Final Answer:
After 5 years, the account balance would be approximately $11,541.20.
Explanation:
To calculate the account balance for a certificate of deposit that has an initial amount of $10,000.00, with an annual interest rate of 2.89% compounded monthly over 5 years, we must use the compound interest formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
- A is the amount of money accumulated after t years, including interest.
- P is the principal amount, which is the initial amount of money ($10,000.00 in this case).
- r is the annual interest rate in decimal form (2.89% or 0.0289 in this case).
- n is the number of times that interest is compounded per year (12 times per year for monthly compounding).
- t is the time the money is invested for, in years (5 years in this case).
Firstly, we convert the annual interest rate from a percentage to a decimal by dividing by 100:
r = 2.89% = 0.0289
Now we substitute the given values into the formula:
[tex]\[ A = \$10,000.00 \left(1 + \frac{0.0289}{12}\right)^{12 \cdot 5} \][/tex]
We calculate the rate per period by dividing the annual interest rate by the number of compounding periods per year:
[tex]\[ \frac{0.0289}{12} = 0.00240833 \][/tex] (rounded to 8 decimal places for precision)
Now calculate the growth factor:
[tex]\[ \left(1 + \frac{0.0289}{12}\right) = 1 + 0.00240833 = 1.00240833 \][/tex]
This growth factor is raised to the power of 60 (since there are 12 months in a year and we are compounding for 5 years):
[tex]\[ (1.00240833)^{60} \][/tex]
Using a calculator, raise 1.00240833 to the power of 60 to get approximately:
[tex]\[ 1.00240833^{60} \approx 1.15412 \][/tex](rounded to 5 decimal places for simplicity)
Finally, multiply this result by the principal amount to find the accumulated amount:
[tex]\[ A = \$10,000.00 \times 1.15412 \approx \$11,541.20 \][/tex]
Therefore, after 5 years, the account balance would be approximately $11,541.20.
If a line is 10 feet long but needs to be reduced to 80% of its original, how long will the new line be?
Answer:
8 feet
Step-by-step explanation:
Select the correct answer
This scatter plot shows the association between time elapsed and distance left to go when John drove from city A to city B. What are the slope
and the y-intercept of the line of best fit on the scatter plot?
Answer:
The y intercept is 80 and the line of the best fit is -3/5
Step-by-step explanation:
The y intercept of the line of best fit is 80 miles with a slope of -0.6 mile per minute
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the graph, the y intercept is 80 miles. The line passes through (0, 80) and (100, 20), hence:
slope = (20 - 80) / (100 - 0) = -0.6 mile per minute
The y intercept of the line of best fit is 80 miles with a slope of -0.6 mile per minute
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Please help!! In radians, what is the period of the function y = .5cos5x
pi/5
(3pi)/2
(2pi)/5
pi/2
Answer:
(2pi)/5
Step-by-step explanation:
The cosine function cos(x) has a period of 2*pi.
If we change the argument of the cosine, the new argument will have a period of 2*pi. If the new argument is 5x, we have that the period will be:
5x = 2*pi
x = 2*pi/5
The period of this function will be (2pi)/5, because for every (2pi)/5 change in the value of x, the function will have the same value. The value of 5 multiplying the cosine does not interfere in the period.
A rectangular prism with a length of 5 centimeters, height of 3 centimeters, and width of 4 centimeters. The rectangular prism shown has a length of 5 cm, a height of 3 cm, and a width of 4 cm. What is the surface area of this prism? square centimeters
Answer:
94cm squared
Step-by-step explanation:
you find the area of each side by doing base times height and you add the six of them all together to get your answer
Answer:
94 cm
Step-by-step explanation:
Each side of a regular pentagon is represented by 4x + 7. Which expression represents the perimeter of the hexagon?
A) 24x + 42
B) 20x + 35
С) 9x + 12
D) 55x
Two cards are randomly chosen, one at time, from a standard deck of 52 playing cards without replacement. What is the probability both cards will be an Ace? A. B. C. D.
