A student takes a 10-question true-or-false quiz and randomly guesses the answer to each question. Suppose that a correct answer is worth 1 point and an incorrect answer is worth -.5 points. Find the probability that

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.

Answer:

Therefore. The correct option is B. Divide the diameter by 2.

Step-by-step explanation:

Diameter of the circle : It is defined a line segment joining two points on the circumference of circles provided the segment passes through the center of the circle.

Radius of the circle : It is defined as a line segment joining any point on the circle to the center of the circle.

So, it can be illustrated that the radius is half of the diameter of the circle.

If we are given the diameter of the circle and we need to find the radius of the circle.

So, we will divide the given diameter of the circle by 2 to obtain the required radius of the circle.

Therefore. The correct option is B. Divide the diameter by 2.

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.

To find two numbers whose GCF is 8 but neither is 8, choose multiples of 8 that are not equal to 8 itself.

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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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.

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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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)

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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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.

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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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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Probability randomly select at least 1 heart is 5 / 14

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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Each friend will get 1/2 of a pie when it is divided into equal.

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?

The remaining piece of the board was [tex]6\frac{3}{4}[/tex]  feet.

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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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.

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.

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

Substitute these values into the equation.

Solve for x.

Hence, the measure of the base angles is 39° respectively.

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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).

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

The solution to the given inequality expression is -1 and 2/3.

To 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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It would cost $756 if orders eight bags of gravel instead.

252x 3= 756

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