An combined area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.
Every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a standard deviation of 1. How do we do that? Use the z-score!
Z = ( x - μ)/σ
if the random variable X has a mean μ and standard deviation σ,
then transforming X using the z-score creates a random variable with mean 0 and standard deviation 1!
With that in mind, we just need to learn how to find areas under the standard normal curve, which can then be applied to any normally distributed random variable.
An area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.
To know more about z-score visit brainly.com/question/15016913
#SPJ4
Every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a standard deviation of 1. How do we do that? Use the z-score!
Z = ( x - μ)/σ
if the random variable X has a mean μ and standard deviation σ,
An area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.
pls help ill mark brainliest
Answer:
Step-by-step explanation:
since you are rotating the image it shows y k j and l so it would be 5.5
This is for my calculus class, please help.
The area bounded by y = x² + 5 and the x-axis from x = 3 to x = -2 is 110/3.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
y = x² + 5
The area bounded by y = x² + 5 from x = -2 to x = 3.
= [tex]\int\limits^{3}_{-2} {(x^2 + 5)} \, dx[/tex]
= [tex][x^3/3]^{3}_{-2}[/tex] + 5 [tex][x]^{3}_{-2}[/tex]
= 1/3 [tex][(3)^3 - (-2)^3][/tex] + 5 [3 + 2]
= 1/3 [27 + 8] + 5 x 5
= 1/3 x 35 + 25
= 35/3 + 25
= (35 + 75)/3
= 110/3
Thus,
The area bounded is 110/3.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
determine whether each pair of triangles is congruent. if so, write a congruence statement and explain why the triangles are congruent. (lesson 5-5) 4. b c n r p f m d 5. a l e
No, these two triangles are not congruent. Congruent triangles have the same shape and size, and Triangle ABC and Triangle DEF do not have the same shape or size.
Congruent triangles are two triangles that have the same shape and size. This means that the angles and the side lengths of the two triangles must be the same. For example, if two triangles have three angles that measure 60°, 60°, and 60°, the two triangles are congruent. Similarly, if two triangles have three side lengths of 5 cm, 6 cm, and 7 cm, the two triangles are also congruent. However, Triangle ABC and Triangle DEF do not have the same shape or size, therefore, they are not congruent. The angles and side lengths of the two triangles are not the same, so they cannot be congruent.
Learn more about triangle here
https://brainly.com/question/2773823
#SPJ4
the complete question is
determine whether each pair of triangles is congruent. if so, write a congruence statement and explain why the triangles are congruent.
Triangle ABC and Triangle DEF
autotrader would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks, cars, and vans. the following data represent the age of a random sample of trucks, cars, and vans. trucks cars vans 12 8 3 8 7 7 9 10 6 11 7 8 the grand mean for these observations is . multiple choice 7.2 8.0 8.9 9.3
The grand mean fir the observations of the age of three different types of vehicles currently on the road: trucks, cars, and vans is Eight . So, correct option is option B.
What is Grand mean ?The overall or pooled average is the average of multiple subsample averages, as long as the subsamples have the same number of data points. In ANOVA, the overall mean for a set of multiple subsamples is the mean of all observations. that is, each data point divided by the common sample size.
∑x = represented by the sum of the averages of all sets. Overall grand mean formula is
Grand mean = sum of all sample mean / total number of sentences
We have given that,
Autotrader would like to test difference exists in the age of three different types of vehicles.
let set A , set B and set C represents the ages of three different vichles i.e trunks , cars and vans respectively.
From table we get,
Mean of ages of trunks , A = 10
Mean of ages of cars , B = 8
Mean of ages of vans , C = 6
Grand mean = (10+8+6)/3 = 8
Hence, the grand mean is 8..
To learn more about Grand mean, refer:
https://brainly.com/question/4523756
#SPJ4
6. Investors buy a studio apartment for $ 240,000. Of this amount, they have a down payment of $ 60,000.
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $ 12,000 down payment be?
If Investors buy a studio apartment for the amount of 240,000.
a. The percent of the purchase price is 25%.
b. The percent of the purchase price is 5%.
