Given is the Principal amount, P = 1600 dollars.
Given the Annual interest is 7% i.e. r = 0.07
Given the Compounding period is semi-annually i.e. n = 2.
Given is the Time of investment, t = 33 years.
It says to find the Final Value of invested amount in the account after 33 years.
We know the formula for Future Value of Money is given as follows :-
[tex] Future \;\;Value = P*(1+\frac{r}{n})^{nt} \\\\
Future \;\;Value = 1600*(1+\frac{0.07}{2})^{(2*33)} \\\\
Future \;\;Value = 1600*(1+0.035)^{66} \\\\
Future \;\;Value = 1600*(1.035)^{66} \\\\
Future \;\;Value = 1600*(9.684185201) \\\\
Future \;\;Value = 15494.69632 \\\\
Future \;\;Value = 15,494.70 \;\;dollars [/tex]
Hence, the final balance would be 15,494.70 dollars.
Answer:
After 33 years balance in the account = A= $15494.696
Explanation:
We will applying the compound interest formula.
[tex] A = P(1 +\frac{r}{n})^{nt} [/tex]
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years
Given that,
P = $1,600
r = 7% = [tex] \frac{7}{100} [/tex] = 0.07
n = 2 (because of twice in a year)
t = 33 years
A= [tex] 1600(1 + \frac{0.035}{2}) ^{2*33} [/tex]
A =[tex] 1600 (1.035)^{66} [/tex]
A= $15494.696
3x squared -42x+9=-5 for completing the square
Can someone help me math homework
Solve for x in the diagram.
A. 25 B. 37 C. 15 D. 14
The value of the hypotenuse x is equal to 12 units.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Use the Pythagorean theorem for this. (a^2+b^2=c^2)
a=9, b=12, c=x
The value of x will be calculated as,
a² + b² = c²
9²+12²=x²
81 + 144 = x²
225 = x²
x =15
Therefore, the measure of x is 15 units.
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the string, that supports the stairs, makes an angle of 50° with the floor. It reaches 3.2 m up the wall. How far is the base od the stringer from the wall?
We use trigonometry to find the distance from the base of the string to the wall. The cosine of an angle in a right triangle is defined as the adjacent side length divided by the hypotenuse length. You can plug the given values into the rearranged formula and solve it.
Explanation:The question is asking about the distance from the base of the string (the part that touches the floor) to the wall. This is a typical trigonometry problem. We know that the string forms an angle of 50° with the floor and that it stretches up to 3.2 m on the wall. Given these values, we can use the cosine function to find the distance between the base of the string and the wall.
The cosine of an angle in a right triangle is defined as the adjacent side length divided by the length of the hypotenuse. In our case, you can think of the 3.2 m wall height as the 'adjacent' and the string length as the 'hypotenuse'. So, we can rearrange this relationship to solve for the base, or 'hypotenuse', of the triangle:
Length of string (hypotenuse) = Adjacent side / cos(angle)
Plugging in the values we know:
Length of string = 3.2 m / cos(50°)
After that, you can plug the numbers into a calculator to find the value in meters of the distance from the base of the string to the wall.
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Find the total cost for a $579 smartphone with 5% sales tax
Final answer:
To calculate the total cost including a 5% sales tax on a $579 smartphone, convert the tax rate to a decimal and multiply it by the price, then add the result to the original price. The total cost would be $607.95.
Explanation:
To find the total cost for a $579 smartphone with a 5% sales tax, you'll need to calculate the amount of sales tax and then add it to the original price of the smartphone. Here's how you would do that step by step:
Firstly, convert the sales tax from a percentage to a decimal by dividing by 100. For 5%, you would calculate 5 ÷ 100 = 0.05.
Next, calculate the sales tax by multiplying the original price by this decimal. You do this by calculating $579 × 0.05 = $28.95 in sales tax.
Finally, add the sales tax to the original price to find the total cost. Add the two amounts together to get $579 + $28.95 = $607.95.
So, the total cost of the smartphone including sales tax would be $607.95.
A plane traveled 972 miles to Berlin and back. The trip there was with the wind. It took 9 hours. The trip back was into the wind. The trip back took 18 hours. Find the speed of the plane in still air and the speed of the wind
Can you help me to find the answer
the first term of a geometric sequence is 2 and the common ratio is -3 find the fifth term
Answer:
With geometric sequences, all you have to do is multiply each term by -3 until you get to the needed term.
