A motorboat travels 210 kilometers in 6 hours going upstream. It travels 366 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current

Answer:

10000000

Step-by-step explanation:

Answer:

1000000

1000  x

10000

-----------

1000000

Before you can multiply two matrices together, the number of COLUMN in the first matrix must equal the number of rows in the second matrix.

The entries of a matrix are a rectangular array of numbers (or other mathematical objects). Standard operations like addition and multiplication can be performed on matrices. A matrix over a field F is often just a rectangular array of F's constituent elements.  Real and complex matrices are those whose entries are real or complex numbers, respectively.

The entries or elements of the matrix are its numbers, symbols, or phrases. In a matrix, the terms "rows" and "columns" refer to the horizontal and vertical rows of entries, respectively.

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The equation -2g+2g has infinitely many solutions.

The method of solving equations involves determining the value of the unknown variable while maintaining the equality of the equation on both sides. When a condition on variable guarantees that two expressions in the variable have the same value, it qualifies as an equation. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. After separating the variable whose value has to be calculated, the solution is found. We can answer it depending on the type of equation we are dealing with. Equations come in a variety of forms, including linear, quadratic, rational, and radical equations.

Consider the given equation

-2g + 2g = 0

Solve the equation,

0 = 0

This means that the equation is valid for all values of g.

Therefore, the equation can have infinitely many solutions.

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Answer:

-1, 0, 1, 2

Step-by-step explanation:

\(\sqrt{5-5} -1\\\sqrt{0} -1\\0-1\\-1\)

\(\sqrt{6-5} -1\\\sqrt{1} -1\\1-1\\0\)

\(\sqrt{9-5} -1\\\sqrt{4} -1\\2-1\\1\)

\(\sqrt{14-5} -1\\\sqrt{9} -1\\3-1\\2\)

Answer:

The x intercept is (-2,0)

the y intercept is (0,4)

Answer:

Step-by-step explanation:

Given,f(x)=3x^2-x+2

now,f(-4)=3(-4)^2-(-4)+

=3(16)+4+2

=48+4+2

=54

So,f(-4) =

Answer:

The solution is 54

Step-by-step explanation:

f(x) = 3x²-x+2

f(-4) = 3(-4)²-(-4)+2

f(-4) = 48+4+2

f(-4) = 52+2

f(-4) = 54

Answer:

-9

Step-by-step explanation:

\((-7)^{2}\) = 49

when you have a negative number to any power make sure you plug it in correctly into the calculator.

\(\frac{49+5}{-7+1}\)  = \(\frac{54}{-6}\)

54÷-6= -9

I hope this helps

Answer:

\(-9\)

Step-by-step explanation:

\(\frac{x^2+5}{x+1}\)

If \(x=-7\) then:

\(\frac{-7^2+5}{-7+1} =\\\\\frac{49+5}{-6} =\\\\\frac{54}{-6} =\\\\-9\)

The expression equals \(-9\) if \(x=-7\)

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

The mathematics curriculum involves examining numbers, the equation the environment we live in, structures, and both actual and hypothetical locations. A function is a variable representation of the relationship between the quantities of intake and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, when combined, provide unique outputs for each input.

Here,

Given :

mass of a population of duckweed is 500g

=>  function m(t)= 500x³^t/45

So,

=> t = 45 hours

Since it is given that the mass of the population of the duckweed triples every 45 hours

it is clear that the time taken for the duckweed to grow a mass triple the original size will be 45 hours .

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

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The largest integer less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13. is 1440

Given, a number less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13.

On using the Chinese remainder theorem. As, the numbers 7, 11, 13 are pairwise coprime.

Firstly, an integer  m  such that  m−5  is divisible by 7 and  m−10  is divisible by 11 .

The Chinese remainder theorem says that all integers that work will be of the form  54+7⋅11⋅k=54+77k  for any integer  k .

Next an integer  n  such that  n−10  is divisible by 13 and  n−54  is divisible by 77.

Then, by the Chinese remainder theorem, all the integers that also work are of the form  439+13⋅77⋅k=439+1001k .