How to find the percent of purchase price?a. Percent of purchase price
Using this formula to find the percentage of purchase price
Percent of purchase price = Down payment / Selling price
Percent of purchase price = $60,000/$240,000
Percent of purchase price = 0.25 × 100
Percent of purchase price = 25%
b. Percent of purchase price
Percent of purchase price = Down payment /Selling price
Percent of purchase price = $12,000/$240,000
Percent of purchase price = 0.05 ×100
Percent of purchase price = 5%
Therefore the percent of the purchase price is 25%, 5%.
Learn more about Percent of purchase price here:https://brainly.com/question/19260405
#SPJ1
Select the correct answer.
Convert 3-3i to polar form.
A. 3√2cis π/4
B. 3√2cis 3π/4
C. 3√2cis 5π/4
D. 3√2cis 7π/4
(Please mark brainliest <3)
Correct option is D.
We have been given a complex number 3-3i we have to convert it in the polar form:
Polar form of a complex number: z=r(cosθ+isinθ)
Where, r=√x^2+ y^2
the general form of complex number is:
x+iy
•Here, x=3 and y=-3
•Hence, r=√3^2+(-3)^2}= √18
•And θ=tan −1 y/x
•θ=tan −1 -3/3
•θ=tan −1 (−1)
•θ=2π− π/4
•θ= 7π/4
•Hence, substituting all the values in polar form formula we get:
z= √18cos( 7π/4) + isin (7π/4)
write and equivalent expression to 24x^2 +56x choose all that apply
Here is the step by step x
The equivalent expression to 24x^2 +56x is : 8x(3x+7)
What is an equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).Using the equality (=) symbol, equivalent phrases are represented. Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18.When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.Given data :
= 24[tex]x^{2}[/tex] + 56
= 24 xx + 56
Rewrite 24 as 8 * 3
Rewrite 56 as 8 * 7
= 8 * 3xx + 8 * 7x
= 8x (3x+7)
Learn more about equivalent expression refer to :
https://brainly.com/question/2972832
#SPJ1
46650 round it to the nearest million
The rounding of 46,650 to the nearest million is given as follows:
0.
How to round a number?To round a number, the number at the next place relative to the rounding place must be looked:
If the number is less than 5, then the number at the previous digit remains constant.If the number is of 5 or greater, then the digit at the previous digit is increased by one.Examples of rounding to the nearest tenth are given as follows:
10.52 = 10.5, as 2 < 5.10.56 = 10.6, as 6 > 5.The numbers to the nearest million are rounded according to the example given as follows:
Less than 500,000: 0.Between 500,000 and 1,500,000: 1.And so on...For this problem, we are given a number that is less than 500,000, hence the rounding of the number to the nearest million is of 0.
More can be learned about rounding at https://brainly.com/question/28128444
#SPJ1
do both and expain please.
The the equation of line in slope - intercept form is [tex]y = -\frac{1}{3}x-3[/tex] and the slope for the given table is 0.
What is slope intercept form of the line?
When you know the slope of the line to be examined and the given point is also the y intercept, you can use the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
Given:
The line passes through the point (3, -4) and having the slope is -1/3.
Consider the point - slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
where, [tex](x_1, x_2)[/tex] is the given point and m is the slope.
Plug [tex](x_1, y_1) = (3, -4)[/tex] and m = -1/3 in the above equation.
[tex]y-(-4)=-\frac{1}{3}(x-3)\\ y+4=-\frac{1}{3}x+1\\ y=-\frac{1}{3}x+1-4\\ y=-\frac{1}{3}x-3[/tex]
This is the equation of line in slope - intercept form.
Now to find the slope of the line that passes through the given points on the table.
Since,
Slope = [tex]\frac{Change In y}{Change In x}[/tex]
From the given table the change in y is 0, and the change in x is 5 for all the values.
So,
Slope = 0/5 = 0
Hence, the the equation of line in slope - intercept form is [tex]y = -\frac{1}{3}x-3[/tex] and the slope for the given table is 0.
To know more about slope - intercept form of the line, click on the link
https://brainly.com/question/24907633
#SPJ1
The current in a wire is defined as the derivative of the charge: l (t) = Q’ (t). (See Example 3 in Section 3.3) What does ∫b l (t) dt represent?
