It takes a ship three hours to sail 72km with the current and 4 hours against it. Find the speed of the ship in still water and find the speed of the current

Answer:

  u = -2.34  or  u = 18.34

Step-by-step explanation:

You want to solve u² -16u = 43 by completing the square.

To complete the square, add the square of half the coefficient of the linear term to both sides.

  u² -16u +(-16/2)² = 43 +(-16/2)²

  u² -16u +64 = 107 . . . . . . . simplify

  (u -8)² = 107 . . . . . . . . . write as a square

  u -8 = ±√107 . . . . . . square root

  u = 8 ± √107  . . . add 8

  u = -2.34  or  u = 18.34 . . . . . find the decimal values

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The volume of the prism is 180 cm³.

A prism is a 3D (three-dimensional) solid which has faces that are identical at both ends. The other faces are flats. A prism is named after its base.

The volume of any prism can be calculated using the formula:

V = A[tex]_{B}[/tex] * h

where A[tex]_{B}[/tex] is area of base and h is height of prism

In this case, we have the following information about the prism:

A[tex]_{B}[/tex]  = 20 cm²

h = 9cm

V = 20 * 9

V = 180 cm³

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Complete Question

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To find the percentage of plants that are exactly 13cm tall using a proportion, you need to first identify the number of plants that are 13cm tall and the total number of plants. Based on your question, let's assume that 2 out of 9 plants are exactly 13cm tall.

Now, set up a proportion with the given information:

(number of plants 13cm tall) / (total number of plants) = (x) / (100)

In this case, the proportion is:
2/9 = x/100

To solve for x, cross-multiply:
2 * 100 = 9 * x
200 = 9x

Now, divide both sides by 9:
x = 200 / 9
x ≈ 22.22
So, approximately 22.22% of the plants in Dorothy's garden are exactly 13cm tall.

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The initial number of video views was (fewer than) the initial number of site visits, and the number of video views grew by (a larger factor) the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is (20,825).

Video views refer to the number of times a video has been watched or viewed by viewers.

A site visit refers to a visit or session by a user to a website. It occurs when a user accesses and interacts with webpages or content on a particular website.

The initial number of video views was (fewer than) the initial number of site visits, and the number of video views grew by (a larger factor) the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is (20,825).

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The reflection of the point P = (-4, 7) in the y-axis is (4, 7).

We have,

To find the reflection of a point P in the y-axis, negate the x-coordinate of the point while keeping the y-coordinate unchanged.

Given that P = (-4, 7),

The reflection of P in the y-axis, denoted as [tex]R_{y-axis}(P),[/tex] can be found by negating the x-coordinate:

[tex]R_{y-axis}(P) = (4, 7)[/tex]

Thus,

The reflection of the point P = (-4, 7) in the y-axis is (4, 7).

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The complete question:

If p = (-4, 7)

R_{y-axis} (P) = ?

The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is  13.58

First using distance calculator we derived the length of TV and the length of VU.

Since TV = Height; and

VU = Base

and the triangle is a right triangle,

Then, area is given by 1/2 base x Height

Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264

So area = 1/2 * 6.40312 * 4.24264

Area = 13.58

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The lowest score that would achieve an A is 10.

To find the lowest score that would achieve an A, we need to find the score corresponding to the 7th percentile of the distribution of scores.

First, we need to find the z-score corresponding to the 7th percentile. We can use a z-table or a calculator to find this value.

The z-score corresponding to the 7th percentile is approximately -1.44. This means that a score at the 7th percentile is 1.44 standard deviations below the mean.

We can use the formula for z-score to find the raw score corresponding to this z-score:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Plugging in the values we have:

-1.44 = (x - 46) / 25

Multiplying both sides by 25:

-36 = x - 46

Adding 46 to both sides:

x = 10

Therefore, the lowest score that would achieve an A is 10.

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The total amount deducted from her gross income health and disability insurance during each pay period is $72.50.

To calculate the total amount deducted from Asako's gross income for health and disability insurance during each pay period, we need to first determine the cost of each insurance plan after the employer's coverage.

For the $3,500 per year disability insurance plan, Asako's employer covers 90% of the cost, which means Asako is responsible for 10% of the cost.

10% of $3,500 is $350, so Asako's cost for the $3,500 per year disability insurance plan is $350 per year.

For the $1,300 per year disability insurance plan, Asako's employer covers 60% of the cost, which means Asako is responsible for 40% of the cost.

40% of $1,300 is $520, so Asako's cost for the $1,300 per year disability insurance plan is $520 per year.

Since Asako gets paid monthly, we need to divide the annual cost of each insurance plan by 12 to determine the cost per pay period.

For the $3,500 per year disability insurance plan, Asako's cost per pay period is $350 / 12 = $29.17.

