$320 is invested in an account earning 8.1% interest (APR), compounded quarterly. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent
Answer:
Step-by-step explanation:
Given that:
The investment amount in account = $ 320
The rate of interest is = 8.1% compounded quarterly
Compunded quarterly means 8.1% / 4 = 0.02025
The time period = t years
The objective is to write a function showing the value of the account after t years.
From compound interest , compounded monthly.
[tex]Amount = Principal * ( 1 + \dfrac{rate}{12*100})^{12*time}[/tex]
[tex]= $320 *(1 + \dfrac{0.02025}{12*100})^{12t}[/tex]
[tex]= 320*(1+ 1.6875*10^{-5})^{12t}[/tex]
[tex]= 320 * ( 1.000016875)^{12t}[/tex]
Thus; the function after t years [tex]= $320 * ( 1.000016875)^{12t}[/tex]
The percentage of growth per year is :
= (1 + 0.02025)^4 - 1
= 1.083493758 - 1
= 0.083493758
= 8.4 % (APY) yearly
Find the value of x in the triangle shown below.
Answer:
58
Step-by-step explanation:
since the triangle has two sides of the same length (6.2cm), this means that it is a isosceles triangle, and that also means that the two angles at the base are the same (both will be 61 degrees)
then just use 180 minus the two angles and you will get x
Solve the inequality, then identify the graph of the
solution
-3x-3<_6
Answer:
First Part is C
The second part is 0,2,4
Step-by-step explanation:
Edge said so
The graph of the solution is option (C) [tex]x\geq -3[/tex] is the correct answer.
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is the condition of being unequal. It is used most often to compare two numbers on the number line by their size.
For the given situation,
The expression is [tex]-3x-3\leq 6[/tex].
The graph below shows the inequality of the expression.
The solution of the expression is
[tex]-3x-3\leq 6[/tex]
⇒ [tex]-3x\leq 6+3[/tex]
⇒ [tex]-3x\leq 9[/tex]
Divide both sides by -3. Then the inequality will also get changed.
⇒ [tex]\frac{-3}{-3}x\geq \frac{9}{-3}[/tex]
⇒ [tex]x\geq -3[/tex]
Hence we can conclude that the graph of the solution is option (C) [tex]x\geq -3[/tex] is the correct answer.
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Find the equation of the line.
Use exact numbers
y=___ x+____
Answer:
y=x-5
Step-by-step explanation:
transformations from parent function:
down 5 units
Answer:
y=x-5
Step-by-step explanation:
slope=rise/run=5/5=1
y -intercept=-5
y=x-5
What is the leading coefficient and constant of this problem?
(8
2/7*3/8>3/8 because 2/7>1
Helllp please someone
Answer: -920
Step-by-step explanation:
-447 - 473 = -920
In this case, smaller means more negative
Answer:
-920
Explanation:
To solve this problem, you simply need to subtract 473 by negative 447. Here is how you solve:
-447 - 473
- (447 + 473)
-920
Therefore, the new dot was on -920.
Sara rolls two dice, one black and one yellow. What is the probability that she will roll a 3 on the black die and 5 on the yellow die?
Answer:
1/6 x 1/6 = 1/36
Step-by-step explanation:
We have to multiply as the odds get smaller as in every experimental probability being from experimental one dice and then trying to achieve that number alongside and same timing another number on an inclusive 2nd dice.
Kiran says we should add the constraint 1 is greater than or less than 0
1. What is the reasoning behind this constraint?
-
2. What other "natural constraint" like this should be added?
(URGENT)Which summation formula represents the series below?
13 + 9 + 5 + 1
Σ-4n+1)
Σ-47-15)
Σ(n-4)
Σ(n-4)
Answer:
Σ-47-15)
Step-by-step explanation:
Option D is correct, the summation formula that represents the series is Σ(n-4) for n=1 to 4.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
A series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
The series can be written as:
13 + 9 + 5 + 1 = (4×3 + 1) + (4×2 + 1) + (4×1 + 1) + (4×0 + 1)
= (4×(3-1) + 1) + (4×(2-1) + 1) + (4×(1-1) + 1) + (4×(0-1) + 1)
= Σ(n-4) from n=1 to 4
Therefore, the summation formula that represents the series is Σ(n-4).
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Vector donated 1/5 of yesterday's sales plus an additional $125. He gave Azul $2,225 total. How much money did the store make in sales yesterday?
Question 3 of 15
2 Points
Solve the equation for x.