The integral [tex]\int\limits^a_b {I (t)} \, dt[/tex]represents the total change in the charge from time t= b to t = a. Or in other words, it is the total amount of charge passed through between t = a and t = b.
What is the Net change Theorem?The ultimate value of a quantity, according to the net change theorem, equals the beginning value plus the integral of the rate of change when a quantity changes. Net change can be either a positive, negative, or zero number.
The Net Change Theorem: The integral of a rate of change is the net change.
[tex]\int\limits^a_b {F'(x)} \, dx[/tex] = F(b) − F(a)
[tex]\int\limits^a_b {I (t)} \, dt[/tex] & I(t) = Q'(t)
Consider the given integral,
[tex]\int\limits^a_b {I (t)} \, dt[/tex], where I(t) = Q'(t)
Now substitute the value I(t) = Q'(t) in [tex]\int\limits^a_b {I (t)} \, dt[/tex]. It becomes[tex]\int\limits^a_b {I (t)} \, dt[/tex] = [tex]\int\limits^a_b[/tex]Q'(t) by using the Net Change Theorem,
[tex]\int\limits^a_b[/tex] Q'(t) dt = Q(b)−Q(a)
[tex]\int\limits^a_b {I (t)} \, dt[/tex] = Q(b)−Q(a)
The integral [tex]\int\limits^a_b {I (t)} \, dt[/tex] represents the change in the charge from time b to a.
Therefore, [tex]\int\limits^a_b {I (t)} \, dt[/tex] represents the change in the charge from time t= b to t= a.
Learn more about Net change Theorum here:
https://brainly.com/question/15867119
#SPJ4
Solve the system of equations graphed on
the coordinate axes below.
y=-3x - 5
y =4/3x-5
Placing a point at the graph's y-intercept offor the equation (0,-5).
How to solve the system of equations graphed?Placing a point at the graph's y-intercept of -4 for the equation y =3x - 5 (0,-5). From the point (0,-5) go one down, three to the right, and then add another point because the slope is -5The two points may be connected by drawing a line using a straightedge. Keep going after the two points. Past them, continue the line.same for y = 4/3x-5. Place a point at since the y-intercept is at 2, (0,-5). Since the slope is 4/3, go up 4and to the right 3 before drawing a second point from (0,-5). The two points may be connected by drawing a line using a straightedge. Don't, once more, end at the two points. Past them, continue the line.To learn more about graph's y-intercept refer to:
https://brainly.com/question/26115667
#SPJ11
math
r,mrkmrkrmkrmkrmkr
When you start from the given set of rules and conditions and determine must be true you are using c) Deductive reasoning.
Define deductive reasoning.In deductive reasoning, conclusions are reached based on premises that are typically taken to be true. It employs a logical premise to arrive at a logical conclusion and is also known as "deductive logic." The term "top-down reasoning" is frequently used to describe deductive reasoning. If something is presumptively true and a different object is connected to the first presumption, then the original truth must also apply to the second. Syllogism is one of the most popular forms of deductive reasoning. A major and a minor assertion coming together to make a logical conclusion is referred to as a syllogism. The fact that the two statements are true indicates that the assertion will probably be true for all further premises belonging to that category.
Given,
When you start from the given set of rules and conditions and determine must be true you are using ___ reason.
c) Deductive reasoning
To learn more about deductive reasoning, visit:
https://brainly.com/question/7284582
#SPJ1
There are only 2.1 x 10^8 metric tonnes of usable fossil fuels existing on Earth.
Assuming an estimated rate of fossil fuel use of 1 x 10^5 metric tonnes per year, calculate an order of magnitude estimation of the time left before the fossil fuel reserves run out.
Give your answer to one significant figure.
The answer is 2000 but I cannot figure out how they got it.
The time left before the fossil fuel reserves run out is 2000years(1significant figure)
What is rate?A rate is a special ratio in which the two terms are in different units. For example, if a 14-ounce can of corn costs 69¢, the rate is 69¢ for 14 ounces. Rate can also be defined as the ratio of two unlike units.
The total metric tonnes of fossil fuel on earth is 2.1×10⁸.
