Answers
Related Questions
Suppose that the function h is defined, For all real numbers, as follows
Please help
Answers
Answer:
5/4; 3; - 19/4--------------------------------
Find the following:
h(-3) = (- 3/4) * (- 3) - 1 = 9/4 - 1 = 5/4, since x ≠ 2h(2) = 3, since x = 2h(5) = (- 3/4) * 5 - 1 = - 15/4 - 1 = - 19/4, since x ≠ 2Answer:
[tex]h(-3)=\boxed{\dfrac{5}{4}}[/tex]
[tex]h(2)=\boxed{3}[/tex]
[tex]h(5)=\boxed{-\dfrac{19}{4}}[/tex]
Step-by-step explanation:
Given piecewise function:
[tex]h(x) \begin{cases} -\dfrac{3}{4}x-1\; &\text{if}\;x\neq 2\\\\3 \; &\text{if}\;x=2 \end{cases}[/tex]
To find h(-3), substitute x = -3 into the function:
[tex]\begin{aligned}\implies h(-3)&=-\dfrac{3}{4}(-3)-1\\\\&=\dfrac{9}{4}-1\\\\&=\dfrac{9}{4}-\dfrac{4}{4}\\\\&=\dfrac{5}{4}\end{aligned}[/tex]
To find h(2), substitute x = 2 into the function:
[tex]\implies h(2)=3[/tex]
To find h(5), substitute x = 5 into the function:
[tex]\begin{aligned}\implies h(5)&=-\dfrac{3}{4}(5)-1\\\\&=-\dfrac{15}{4}-1\\\\&=-\dfrac{15}{4}-\dfrac{4}{4}\\\\&=-\dfrac{19}{4}\end{aligned}[/tex]
2. Which system has an infinite number of solutions?
a. x ÷ 2=y
4=2y - x
b. 2y ÷ 6 = 4x
-3 = y - 2x
c. y ÷ 3 = 2x
4x = 2y - 3
d. y = 2x - 5
-2 = y - 2x
Answers
A set of two or more linear equations involving the same set of variables make up a linear system of equations, which is the type of system of equations in question.
Substitution methodAnswer: d. y = 2x - 5; -2 = y - 2xy = 2x - 5 and -2 = y - 2x has an infinite number of solutions.This system can be written as y = 2x - 5 and -2 = y - 2x.Since they have the same equation, they have an infinite number of solutions.The equation y = 2x - 5 can be rearranged to x = (y + 5)/2, and when this is substituted into -2 = y - 2x, the equation becomes -2 = y - 2(y +5)/2, simplifying to 0 = 5y + 10.This equation has an infinite number of solutions, since any value of y will satisfy the equation.For example, if y = -2, then x = 0; and if y = 6, then x = 4. All real numbers satisfy the equation, so the system has an infinite number of solutions.To learn more about infinite number of solutions refer to:
https://brainly.com/question/4710192
#SPJ1
46650 round it to the nearest million
Answers
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
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.
Answers
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?
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
Answers
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
math
r,mrkmrkrmkrmkrmkr
Answers
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
Given the linear function g(x)= 1/4x-2, which domain value corresponds to the range value of 1/8?
Answers
Answer: x = 8 1/2 i believe
Step-by-step explanation:
PLS HELP Ana Maria has the length of
1/3
ribbon Jolie has.If represents the
length of ribbon Jolie has, which
expression represents the length
of Ana Maria's ribbon?
OA)3r
OB)r/3
OC)3/r
OD) 3+r
Answers
The expression that represents the length of Ana Maria's ribbon is r/3
How to determine which expression can be used to represent the length?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation. It should be noted that an expression shows the relationship between the variables.
Ana Maria has the length of 1/3 ribbon Jolie has.
Let r represent the length of ribbon Jolie has
Since Ana Maria's ribbon length is 1/3 that of Jolie ribbon. We can write:
Ana Maria's ribbon length = 1/3 × r = r/3
Thus, the expression for Ana Maria's ribbon length is r/3.
Learn more about word problems on:
brainly.com/question/1781657
#SPJ1
The expression that represents the length of Ana Maria's ribbon is r/3
How to determine which expression can be used to represent the length?
A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation. It should be noted that an expression shows the relationship between the variables.
Ana Maria has the length of 1/3 ribbon Jolie has.
