Answer:
160
Step-by-step explanation:
Which is the graph of f(x)=2(3)^x
Answer-
The first graph represents [tex]f(x)=2(3)^x[/tex]
Solution-
The given function is,
[tex]f(x)=2(3)^x[/tex]
Putting x = 1,
[tex]f(x)=2(3)^1=2(3)=6[/tex]
So, the point (x, f(x)) i.e (1, 6) must satisfy or lie on the curve of the function.
Only in case of the first graph, the point (1, 6) lies on the curve.
Therefore, the first graph represents the function [tex]f(x)=2(3)^x[/tex] correctly.
Answer: the first answer is correct
Which of the following is a description of the data with a correlation coefficient of -0.3?
A.)low positive correlation
B.)low negative correlation
C.)high positive correlation
D.)high negative correlation
The measure of ______________ in a circle is half the measure of the intercepted arc.
A. a central angle
B. an interior angle
C. an inscribed angle
YES slay5 is correct the answer is : C. an inscribed angle
Answer: C. An inscribed angle
Step-by-step explanation:
Central angle is an angle that is subtended by an arc in a circle, it is also known as the arc's angular distance.
Interior angle is an angle between two sides inside a polygon or a shape.
Inscribed angle is an angle formed by two chords in a circle which have a common endpoint, and by the inscribed angle theorem, the measurement of inscribed angle is half the measure of the intercepted arc.
Find the exact length of the curve. y = 3 + 2x3/2, 0 ≤ x ≤ 1
The exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\(\frac{2}{27} (10\sqrt{10} - 1)\)[/tex].
To find the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex], we can use the formula for arc length of a curve:
[tex]\[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx \][/tex]
where a and b are the lower and upper bounds of the interval, respectively.
First, we need to find [tex]\(\frac{dy}{dx}\)[/tex], which represents the derivative of y with respect to x:
[tex]\[ \frac{dy}{dx} = \frac{d}{dx}(3 + 2x^\frac{3}{2}) = 0 + 3x^\frac{1}{2} = 3\sqrt{x} \][/tex]
Next, we substitute this derivative into the formula for arc length:
[tex]\[ L = \int_{0}^{1} \sqrt{1 + (3\sqrt{x})^2} dx = \int_{0}^{1} \sqrt{1 + 9x} dx \][/tex]
Now, we need to integrate [tex]\(\sqrt{1 + 9x}\)[/tex]L with respect to \(x\). We can do this by making a substitution. Let u = 1 + 9x, then du = 9dx and \(dx = \frac{du}{9}\). Substituting these into the integral, we get:
[tex]\[ L = \frac{1}{9} \int_{1}^{10} \sqrt{u} du \][/tex]
Now, we can integrate [tex]\(\sqrt{u}\)[/tex]:
[tex]\[ L = \frac{1}{9} \left[\frac{2}{3}u^\frac{3}{2}\right]_{1}^{10} = \frac{2}{27} \left[10^\frac{3}{2} - 1^\frac{3}{2}\right] \][/tex]
[tex]\[ L = \frac{2}{27} (10^\frac{3}{2} - 1) \][/tex]
[tex]\[ L = \frac{2}{27} (10\sqrt{10} - 1) \][/tex]
So, the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\( \frac{2}{27} (10\sqrt{10} - 1) \)[/tex].
The function f(x) is represented by this table of values .Match average rate of change of f(x) with corresponding intervals
To which part of the prism are the arrows pointing
A jacket that regularly cost $40 is on sale for $32 what is the percent decrease in the price of the jacket?
You give your friend a head start of 20 feet in a race. A linear equation representing your friend’s progress (in feet) after x seconds is y = 9x + 20. A linear equation representing your progress (in feet) after x seconds is y = 9x. Will you catch up to your friend? Explain.
To catch up to your friend or not in a race explained with equations and steps.
The question is: Will you catch up to your friend? Explain.