The rate of usage is 1×10⁵ metric tone of fossil fuel per year
as been said rate = total metric tone of fuel/ number of years to use
1×10⁵= 2.1×10⁸/no of years
no of years = 2.1×10⁸/1×10⁵
no of years = 2.1×10³years= 2100years
to 1 significant figure = 2000years
therefore the number of years for the fossil fuel to run out is 2000years
learn more about rate from
https://brainly.com/question/25793394
#SJ1
Im lost can I get help with this
Answer:
see explanation
Step-by-step explanation:
y = - x² + 4
can be expressed in functional notation as
f(x) = - x² + 4
to find the range value, substitute the domain value into f(x) , that is
f(3) = - 3² + 4 = - 9 + 4 = - 5
range value is then - 5
Erika drives from school to soccer practice 1.3 miles away. It takes her 7 minutes.
a.
b.
C.
d.
What fraction represents her constant speed, C?
What fraction represents her constant speed, C, if it takes her x minutes to drive exactly 1 mile?
Write a proportion using the fractions from parts (a) and (b) to determine how much time it takes her to drive
exactly 1 mile. Round your answer to the tenths place.
Write a two-variable equation to represent how many miles Erika can drive over any time interval.
a. Constant speed, C = 0. 19 miles/minutes
b. The fraction representing her constant speed is 1/x miles/minutes
c. The time it takes her to drive exactly 1 mile is 5. 38 minutes
How to determine the valueThe formula for calculating constant speed is expressed as;
Constant speed = total distance covered/ total time taken
From the information given, we have that;
Total distance = 1. 3milesTime taken = 7 minutesNow, substitute the values into the formula
Constant speed = 1. 3 / 7
Divide the values
Constant speed = 0. 19 miles/minutes
When distance 1 mile, time taken = x minutes
Constant speed = 1/x miles/minutes
If 1. 3 miles = 7 minutes
Then, 1 mile = x
cross multiply
x = 7/1. 3
x = 5. 38 minutes
Hence, the constant speed is 0. 19 miles/minutes
Learn more about constant speed here:
https://brainly.com/question/2681210
#SPJ1
Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. The time t is measured in seconds and the units for r(t) are measured in tonnes (metric tons) per second. Note that r(t) is increasing over the interval [0, 6]. t 0 1 2 3 4 5 6 r(t) 28 18 34 48 54 60 (a) Give upper and lower estimates (in tons) for the total quantity Q(6) of erupted materials after six seconds. (Use six equal subintervals.) lower estimate Q(6) tons upper estimate tons = 016) (b) Use the midpoint rule to estimate Q(6) (in tons). (Use three equal subintervals.) Q(6) = tons Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table. t(h) 0 2 4 6 8 10 r(t) (L/h) 8.6 7.5 6.7 6.4 5.7 5.1 Find lower and upper estimates for the total amount of oil in liters) that leaked from the tank over the interval [0, 10]. (Use five equal subintervals.) lower estimate upper estimate
Lower estimate obtained would be = 35.4 liters
Upper estimate obtained would be = 35.4 liters
What is Estimate?
Estimation finds an estimate or approximation.
An approximation is a value, amount, or size closest to the true value found by rounding off.
To find upper and lower estimates for the total quantity of erupted materials after six seconds using six equal subintervals, we can use the left endpoints and the right endpoints of the subintervals to find the estimates.
The lower estimate is obtained by using the left endpoints of the subintervals to estimate the value of r(t) at each subinterval. Since there are six subintervals, we have:
lower estimate = (28 + 18 + 34 + 48 + 54 + 60) * (6/6) = 324 tons
The upper estimate is obtained by using the right endpoints of the subintervals to estimate the value of r(t) at each subinterval. We have:
upper estimate = (18 + 34 + 48 + 54 + 60 + 60) * (6/6) = 324 tons
To use the midpoint rule to estimate Q(6) using three equal subintervals, we need to find the midpoints of the subintervals. The subintervals are [0,2], [2,4], and [4,6]. The midpoints are 1, 3, and 5. The value of r(t) at these points is 18, 48, and 54 respectively. The midpoint rule estimate is given by:
Q(6) = (18 + 48 + 54) * (6/3) = 180 tons
To find lower and upper estimates for the total amount of oil leaked over the interval [0, 10] using five equal subintervals, we can again use the left endpoints and the right endpoints of the subintervals to find the estimates. The lower estimate is obtained by using the left endpoints of the subintervals to estimate the value of r(t) at each subinterval. The upper estimate is obtained by using the right endpoints of the subintervals to estimate the value of r(t) at each subinterval.
