Part A. An explicit expression for the function A(n), the final amount (future value) after n years is 1,500 x 1.0235^n.
Part B. The function for determining the future value of the CD at 2.35% annual compounded interest rate is derived by comparing the present value and the future value and using the difference to calculate the compound interest rate.
What is the future value?The future value is the present value compounded at an interest rate.
The future value formula or function is as follows:
FV = PV(1+r)^{n}
FV = future value
PV = present value
r = annual interest rate
{n} = number of periods interest held
Initial deposit in a ten-year certificate of deposit (CD) = $1,500
Deposit period = 10 years
Amount after 1 year = $1,535.25
Compound interest rate = 2.35% annually ($1,535.25 - $1,500)/$1,500 x 100)
Function for A(n) = 1,500 x 1.0235^n
Thus, from the future value after 1 year, we can derive the compound interest rate.
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According to this diagram, what is sin 28°?
28°
OA. 17
15
OB.
B. 15
8
O C. 17
D. 15
OE
F.
8
15
8
17-
15
62°
90°
00
8
Answer:
sin 28 = 8 /17
Step-by-step explanation:
Since this is a right triangle, we can use trig functions.
sin theta = opp side / hypotenuse
sin 28 = 8 /17
U= (1,2,3,4,5,6,7,8,9)
A=(1,2,5,6)
B=(2,3,4,6,7)
C=(5,6,7,8
Find (B’ n A) u c
Answer:
[tex](B'\cap A)\cup C=\{1,5,6,7,8\}[/tex]
Step-by-step explanation:
[tex]B'=\{1,5,8,9\}[/tex]
[tex](B'\cap A)=\{1,5\}[/tex]
[tex](B'\cap A)\cup C=\{1,5,6,7,8\}[/tex]
The complement of a set, notated with a prime symbol ('), are all other elements that are not in that set.
The intersection of two sets, notated by [tex]\cap[/tex], are just the elements that are contained in both sets.
The union of two sets, notated by [tex]\cup[/tex], are all the elements that are contained in both sets (any duplicates are not included).
What is the range of the function shown on the graph above?
From the graph the range of the function is obtained as option 1: -5 ≤ y ≤ 8.
What is the range of data?
The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.
From the graph, the following observations are made -
The endpoints of the graph have closed circles this means that, the endpoints are inclusive of the range.
For closed circles the inequality symbols used is (≤,≥).
The y-axis values suggests the range of the function.
The minimum y-axis value in the fourth quadrant is -5.
The maximum y-axis value in the first quadrant is 8.
The range of the function is [-5 , 8]
Therefore, the range is found to be -5 ≤ y ≤ 8.
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3 over 5 meters =. centimeters
Answer:
60
Step-by-step explanation:
3/5 = 0.6 meters = 60 cm
Given a2 = 6 and a5 = –384 of a geometric sequence, what is the recursive equation for the nth term?
an = –4(an – 1), a1 = –1.5
an = –4(an – 1), a1 = 1.5
an = 4(an – 1), a1 = –1.5
an = 4(an – 1), a1 = 1.5
Answer:
[tex]a_n = (-4)^{n - 1}; a_1 = -1.5[/tex]
Step-by-step explanation:
[tex] a_1 = a_1 [/tex]
[tex] a_2 = a_1 \times r [/tex]
[tex] a_3 = a_1 \times r^2 [/tex]
[tex] a_4 = a_1 \times r^3 [/tex]
[tex] a_5 = a_1 \times r^4 [/tex]
[tex] a_1 \times r = 6 [/tex]
[tex] a_1 \times r^4 = -384 [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] a_1 \times (\dfrac{6}{a_1})^4 = -384 [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] \dfrac{1296}{a_1}^3} = -384 [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] \dfrac{1}{a_1}^3} = -\dfrac{384}{1296} [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] a_1^3 = -\dfrac{27}{8} [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] a_1 = -1.5 [/tex]
[tex] r = \dfrac{6}{-1.5} [/tex]
[tex] a_1 = -1.5 [/tex]
[tex] r = -4 [/tex]
[tex] a_1 = -1.5 [/tex]
[tex]a_n = (-4)^{n - 1}; a_1 = -1.5[/tex]
If a figure is dilated by a factor of 3, the sides of the pre-image will be _ of the image's sides.