First term: 2
Second term: 2 * -3 = -6
Third term: -6 * -3 = 18
Fourth term: 18 * -3 = -54
Fifth term: -54 * -3 = 162
The fifth term of the sequence is 162.
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In this right triangle what is the approximate length of the hypotenuse side AC
A) 22.5 cm
B) 3.56 cm
C) 45 cm
D) 6.71 cm
Erma maintains an active blog about her seashell collection. She has 500 white shells, 325 yellow shells, 115 pink shells, and 60 green shells in her jar. She asks Sweet T to reach into her jar and randomly selects a shell. Then she replaces it and shakes up the jar before asking Sweet T to pick another shell. Which model shows the probability of a randomly selecting each color shell from her jar?
A. White 60% Pink: 10% yellow: 20% Green: 10%
B.White: 50% Pink: 11% yellow: 32.5% green: 6%
C. White: 25% Pink: 25% Yellow: 25% Green: 25%
D. White: 100% Pink: 23% Yellow: 65% Green: 12%
Brian read 8 I/4 pages of a book in 1/6 hour at this rate what is the total number of pages of the book he will read in 1 hour
The library is having a book sale. Hardcover books sell for $4 each, and paperback books are $2 each. If Connie spends $26 for 8 books, how many hardcover books did she buy?
There were 3 apple, 1 mixed fruit, 2 grape, and 4 tropical fruit juice boxes in the cooler at the picnic. What is the probability that, when Jill reaches into the cooler to grab two juice boxes without replacing them, she grabs two that are grape?
1/100
1/50
1/45
1/25
Answer:
1/45
Step-by-step explanation:
PLEASE HELP.
There is a 40% chance that you will lose $25,000 if you invest...
What is 8,663,943,526 rounded to the nearest million? A. 8,663,000,000 B. 8,663,944,000 C. 8,664,000,000 D. 9,000,000,000
BRAINLIEST if right!
Find the area of the circle. Use 3.14 for π. Round to the nearest square foot.
3 to the power of n = 81. Pls explain
The sketch shows two parallel lines cut by a transversal. Angle 1 is 58° . What is the measure of angle 7 ?
Answer: 122
Step-by-step explanation: its right on imagine math (ttm)
Please need help on this
write the equation in standard form y+2=3/5(x + 5)
If a girl take algebra in 8 grade and she fail , she gonna retake it in 9 grade so that will be affect to the credit high school or same ? I need the answer for algebra
im need HELP!!!
m<JEF=40°
Answer:JEF has a 50 degree complement
140 degrees is the supply of JEF
If your teacher says NONE, then the complement of DON is -34 degrees.
DON is 56 degrees when supplemented
Anastasia had 10 buckets of mulch for her garden. If Colby used 3 2/7 buckets of Anastasia's mulch, how many buckets were left? Leave answer as a mixed number with a space between the whole number and the fraction
After Colby used 3 2/7 buckets out of Anastasia's 10 buckets of mulch, Anastasia has 6 5/7 buckets left. The subtraction was performed by converting mixed numbers to improper fractions, performing the operation, and then converting back to a mixed number.
Anastasia had 10 buckets of mulch for her garden. After Colby used 3 2/7 buckets, we need to subtract that amount from the total to find out how many buckets are left. To subtract the mixed number, we can convert it into an improper fraction and then perform the subtraction.
First, convert 3 2/7 to an improper fraction:
3 2/7 = 3 x 7 + 2 which is 21/7 + 2/7 = 23/7.
Now subtract the improper fraction from the total number of buckets:
10 - 23/7
Change 10 to a fraction with a denominator of 7 to get 70/7.
Subtract the two fractions:
70/7 - 23/7 = (70 - 23) / 7 = 47/7.
Convert the improper fraction back to a mixed number:
47/7 = 6 5/7 (since 47 divided by 7 is 6 with a remainder of 5).
So, Anastasia has 6 5/7 buckets of mulch left.
what is distribution property
help me.................