The subintervals are [0,2], [2,4], [4,6], [6,8], and [8,10]. The left endpoints are 0, 2, 4, 6, and 8, and the right endpoints are 2, 4, 6, 8, and 10. The lower estimate is obtained by using the left endpoints:
lower estimate = (8.6 + 7.5 + 6.7 + 6.4 + 5.7) * (10/5) = 35.4 liters
The upper estimate is obtained by using the right endpoints:
upper estimate = (7.5 + 6.7 + 6.4 + 5.7 + 5.1) * (10/5) = 35.4 liters
Hence, The Lower estimate obtained would be = 35.4 liters and
Upper estimate obtained would be = 35.4 liters
To know more about Estimate visit,
https://brainly.com/question/28416295
#SPJ4
What is the slope of the line passing through the points (-1, 3) and (4, - 7)?
02
O-2
O
O
ده | ر
Answer:
Step-by-step explanation:
m = slope
m = (-7 -3 ) / (4 -(-1)
m = -10 / 5
m = -2
ask, if you want to understand how I got that. :)
Find all values of x that make the equation true. 3/x+3 = x-4/x
Answer:
X = -2 - 2(square root)3 or x = -2 + 2 (square root )3
Step-by-step explanation:
According to the United States Census Bureau the population of Utah was 2.12 million people in 1997 and 2.53 million people 9 years later in 2006. Use an explicit exponential model P t = P 0 ( 1 + r ) t to calculate the rate of growth of the population over this time period.
The rate of growth in the exponential function is 1.98%
Exponential FunctionAn exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
To solve this problem, we have to model the growth in an exponential function.
Population in 1997 = 2.12 million
Population in 2006 = 2.53 million
Time = 9
Since this is an exponential growth function, we can write this as;
2.53 = 2.12(1 + r)⁹
where r = rate of growth
2.53 = 2.12(1 + r)⁹
r = 0.0198
r = 1.98%
The rate of growth is 1.98%
Learn more on exponential function here;
https://brainly.com/question/2456547
#SPJ1
you have to choose a number between 0 and 100. the winner of the game is the person whose number is closest to 2/3 times the average of all chosen numbers.
The "winning" guess when played this game has been around 18.
What is rationality?The quality of being guided by or based on reasons is referred to as rationality. In this sense, a belief is rational if it is based on strong evidence, and an individual acts rationally if they have a good reason for doing so. This quality can be applied to a skill, like reasoning in a rational animal, a psychological process, like reasoning, mental states, like beliefs and intentions, or people who have these other kinds of rationality. If something does not meet the standards of rational evaluation, it is either irrational or rational, depending on where it falls outside the realm of rational evaluation.
Given you have to choose a number between 0 and 100. the winner of the game is the person whose number is closest to 2/3 times the average of all chosen numbers,
Theoretically, concur that the answer is 0. As stated, this is due to widespread rationality knowledge. You should guess 2/3*50=33 if everyone chose equally between 0 and 100. The average would be 50. Everyone ought to guess 33 if they are all aware of this. However, if I know that everyone correctly predicted 33, then 33 is the average, and should seek 2/3*33=22. This logic continues until everyone should correctly guess 0.
People actually don't think this way, but I disagree that you should guess between 5 and 10, which I believe is too low. depending on who you play with, as a group of game theorists might get a lower average than a group of people from the average population.) In a real-world setting, you need to consider how many iterations the others will make. You should guess 22 if you think they will only do one, which would result in everyone guessing 33. If you assume that they iterate the reasoning twice on average and guess 22, you should estimate 15 and so on.
The "winning" guess when played this game has been around 18.
Hence the guess should be 18.
