In order to conduct a certain experiment, four students are randomly selected from a class of 20. how many different groups of four stdents are possible
i need help!!!!!!!!!!!!!!?!!!
What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?
Final answer:
The total amount on a $6,500 investment at a 6% annual interest rate compounded yearly for 25 years is approximately $28,353.25, with the interest earned being about $21,853.25.
Explanation:
To calculate the total amount and the amount of interest earned on $6,500 at 6% for 25 years, we need to identify whether the interest is compounded annually, monthly, or if it's simple interest. Since the type of interest isn't specified, we'll assume it's compounded annually, which is common in savings accounts. The formula for compound interest is:
A = P(1 + r/n)nt
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($6,500)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time the money is invested or borrowed for, in years (25 years)
For this example, since the interest is compounded annually, n = 1. First, convert the interest rate from a percentage to a decimal by dividing by 100: 6% / 100 = 0.06. Now, plug the values into the formula:
A = $6,500(1 + 0.06/1)1*25
A = $6,500(1 + 0.06)25
A = $6,500(1.06)25
Calculating this out, A, which is the total future amount, comes out to:
A = $28,353.25 approximately
To find out the total interest earned, subtract the principal from the final amount:
Total interest = A - P
Total interest = $28,353.25 - $6,500
Total interest = $21,853.25 approximately
The total amount is about $28,353.25 and the amount of interest earned is about $21,853.25.
Which box plot represents the data?
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
The box plot that represents the data is option B.
What is a box plot?A box plot is known to be a method that is employed to demonstrate the locality and skewness of numerical data. This is carried out graphically and done through the quartiles of the given numerical data.
Rearranging the given data, we have:
112,116, 134, 134, 135, 141, 149, 154, 156, 156
The minimum value after rearranging = 112.
First Quartile, Q1 = 134.
Second Quartile, Q2 or Median = 135+141/2 = 276/2 = 138
Third Quartile, Q3 = 154
Largest figure = 156
The answer is the second figure.
Learn more about box plot on https://brainly.com/question/14277132
The first term of an arithmetic sequence is -5 , and the twelfth term is 1.7 .find the common difference
The equation of a circle is (x−2)2+(y−16)2=169 .
What is the circle's radius?
Enter your answer in the box.
units
The radius of the circle with the equation (x−2)^2+(y−16)^2=169 is 13 units.
The equation of the circle provided is (x−2)2+(y−16)2=169. In the standard form of a circle's equation, (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius, we see that 169 represents r2. Hence, to find the radius of the circle, we take the square root of 169.
The radius r is calculated as r = √169 = 13 units. Therefore, the circle's radius is 13 units.
On a rectangular soccer field, Sang is standing on the goal line 20 yards from the corner post. Jazmin is standing 99 yards from the same corner post on the nearest adjacent side of the field. What is the distance from Sang to Jazmin?
A.119 yards
B.101 yards
C.10,201 yards
D.1,980 yards
I am wondering if the answer to this question is Table B. At x = 1, f'(x) = 1/2. At x = 2, f'(x) = 3. Does this mean that, between 1 and 2, the slope should be greater than 1/2 and less than 3? (e.g. graph B)?
Using the discriminant, how many real number solutions does this equation have? 3x^2 – 2 = 5x
The height of a tree in feet over x years is modeled by the function f(x). f(x)=301+29e−0.5x which statements are true about the growth of the tree? select each correct answer. the tree's maximum height is limited to 30 ft. the tree is initially 2 ft tall. between the 5th and 7th years, the tree grows approximately 7 ft. after growing 15 ft, the tree's rate of growth decreases.
Final answer:
The tree's maximum height is not limited to 30 ft but approaches 301 ft. Initially, the tree is 30 ft tall, not 2 ft. To verify the growth between the 5th and 7th years, one must calculate f(5) and f(7). The rate of growth indeed decreases over time.
Explanation:
When analyzing the function f(x) = 301 + 29e^{-0.5x} to understand the growth pattern of a tree, it is apparent that some statements about the tree's growth can be identified as true or false.
The tree's maximum height is not limited to 30 ft; instead, the model suggests that the height approaches 301 ft as x increases indefinitely, because the exponential term decreases towards zero.The tree is initially 30 ft tall, not 2 ft tall, since f(0) = 301 + 29 × 1 = 330 ft.Between the 5th and 7th years, the growth can be calculated using f(5) and f(7) to determine if it grows approximately 7 ft during that period.After growing 15 ft, the rate of growth would decrease since the exponential function's growth rate decreases as x increases.The amounts of 8 charitable contributions are $100, $80, $250, $100, $500, $1000, $100, and $150.
The mean, median, and mode of the amounts are given below. mean = $285 median = $125 mode = $100
Which value describes the amount received most often?
What is the equation of the circle whose center and radius are given.
center ( 7, -3), radius = 7
2x + 4y = 12 converted into slope intercept form (y=mx+b)??
