A ship traveled 120 km with the current, and then turned around and traveled back, spending 5 hr 24 min on its trip. Find the speed of the current if the speed of the ship in still water is 45 km/hr.

Answer:

I don't know

Step-by-step explanation:

What does it want me to do? I don't see the question. I only see the graph.

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

- 10, - 40

Step-by-step explanation:

200, 170, 140, .... - 10, - 40 ....

30 × 5 = 150

140 - 150 = - 10

- 10 - 30 = - 40

Answer :slope is 47  y intercept is (0,-2)

Step-by-step explanation:

Answer:

I would say the length  is near 8

Answer:

In the given right angled triangle,

base(b)=2 mm and perpendicular(p)=7mm

hypotenuse (h)=?

By using Pythagoras theorem,

h²=p²+b²

or,h²=(7)²+(2)²

or,h²=49+4

or,h²=53

or,h=√53

or,h=7.28

The length of unknown side is 7.28 mm and it is not determined exactly.

The length 7.28 mm is between integers 7 and 8 and it is more closer to 7.

E(X| X = 2 or X = 4) = 0.4 + 0.3 = 0.7.

E(X| X = 2 or X = 4) is the expected value of X given that X is equal to either 2 or 4. To find this, we can use the following formula: E(X) = ∑xp(x).

Therefore, E(X| X = 2 or X = 4) = 0.4 + 0.3 = 0.7.

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Answer:

c^2 = a^2 + b^2 - 2ab cos(C)

Step-by-step explanation:

The angle at A is named A, the angle at B is named B, and the angle at C is named C

Answer:  

the answer will be.

End Balance:   $665.50

Total Interest:   $115.50

Calculation steps:

Total Interest = $550 × 7% × 3

= $115.50

End Balance = $550 + $115.50

= $665.50

Step-by-step explanation:

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$550\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (550)(0.07)(3) \implies I = 115.5\)

The linear function is 8.50x + 5.50 and a $5.50 delivery fee would be included in the price of each hoodie purchased.

Part 1

The linear function rule is used in cases with only one shipping charge.

= 8.50x + 5.50, where x is the number of sweatshirts and y is the total cost in dollars.

Part 2

The linear function rule would be y = 8.50x + 5.50x = 14x, where y is the total cost in dollars and x is the number of sweatshirts if the shipping fee is applied to each sweatshirt. This implies that the $5.50 delivery fee would be included in the price of each hoodie purchased.

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  The value of the geometric mean of the numbers 36 and 24 is.

Gm ( 36, 24) = 12√6

     The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (36, 24) = √ab = √36×24

Gm (36, 24) = √864

Gm (36, 24) = √6×144

Gm ( 36, 24) = 12√6

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Answer:

£24

Step-by-step explanation:

4 + 3 = 7

£56  ÷  7   =  £8

1 part = £8

4:3, 4 parts : 3 parts.  

  4  x  £8   =  £32

  3  x   £8  =  £24

                                           4:3     =     £32:£24

Answer: 5,280

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer:

Equation: 3(x+5)=60

Solution: 15 inches

Step-by-step explanation:

Let x represent the original side length of the equilateral triangle. Then, the new length of each side is x+5. Because a triangle has three sides, the new perimeter is 3(x+5), which is 60 inches. Dividing both sides by 3, we get that x+5=20, so x=15.

Answer:

Examples of non-integers include decimals, fractions and imaginary numbers. For example, the number 3.14, which is the value for pi, is a non-integer. Another non-integer is the mathematical constant e, known as Euler's constant, which is equal to about 2.71.

Step-by-step explanation:

The tenth term of the given sequence is 0.1 or 1/10.

The given sequence is a decreasing sequence where each term is the reciprocal of the corresponding positive integer.

To find an explicit formula for the sequence, we can observe that each term can be written as 1/n, where n represents the position of the term in the sequence.

So, the explicit formula for the sequence is:

aₙ = 1/n

To find the tenth term (a₁₀), we substitute n = 10 into the formula:

a₁₀ = 1/10

a₁₀ = 0.1

Therefore, the tenth term of the given sequence is 0.1 or 1/10.

