Final answer:
Pierre earns $360 in interest on his $9,000 certificate of deposit after the first six months, with a balance of $9,360.
Explanation:
Pierre deposits $9,000 in a certificate of deposit (CD) that pays an 8% interest rate, compounded semiannually. To calculate the interest earned in the first six months and the balance after six months, we follow these steps:
Determine the semiannual interest rate by dividing the annual rate by two. Since the annual rate is 8%, the semiannual rate is 4% or 0.04 in decimal form.
Calculate the interest for the first semiannual period (first six months) by multiplying the principal amount by the semiannual interest rate: $9,000 * 0.04 = $360.
The interest earned in the first six months is $360.
To find the new balance after six months, add the interest earned to the initial deposit: $9,000 + $360 = $9,360.
The balance of Pierre's certificate of deposit after six months is $9,360.
An incompressible steady flow pattern is given by u=x^3+2z^2 and w=y^3-2yz. what is the most general form of the third component v(x,y,z) which satisfies continuity?
Final answer:
For an incompressible steady flow with u and w components as [tex]x^{3} +2z^{2}[/tex] and [tex]y^{3}-2yz[/tex], respectively, the v component of the velocity that satisfies continuity is of the form [tex]v(x,y,z)=y^{2}-3x^{2y}+f(x,z)[/tex], where f(x, z) is an arbitrary function of x and z.
Explanation:
The question is asking for the most general form of the third component v(x, y, z) of a velocity vector field that satisfies the continuity equation for an incompressible steady flow. Given that the u and w components of the velocity are
u = [tex]x^{3} +2z^{2}[/tex] and
w = [tex]y^{3}-2yz[/tex],
respectively, we can use the continuity equation for incompressible flow, which is
∇ ⋅ β = 0,
or written out,
∂u/∂x + ∂v/∂y + ∂w/∂z = 0.
By substituting the given components into the continuity equation, and taking the respective partial derivatives, we get:
∂u/∂x = [tex]3x^{2}[/tex],
∂w/∂z = -2y,
So, the continuity equation becomes: [tex]3x^{2}[/tex] + ∂v/∂y - 2y = 0.
Rearranging terms we get: ∂v/∂y = 2y - [tex]3x^{2}[/tex]
Integrating with respect to y, we find that v must generally be of the form: [tex]v(x,y,z)=y^{2}-3x^{2y}+f(x,z)[/tex], where f(x, z) is an arbitrary function of x and z since the partial derivative with respect to y of any function that does not contain y will be zero, preserving the continuity.
6 friends share 3 small pies equally
Each friend will get 1/2 of a pie when it is divided into equal.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that, 6 friends share 3 small pies equally.
Total number of pies = 3
Total number of friends = 6
Since, the number of pie is less than number of friends, no one will get 1 pie each.
Divide 3 pies in to 6 equal parts.
Each friend will get 3/6 pies.
After simplifying, each friend will get 1/2 pie.
That is, each will get half of a pie.
Hence each of the friend will get one half of a pie.
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Your question is incomplete. Probably, the correct question is as follows.
6 friends share 3 small pies equally. What fraction of a pie does each friend get?
Elly buys 75 shares of stock in a mutual fund for a total investment of $450. She sells 50 shares of her stock for total proceeds of $400. Determine if Elly made a profit or loss, and how much per share.
Answer:
She made a profit of $ 2 on each share of stock
Step-by-step explanation:
Elly buys 75 shares of stock in a mutual fund for a total investment of $450.
cost of 1 share of stock= $ 450/75
= $ 6
She sells 50 shares of her stock for total proceeds of $400.
selling price of 1 share of stock=$ 400/50
= $ 8
Hence, She made a profit of $ 2 on each share of stock ($8-$6=$2)
what do you think the sum of the probabilities for all the possible outcomes must be for any situation. explain
Timmy writes the equation f(x) = 1/4x – 1. He then doubles both of the terms on the right side to create the equation g(x) = x – 2. How does the graph of g(x) compare to the graph of f(x)? The line of g(x) is steeper and has a higher y-intercept. The line of g(x) is less steep and has a lower y-intercept. The line of g(x) is steeper and has a lower y-intercept. The line of g(x) is less steep and has a higher y-intercept.
Solve for c: 6/13=3/c
Can you show me the formula for this?
The wall at the front entrance to the rock and roll hall of fame and museum in cleveland, ohio, is an isosceles triangle. the triangle has a vertex angle of 102 degrees. what is the measure of the base angles? answer
The measure of the base angles is 39° respectively.
An Isosceles triangle is a triangle that has two equal sides.
Note: The base angle of an isosceles triangle is equal.
From the question,
The sum of the angle in a triangle is 180°.
⇒ a+b+c = 180°............... Equation 1
Given:a = 102°b = c = x = base angle of the isosceles triangle.Substitute these values into the equation.
102+x+x = 180102+2x=180Solve for x.
2x = 180-1022x = 78x = 78/2x = 39°Hence, the measure of the base angles is 39° respectively.
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How much would $400 be worth after 16 years, if it were invested at 3% interest compounded annually? (Use the formula below and round your answer to the nearest cent.)
A(t)=P(1+ r/n)^nt
Final answer:
Using the compound interest formula A(t) = P(1 + r/n)^(nt) with the values P = $400, r = 3%, n = 1, and t = 16 years, the investment would grow to $722.44.
Explanation:
To calculate how much $400 would be worth after 16 years when invested at a 3% interest rate compounded annually, we can use the compound interest formula A(t) = P(1 + r/n)^(nt). In this formula, P represents the principal amount ($400), r is the annual interest rate (3% or 0.03), n is the number of times interest is compounded per year (1 for annually), t is the number of years the money is invested (16 years), and A(t) is the amount of money accumulated after t years, including interest.
To solve for A(t), we substitute the values into the formula:
A(t) = 400(1 + 0.03/1)^(1×16)
A(t) = 400(1 + 0.03)^16
A(t) = 400(1.03)^16
After calculating the power term:
A(t) = 400(1.80611123467)
Finally, we multiply the principal amount by the factor:
A(t) = $722.44
The $400 investment at 3% interest compounded annually would be worth $722.44 after 16 years.
Cassie has 1/2 pound of sugar in her cabinet. Her cake recipe calls for 2/10 of a pound of sugar. How many cakes can she make?
what fraction did she spend on petrol ,she spent £30 on petrol in total ,how much did she spend
A carpenter cut a board 3 3/4 feet long to make a shelf. Before he cut the board, it was 10 1/2 feet long.
How long is the remaining piece of the board?
Enter your answer, as a mixed number in simplest form
The remaining piece of the board was [tex]6\frac{3}{4}[/tex] feet.
What are mixed fractions?A fraction represented with its quotient and remainder is a mixed fraction.
Given that, a carpenter cut a board 3 3/4 feet long to make a shelf, before he cut the board, it was 10 1/2 feet long.
[tex]3\frac{3}{4} = \frac{15}{4} \\10\frac{1}{2} = \frac{21}{2}[/tex]
[tex]\frac{21}{2} - \frac{15}{4} \\= \frac{27}{4} \\= 6\frac{3}{4}[/tex]
Hence, The remaining piece of the board was [tex]6\frac{3}{4}[/tex] feet.
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solve the equation.
| 2z - 3| = 4z - 1
The solution to the given inequality expression is -1 and 2/3.
Solving inequality expressionTo solve the equation |2z - 3| = 4z - 1, we need to consider two cases: one where the expression inside the absolute value is positive and another where it is negative. Remember that the absolute value of a number is always non-negative.
Case 1: (2z - 3) is non-negative (greater than or equal to zero).
In this case, |2z - 3| = 2z - 3. So we have:
2z - 3 = 4z - 1
Now, let's solve for 'z':
2z - 4z = -1 + 3
-2z = 2
z = 2 / -2
z = -1
Case 2: (2z - 3) is negative (less than zero).