Hence, the positive integers satisfying the condition are: 439, 439 + 1001 = 1440, 1440 + 1001 = 2441, and so on.

The largest integer less than 2010 is 1440.

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create your own scale, it could be 2cm=40mm, so 3cm=60mm and 2.5cm=50mm.

then draw your trapezium in the given space using your scale

Given:

Required:

To find the quotient and remainder using synthetic division.

Explanation:

Consider

Here the quotient is

And the remainder is

Final Answer:

Quotient :

Remainder : -9.

Answer:

The % increase is 7.179 but see the remark I made below. What I have given and what it could be is a rounding error. Less than 2 dollars error is not much when you are calculating something for someone just to show them how to do it.

Step-by-step explanation:

242,555 * x/100 = 259,970           Multiply by 100

242,555 * x = 259970 * 100

242,555 * x = 25997000            Divide by 242555

x = 24997000/242444

x = 107.179

That's the total increase.

What you want is 7.179%

If you take 7.179% of 242,555 and add it onto 242555 you should get 259,970

7.1797/100 * 242555 = 17413.02

17413.02 + 242555 = 259968.02

Why isn't it exact. I'm out just about 2 whole dollars. The reason is that the % isn't exact. It's only out to 3 decimal places which apparently is not enough. You can go over my numbers if you want more exactness us use something that is rounded to 7.180 if you like.

That would be, 45, 56, 67, and on, the sequence is to add 11.

Answer:Once you have the value of a variable you can check by plugging it into the equation and seeing if it’s right or not

Step-by-step explanation:

The required value of the missing sides with the help of trig ratios we have x = 19.9.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
To find the missing side in the given right triangle, we can use trigonometric ratios. Specifically, we can use the tangent ratio:

Cosine of an angle = opposite side / adjacent side

In this case, we know the measure of one acute angle (19 degrees) and the length of the adjacent side (21). We want to find the length of the opposite side, which we can represent as x.

cos(19°) = x / 21

Multiplying both sides by 21, we get:

x = 21 cos(19°)

Using a calculator, we can evaluate the right-hand side to get:

x ≈ 19.85

Rounding to the nearest tenth, the missing side is approximately 19.9 units long.

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Answer:

the answer is B) 1/2, 3.

Step-by-step explanation:

To solve the system of linear equations by graphing, we need to graph both lines and find the point where they intersect. This point will be the solution to the system.

The equation y = -1/2x+2 has a y-intercept of 2 and a slope of -1/2. We can plot this on a graph by starting at the y-intercept (0, 2) and then going down 1 unit and to the right 2 units to get another point on the line. We can then draw a straight line through these two points.

The equation y=1/2x-1 has a y-intercept of -1 and a slope of 1/2. We can plot this on the same graph by starting at the y-intercept (0, -1) and then going up 1 unit and to the right 2 units to get another point on the line. We can then draw a straight line through these two points.

The point where these two lines intersect is the solution to the system of equations. From the graph, we can see that this point is approximately (1/2, 3).

the answer is B) 1/2, 3.

To solve the system of linear equations by graphing, we need to plot the lines represented by the equations on the same coordinate plane and find the point of intersection.

|

3 | .

| \

2 | \

| \

1 | . \

| \

0 |_____________

0 1 2 3 4

Answer:

Its C because it passes through the origin. I learned about this.

C. 35 minutes

300 words in 10 minutes

words/minutes = 300/10

For 1050 words:

1050 words / x minutes

1050 /x

Equal both rates:

300/10 = 1050/x

Solve for x (minutes)

30 =1050/ x

x = 1050/30

x= 35

Answer:

My answer is 13 units

Step-by-step explanation:

Hope it helps

answer!

49 cookies were sold!

explaination!

42÷6= 7

42 plus 7 = 49

the amount of cookies sold was 49

(Sorry if it's wrong)

To find the critical points at which profit is maximized given the total revenue TR = 4700 - 302 and total cost TC = 320/10,500, we need to compute the marginal revenue and marginal cost, equate MR = MC to find the optimal quantity Q∗, verify if Q∗ is a relative maximum point, and compute the maximum profit level (π) by evaluating π∗ = 9(π(Q∗)).