A. one-ninth the size
B. one-third the size
C. nine times the size
D. three times the size
The equation and the graph represent two functions. Use the equation y=4 and the graph to answer the questions.
When x is 4, is the output of the equation or graph greater?
What value for x produces the same output in both the graph and the equation?
When x is 4, the output of the equation is greater.
The value for x that produces the same output in both the graph and the equation is equal to 6.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.
By critically observing the graphs of the equations, we can reasonably infer and logically deduce that they both would produce the same output (dependent value or y-value) at the ordered pair (4, 6).
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Mario has 5 gallons of paint. He uses 1/4 gallon to paint a door. He uses 3/8 gallon to paint a wall. How much paint does Mario have left?
(100 POINTS!) The measures of the exterior angles of an octagon are x°,2x°,3x°,4x°,5x°,6x°,7x°, and 8x°. Solve for X.
[tex]\textit{sum of all exterior angles in a polygon}\\\\ S=360^o \\\\[-0.35em] ~\dotfill\\\\ x+2x+3x+4x+5x+6x+7x+8x=360\implies 36x=360 \\\\\\ x=\cfrac{360}{36}\implies x=10[/tex]
Answer:
The exterior angles of an octagon add up to 360°. So, 8x° = 360°, and x = 45°.
Please solve for in this equation
Answer:
x = 4 rounded to the nearest whole number (actually 4.0801)
Step-by-step explanation:
The triangle formed by the sides of length 0.9x, 2.8x and 12 form a right triangle with the side of length 12 as they hypotenuse
By the Pythagorean theorem
c² = a² + b² where c = hypotenuse, a and b being the other two sides
Plugging in values we get
12² = (0.9x)² + (2.8x)²
144 = 0.81x² + 7.84x² = 8.65x²
Switching sides:
8.65x²= 144
x² = 144/8.65 = 16.6473
x = √16.6473= 4.0801
Rounded to the nearest integer, x = 4
HELPP WITH ALL 4 OF THESE ? PLEASE!! each is worth 10 points!!
Answer: 1.+900
2. -24
3. -5
4. +10
Step-by-step explanation:
A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. A 3-column table with 10 rows. Column 1 is labeled volunteer with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Column 2 is labeled Treatment A with entries 10, 13, 13, 9, 13, 12, 14, 10, 8, 7. Column 3 is labeled Treatment B with entries 19, 18, 19, 15, 20, 16, 16, 16, 13, 17. What is the mean difference (A – B) and the standard deviation of the differences?
I think that it could be b but I'm not 100 percent sure
Nolan shoveled driveways over the weekend. He made a total of $82. If he earned the same amount of money on both days, how much money did he make on Saturday alone?
Answer: $41
Step-by-step explanation: $82 all total. 2 days. 82/2=41. He made $41 on Saturday
write the following expression in terms of logs of x, y and z: log x√√x/z
The equation in terms of log(x), log(y) and log(z) is,
log x + 1/4 log y -1/2 log z.
What is logarithmic expression?A logarithmic equation is one in which a variable-containing expression's logarithm is used as a solution. If you can write both sides of the equation as powers of the same number, that will help you answer exponential equations.
here, we have,
log x√√y/z = log(x√(√y)/z)
Consider, the given logarithmic expression,
we get,
By using the logarithmic rule: log(ab) = log(a) + log(b)
So, log(x√(√y)/z)
=logx + log(√(√y)/z)
=log x + 1/2 log (√y)/z
=logx + 1/2 log (√y) - 1/2 log z
= log x + 1/4 log y -1/2 log z
Hence, the expression in terms of x , y and z is, log x + 1/4 log y -1/2 log z.
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Which of the following situations represent direct variation?
y = -5x
2y = x
y/x = 12
x/y = 4
All the equations are direct variation equations
How to determine the equations of direct variationA relationship between two variables is said to be a direct variation if one of the variables is proportional to the other, meaning that their ratio is always constant.