Answer:
C
Step-by-step explanation:
I remember the answer
An observer at the top of a skyscraper sees a car on the road below. The angle of depression to the car is 29°. If the car is about 62 m from the skyscraper when it is seen, how tall is the skyscraper?
The height of the skyscraper is 34.4m
Step-by-step explanation:
Let the height of the skyscraper be 'h'
Distance between the skyscraper and the car = 62 m
Angle of depression = 29°
Angle = 61°
tan 61° = 62/h
1.80 = 62/h
h = 62/1.80
h = 34.4m
The height of the skyscraper is 34.4m
Evaluate the expression when x=-6.
x² + 5x-5
Answer:
1
Step-by-step explanation:
x² + 5x-5
Let x = -6
(-6)^2 + 5(-6) -5
36 -30 -5
6-5
1
To evaluate the expression x² + 5x - 5 for x=-6, substitute -6 into the expression and follow the order of operations to obtain a result of 1.
Substitute -6 for x in the expression, which gives us (-6)² + 5(-6) - 5.Calculate the square of -6, which is 36.Multiply 5 by -6, which is -30.Add these results and subtract 5: 36 - 30 - 5 = 1.Therefore, the value of the expression when x = -6 is 1.
Set of integer solutions of x^2≤3
Answer:
[tex]-1,0,1,[/tex]
Step-by-step explanation:
x²≤3
|x|≤√3
Hence, $x\leqslant \sqrt 3$ or $ x\geqslant -\sqrt 3$
Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.
Answer:
So when two lines intersect, it creates 4 angles. The angles that lie opposite to each other are congruent
If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.
Step-by-step explanation:
The height of a trapezoid is 6 in. and it’s area is 72 in to the 2nd power. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases? Complete the explanation of how you found your answer.
One base is __ inches for one of the bases and __ inches for the other base.
Use the formula for the area of a trapezoid. Substitute 72 for A and 6 for h and simplify the equation to find __ = (b1 + b2). Use guess and check to find two numbers that add to __ with one number 6 more than the other to get __ inches for one of the bases and __ inches for the other base.
Given:
The height of the given trapezoid = 6 in
The area of the trapezoid = 72 in²
Also given, one base of the trapezoid is 6 inches longer than the other base
To find the lengths of the bases.
Formula
The area of the trapezoid is
[tex]A=\frac{1}{2} (b_{1} +b_{2} )h[/tex]
where, h be the height of the trapezoid
[tex]b_{1}[/tex] be the shorter base
[tex]b_{2}[/tex] be the longer base
As per the given problem,
[tex]b_{2}=b_{1} +6[/tex]
Now,
Putting, A=72, [tex]b_{2}=b_{1}+6[/tex] and h=6 we get,
[tex]\frac{1}{2} (b_{1} +b_{1}+6)(6) = 72[/tex]
or, [tex]b_{1}+b_{1}+6 = \frac{(72)(2)}{6}[/tex]
or, [tex]2b_{1}+6 = 24[/tex]
or, [tex]2b_{1}=24-6[/tex]
or, [tex]b_{1}= \frac{18}{2}[/tex]
or, [tex]b_{1}=9[/tex]
So,
The shorter base is 9 in and the other base is = (6+9) = 15 in
Hence,
One base is 9 inches for one of the bases and 15 inches for the other base.
please help me with this problem
Answer:
-3
Step-by-step explanation:
Negative reciprical
In the diagram, DC is tangent to the circle, AC = 12 cm, and BD=2134 cm. Find AD.
A. 10 cm
B. 12 cm
C. 2/61 cm
D. 130 cm
Felicia has a garden in the shape of a parallelogram as shown. What is the area of her garden?
O 72 ft²
O 75 ft²
O 92 ft²
O 96 ft²
Answer:
72 ft²
Step-by-step explanation:
base=9
height=8
9*8=72
Area of parallelogram= base*height
Answer:
O 72 ft²
Step-by-step explanation:
Formula for Area of a Parallelogram:
[tex]A = bh[/tex]
The base (b) is 9 ft.
The height (h) is 8 ft.