14x = 28
X =
Answer here
Answer:
x = 2
Step-by-step explanation:
[tex]14x = 28\\\mathrm{Divide\:both\:sides\:by\:}14\\\frac{14x}{14}=\frac{28}{14}\\Simplify\\x=2[/tex]
Evaluate \sqrt{-75s}
−75s
square root of, minus, 75, s, end square root where s = -3s=−3s, equals, minus, 3.
Answer:
Step-by-step explanation:
the answer is 15!
The square root of the number -√75 will be -3√5.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The square root of the number will be calculated as below:-
-√75 = - √( 3 x 3 x 5 )
= -3√5
Therefore, the square root of the number -√75 will be -3√5.
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if cos 67 degrees is close to 2/5 which is closest to the length of no
PO=100cm
P=23 degrees
Answer:
40 cm
Step-by-step explanation:
In the right triangle PNO:
∠N = 90°PO = 100cm (the hypotenuse of the triangle)∠P = 23°∠O = 90° - 23° = 67°side NO is adjacent to ∠OBy definition:
cos(β) = adjacent/hypotenuse
Replacing with data and solving for NO:
cos(∠O) = NO/PO
2/5 = NO/100
NO = (2/5)*100
NO = 40
HI!!! I just finished the unit 7 lesson 11 unit test!! Here are the answers: :)
1. A: 2
2. C: 225
3. C: pi/4
4. A: -465
5. C: 0
6. B: 210
7. B: 2pi
8. A: 52
9. C: 40
10. C: 3rd graph
11. A: y=sin pi/265
12. B: 1/4pi
13. D: y=3cos2
14. A: sqrt3/3
15. C: 0
16. C: 3rd graph
17. A: 187
18. C: sqrt2/2
19. B: 1+sin theta
20. D: 45
21. D: 0.64
22. A:80
23. C: pi/2, 5pi/4, 3pi/2, 7pi/4
24. C: csc theta =13/12, sec theta= 13/5
hope this helps someone :)))
Consider the table showing the given, predicted, and residual values for a data set.
A 4-column table with 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled given with entries negative 1.6, 2.2, 4.5, 6.1. The third column is labeled predicted value with entries negative 1.2, 1.5, 4.7, 6.7. The fourth column is labeled residual value with entries negative 0.4, 0.7, negative 0.2, negative 0.6.
Which point would be on the residual plot of the data?
Answer:
(4, -0.6)
Step-by-step explanation:
The table is:
x Given Predicted Residual value
1 -1.6 -1.2 0.4
2 2.2 1.5 0.7
3 4.5 4.7 -0.2
4 6.1 6.7 -0.6
The points on the residual plot must be the pairs (x, residual value). This is:
(1, 0.4)
(2, 0.7)
(3, -0.2)
(4, -0.6)
Thus, the correct choice is the last one: (4, -0.6)
The point that would be on the residual plot of the data is (4, -0.6). See the explanation below.
What is a residual plot?A residual plot is a graph in which the residuals are displayed on the vertical axis and the explanatory variables is displayed on the horizontal axis.
From the analysis of the table attached, we have the following points on the residual plot:
(1, 0.4)
(2, 0.7)
(3, -0.2)
(4, -0.6)
Point on the residual plot must include the point on x and a residual value, hence, the correct answer is (4, -0.6).
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2. Determine if the two quadrilaterals are similar,
if they are, state the scale factor.
Answer:
Yes, they are similar. The scale factor is 5/3
Step-by-step explanation:
The longest to the shortest side of quadrilateral KLMJ are: JM, ML, KJ, LK
The longest to the shortest side of quadrilateral QPSR are: QP, PS, RQ, SR
If the two quadrilaterals are similar, the following proportion must be satisfied:
JM = k*QP
ML = k*PS
KJ = k*RQ
LK = k*SR
where k is the scale factor. Solving for k and replacing with lengths:
k = 25/15 = 24/14.4 = 20/12 = 15/9 = 5/3
From the figure, we can also see that:
∠M ≅ ∠P
∠L ≅ ∠S
∠R ≅ ∠K
∠Q ≅ ∠J
Therefore, the two quadrilaterals are similar.
Bryan and his son, and Elton and his son all went fishing. Bryan caught as many fish as his son and Elton caught three times as many fish as his son. All together, they caught 25 fish. How many fish did Bryan catch?
Answer:
The answer is explained below
Step-by-step explanation:
This is a word problem, therefore to solve it the statement have to be writing in form of an equation and then solved.