Using the above as a guide, we have the following:
y = -5x:
Direct variation
Constant of variation = -5
2y = x
Direct variation
Constant of variation = 1/2
y/x = 12
Direct variation
Constant of variation = 12
x/y = 4
Direct variation
Constant of variation = 1/4
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Eli's basketball team is having a Free-Throw Challenge in order to raise money for new uniforms. Eli's grandma pledges to give $10 as well as $2 for every free throw he makes. Which equation represents how much money (M) Eli's grandma will give depending on how many free throws (f)
Eli makes?
Answer:
M = 10 + 2f
Step-by-step explanation:
Please see the attachment for detail explanation
Find the perimeter of the figure.
Answer:
30
Step-by-step explanation:
Add all the sides and you get 30.
Hope this helps! Pls give brainliest!
Answer:
30
Step-by-step explanation:
6+9.5+6.5+4+4 = 30
Amy will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. The second plan has no initial fee but costs $0.90 per mile driven.
For what amount of driving do the two plans cost the
same?
What is the cost when the two plans cost the same?
The two plans cost the same when the amount is $200.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
Let us suppose the miles driven = x.
Given that,
The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. This is represented as:
A = 40 + 0.70x
The second plan has no initial fee but costs $0.90 per mile driven.
B = 0.90x
The two plans cost the same when A = B:
40 + 0.70x = 0.90x
40 = 0.90x - 0.70x
40 = 0.20x
x = 200
The two plans cost the same when the amount is $200.
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A small fair charges different admission for adults and children; it charges $2.75 for adults, and $0.25 for children.
On a certain day, the total revenue is $6,962.50 and the fair admits 4900 people.
How many
adults and children were admitted?
Answer: Let's call the number of adults admitted "A" and the number of children admitted "C". We know that:
A + C = 4900 (total number of people admitted)
And the total revenue is:
2.75A + 0.25C = $6,962.50
We can use the first equation to solve for one of the variables in terms of the other:
C = 4900 - A
Substitute this expression for C into the second equation:
2.75A + 0.25(4900 - A) = $6,962.50
Expand and simplify the right side:
2.75A + 1225 - 0.25A = $6,962.50
2.5A = 5737.5
Solve for A:
A = 2298
So there were 2298 adults and 4900 - 2298 = 2602 children admitted.
Step-by-step explanation:
Find the scale factor.
ABCD~EFGH
Answer:
0.67
Step-by-step explanation:
10/15＝0.666666......
＝0.67
Draw 2 isosceles triangles ABC and DEF where AC=BC and DF=EF
The conclusions reached in steps 4 and 5 are invalid. This is a flawed argument for the existence of isosceles triangles.
An isosceles triangle contains what?An isosceles triangle has two equal sides and two equal angles as a result. The term comes from the Greek words iso (same) and skelos (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Each step is valid, but the conclusion is not. At the end of step 4,
here are a series of isometric maps that lead A to D and C to F, as claimed..
After the final rotation in Step 5, the sequence of isometries takes B to E and C to F —but here’s the hitch—there is no reason why it should still take A to D, in fact it can’t take A to D unless the rotation angle is zero.
If the rotation angle in Step 5 is zero, then the isometries take [A,B,C] to [D,E,F] and the two triangles are indeed similar
But this requires the dilation in Step 2 to have made A′B′ congruent to DE , in other words, it requires assuming the triangles are similar before performing any of of the transformations.
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Question:
This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why. 1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF. 2. Dilate triangle ABC to a new triangle A'B'C' using center C and scale factor DF/AC so that A'C= BC - DF = EF. 3. Translate by directed line segment CF to take A'B'C' to a new triangle A" B" F. Since translation preserves distance, A"F = A'C=DF and B" F = BC = EF. 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B" F = EF, we can rotate using center F to take B" to E. 6. We have now established a sequence of dilations, translations, and rotations that takes A to D, B to E, and C to F, so the triangles are similar.
Demarco and Tanya have received information about three separate mortgage offers. In two or three paragraphs, describe your recommendation for the best financial choice in their situation. Evaluate each of the three offers, compare and contrast their effectiveness, and explain the offer that works best. As you explain your answer, support it using reasons and evidence from the calculations you made based on the information provided in this guide for Analyzing Mortgage Options. pls try to be original
Best Mortgage Option 3 because this mortgage option offers a lower interest rate.