Let r represent the length of ribbon Jolie has
Since Ana Maria's ribbon length is 1/3 that of Jolie ribbon. We can write:
Ana Maria's ribbon length = 1/3 × r = r/3
Thus, the expression for Ana Maria's ribbon length is r/3. :)
If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle, then are the triangles congruent?
Answers
The triangles are considered to be congruent if one right triangle's hypotenuse and another right triangle's hypotenuse are equal.
Given, assuming that the hypotenuse of one right triangle is equivalent to the hypotenuse of another right triangle, then the triangles are harmonious.
The given statement must be verified as true or false by us.
According to the RHS congruence theorem, two right-angled triangles are congruent if the hypotenuse and side of one triangle are equal to the hypotenuse and side of another.
The hypotenuse and the side of the triangle that corresponds to it must be equal according to the RHS rule.
The hypotenuses of the two triangles are equal, per the question.
To learn more about right triangle's hypotenuse here
https://brainly.com/question/2869318
#SPJ4
Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
1
x + 7 = 8
X=
Answers
Answer:
x = 1
Step-by-step explanation:
x + 7 = 8 ( isolate x by subtracting 7 from both sides )
x = 8 - 7 = 1
feet is given by h
Layla launches a toy rocket from a platform. The height of the rocket in
-16t² + 136t + 72 where t represents the time
in seconds after launch. How many seconds have gone by when the
rocket is at its highest point?
Answer:
=
seconds
Submit Answer
Answers
Answer:
The time when the rocket is at its highest point is 8.5 seconds.
Find length,width,perimeter,and area of the rectangle
Answers
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
What is the slope of the line passing through the points (-1, 3) and (4, - 7)?
02
O-2
O
O
ده | ر
Answers
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. :)
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?
Answers
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
how many solutions are there for linear equations? what are they and how can you tell?
Answers
Answer:
Step-by-step explanation: There are three possible solutions for a linear equation: no solution, one unique solution, and infinitely many solutions.
A linear equation is an algebraic equation in which the highest exponent of the variables is 1. For example, 2x + 3 = 5 is a linear equation because the highest exponent of the variable x is 1.
If a linear equation has no solutions, this means that the equation is contradictory and there is no possible value of the variable that can make the equation true. For example, the equation 2x + 3 = 5 has no solutions because it is already true for all possible values of x.
If a linear equation has a unique solution, this means that there is only one possible value of the variable that can make the equation true. For example, the equation 2x + 3 = 5 has a unique solution because there is only one value of x that can make the equation true (in this case, x = 1).
If a linear equation has infinitely many solutions, this means that there are an infinite number of possible values of the variable that can make the equation true. This typically happens when the equation has the form of 0 = 0, which is always true for any value of the variable. For example, the equation 0 = 0 has infinitely many solutions because it is true for all possible values of x.
In general, you can tell whether a linear equation has no solutions, a unique solution, or infinitely many solutions by solving the equation. Solving a linear equation involves isolating the variable on one side of the equation and then using algebraic techniques to find its value. If you are able to find a unique value for the variable, then the equation has a unique solution. If you are unable to find a unique value for the variable, then the equation either has no solutions or infinitely many solutions.
Chris completed a 100-meter breaststroke swimming race in 92.542 seconds.
Michael completed the 100-meter breaststroke swimming race in 95.6 seconds.
How much faster was Chris's time than Michael's? . I don’t need an explanation just tell me the answer it is not a… A B C D Type question just give me an answer
Answers
Chris's time 3.058 sec faster than Michael's.
What is meaning of faster?
Fast and fast refer to moving quickly. Fast can be used as an adverb or an adjective. Quick is an adjective, while rapidly is its adverbial counterpart.
Given that,
Chris completed a 100-meter breaststroke swimming race in 92.542 seconds.
Michael completed the 100-meter breaststroke swimming race in 95.6 seconds.
The difference of time between Chris and Michael to complete 100-meter breaststroke swimming is = (95.6 - 92.542) = 3.058 sec.
Since both are completed 100 meter breaststroke, thus the difference of time denotes the faster time.
Thus Michael's timing was 3.058 seconds slower than Chris'.
To learn more about faster time, click on below link:
https://brainly.com/question/11612898
#SPJ1
Im lost can I get help with this
Answers
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
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
Answers
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
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?