Let the number of fishes caught by Bryan's son be x fishes. Since Bryan caught as many fish as his son, Bryan caught x fishes
Let the number of fishes caught by Elton's son be y fishes. Since Elton caught three times as many fish as his son, Bryan caught 3y fishes
All together, they caught 25 fish
Therefore it can be represented by the equation:
x + x + y + 3y = 25
2x + 4y = 25
2x = 25 - 4y
x = (25 - 4y)/2
The number of fish caught by Bryan is half of the difference between the total fish caught and four times the number of fish caught by Elton son
Miguel’s savings account balance changed by -$48 over a year because a banking fee was withdrawn every month. He wants to find the monthly change to his account.
Answer:
-48 ÷ 12
Step-by-step explanation:
account balance changed over a year = -$48
In a year, there are 12 months. Above statement can also be written as
account balance changed in 12 months = -$48
we have to find monthly change, so we divide LHS and RHS by 12
account balance changed in 12 /12 months = -$48/12
Thus, account balance changed in 1 months = -$48/12
which is represented option 4 i.e -48 ÷ 12
QI - The sum of the distance of a moving
point from the points (c,0) and (-c,0) is
always 2a units. Find the equation to the locus
of the moving point.
Answer:
[tex]\frac{x^2}{a^2}+\frac{y^2}{a^2-c^2}=1[/tex]
Step-by-step explanation:
Let P be the moving point and the given points be A (c,0) and B (-c, 0). If (h, k) be the co-ordinates of any position of P on its locus then:
PA + PB = 2a
PA = 2a - PB
PA² = 4a² + PB² – 4a ∙ PB
PA² – PB² = 4a² – 4a ∙ PB
[(h - c)² +(k - 0)²] - [(h + c)² +(k - 0)²] = 4a² – 4a. PB
-4hc = 4a² – 4a∙PB
a ∙ PB = a² + hc
Taking square
a² ∙ PB² = (a² + hc)²
a² [(h + c)² + (k - 0)²] = (a² + hc)²
a² [h² + c² + 2hc + k²] = a⁴ + 2a²hc + h²c²
a²h² – h²c² + a²k² = a⁴ – a²c²
(a² – c²)h² + a²k² = a² (a² – c²)
h²/a² + k²/(a² – c²) = 1
Therefore, the required equation to the locus of P is
[tex]\frac{x^2}{a^2}+\frac{y^2}{a^2-c^2}=1[/tex]
Billy’s Boat Rentals charges a yearly fee of $105 and $9.50 each time a member wants to rent a boat. Lisa’s Boat Rentals does not charge a yearly fee but charges $14.75 every time a member rents a boat. How many times does a person have to rent a boat for Billy’s and Lisa’s to cost the same amount?
A.10
B.15
C.20
D.30
Answer:
C. 20
Step-by-step explanation:
105 + 9.5x = 14.75x
105 = 5.25x
20 = x
Help please! Will give brainly! Take a look at the figure below, which is made up of many small squares. How does each expression (A-D) represent the number of small squares in the figure? Explain?
Answer:
Step-by-step explanation:
A: Take 8*6 which build a rectangle, then take out 2*3 squares to create the same shape as in the picture
B: split the shape into two pieces, so one rectangle has the sides 4 and 8 and the rectangle has 2 and 5. Multiply the 4 with 8 and 2with 5 then add them together
C: Add the amount of squares in a layer one by one together
D: split the shape into 2 rectangles but instead of a horizontal split, do a vertical split so first rectangle has the sides 5 and 6 and the other has 3 and 4. Multiply 5 with 6 and 3 with 4 and add both results together
you may have to change the english a bit since english is not my first language
In the diagram, measure angle 3 = 120° and measure angle 12 = 80°. Which
angle measures are correct? Check all that apply
measure angle 1 = 60°
measure angle 13 = 80
measure angle 6 = 80°
measure angle 5 = 60°
measure angle 10 = 120
measure angle 14 = 100
Answer:
1, 13, 5 are correct
Step-by-step explanation:
Answer: A,B,D,F are correct
Step-by-step explanation:
A line of best fit is drawn for the set of points shown on the graph.
A 2-column table with 10 rows. The first column is labeled x with entries 5, 6, 8, 8, 10, 11, 14, 15, 16, 18. The second column is labeled y with entries 8.9, 11.4, 13.6, 14, 15.3, 12.25, 22.1, 21.8, 20.8, 24.5. A graph shows the horizontal axis numbered 4 to 16 and the vertical axis numbered 4 to 24. A line increases from 0 to 17.
Which point is an approximate extrapolation for x = 30 from the line of best fit?