Learn more about rationality;
https://brainly.com/question/1310146
#SPJ4
the complete question is,
Several people choose an integer between 0 and 100. The winner is the person whose integer is closest to 2/3 of the average of the numbers reported by all seven participants. What value would you choose?
Find length, width, perimeter, and area
Answer:
length is 4 units
width is 2 units
Perimeter is 12 units
Area is 8 sq units
Step-by-step explanation:
Since you have a graph of the points, you can see the shape is a rectangle. Count to find the measure of the length and width.
Perimeter is the distance all the way around the shape.
length + width + length + width
Or 2(length)+2(width)
= 2 + 4 + 2 + 4
= 12
Area is
length × width
= 4 × 2
= 8 sq units.
I’ll give BRAINLIEST if correct I need asap question is in the photo attached
The domain and range of the function will be Real number and [0, ∞). The parent function f(x) is get shifted down by 2 units.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = |x - h| + k
The function is given below.
g(x) = |x + 3|
The graph of the function g(x) is given below. From the graph, the domain and range of the function will be Real number and [0, ∞).
The parent function and translated function are given below.
f(x) |x| and h(x) = |x| - 2
The parent function f(x) is get shifted down by 2 units.
More about the absolute function link is given below.
https://brainly.com/question/10664936
#SPJ1
Find length,width,perimeter,and area of the rectangle
By using distance formula, it can be calculated that
Length of the rectangle is 4 units
Width of the rectangle is 2 units
Perimeter of the rectangle is 12 units
Area of the rectangle = 8 sq. units
Distance between (0, 0) and (4, 0) = [tex]\sqrt{(4-0)^2 + (0 - 0)^2}[/tex]
= [tex]\sqrt{16}[/tex]
= 4 units
Length of the rectangle is 4 units
Distance between (0, 0) and (0, 2) = [tex]\sqrt{(0-0)^2 + (0 - 2)^2}[/tex]
= [tex]\sqrt{4}[/tex]
= 2 units
Width of the rectangle is 2 units
Perimeter of the rectangle = 2 [tex]\times[/tex] (4 +2)
= 12 units
Area of the rectangle = 4 [tex]\times[/tex] 2 = 8 sq. units
To learn more about distance formula, refer to the link-
https://brainly.com/question/661229
#SPJ1
NO LINKS!! Please help me with these questions. Part 1cc
Problem 1
With simple interest, we take a percentage of the loan amount (or deposit depending how you frame things) to determine the interest paid or earned.
The simple interest formula is
i = P*r*t
Let's look at an example: You deposit $100 into an account earning 5% simple interest. You want to know how much interest you earn over 2 years.
i = P*r*t
i = 100*0.05*2
i = 10
You've earned $10 in simple interest. Notice how this is 10% of the original deposit ($100). You can think of the 5% interest rate doubling to 10% because we're working over a 2 year period.
---------------------------------
Compound interest is where we can't take a simple percentage of the deposit. This is because we must use this formula
A = P*(1+r/n)^(n*t)
variables are:
A = final amount after t yearsP = depositr = interest rate in decimal formn = compounding frequencyt = number of yearsAn example: You deposit $100 at an interest rate of 5%. The interest is compounded quarterly (4 times a year). How much interest have you made in 2 years?
The input values will be
P = 100r = 0.05n = 4t = 2So,
A = P*(1+r/n)^(n*t)
A = 100*(1+0.05/4)^(4*2)
A = 110.448610118141
A = 110.45
i = interest
i = A - P
i = 110.45 - 100
i = 10.45
You've made $10.45 in interest over the two year period.
As you can see, we used an exponential function to determine compound interest. Whereas with simple interest, the function was linear. Exponential functions grow much faster compared to linear functions.
======================================================
Problem 2
Savings accounts offer higher interest rates, which encourages people to save their money (hence the name). Checking accounts on the other hand are used to write checks and are there for immediate withdrawals of cash. Checking accounts are also used for debit cards, such as for online shopping.
Both types of accounts are useful in their own different ways. Linking them together is handy to quickly move money without having to deal with tons of paperwork and/or lots of time spent.
