[tex]A=\frac{a+b}{2} h\\\\A=\frac{6+10}{2} *8\\\\A=\frac{16}{2} *8\\\\A=8*8\\A=64[/tex]
The hypotenuse function is correct, but the main function has a problem. Explain why it may not work, and show a way to fix it. Your fix must be to the main function only; you must not change the hypotenuse function in any way.
Answer: hello your question is incomplete attached below is the missing codes
Answer : It may not work because; the double pointer P was not allotted a double using a new double ( I.e. Error in the main function ) also the cout statement was not written in the main function
Step-by-step explanation:
It may not work because; the double pointer P was not allotted a double using a new double ( I.e. Error in the main function ) also the cout statement should be moved to the Main
The correction is below
{
double* p = new double;
hypotenuse(1.5, 2.0, p);
cout << "The hypotenuse is " << *p << endl;
}
What is 8.75% of 172?
Answer:
15.05 is your answer.
Step-by-step explanation:
To find our answer we will first divide 8.75 by 100 since it is a percentage. 8.75 ÷ 100 = 0.0875
Now we will take 0.0875 and multiply it by 172 and we get 15.05. Therefore, 15.05 is our answer
Hey there!
8.75% of 172
The word “of” means multiply in mathematical terms.
8.75% * 172
8.75% = 8.75/100 = 0.0875
0.0875 * 172
= 301/20
= 15.05
Answer: 301/20 OR 15.05
(BOTH ANSWERS WORK because they are both equivalent)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
plsss help!! is this a right triangle if no or yes please explain why??
Answer:
yes, it is a right triangle
Step-by-step explanation:
the other two angles are 35 and 55 degrees
Answer:
is NOT a right triangle
Step-by-step explanation:
is a right triangle if it checks the Pythagorean Th.
12² = 10² + 7²
144 = 100+49
144 = 149 False
Two puppies from the same litter name Bruno in Jasper there ways during the first six weeks are plotted on the coordinate grid at which age did Bruno in Jasper Way the same
Answer:
3 weeks
Step-by-step explanation:
Two puppies from the same litter are named Bruno Puppy Weight and Jasper. Their weights during the first weeks are plotted on the coordinate grid. At which age did Bruno and Jasper weigh the same?
Solution:
We can see that Bruno and Jasper weight is represented by a straight line. Let y represent the weight of the puppies in ounce and x represent the age in weeks.
For Bruno:
The line passes through (1, 10) and (5, 16), hence the equation of the line is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{16-10}{5-1} (x-1)\\\\y-10=\frac{3}{2}(x-1)\\\\y=1.5x+8.5\ \ \ (1)[/tex]
For Jasper:
The line passes through (0, 12) and (3, 13), hence the equation of the line is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-12=\frac{13-12}{3-0} (x-0)\\\\y-12=\frac{1}{3}(x)\\\\y=\frac{1}{3} x+12\ \ \ (2)[/tex]
To find the age at which both puppies weighed the same, we have to solve equation 1 and 2 simultaneously. Subtract equation 1 from 2:
-1.167x + 3.5 = 0
1.167x = 3.5
x = 3
Put x = 3 in equation (2)
y = (1/3)(3) + 12 = 13
The solution is (3, 13)
Therefore both Jasper and Bruno weigh the same weight of 13 ounce at 3 weeks of age
Select the false statement about inverse relations.
a. The range of a function will be the domain of its inverse.
b. The graphs of inverse relations are reflections in the line y=x.
c. The inverse of a function will always be a function.
d. The domain of a function will be the range of its inverse.
Answer:
THE ANSWER IS B
Step-by-step explanation:
B mine please im so single
jack bought a mother bike the original price was 1300 but he got a discount of 20% what was the discounted price of the bike
The product of b and 3
Answer and Step-by-step explanation:
The product of a two numbers/values is the result of multiplying two numbers/values.
So, multiply b and 3 together.
3b is the answer.
#teamtrees #PAW (Plant And Water)
Determine the missing angle in the picture below.
Answer:
x =41.18114952
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
We know the hypotenuse and adjacent sides
cos theta = adjacent / hypotenuse
cos x = 14.3/19
taking the inverse cos of each side
cos^-1 (cos x) = cos ^-1 ( 14.3/19)
x =41.18114952
Answer:
Step-by-step explanation:
take x degree as reference angle
using cos rule
cos x=adjacent/hypotenuse
cos x=14.3/19
cos x=0.75
x=cos 41
x= 41 degree
Choose the best estimate for the multiplication problem below. 56 x 51
A. 2000
B. 3000
C. 4100
Answer:
B
Step-by-step explanation:
Pedro solves the quadratic equation x^2+6x –14 using the quadratic formula. In which step did Pedro make an error?