(23, 30)
(30, 38)
(44, 30)
(30, 72)
yo hice el examen y la tuve mal pero me dijo cual era la correcta y es (30,38)
I do the exam and I heve it wrong but the exam put what was the correct answer and it is (30,38)
option B
Equation of Linear Regression line is
y=1.14 x + 3.805
so, (30,38) is an approximate extrapolation for x = 30 from the line of best fit.
What is line of regression?A line of regression is that line which passes through none of the points, few points or all the points in the two dimensional coordinate plane.It tells value of one variable when another variable is known.
here, we have,
A line of best fit is drawn for the set of points shown on the graph.
from the given information,
we get,
for, x=30
y=1.14 × 30 +3.805
y=34.20 +3.805
y=38.005
y=38 (approx)
Equation of Linear Regression line is
y=1.14 x + 3.805
so, (30,38) is an approximate extrapolation for x = 30 from the line of best fit.
So, Ordered pair is , (30,38)
Option B
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completely factor -6x^3+11x^2+10x
Answer:
-x (2 x - 5) (3 x + 2)
Step-by-step explanation:
Factor the following:
-6 x^3 + 11 x^2 + 10 x
Factor -x out of -6 x^3 + 11 x^2 + 10 x:
-x (6 x^2 - 11 x - 10)
Factor the quadratic 6 x^2 - 11 x - 10. The coefficient of x^2 is 6 and the constant term is -10. The product of 6 and -10 is -60. The factors of -60 which sum to -11 are 4 and -15. So 6 x^2 - 11 x - 10 = 6 x^2 - 15 x + 4 x - 10 = 2 x (3 x + 2) - 5 (3 x + 2):
-x 2 x (3 x + 2) - 5 (3 x + 2)
Factor 3 x + 2 from 2 x (3 x + 2) - 5 (3 x + 2):
Answer: -x (2 x - 5) (3 x + 2)
Can someone please answer this?
Answer: it is a parallelogram
Step-by-step explanation:
the coordinates form a parallelogram as you can see on the grid.
the shapes edges are joined together to form a parallelogram
there you go
Solve for x and y adding
2x + 4y = 16
-5x-4y = 16
Show work
Answer:
x = -32/3
y =28/3
Step-by-step explanation:
2x + 4y = 16
-5x-4y = 16
Add the equations
2x + 4y = 16
-5x-4y = 16
--------------------
-3x = 32
Divide each side by -3
x = -32/3
Now solve for y
2x+4y = 16
2(-32/3) +4y = 16
-64/3 +4y = 16
Multiply each side by 3 to get rid of the fractions
-64 +3*4y = 16*3
-64 + 12y = 48
Add 64 to each side
12y = 112
Divide by 12
12y/12 = 112/12
y =28/3
Given a = -3 and b= 4 and c=-5, evaluate
atb
C
-1/5
O 1/5
0 -7/5
Answer:
I got - 5 as an answer.
I don't think I made a mistake.
Please if you find any error, contact me in the comment section.
Step-by-step explanation:
[tex]a = -3 , b= 4 ,c= - 5\\(a+b)c\\(-3+4)-5\\(1)*(-5)\\Answer = -5[/tex]
Evaluate the following expression. 6 squared -1
Answer:
35
Step-by-step explanation:
[tex]6^2 - 1\\36-1\\35[/tex]
Natasha uses 2.5 feet of twine to tie campfire wood into bundles. The proportional relationship between the number of bundles, x, and the amount of twine, y, in feet she uses is shown in the graph. What does the point (3, 7.5) represent in a graph?
Answer:
She uses 7.5 feet of twine to make 3 bundles of wood.
Find the volume of a cone with the radius of 14, and a height of 9. (Hint:
the volume of a cone is 1/3*b*h where the "b" is the area of the base of
the cone or a circle). DO NOT ROUND!!!!! USE 3.14 for PI!!!*
Answer:
The answer is 1846.32 units³.
Step-by-step explanation:
Given that the base of a cone is a circle so the area of circle is A = πr². You have to substitute the following values into the formula :
[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
Let π = 3.14,
Let r = 14,
Let h = 9,
[tex]v = \frac{1}{3} \times 3.14 \times {14}^{2} \times 9[/tex]
[tex]v = 1846.32 \: {units}^{3} [/tex]
Which symbol correctly compared these two fractions
Answer:
B
Step-by-step explanation:
> = greater than
= this means equal to
< = less than
[tex]\frac{8}{13} =\frac{8}{13}[/tex]