To convert 2x + 4y = 12 into slope-intercept form, we must put it into y = mx + b form, where m represents the slope of the line and b is the y intercept of the equation. To begin, we should subtract 2x from both sides so that we can get the variable y alone on the left side of the equation.
2x + 4y = 12
4y = -2x + 12
Next, because there cannot be a coefficient on the variable y in this form, we must divide both sides of the equation by 4.
y = -2/4x + 3
Because 2 and 4 are both divisible by 2, we can divide both the numerator and the denominator by 2 to further simplify the equation.
y = -1/2x + 3
Therefore, the answer is y = -1/2x + 3.
Hope this helps!
To convert the equation 2x + 4y = 12 into slope-intercept form (y=mx+b), you subtract 2x from both sides and then divide by 4 to isolate y, resulting in y = -1/2x + 3, where the slope (m) is -1/2 and the y-intercept (b) is 3.
Explanation:To convert the equation 2x + 4y = 12 into slope-intercept form (y=mx+b), we need to solve for y. Here's how you can do it step by step:
Begin with the original equation: 2x + 4y = 12.Subtract 2x from both sides to isolate the y-term: 4y = -2x + 12.Divide each term by 4 to solve for y: y = -½x + 3.Now the equation is in slope-intercept form where m (the slope) is -1/2 and b (the y-intercept) is 3. The slope m is defined as the rise over the run of the straight line, and the y-intercept b is the point where the line crosses the vertical axis, which in this case is when x=0 and y=3.
A card is drawn randomly from a standard deck of cards. you win $10 if the card is a spade or an ace. what is the probability that you will win the game?
You are selling cookies for your organization. One box of cookies is sold for $3. Thirty percent of the sale price goes to the bakery to pay for the cookies. The rest of the sale price is split evenly between the regional headquarters for your organization, and your local chapter. How much does your local chapter earn for each box of cookies that are sold? How many boxes of cookies do you have to sell to earn $100 for your local chapter?
Write a single algebraic rule for the series of transformations: a reflection about the x-axis, a rotation of 90 degrees clockwise, and a translation of 4 units right and 2 units down.
Which transformation is a rotation?
Answer:
the answer is c.
Step-by-step explanation:
Let d(t) =6t^2 be the distance function, find the average velocity from (4, 4.1)
Can someone help me please?
Write the equation for finding the nth term of the sequence. 18, 14, 10
The diagram shows the locations of John and Mark in relationship to the top of a tall building labeled A.
A) Describe < 4 as it relates to the situation
B) Describe < 3 as it relates to the situation
The center of a circle is at (2, -5) and it's radius is 12. What is the equation of the circle?
A.) (x+2)^2 + (y-5)^2 =24
B.) (x-2)^2 + (y+5)^2 = 24
C.) (x+2)^2 + (y-2)^2 = 144
D.) (x-2)^2 + (y+5)^2 = 144
Answer:
The answer is D
Step-by-step explanation:
It is D
whats the equation of the line that passes through (3,8) and (6,0)
To begin this problem, we need to use the two points that we are given to find the slope of the line. Slope is defined as the change in y values divided by the change in x values, or rise/run, and is represented by the variable m.
m = (y1-y2)/(x1-x2) = (8-0)/(3-6) = 8/(-3) = -8/3
Now, we can use the slope and one of the points from our given values to create an equation of the line in point-slope form.
y = m(x-h) + k, where a point on the line is (h,k)
y = -8/3(x - 3) + 8
Now, we can distribute our slope and simplify through addition.
y = -8/3x + 8 + 8
y = -8/3x + 16
Therefore, your answer is y = -8/3x + 16.
Hope this helps!
An equation of the line passing through (6,−3) having slope −35 is
If arc AXC = 235°, what is m∠ABC?
a. 117.5°
b. 60°
c. 55°
d. 125°
Answer:
The correct option is c.
Step-by-step explanation:
Given information: The measure of arc AXC is 235°. Let the center of the circle be O.
The sum of all disjoint arcs is 360°. So,
[tex]Arc(AXC)+Arc(AC)=360^{\circ}[/tex]
[tex]235^{\circ}+Arc(AC)=360^{\circ}[/tex]
[tex]Arc(AC)=360^{\circ}-235^{\circ}[/tex]
[tex]Arc(AC)=125^{\circ}[/tex]
[tex]\angle AOC=125^{\circ}[/tex]
The measure of arc AC is 125°.
Line BA and BC are tangent on the circle O from the same point, so the sum of opposite angles of the quadrilateral is 180°.
[tex]\angle AOC+\angle ABC=180^{\circ}[/tex]
[tex]125^{\circ}+\angle ABC=180^{\circ}[/tex]
[tex]\angle ABC=180^{\circ}-125^{\circ}[/tex]
[tex]\angle ABC=55^{\circ}[/tex]
The measure of angle ABC is 55°. Therefore the correct option is c.