For the $1,300 per year disability insurance plan, Asako's cost per pay period is $520 / 12 = $43.33.

Therefore, the total amount deducted from Asako's gross income for health and disability insurance during each pay period is $29.17 + $43.33 = $72.50.

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We know that the indicated probability is approximately 0.1210.

To use the normal approximation, we need to check if the conditions for a normal approximation are met. In this case, we have:

np = 81 * 0.5 = 40.5 ≥ 10
n(1-p) = 81 * 0.5 = 40.5 ≥ 10

Since both conditions are met, we can use the normal approximation to find the probability.

First, we need to find the mean and standard deviation of the sampling distribution of sample proportions:

mean = np = 81 * 0.5 = 40.5
standard deviation = sqrt(np(1-p)) = sqrt(81 * 0.5 * 0.5) = 4.5

Next, we need to standardize the value of x:

z = (x - mean) / standard deviation
z = (46 - 40.5) / 4.5 = 1.22

Finally, we can use a standard normal table or calculator to find the probability:

P(z ≥ 1.22) = 0.1118

Therefore, the answer is approximately 0.1210.

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Mike's bonus for the year is between $15,000 and $19,500.

The inequality that best represents Mike's bonus, B, for the year is:

$15,000 [tex]\leq B \leq[/tex] 19,500$

to see why, we are able to use the given data that Mike's bonus is calculated as 3 percent of his corporation's overall profits.

If we let P be the organization's general income, then Mike's bonus B can be expressed as:

$B = 0.03P$

We recognise that the organization's total profits are between $500,000 and $650,000, so we will write:

$500,000 [tex]\leq P \leq[/tex] 650,000$

Substituting this inequality into the equation for Mike's bonus, we get:

$15,000 [tex]\leq B \leq[/tex] 19,500$

Therefore, Mike's bonus for the year is between $15,000 and $19,500.

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The investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.

To solve this problem, we need to use the formula for continuous compound interest:
A = Pe^(rt)

Where A is the amount after t years, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.

Using the given information, we can fill in the table as follows:

Interest Rate | Amount after 4 years
--------------|---------------------
2%            | $4,493.29
3%            | $4,558.56
4%            | $4,625.05
5%            | $4,692.79
6%            | $4,761.81

To find the amount after 4 years at each interest rate, we plug in the values of P, r, and t into the formula and simplify:

2%: A = $4000 * e^(0.02*4) = $4,493.29
3%: A = $4000 * e^(0.03*4) = $4,558.56
4%: A = $4000 * e^(0.04*4) = $4,625.05
5%: A = $4000 * e^(0.05*4) = $4,692.79
6%: A = $4000 * e^(0.06*4) = $4,761.81

Therefore, the investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.

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The solution to the given initial value problem is (d) y = 4x^(1/4) - 1.

Given the initial value problem,

dy/dx = 4x^(-3/4), y(1) = 3

Integrating both sides with respect to x, we get

∫dy = ∫4x^(-3/4)dx

y = -8x^(-1/4) + C

where C is the constant of integration.

To find the value of C, we use the initial condition y(1) = 3

3 = -8(1)^(-1/4) + C

C = 3 + 8 = 11

Therefore, the solution to the initial value problem is

y = -8x^(-1/4) + 11

Simplifying further,

y = 11 - 8/x^(1/4)

Hence, the correct option is d) y = 4x^(1/4) - 1 is not the solution to the given initial value problem.

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The volume of the larger box is 200 cubic inches, and the volume of the smaller box is 150 cubic inches.

To find the volume of each box, we use the formula for the volume of a rectangular prism, which is V = lwh, where l is the length, w is the width, and h is the height.

For the larger box, we have l = 8 inches, w = 2.5 inches, and h = 10 inches, so

Volume of large box = = 8 x 2.5 x 10 = 200 cubic inches.

For the smaller box, we have l = 0.75 x 8 = 6 inches, w = 2.5 inches, and h = 10 inches, so

Volume of small box= 6 x 2.5 x 10 = 150 cubic inches.

The difference in the volumes of the two boxes is

Volume of large box - Volume of small box = 200 - 150 = 50 cubic inches.

The units for the volumes are cubic inches, since we are dealing with three-dimensional space.

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Answer:

The correct system of inequalities that models the constraints is:

6.00b + 7.75s ≥ 250

b + s ≤ 40

Explanation:

The first inequality represents the requirement that Jason needs to earn at least $250 each week. The earnings from babysitting are $6.00 per hour, and the earnings from working at the store are $7.75 per hour.

Therefore, the total earnings from both jobs can be represented by the expression 6.00b + 7.75s. This expression must be greater than or equal to $250, hence the first inequality.