======================================================
Problem 3
APR = annual percentage rate
APY = annual percentage yield
The APR value is often the stated item on a loan, since it is the smaller of the two values. When it comes to savings accounts in banks, they tend to state the APY value since it is larger.
Let's look at an example:
The APR is 5% and the money is compounded monthly (12 times a year). Compute the APY.
----------
Solution:
The formula we use is
y = (1+r/n)^n
where y is the APY and r is the APR
In this case we have
r = 0.05n = 12Giving us the following
y = (1+r/n)^n - 1
y = (1+0.05/12)^12 - 1
y = 1.05116189788173 - 1
y = 0.0512
Then multiply that by 100, aka move the decimal point two spots to the right, to arrive at an APY of approximately 5.12%
This example demonstrates how compound interest slightly bumps up the amount of return. We've gone from 5.00% to 5.12%
This slight increase is because the money is compounded 12 times a year. Each time we compound, we're adding to the pile ever so slightly. There's a limit to this process (see the continuous compounding interest formula); i.e. we can't grow the APY forever.
If we were using simple interest, then the APY formula shown above would not apply. For simple interest situations, the APY and APR are the same value.
PLEASE HELP
An equation of a line is shown. A second line is perpendicular to the given line and passes through the point (0,1).
Which is the equation of the perpendicular line?
Answer:
C
Step-by-step explanation:
slope of the first line = -9/2
slope of a perpendicular line = 2/9
y-(-1)= 2/9(x-0)
y + 1 = 2/9 x
y = 2/9 x -1
write the ratio as a fraction in simplest form 35 to 112
Answer:
5 :16
Step-by-step explanation:
35:112 <===== divide both by '7 ' to get 5/16
Find f'(x) and simplify.
f(x)=x²+5/3x-2
Which of the following shows the correct application of the quotient rule?
A. (3x-2)(2 x)-(x²+5)(3)/(3 x-2)²
B. (3 x-2)(2 x)-(x²+5)(3)/(x²+5)²
C. (x²+5)(3)-(3 x-2)(2 x)/(x²+5)²
D. (x²+5)(3)-(3 x-2)(2 x)/(3 x-2)²
The correct application of the quotient rule is f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
What is the derivative of a function?The derivative of a function f'(x) is the rate of change of the function with respect to a variable.
How to find the correct application of the quotient rule?Since we have f(x) = (x²+5)/(3x-2), to find its derivative f'(x), we use the quotient rule.
What is the quotient rule?Given a function f(x) = u(x)/v(x) then the derivative of f(x) which is f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]²
So, with f(x) = (x²+5)/(3x-2)
u(x) = (x²+5) and v(x) = (3x-2)
So, du(x)/dx = d(x²+5)/dx
= d(x²+5)/d(x²+5) × d(x²+5)/dx
= 2x
and
dv(x)/dx = d(3x - 2)/dx
= d3x/dx - d2dx
= 3 - 0
= 3
Since f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]², substituting the values of the variables into the equation, we have that
f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]²
f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
So, the quotient rule is f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
Learn more about quotient rule of derivative here:
https://brainly.com/question/29232553
#SPJ1
What is the solution and how can I solve it? I an super confused
whats the question im getting off camera blind explain it to me
The graph is the boundary line for the inequality y ≤ 2/3x + 1. Which of the points is a solution for this inequality?
A (-4,5)
B (-10, -2)
C (0,-3)
D (1,3)
The points is a solution for this inequality is (0, -3).
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Switch sides
[tex]\frac{2}{3} x+1 \geq y$$[/tex]
Move 1 to the right side
[tex]\frac{2}{3} x \geq y-1$$[/tex]
Multiply both sides by 3
[tex]3 \cdot \frac{2}{3} x \geq 3 y-3 \cdot 1$$[/tex]
Simplify
[tex]2 x \geq 3 y-3$$[/tex]
Divide both sides by 2
[tex]\frac{2 x}{2} \geq \frac{3 y}{2}-\frac{3}{2}$$[/tex]
Simplify
[tex]x \geq \frac{3 y-3}{2}$$[/tex]
To learn more about inequalities visit:https://brainly.com/question/28823603
#SPJ1
What is the value for k