9514 1404 393
Answer:
correct choice is marked
Step-by-step explanation:
The error is in step 2. The square root cannot be distributed to a sum.
Find the solution of the differential equation f' (t) = t^4+91-3/t
having the boundary condition f(1) =1/4
Answer:
[tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Antiderivatives - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f'(t) = t^4 + 91 - \frac{3}{t}[/tex]
[tex]\displaystyle f(1) = \frac{1}{4}[/tex]
Step 2: Integration
Integrate the derivative to find function.
[Derivative] Integrate: [tex]\displaystyle \int {f'(t)} \, dt = \int {t^4 + 91 - \frac{3}{t}} \, dt[/tex]Simplify: [tex]\displaystyle f(t) = \int {t^4 + 91 - \frac{3}{t}} \, dt[/tex]Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle f(t) = \int {t^4} \, dt + \int {91} \, dt - \int {\frac{3}{t}} \, dt[/tex][1st Integral] Integrate [Integral Rule - Reverse Power Rule]: [tex]\displaystyle f(t) = \frac{t^5}{5} + \int {91} \, dt - \int {\frac{3}{t}} \, dt[/tex][2nd Integral] Integrate [Integral Rule - Reverse Power Rule]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - \int {\frac{3}{t}} \, dt[/tex][3rd Integral] Rewrite [Integral Property - Multiplied Constant]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3\int {\frac{1}{t}} \, dt[/tex][3rd Integral] Integrate: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex]Our general solution is [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex].
Step 3: Find Particular Solution
Find Integration Constant C for function using given condition.
Substitute in condition [Function]: [tex]\displaystyle f(1) = \frac{1^5}{5} + 91(1) - 3ln|1| + C[/tex]Substitute in function value: [tex]\displaystyle \frac{1}{4} = \frac{1^5}{5} + 91(1) - 3ln|1| + C[/tex]Evaluate exponents: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3ln|1| + C[/tex]Evaluate natural log: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3(0) + C[/tex]Multiply: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91 - 0 + C[/tex]Add: [tex]\displaystyle \frac{1}{4} = \frac{456}{5} - 0 + C[/tex]Simplify: [tex]\displaystyle \frac{1}{4} = \frac{456}{5} + C[/tex][Subtraction Property of Equality] Isolate C: [tex]\displaystyle -\frac{1819}{20} = C[/tex]Rewrite: [tex]\displaystyle C = -\frac{1819}{20}[/tex]Substitute in C [Function]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]∴ Our particular solution to the differential equation is [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex].
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
5(2b + 3) + 8(b - 6)
Answer:
Step-by-step explanation:
5(2b+3)+8(b-6)
=10b+15+8b-48
=18b-33
=3(6b-11)
Which is the volume of a sphere with diameter
50 cm?
Answer:
V =65416.666666 cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The diameter is 50 so the radius is 1/2 of the diameter
r = 1/2 (50) = 25
V = 4/3 ( pi) (25)^3
V = 4/3 (pi) 15625
V =20833.3333 pi
Using 3.14 for pi
V =65416.666666 cm^3
Answer:
V =65416.666666 cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The diameter is 50 so the radius is 1/2 of the diameter
r = 1/2 (50) = 25
V = 4/3 ( pi) (25)^3
V = 4/3 (pi) 15625
V =20833.3333 pi
Using 3.14 for pi
V =65416.666666 cm^3
Exponential Growth/Decay
Plz help!!!
Answer:
a) 82.
b) So a growth factor of 0.025
c) 2.5%.
d) f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.
Step-by-step explanation:
Exponential equation of population growth:
The exponential equation for population growth has the following format:
[tex]f(x) = x(0)(1+r)^x[/tex]
In which x(0) is the initial value and r is the growth factor, as a decimal.
In this question:
In x years after 2021:
[tex]f(x) = 82(1.025)^x[/tex]
a)
This is f(0). So
[tex]f(0) = 82(1.025)^0 = 82[/tex]
So 82.
b)
We have to find r. So
[tex]1 + r = 1.025[/tex]
[tex]r = 1.025 - 1 = 0.025[/tex]
So a growth factor of 0.025.
c)
Growth factor multiplied by 100%.
So 0.025*100% = 2.5%.
d)
f(5) = population in 5 years after January 1st 2021, that is, January 1st 2026.
