The better deal between the offer at Mystic Bank and Four Rivers Bank is the deal at Mystic Bank.
What is the better deal?In order to determine which bank has the better offer, the future value of the investment options have to be determined.
The future value of an investment is a function of the amount investment, the number of compounding, the years of the investment and the interest rate.
When an investment is compounded semi-annually, it means that it grows exponentially twice in a year. When an investment is compounded quarterly, it means that is grows exponentially four times in a year.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsInterest rate at Mystic bank = 10% /2 = 5%
Interest rate at Four Rivers Bank = 8% / 4 = 2%
Future value of the investment at Mystic bank :
$10,000 x (1.05)^(2 x 4) = $14,774.55
Future value of the investment at Four Rivers Bank :
$10,000 x (1.02)^(4 x 4) = $13,727.86
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just 34 unless you want to help me with more?
M is the midpoint of the line segment FG.
Being the midpoint means that M divides the line in two equal halves so you know that the distance between F and M is equal to the distance between M and G, symbolically:
FM=MG
And of you add them you'll be able to calculate the length of the whole line FG
34.
Given the expressions
FM= 5y+13
MG=5-3y
We know that FM=MG, so the first step is to replace this equivalency with the given expressions. This way you'll determine an equation with one unknown y.
Once you have the equation you can clear the value of y:
[tex]\begin{gathered} FM=MG \\ 5y+13=5-3y \end{gathered}[/tex]Pass all terms with the unknown to one side of the equation and all others to the other side:
[tex]\begin{gathered} 5y+3y=5-13 \\ 8y=-8 \\ y=-1 \end{gathered}[/tex]y=-1
Now that you know the value of y, you can replace it in the given expressions to calculate the length of FG
[tex]\begin{gathered} FG=FM+MG \\ FG=(5y+13)+(5-3y) \\ FG=5y+13+5-3y \\ FG=2y+18 \\ \text{Replace with y=-1} \\ FG=2(-1)+18 \\ FG=16 \end{gathered}[/tex]The length of the line segment FG is 16 units.
The formula for the area of a triangle is A = -bh, in which b represents the length of the base and h2represents the height. If a triangle has an area of 115 mm2 and the height is 10 mm, what is the measureof the base?The measure of the base ismm.
The formula for the area of a triangle is A is;
Evaluate: base 6 exponent 0
Answer:
1
Explanation:
Given:
[tex]6^0[/tex]To evaluate the expression above, apply the law of indices below.
[tex]a^0=1,a\neq0[/tex]That is, whenever a number (except 0) is raised to the power of 0, the result is always 1.
Therefore:
[tex]6^0=1[/tex]Hello I need help please.The choices for f(-6): A. f(-6) ; B. The answer is not a real number
Given the function:
[tex]f\mleft(x\mright)=\sqrt{x-1}[/tex]First part:
You need to substitute the following value of "x" into the function:
[tex]x=1[/tex]In order to find:
[tex]f(1)[/tex]Then, substituting and evaluating, you get:
[tex]\begin{gathered} f(1)=\sqrt[]{1-1} \\ f(1)=\sqrt[]{0} \\ f(1)=0 \end{gathered}[/tex]Second part:
Substitute this value of "x" into the function:
[tex]x=-6[/tex]And then evaluate, in order to find:
[tex]f(-6)[/tex]You get:
[tex]\begin{gathered} f(-6)=\sqrt[]{-6-1} \\ f(-6)=\sqrt[]{-7} \end{gathered}[/tex]Since the Radicand is negative, it is not a Real Number.
Therefore, the answers are:
First part:
A.
[tex]f(1)=0[/tex]Second part:
B. The answer is not a real number.
Help please and thank you
HELP ME WITH IS PROBLEM THANK YOU
The solution to the given expression is 10√5 - 4√10 which is the correct answer would be an option (C)
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
The given expression as:
⇒ √5(10 - 4√2)
Open the parentheses and apply the distributive property of multiplication to get,
⇒ 10√5 - 4√5√2
⇒ 10√5 - 4√(5 × 2)
⇒ 10√5 - 4√10
Therefore, the solution to the given expression is 10√5 - 4√10.