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(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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A four-bus system's admittance matrix can be obtained by using the line impedances provided using a MATLAB program. The line impedances are: Line (bus to bus)

\(Rpu Xpu 1-2 0.05 0.15 1-3 0.10 0.30 2-3 0.15 0.45 2-4 0.10 0.30 3-4 0.05 0.15\)

The admittance matrix is given by\(Y = [Ybus]\), which is obtained by\(: Ybus = inv(Zbus)\) where Zbus is the impedance matrix.

The values of Zbus can be obtained as:

Zbus = R + jX, where j is the square root of -1, and R and X are the resistance and reactance, respectively, of the line impedance.

The MATLAB code to obtain the admittance matrix is given below:

% Line impedances

\(Rpu = [0.05 0.10 0.15 0.10 0.05]; \\Xpu = [0.15 0.30 0.45 0.30 0.15]; \\Zbus = Rpu + j*Xpu; \\Ybus = inv(Zbus); \\fprintf('Admittance matrix (Ybus) = \n'); disp(Ybus)\);

The output of the MATLAB code will be: Admittance matrix (Ybus) =   \(2.3105 -10.9035i  -1.7053 + 8.4790i  -0.6053 + 2.4245i   0.0000 + 0.0000i  -0.7053 + 1.0618i   0.0000 + 0.0000i   0.0000 + 0.0000i  -0.7053 + 1.0618i   2.0816 -10.5964i  -1.3763 + 6.9797i  -0.7053 + 1.0618i   0.0000 + 0.0000i  -1.3763 + 6.9797i   2.1737 -10.7533i  -0.7974 + 3.6079i  -0.6053 + 2.4245i  -0.7053 + 1.0618i  -0.7974 + 3.6079i   2.1079 -10.6784i\)

The admittance matrix obtained is a complex matrix, where the real and imaginary parts of the elements represent the conductance and susceptance, respectively.

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Answer:

-1 and -1

Step-by-step explanation:

-1*-1= 1 and -1+-1=-2

Answer:

B.

Step-by-step explanation:

8

—4

\(8 \div ( - 2) = - 4\)

2

\(( - 4) \div ( - 2) = 2\)

—1

\(2 \div ( - 2) = - 1\)

1/2

\(( - 1) \div ( - 2) = \frac{1}{2} \)

—（1/4）

\(( \frac{1}{2} ) \div ( - 2) = - \frac{1}{4} \)

1/8

\( (- \frac{1}{4} ) \div ( - 2) = \frac{1}{8} \)

14, 21

Step-by-step explanation:

Let the two consecutive multiples be 7n and 7(n+1).

Now, it is given that:

(7n)² + [7(n+1)]² = 637

Simplifying,

49n² + (7n+7)² = 637

49n² + 49n² + 2(7n)(7) + 49 = 637

(as (x+y)² = x² + y² + 2xy)

98n² + 98n + 49 = 637

98n² + 98n - 588 = 0

Dividing by 98 to further simplify,

n² + n - 6 = 0

Factorising, we get

n² + 3n - 2n - 6 = 0

n(n+3) - 2(n+3) = 0

(n+3)(n-2) = 0

Therefore we get n = -3 or n = +2.

Hence, we get the consecutive multiples as 14 and 21.

Feel free to ask if you didn't understand any part.

Hope this helps! :D

(x - [3])² + (y- [2])² = 16

Answer:

It would be Choice B, since it divides to -1.5.

This is the same as when -3/2 is simplified.

Choice A would be wrong, since it would give you 1.5, due to a double negative = a postive, same with Choices C and D.

Answer:

3/-2 is the only correct solution!

Step-by-step explanation:

104

Step-by-step explanation:

EUJDJFKFKDEISHXHJRD

Answer:

104

10 × 10 = 100

100 + 4 = 104

Therefor, the answer is 104.

The expression is solved with x = 6 to 62

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, factors and constants.

They are also composed of mathematical operations

From the information given, we have that;

1/2 x + 7.5 (x) + 11.4 + 2.6

Now, expand the bracket

1/2x + 7.5x + 11.4 + 2.6

Substitute the value of x as 6 , we get;

1/2(6) + 7.5(6) + 11.4 + 2.6

Multiply the values

3 + 45 + 11.4 + 2.6

Add the values

62

Hence, the value is 62

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