In this case, |2z - 3| = -(2z - 3) = -2z + 3. So we have:
-2z + 3 = 4z - 1
Now, let's solve for 'z':
-2z - 4z = -1 - 3
-6z = -4
z = -4/-6
z = 2/3
Therefore, we have two possible solutions: z = -1 and z = 2/3.
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Why is simple interest useful for planning parts of your financial future?
Simple interest is useful for planning parts of your financial future because it helps you calculate how much interest you will earn or owe on a loan or investment.
Explanation:Simple interest is useful for planning parts of your financial future because it helps you calculate how much interest you will earn or owe on a loan or investment. It is a straightforward calculation that only takes into account the principal amount and the interest rate. By using simple interest, you can make informed decisions about saving, borrowing, or investing money.
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The perimeter of parallelogram WXYZ is 50 millimeters. What is WZ?
The mean of the scores obtained by a class of students on a physics test is 42. The standard deviation is 8%. Students have to score at least 50 to pass the test. Assuming that the data is normally distributed, % of the students passed the test.
Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3. How much of each juice is needed to make 25 liters of this punch?
Answer:
5:2:3....added = 10
Step-by-step explanation:
5/10(25) = 125/10 = 12.5 liters of pear juice
2/10(25) = 50/10 = 5 liters pineapple juice
3/10(25) = 75/10 = 7.5 liters plum juice
Nitrogen and oxygen are the most abundant gases in Earth’s atmosphere. A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule. Which statements describe writing 0.00000000003 in scientific notation? Check all that apply.
Answer:
(these are the answer choices ppl)
The exponent is negative.
The exponent is positive.
The coefficient is 0.3.
The exponent represents the number of places the decimal moves.
The decimal moves to the right.
(its a, d, e)
0.00000000003 in scientific notation is 3.0 x 10^-11.
Explanation:The number 0.00000000003 can be converted to scientific notation by moving the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, we would move the decimal point 11 places to the right to get 3.0 x 10-11. The exponent, -11, indicates how many places the decimal point was moved.
So, the correct statement would be:
0.00000000003 in scientific notation is 3.0 x 10-11.
Upon graduation from college, Warren Roberge was able to defer payment on his $22,000 student loan for 3 months. Since the interest will no longer be paid on his behalf, it will be added to the principal until payments begin. If the interest is 6.94 % compounded monthly , what will the principal amount be when he must begin repaying his loan?
Using the compound interest formula, we calculate that after 3 months, the new principal amount that Warren Roberge will owe on his student loan is $22,000(1 + 0.0694/12)^(12*0.25).
Explanation:To find the principal amount that Warren Roberge will owe when he begins repaying his student loan, we need to consider the interest compounding monthly over the 3-month deferment period. The formula for compound interest is: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time in years.
In this case, P = $22,000, r = 6.94/100 = 0.0694, n = 12 (since the interest is compounded monthly), and t = 3/12 = 0.25 (since the deferment period is 3 months, or 0.25 years).
Substituting these values into the formula, we find that A = $22,000(1 + 0.0694/12)^(12*0.25).
Therefore, after 3 months, the principal amount that Warren will owe on his student loan will be A.
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When Warren Roberge begins repaying his student loan after a 3-month deferment, the principal amount will be $22,038.07.
To calculate the principal amount when he starts repaying, we need to account for the accrued interest during the deferment period.
Calculate the monthly interest rate,Calculate the interest accumulated over the 3-month deferment period,Add the accrued interest to the principal:
Interest rate,
6.94% / 12 (months)
= 0.579%
$22,000 * 0.579% * 3 months
=127.38*3
= $38.07
Principal amount,
$22,000 + $38.07
= $22,038.07
what is the vertex of the quadratic function: y=-3(x+5)^2-4
Elle wanted to order candy online. Company A is offering 2 1/2 pounds of chocolate for $32.50, while Company B is offering 2 3/4 pounds of the same chocolate for $35.00. Which company is offering the lowest price per pound. Justify your answer.
Based on the price offered per company, we can infer that the cheaper company is Company B.
