1. Anya is at camp and walks 2km due north and then turns and walks another 3km at a bearing angle of 35° . Find her distance back to camp and the bearing angle from her starting point. ​

Let x be the crew rowing rate and y the rate of the current.

When the boat goes downstram the rates add up, then we have:

Now, we know that it took 2 hours to travel 12 miles, this means that the speed is 6 miles per hour, hence we have the equation:

Now, when the boats go downstream the rate of the current substract from the rowing rate, then we have:

Since it took them 3 hours to travel 12 miles the speed in this case is 4 miles per hour, then we have the equation:

Then we have the system of equations:

To solve this system we add the equation, then we get:

now that we know the value of x we plug it on the first equation and solve for y:

Therefore the rowing rate is 5 miles per hour and the current rate is 1 mile per hur.

The price per unit when the demand equals 7000 units is $0, while the number of units demanded at a price $13.78 is 2000 units.

The correct equation of the question is as follows:

p = 50(5^(−q/2)) ................................... (1)

Where p is the price per unit and q is a thousand units of the commodity.

a.) The price p per unit at which the demand will equal 7000 units can be calculated as follows:

Substituting q = 7000 into equation (1) we have:

p = 50(5^(−700/2))

p = 50 * 5^(-450)

p = 50 * 0

p = $0

b.) The number of units, to the nearest thousand units, that will be demanded if the price is $13.78 can be calculated as follows:

Substituting p = 13.78 into equation (1) and solving for q, we have:

13.78 = 50(5^(−q/2))

13.78 / 50 = 5^(−0.5q)

0.2756 = 5^(−0.5q)

Taking the log of both sides, we have:

log0.2756 = −0.5q * log5

−0.559720786764412 = −0.5q * 0.698970004336019

−0.5q = −0.559720786764412 / 0.698970004336019

−0.5q  = −0.80077940869024

q = −0.80077940869024 / −0.5

q = 1.60155881738048

Since q is a thousand units, we have:

q = 1.60155881738048 * 1000 = 1601.55881738048

Rounding to the nearest thousand units, we have:

q = 2000

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Answer:

\(\frac{1}{3}\ of\ Rs.30 = Rs.10\)

Step-by-step explanation:

Given

\(\frac{1}{3}\ of\ Rs.30\)

Required

Solve

of means *. So, we have:

\(\frac{1}{3}\ of\ Rs.30 = \frac{1}{3}\ *\ Rs.30\)

\(\frac{1}{3}\ of\ Rs.30 = \frac{1\ *\ Rs.30}{3}\)

\(\frac{1}{3}\ of\ Rs.30 = \frac{Rs.30}{3}\)

\(\frac{1}{3}\ of\ Rs.30 = Rs.10\)

Answer:

D

Step-by-step explanation:

The amount of time that will take him to swim the remaining distance will be [2,000 (1/5)] / (3/4). Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

Mateo has proactively swum Four-fifths of the 2,000 meters he is swimming today. On the off chance that he keeps swimming at a speed of Three-fourths of a meter each second.

3/4 = 2,000 (1 - 4/5) / T

T = [2,000 (1/5)] / (3/4)

The amount of time that will take him to swim the remaining distance will be [2,000 (1/5)] / (3/4). Then the correct option is D.

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The surface areas generated by rotating the given curves around the x-axis are approximately 232.35 units², 9.25 units², 88.38 units², 27.22 units², and 16.77 units².

To find the surface area of the volume generated by rotating curves around the x-axis, we need to use the formula 2π ∫f(x) √(1 + [f'(x)]²) dx, where f(x) is the curve being rotated. For the given exercises, we have:

The curve y = x is being rotated from x = 2 to x = 6. Using the formula, we get the integral 2π ∫2x √(1 + 1²) dx from 2 to 6. Evaluating this integral gives us a surface area of approximately 232.35 units².

The curve y = x³ is being rotated from x = 0 to x = 1. Using the formula, we get the integral 2π ∫x³ √(1 + 9x⁴) dx from 0 to 1. This integral cannot be evaluated exactly, but using a calculator, we get a surface area of approximately 9.25 units².

The curve y = 7x is being rotated from x = -1 to x = 1. Using the formula, we get the integral 2π ∫7x √(1 + 49) dx from -1 to 1. Evaluating this integral gives us a surface area of approximately 88.38 units².

The curve y = √x is being rotated from x = 1 to x = 3. Using the formula, we get the integral 2π ∫√x √(1 + 1/(4x)) dx from 1 to 3. This integral cannot be evaluated exactly, but using a calculator, we get a surface area of approximately 27.22 units².

The curve y = √(4 - x²) is being rotated from x = 0 to x = 2. Using the formula, we get the integral 2π ∫√(4 - x²) √(1 + x²/(4 - x²)) dx from 0 to 2. This integral cannot be evaluated exactly, but using a calculator, we get a surface area of approximately 16.77 units².

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Answer:

7w

Step-by-step explanation:

Answer: $18.6

Step-by-step explanation: If we take a look at the sale off the shoes cost which is $43.4 and look at the sale amount (30%) which is 18 dollars and 60 cents the answer is: 18.6 or $18.6 off

The way to convert counts into relative frequencies in a Two Way Relative Frequency Table is to divide the count by the total number of items

This refers to the depiction of the number of times in which an event occurs in the form of a table.

Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.

Please note that your question is incomplete as you did not provide the frequency table needed and also the trends and generalizations to find, so a general overview was given.

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Answer:

The relative frequency table shows a trend that a majority of people prefer coffee over tea: the ratio in the total row for coffee is 0.65 and just 0.35 for tea. Similarly, more people are night owls than early birds: the total column for night owl is 0.6, but the early bird column is only 0.4.

Answer: I think it’s 30

Step-by-step explanation:

Answer:

11th floor

Step-by-step explanation:

3rd floor +6 =9

9 -2 =11

11th floor

Answer:

))))))

Step-by-step explanation:

43+2(3-2)=43+2*3-2*2=43+6-4=45

Answer:

45

Step-by-step explanation:

43 + 2(3-2)

43 +2 (1)

43 + 2

45

1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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In triangle CDE, the sides CD is equal to side CE, so angle opposite to side CD is equal to angle opposite to side CE, means

Determine the measure of angle CDE (or angle CED) by using angle sum property of triangle.

The measure of angle CDE is 65 degrees.

The angle CDE and angle CDA are linear pair of angles. So,

Substitute the measure of angle CDE to obtain the measure of angle CDA.

Consider the triangle CAD.

Determine the measure of angle DCA by using angle sum property of triangle.

So measure of angle DCA is 25 degrees.

Ok, lets solve this

The lines are y = 4x+5 and y= 4x-2

When we put this into line intercept form i,.e y= mx +b

we see that the slopes are equal, hence both lines are parallel, they have no intersection point, lets try solving for this algebraically,

The intersection point of the two lines occurs when 4x+5 =4x-2

collecting like terms , wee have

4x-4x = -5-2

i.e 0= -7

This clearly is impossible so the lines never intersect, even if drawn till infinity.

If you try sketch the lines, you will see

Answer:

I am also wonder what do we explain.

Step-by-step explanation:

There is nothing here.

The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Answer:

642

Step-by-step explanation:

The area of the rectangle is 27/70 square feet.

The area of a rectangle is given by the formula:

Area = base x height

Plugging in the given values, we get:

Area = (3/7) x (9/10)

Simplifying, we get:

Area = (27/70) square feet

Therefore, the area of the rectangle is 27/70 square feet.

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Step-by-step explanation:

Fifty flats in base ten is equal to 5000 units.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object

Given, with base-ten blocks,

1 long = 10 units, 1 flat = 10 longs and 1 block = 10 flats.

We have to find the number of units corresponding to fifty flats in base ten.

1 flat = 10 longs

50 flats = 50 × 10 longs

            = 500 longs

Also, we have,

1 long = 10 units

500 longs = 500 × 10 units

                 = 5000 units

The conversion for base eleven is not given.

Hence fifty flats in base ten is equal to 5000 units.

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Answer:

Step-by-step explanation:

\(\mathrm{6n - 9 \; when\;n = 4}\)

Let's substitute n with 4 :-

Multiply 6*4 = 24:-

Subtract:-

____________________

Hope this helps!