[tex]f(5) = 82(1.025)^5 = 93[/tex]
f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.
Last week at the business where you work , you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items
Answer:
240
Step-by-step explanation:
They spent $120 buying 120 items, so they have -$120. By selling the items at 3x the price, they gained the 120 back and made a profit of 240 (120 x 2).
Suppose you are investigating the relationship between two variables, traffic flow and expected lead content, where traffic flow is a predictor of lead content. You find the 95% CI for expected lead content when traffic flow is 15, based on a sample of n= 10 observations, is (461.7, 598.1).
Required:
What parameter is this interval estimating?
Answer:
The answers is " Option B".
Step-by-step explanation:
[tex]CI=\hat{Y}\pm t_{Critical}\times S_{e}[/tex]
Where,
[tex]\hat{Y}=[/tex] predicted value of lead content when traffic flow is 15.
[tex]\to df=n-1=8-1=7[/tex]
[tex]95\% \ CI\ is\ (463.5, 596.3) \\\\\hat{Y}=\frac{(463.5+596.3)}{2}\\\\[/tex]
[tex]=\frac{1059.8}{2}\\\\=529.9[/tex]
Calculating thet-critical value[tex]t_{ \{\frac{\alpha}{2},\ df \}}=-2.365[/tex]
The lower predicted value [tex]=529.9-2.365(Se)[/tex]
[tex]463.5=529.9-2.365(Se)\\\\529.9-463.5=2.365(Se)\\\\66.4=2.365(Se)\\\\Se=\frac{66.4}{2.365} \\\\Se=28.076[/tex]
When [tex]99\%[/tex] of CI use as the expected lead content: [tex]\to 529.9\pm t_{0.005,7}\times 28.076 \\\\=(529.9 \pm 3.499 \times 28.076)\\\\=(529.9 \pm 98.238)\\\\=(529.9-98.238, 529.9+98.238)\\\\=(431.662, 628.138)\\\\=(431.6, 628.1)[/tex]
HELPPPP PLZZZZZzz HELLP FAST I NEED TO PASS
Answer:
✬ m∠Q= 105°➬➬➬➬➬➬➬➬
[tex]6x+5+(11x-5)+x=180^o[/tex]
[tex]18x=180[/tex]
[tex]x=10[/tex]
☄m∠Q=105°
❆❆❆❆❆❆❆❆❆❆❆❆
hope it helps....
have a great day!!
how do you estimate 10.43
Answer:
Step-by-step explanation:
Given 10.43, you can 'estimate' it only by rounding off:
10.43 to the nearest tenth is 10.4.
10.43 to the nearest whole number is 10; we drop the fraction 0.43.
1
Help will be appreciated
Answer:
48
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
48
the picture 20 words or longer for the answer so this is extra text
The heart rate of 10 football players is sampled. The rates measured in beats per minute are 62,74,74,64,76,6480,76,68,76
What is the best estimate of the population mean for heart rate among football players?
Enter your answer in the box.
Answer:
The best estimate of the population mean for heart rate among football players is of 71.4 beats per minute.
Step-by-step explanation:
The best estimate for the population mean is the sample mean.
Sample mean:
Sum of all values in the sample divided by 10(size of the sample). So
[tex]\overline{x} = \frac{62+74+74+64+76+64+80+76+68+76}{10} = 71.4[/tex]
The best estimate of the population mean for heart rate among football players is of 71.4 beats per minute.
Answer: 71.4
Just a confrimation to the below anwser.
Can someone help me pls pls help with this question
Answer:
D.
Step-by-step explanation:
The mean is 11,000
GIVING OUT BRAINLIEST PLS HELP! ALMOST DUE
Answer:
I think it's option B
What combination of transformations is shown below?
Explanation:
To go from figure 1, to figure 2, we apply a translation (aka "shifting"). Specifically, we translate 3 units to the right and 4 units up.
To go from figure 2 to figure 3, we apply a reflection. The mirror line is vertical and it is along the shared segment of figures 2 and 3.
Anybody know this one? I was leaning towards D but not sure
Answer:
You would be correct!
Step-by-step explanation:
10 × 4 = 40 40 + 15 = 55 therefore D is the answer great job!
I need help with this three problems (with procedure)
Answer:
13. [tex]x^{3} y^3[/tex] cubic units
14. 43 million; 79 million; 3.6 × [tex]10^7[/tex]
15. 2.68 × [tex]10^5[/tex]
Step-by-step explanation: