General Idea:
We need to make use of the below formula to find the present value.
[tex] PV=\frac{FV}{(1+\frac{r}{n})^{nt}} \\ \\ Where:\\ FV \; is \; Future\; Value\; of \; money\\ r \; is\; Annual\; rate\; of\; interest\\ t\; is\; number\; of\; years\\ n\; is\; Number\; of\; periods\; based\; on\; compounding \; frequency [/tex]
Applying the Concept:
We are given the below information:
[tex] FV= \$11,500\\ \\ t=5\; years\\ \\ r=4.5 \%\\ \\ n=2\; (because\; given\; compounded\; semi-annually) [/tex]
We need to substitute the above information in the formula to find the Present value.
[tex] PV=\frac{11500}{(1+\frac{0.045}{2})^{2 \times 5}} =\frac{11500}{(1+0.0225)^{10}} =\frac{11500}{1.0225^{10}} \\ \\ PV \approx \$9206 [/tex]
CONCLUSION:
The present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually is approximately 9206 dollars
Kiera wanted to find the approximate number of historical books at the library she works at. She used the computer to randomly take a sample of 80 books and found that 6 of them were considered historical books. There are 21,360 books at this library. What is the best estimate of the amount of historical books at this library?
A sample of 80 books was taken randomly using a computer and 6 of them were considered to be historical books.
It means probability of sample would be 6 out of 80 i.e. P = 6 over 80 = 0.075 or 7.5%.
It says there are 21,360 books in the library, so Population would be 21,360 books. We can use outputs of the sample survey to represent complete collection of books in the library.
So best estimate of total historical books in the library would be 7.5% of total population.
Best estimate = 7.5% of 21,360
Best estimate = 0.075 x 21,360
Best estimate = 1602 books.
Hence, there are approximately 1602 historical books in the entire library.
What is the simplified form of the expression? x8 - 2y10 - 5x5
What is the length of the segment with endpoints (-3,4) and (5,4)?
In the regular nonagon shown, what is the measure of angle x?
an athlete is training to run a marathon. she plans to run 2 miles the first week. she increases the distance by 8% each week. which function models how far she will run in the nth week?
The sum of a number divided by 8 and 7 is equal to 9 .
[tex]n-the\ number\\\\\dfrac{n}{8}+7=9\qquad\text{subtract 7 from both sides}\\\\\dfrac{n}{8}=2\qquad\text{multiply both sides by 8}\\\\\boxed{n=16}[/tex]
I = $1,200 * 8/100 * 240/360 =
Answer:
$ 64
Step-by-step explanation:
I=$ 1200×8/100×240/360
Which could also be written as:
I=
[tex]1200\times \dfrac{8}{100}\times \dfrac{240}{360}\\ \\= 12\times 8\times \dfrac{24}{36}\\ \\=12\times 8\times \dfrac{2}{3}\\ \\=4\times 8\times 2[/tex]
=$ 64
What is the solution to this inequality 2(x-4)+14<= x-1
In a circle with radius 4 cm the diameters AC and BD are perpendicular to each other. Prove that ABCD is a square. Find the area of ABCD.
the width of rectangle is 12cm less than the length . the perimeter is 156cm find the width and the length
A wedding cake has a diameter of 12 inches. The cake decorator needs to know how many strawberries he will need to put around the outside, so he needs the circumference. What is the circumference? Leave the answer in terms of π.
A square pyramid has a base area of 64ft2. The pyramids total surface area is 224ft2. What is the area of each triangular face?
The unit used to measure an angle is called
Estimate it’s the length in meters for poster. Explain
The price has changed from $120 to $75. by how many percent did it change?
The price has changed by 37.5% from $120 to $75.
Explanation:To find the percentage change, we can use the formula:
Percentage change = ((new value - old value) / old value) * 100
In this case, the old value is $120 and the new value is $75. Plugging these values into the formula, we get:
Percentage change = (($75 - $120) / $120) * 100 = (-$45 / $120) * 100 = -0.375 * 100 = -37.5%
Therefore, the price has changed by 37.5%.
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The percentage change in price from $120 to $75 is calculated by subtracting the initial price from the final price, dividing the result by the initial price, and then multiplying by 100. The price has decreased by 37.5%.
Explanation:The question involves calculating the percentage change in price. To do this, you start by subtracting the final price ($75) from the initial price ($120) to determine the difference. In this case, the difference is $120 - $75 = $45. This represents the total change in price.
To find out the percentage change represented by this difference, you divide the difference ($45) by the original price ($120) and then multiply the result by 100 to convert it to a percentage. This can be represented by the formula:
((Final Price - Initial Price) / Initial Price) x 100.
So, the percentage change would be calculated as follows: ((120 - 75) / 120) * 100 = 37.5%. Therefore, the price has decreased by 37.5%.
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The length of the longer leg of a right triangle is 19ft more than five times the length of the shorter leg. the length of the hypotenuse is 20ft more than five times the length of the shorter leg. find the side lengths of the triangle.
This problem can be solved by creating and solving a quadratic equation based on the Pythagorean theorem. We denote the length of the shorter leg as 'x', and substitute '5x+19' and '5x+20' as lengths of the longer leg and hypotenuse in the theorem.
Explanation:The entire problem revolves around the application of the Pythagorean theorem, which in a right-angled triangle gives the relationship a² + b² = c², were a and b are the lengths of the shorter sides (legs) and c is the length of the longest side (hypotenuse).
Let's denote the length of the shorter leg as 'x'. From the problem, we know that the longer leg is 5x+19 and the hypotenuse is 5x+20. Using the Pythagorean theorem, we have:
((5x+19)² + x²) = (5x+20)².
You can solve this equation to find out the value of 'x', following which you can substitute this value back into 5x+19 and 5x+20 to find lengths of the longer leg and hypotenuse.
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In a circle with a radius of 3 ft, an arc is intercepted by a central angle of 2π3 radians. What is the length of the arc?
2π ft
3π ft
6π ft
9π ft
Answer:
The correct answer is 2π ft.
Step-by-step explanation:
Verified by correct test results.
The sum of 2 numbers is 80. The ratio of the numbers is 3 to 5. Find the large number
How do you write 4.5 with the same number of decimal places as 6.25
What triangle has 0 reflectional symmetries?
Answer:
A. right scalene triangle
A triangle with 0 reflectional symmetries is a scalene triangle. Equilateral triangles, such as those on an icosahedron, have multiple symmetries. Symmetry in different contexts, like physics and chemistry, can result in a net effect of zero.
Explanation:A triangle that has 0 reflectional symmetries is a scalene triangle, where all three sides and all three angles are of different lengths and magnitudes, respectively. An equilateral triangle, like the ones that form the faces of an icosahedron, has multiple lines of symmetry because of its equal sides and angles. On another note, in vector algebra, a null vector has all components equal to zero, which implies it has no direction or magnitude. Similarly, the molecular geometry of BF3 is described as trigonal planar and possesses symmetry, resulting in a net dipole moment of zero despite having polar B-F bonds.
In physics-related symmetry, charges or forces can cancel each other out leading to a net force of zero. For instance, if equal charges are placed at the corners of a square with a charge at the center, the net Coulomb force on the center charge will be zero due to the symmetry. Similarly, in collisions, certain angles or scenarios can result in a term becoming zero, like having a head-on collision where the incoming ball stops (v1 = 0), or the balls deflect at a 90-degree angle resulting in cos(θ1 - θ2) being zero.
a medication is supplied in a mixture that contains 7.5 mg of medication per millimeter of solution. the dosage rate is 10.0 mg of active ingredient per kilogram of body weight. calculate the number of millimeters of medication that should be given to a patient weighing 187 lb.
3) Ashley uses the two points on the coordinate plane to represent the location of her house and the public library. Each unit on the graph represents 1 mi. How far is the public library from Ashley’s? Show your work.
Find the interest on the loan if you borrowed $2,000 at 8% for 1 year.
A number devised by six is 306. What is the number?
Mary had some cookies.she gave 2/9 of them to matthew and ate 1/3 of them. she had 8 cookies left. how many did she have at first?
Mary originally had 18 cookies. This is determined by creating and solving a ratio based on the fractions of cookies Mary had left after giving some away and eating some.
Explanation:The subject of this question is mathematics and it involves fractions. We can think of Mary's original number of cookies as 1 whole or 100%. We're told she gave away 2/9 of them and ate 1/3 of them, which means she hasn't touched 1 - 2/9 - 1/3 of the cookies.
First, we calculate the common denominator, which is 9. So, we must convert 1/3 to 3/9. Now, we have 1 whole - 2/9 - 3/9. This addition simplifies to: 9/9 - 2/9 - 3/9 = 4/9.
The 4/9 is equal to the 8 cookies she has left over. To find the original amount of cookies, we set up the following ratio: 4/9 = 8/x. Solve this ratio for x (which represents Mary's original number of cookies) by cross multiplying: 4x = 72. Divide both sides by 4 to get: x = 18 cookies.
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Convert the following measurements.
a. 2 cubic yards to cubic feet
b. 135 cubic feet to cubic yards
c. 6,912 cubic feet to cubic inches
d. 279,936 cubic inches to cubic feet
Solve the following addition problem. Remember to carry as necessary.
7 cu. yd. 9 cu. ft. 134 cu. in. + 1 cu. yd. 12 cu. ft. 200 cu. in.
Solve the following subtraction problem. Remember to borrow as necessary.
9 cu. yd. 113 cu. in. – 4 cu. ft. 129 cu. in.
Solve the following multiplication problem.
11 cu. yd. 17 cu. in. × 135
What’s the capacity of a 3 cubic foot carton in cubic inches?
The Great Pyramid was built in Egypt more than 4,000 years ago. It was built by King Khufu, or Cheops, who intended to use it as a tomb. The pyramid contains about 2,300,000 blocks of stone, each weighing 2 1⁄2 tons. Can you calculate the approximate total weight of the Great Pyramid, in pounds?
Convert the following liquid measures.
a. 5 gallons to pints
b. 128 tablespoons to fluid ounces
c. 93 pints to quarts
d. 13 quarts to cups
e. 69 teaspoons to tablespoons
f. 112 cups to gallons
g. 18 fluid ounces to teaspoons
h. 3 gallons to fluid ounces
A local dairy farmer collects 490 gallons of milk a day from his cows. He keeps 1⁄35 of the milk for his own use, and sells the rest. Each quart of milk sells for 35 cents. In dollars, how much does he earn from selling his milk each day? (There are 100 cents in a dollar.)
A swimming pool has a capacity of 1,386 cubic feet. One gallon of water will fill 231 cubic inches of space. How many gallons of water will it take to fill the entire pool? (Hint: Convert the capacity of the pool to cubic inches first.)
The instructions on a bottle of laundry detergent tell you to add two capfuls of detergent to each gallon of water. One capful of detergent is equal to about one tablespoon. If your washing machine holds 11 gallons of water, how many tablespoons of detergent will you need to add? How many fluid ounces of detergent?
Convert the following dry measurements.
a. 11 bushels to quarts
b. 3 pecks to pints
c. 97 quarts to bushels
d. 1,120 quarts to pecks
Twelve apple pies can be made from one bushel of apples. How many apple pies can be made from one peck of apples?
Mr. Osaka sprinkles 1.694 pints of dry, powdered plant food on his garden three times a year. In quarts, what’s the total amount of plant food he uses in one year?
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Which sentence contains a punctuation error?
One-quarter cup of chocolate chips does not seem like enough.
She is a well known basketball player.
This well-known recipe is the one I always use for oatmeal cookies.
He bakes loaves of the best-tasting bread we have ever eaten.
Thanks for helping.
Melinda rents paddle boats down at the pier. She uses 5.5 feet of nylon rope to tie off each boat. She started with 80 feet of rope. After securing all the boats, she was left with more than 3 feet of rope. How many boats did Melinda tie off?
Answer: Less than 14
Step-by-step explanation: My teacher helped me on this problem and i got less then 14 and i submitted it and it was right i really this helped
the graph shows y in direct variation with x. Find the value of Y when X=-15
A.) -30
B.) -24
C.)-18
D.) -12
Answer:
A -30
Step-by-step explanation:
If you pay attention you will see I did this on USATestPrep and I know the answer
Anna is buying trim to go around her rug. Her rug measures 54 inches by 42 inches. How many inches of trim will Anna need to buy