Step-by-step explanation:
Friend's progress equation: y = 9x + 20
Your progress equation: y = 9x
To catch up, set the equations equal: 9x + 20 = 9x
Solve for x: 20 = 0 (This equation has no solution)
You will not catch up to your friend.
f(x) = 16x4 – 81 = 0 Select all of the zeroes of the function.
3/2
-3/2
3/2i
-3/2i
Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.
The zeros are:
x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*iFirst, for a given function f(x), we define the zeros as the values of x such that:
f(x) = 0.
Then we must solve:
f(x) = 16*x^4 - 81 = 0
Solving this for x leads to:
16*x^4 = 81
x^4 = 81/16
x^2 = ±√(81/16) = 9/4
x = ±√±(9/4) = ±3/2 and ±(3/2)*i
So there are 4 zeros, and these are:
x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*iWhere the two complex zeros come from evaluating the second square root on -9/4.
If you want to learn more, you can read.
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ms johnson and ms smith were folding report cards to send home to parents. the ratio of the number of report cards ms johnson folded to the number of report cards ms smith folded is 2:3. At the end of the day , ms Johnson and ms smith folded at total of 300 report cards. How many did each person fold?
Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half hour. how many bacteria will the colony contain at the end of 24
A colony of bacteria that starts with 1 bacterium and doubles in number every half hour will contain approximately 281,474,976,710,656 bacteria at the end of 24 hours.
Explanation:The number of bacteria in a colony that starts with 1 bacterium and doubles in number every half hour can be calculated using the formula 2ⁿ, where n is the number of generations. Since each generation is half an hour, there are 48 generations in 24 hours. Plugging in n=48 into the formula, we get 2⁴⁸, which is approximately 281,474,976,710,656 bacteria.
Learn more about Bacterial growth rate here:https://brainly.com/question/29885707
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THIS IS TIMED AND I NEED HELP!!!
Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)
(25 points) A weather reporter in your area said that the speed of sound in air today is about one thousand one hundred feet per second. What is that speed in scientific notation?
Answer:
1.1 × 103 feet per second
What is the value of S4 for
A. 5 5/64
B. 5 1/4
C. 5 5/16
D. 5 5/6
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
[tex]S_n=\sum^{\infty}_{n=1}4(\dfrac{1}{4})^{n-1}[/tex]
We need to find the value of S₄.
So, it means sum of 4 terms.
Here it form a geometric series:
a = 4 = first term
r = [tex]\dfrac{1}{4}[/tex] = Common ratio
And sum of n terms whose ratio is less than 1 is given by
[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\S_4=\dfrac{4(1-\dfrac{1}{4}^{4})}{1-\dfrac{1}{4}}\\\\S_4=\dfrac{4(1-0.25^4)}{1-0.25}\\\\S_4=\dfrac{4(1-0.0039)}{0.75}\\\\S_4=5.3125\\\\S_4=5\dfrac{5}{16}[/tex]
Hence, Option 'C' is correct.
Answer: Option 'C' is correct.
Step-by-step explanation:
Which expression is equivalent to 34 ⋅ 3−9?
1 over 3 to the 13th power
1 over 3 to the 5th power
35
313
Answer:
b.1 over 3 to the 5th power.
Step-by-step explanation:
We are given that an expression
[tex]3^4\cdot 3^{-9}[/tex]
We have to find that which expression is equivalent to given expression
[tex]3^4\cdot 3^{-9}[/tex]
We know that [tex]a^b+a^c=a^{b+c}[/tex]
Using this identity
Then, we get [tex]3^4\cdot 3^{-9}=3^{4-9}=3^{-5}[/tex]
[tex]3^4\cdot 3^{-9}=\frac{1}{3^5}[/tex]
Using [tex]a^{-b}=\frac{1}{a^b}[/tex]
Hence, option b is true.
Answer:b.1 over 3 to the 5th power.
The sum of two numbers is 49 . the smaller number is 17 less than the larger number. what are the numbers?
Final answer:
To solve the student's algebra problem, we defined variables, set up an equation based on the given conditions, and then solved for the larger number. Ultimately, we found the two numbers to be 33 and 16.