Answers
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
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
Answers
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
Graph TU with endpoints T(1,2) and U(4,6) and its image after the composition.
Translation: (x, y) → (x-2, y-3)
Translation: (x, y) → (x-4, y + 5)
Answers
The graph of the line segment after the translation (x, y) → (x-2, y-3) and (x, y) → (x-4, y + 5) has been drawn.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As per the given coordinate,T(1,2) and U(4,6)
Apply the translation (x, y) → (x-2, y-3)
T(1,2) → T'(1 - 2,2 - 3) = T'(-1,-1)
U(4,6) → U'(4 - 2,6 - 3) = U'(2,3).
Apply the translation (x, y) → (x-4, y + 5)
T(1,2) → T'(1 - 4,2 + 5) = T'(-3,7)
U(4,6) → U'(4 - 4,6 + 5) = U'(0,11)
All points have been plotted below.
Hence"After the translations (x, y) → (x-2, y-3) and (x, y) → (x-4, y + 5), the graph of the line segment has been drawn.".
To learn more about the transformation of graphs,
brainly.com/question/3099136
#SPJ1
Answer:
Translation (x, y) → (x - 2, y - 3):
T' (-1, -1)U' (2, 3)Translation (x, y) → (x - 4, y + 5):
T'' (-3, 7)U'' (0, 11)Step-by-step explanation:
Given endpoints of line segment TU:
T = (1, 2)U = (4, 6)Translation 1 (blue on attached diagram)
(x, y) → (x - 2, y - 3)This means to subtract 2 from the x-values of the endpoints, and subtract 3 from the y-values of the endpoints:
Therefore:
T' = (1 - 2, 2 - 3) = (-1, -1)U' = (4 - 2, 6 - 3) = (2, 3)Translation 2 (red on attached diagram)
(x, y) → (x - 4, y + 5)This means to subtract 4 from the x-values of the endpoints, and add 5 to the y-values of the endpoints:
Therefore:
T'' = (1 - 4, 2 + 5) = (-3, 7)U'' = (4 - 4, 6 + 5) = (0, 11)do both and expain please.
Answers
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
NO LINKS!! Please help me with these questions. Part 1cc
Answers
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.
A bag contains 1 gold marbles, 6 silver marbles, and
28 black marbles. Someone offers to play this game:
You randomly select one marble from the bag. If it
is gold, you win $3. If it is silver, you win $2. If it is
black, you lose $1.
Answers
To calculate the expected value of playing this game, we need to multiply the value of each possible outcome by its probability of occurring and then add these values together. In this case, there is 1 gold marble, 6 silver marbles, and 28 black marbles in the bag, for a total of 35 marbles. So, the probability of selecting a gold marble is 1/35, the probability of selecting a silver marble is 6/35, and the probability of selecting a black marble is 28/35. The value of winning $3 if a gold marble is selected is $3 * (1/35) = $0.09. The value of winning $2 if a silver marble is selected is $2 * (6/35) = $0.34. And the value of losing $1 if a black marble is selected is -$1 * (28/35) = -$0.80. Adding these values together, we get $0.09 + $0.34 - $0.80 = -$0.37. Therefore, the expected value of playing this game is approximately -$0.37.
The length of the longest side of a quadrilateral is 5 cm more than three times the cube of the length of the shortest side. The length of another side is 6 cm less than the square of the length of the shortest side. The length of a third side is 7 cm more than four times the length of the shortest side. What is the perimeter of the quadrilateral, in terms of , the length of the shortest side?
Answers
The Perimeter of the Quadrilateral will be P = 3s³ + s² + 5s + 1
What is Quadrilateral?
A quadrilateral is a four-sided polygon with four edges and four corners in geometry. The name derives from the Latin words quadri (a variation of four) and latus (a side).
Solution:
Given:
Length of Longest side is three times more than the cube of shortest side
Length of Another side is 6cm less than square of shortest side
Length of Third side is 7cm more than four times the length of shortest side
To Find:
Perimeter of the Quadrilateral in terms of Shortest Side
Let, Shortest Side be s
So, longest side will be 3 * s³
Another Side will be s² - 6
Third Side will be 4s + 7
Perimeter of the Quadrilateral will be s + 4s +7 + s² - 6 + 3s³
5s + 1 + s² + 3s³
P = 3s³ + s² + 5s + 1
To learn more about Quadrilateral from the given link
https://brainly.com/question/23935806
#SPJ1
What is the value for k
Answers
Simplify and u get
-36
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 290 feet of If
antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.
