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Related Questions
There are 21 different coffee flavours at the cafe. oddly, each student in my 8 am class has a favourite flavour there. there are just enough students in the class so you can be absolutely sure that 7 students all have the same favourite. how many students are there in the class?
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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)
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y = x - 1
x^2 + 2x - 3 = x - 1
x^2 + 2x - x - 3 + 1 = 0
x^2 + x - 2 = 0
(x + 2)(x - 1) = 0
x + 2 = 0 y = x - 1
x = -2 y = -2 - 1
y = -3
x - 1 = 0 y = x - 1
x = 1 y = 1 - 1
y = 0
ur solutions are : (-2,-3) and (1,0)
You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
(I know it's 119.954 years, but I have no idea how to get that)
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A=p (1+r/k)^kt
A future value 3000
P present value 150
R interest rate 0.025
T time?
3000=150 (1+0.025/12)^12t
Solve for t
3000/150=(1+0.025/12)^12t
Take the log
Log (3000/150)=log (1+0.025/12)×12t
12t=Log (3000/150)÷log (1+0.025/12)
T=(log(3,000÷150)÷log(1+0.025÷12))÷12
T=119.95 years
Answer:
It take 119.954 years to earn $ 3000 without depositing any additional funds.
Step-by-step explanation:
Given:
Principal Amount, P = $ 150
Amount, A = $ 3000
Rate of interest, R = 2.5% compounded monthly.
To find: Time, T
We use formula of Compound interest formula,
[tex]A=P(1+\frac{R}{100})^n[/tex]
Where, n is no time interest applied.
Since, It is compounded monthly.
R = 2.5/12 %
n = 12T
[tex]3000=150(1+\frac{\frac{2.5}{12}}{100})^{12T}[/tex]
[tex]\frac{3000}{150}=(1+\frac{2.5}{1200})^{12T}[/tex]
[tex]20=(1+\frac{2.5}{1200})^{12T}[/tex]
Taking log on both sides, we get
[tex]log\,20=log\,(1+\frac{2.5}{1200})^{12T}[/tex]
[tex]1.30103=12T\times\,log\,(1.002083)[/tex]
[tex]T=\frac{1.30103}{12\times\,log\,(1.002083)}[/tex]
[tex]T=119.954[/tex]
Therefore, It take 119.954 years to earn $ 3000 without depositing any additional funds
A. 15
B. 125
C. 135
D. 45
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They are corresponding angles)
so 3x + 9x = 180
x = 180/12 = 15
So angle 1 = 3x = 3*15 = 45 degrees
D
12x = 180°
x = 15°
9x + 1 = 180°
9(15°) + 1 = 180°
135° + 1 = 180°
1 = 180° - 135° = 45°
Answer is D
Hope it helped!
(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?
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In scientific notation, it's 1.1*10^3
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
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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:
How do I find the terms?
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[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=4\\ a_1=-2\end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=-2+(2-1)4\\ 3&a_3=-2+(3-1)4\\ 4&a_4=-2+(4-1)4\\ 5&a_5=-2+(5-1)4 \end{array}[/tex]
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A(n)= 1/4 * A(n) is just a way of saying, you get the next term by multiplying the current one by 1/4, and A(1) = 8, simply means the first term's value is 8.
[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=\frac{1}{4}\\ a_1=8 \end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=8\left( \frac{1}{4} \right)^{2-1}\\\\ 3&a_3=8\left( \frac{1}{4} \right)^{3-1}\\\\ 4&a_4=8\left( \frac{1}{4} \right)^{4-1}\\\\ 5&a_5=8\left( \frac{1}{4} \right)^{5-1}\\ \end{array}[/tex]
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?
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hope that helps
f(x) = 16x4 – 81 = 0 Select all of the zeroes of the function.
3/2
-3/2
3/2i
-3/2i
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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.
https://brainly.com/question/8815381
Write the standard form of the line that contains a y-intercept of -3 and passes through the point (3, 0). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
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m=(y2-y1)/(x2-x1)
m=(-3-0)/(0-3)
m=-3/-3
m=1 so far for the line y=mx+b we have:
y=x+b, b is the y intercept which we were told is -3 so
y=x-3
The above is called the slope-intercept form of a line, y=mx+b, the standard form of a line is ax+by=c, so we need to get both variables on one side of the equation..
y=x-3 subtract x from both sides
-x+y=-3
While the above may be acceptable to some, technically the coefficient of x should be expressed as a positive value, so we should divide the above "solution" by -1 to get:
x-y=3
The equation of the line in standard form that has a y-intercept of -3 and passes through the point (3, 0) is y = x - 3.
Explanation:The standard form of a line can be found using the formula y = mx +b, where 'm' is the slope and 'b' is the y-intercept. The y-intercept in this problem is -3, but we need to find the slope to complete the standard form of the line. Since our line passes through the point (3,0) and (0,-3), the slope, m, can be found by using the formula (y2-y1)/(x2-x1), which gives us a slope of 1. So the equation of our line in standard form is y = x - 3.