Marginal Revenue (MR) is the derivative of the total revenue function with respect to quantity (Q). In this case, MR = dTR/dQ. By taking the derivative of TR = 4700 - 302 with respect to Q, we can find the expression for MR.

Marginal Cost (MC) is the derivative of the total cost function with respect to quantity (Q). In this case, MC = dTC/dQ. By taking the derivative of TC = 320/10,500 with respect to Q, we can find the expression for MC.

To find the optimal quantity Q∗, we equate MR and MC by setting MR = MC and solve for Q. This is because profit is maximized when MR equals MC.

Once we have found Q∗, we need to verify if it is a relative maximum point. This can be done by checking the second derivative of the profit function and determining if it is negative at Q∗. If the second derivative is negative, it confirms that Q∗ is a relative maximum point.

Finally, to compute the maximum profit level (π∗), we evaluate π(Q∗) by substituting Q∗ into the profit function. In this case, we can multiply the value of π(Q∗) by 9 to obtain the maximum profit level (π∗).

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Complete question is;

Determine whether the experiment is blind or double blind.

Is the aspirin produced by the World’s Best Pharmaceutical Company better than that of a competitor at relieving headaches? 200 headache sufferers are chosen at random. Migrained Testing Service administers the experiment and provides the results evaluation. Three levels are made: participants receive contents from Bottle A, Bottle B, or Bottle C. Other than the fact that one bottle contains placebo aspirin, no other information is given to the testing service regarding the bottles’ contents.

a) blind study

b) double blind study

C) Neither

Answer:

Double blind study.

Step-by-step explanation:

We are told that participants receive contents from Bottle A, Bottle B, or Bottle C.

However, the testing service only knows that one bottle contains placebo aspirin but they don't know the other contents nor which of the participants is taking the one with placebo aspirin.

Thus, this is a double blind experiment because neither the participants nor the testing service have knowledge of who is taking the bottle that contains placebo aspirin unlike a blind experiment where the testing service will know which participants got the bottle containing aspirin.

Answer:

60 degrees

Step-by-step explanation:

It measures 60 degrees

Tip: the wider the angle, the bigger the degree.

Hope this helps!

Answer:

23.2

12

..........................................

Given:

One of the angle of a triangle is 104°.

The objective is to find the missing angle x.

If two sides of a triangle are equal, then it is an isosceles triangle.

In an isosceles triangle, the angle formed by the equal sides is also equal.

Then, the value of angle x can be calculated angle sum property of triangle.

Hence, option (A) is the correct answer.

Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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The probability that the sample average amount of time taken on each day is at most 11 min is 0.5167

To solve for the probability proportion, we make use of the z statistic. The procedure to do is to calculate for the z value and using the standard probability tables, we can look up for the p value. The formula for z score is:

z =(x – μ) / (σ / √n))

where,

x = sample score = 11

μ = sample mean= 10

σ = standard deviation = 4

n = sample size

Calculating for the z and p value when n = 5:

z =(11 – 10) / (2 /√(5))

z = 0.55

Using the tables, p(5) = 0.7088

Calculating for the z and p value when n = 6:

z =(11 – 10) / (4/ √6))

z = 0.61

Using the tables, p(6) = 0.7290

If both days should be occurring, therefore the total probability that each day is at most 11 min is:

p total = p(5) * p(6)

p total = 0.7088 * 0.7290

p total = 0.5167

Hence the average amount of time taken on each day is at most 11 min.

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Answer:

A=200 ft²

Step-by-step explanation:

let the Length be L and the Width be W

We know that Perimeter = Length + Length + Width + Width

or,

Perimeter = 2(L + W)  

given that Perimeter = 60 ft,

60 = 2(L+W)    (divide both sides by 2)

60/2 = (L+W)

L + W = 30 ---------------------eq 1

we are further given that the length is twice the width, or,

L = 2W ---------------------- eq 2

substituting eq2 into eq 1,

L + W = 30

(2W) + W = 30

3W = 30

W = 10  (substitute this into eq 2)

L = 2W

L = 2(10)

L = 20

Area = Length x Width

= 20 x 10

= 200 ft²