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Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the around it to two decimal places if necessary.8i4 + 5i
SOLUTION
The given complex expression is:
[tex]\frac{-8i}{4+5i}[/tex]Rationalize the denominator
This gives
[tex]\begin{gathered} \frac{-8i}{4+5i}\times\frac{4-5i}{4-5i} \\ =\frac{-32i-40}{16+25} \\ =-\frac{40}{41}-\frac{32i}{41} \end{gathered}[/tex]twice the difference of a number 4 is 5.
Answer:25
Step-by-step explanation:
The slope of like A is m=9 & the slope of line B is m-9. What is their relation?
O Parallel
O Perpendicular
O Neither
please help and could u give all the steps if there’s more after this thank you so much
Angle IJL is 54 because congruent angles have equal measure.
What are congruent angles?
Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.
According to question, angle m IKL = 54
And AB// CD and EF// GH
Angle IKL is alternate interior angle to angle HLK
m angle HLK= m angle IKL (congruent angles have equal measure)
m angle HLK= 54
Similarly, m angle IJL = m angle HLK
Hence, angle IJL= 54
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Which of the following would result in an integer?
O a.) 120
O b.) √144
O c.) √52
O d.) √24
The answer is either Option (a) or option(b) or both the options i.e, 120 or √144
What is Integer ?
An integer is a whole number from the set of -ve , non-negative , +ve and 0 numbers.
Let's see how both the option is correct
we know, integers are 0,1, 2, 3, .... or -1, -2 , -3 ......
Means the number which is not in fraction or decimal value or root.
so, by seeing option(a) we can say it's an integer
but in option(b) it's the root so how it is integer
The answer is simple it's perfect square of 12 so √144 = 12 so that means it have the value which is not in fraction. By that we can say that option(b) is also an integer
Now, in option(c) and (d) they are not the perfect square and their root results in decimal values. so we cannot tell them as an integer value.
Hence, the answer is either Option (a) or option(b) or both the options.
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Use the law of cosines to solve the following problem.The robot arm shown in the figure places packages on a conveyer belt. What is the distance x?
SOLUTION
Using cosine rule it follows:
[tex]x^2=3.00^2+2.25^2-3(2.25)\cos110[/tex]Simplify the equation for x
[tex]x=\sqrt{3.00^2+2.25^2-3(2.25)\cos110}[/tex]Therefore the required answer is
[tex]x=\sqrt{3.00^2+2.25^2-3(2.25)\cos(110)}[/tex]Find the range PLEASE HELP!!! EXTRA POINTS
the domain is the interval or set of all valid values for x (the input variable).
the range is the interval or set of all valid values for y or f(x) (the function result variable).
the functional result values for the first piece :
x - 4 for 0 <= x < 2
for x = 0 we get y = -4
for x = 2 we get y = -2
the range for this piece is [‐4, -2).
we use the round bracket to indicate -2 itself is not included, as we have x < 2 (and not x <= 2).
the functional result values for the second piece :
x² - 3x + 4 for 2 <= x < 4
for x = 2 we get 4-6+4 = 2
for x = 4 we get 16-12+4 = 8
the range for this piece is [2, 8)
again, because of x < 4 we use the ")" for 8 (not included).
the functional result values for the third piece :
5 for 4 <= x < 7
the range is simply [5) = [5] because the set contains only one element.
and 5 is already contained in the range of the second piece.
so, the range is just the combination of the ranges of the first 2 pieces :
[-4, -2) U [2, 8)
The table shows a proportional relationship.
x 12 8 24
y 3 2 6
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
A graph of which best describes what the proportional relationship would look like is: D. A line passes through the point (0, 0) and continues through the point (12, 3).
What is a graph?In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Additionally, a graph that represents a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).
Since the graph represents a proportional relationship we have:
Constant of proportionality, k = 12/3 = 8/2 = 24/6 = 4
Ratio = 24:6 = 12:3.
Therefore, (0, 0) and (12, 3) are points on this graph that represents a proportional relationship.
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Answer:d
Step-by-step explanation:trust
I need help with the question above. I took a picture of it.
The answer is: It will be a line.
Translate Pre image coordinates right 14 units and up 13 units.
We will have the following:
We translate the points:
A(-12, 3)
B(-6, -3)
C(-12, -9)
The transformation rule is (x, y) -> (x + 14, y + 13); so:
A'(2, 16)
B'(8, 10)
C'(2, 4)
Find the percentage decrease and round to the nearest tenth
Answer:
16.6%
Step-by-step explanation:
First, find the difference between the prices:
$3.95 - $3.45 = $0.50
Then, divide the difference by yesterday's price.