Learn more about Standard Form of a Line here:https://brainly.com/question/32638435
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
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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
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Each year the number of students is 1.2 times the number the year before. Or you could say that each year the enrollment increases by 20%.
Step-by-step explanation: Apex 9/25/19
What is equivalent to xy/a - 1/b
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1. The least common multiple of the denominators of the terms of the given is ab.
2. Multiply the expression with ab, such that,
(xy/a - 1/b) x (ab)
3. Simplifying,
xyb - a
4. Writing ab as the denominator of the expression in number, we get the final answer which is equal to,
(xyb - a)/ab
The sum of two numbers is 49 . the smaller number is 17 less than the larger number. what are the numbers?
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So the smaller number will be x-17
Since the sum of the two numbers is 49
x-17+x=49
2x-17=49
2x=49+17
2x=66
x=33
The larger number is 33 while the smaller number is 33-17=16
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.
Which is the graph of f(x)=2(3)^x
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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
What are the solutions of 4x4 – 4x2 = 8?
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and
x=+-sqrt2
so its A anc C
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.
Roger owns a one acre piece of land . The length of the land is 484 feet. What is the width of his property
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1 acre = 43560 square feet
43560 = 484 * X
X=43560/484 = 90
the width = 90 feet
Answer:
90 feet
Step-by-step explanation:
How many equations are needed to solve for 1 unknown variable?
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For number of variables greater than 1, as stated above, the number of equations should be equal to that number. However, it has to be noted that the equations should be independent and not the multiplicative of another.
For the concept of multiplicity,
x + y = 0 and 2x + 2y = 0 are just the same equations.
Hence, the answer to this item is one (1).
The statement “Angles that measure more than 90 degrees are obtuse angles” has a counterexample
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How old am i if i was born in 05/22/1965?
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2017 - 1965 = 52
And since May already passed (05/22), you're birthday already passed.
So you are 52 years old if you were 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
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
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Since it's negative, so it's low negative correlation
Which expression is equivalent to 34 ⋅ 3−9?
1 over 3 to the 13th power
1 over 3 to the 5th power
35
313
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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.
Find the exact length of the curve. y = 3 + 2x3/2, 0 ≤ x ≤ 1
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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].
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?
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The range of a relation is
A: the output (y) values of a relation
B: the input (x) values of the relation
C: a set of points that pair input values with output values
D: x and y values written in the form (x,y)
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Consider a relation R, from M to N
that is:
R:M→N
R(x)=y
so x is taken from set M, and the product y, is in set N
The set of all output of R,so all possible y, is called the Range of y:
Answer: A: the output (y) values of a relation
A jacket that regularly cost $40 is on sale for $32 what is the percent decrease in the price of the jacket?
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now, if we take 40 to be the 100%, how much is 8 off of it in percentage?
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 40&100\\ 8&x \end{array}\implies \cfrac{40}{8}=\cfrac{100}{x}[/tex]
solve for "x".
The integral represents the volume of a solid. describe the solid. π π 0 sin(x) dx
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The function f(x) is represented by this table of values .Match average rate of change of f(x) with corresponding intervals
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If fx(x) changes from f(x₁) to f(x₂), the rate of change is
Rate = [f(x₂) - f(x₁)]/(x₂ - x₁)
From the table, we can compute rates of change as follows:
Change in x Change in f(x) Change in x Rate
----------------- -------------------- ----------------- ---------
[-4,-2] 0 - (-12) = 12 0 - (-2) = 2 6
[-2, 1] 3 - 0 = 3 1 - (-2) = 3 1
[-3, 1] 3 - (-5) = 8 1 - (-3) = 4 2
[-4, 0] 4 - (-12) = 16 0 - (-4) = 4 4
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)
Answers
The 'line of best fit' shows a negative gradient
Part A: The most likely coefficient is -0.98.
If the coefficient is -1, then each point would be exactly on the straight line (which they are not as shown on the graph). The graph however still shows a strong negative coefficient. It can be seen from the close distance of each point from the line of best fit. So -0.5 and -0.02 is unlikely as they show weak negative correlation
Part B: Refer to the second picture to see the horizontal and vertical distance between day 15 and day 20
The horizontal distance is 5 units
The vertical distance is read between 61 and 71.5, hence it's 10.5
The slope = Vertical distance ÷ Horizontal Distance = 10.5÷5 = 2.1
The 'downhill' slope shows a negative gradient, hence the value of the slope is -2.1
The value of the slope shows that the surface area of the lake shrinks by 2.1 for every one day
Part C: The data in the table represents the relation between two variables. Since one variable doesn't cause the change in the other variable, the data table represents correlation rather than a causation.
Which statement is 1?
option 5 btw is none of these