[tex]A = 9 * 8\\A = 72[/tex]
First, she needs to find her resting heart rate by counting her pulse for one minute immediately after she wakes up for 5 days in a row. She finds her average resting heart rate to be 62 after
5 days and she remembers the last day's pulse was 58 and all the others were the same. Write and solve an equation to find what her pulse was on all the other days. Justify your answer by showing your steps. Put in Simple equation
Answer:
63
Step-by-step explanation:
She finds her average resting heart rate to be 62 after 5 days.
That means, average of the 5 heart rate pulse=62
If the last day was 58 and all the other days were the same.
Let x be her pulse on the other days,
Then,
[tex]Average, 62=\dfrac{58+4x}{5}\\\text{Cross Multiply}\\58+4x=62 X 5\\\text{Suntract 58 from both sides}\\4x=(62X5)-58\\4x=310-58\\4x=252\\\text{Divide both sides by 4}\\x=63[/tex]
Her pulse on all the other days is 63.
Frank averages a speed of 19 miles per hour during his bike race. The race is 60 miles long.
Answer:
3 hours and 16 minutes or 3.16 for Frank to finish the race
Step-by-step explanation:
60 miles long Frank is going 19 miles an hour
60 divided by 19 3.157 rounded up 3.16
Using the distance and speed, we calculate the time it takes for Frank to complete the bike race. He averages a speed of 19 miles per hour for a 60-mile race, which means it will take him approximately 3.16 hours to finish.
Explanation:This question is about solving a typical problem in math - specifically, calculating time with information on distance and speed. To figure out how long it would take Frank to finish the 60-mile bike race, we use the formula Time = Distance / Speed. Given that Frank averages a speed of 19 miles an hour, we divide the total distance (60 miles) by his average speed (19 mph).
So, 60/19 ≈ 3.16. That means Frank will take approximately 3.16 hour to complete the bike race.
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PLEASE HELP ASAP.
The difference of 3 times a number and 15 is no less than the square of the number.
Select the inequality that represents this relationship.
P
Answer:
d
Step-by-step explanation:
At a summer camp, 72% of the campers participate in rope climbing and 26% participate in canoeing. 83% of the campers participate in rope climbing, canoeing, or both. What is the probability that a randomly selected camper participates in both rope climbing and canoeing
Answer:About 60%
Step-by-step explanation:
Answer:
.15
Step-by-step explanation:
0.83 = 0.72 + 0.26 - P(R and C)
P(R and C) = 0.15.
*2.6-(5.85)
Evaluate It
Answer: -3.25
Step-by-step explanation:
2.6-(5.85)
remove parentheses
2.6-5.85
answer: -3.25
Tickets for the concert cost $47 each. There is also a $5.95 service fee for each ticket. Bernie's aunt buys tickets for 5 people. How much money does she spend in all?
Answer:
$264.75
Step-by-step explanation:
47*5=235
5.95*5=29.75
29.75+235=264.75
(Can i get the Brainliest?)
Answer:
$264.75
Step-by-step explanation:
You multiply 47 to 5, because it's 5 tickets and $47 each. You should get $235. Then, you multiply 5 and 5.95. you should get $29.75. Then you add 29.75 to 235. Your final answer is $264.75.
What are the coordinates of A’ after reflecting across the line x = 3?
On a coordinate plane, figure A B C D has points (3, 2), (2, 4), (6, 3), and (1, 0).
(2, 3)
(3, 2)
(3, 4)
(3, –2)
Answer:
(3,2)
Step-by-step explanation:
A: (3,2)
Since A lies on the mirror line, it will mapped onto itself
A': (3,2)
The required coordinate of image A' is given as (3, 2). Option B is correct.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
Here,
The Coordinate of A is (3, 2) and the equation of a line is x = 3, since
Point A lies on line x = 3, so the image of the point overlapped the original point. Although the coordinate of the image A' is given as (3, 2)
Thus, the required coordinate of image A' is given as (3, 2). Option B is correct.
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The coordinate plane shows dig sites for archaeological research. Each unit on the grid represents 1 square foot. What is the distance from Site A to Site C?