What is the solution set of (x - 2)(x - 3) = 2?
a. {1, 4}
b. {2, 3}
c. {4, 5}
A residual plot is shown. Which statements are true about the residual plot and the equation for the line of best fit for the data? Check all that apply.
The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern.
The equation for the line of best fit is a good approximation for the data because the points are random, having no pattern.
The residual plot has a linear pattern.
The points of the residual plot are spread evenly above and below the x-axis.
The residual plot has the pattern of a curve.
The equation for the line of best fit is not a good approximation for the data because the points have a linear pattern
Only right answers, please. This is important for my grade.
Answer:
answer is 1 & 3 on edg
Step-by-step explanation:
Factor this trinomial completely.
10x2 + 7x – 12
A. (2x + 3)(5x – 4)
B. (x + 4)(10x – 3)
C. (x + 3)(10x – 4)
D. (2x + 4)(5x – 3)
The trinomial "10[tex]x^2[/tex] + 7x - 12" is factored by finding two numbers that multiply to -120 and add up to 7, which are 15 and -8. Split the middle term, group, and factor by grouping to get (2x + 3)(5x - 4), which is option A.
Explanation:To factor the trinomial "10x2 + 7x − 12" completely, you want to find two binomials that, when multiplied together, will give you the original trinomial. To do this, you will need two numbers that multiply to give you the product of the coefficient of the x2 term (which is 10) and the constant term (which is −12), which equals −120, and also add up to the coefficient of the x term (which is 7).
The two numbers that meet these criteria are 15 and −8, since (15)(−8) = −120 and 15 + (−8) = 7. Next, split the middle term of the trinomial using these two numbers:
10x2 + 15x − 8x − 12
Now, group the terms:
(10x2 + 15x) − (8x + 12)
Factor out the greatest common factor from each group:
5x(2x + 3) − 4(2x + 3)
Finally, factor out the common binomial factor:
(2x + 3)(5x − 4)
Therefore, the correct factorization of the trinomial 10x2 + 7x − 12 is (2x + 3)(5x − 4), which corresponds to option A.
If you round off 23 to nearest ten.what is the answer
Please help!!!
Use DeMoivre's theorem to evaluate the expression
[sqrt 3( cos 5pi/3 + i sin 5pi/3)]^4 ? write the answer in rectangular form
a. 9sqrt3/2 + 9/2 i
b. 9sqrt3/2 - 9/2 i
c. -9/2 - 9sqrt3/2 i
d. -9/2 + 9sqrt3/2 i
Answer:
Option d - [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]
Step-by-step explanation:
Given : [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]
To find : Use DeMoivre's theorem to evaluate the expression?
Solution :
DeMoivre's theorem state that, for complex number
If [tex]z = r(\cos\theta+ i\sin \theta)[/tex] then [tex]z^n = r^n(\cos n\theta+ i\sin n\theta)[/tex]
We have given,
[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]
On comparing [tex]r=\sqrt3[/tex] and n=4
Applying DeMoivre's theorem,
[tex]=(\sqrt3)^4(\cos 4(\frac{5\pi}{3})+i\sin4(\frac{5\pi}{3}))[/tex]
[tex]=9(\cos (\frac{20\pi}{3})+i\sin(\frac{20\pi}{3}))[/tex]
[tex]=9(\cos (6\pi+\frac{2\pi}{3})+i\sin(6\pi+\frac{2\pi}{3}))[/tex]
[tex]=9(\cos (\frac{2\pi}{3})+i\sin(\frac{2\pi}{3}))[/tex]
We know, the value of
[tex]\cos (\frac{2\pi}{3})=-\frac{1}{2},\sin (\frac{2\pi}{3})=\frac{\sqrt3}{2}[/tex]
[tex]=9(-\frac{1}{2}+i\frac{\sqrt3}{2})[/tex]
[tex]=-\frac{9}{2}+i\frac{9\sqrt3}{2}[/tex]
Therefore, Option d is correct.
[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]
Find the value of the lesser root of x^2-6x+8=0
Answer:
The value of lesser root is:
x=2
Step-by-step explanation:
We are given a quadratic equation in terms of variable " x " as:
[tex]x^2-6x+8=0[/tex]
We know that for any quadratic equation of the type:
[tex]ax^2+bx+c=0[/tex]
The roots of x are calculated as:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here we have:
a=1 , b=-6 and c=8
Hence, on solving for roots:
[tex]x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 1\times 8}}{2\times 1}\\\\\\x=\dfrac{6\pm \sqrt{36-32}}{2}\\\\\\x=\dfrac{6\pm \sqrt{4}}{2}\\\\\\x=\dfrac{6\pm 2}{2}[/tex]
Hence, we have:
[tex]x=\dfrac{6+2}{2}\ or\ x=\dfrac{6-2}{2}\\\\x=\dfrac{8}{2}\ or\ x=\dfrac{4}{2}\\\\\\x=4\ or\ x=2[/tex]
Hence, the value of lesser root is:
x=2