The cheaper company is the one that is selling a pound of chocolate for a lower price than the other company.
First convert the mixed fractions to decimals for easier calculation:
Company A = 2 ¹/₂ = 2.5 pounds
Company B = 2 ³/₄ = 2 + (3/4) = 2.75 pounds
The cost per pound is:
= Cost of chocolate / Number of pounds
Company A: Company B:
= 32.50 / 2.5 = 35 / 2.75
= $13 per pound = $12.73
In conclusion, Company B is cheaper for selling at $12.73.
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Solve |a| = -6
{-6}
{-6, 6}
Ø
Mathematically, the absolute value of a number is always non-negative, which means it can never be equal to a negative number. Hence, there's no possible value for 'a' in the equation |a| = -6, making the correct answer Ø.
Explanation:To solve |a| = -6, it’s important to understand the concept of absolute values. The absolute value of a number is its distance from zero on the number line. Therefore, it's always non-negative, because distances cannot be negative. Thus, there are no values of 'a' that would make |a| = -6, because absolute values cannot be negative.
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of the 125 students in 5th grade, 3/5 of them have a mobile phone. How many students do not have a mobile phone.
Leo is adding gravel to the edge of his driveway he order six bags of gravel for $252 how much would it cost if orders eight bags instead
It would cost $756 if orders eight bags of gravel instead.
252x 3= 756
Write two numbers, neither of which is 8, whose GCF is 8.
To find two numbers whose GCF is 8 but neither is 8, choose multiples of 8 that are not equal to 8 itself.
Explanation:To find two numbers whose GCF is 8 and neither of which is 8, we need to find two numbers that have 8 as their largest common factor.
The easiest way to do this is to select a number that is a multiple of 8, such as 16, and then choose another number that is also a multiple of 8, but not equal to 8 itself, such as 24.
So, the two numbers whose GCF is 8 and neither of which is 8 are 16 and 24.
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What is the volume in cubic meters of a greenhouse that is 30 feet long, 15 feet wide, and 8 feet high
The volume of the greenhouse is approximately 101.952 cubic meters.
To calculate the volume of the greenhouse in cubic meters, we first need to convert the measurements from feet to meters.
1 foot is approximately equal to 0.3048 meters.
Given measurements:
Length = 30 feet
Width = 15 feet
Height = 8 feet
Converting to meters:
Length = 30 feet * 0.3048 meters/foot ≈ 9.144 meters
Width = 15 feet * 0.3048 meters/foot ≈ 4.572 meters
Height = 8 feet * 0.3048 meters/foot ≈ 2.4384 meters
Now, we can calculate the volume in cubic meters:
Volume = Length * Width * Height
Volume ≈ 9.144 meters * 4.572 meters * 2.4384 meters ≈ 101.952 cubic meters
The volume of the greenhouse is approximately 101.952 cubic meters.
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Carla and Ross competed in the long-jump at a track meet. Carla jumped 3.5 meters. Ross jumped 99 inches. Who jumped farther and by approximately how many feet? Use 1 m = 3.27 ft. Explain how you solved this problem.
The solution of d + s > -3 is d > -7. What is the value of s?
21k – 3n + 9p > 3p + 12
Eleven years ago, you deposited $3,200 into an account. seven years ago, you added an additional $1,000 to this account. you earned 9.2 percent, compounded annually, for the first 4 years and 5.5 percent, compounded annually, for the last 7 years. how much money do you have in your account today? $8,666.67 $7,411.90 $7,717.29 $8,073.91 $8,708.15
Dipping your spoon into the bowl 4 times, what is the probability that you randomly select at least 1 heart
Probability randomly select at least 1 heart is 5 / 14
Probability based questions:Given question is incomplete, complete question is as follows;
Number of hearts = 5
Number of clover = 3
Number of stars = 4
Number of moons = 2
Find:
Probability randomly select at least 1 heart
Computation:
Total item = 5 + 3 + 4 + 2
Total item = 14
Probability randomly select at least 1 heart = 5 / 14
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