The second inequality represents the constraint that Jason can work no more than 40 hours each week. The variables b and s represent the number of hours worked babysitting and working at the store, respectively.

The sum of these hours must be less than or equal to 40, hence the second inequality.

Therefore, the correct system of inequalities is:

6.00b + 7.75s ≥ 250

b + s ≤ 40

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The probability that a student at Kennedy High School plays on the football team given that they already play in the band is 2/1 or simply 2.

To solve this problem, we can use conditional probability. We want to find the probability that a student plays on the football team given that they already play in the band.

Let's use the formula for conditional probability:

P(Football | Band) = P(Football and Band) / P(Band)

We know that P(Band) = 0.15, and P(Football and Band) = 0.3.

So,

P(Football | Band) = 0.3 / 0.15

Simplifying, we get:

P(Football | Band) = 2

Therefore, the probability that a student at Kennedy High School plays on the football team given that they already play in the band is 2/1 or simply 2.

Note: This answer may seem unusual because probabilities are typically expressed as fractions or decimals between 0 and 1. However, in this case, we can interpret the result as saying that students who play in the band are twice as likely to also play on the football team compared to the overall population of students.

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The probability that a randomly selected admission charge is less than $3. 50 is 0.23% or 0.0023.

To find the probability that a randomly selected admission charge is less than $3.50, we will use the z-score formula and a standard normal table. The z-score formula is:

Z = (X - μ) / σ

Where X is the value we are interested in ($3.50), μ is the average admission charge ($5.81), and σ is the standard deviation ($0.81).

Z = (3.50 - 5.81) / 0.81 ≈ -2.84

Now, look up the z-score (-2.84) in a standard normal table, which gives us the probability of 0.0023. Therefore, the probability that a randomly selected admission charge is less than $3.50 is approximately 0.23% or 0.0023.

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The equation in slope-intercept form that models the total cost of attendance is: y = 2,633x + 275.


1. Add up the annual costs: tuition and fees ($4,934), room and board ($1,424), and cost of books and supplies ($1,250) to get the total annual cost: $4,934 + $1,424 + $1,250 = $7,608.

2. Subtract the annual scholarship and grants from the total annual cost: $7,608 - $5,250 = $2,358. This is the slope (x) of the equation, as it represents the cost per year.

3. The other one-time fee ($275) is the y-intercept of the equation, as it's a fixed cost that does not change with the number of years.

4. Put the slope and y-intercept into the slope-intercept form (y = mx + b) to get: y = 2,633x + 275.

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By using Numerical integration method such as Simpson's rule or Monte Carlo simulation, we will get the area

To calculate the area of surface S, we first need to find the limits of integration. The paraboloid hyperbolic is located between the cylinders x + y = 1 and x = 2. This means that the limits of integration for x are 1 and 2, and for y they are -sqrt(4-[tex]x^2[/tex]) and sqrt(4-[tex]x^2[/tex]).

Calculation of area:
Using the formula for the surface area of a paraboloid hyperbolic, which is given by:
A = 2π ∫∫ (1 + (∂z/∂x[tex])^2[/tex] + (∂z/∂y[tex])^2[/tex][tex])^{(1/2)[/tex] dA
We can calculate the area of surface S. First, we need to find the partial derivatives of z with respect to x and y:
∂z/∂x = -2x/(2+[tex]y^2[/tex])
∂z/∂y = -2y/(2+[tex]x^2[/tex])
Substituting these values into the formula for surface area, we get:
A = 2π ∫[tex]1^2[/tex] ∫-sqrt(4-[tex]x^2[/tex])^sqrt(4-[tex]x^2[/tex]) (1 + (-2x/(2+y^2)[tex])^2[/tex]+ (-2y/(2+[tex]x^2)[/tex][tex])^2[/tex][tex])^{(1/2)[/tex]dydx
Using a numerical integration method such as Simpson's rule or Monte Carlo simulation, we can calculate this integral to get the area of surface S.

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Answer: 1.3

Step-by-step explanation:

Step-by-step explanation:

= sqrt ( 28 ÷7) = sqrt (4) = 2

Answer:

2

Step-by-step explanation:

First we put the two equations together so it would be like this

[tex]\sqrt \frac{28}{7}[/tex]

the square root of that is 4 because 7 goes into 28 four times

so now we have this [tex]\sqrt{4}[/tex]

and the square root of 4 is 2

Answer:

$15.92

Step-by-step explanation:

We Know

2 liters of Gatorade cost $3.98

How much do 8 liters cost?

We take

3.98 x 4 = $15.92

So, 8 liters cost $15.92

Answer:

P(t)=26.5 (0.1)^t

Step-by-step explanation:

When i (x) = 3, the value of y is approximately -6.67. The equation relating i (x) and y in this inverse variation is xy = -20.

The given information states that the variables x and y vary inversely. To write an equation relating i (assuming it's x) and y, we first need to understand the concept of inverse variation.

In inverse variation, the product of the two variables remains constant. Mathematically, it can be represented as xy = k, where k is the constant of variation. We are given the values i (x) = 5 and y = -4. Using these values, we can find the constant of variation, k:

5 * -4 = k
k = -20

Now that we have the constant of variation, we can write the equation relating i (x) and y as:

xy = -20

Next, we want to find the value of y when i (x) = 3. We can use the equation we just derived to find the value of y:

3 * y = -20

Now, we can solve for y:

y = -20 / 3
y ≈ -6.67

So, when i (x) = 3, the value of y is approximately -6.67. The equation relating i (x) and y in this inverse variation is xy = -20.

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Answer:

The expression 625y^2 + 400y - 36 + 20z - z^2 can be rearranged and simplified as follows:

625y^2 + 400y - 36 + 20z - z^2

= (25y)^2 + 2(25y)(8) + 8^2 - 8^2 - 36 + 20z - z^2 (adding and subtracting (25y)(8) and 8^2 inside the parentheses)

= (25y + 8)^2 - (8^2 + 36) + 20z - z^2 (expanding the squared term and simplifying)

= (25y + 8)^2 - 100 + 20z - z^2 (simplifying)

Therefore, the simplified form of the expression is:

(25y + 8)^2 - 100 + 20z - z^2.

Note that this expression can also be written as:

(5y + 2)^2(5y - 12)^2 - (z - 10)(z + 10),

Using the difference of squares factorization. However, this is not necessarily simpler than the previous form, and it depends on the context and the purpose of the expression.

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Size of triangles doesn't determine slope, mq slope=-2, qs slope=-0.5

Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. The slope is calculated by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. Therefore, we need to find two points on the lines mq and qs to calculate their slopes.

Let's start by finding the slope of mq. We can identify two points on the line, (0,6) and (2,2). Using these points, we can calculate the slope as:

slope of mq = (change in y-coordinates) / (change in x-coordinates)

slope of mq = (2 - 6) / (2 - 0)

slope of mq = -4 / 2

slope of mq = -2

Now let's find the slope of qs. We can identify two points on the line, (2,2) and (6,0). Using these points, we can calculate the slope as:

slope of qs = (change in y-coordinates) / (change in x-coordinates)

slope of qs = (0 - 2) / (6 - 2)

slope of qs = -2 / 4

slope of qs = -0.5

Therefore, the slope of mq is -2 and the slope of qs is -0.5.

In summary, Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. We calculated the slopes of lines mq and qs by finding two points on each line and using the formula for slope, which is the change in y-coordinates divided by the change in x-coordinates. The slope of mq is -2, and the slope of qs is -0.5.

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Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.

To find how many card ,We see Curtis has 9 cards at school after trading with Dino again, which means he had 12 cards before the trade.

Before his mom bought him another pack of 12 cards, he had 10 missing, so he must have had 24 cards in total (12 + 12).

He hid half of his cards at home, so he has 12 cards at home.

He traded ¼ of the cards he brought to school to Dino and got back 3 of Dino's cards. Let's call the number of cards he brought to school "x".

So, he traded x/4 cards to Dino, and got back 3 cards, which means he now has (x/4) - 3 cards.

We know that he now has 9 cards at school, so we can set up an equation:

(x/4) - 3 = 9

Solving for x, we get:

x/4 = 12

x = 48

So, Curtis brought 48 cards to school, which means he started with 24 + 12 + 48 = 84 cards in total.

Therefore, Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.

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Lillian would have approximately $14,599 in her account after 3 years, to the nearest dollar.

To find out how much Lillian would have in her account after 3 years, we need to use the future value of a series formula, which is:

[tex]FV = P \frac{(1 + r)^nt - 1)}{r}[/tex]

where:
FV = future value of the series
P = monthly deposit ($430)
r = monthly interest rate (annual interest rate / 12)
n = number of times interest is compounded per year (12)
t = number of years (3)

First, we need to find the monthly interest rate by dividing the annual interest rate (4.5%) by 12:
[tex]r =\frac{0.045}{12} = 0.00375[/tex]

Now we can plug the values into the formula:
[tex]FV = 430 \frac{(1 + 0.00375)^{12x3}  - 1)}{0.00375}[/tex]

Calculating the future value:
[tex]FV = 430\frac{(1.127334 - 1) }{0.00375} = 430 \frac{0.127334}{ 0.00375} = 430 (33.955)[/tex]
[tex]FV =14,598.65[/tex]

So, Lillian would have approximately $14,599 in her account after 3 years, to the nearest dollar.

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