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Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 20 min. If the current in

that part of the river is 4 km per hr, what was her boat speed in still water?

Her boat speed in still water was km per hr.

First, notice that since the point (a,1) belongs to the circumference x^2+y^2=5, then:

Since the point (a,1) is in the second quadrant, then:

Remember that the coordinates of a point on a circle of radius r can be written in terms of the angle as:

The radius of the circle in this case is the square root of 5. Then:

Therefore:

On the other hand, remember the following identity:

Substitute the value for the cosine of θ:

Therefore:

Answer:

B,

Step-by-step explanation:

Answer:

I think the answer is 43.8

Answer:

198.4

Step-by-step explanation:

Right side is a rectangle   12.8 * 12.8 = 163.84 cm^2

Left side is triangle   area = 1/2 Base * height = 1/2 * 12.8 * (18.2-12.8) =

         34.56 cm^2

summed = 198.4  cm^2

Answer:

936.58

Step-by-step explanation:

Answer:

  yes

Step-by-step explanation:

You want to know if Kayla can earn an average of 90, given that her first four test grades are 94, 82, 96, and 78.

The average of Kayla's grades is found by adding them up and dividing by their number. If we let x represent the grade on her 5th test, then her average would be ...

  average = (94 +82 +96 +78 +x)/5 = (350 +x)/5 = 70 +x/5

For this to have the value 90, we must have x ...

  90 = 70 +x/5

  20 = x/5

  100 = x

It is mathematically possible for Kayla to earn an A for the course if she gets a perfect score (100) on her last test.

The percentage of our new facility's seating is full will be 76%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

Our new training room can seat 150 employees.

If 6 tables consisting of 6 chairs are now taken.

Then the number of occupied seats by tables will be

⇒ 6 x 6

⇒ 36

Then the percentage of our new facility's seating is full will be

P = [(150 - 36) / 150]  x 100

P = (114/150) x 100

P = 0.76 x 100

P = 76%

The percentage of our new facility's seating is full will be 76%.

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The time required for the amount to double and triple are 19.53 and 30.95 respectively.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

\(f(t) = P_{0}e^{rt}\)

Where:

Based on the information provided above, we can reasonably infer and logically deduce that a function for the time required for the amount to double is given by;

\(2(1500) = 1500e^{0.0355t}\\\\3000= 1500e^{0.0355t}\\\\2=e^{0.0355t}\)

Taking the natural log (ln) of both sides of the equation, we have:

0.0355t = ln(2)

Time, t = 19.53

Similarly, a function for the time required for the amount to triple is given by;

\(3(1500) = 1500e^{0.0355t}\\\\4500= 1500e^{0.0355t}\\\\3=e^{0.0355t}\)

Time, t = 30.95

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Answer:

1/5 = 3/15

2/3 = 10/15

When all Added up

= 13/15

Step-by-step explanation:

So our LCD here is 15.

So in order to go from 5 to 15, we multiply by 3, and In order to go from 3 to 15, we multiply by 5. What we do to the denominator we also do to the numerator.

So,

\(\frac{1}{5} x \frac{3}{3} = \frac{3}{15}\)

And,

\(\frac{2}{3} x \frac{5}{5} = \frac{10}{15}\)

So there you go, multiply for what you need to get to the LCD, and what is done to the numerator is also done to the denominator. Enjoy

*If this Helped I'd Also Appreciate 5* and a ♥ Thanks!*

Answer:

approximately 254.5

btw area of circle= pi multiplied by radius

Step-by-step explanation: I got you bro

Answer: Circle area = π * r² = π * 81 [inch²] ≈ 254.47 [in²]

but because it asks for nearest tenth

254.5 in²

this is your real answer

The  volume of the sphere is calculated as  8,788 cm³.

The volume of the sphere is calculated using the following formulas as shown below;

V = ⁴/₃πr³

where;

The radius of the sphere is given as 13 cm

π is given as 3

The  volume of the sphere is calculated as follows;

V =  ⁴/₃πr³

V = ⁴/₃ x 3 x 13 x 13 x 13

V = 8,788 cm³

Thus, The  volume of the sphere is calculated by using the formula for volume of sphere.

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Step-by-step explanation:

By the Right Triangle Altitude Theorem, the two triangles formed by the altitude of a right triangle are similar to the original triangle and to each other.

In this case, triangle ABC is the original right triangle and CE is the altitude. Therefore, the similarity statement that is true is:

△ABC ∼ △AEC

This is because triangles ABC and AEC are both right triangles that share the angle at C, and the altitude CE creates two pairs of congruent angles (the right angles and the angle at A and E) and a pair of proportional sides (CE and AE are corresponding altitudes).