$0.50 ÷ $3.95
≈ 0.166
≈ 16.6%
Answer:
12.7%
Step-by-step explanation:
$3.95 - $3.45 = $.50
$.50 / $3.95 = .127 = 12.7%
Question 2-20
Mrs. Kimsey purchased a bushel of large apples that weighs about 48 pounds. The bushel contains 96 apples. What is the approximate
weight, in ounces, of one apple?
02
O 16
32
Weight of one apple is 8 ounces.
We have to calculate the weight of one apple. For that firstly, we have to calculate the weight of one apple in pounds because we have been given the weight of 96 apples in pounds. After that, we will convert it into ounces and we know that one pound is equal to 16 ounces.
A bushel has 96 apples.
We have been given weight of 1 bushel which is 48 pounds.
Weight of 96 apples = 48 pounds
We have to calculate weight of one apple.
Weight of one apple = 48/96 = 1/2 pound
1 pound = 16 ounces.
Now, we have to convert pounds into ounces
Weight of one apple = 1/2 * 16 ounces
= 8 ounces
Hence, the answer is 8 ounces.
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The half life of iron-59 is 44.5 days. How much of
a 50g sample would remain after 178 days?
Answer:
If the half-life of a nuclide is 44.5 days, then 178 days is four half-lives.
explanation:
After four half-lives, 0.0625 (0.54) of the original nuclides remains. If 50g is the original mass, then the mass after 4 half-lives is 3.125g.
AT = A0 2(-T/H)
A178 = (50) 2(-44.5/178)
A178 = 3.125
I NEED HELP ASAP, I DONT KNOW HOW TO DO THIS.
Answer:
slope = 5/2
Step-by-step explanation:
Locations of points: (-4 , -4) and (-2 , 1)
slope = rise / run
between two plotted points this means that:
slope = change in y / change in x
slope = (1 - (-4)) / (-2 - (-4))
slope = 5/2
1. A piece of power transmission equipment is being designed. The design includesa set of three different meshed gears with a total of 107 teeth between them. If thesecond gear has 13 more teeth than the first gear. The third gear has 15 more teeththan the second gear.How many teeth does the second gear have?
where x is the first, y the second and z the third
the second gear has 13 more teeth than the first gear
[tex]x+13=y[/tex]The third gear has 15 more teeth than the second gear
[tex]y+15=z[/tex]we need solve z form the third equation and solve x from the second equation an replace on the first
[tex]\begin{gathered} z=y+15 \\ x=y-13 \end{gathered}[/tex]replacing
[tex]\begin{gathered} (y-13)+y+(y+15)=107 \\ y-13+y+y+15=107 \\ 3y+2=107 \\ 3y=105 \\ y=35 \end{gathered}[/tex]so, the second gear have 35 teeth
a. If Ax = b has a solution and Aᵀy = 0, then y is perpendicular to ___.
b. If Aᵀy = c has a solution and Ax = 0, then x is perpendicular to ___.
The answer to question (a) that is if Ax = b has a solution and [tex]A^{T}[/tex] y = 0 then y is perpendicular to b
Answer to question (b) that is if [tex]A^{T}[/tex] y = c has a solution and Ax = 0 then x is perpendicular to c.
a) As Ax = b has a solution for x this means b lies in the column space of A. We also know that [tex]A^{T}[/tex] y = 0. This means y lies in the orthogonal complement of the column space of A or in the left null space of A. Therefore y is perpendicular to b
b) We see [tex]A^{T}[/tex] y = c has a solution. This tells us that c lies in the row space of A and also from the given Ax = 0 we can deduce that x lies in the null space of A or the orthogonal complement of row space of A. Therefore evidently x will be perpendicular to c
Determine whether AT has a row space same as column space of A
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Solve and check the equation X-23=16
Answer:x=39
Step-by-step explanation:
x-23=16
x=16+23
x=39
The state transportation commission counted cars traveling east and west across a toll bridge. 75% of the 588 cars counted were traveling east. How many eastbound cars did the commission count?
Answer: the answer is 441
Step-by-step explanation: 75% of 588 is 441
From 1982 to 2004, the number
B
of federally insured banks could be approximated by
B
(
t
)
=
−
326.6
t
+
13783
where t is the year and t=0 corresponds to 1982.
How many federally insured banks were there in 1987?
Find the slope of the graph of B.