What is the length of the garden?
The length of the garden is
What is the width of the garden?
The width of the garden is
Answers
In order to enclose the garden's perimeter, vintage fence will be used. The perimeter of a rectangle-shaped garden is equal to the sum of the garden's two lengths and two widths.
Do the length and breadth calculations?In order to enclose the garden's perimeter, vintage fence will be used. The perimeter of a rectangle-shaped garden is equal to the sum of the garden's two lengths and two widths.
According to their estimates, our perimeter fence measures 220 feet, hence 220 = 2L + 2W.
We can make this more manageable if we divide everything by two: 110 = L + W
The width is now specified as being "exactly two-thirds of the length."
In math, the letter "=" equals the word "IS". Consequently, "the width is" becomes "W =," and "the two-thirds of the length" is precisely what it says, "(2/3) L."
W = (2/3)L is the result of adding these.
and we will add this W to the formula above (110 = L + W) to make 110 = L + (2/3)L.
If we substitute L with (3/3) L (that is, 1*L with 1 written 3/3) now we can add (3/3) as adding fractions requires a "common denominator."
L + (2/3)
L = (5/3)L
At this point, our equation is 110 = (5/3)L.
The right side (3/5) is now multiplied by the reciprocal on both sides, yielding (3/5)(110) = (3/5)(5/3)
L66 = L and W=2/3
L = (2/3)(66) = 44 = W
66 feet by 44 feet are the measurements of the square flower garden.
To learn more about Lengths refer to:
https://brainly.com/question/2217700
#SPJ1
4. Suppose a firm’s short-run total cost curve is given by TC = 6Q2 + 5Q + 10
a) Derive the ATC, AVC, AFC, and MC functions (8 pts)
b) How many units will the firm supply if market price is 29 ? (2 pts)
c) How much is TR? How much is the profit? (4 pts)
Answers
The value of ATC, AFC, TVC if TC = 6Q² + 5Q + 10, are 6Q + 5 + 10/Q, 5 + 6Q, 5Q + 6Q² respectively.
What is ATC?Average total cost (ATC) is calculated by dividing the entire cost by the total amount of output produced. The additional cost incurred by creating one more unit of output is known as marginal cost (MC).
Given:
TC = 6Q² + 5Q + 10,
Calculate the value of AFC as shown below,
AFC = 10 / Q
Calculate the value of TVC as shown below,
TVC = TC - TFC
TVC = 5Q + 6Q²
Calculate the value of AFC as shown below,
AFC = TVC / Q
AFC = 5Q + 6Q² / Q
AFC = 5 + 6Q
Calculate the value of ATC as shown below,
ATC = TC / Q
ATC = 6Q² + 5Q + 10 / Q
ATC = 6Q + 5 + 10/Q
To know more about ATC:
https://brainly.com/question/28194689
#SPJ1
Guests who appear on talk shows and interact with other guests for the benefit of an audience are participating in a
a. symposium. b. forum.
c. panel discussion.
d. governance group. e. service group.
Answers
Guests who appear on talk shows and converse with one another for the benefit of the audience make up a (C) panel discussion.
What is a panel discussion?Participants in a panel discussion are guests who appear on talk shows and engage in conversation with one another for the benefit of the audience.
A panel discussion, or simply a panel, is a gathering of people who talk about something in front of an audience, usually at fan conventions, conferences for business or academia, or on television.
Panels often have a moderator who leads the conversation and occasionally solicits questions from the audience with the intention of being both educational and entertaining.
Fan convention film panels have been attributed with increasing box office revenues by creating anticipation.
Therefore, guests who appear on talk shows and converse with one another for the benefit of the audience make up a (C) panel discussion.
Know more about the panel discussion here:
https://brainly.com/question/2290843
#SPJ4
Given the following functions, find and simplify (f- g) (8.5).
f(x) = -x +3
g(x) = -10x - 9
Answers
Step-by-step explanation:
an arithmetic operation (like "-") on functions is the same as using the same operation on the functional excursions themselves.
(f - g)(x) = -x + 3 - (-10x - 9) = -x + 3 + 10x + 9 =
= 9x + 12
(f - g)(8.5) = 9×8.5 + 12 = 76.5 + 12 = 88.5