Explanation:
The student asked a problem that involves finding two numbers given that their sum is 49 and the smaller number is 17 less than the larger number. To solve this problem, we will use algebra.
Let the larger number be x and the smaller number be x - 17. According to the problem, the sum of these two numbers is 49:
x + (x - 17) = 49
Combine like terms: 2x - 17 = 49
Add 17 to both sides: 2x = 66
Divide by 2: x = 33
Since the larger number is 33, the smaller number is 33 - 17, which is 16.
Therefore, the two numbers are 33 and 16.
What is equivalent to xy/a - 1/b
Express -2 in triganomic form
Final answer:
To express -2 in trigonometric form, we find the magnitude (absolute value) and the argument (angle) of the complex number.
Explanation:
The trigonometric form of a complex number is expressed in the form r(cosθ + isinθ), where r is the magnitude of the complex number and θ is the argument or angle.
In this case, to express -2 in trigonometric form, we first find the magnitude, which is the absolute value of -2, so |-2| = 2. The argument can be found using the arctan function, which is θ = arctan(b/a), where a is the real part and b is the imaginary part.
For -2, the real part is -2 and the imaginary part is 0. Thus, the argument is θ = arctan(0/(-2)) = arctan(0) = 0. Therefore, -2 in trigonometric form is 2(cos0 + isin0), which simplifies to just 2.
Alicia drove 265 miles in 5 hours What is the average rate that she traveled 49 miles per hour 51 miles per hour 53 miles per hour 55 miles per hour
Which statement is 1?
option 5 btw is none of these
What are the solutions of 4x4 – 4x2 = 8?
Final answer:
To find the solutions of the equation 4x^4 - 4x^2 = 8, we can rearrange the equation and solve the resulting quadratic equation. The solutions are x = ±√2.
Explanation:
To find the solutions of the equation 4x^4 - 4x^2 = 8, we can rearrange the equation to get 4x^4 - 4x^2 - 8 = 0. This is a quadratic equation in terms of x^2. We can solve this quadratic equation by factoring or by using the quadratic formula.
Factoring the equation, we get (2x^2 - 4)(2x^2 + 2) = 0. Setting each factor equal to zero, we have 2x^2 - 4 = 0 and 2x^2 + 2 = 0.
Solving each equation separately, we get x^2 = 2 and x^2 = -1. Taking the square root of both sides, we get x = ±√2 and x = ±i. Therefore, the solutions of the original equation are x = ±√2.
the function f (x) =830(1.2)x represents the number of students enrolled at a university xyears after it was founded. each year the number of students is ----- the number the year before
Step-by-step explanation: Apex 9/25/19
How do I find the terms?
If you put down 20% on a $7000 car and pay monthly payments of $109.40 for 60 months, what is the total price of the car?
Answer:
7964
Step-by-step explanation:
How old am i if i was born in 05/22/1965?
Answer:
In 2021 you would be 56 or 55 years old
Step-by-step explanation:
2021-1965=56 or the other way you could do it 52+4 because the other person said you would be 52 in 2017 so 4 years after you would be 55 or 56
Roger owns a one acre piece of land . The length of the land is 484 feet. What is the width of his property
1 acre = 43560 square feet
43560 = 484 * X
X=43560/484 = 90
the width = 90 feet
Answer:
90 feet
Step-by-step explanation:
A. 15
B. 125
C. 135
D. 45
Melanie is flying from washington,
d.c., to seattle. her flight leaves at 10
a.m. when her plane lands, the pilot announces that it is 2 p.m. in seattle. how long did her flight take
If a triangle has legs measuring 8 inches and 15 inches and has a hypotenuse measuring 17 inches, what is the ratio, in simplest form, of the shorter leg to the hypotenuse?
The table below shows the surface area y, in square feet, of a shrinking lake in x days:
Time (x)
(days) 5 10 15 20
Surface area (y)
(square feet) 90 85 70 61
Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] (4 points)
Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points)
Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)