At 7:00 AM there were 14,000 gallons of water in Lance’s pool when he noticed there was a leak. After 6 hours there were only 5,000 gallons of water remaining in his pool. Write an equation that describes the number of gallons of water as a function of the time the pool has been leaking.
y = -5,000x + 14,000
y = -1,500x + 14,000
y = -9,000x + 14,000
Is it possible for a vertical line to have a negative slope?
no
yes
Answer: -5000x + 14,000 = 9000 and yes
Step-by-step explanation:
The equation is y = - 1500x + 14000, then the option B is correct. And yes, the slope of the line is negative.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more variables.
At 7:00 AM there were 14,000 gallons of water in Lance’s pool when he noticed there was a leak.
After 6 hours there were only 5,000 gallons of water remaining in his pool.
Let y be the amount of water in the pool and x be the time.
Then the coordinate will be (0, 14000) and (6, 5000)
We know that the equation of a line is given as
[tex]\rm y - y_1 = \dfrac{y_2 - y_1}{x _2 - x_1} \times (x -x_1)[/tex]
Then we have
[tex]\rm y - 14000 = \dfrac{5000 - 14000}{6 - 0} (x - 0)\\\\y = -1500x + 14000[/tex]
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How to know that number is irrational list all things . plz
What is the exact volume of the cone?
40π cm³
803π cm³
1603π cm³
160π cm³
Outline of cone with dotted line rising from middle of base to the point. Line is labeled ten centimeters. A second dotted line extends horizontally from middle of base to its edge. Line is labeled four centimeters.
Answer:
it is c
Step-by-step explanation:
The exact volume of the cone in which the outline of cone with dotted line rising from middle of base to the point is 160/3π cm³.
What is of volume of solid?Volume of solid is the amount of quantity, which is obtained by the solid or object in the 3 dimensional space.
The volume of the cone can be given with the following formula as,
[tex]V=\dfrac{\pi r^2 h}{3}[/tex]
Here, (r) is the radius of the base of the cone and (h) is the height of the cone.
The image of the cone, whose volume has to be find out, is attached below.
The height of the cone is 10 cm long and the radius is 4 cm long. Thus put these values in the above formula as,
[tex]V=\dfrac{\pi (4)^2 (10)}{3}\\V=\dfrac{160}{3}\pi \;\;\tm cm^3[/tex]
Hence, the exact volume of the cone in which the outline of cone with dotted line rising from middle of base to the point is 160/3π cm³.
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an observer on a cliff 1200 feet above sea level sights two ships due East. The angle of depression to the shops are 48° and 33°. What is the distance between the ships?
The problem involves using trigonometry, specifically the tangent function, to determine the distance between the two ships. By calculating the distance from the observer to each ship separately and finding the difference, we find the distance between the two ships to be approximately 814.61 feet.
Explanation:The problem at hand involves the use of trigonometry, specifically tangent of an angle in a right triangle. Since we are dealing with angles of depression, we must understand that these angles are taken from a horizontal line - in this case, the line of sight from the cliff's edge.
First, let's consider the observer and the further away ship using tangent as follows:
tangent of 33° = height/distance, thus distance to the further ship = height / tangent of 33° = 1200 / tan(33) approximately equals to 1809.54 feet.Similar steps for nearer ship with angle of 48 degrees:
tangent of 48° = height/distance, hence distance to the closer ship = height / tangent of 48° = 1200 / tan(48) approximately equals to 994.93 feet.Therefore, the distance between the ships is the difference between the two distances calculated above, which will be 1809.54 - 994.93 = 814.61 feet.
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To determine the distance between the two ships, use the angles of depression and the observer's height above sea level to find the horizontal distances to each ship with trigonometry and subtract the smaller from the larger.
Explanation:To calculate the distance between two ships using their angles of depression from an observer's viewpoint atop a cliff, we can employ trigonometry. Let us denote the observer's vertical distance above sea level as height (h), which is 1200 feet in this case. The angles of depression to the first and second ship are 48° and 33° respectively.
We will use the tangent of these angles to find the horizontal distances (d1 and d2) from the base of the cliff to each ship:
Using the tangent of the angle of depression 48° to find distance to first ship (d1):After finding d1 and d2, we subtract the smaller distance from the larger to get the distance between the two ships:
Distance between ships = d2 - d1
Finally, we convert the answer from feet to the desired unit if necessary.
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