Answer:
25
Step-by-step explanation:
The distance between the two points A and C is 25 units.
What is coordinate geometry?A coordinate plane is a 2D plane created by the junction of the x-axis and y-axis, two perpendicular lines. A coordinate system in geometry is a way to use one or more integers or coordinates to determine the positions of the points.
Given points are (5, 20) and (25,5). The distance between the points will be calculated as below:-
D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]
D = √ [ ( 25 - 5 )² + ( 20 - 5)² ]
D = √ ( 400 + 225 )
D = 25 units
Therefore, the distance between points A and C is 25 units.
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Which sentence illustrates the Inverse Property for Multiplication?
A. 6 + (-6) = 0
B. 1/6 x 6 = 1
C. 1 x 6 = 6
D. 1 x 6 = 6 x 1
Answer:
the answer is .143728353
Step-by-step explanation:
answer
9. Mrs. Kenny teaches a ceramics class. She finds
that she has of a pound of clay for a project. The
project requires of a pound. How many projects
can Mrs. Kenny complete without running out of clay?
To find how many projects can be completed, divide the total amount of clay Mrs. Kenny has by the amount of clay required for each project. However, the question seems to be missing the values for the total amount of clay and the amount required per project.
Explanation:Mrs. Kenny is teaching a ceramics class where she uses clay for her projects. As stated, it seems there is a portion of the question omitted which is the number of pounds of clay Mrs. Kenny has and the amount required for each project. Ideally, the number of projects Mrs. Kenny can complete is determined by dividing the total weight of the clay she has by the weight of clay required for each project. For instance, if Mrs. Kenny has 3 pounds of clay and each project requires 1/2 pound of clay, she would be able to complete 6 projects (3 divided by 1/2 = 6).
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Nancy's spaghetti and meatballs recipe calls for 2 cloves of garlic the recipe makes 8 servings how much garlic is in each serving
Answer:
1/4 clove
Step-by-step explanation:
Each serving of Nancy's spaghetti and meatballs recipe contains a quarter (or 0.25) of a garlic clove.
Explanation:In the given scenario, Nancy's spaghetti and meatballs recipe asks for 2 cloves of garlic and yields 8 servings. Hence, to find out the amount of garlic in each serving, we need to divide the total cloves of garlic by the number of servings. Hence,
Garlic per serving = Total garlic / Number of servings
Here's how to do the math:
Garlic per serving = 2 cloves / 8 servings = 0.25 cloves per serving
So, there is 0.25 or a quarter of a garlic clove in each serving of Nancy's spaghetti and meatballs recipe.
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What is the value log5 25?
Answer:
2
Step-by-step explanation:
You can think of logarithms as a rewritten exponent.
So exponents are in the form of a^b=c
Logarithms are [tex]log_a c=b[/tex]
Here, we have [tex]log_{5} 25[/tex]
Basically we have to figure out 5 to the power of what is 25.
So our answer is 2.
5^2=25
The value of log5 25 is 2, as 5 to the power of 2 equals 25.
The value of log₅ 25 is determined by asking the question: 'to what power do we need to raise 5 to get 25"
Since 5 squared is 25 (5² = 25).
The power of 5 is 2.
Therefore, log₅ 25 = 2
Hey y’all please help me with this
Answer:
-12
Step-by-step explanation:
I try to think of it as how many steps would I need to get to zero
-12 would take 12 steps to get to 0
7 would take 7 steps to get to 0
-9 would take 9 steps to get to 0
1 would take 1 step to get to 0
-12 would take the most steps to get to 0 so it is the farthest from 0 on the number line
PLEASE HELP I ONLY HAVE 14 MINS LEFT!!!
Answer:
0 and 0.695
Step-by-step explanation:
0=(0.695)- 14= 0.95
There are 32 students in choir, and 44 students in band. Out of those in choir, 5 are in band. What is the probability that a student is in band, given that they are in choir.
What numbers should be placed in the boxes from left to right ?
Answer:
3 and 6
Step-by-step explanation:
hello
i hope it help