Why Option 3 was recommendedAfter reviewing all three mortgage options available to Demarco and Tanya, I would recommend that they choose option 3. This option offers a lower interest rate compared to the other two options and a longer loan term, which means that their monthly payments will be lower and more manageable for their budget. Additionally, option 3 offers a fixed interest rate, which provides them with more stability and predictability in their mortgage payments, as opposed to options 1 and 2 that offer adjustable interest rates.
Option 1 has the highest interest rate and the shortest loan term, making their monthly payments the highest of all three options. Option 2 offers a slightly lower interest rate, but it still higher compared to option 3, and has a shorter loan term compared to option 3, making their monthly payments still relatively high.
In conclusion, the best financial choice for Demarco and Tanya would be option 3. Its lower interest rate, longer loan term, and fixed interest rate make it the most affordable and stable option for them in the long run.
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Explain how you can use a table or graph to find the y-intercept.
The y-intercept is calculated using a table or a graph by substituting x = 0.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The y-intercept value is calculated when the x-coordinate is zero.
Now,
Example:
(0, 3), (0. 5), (0, 7) are all y-intercepts of the graph.
Thus,
The y-intercept is calculated when x = 0.
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If f(x) = x² + 3x - 5, find the value of f(3).
Hey there!
[tex]\huge\textbf{Assuming:}[/tex]
[tex]\mathsf{f(x) = x^2 + 3x - 5}[/tex]
[tex]\mathsf{f(x) = 3^2 + 3(3) - 5}[/tex]
[tex]\mathsf{f(x) = 3 \times 3 + 9 - 5}[/tex]
[tex]\mathsf{f(x) = 9 + 9 - 5}[/tex]
[tex]\mathsf{f(x) = 18 - 5}[/tex]
[tex]\mathsf{f(x) = 13}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\mathsf{f(x) = 13}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Divide. (54t2−81t)÷(9t)
Answer:
The answer is 6t-9. This can be calculated by dividing the numerator (54t2−81t) by the denominator (9t). This gives 6t-9.
Step-by-step explanation:
Answer:
81t2+16
Step-by-step explanation:
(9t-4)(-9t-4) : Equation
Distribute parentheses using:(a + b)(c + d) = ac + ad + bc + bd.
Where : a=9t, b=-4, c=-9t, d=-4.
This leads to 9t(-9t) +9t (-4) -4- (9t) -4 (-4).
Now we have to Apply minus-plus rule.
Where: -(-a)=a.+(-a)=-a
-9t.9t - 9t.4 + 4.9t = 4.4
=81t2+16
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Laura is the fund raising manager for a local charity she is ordering caps for an upcoming charity walk. The company that makes the caps chargers $6 per cap plus a $25 shipping fee . Laura had buaght of $1000 WhT is the greatest number of caps she can buy?
the maximum number of caps she can order is 162.
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.
Given, Laura is the fundraising manager for a local charity she is ordering caps for an upcoming charity walk.
Let "x" be the number of caps she ordered.
Since, manufacturing cost for a cap = $6
shipping charges for the lot = $25
Thus,
Total price she paid for x caps = 6*x + 25
Since she had only 1000$
So,
6x + 25 ≤ 1000
6x ≤ 975
x ≤ 975/6
x ≤ 162.5
therefore, the maximum number of caps she can order is 162.
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Instructions Type an essay response to the following prompt. Completely explain all parts of your response and use the rubric to determine what you need to include in your essay. 1) In your own words, write a definition for sales tax. 2) If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, how much do you pay in taxes? - Explain in detail, the steps you would take to solve this sales tax question.
1) The sales tax is an additional rate that is paid along with the cost of the meal.
2) The amount paid in taxes for a meal costing $15.00 and a rate of 7% is given as follows: $1.05.
How to obtain the sales tax?The sales tax is obtained applying the proportions in the context of this problem.
A proportion is applied as the sales tax is obtained with the multiplication of the cost of the meal by the decimal equivalent of the percentage of tax.
The decimal equivalent for a percentage of 7% is given as follows:
7/100 = 0.07.
Hence the amount of tax paid is given as follows:
0.07 x 15 = $1.05.