There were 120150 federally insured bank in the year 1987. The slope of the graph of B is -326.6.
The provided function B(x) states the number of federally insured banks from 1982-2004.
The function B(x) is,
B(x) = -326.6t + 13783
Here t is representing the year,
This function is a linear function corresponding to an equation of line,
If according to the situation,
t = 0, signifies the year 1982,
Then the year 1983 should be represented by t = 1.
On continuing the pattern the year 1987 should be represented by t = 5.
So, the number of federally insured banks in year 1987 can be found by putting t = 5 in B(x),
B(5) = -326.6(5) + 13783
B(5) = 12150.
The number of banks federally insured in year 1987 is 12150.
The function is B(x)= -326.6t + 1783,
This is representing the point-slope form of the line,
y = mx + c,
On comparing the provided function with the standard equation we can see,
Slope m = -326.6
So the slope of the function is -326.6.
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Maria expandió el siguiente cuadrado (x+3)^2=x^2 Está correcta la forma que usò?
No, the form that Maria expanded is not correct.
What does it mean to "extend and simplify"?
We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression. We take out brackets by expanding them, often known as multiplying out.
Given:
(x+3)²
= x² + 2 . 3 . x + 3²
= x² + 6x + 9
Therefore the correct expansion is x² + 6x + 9.
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Question:
Maria expanded the following square (x+3)^2=x^2 Is the form she used correct?
The mass of an atom or molecule is measured in atomic mass units. Which is greater, a carat or a milligram?
Notice that:
[tex]\begin{gathered} -23<-21, \\ 8.3<10. \end{gathered}[/tex]Therefore:
[tex]8.3\times10^{-24}<10\times10^{-24}=10^{-23}<10^{-21}<1.66\times10^{-21}\text{.}[/tex]Then a carat is greater.
Now, since:
[tex]1atomic\text{ mass unit=8.3}\times10^{-24}carat.[/tex]Then:
[tex]\frac{1}{8.3}\times10^{24}\text{atomic mass unit=1carat.}[/tex]Simplifying the above result we get:
[tex]1\text{carat}=1.20\times10^{23}\text{atomic mass units.}[/tex]Also, since:
[tex]1\text{atomic mass unit=1.66}\times10^{-21}milligram[/tex]then:
[tex]\frac{1}{1.66}\times10^{21}\text{atomic mass unit=1 milligram.}[/tex]Simplifying the above result we get:
[tex]1\text{ milligram=6.02}\times10^{20}atomic\text{ mass units.}[/tex]Answer:
A carat is greater.
[tex]1\text{carat}=1.20\times10^{23}\text{atomic mass units.}[/tex]and
[tex]1\text{ milligram=6.02}\times10^{20}atomic\text{ mass units.}[/tex]and
Roseanne makes 1 1/2 of strawberry lemonade. She pours 1/4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2/5 of the remaining lemonade. How much lemonade does Roseanne's brother drink? Which expression can be used to determine the amount of lemonade Roseanne's brother drank? A. 1 1/2 - (1/4 x 2/5) B. (1 1/2 + 1/4) x 2/5 C. (1 1/2 - 1/4) x 2/5 D. (1 1/2 - 1/4) ÷ 2/5
we know that
the total lemonade is 1 1/2 liter
She pours 1/4 of a liter of lemonade into a thermos
Her brother drinks 2/5 of the remaining lemonade
the remaining lemonade is equal to
1 1/2-1/4=3/2-1/4=5/4 liters
Multiply by 2/5
(5/4)(2/5)=10/20=1/2 liter
therefore
answer is option
C. (1 1/2 - 1/4) x 2/5
what is the shape of a cross section that is perpendicular to the basis
If we get the cross section perpendicular to the base of this image, we would get the same shape as the image.
Through the diagram, we can see that if we cut the image to get the cross section perpendicular to its base, we would get the same shape as the image, which is a pentagon.
can you give me some examples of how to simplify
Let's check out the expression
[tex]2x+4+6y+7+2+3x[/tex]To simplify, you have to add up similar terms. That is, add up everything that has an x, add up everything that has a y, and add up every independent term (no variable), as following:
[tex]\begin{gathered} 2x+4+6y+7+2+3x\rightarrow2x+3x+6y+4+7+2 \\ \rightarrow5x+6y+13 \end{gathered}[/tex]And there we have the simplified expression.