So, we can write the similarity statement as:

△ABC ~ △AEC

Answer:

5 < x

Step-by-step explanation:

I just learned this stuff in class yw

ASA stands for "Angle-Side-Angle." Triangles classified as ASAs have two known angles and a common side. The ASA triangle ABC, with provided angles B and C and their common side a between them, is depicted below.

What does a congruence mean in mathematics?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

Describe ASA congruence through an example.

ASA (Angle-Side- Angle) 

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

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Answer:

A

Step-by-step explanation:

Answer:

x-intercept = 6

y-intercept = -4

Slope: m = ⅔

f(3) = -2

Step-by-step explanation:

✔️The x-intercept is the value of x when y = 0. It is the point at which the line of the function intercepts the x-axis. Thus,

x-intercept = 6

✔️The y-intercept is -4. At this point, x = 0. The line intercepts the y-axis at y = -4. Thus,

y-intercept = -4

✔️Slope can be calculated using two points, (0, -4) and (6, 0).

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 -(-4)}{6 - 0} = \frac{4}{6} = \frac{2}{3} \)

Slope: m = ⅔

✔️f(3) means, what is the value of y when x = 3.

From the graph, when x = 3, y = -2.

Therefore,

f(3) = -2

Answer:  When you solve for w the equation is \(w= \frac{p-2l}{2}\)

Step-by-step explanation:

p = 2L + 2w  subtract 2L from both sides

p -2L = 2L -2L + 2w     2L-2L = 0 om the right; they cancel

p - 2L = 2w     now get w alone

(p - 2L)/2  = 2w/2   divide both sides by 2  2w/2 = w  2/2=1  it "cancels"

\(\frac{p +2L}{2} = w\)  rewrite Reverse sides to put w alone on the left side

\(w= \frac{p-2l}{2}\)

The percentage population increase from 2001 to 2011 is 50%.

To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.

The formula to calculate the percentage increase is:

Percentage Increase = ((New Value - Old Value) / Old Value) * 100

Plugging in the values:

Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%

Therefore, the percentage population increase from 2001 to 2011 is 50%.

Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.

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Answer:

-5/6

Step-by-step explanation:

(9, 5) and (21, -5)

slope = m = (difference in y)/(difference in x)

m = (-5 - 5)/(21 - 9)

m = -10/12

m = -5/6

Answer: -5/6

The slope of the line that passes through points (9,5) and (21,-5) is -5/6.

We can use the two-point formula to find the slope for the given line. The formula is as follows:

(y2 - y1) = m*(x2 - x1)

Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.

In the given case:

x1=9, x2=21

y1=5, y2=-5

Using these values in the two-point formula, we get:

(-5-5)=m*(21-9)

-10=m*12

m=-10/12

m=-5/6

Hence the slope of the line is -5/6.

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Answer:

490849.9

Step-by-step explanation:

Answer:

490849.92 centimeters

Answer:

Number of 2-point questions on the test as per given condition is equals to 8.

Total number of questions in a test = 28

Total points allotted for test = 100

Questions distribution as per points :

2-point questions, 4-point questions, and 5-point questions

'x' represents the 5-point questions

As per condition given,

Number of 2-point questions = 2x

Number of( 2-point  +  4-point +  5-point ) questions = 28

⇒ 2x + 4-point questions  + x = 28

⇒ 4-point questions  = 28 - 3x

Substitute the value in the given condition of the equation we get,

2(2x)+4(28-3x)+5(x) = 100

4x+112-12x+5x=100

112-3x=100

x=4

The point which is on the y-axis and is the y axis and is 7 units from the point (-7, -5) is;

Since the point is on the y-axis, it follows that it's x-coordinate is zero and hence; the point is; (0, y).

The distance is therefore 7 units and hence;

7² = (-7-0)² + (y - (-5))²

49 -49 = (y +5)²

0 = y +5

y = -5

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Answer:

the base is 7 and the height is seven so the first answer

Answer:

The square root of 50 is approximately 7.07.

Answer:

7.07106781187...

Step-by-step explanation:

its an irrational number

Answer:

5

Step-by-step explanation:

-9 + x = -4

( move +x to right and -4 to left)

-9 +4= -x

[sign changes when number is moved]

-5= -x

[negative signs cancel out each other/ divide both sides by negative sign]

x = 5

The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.

The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.

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Answer:

hhhhhhhdjskafwlsgsksyskdkhdjdjjdjh

Answer:

78r²s

Step-by-step explanation:

well you add 49 and 42 and 28 and subtract 41 bc they have the same symbols afterwards, and you get that

Step-by-step explanation:

\((9\pi \frac{2}{2} )\div 3\pi \\ \)

\( \frac{9\pi}{3\pi} \\ \)

\(3\pi\)

3π is the answer