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Trigonometric Identities (HELP)
Use the Reciprocal and Quotient Identities for 1&2
1: Find cscX if sinX= 2√5/5
2: Find cosA if tanA= √2/2 and sinA= -√3/3
Use the Pythagorean Theorem identities for 3&4
3: Find sinX if cotX= -√3/2 and cosX < 0
4: Find cotθ if cosθ= 1/7 and sinθ < 0
Use the cofunction and even-odd identities for 5&6
5: Find tan(-x) if cot(π/2 -x)= -1.84
6: Find cos(θ-π/2) if sinθ= -0.57
Simplify the Trigonometric expressions
7: secX ⋅ sin^2X + cosX
8:(sinθ + 1)(tanθ - secθ)
Prove the Trigonometric expression
1+sec^2X / 1+tan^2X= 1+cos^2X
1: cscX = 1/sinX = 5/2√5.
2: Using the reciprocal identity of tanA and sinA,
tanA/sinA = 1/cosA
√2/2 / -√3/3 = 1/cosA
-2√2/2√3 = 1/cosA
cosA = -2√3/2√2.
What are the responses to other questions?3: Using the Pythagorean theorem, sinX = √(1 - cos^2X)
√(1 - cos^2X) = √((1/cot^2X) - 1) = √((√3/2)^2 - 1) / (-√3/2)
sinX = √2/2.
4: Using the Pythagorean theorem,
cotθ = cosθ / sinθ = 1 / tanθ = 1 / (√(1 - cos^2θ) / cosθ) = cosθ / √(1 - cos^2θ) = 1 / (√(1 - (1/7)^2)) = √(48) / 7.
5: Using the cofunction identity, tan(-x) = -tan(x).
Using the identity that tan(π/2 -x) = cot(x),
-tan(x) = -1/cot(π/2 -x) = -1/(-1.84) = 1.84.
6: Using the even-odd identity, cos(-θ) = cos(θ), and
sin(-θ) = -sin(θ),
cos(θ-π/2) = cosθcos(π/2) + sinθsin(π/2) = 0cos(π/2) + (-0.57)sin(π/2) = -0.57.
7: Using the identity sin^2X + cos^2X = 1,
secX ⋅ sin^2X + cosX = secX ⋅ (1 - cos^2X) + cosX = secX - secXcos^2X + cosX = secX + cosX.
8: Using the identity 1 + tan^2θ = sec^2θ,
(sinθ + 1)(tanθ - secθ) = (sinθ + 1)(tanθ - 1/cosθ) = (sinθ + 1)(tanθcosθ - 1) = (sinθ + 1)sinθ(tanθ/sinθ) - (sinθ + 1) = sinθ + sin^2θ - sinθ - 1 = sin^2θ - 1.
Proof:
Using the identity tan^2X = sin^2X / cos^2X,
1+sec^2X / 1+tan^2X = (1 + 1/cos^2X) / (1 + sin^2X / cos^2X) = cos^2X / (cos^2X + sin^2X) = cos^2X / (1) = 1 + cos^2X.
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Lexi MUST spend $100 and get 100 animals. $15 for 1 dog, $1 for 1 cat, and 25 cents for each mice.
thank you to whoever helps <33
Info on the graph with needing the slopes:
PLEASE HELP I REALLY AM STRUGGLING WITH THIS
I added photos of both graphs to be looked at
Using this formula, the tax on 9701 will be 970 + 0.12(9701 − 9700) = 970 + 0.12(1) = $. . This means that your tax only goes up 12 cents instead of almost $200. The graphs show these two scenarios. The correct scenario is shown on Graph 1. The incorrect scenario is shown on Graph 2.
What is the slope of the first piece of the tax function? (Graph 1)
I got y=1x+0 but I don't know if I am correct.
What is the slope of the second piece of the tax function? (Graph 2)
What do these slopes tell us??
The slope for the first piece of the tax function is given as follows:
0.1.
The slope for the second piece of the tax function is given as follows:
0.2.
It tells that for smaller salaries, the tax rate is of 10%, while for salaries on a second range, the tax rate is of 20%.
How to obtain the slope of a linear function?The slope of a linear function represents the rate of change of the output variable relative to the input variable.
For the first piece, when x increases by 5000, the output increases by 500, hence the slope m is given as follows:
m = 500/5000
m = 0.1.
For the second piece, when x increases by 5000, the output increases by 1000, hence the slope m is given as follows:
m = 1000/5000
m = 0.2.
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